T.C.

MARMARA ÜNİVERSİTESİ SOSYAL BİLİMLER ENSTİTÜSÜ İŞLETME ANABİLİM DALI

SAYISAL YÖNTEMLER (İNG) BİLİM DALI

EXPLORING THE BEST METHOD OF FORECASTING FOR

SHORT TERM ELECTRICAL ENERGY DEMAND

(A RESEARCH ON ENERGY DEMAND OF TRAKYA REGION IN

TURKEY)

Yüksek Lisans Tezi

MESUT GÜNEŞ

İstanbul, 2009

T.C.

MARMARA ÜNİVERSİTESİ SOSYAL BİLİMLER ENSTİTÜSÜ İŞLETME ANABİLİM DALI

SAYISAL YÖNTEMLER (İNG) BİLİM DALI

EXPLORING THE BEST METHOD OF FORECASTING FOR

SHORT TERM ELECTRICAL ENERGY DEMAND

(A RESEARCH ON ENERGY DEMAND OF TRAKYA REGION IN

TURKEY)

Yüksek Lisans Tezi

MESUT GÜNEŞ

SUPERVISOR: PROF. DR. RAUF NURETTİN NİŞEL

İstanbul, 2009

I

II

GENEL BİLGİLER

İsim ve Soyadı : Mesut Güneş Anabilim Dalı : İşletme Programı : Sayısal Yöntemler Tez Danısmanı : Prof. Dr. Rauf Nurettin Nişel Tez Türü ve Tarihi : Yüksek Lisans – Temmuz 2009 Anahtar Kelimeler : Tahmin yöntemleri, zaman serileri, elektrik enerjisi tüketimi, SPSS, Minitab, Matlab

ÖZET

KISA SÜRELİ ELEKTRİK ENERJİSİ İHTİYACI İCİN EN İYİ YÖNTEMİN

BELİRLENMESİ (TRAKYA BÖLGESİ ENERJİ İHTİYACI ÜZERİNE BİR

ÇALIŞMA)

Bu çalışma belli bir bölgeye ait saatlik tutulmuş elektrik enerjisi tüketimine ilişkin

veriler üzerine kurulu tahmin yöntemlerinin uygulanmalarını kapsamaktadır. Bu kapsamda

öncelikle elektrik sistemleri ve tahmin yöntemleri üzerine bilgi verilerek mevcut durum

ortaya konmuştur. Bölge olarak Türkiyenin Avrupa kıtasında kalan kesimi yani Trakya

bölgesi amaç olarak ele alındı. Mevcut elektrik tüketim verilerinin saatlik tutulması ve 2005

yılının tamamı, 2006 ve 2007 yıllarının bazı ayları olmak üzere toplam 23 aylık büyük bir

veri üzerinde çalışılmasından dolayı “Quantitative” sayısal tahmin yöntemleri daha tutarlı

sonuç vermesi acısından kullanıldı. Bu bölgeye yönelik her bir ayın son gününü takip eden

12 saatlik elektrik enerji tüketimine ilişkin tahmin teknikleri geliştirildi ve elde edilen

veriler ışığında en uygun modeller belirlendi. Elde edilen tahmin modelleri elektrik enerjisi

verilerine uygulandı ve sonuçlar tartışıldı.

III

GENERAL KNOWLEDGE

Name and Surname : Mesut Güneş Field : Management Programme : Quantitative Science Supervisor : Prof. Dr. Rauf Nurettin Nişel Degree Awarded and Date : Master - May 2009 Keywords : Forecasting methods, time series, electrical power consumption, SPSS, Minitab, Matlab

ABSTRACT

EXPLORING THE BEST METHOD OF FORECASTING FOR SHORT TERM

ELECTRICAL ENERGY DEMAND (A RESEARCH ON ENEGRY DEMAND OF

TRAKYA REGION IN TURKEY)

This study includes applications of forecasting models established on the data that

contain the electrical power consumption of a specific region which are observed hourly.

At the beginning of the research, basic information about the electrical power system and

the forecasting methods are given and the situation is clarified. Trakya region in Turkey

which is in European side of Turkey is selected as the target region. The data is composed

of hourly observed electrical energy values for the whole year of 2005 and some months of

2006 and 2007 which is 23 months in total. Because the data is large enough and the aim

of the research is to establish accurate forecasting models for short term forecasting,

quantitative methods are used. For this region, forecasting methods are improved for the

short term electrical energy consumption that is the next 12 hours of the last day of each

months and the best fitted model is determined for each months. The best fitted models are

applied to the data and the related results are discussed.

IV

ACKNOWLEDGE

I am appreciated to represent my special thanks to my supervisor and teacher Prof. Dr.

Rauf Nurettin Nişel, my teacher Ass. Prof. Dr. Özcan Baytekin and my friend Betül

Özdemir.

V

ABBREVATION

AC : Alternative Current

ACF : Autocorrelation Function

ADF : Augmented Dickey Fuller Test

AIC : Akaike Information Criteria

AICF : Akaike Information Criteria Function

ANSI : American National Standards Institute

AR : Auto Regression

ARIMA : Auto Regressive Integrated Moving Average

BEDAS : Turkish Electricity Distribution CO.

BIC : Bayesian Information Criteriation

DC : Direct Current

df : Degrees-of-freeedom

LBQ : Indicator for Ljung-Box Q test

MA : Moving Average

MAD : Mean Absolute Deviation

MAPE : Mean Absolute Percentage Error

MSD : Mean Squared Deviation

MW : Unit of Electrical Power (equals to 106 Watt)

PACF : Partial Autocorrelation Function

TEIAS : Turkish Electricity Transmission CO.

VI

TABLE OF CONTENTS

ÖZET……. ...........................................................................................................................II

ABSTRACT ........................................................................................................................ III

ACKNOWLEDGE............................................................................................................. IV

ABBREVATION ..................................................................................................................V

INTRODUCTION........................................................................................................... XIV

SECTION 1............................................................................................................................1

1 ELECTRICAL POWER SYSTEMS ............................................................................1

1.1 Basics Of Electrical Power .....................................................................................1

1.2 Electrical Power System .........................................................................................4

1.2.1 Generators ...........................................................................................................6

1.2.2 Transmission And Subtransmission....................................................................8

1.2.3 Distribution .........................................................................................................9

1.2.4 Loads .................................................................................................................10

SECTION 2..........................................................................................................................13

2 FORECASTING METHODOLOGY.........................................................................13

2.1 Basics of Forecasting Methods .............................................................................14

2.1.1 Qualitative Methods ..........................................................................................16

2.1.1.1 Delphi Methods.................................................................................................18

2.1.1.2 Scenario Writing ...............................................................................................18

2.1.1.3 Market Search ...................................................................................................19

2.1.1.4 Focus Groups ....................................................................................................19

2.1.2 Quantitative Methods ........................................................................................20

VII

2.1.2.1 Naïve Models ....................................................................................................25

2.1.2.2 Autoregressive Process (AR) ............................................................................26

2.1.2.3 Moving Average (MA) .....................................................................................28

2.1.2.4 Autoregressive And Moving Average Process (ARMA) .................................30

2.1.2.5 Smoothing Methods ..........................................................................................32

2.1.2.6 Simple Exponential Smoothing Methods .........................................................35

2.1.2.7 Exponential Smoothing Adjusted For Trend: Holt’s Method...........................37

2.1.2.8 Exponential Smoothing Adjusted For Trend And Seasonality Variation: Winter’s Method ...............................................................................................39

2.2 Test Of Stationarity ...............................................................................................42

2.3 Model Checking ....................................................................................................45

2.4 Model Selection Criteria .......................................................................................48

2.5 Testing Of Forecasting Accuracy .........................................................................49

2.6 Analysis Of Outlier ...............................................................................................51

2.6.1 Univariate Detection Of Outlier........................................................................53

2.6.2 Bivariate Detection Of Outlier ..........................................................................54

2.6.3 Multivariate Detection Of Outlier.....................................................................55

SECTION 3..........................................................................................................................57

3 APPLICATIONS OF FORECASTING METHODS TO THE ELECTRICAL ENERGY DATA OF TRAKYA REGION FOR SHORT TERM ENERGY DEMAND ......................................................................................................................57

3.1 Exploring Data Pattern..........................................................................................58

3.2 Test Of Stationarity ...............................................................................................65

3.3 Applications Of Autoregressive Moving Average Models For January 2005 .....72

3.3.1 Model 1: ARIMA(1, 1, 0)(0, 1, 2)24..................................................................82

VIII

3.3.2 Model 2: ARIMA(1, 1, 0)(1, 1, 1)24..................................................................84

3.3.3 Model 3: ARIMA(1, 1, 0)(0, 1, 1)24..................................................................86

3.3.4 Model 4: ARIMA(0, 1, 1)(0, 1, 1)24..................................................................88

3.3.5 Model 5: ARIMA(0, 1, 2)(1, 1, 0)24..................................................................90

3.3.6 Model 6: ARIMA(0, 1, 0)(2, 1, 0)24..................................................................92

3.3.7 Model Selection For ARIMA Models ..............................................................94

3.4 Applications Of Smoothing Methods For January 2005 ......................................96

3.4.1 Application Of Simple Exponential Smoothing For January 2005 ..................96

3.4.2 Application Of Exponential Smoothing Adjusted For Trend: Holt’s Methods For January 2005................................................................................99

3.4.3 Application Of Exponential Smoothing Adjusted For Trend And Seasonal Variation: Winter’s Methods For January 2005 .............................................102

3.4.3.1 Application Of Winter’s Additive Method For January 2005 ........................102

3.4.3.2 Application Of Winter’s Multiplicative Method For January 2005 ...............104

3.5 Exploring The Best Fitted Forecasting Model For January 2005 .......................107

3.6 Re-Modeling Of January 2005 By SPSS 17 “Time Series Modeler”.................108

SECTION 4........................................................................................................................115

4 EXPLORATION AND APPLICATION OF THE BEST FITTED FORECASTING MODEL FOR EACH MONTHS BY SPSS TIME SERIES MODELER .................................................................................................................115

4.1 Application Of The Best Fitted Forecasting Model For February 2005.............123

4.2 Application Of The Best Fitted Forecasting Model For March 2005.................125

4.3 Application Of The Best Fitted Forecasting Model For April 2005...................127

4.4 Application Of The Best Fitted Forecasting Model For May 2005 ....................129

4.5 Application Of The Best Fitted Forecasting Model For June 2005 ....................131

IX

4.6 Application Of The Best Fitted Forecasting Model For July 2005 ....................133

4.7 Application Of The Best Fitted Forecasting Model For August 2005................135

4.8 Application Of The Best Fitted Forecasting Model For September 2005 ..........137

4.9 Application Of The Best Fitted Forecasting Model For October 2005 ..............139

4.10 Application Of The Best Fitted Forecasting Model For November 2005 ..........141

4.11 Application Of The Best Fitted Forecasting Model For December 2005...........143

4.12 Application Of The Best Fitted Forecasting Model For August 2006................145

4.13 Application Of The Best Fitted Forecasting Model For September 2006 ..........147

4.14 Application Of The Best Fitted Forecasting Model For October 2006 ..............149

4.15 Application Of The Best Fitted Forecasting Model For November 2006 ..........151

4.16 Application Of The Best Fitted Forecasting Model For January 2007...............153

4.17 Application Of The Best Fitted Forecasting Model For February 2007.............155

4.18 Application Of The Best Fitted Forecasting Model For March 2007.................157

4.19 Application Of The Best Fitted Forecasting Model For April 2007...................159

4.20 Application Of The Best Fitted Forecasting Model For May 2007 ....................161

4.21 Application Of The Best Fitted Forecasting Model For June 2007 ....................163

4.22 Application Of The Best Fitted Forecasting Model For July 2005 ....................165

5 CONCLUSION ...........................................................................................................167

REFERENCE ....................................................................................................................169

BOOKS………….. ............................................................................................................169

ARTICLES AND WEB PAGES ......................................................................................172

X

LIST OF TABLES

Table 1.1: Components of A Modern Electrical Distribution System ...................................5

Table 1.2: Heating Values of the Sources of Power Generation Used in Turkey..................7

Table 1.3: Sources of Power Generation in Turkey From 1970 to 2007 ...............................8

Table 1.4: Capacitive (a) and Inductive (b) Loads...............................................................10

Table 2.1: Organization Chart of Forecasting ......................................................................16

Table 2.2: Elements of Focus Groups ..................................................................................20

Table 2.3: Summary of ACF and PACF in AR(p), MA(q) and ARMA(p, q) Processes.....31

Table 2.4: The Route of AR(p), MA(q) and ARMA(p, q) Processes ..................................32

Table 2.5: Two Filter for Time Series..................................................................................33

Table 2.6: The Process of Smoothing A Data Set................................................................34

Table 2.7: Smoothing Methods – ARIMA...........................................................................35

Table 2.8: Comparison of Smoothing Constants .................................................................37

Table 2.9: Critical Values for ADF Test ..............................................................................44

Table 3.1: Autocorrelation of January 2005 with Lag 1 Difference ....................................60

Table 3.2: Autocorrelation of January 2005 with Seasonal Difference ...............................61

Table 3.3: Seasonally Differentiated Time Series, Seasonal Index: 24 ...............................69

Table 3.4: Autocorrelation of power0105_Bus_Dif1 ..........................................................80

Table 3.5: Partial Autocorrelation of power0105_Bus_Dif1 ...............................................81

Table 3.6: Comparison of ARIMA Models .........................................................................94

Table 3.7: Comparing ARIMA(0, 1, 1)(0, 1, 1)24 and Smoothing Methods ......................107

Table 3.8: Forecasting Boundary of ARIMA(0, 1, 1)(0, 1, 1)24 ........................................108

XI

Table 3.9: Definition of Time Series Modeler Function ....................................................109

Table 3.10: Definition of Time Series Modeler Function ..................................................111

Table 4.1: Model Description of Raw Data, Outlier Detection is off ................................116

Table 4.2: Model Statistics of Raw Data, Outlier Detection is off.....................................117

Table 4.3: Model Description of Raw Data, Outlier Detection is on.................................118

Table 4.4: Model Statistics of Raw Data, Outlier Detection is on .....................................119

Table 4.5: Model Description of Data of Business Day, Outlier Detection is off..............120

Table 4.6: Model Statistics of Data of Business Day, Outlier Detection is off ..................121

Table 4.7: Model Description of Data of Business Day, Outlier Detection is on ..............121

Table 4.8: Model Statistics of Data of Business Day, Outlier Detection is on ..................122

Table 4.9: Summary of Forecasting Models for All Months .............................................168

XII

LIST OF FIGURES

Figure 2.1: Electrical Energy Consumption of Trakya Region January 2005 .....................23

Figure 2.2: Electrical Energy Consumption of Trakya Region 2005...................................24

Figure 2.3: Time Series Analysis Process ............................................................................25

Figure 2.4: Scatterplot for Bivariate Outlier Detection........................................................55

Figure 2.5: Multivariate Detection of Outlier ......................................................................56

Figure 3.1: Scatter plot of January 2005 with Lag 1 Difference..........................................59

Figure 3.2: Scatter plot of January 2005 with Seasonal Difference.....................................61

Figure 3.3: Trend Line Plot for January 2005 ......................................................................62

Figure 3.4: Growth Curve Trend Model Plot for January 2005...........................................63

Figure 3.5: Quadratic Trend Mode for January 2005 ..........................................................63

Figure 3.6: Component Analysis of January 2005. ..............................................................65

Figure 3.7: Consumption of Electrical Power Over Jan. 2005 ............................................66

Figure 3.8: Autocorrelation Function for powerJan2005.....................................................71

Figure 3.9: Partial Autocorrelation Function for powerJan2005 .........................................71

Figure 3.10: Autocorrelation Function for powerJan2005_sDiff ........................................72

Figure 3.11: Partial Autocorrelation Function for powerJan2005_sDiff .............................73

Figure 3.12: Power Consumption Business Days versus Holidays .....................................74

Figure 3.13: Power Consumption of Business Day .............................................................75

Figure 3.14: Autocorrelation Function for power0105_Bus ................................................75

Figure 3.15: Seasonally Differentiated Power Consumption of Business Day ...................76

Figure 3.16: Autocorrelation Function for power0105_Bus_Dif ........................................77

XIII

Figure 3.17: Seasonal+ Lag1 Differentiated Power Consumption ......................................78

Figure 3.18: Autocorrelation Function for power0105_Bus_Dif1 ......................................79

Figure 3.19: Partial Autocorrelation Function for power0105_Bus_Dif1 ...........................79

Figure 3.20: Forecasting Boundary of ARIMA(0,1,1)(1,1,0)24 .........................................114

XIV

INTRODUCTION

Since there has been an increasing trend for the use of energy, the consumption

values are getting higher and higher if we don’t regard the economic crises. For any part of

life, the electrical energy is a non-replaceable item because the advantages of practically

use of electrical power in our smart home. Therefore for the government or any firms who

have the responsibility of the electrical power supplying from generation to distribution

have an import task for people’s needs. The energy for the people should be always eligible

in security. Any interruption can cause stopping the surgery operation or shutting down the

main server of a web provider if they haven’t taken any preventative action. Therefore

using the sources of electrical power efficiently is a must. Automation of the power flow

and estimating the fluctuation in the usage amount should be reinforced with the short term

power forecasting.

As I want to mention the importance of the electrical energy for ordinary life,

this research is aiming to develop forecasting models for short time forecasting like as

twelve hours energy demands. To achieve that, in the first section of the research, the basics

of electrical power and the components of electrical power distribution system are given

because we will use the data of electrical power consumption of Trakya region in Turkey.

XV

Correspondingly, in section two, the basics of forecasting methods are given and structures

of forecasting iteration are explained. In the section three, the forecasting methods given in

the section two are separately applied to the data of the first month and the related result is

given by the help of SPSS, Minitab, Matlab, Excel, and some other sources. You can also

find the discussion of the each model in this section. In the section four, by the application

of the SPSS Time Series Modeler, forecasting result are found for the rest of the 22 months.

And again the results of the each moth are discussed here.

In the conclusion part, the best fitted forecasting methods are represented in a table

with outlier information. At the end of the research, you can find the data used in the

analysis.

SECTION 1

1 ELECTRICAL POWER SYSTEMS

1.1 Basics Of Electrical Power

The history of electrical power system goes back to the 18th century and it starts

with Benjamin Franklin; by a kite string, electrical spark is understood as the base of the

electrical power then the principles of electricity become understandable gradually1. After

that the first electrical distribution system was established by Tomas Edison in 1882 which

was supplying direct current (DC Power) at Pearl Street Station in New York City. Then, in

1885, by William Stanley, transformer that regulates the magnitudes of current and voltage

level was invented and by Nicola Tesla, induction motor that uses alternative current (AC

Power) was invented in 1888.

The basic difference of AC power system and DC power system is that the DC

power system is supplied by DC current generators but the AC power system is supplied by

1 Robert H. Miller, James H. Malinowski, Power System Operation, Edition: 3, McGraw-Hill Professional, 1970, ISBN 0070419779, 9780070419773

2

AC current generator. Basically the DC system has a constant current level over time but

the AC system produces a current which changes sinusoidally over the time. The unit of

power is called watt which defines by the formula below for the DC power system;

P V I= (1.1)

V

IR

= (1.2)

2P I R= (1.3)

Where, P is the power which is in Watt, V is the potential which is in Volt, I stands for the

current which is in Ampere and the R stands for the resistance of the system which is given

in Ohm. Then the result of the equation is given by watt. If we expand the formulation for

the AC power system then the every components must be given in time domain t. The

following equations are defined for AC systems2;

( ) ( ) ( )P t V t I t= (1.4)

( )( )

( )

V tI t

Z t= (1.5)

( )Z t R j X= + (1.6)

2( ) ( ) ( )P t I t Z t= (1.7)

Where, ( )Z t is the impedance of the AC power system which is given in ohm with

complex numbers. Since the AC power is in discussion the resistance is not only R, inactive

power components which are inductance and capacitance are added to the total resistance

and then the new component is called as impedance.

2 Mahmood Nahvi, Joseph Edminister, Schaum's outline of theory and problems of electric circuits, Edition: 4, McGraw-Hill Professional, 2002, ISBN 0071393072, 9780071393072, p.219

3

The AC power system has two components, the first one is active power and the

second one is reactive power. In the street, power generally has the meaning of the active

power. The active power is used to run any kind of electrical machines, but the reactive

power is used to generate electromagnetic field in the winding of the motors. Wherever the

inductive and capacitive loads are present in a system, reactive power is consumed by the

system. The active and reactive powers are defined by the formulas given below3;

2( ) ( ) ( ) c o sP t I t Z t j= … (W) (1.8)

2( ) ( ) ( ) s i nQ t I t Z t j= … (Var) (1.9)

2 2S P j Q P Q= + = + … (VA) (1.10)

Where, the S is known as the complex power. Since the I in ampere, Z in ohm, V in volt the

result of the these powers are observed in Watt, Var and VA (volt-ampere). In generally

power is associated kilo so the powers are given in kilowatt, kWh which means that a

system consumes 1.000 Watt electrical power per hour. If the system works 5 hours, it

consumes 5.000 Watts, in another word, it consumes 5 kW.

In this research, active power consumptions of the Trakya region in Turkey are

observed by the TEIAS4 so the analysis is establish on active power consumption. Because

we will discuss the power consumption of a very large area of Turkey, the powers are given

by megawatt, MWh which is 1.000 times of kWh or 1.000.000 Watt.

3 Nahvi, Edminister, p.224 4 TEIAS stands for the Turkish Electrical Power Distribution Anonym Firm

4

1.2 Electrical Power System

By the invention of Tesla the DC electrical distribution system was replaced to the

AC electrical distribution system because of many advantages of AC system5. The

advantages of AC distribution system can be summarized as below6:

1. Voltage level can be easily transformed in AC systems, thus providing the

flexibility for use of different voltage for generation, transmission and

consumption.

2. AC generators are much simpler than DC generators.

3. AC motors are much simpler and cheaper than DC motors

Basically, the electrical power in the distribution system is supplied by the

generators. In modern electrical distribution system, the distribution system is designed as

to supply the needs for electrical power without interruption. Therefore the system that the

generators are connected each other is called interconnected network is used for the modern

distribution system7.

5 Hadi Saadat, Power Transmission System, ISBN10: 0070122350 ISBN13: 9780070122352, 1/1/1998, Mcgraw Hill Book Company, p.1

6 Prabha Kundur, Neal J. Balu, Mark G. Lauby, Power system stability and control, McGraw-Hill Professional, 1994, ISBN 007035958X, 9780070359581, p.4

7 Saadat, p.4

5

Table 1.1: Components of A Modern Electrical Distribution System

Reference: Alan Elliott Guile, William Paterson, D. Das, Electrical Power Systems, New Age International, 2006, ISBN 8122418856, 9788122418859, p.2

By interconnecting, the large generators (MW) that produce electrical power at

cheaper cost than the small generators feed the whole system not a particular area so if

there is a fault in one area, this area is supplied by borrowing adjoining interconnected

areas. Therefore, the interconnected distribution system is not only economical but also it is

more reliable8. The basic components of the modern electrical system can be listed as

below

8 Alan Elliott Guile, William Paterson, D. Das, Electrical Power Systems, New Age International, 2006, ISBN 8122418856, 9788122418859, p.3

6

· Generators

· Transmission and subtransmission

· Distribution

· Loads

1.2.1 Generators

Generator is a kind of machine that if the stator is turned by applying a power from

outside, called mechanical power, and giving a direct current to exciting winding called as

excitation currrent, it generates electrical power. Therefore, they are one of the basic

components of an electrical system. There are made up as one phase or three phases.

Generally three phase generators are higher capacity than one phase generators and one

phase generators are used for local needs for electricity, not for a distribution system.

Capacities of generators are changed from 50 MW to 1500 MW9.

The sources to produce mechanical power to turn the generators are obtained a

variety of way. These are hydro, geothermal, wind, tidal, biomass, fossil fuels and nuclear

power10. Traditionally, damps have been used to produce electrical power but since the

trend of needs for electrical power had overcame the capacity of damps in many countries;

many of the countries have invoked other sources to provide their needs for electrical

energy. In the Table 1.1, summarizes the energy sources and their heating content and the

component of the chemical compounds in Turkey.

9 Saadat, p.4 10 Anthony J. Pansini, Kenneth D. Smalling, Guide to electric power generation Edition: 2, Press: Marcel

Dekker, 2002, ISBN 0824709276, 9780824709273, p.13

7

Table 1.2: Heating Values of the Sources of Power Generation Used in Turkey

Heating Values of Sources

Source 2006 2007

Hard Coal+Imported Coal 29.504 32.115

Lignite 83.932 100.320

Total 113.436 132.435

Fuel Oil 16.769 21.434

Diesel Oil 627 517

Lpg 0 0

Naphta 141 118

Total 17.537 22.069

Natural Gas 150.588 179.149

Total 281.561 333.653

Main Fuel 2.480 5.292

Auxiliary Fuel 1.505 1.601

Total 3.985 6.893

Main Fuel 80 37

Auxiliary Fuel 468 477

Total 548 514

Reference: The table formed by the data obtained from the source: http://www.teias.gov.tr/ist2007/45.xls

Figure 1.2 shows the percentage of the sources of power generation during 1970 to

2007. We can see that in 1970 the percent of the total heating sources is double of the total

hydro source and the years later, 1982 and 1988 the percent of the hydro power are greater

than the percent of the heating sources. However there is an increasing trend of using

heating sources, we can see that in 2007, the percent of the total heating sources is 5 times

bigger than the total hydro source. Another important point is that after 1984 geothermal

power and wind power started to use and in the recent years it is doubled but the percent of

the total of them is not satisfactory.

8

Table 1.3: Sources of Power Generation in Turkey From 1970 to 2007

Reference: Formed by the data obtained from the source: http://www.teias.gov.tr/ist2007/7.xls

1.2.2 Transmission And Subtransmission

Transmission of the power is performed by the transformers. By the meaning of the

transmission is that the depending on the ratio of transformer the voltage level or the

current level of the system or both is converted to another values. By transferring the

absolute value of the voltage level of the electric, transmission of the electrical power for

9

long distance become more effective11. Transmission of the high voltage of electric is more

effective in terms of loses but the insulation and design problems set limit of current level

for generation, which is usually 30kV. Therefore to make the transmission of electricity for

long distance with high voltage, step-up transformers are used to get higher voltage level

before transmission12.

By the term transmission, it is wanted to express, transferring the power for long

distance and by the term subtransmission, after the power transferred to long distance the

power should be reduced to voltage level of electric which can people use in their smart

home. In the transmission line the voltage level of the electricity which is called high

voltage or very high voltage are generally available in 60 kV, 69 kV, 115 kV, 138 kV, 161

kV, 230 kV, 345 kV, 500 kV, 765 kV13 for ANSI standard14. For the subtransmission line

the voltage level should be finally decreased to 230 Volt for Europe, Middle East and

Africa and 110 Volts for USA, Japan, Australia and some of other countries.

1.2.3 Distribution

Distribution is the last component of the power transmission. Since the electricity is

transmitted by transmission and subtransmission lines to the location where the power is

need, to serve for the people is performed by distribution system. The distribution system

can be underground and overhead because of the weather condition. The convenience of the

underground system makes it popular around the world; the 70 percent of the newly

building areas are equipped by underground system15. Generally distribution of electricity

is run by local government because the controlling of the system some times becomes

difficult. The distribution of the electricity is run by BEDAS in Turkey.

11 Robert H. Miller, James H. Malinowski, Power System Operation, Edition: 3, McGraw-Hill Professional, 1970, ISBN 0070419779, 9780070419773, p.2

12 Saadat, p.5-6 13 Saadat, p.6 14 ANSI: American National Standart Institute 15 Saadat, p.8

10

1.2.4 Loads

As it is defined in the basics of electrical power, the load of the system is the total

impedance of the system. If the system is supplied by the AC power system then load has

three components which are resistive loads, inductive loads and capacitive loads. The

inductive and the capacitive loads make an angle difference between the current and the

voltage in sinusoidal wave form. The angle is called as load factor which takes minus, plus

value. For inductive load, load factor becomes minus and lags the voltage wave and for

capacitive loads, it takes positive values which mean that the current angle is leading the

voltage angle. For the resistive load, there is no angle in AC system16.

Table 1.4: Capacitive (a) and Inductive (b) Loads

Reference: Dale R. Patrick, Stephen W. Fardo, Rotating Electrical Machines and Power Systems, Edition: 2, The Fairmont Press, Inc., 1997, ISBN 0881732397, 9780881732399, p.35-38

In AC system, the load factor is wanted to be higher as much as possible because of

the power conservation. In the last review of the “Electrical Installation on Residential

Constructions for Low Voltage” the power factor is adjusted to 0.90 – 1. The meaning of

16 Dale R. Patrick, Stephen W. Fardo, Rotating Electrical Machines and Power Systems, Edition: 2, The Fairmont Press, Inc., 1997, ISBN 0881732397, 9780881732399, p.40-41

11

this change is that the people must repair their system and then they profit in terms of

money by this changing17.

17 Ahmet Becerik, Ülkemizdeki Reaktif Güç Kompanzasyonuna Bir Bakis-I, Elektrik Mühendisleri Oda, Izmir, 12 March 2008, http://www.emo.org.tr/ekler/6556dfe948f58c5_ek.pdf?dergi=4, p.1-2

13

SECTION 2

2 FORECASTING METHODOLOGY

Forecasting is the art of saying what will happen, and then explaining

why it didn’t. - Anonymous.

Forecasting is a systematic effort to anticipate future events, condition, amount of

anything, establishment of future expectation by the analysis of past data, or information of

opinions18. Selecting a proper forecasting method is the critical point for a successful

forecasting model for all type of the data and subjects. The importance of selecting the

correct forecasting methods can be explained by the internal result of forecasting. In the

forecasting process, every step is an observation for the success of the step performed one

before.

18 Chatfield, p.73

14

Forecasting methods can be applied every data with regarding the trend, cycle,

seasonality and irregular component. However every method has both advantages and

disadvantages so the selecting the appropriate methods is one of the most important issue.

For example, regarding a manufacturer, any significant over-or-under sales forecast error

may cause the firm to be overly burdened with excess inventory carrying costs or else

create lost sales revenue through unanticipated item shortages. When demand is fairly

stable, e.g., unchanging or else growing or declining at a known constant rate, making an

accurate forecast is less difficult than the situation includes unknown trend and unexpected

events. If, on the other hand, the data has historically experienced an up-and-down sales

pattern, then the complexity of the forecasting task is compounded. In this research we

ignore the unexpected events because it is not known how the situation changes and how it

would affect the forecast. This can be estimated by applying some methods but it is not a

subject of this research.

Time series methods are especially good for short-term forecasting where, within

reason, the past behavior of a particular variable is a good indicator of its future behavior, at

least in the short-term. The typical example here is short-term demand forecasting. Note the

difference between demand and production - demand should be zero.

2.1 Basics of Forecasting Methods

By the explanation it is a reality that modern economic system is based on the

explanation for the amount of future needs by analyzing the up to date data. Forecasting

methods are divided into two categories. First one is based on the explanation of the

behavior of the data collected until the time forecasting would be performed; this category

is called extrapolation method. The second one is called explanatory method which is based

on the factors that can affect the amount of the product or service. For example, the belief

that the sale of doll clothing will increase from current levels because of a recent

advertising blitz rather than proximity to Christmas illustrates the difference between the

15

two philosophies19. Both methods can produce successful result but the former method,

explanatory method, is more difficult to apply.

In this study, the extrapolation method will be used because, for short term

electrical energy consumption, it is important to recognize the fluctuation of the demand. In

addition to this it is also not easy to understand for what purposes people use electrical

energy just because we have the past related data. Since the power consumption data is

observed over time, it is supposed that the time series methods are best for the explanation

of the series. Time series methods are especially good for short-term forecasting where,

within reason, the past behavior of a particular variable is a good indicator of its future

behavior, at least in the short-term. The typical example here is short-term demand

forecasting. Note the difference between demand and production - demand should be zero.

Forecasting techniques are based on systematic effort so that the expectation can

be corrected by the correction of the errors done during the forecasting process. Basically

forecasting techniques are listed below in a table.

19 Peter Kenedy, A Guide to Econometrics, Edition: 5, MIT Press, 2003, ISBN 026261183X, 9780262611831, p.201-202

16

Table 2.1: Organization Chart of Forecasting

2.1.1 Qualitative Methods

Qualitative methods are primarily based on judgments of past experience when

there is no past data to take an appropriate estimation formula and qualitative methods used

for the long term forecasting. However the people studying on qualitative methods don’t

have health or medical educational background, qualitative methods are generally used for

Forecasting Techniques

Techniques Routes

Qualitative Quantitative 1 - Top-down route

2 – Bottom-up route

1 - Delphi Methods 2 - Nominal Groups Techniques

3 - Jury of Exclusive Opinion

4 - Scenario Projection

1 – Naïve Model

2 – Auto Regressive

3 - Moving Average

4– Autoregressive Moving Average

5 – Simple Exponential Smoothing

6 – Holt’s Method

7 – Holt-Winters Method

17

the health and medical study20. As it is defined by Catherine P., Nicholas M. qualitative

research asks qualitative question as follows:

“Measurement in qualitative research is usually concerned with taxonomy or

classification. Qualitative research answers questions such as, ‘what is X, and how

does X vary in different circumstances, and why?’ rather than ‘how big is X or how

many X’s are there?’”

The differences between quantitative and qualitative methods are not only the

quantitative method uses the observed data or the numbers. Sometimes the qualitative gives

more accurate result by eliminating the misunderstanding of language or terms of a specific

disciplinary by asking the question face-to- face21. Well known qualitative methods are

listed below.

1. Delphi Method

2. Growth Curves

3. Scenario Writing

4. Market Search

5. Focus Groups

20 Catherine Pope, Nicholas Mays, Qualitative Research in Health Research, Blackwell Publishing Ltd. 2006, ISBN-13: 978-1-4051-3512-2, ISBN-10: 1-4051-3512-3, p.1

21 Pope and Mays, p.5-6

18

2.1.1.1 Delphi Methods

The Delphi method is an iterative process which gathers the expert’s options22 .

All experts or forecasters are meted together to make a future forecast on specific products

or services but the result of the consensus possibly may not be acceptable for all experts. As

in the continue time, everyone defends their point of view and poses their opinions to the

investigating team. Then the team sends the summary of the comments and mails the all

participants. This time every participant can see the others opinion and they can evaluate

themselves and modify the thoughts regarding the others opinions.

The procedures last when the majority of the experts reach the same point of view

after these procedures, all participants are invited to debate their opinion again and then the

result of the consensus are announced for the future expectations.

Nowadays the Delphi technique has a different meaning. It involves asking a body

of experts to arrive at a consensus opinion as to what the future holds. Underlying the idea

of using experts is the belief that their view of the future will be better than that of non-

experts (such as people chosen at random in the street). One of the most important problem

of qualitative methods which cause the models to be biased is that the qualitative methods

depends on people opinion, let say the models are subjective23.

2.1.1.2 Scenario Writing

Scenario writing is a special estimation for the specific un-clear future which

includes an organization of long term forecasting. This scenario writing is based on the

trends, people needs, new technology and also political view of the government. These

factors are important long years before the issue comes out.

22 Kenneth Lawrence, Ronald K. Klimberg, Fundamentals of Forecasting Using Excel Industrial Press, Inc.,1’st edition, November 15, 2008, p.4

23 Lawrence and Klimberg, p.4-5

19

Scenario writing is established, in general, for the forecast of the many years in the

future. For example, if a company wants to write a scenario for long-term profitability,

generally planning department, should not focus on the short-term profitability which they

need to ignore short-term indicators. After discussion by employees of the planning

department, top management team reacts to important environmental changes.

2.1.1.3 Market Search

Market research is an affair that collects the customer information about new or old

products. After the research is completed, the result is used to profile of the product in the

market. Therefore the market research is aiming to collect general information about the

product, which is different than the focus group that is aiming to collect this kind of

information from the group of people who were already selected or determined by a group

of expert. However by the focus group detailed information which is not appropriate to

collect by survey can be collect by the help of a moderator, collected information can not

be generalized24.

2.1.1.4 Focus Groups

The focus group method is an interview which is performed by group of people. In

the social sciences, focus groups allow interviewers to study people in a more natural

setting than a one-to-one interview so the result of the method generally become more

natural and deterministic. Because the participants are not restricted for the answers, they

can say anything, by this way, the researchers gain any type reflection about the product

and also the feelings behind the facts can also be illustrated25. If the question is easy to

24 Lawrence and Klimberg, p.4 25 Nancy Grudens-Schuck, Beverlyn Lundy Allen, Kathlene Larson, Focus Group Fundamentals, Iowa State

University, May. 2004, p.2

20

understand, the results are believable and also it is cost and time effective to get sample

size. The element of Focus Groups is given in the Table 2.2

Table 2.2: Elements of Focus Groups

Reference: Grudens, Allen and Larson, p.7

2.1.2 Quantitative Methods

Quantitative methods are research techniques that are used to gather quantitative

data - information dealing with numbers and anything that is measurable. Statistics, tables

and graphs, are often used to present the results of these methods. They are therefore to be

distinguished from qualitative methods. Past time data are needed to use to anticipate the

21

future by quantitative forecasting methods. Further more, quantitative methods are divided

into two groups time series methods which uses just the past time data and causal

methods26. In this research, time series forecasting techniques are used to produce better

result.

The data that is collected or observed during incremental time period is named as

time series data27. Since time series methods are used, frequency which represents the

number of occurrences over time may be defined by minute, half-hour, hour, day, week,

mouth, and so on28. Depends on the frequency, we can see time series components or

patterns on the time series data. As in the quantitative methods, numerical indicators must

be observed successfully. However, we can not assume that the data is random because

collecting the data over time are disposed to have trend, seasonal pattern and the other time

series characteristics29. These are the basic issue in the quantitative methods application;

trend, cycle, seasonality and irregularity. The time series characteristic features can be

described as below:

1. Trend: It is a component which can be seen locally or globally but it lies on the

time series for long time. Trend can be upward or downward in the series. It is

important to estimate the trend because the mean of the changes in the series is

calculated by the slope of the trend. The more the slope of the trend line is, the more

the difference between next occurrences, and vice wise30.

2. Seasonality: In a time series, the seasonality occurs in a period of time

consecutively. Generally, economic pattern and the time series which is observed by

hourly, daily, weekly, yearly, and so on have this component. In engineering,

26 Lawrence and Klimberg, p.5 27 Bovas Abraham, Jhonnes Ledolter, Statistical Methods for Forecasting, Wiley Series in Probability and

Statistics”, John Willey &Sons, p.58-59 28 Lawrence and Klimberg, p.33 29 John E. Hanke, Dean W. Wichern, Business Forecasting, Pearson, Prentice Hall, New Jersey, 2005, ISBN

0-13-122856-0, pp.327 30 Lawrence and Klimberg, p.34

22

demand of power, gas, water, and any kind of needs have the problems of

seasonality which is always be clarified and be well estimated31.

3. Cyclical: It is described as long-term data pattern that repeat themselves. In

electrical energy demand, cyclical components occur as annual, weekly and daily

cycles32.

4. Irregular: In time series, after the trend, seasonality, cycles are removed, the

irregular component of the series is observed. It is the pattern which is not described

by the rules.

The series may have all of the components, or one or more of the components

together. We can see these indicators from the electrical energy distribution of the Trakya

region in Turkey.

31 Ajoy K. Palit, Dobrivoje Popović, Computational intelligence in time series forecasting: theory and engineering applications, Springer, London, 2005, ISBN:1852339489, p.21

32 Michael P. Clements, David F. Hendry, A Companion to Economic Forecasting, Blackwell Publishing, 2002, ISBN 0631215697, 9780631215691, p.81

23

0 100 200 300 400 500 600 700 8001000

1500

2000

2500

3000

3500

4000

4500Consumption of Electrical Power During Jan. 2005

Ele

ctrica

l Po

we

r (M

Wh

)

Time Interval Jan. 2005 (Hour)

Figure 2.1: Electrical Energy Consumption of Trakya Region January 2005

According to Figure 2.1, power demand changes with the time, the data pattern

includes seasonality which the needs reach the maximum and minimum values in every 24

hours. This chart also shows that at night from 6pm to midnight, electrical energy demand

is at maximum. We can also see that 2 days for per weeks have less consumption, this

should be weekends.

24

0 1000 2000 3000 4000 5000 6000 7000 8000 90001000

1500

2000

2500

3000

3500

4000

4500

5000Consumption of Electrical Power During 2005

Ele

ctrica

l Po

we

r (M

Wh

)

Time Interval Jan. 2005 - Dec. 2005

Figure 2.2: Electrical Energy Consumption of Trakya Region 2005

Furthermore, if we calculate a larger time series, Figure 2.2, it is also seen that the

electrical energy demand has annually cycle. The demand goes to maximum level at winter

time and lowest level at spring and autumn but in summer time, the consumption is higher

than spring and autumn but lower than winter time. In addition to these, there are two

lowest points in January and November. There are the Islamic vacation33 celebrated

annually.

Quantitative methods can be applied the data after the needed process has been

done. Upon starting to analysis, we need to estimate/find the seasonality and then eliminate

the trend and cycle at the end of the procedure data has to become stationary. Then we can

25

apply the forecasting techniques to find the electrical consumption for any demanded

intervals.

Figure 2.3: Time Series Analysis Process

2.1.2.1 Naïve Models

Basically Naïve forecasting model is the easiest model to understand the base of

forecasting techniques. The Naïve model depends on the last observed data to calculate the

forecasting values34. The Naïve forecasting model is described as below:

1ˆt tY Y+ =

Where, tY is the observed data at the time period t and 1ˆtY + is the forecasted value for time

period t. By this method one hundred percent of forecasting values is imposed by the

current value of the series, having this feature the method is sometimes called as “no

change” forecast35. Since the Naïve model is accepted as the base of the forecasting

techniques, it is used to test the accuracy of the forecasting models by determining the

accuracy ratio36.

33 www.yildizliblok.com.tr/2005Takvimi.asp 34 Edwin J. Elton, Martin Jay Gruber, Investments: Portfolio theory and asset pricing, MIT Press, 1999, ISBN

0262050595, 9780262050593, p.378 35 John E. Hanke, Dean W. Wichern, Business Forecasting, Pearson, Prentice Hall, New Jersey, 2005, ISBN

0-13-122856-0, p.102 36 Charles W. Ostrom, Time series analysis: regression techniques, Second edition SAGE, 1990, ISBN

0803931352, 9780803931350, p.85

26

Accuracy Ratio = _ m o d

_ m o d

f o r e c a s t i n g e l

n a i v e e l

R M S E

R M S E (2.1)

Where, RMSE is stand for root-mean-squared-error, which is explained later of the

research.

2.1.2.2 Autoregressive Process (AR)

Basically, autocorrelation is described as values of dependent variable in one time

period are linearly related to values of the dependent variable in another time period37. An

AR model is represented as the function of dependent past data38. Therefore time series

forecasting model can be defined by a function of time which contains constant, predictor

and error term as following:

ttt xfY eb ++= )( (2.2)

Where, tY is the desired data point to be forecasted, tx is the predictor variable or function

of time, b is the constant for over the time and te is the error term as well.

ttt aYY =--- - )()( 1 mfm (2.3)

Where, tf is the coefficient and ta is the uncorrelated random variable. Then, we need a new

operator B which is called as backward-shift to shift the time series one step back. This

operator for one shift can be defined as 1-= tt YBY , and it is in general form:

mttm YYB -= (2.4)

37 Hanke and Wichern, p.345 38 Bovas Abraham, Jhonnes Ledolter, Statistical Methods for Forecasting, Wiley Series in Probability and

Statistics”, John Willey &Sons, p.192

27

Combining the formulation (2.3) and (2.4) auto regression model turns into more

representative formulation for the time series.

tt aYB =-- ))(1( mf (2.5)

Estimation of sufficient p for AR models is ca l led as determination of AR. For

determination there have been two ways, first is using autocorrelation function (PACF) and

the second one is information criterion function (AICF). This step can be made by

empirically39. In this research, because it is easy to apply to the series, PACF is used to

determine the order of the AR models. Therefore before deciding to use an AR model,

these two questions should be asked to the data40:

1. What is the order of process?

2. How can the parameters of the process be estimated

To describe the Partial autocorrelation function, following AR models is used to find the

order of the partial autocorrelation...

ttpp 111,11,01 eff ++= -

ttt ppp 222,212,12,02 efff +++= --

tttt pppp 333,323,213,13,03 effff ++++= --- (2.6)

…

39 Ruey S. Tsay, Analysis of Financial Time Series, John Wiley and Sons, 2001, ISBN 0471415448, 9780471415442, p.36

40 Christopher Chatfield,The Analysis of Time Series: An Introduction, Edition: 6, CRC Press, 2004, ISBN

1584883170, 9781584883173, p.59

28

Where, j,0f is the constant term, ji ,f is the coefficient of jtp - and jte is the error of AR(j)

model. in the process, the partial autocorrelation which is highest than the order of the AR

is going to be zero41.

2.1.2.3 Moving Average (MA)

Moving average is described as an average shift of the body of the data. As an

instance, a 12-hour moving average is produced by dividing 12 the sum of the nearest data

in the series. End of this procedure, the average of the series is shifted forward by 12 times.

The moving average method is defined as following for the MA(1):

11 --=- ttt aaY qm or tt aBY )1( qm -=- (2.7)

Where, finite number of non-zero 1y weight is 11 qy -= and 1-= tt aBa . This is for the first

order moving average but if we consider the order q moving average, then the weight is

rewritten for the order q:

ttq

qtt aBaBBY )()...1( qqqm =---=- (2.8)

After that autocorrelation function is defined as

211 q

q

+

-=p (2.9)

Where, 0=kp for k > 1. This shows that observations more than one step are not

correlated but one step observations should be correlated42. Furthermore, if we expand the

autocorrelation model for the order q, then we observe the following equation:

41 Tsay, p.36

42 Abraham and Ledolter, p.215

29

q

qkqkk

kp2

12

11

1 qq

qqqqq

L

L

++

+++-=

-+ k=1, 2, . . . ,q (2.10)

As a result, because the MA models are time invariant and they are produced by

finite linear combination of white noise, the MA models are always said to be weakly

stationary43.

To determine the sufficient order of the MA models, partial autocorrelation function

is also used as AR models with some differences. While PACF of MA process at the order

of q is waving like a sinusoidal or exponential, ACF of the model cuts immediately after

lag q. However, it is difficult to determine the partial autocorrelation for the higher degree

of the MA model because the model is dominated by the disruption in exponential and

sinusoidal wave.

PACF for the MA models is defined as follows:

4

2

211,11

)1(

1 q

qq

q

qf

+

--=

+

-== p (2.11)

6

22

42

2

21

21

21

212

2,21

)1(

111 q

qq

qq

qf

-

--=

++

-=

+

-=

+

-=

p

p

p

pp

8

23

21

31

2,21

)1(

21 q

qqf

-

--=

-=

p

p (2.12)

For the thk order, the PACF should be,

)1(2

2

.1

)1(+-

--=

k

k

kkq

qqf (2.13)

43 Tsay, p.43

30

The difference in terms of the PACF and the ACF functions between AR(p) and

MA(q) is that in AR(p) models while ACF is going to infinity, the PACF cuts of after lag p,

however, for the MA(q) models while PACF is going to infinity and dominated by damped

exponentials and sinusoidal wave, ACF cuts off after lag q44.

2.1.2.4 Autoregressive And Moving Average Process (ARMA)

A useful model is composed of the advantages of both autoregressive and moving

average process so this process is called mixed autoregressive and moving average process

(ARMA). The model of ARMA(p, q) is the representation of AR model with the order of p

and MA model with the order of q. The ARMA process is defined as following:

tq

qtp aBBYBB )1())(1( 111 qqmff ---=---- LL (2.14)

Then if we redefine the AR and MA process as following:

AR(p): 1 1( ) 1 pB B Bf f f= - - -L (2.15)

MA(q): 1( ) 1 qqB B Bq q q= - - -L (2.16)

Such a way, a pure MA process is described as

( )t tY B am y- = ( )

( )( )

BB

B

qy

f= (2.17)

And a pure AR process is described as

( ) ( )t tB Y ap m- = ( )

( )( )

BB

B

fp

q= (2.18)

44 Abraham and Ledolter, p.218

31

In ARMA process, autoregressive parameters ( 1f , 2f , 3 , , pf fL ) manage the

autocorrelation of the model, but the moving average parameters ( 1q , 2q , 3 , , qq qL ) don’t

have such an effect on the process45. We should also be sure that the roots of ( ) 0Bf = are

outside the unit circle for stationarity and the roots of ( ) 0Bq = are outside the unit circle

for invertibility46.

For ARMA(p, q) model, the ACF and the PACF have the behaviors of both AR(p)

and MA(q) process. In addition to this we can estimate the parameter of I(q) by the PACF,

as it is indicated by Wei, PACF invokes that time series needs to be differentiated if the

PACF of the time series declines very slowly47. For a non-stationary data ARIMA(p, d, q)

model has the ability to represent the model efficiently. There is a close relationship

between AR(p), I(d) and MA(q), however there is not an algorithm to find the correct

model for forecasting48. Determination of the orders of the AR(p), MA(q) and ARMA(p, q)

processes are summarized in the table below.

Table 2.3: Summary of ACF and PACF in AR(p), MA(q) and ARMA(p, q) Processes

45 James Douglas Hamilton, Time Series Analysis, Princeton University Press, 1994, ISBN 0691042896, 9780691042893, p.60

46 Abraham and Ledolter, p.223 47 Kadri Yürekli, Osman Çevik, Detection of Whether The Autocorrelated Meteorological Time Series

Have Stationarity by Using Unit Root Approach: The Case of Tokat, Gaziosmanpasa University, Magazine of Faculty of Agriculture, 2005, 22 (1), 45-53, p.46

48 SPSS User Manul, “SPSS® Trends 13.0”

32

Table 2.4: The Route of AR(p), MA(q) and ARMA(p, q) Processes

Reference: http://www.shef.ac.uk/pas/TimeSeries/Fitnew.pdf, p.51

2.1.2.5 Smoothing Methods

Smoothing means averaging the data into more representative value this sometimes

become the average of the past data equally or sometimes there is weighting parameters

between old and newly observed data. Generally, smoothing methods are useful for short

term forecasting. Base of smoothing methods are depends on identifying historical trends in

http://webs.edinboro.edu/EDocs/SPSS/SPSS%20Trends%2013.0.pdf

33

the time series to be forecasted, then the smoothing method produce forecasting by

extrapolating the patterns.

Table 2.5: Two Filter for Time Series

Reference: Chatfield, p.18

Another meaning of smoothing is that the noise or unpredicted fluctuations which

are not desirable throughout a time series so this kind of errors should be eliminated by the

smoothing parameters for every smoothing period49. For example, if we want to remove

local fluctuation we may use a smoothing method which is called low-passed filter, or if we

want to remove long-term fluctuation we may use a smoothing method which is called

high-passed filter50. In the Table 2.6, there are some filtering models for different

situations; it also shows the different smoothing models.

49 Douglas C. Montgomery, Chery L. Jennings, Murat Kulahci, Introduction to Time Series Analysis and Forecasting, John Wiley & Sons Inc., 2008, p.171

50 Chatfield, p.18

34

Table 2.6: The Process of Smoothing A Data Set

There are three main smoothing models which are the subjects of the this research

1. Simple exponential smoothing method

2. Holt’s methods or double exponential smoothing method

3. Holt-Winters methods or triple exponential smoothing method

As it is shown in the Table 2.7, there is equality between the optimal one-step-ahead

ARIMA model and single exponential smoothing and the double exponential smoothing

methods51.

51 Minitab Inc. Single And Double Exponential Smoothing, May. 15, 2001, p.4

35

Table 2.7: Smoothing Methods – ARIMA

2.1.2.6 Simple Exponential Smoothing Methods

Exponential smoothing is a forecasting method which can be also applied to time

series to produce smoothed data. The Exponential Smoothing model is based on weighted

average of past and current values so we can adjust the weight of smoothing. In terms of

seasonality, it adjusts the weight on current values to account for the effects of swings in

the data. The weight of the model is represented by a new term alpha a which takes the

values between 0-1 so that the sensitivity of the model can be adjusted. Therefore, in

addition to the moving average model, exponential smoothing provides an exponentially

weighted moving average of all previously observed data52. When the sequence of

observations begins at time t = 0, the simplest form of exponential smoothing is given by

the formulas:

New Forecast = [a X (new observation)] + [(1-a ) X (old observation)]

Formal exponential smoothing equation:

1ˆ ( 1 )t t tY Y Ya a+ = + - (2.19)

Where, the variables are defined as:

1ˆtY + = new smoothed value or the forecasted value for the next period

a = smoothing constant (0 < a < 1)

36

tY = new observation or actual values of series in period t

ˆtY = old smoothed value or forecast for period t

If the equation (2.19) is rewritten, we can get this equation:

1ˆ ˆ ˆ ˆ( 1 )t t t t t tY Y Y Y Y Ya a a a+ = + - = + -

1ˆ ˆ ˆ( )t t t tY Y Y Ya+ = + - (2.20)

Since a time series has a trend and the forecasting model doesn’t accept a time

delay, exponential smoothing model carries very important advantage over simple

forecasting models, which is that the exponential smoothing model does not have a time

delay or phase effect53.

Selecting the optimal a is one of the biggest issues for exponential smoothing

method. It is suggested by Brown that the constant discount efficient ( 1w a= - ) should be

lies between 1 /( . 7 0 )g and 1 /( . 9 5 )g where g is the number of parameters, or the value of the

1w a= - should be traced and the value of smoothing constant which makes the sum of the

squared one-step ahead forecasting error (SSE) minimum should be selected54.

21

1

ˆ( ) [ ( 1 ) ]n

t tt

S S E Y Ya -=

= -å (2.21)

Upon selecting optimal a , the value sample autocorrelation function of one step

ahead forecasting error should be calculated for adequacy of the model if the value is found

52 Hanke and Wichern, p.114 53 D. G. Infield, D. C. Hill, Optimal Smoothing for Trend Removal in Short Term Electricity Demand

Forecasting, IEEE Transaction on Power Systems, Vol. 13, No. 3, August 1998, p.1116 54 Abraham and Ledolter, p.158

37

to be significant then it means the model is not appropriate for forecasting55. Final model

for the exponential smoothing is given below:

2 31 2 3

ˆ ( 1 ) ( 1 ) ( 1 )t t t t tY Y Y Y Ya a a a a a a+ - -= + - + - + - + K (2.22)

Table 2.8: Comparison of Smoothing Constants

a = 0.1 a = 0.6

Period Calculation Weight Calculation Weight

t 0.1 0.100 0.6 0.600

t-1 0.9x0.1 0.090 0.4x0.6 0.240

t-2 0.9x0.9x0.1 0.081 0.4x0.4x0.6 0.096

t-3 0.9x0.9x0.9x0.1 0.073 0.4x0.4x0.4x0.6 0.038

t-4 0.9x0.9x0.9x0.9x0.1 0.066 0.4x0.4x0.4x0.4x0.6 0.015

All others 0.059 0.011

Reference: Hanke and Wichern, p.114

2.1.2.7 Exponential Smoothing Adjusted For Trend: Holt’s Method

For a simple exponential smoothing method, the level of mean is constant over the

time series. However, if the mean changes locally and the mean needs to be recalculated,

the simple exponential smoothing methods become incapable of handling the trend. The

Holt’s technique is regarded as capable of handling trend but not seasonality56. To identify

the Holt’s method (sometimes called as double exponential smoothing), two parameters are

used. First parameter a which is previously used for simple exponential smoothing model

and the second parameter is g . By the Holt’s method the newer observation takes higher

weight than the old observation for forecasting model because the an equally weighted

model means that decaying the weight of observation exponentially in time series makes

55 Abraham and Ledolter, p.158 56 Chatfield, p.78

38

the newer observation more important. The weighting of observation is defined by the

parameter of a 57.

The three equations used in Holt’s methods are:

1. The exponential smoothed series, current level estimation:

1 1( 1 ) ( )t t t tL Y L Ta a - -= + - + (2.23)

2. The trend estimate:

1 1( ) ( 1 )t t t tT L L Tg g- -= - + - (2.24)

3. forecast p period into the feature:

ˆt P t tY L p T+ = + (2.25)

Where the parameters are defined as:

tL = new smoothed value (estimated of current level)

a = smoothing constant for the level (0 < a < 1)

tY = new observation or actual value of series in period t

g = smoothing constant for trend estimate (0 < g < 1)

tT = trend estimate

p = periods to be forecast into the future

57 Joseph J. La Viola Jr., Brown University Technology Center for Advanced Scientific Computing and Visualization, Double Exponential Smoothing: An Alternative to Kalman Filter-Based Predictive Tracking, The Eurographics Association 2003. www.cs.brown.edu/~jjl/pubs/kfvsexp_final_laviola.pdf, p.2

39

ˆt pY + = forecast for p period into the future

The smoothing parameters a and g are optimized using the minimum one step

ahead mean squared error criterion (MSE) or mean absolute percentage error (MAPE).

Amount of change is subject to the weight of the parameters for example large weight

causes rapid change in the component, besides a small weight in the parameters cause a less

rapid change in the component. Therefore, more smoothed values is placed in the data if the

weight is larger58.

2.1.2.8 Exponential Smoothing Adjusted For Trend And Seasonality Variation:

Winter’s Method

As previously defined Holt’s methods can not deal with only trend but it can be

enhanced to be efficient for trend plus seasonality. In 1957, C.C. Holt suggest a model for

non-seasonal time series with no trend then he again presented a procedure which can

handle the trend. In 1965, Winter generalized the Holt’s formula to add a functionality to

handle the seasonality59. The enhanced method is called Winter’s method or Holt-Winters

method. Winter’s method uses three parameters which are a for updating the level, g for

slope and d for the seasonal component60. The minimum one step ahead mean squared

error are used for determining the optimal smoothing hyper parameters, it is never

forgotten that if the parameters are set to be 1 then it means that the naïve model is used for

selection criteria and only the last observation takes the meaning full of the model61. The

Holt-Winters method has two versions first one is additive and the second one

58 Hanke and Wichern, p.122 59 http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc437.htm, Acces Date: 19.05.2009 60 Abraham and Ledolter, p.167 61 Reinaldo C. S., Mônica B., Cristina Vidigal C. de Miranda, Short Term Load Forecasting Using Double

Seasonal Exponential Smoothing and Interventions to Account for Holidays and Temperature Effects http://www.ecomod.org/files/papers/294.pdf, p.4

40

multiplicative. The use of a version of Holt-Winters method depends on the characteristics

of the particular time series.

The Winter’s method for a model with linear trend and multiplicative seasonality is applied

to the formula below:

Forecast = (Level + Linear Trend)* Seasonal

1. The exponentially smoothed series or level estimate:

1 1( 1 ) ( )tt t t

t s

YL L T

Sa a - +

-

= + - + (2.26)

2. The trend estimate:

1 1( ) ( 1 )t t t tT L L Tg g- -= - + - (2.26)

3. The seasonality estimate:

( 1 )tt t s

t

YS S

Ld d -= + - (2.27)

4. Forecast for p periods into the future:

ˆ ( )t p t t t s pY L p T S+ - += + (2.28)

Where the parameters are defined as:

tL = new smoothed value for current level estimate

a = smoothing constant for the level

tY = new observation or the actual value in period t

41

g = smoothing constant for trend estimate

tT = trend estimate

d = smoothing constant for seasonality estimate

tS = seasonal estimate

p =periods to be forecast into the future

s = length of seasonality

t pY + = forecast for p period into the future

The Winter’s method for a model with linear trend and additive seasonality is applied to the

formula below:

Forecast = Level + Linear Trend + Seasonal

5. Forecast for p periods into the future:

ˆt p t t t s pY L p T S+ - += + +

While applying Holt-Winter method to the seasonal data, the things needs to be

done with a great care are given in “The Analysis of Time Series” by Christopher C. they

are listed as below62:

1. Examine a graph of the data to see whether an additive or a

multiplicative seasonal effect is the more appropriate

62 Reinaldo Castro Souza, Mônica Barros, Cristina Vidigal C. de Miranda, Short Term Load Forecasting Using Double Seasonal Exponential Smoothing and Interventions to Account for Holidays and Temperature Effects http://www.ecomod.org/files/papers/294.pdf, p.79-80

42

2. Provide starting values for 1L and 1T as well as seasonal values for

the first year, here it is hour, say 1 2, , ,sI I IK , using the first few

observation in the series in a fairly simple way; for example, the

analyst could choose 1 1/

s

iL x s= å .

3. Estimate values for , ,a g d by minimizing 2teå over a suitable

fitting period for which historical data are available.

4. Decide whether to normalize the seasonal indices at regular

intervals by making they sum to zero in additive case or have

average of one in the multiplicative case.

Choose between a fully automatic approach (for a large number of series) and a

non-automatic approach. The later allows subjective adjustments for particular series, for

example, by allowing the removal of outliers and a careful selection of the appropriate form

of seasonality.

2.2 Test Of Stationarity

Since we have time series analysis, we first determine if the series is stationary

otherwise spurious regression may be observed because of non-stationary situation63. The

reason that makes the series to be non-stationary is the effect of the one or more of the

following time series conditions: outliers, random walk, drift, trend or changing variance64.

As it is seen in the Figure 2.1, hourly electrical energy consumption series has a

seasonality, trend and also cycle so if the series is found to be non-stationary, we should

63 Ferhat T., Serdar K., İşsiz ve Boşanma İlişkisi 1970-2005 VAR Analizi, p.6 64 Yaffee and McGee, p.78

43

make it stationary before the forecasting techniques can be applied to the series65. The

series is called stationary if its mean and variance of observed data are constant and the

difference between two observed data tY and dtY - are the base of the covariance and it

doesn’t change over time66. To test the series in terms of stationarity, “Augmented Dickey-

Fuller” (ADF - Test) which was improved by Dickey and Fuller in 1981 or Philips-Perron

test (PP - Test) can be used. However the two methods give same result, ADF test is

preferred because ADF test is more applicable.

ADF test is applied to the following formula:

å=

-- +D+++=Dm

itititt YYtY

1121 eadbb t = 1, 2, 3, … T (2.29)

Where tYD ; first-difference operator of the series, t; trend variable, itY -D ;

difference between observed and following times, te is the error term of the process, m is

the lag length of the sum. Selecting an optimal lag length is very important for the

adequacy. If m is chosen very large then it is a possible danger to reduce adequacy of the

test; on the other hand, if the m is chosen too small the result of the ADF test might be

wandered by the remaining serial autocorrelation in the errors67. For the optimum lag

length, Ng and Perron suggest that m a xp p= should be selected and check if the absolute

value of the last lag is greater than 1.6 and the lag length is reduced by one and repeating

the process68.

1 / 4

m a x 1 2 .1 0 0

Tp

é ùæ ö= ê úç ÷

è øê úë û (2.30)

65 Peter Kenedy, A Guide to Econometrics, Edition: 5, MIT Press, 2003, ISBN 026261183X, 9780262611831, p.350

66 Ajoy K. Palit, Dobrivoje Popović, Computational intelligence in time series forecasting: theory and engineering applications, Springer, London, 2005, ISBN:1852339489, p.18

67 Eric Zivot, Lecturer Notes: Choosing the Lag Length for the ADF Test, http://faculty.washington.edu/ezivot/econ584/notes/unitrootLecture2.pdf, p.1

68 Zivot, p.1

44

In the equation (2.29), both a constant or intercept 1b and time trend variable t

are included. The term ( t2b ) is omitted from equation (2.29), i f the series has a constant

term 1b but no time trend69. Augmented Dickey-Fuller test also eliminates the possibility

of an auto correlated error70.

Table 2.9: Critical Values for ADF Test

Number of Observation

Significance Level

1% 2,5% 5% 10%

25 -3.75 -3.33 -3.00 -2.63

50 -3.58 -3.22 -2.93 -2.60

100 -3.51 -3.17 -2.89 -2.58

250 -3.46 -3.14 -2.88 -2.57

500 -3.44 -3.13 -2.87 -2.57

inf -3.43 -3.12 -2.86 -2.57

Reference: MacKinnon, James (1991), Critical Values for Cointegration Tests, Chapter 13 in Robert Engle & Clive Granger, eds., Long-run Economic Relationships: Readings in Cointegration, Oxford University Press, Oxford, pp. 267-276, p.272

ADF test defined by equation (2.29), is aiming to test the value of d is statistically

equal to zero or not. Zero hypotheses, the series which are not differentiated have unit-root

so they are not stationary. If the coefficient d is statistically significant; then it means to

reject the hypothesis and let’s say that the series is stationary. If the coefficient d is

statistically not significant; then it means to accept the zero hypotheses. To test the result of

the ADF test, the result is compared to the values in the Table 2.9 which is obtained from

MacKinnon (1990). If the absolute value of the ADF test is less than the value in the Table

2.9, we will accept the null hypothesis and say that the series is not stationary.

0H : The series is not stationary.

69 Wang Baotai, Tomson Ogwang, Is the Size Distribution of Income in Canada a Random Walk?,

45

1H : The series is stationary.

If the series is found to be non-stationary, one way to make the series stationary is to

difference the series until the series is accepted as stationary. However in every

differentiation, the series looses one observed data. After this process, the series is called as

differentiated time series, which is represented as ‘I’ in ARIMA process. The ARIMA

(Auto Regressive Integrated Moving Average) process is an addition to ARMA process.

2.3 Model Checking

Before starting forecasting with possible forecasting models, the most important

thing should be done is to test the adequacy of each models. For the adequacy of model,

two plots are needed. First plot is the time plot which helps to determine if the time series

has any outlier data, and the second plot is the correlogram of the residuals which assists to

test the effect of the autocorrelation. The correlogram of such model which is acceptable as

an adequate model should be normally distributed, with mean zero and the variance 1 /N ,

where, N is the number of observation. Another meaning of ACF function is that if all the

ACFs are statistically equal to zero the time series is called as Gaussian white noise71. For

an adequate model, the residual autocorrelation, the autocorrelation should lies in the

interval calculated by the formula below72.

2 /Nm (2.31)

The portmanteau lack-of-fit test can be used to test the residual autocorrelation. The

portmanteau lack-of-fit test is considered to test the first K values of the residual

correlogram all at once. The test statistic is defined by the formula below:

Economics Bulletin, Vol. 3, No. 29, 2004, p.3 70 Kenedy, p.350 71 Tsay, p.31 72 Chatfield, p.68

46

2,

1

K

z kk

Q N r=

= å (2.32)

Where, N is the number of term in the difference series and the K is chosen as a

number between15 to 30, 2,z kr is the autocorrelation coefficient at lag k of the residuals. if

the result of the test says that the model successfully fits to the series, the Q is distributed as

2c with (K – p - q) degrees of freedom where p and q are the parameters of AR and MA

process respectively73. The checks for the model estimation is listed by John E. H., Dean

W. W as:

1. Many of the same residual plots that are useful in regression analysis can be

developed for the residual from an ARIMA model. A histogram and a normal

probability plot (to check for normality) and a time sequence plot (to check for

outliers) are particularly helpful.

2. The individual residual autocorrelation should be small and generally be within

2 /Nm of zero. Significant residual autocorrelations at low lag or seasonal

lags suggest the model is inadequate and a new or modified model should be

selected.

3. The residual autocorrelations as a group should be consistent with those

produced by random errors.

An enhancement type of portmanteau test as called Ljung-Box Q test is used to

examine the adequacy of the model. Ljung-Box Q test is applied to the formula below:

2

1

( )( 2 )

Kk

mk

r eQ N N

N k=

= +-

å (2.33)

Where the parameters are :

47

( )kr e = the residual autocorrelation at lag k

n = the number of residuals

k = the time lag

K = the number of time lag to be tested

As it is indicated by Ruey S. Tsay, the residuals of a model should behave like a

white noise. The ACF and the LBQ statistic of the residuals can be used for the checking of

the closeness of the model to white noise. For example, the correlations of the series whose

residual autocorrelation function illustrates an additive serial autocorrelation are examined

with spending more attention. For an AR(p) model, the Ljung-Box statistic Q(m) follows

asymptotically a chi-square distribution with d f m g= - degrees of freedom. Where, g is

the number of coefficient. If a fitted model is found to be inadequate, it must be redefined

so that to remove the significant coefficients by simplifying the model74.

By the result of the test, we can test the hypothesis that the model is adequate for

the time series data and the model can be used for forecasting. If the p value is greater than

significance level (p-value < .05 for 5 percent significance level) than the null hypothesis is

accepted75.

· H0 : The model adequately describes your data

· H1: The model does not adequately describe your data

Upon accepting the null hypothesis, the next step is to selection of the model among

the adequate models. Next section summarizes the model selection criteria.

73 Chatfield, p.68 74 Tsay, p.44 75 Hanke and Wichern, p.392

48

Another important test for model checking is called by Goodness-of-Fit test. The

test is used to test whether the model fits the time series. In the goodness-of-fit test, the test

parameter is R-square ( 2R ), which is defined as following formula;

2 R e _ _ _1

_ _ _

s i d u a l s u m o f s q u a r e sR

T o t a l s u m o f s q u r e s= - (2.34)

2

12

2

1

1

( )

T

t p

T

tt p

e

R

r r

= +

= +

= -

-

å

å (2.35)

1

T

tt p

r

rT p

= +=

-

å (2.36)

Where, T is the number of observation. The 2R has a value in the interval from 0 to

1, which is 0< 2R <1. The model which has larger R-square value fits better to the time

series. However the goodness-of- fit test is valid for only stationary time series76.

2.4 Model Selection Criteria

Akaike selection criterion (AIC)77 or Schwarz selection criterion (BIC)78 enable us

to determine the most accurate forecasting model. These criteria are defined as below,

where, 2s is the residual sum of squares divided by the number of observations, T is the

76 Tsay, p.46-47 77 Hirotsugu Akaike, A New Look At Statistical Model Identification, IEEE Trans. Automatic Control AC-

19, 1974, p.716-723 78 Gideon Schwartz, Estimating the Dimension of a Model, Annual of Scientist, Vol. 6, No. 2, March 1978,

p.461-464

49

number of observation (residual), r is the total number of parameters (including the

constant term) in the ARIMA model:

Mean Square Error (MSE)2

1

Tt

t T

e

=

= å (2.37)

Akaike Information Criteria (AIC) 2 2ˆl n r

Ts= + (2.38)

Swartz - Bayesian Information Criteria (BIC) 2 l nˆl n

nr

Ts= + (2.39)

Both AIC and BIC are tent to give same result so we can use one of the criteria for

the selection of model. However, because of the “penalty factor” for including additional

parameter in the model, if there is a conflict in the result of AIC and BIC choosing the

model BIC is suggested if the number of parameter by BIC is greater than the model AIC

suggests. The AIC and BIC should be thought as the additional procedures to help during

the selection of the accurate model but they are not thought as testing procedure for sample

autocorrelation and partial autocorrelation79. However, the AIC or BIC suggest the best

model of forecasting for the time series, the other descriptive indicator should be kept in

mind for the performance of the forecasting model. In the next section, other indicators for

the testing of model accuracy are represented.

2.5 Testing Of Forecasting Accuracy

The accuracy of a model can be tested by the comparison of the input variables

versus output variables80. For a forecasting model the input variables are the observed data

until the time of forecasting and the output variables are the forecasting results for desirable

period of time. Basically the forecasting error is the difference between the forecasting

79 Hanke and Wichern, p.413

50

values and the actual values. The listed formulas should be always kept in mind during

forecasting procedure.

1. Mean percentage error (MPE):

1

ˆ( )1 nt t

t t

Y YM P E

T Y=

-= å

2. Mean absolute percentage error (MAPE):

1

ˆ| |1 nt t

t t

Y YM A P E

T Y=

-= å

3. Mean squared error (MSE):

2

1

1 ˆ( )n

t tt

M S E Y YT =

= -å

4. Root mean squared error (RMSE):

2

1

1 ˆ( )n

t tt

R M S E Y YT =

= -å

5. Mean absolute deviation (MAD):

1

1 ˆ| |T

t tt

M A D Y YT =

= -å

6. Forecast error, or residual (e):

ˆt t tY Ye = -

80 Minitab Inc. Single And Double Exponential Smoothing, May. 15, 2001, p.7

51

7. t statistic for testing the significance of lag 1 autocorrelation (t):

1

1( )

rt

S E r=

8. Random model (Y):

t tY c e= +

9. Ljung-Box (Modified Box – Pierce) Q statistic (Q):

2

1

( 2 )m

k

k

rQ T T

T k=

= +-

å

10. Standard error of autocorrelation coefficient (SE):

12

1

1

( )

k

ii

k

r

S E rT

-

=

+

=å

2. kth order autocorrelation coefficient (r)

1

2

1

( ) ( )

( )

T

t t kt k

k n

tt

Y Y Y Y

r

Y Y

-= +

=

- -

=

-

å

å

2.6 Analysis Of Outlier

The success of an analysis starts with the successive data observation. Such an error

or a kind of lack of attention may deeply affect the analysis. Outlier is described by

Hawkins (1980) that an outlier is an observation that deviates so much from other

52

observations as to arouse suspicion that it was generated by a different mechanism81. At

this point, any outlying data points in a time series data may mislead analysis in modeling

process. Since there has been unpredictable event such as strikes, outbreaks of war, and

sudden changes in the marketing strategy can occur any time, time series data is directly

affected by this intervention. Because the effect of such unpredictable events can deviate

the parameter estimation, forecast and seasonal adjustment, the outliers should be

determined before starting to apply forecasting model82. The reasons for the outlier can be

classified into four classes83:

· Procedural error, generally this kind of error occurs by the lack of attention

during data entry. Procedural error can be eliminated in data cleaning.

· Extraordinary event, such an event that explains the uniqueness of the

situations. The researcher must decide if the observation during extraordinary

event is taken into the analysis or not.

· Extraordinary event, such an event can not be explained the origin of the event.

Generally this kind of extraordinary event should be omitted.

· Outlier in the range of population, sometimes the outliers can lie in the range of

population. If there is a specific reason for the cause of data is not a member of

valid population then the outliers must be eliminated.

In the time series analysis, if we think an AR(p) model, possibly there two kinds of

outliers are presence in the series. First one is additive outliers (AO) which affects the time

series from a single point and the second one is innovative outliers (IO) which affects the

subsequent series and an observation by an innovation. The affects of the outliers, named

81 Irad Ben-Gal, Outlier Detection, Department of Industrial Engineering, Tel-Aviv University, p.1 82 Abraham and Ledolter, p.356 83 Hanke and Wichern, p.64-65

53

AO and IO are evaluated and measured separately84. Mathematically, an additive outlier hy

is defined as;

,h

t

t

x w i f t hy

x o t h e r w i s e

+ ® =ì= í

®î

Where, w is the magnitude of the outlier and tx is an outlier free time series. According to

Tsay, the other type of outliers can be listed as85;

· Additive outliers (AO)

· Innovative outliers (IO)

· Level Shift (LS)

· Permanent level change (LC)

· Transient level change (TC)

· Variance change (VC)

The identification of outlier can be performed as univariate, bivariate and

multivariate structure.

2.6.1 Univariate Detection Of Outlier

Detection of univariate outlier depends on a known distribution of data. The

analysis is performed under the condition that the a generic model for which the number of

84 Watson S. M., Tight M., Clark S., Redfern E., Detection of Outlier in Time Series, Institute od Transport Studies, University of Leeds, Working Paper 362, 1991, p.1.3

85 Watson S. M., Tight M., Clark S., Redfern E., p.5

54

observation become smaller and distributed form the distribution 1, , kG GK , which is

differentiated, as accepting normal distribution F, from target distribution86.

{21 / 2( , , ) : | |o u t x x Z aa m s m s-= - >

Where, the confidence level a , 0 1a< < ; and the a -outlier region of 2( , )N m s .

The x is an outlier with respect to F.

The method of univariate detection depends on the standard scores, comparison of the

observed data versus the standard score determines the data as outlier. Typically for the

small number of sample, let’s say 80, the boundary for the valid data sets 2.5 of standard

score or greater. For the large number sample of data the range can be extended to 3 or4

times of standard score87.

2.6.2 Bivariate Detection Of Outlier

In univariate detection of outlier, the outlier boundary is estimated by the standard

score Z, for the univariate detection of outlier there are two variables are used to draw a

scotterplot and a boundary for the valid value of data88. The data which is outside of the

confidence boundary is accepted as outlier.

86 Ben-Gal, p.2 87 Hanke and Wichern, p.65 88 Hanke and Wichern, p.65

55

Figure 2.4: Scatterplot for Bivariate Outlier Detection

2.6.3 Multivariate Detection Of Outlier

This type of outlier detection is used for multivariate data set. The method depends

on the test of the Mahalanobis Distance (Mahalanobis D2) which is suggested by P. C.

Mahalanobis in 193689. The application of the Mahalonobis distance is performed on linear

regression model. As it is shown in the Figure 2.11, on the model one liner line is

determined and mahalanobis distance for each variable is calculated. The observation

which has greater value has more influence on the slope or the coefficient of regression

model. Mahalanobis distance is defined by the formulation below90, where S is the

covariance matrix;

2 11 2 1 2( ) ' ( )D Y Y S Y Y-= - - (2.40)

89 Alvin C. Rencher, Methods of multivariate analysis, Edition: 2, John Wiley and Sons, 2002, ISBN 0471418897, 9780471418894, p.76

90 Rencher, p.76

56

Figure 2.5: Multivariate Detection of Outlier91

91 http://matlabdatamining.blogspot.com/2006/11/mahalanobis-distance.html

57

SECTION 3

3 APPLICATIONS OF FORECASTING METHODS TO THE

ELECTRICAL ENERGY DATA OF TRAKYA REGION FOR

SHORT TERM ENERGY DEMAND

In this section, the forecasting techniques introduced in the previous section will be

applied to the data. As it is described, forecasting methods are classified as quantitative and

qualitative methods. Qualitative methods are basically used for any cases that don’t have

enough observation and generally for the long term forecasting. More about the qualitative

methods, Delphi Method generates forecasts depend on the expert’s opinion. After a

consensus, if the result is accepted then the forecasting model can be used for only the case

being discussed. The second qualitative method Scenario Writing aims to produce forecasts

for the long term forecasting for the subjects like new marketing strategy or technological

improvement on a product. Therefore the method is not practical for number based

structure. Market Research and Focus Group are a kind of survey to demonstrate people's

thought about present product or services to find out the effect of new product or service.

Behind the disadvantages of qualitative methods for short term forecasting, they are

systematical ways to generate long term forecasting even if there is no eligible data. Since

the quantitative methods are more efficient to represent number based structure, they are

58

used to generate forecasting with some performance terms which enable us to compare

them. At the end of each method’s application, advantages and disadvantages of the method

will be introduced with error terms.

In the research, we have the electrical consumption data of Trakya region in

Turkey for whole year of 2005, half of 2006 and 2007, it is totally 23 months. This data

includes both the sum of active energy and the sum of reactive energy which are hourly

taken from transformers located in Trakya region to provide energy for Trakya region and it

also includes hourly load of each transformers. However, for the sum of the reactive

energy, there are some empty fields to make a forecasting model. Therefore, the research

focus on forecasting of active power, the data is converted into one column and it just

contains active energy information for the whole year 2005 and from August to December

of 2006 and from January to June 2007. However the data contains the whole year active

energy stored as hourly, the data of the first moth is used to establish the best fitted

forecasting model such as ARMA(p, q) models or a smoothing method for sort term

electric energy forecast. It is good enough information/observation to make an accurate

forecasting model. Furthermore, for the first month, January 2005, all the models are

established and related result will be given in the analysis if each forecasting model

separately. By this way at the end of the forecasting process, we will have a chance to

compare the each result of the forecasting models against to the real consumption values.

3.1 Exploring Data Pattern

Time series is the observation of the variable during time so the data which comes

after the previous one has the information about the previous one. This kind of relation is

called as correlation. Autocorrelation coefficient gives the correlation function of the series

and also gives information about the pattern of the estimated model92. Therefore upon

92 Ajoy K. Palit, Dobrivoje Popović, Computational intelligence in time series forecasting: theory and engineering applications, Springer, London, 2005, ISBN:1852339489, p.60

59

starting to the time series analysis it is needed to analyze the autocorrelation and the data

pattern of the series.

1

2

( ) ( )

( )

n

t t kt k

k n

tt k

Y Y Y Y

r

Y Y

-= +

=

- -

=

-

å

å k = 0, 1, 2, … (3.1)

Where,

kr = autocorrelation coefficient for lag k

t kY - = observation at time period t-k

Y = mean of the series

tY = observation at time period t

125010007505002500-250-500

4500

4000

3500

3000

2500

2000

1500

powerJan2005_Diff1

po

we

rJa

n2

00

5

Scatterplot of powerJan2005 vs powerJan2005_Diff1

Figure 3.1: Scatter plot of January 2005 with Lag 1 Difference

60

Table 3.1: Autocorrelation of January 2005 with Lag 1 Difference

Lag ACF T LBQ Lag ACF T LBQ

1 0,959742 26,18 688,07 16 0,109403 1,09 2425,82

2 0,876469 14,18 1262,69 17 0,195377 1,95 2454,96

3 0,765886 9,98 1702,05 18 0,294581 2,92 2521,3

4 0,642767 7,44 2011,93 19 0,399198 3,92 2643,3

5 0,517686 5,59 2213,21 20 0,502832 4,83 2837,13

6 0,392552 4,07 2329,1 21 0,601329 5,61 3114,71

7 0,274712 2,79 2385,93 22 0,686268 6,15 3476,76

8 0,170672 1,71 2407,9 23 0,74461 6,35 3903,57

9 0,08651 0,87 2413,55 24 0,762993 6,18 4352,33

10 0,023943 0,24 2413,98 25 0,721686 5,57 4754,38

11 -0,01311 -0,13 2414,11 26 0,640737 4,75 5071,74

12 -0,0283 -0,28 2414,72 27 0,534974 3,85 5293,28

13 -0,02622 -0,26 2415,24 28 0,41895 2,96 5429,34

14 -0,00294 -0,03 2415,25 29 0,300678 2,1 5499,52

15 0,043561 0,44 2416,69 30 0,183286 1,27 5525,63

As a result of the autocorrelation plot, the correlation between tY and 1tY - at the lag

1 is positive and the lag 1 autocorrelation coefficient is kr = 0,959742 which means that

there is a high correlation between two corresponding data point. However when the lag is

higher the correlation becomes lower. As it is seen form Figure.3.4, the scatter plot is not a

straight line, the correlation distributes in a very large of scale the reason for this is having

the very small autocorrelations for the higher order of lag. What is more, from the Table

3.1, while the correlation decreases, at the lag 24 the autocorrelation gets the highest value

which is 0,762993 for the rest of the series. Therefore this means that there is a seasonality

which occurs every 24 observed data.

61

37503500325030002750250022502000

4500

4000

3500

3000

2500

2000

1500

powerJan2005_sDiff

po

we

rJa

n2

00

5

Scatterplot of powerJan2005 vs powerJan2005_sDiff

Figure 3.2: Scatter plot of January 2005 with Seasonal Difference

Table 3.2: Autocorrelation of January 2005 with Seasonal Difference

Lag ACF T LBQ Lag ACF T LBQ

1 0,996995 26,77 719,66 16 0,816886 4,23 9972,45

2 0,992384 15,42 1433,67 17 0,800025 4,04 10446,37

3 0,986248 11,89 2139,86 18 0,782776 3,87 10900,73

4 0,978706 10 2836,26 19 0,765163 3,7 11335,48

5 0,969866 8,77 3521,09 20 0,747226 3,55 11750,68

6 0,959833 7,88 4192,77 21 0,729033 3,4 12146,48

7 0,94871 7,19 4849,88 22 0,710624 3,27 12523,07

8 0,936612 6,64 5491,25 23 0,69209 3,13 12880,79

9 0,923671 6,18 6115,88 24 0,673506 3,01 13220,05

10 0,909977 5,79 6722,99 25 0,65491 2,89 13541,29

11 0,895666 5,45 7311,98 26 0,636295 2,78 13844,96

12 0,880812 5,15 7882,4 27 0,617661 2,67 14131,52

13 0,865456 4,89 8433,88 28 0,599049 2,56 14401,46

14 0,849652 4,65 8966,16 29 0,580485 2,46 14655,29

15 0,833443 4,43 9479,04 30 0,561976 2,36 14893,54

62

The autocorrelation at lag 1 between the seasonally differentiated data and raw data

is kr = 0,996995 and the correlation values is decreasing very slowly relatively to the

autocorrelation table for the raw data and lag differentiated data. This means that between

two data, there is a very high correlation so it can be said that there is seasonality of 24

hours between in the series. As it is seen form Figure 3.2, the scatter plot is not a straight

line but comparing the Figure 3.1 the autocorrelations are handled more efficiently.

44039635230826422017613288441

4500

4000

3500

3000

2500

2000

Index

po

we

r01

05

_B

us

MAPE 21

MAD 627

MSD 497039

Accuracy Measures

Actual

F its

Forecasts

Variable

Trend Analysis Plot for power0105_BusLinear Trend Model

Yt = 3344,9 + 0,374*t

Figure 3.3: Trend Line Plot for January 2005

63

44039635230826422017613288441

4500

4000

3500

3000

2500

2000

Index

po

we

r01

05

_B

us

MAPE 21

MAD 645

MSD 503538

Accuracy Measures

Actual

F its

Forecasts

Variable

Trend Analysis Plot for power0105_BusGrowth Curve Model

Yt = 3264,61 * (1,00011**t)

Figure 3.4: Growth Curve Trend Model Plot for January 2005

44039635230826422017613288441

4500

4000

3500

3000

2500

2000

Index

po

we

r01

05

_B

us

MAPE 21

MAD 627

MSD 496947

Accuracy Measures

Actual

F its

Forecasts

Variable

Trend Analysis Plot for power0105_BusQuadratic Trend Model

Yt = 3323 + 0,67*t - 0,00069*t**2

Figure 3.5: Quadratic Trend Mode for January 2005

64

To call a time series as stationary time series, the basic statistic such as mean,

variance should be constant over the time. As it is defined in Section.2, the stationarity is

test by ADF test, which is performed in the test of stationarity. However we see that from

the Figure 3.3, Figure 3.4 and Figure 3.5, the different type trend model is illustrated with

the descriptive statistic values such as MAPE, MAD and MSD. Since the trend models are

slightly different, the quadratic trend model best describes the time series depends on the

descriptive statistics show in the each figure. The quadratic trend model’s equation is

determined by Minitab with the MAPE, MAD and MSD are 21, 627, and 496.947

respectively as below;

23 3 2 3 0 . 6 7 0 . 0 0 0 6 9tY t t= + -

Since the seasonality and the trend are determined, the rest of the time series

includes the cyclical and irregular components. The irregular and the cyclical component

are easy to calculate but they can be inspected by visual inspection. The Figure 3.8 shows

that the seasonally adjusted data and de-trended data below;

65

440352264176881

4000

3000

2000

Index

440352264176881

4000

3000

2000

Index

440352264176881

1,25

1,00

0,75

0,50

Index

440352264176881

300

0

-300

-600

Index

Component Analysis for power0105_BusMultiplicative Model

Original Data

Seasonally Adjusted Data

Detrended Data

Seas. Adj. and Detr. Data

Figure 3.6: Component Analysis of January 2005.

3.2 Test Of Stationarity

There are two kind of stationarity, first one is local and the second one is global

stationarity. Global stationarity means that the time series is stationary for along the whole

data. There is not enough information in the Figure 3.7 to prove that the series isn't

stationary. The average of the data appears constant in time, and the variability doesn't

seem to be changing with time. However it is difficult to assess from this plot if the

autocorrelation only depends on the lag so ADF test should take a place to analyze series in

terms of stationarity.

>> plot(powerJan2005) >> title('Consumption of Electrical Power Over Jan. 2005', 'color', 'b', 'fontsize', 12); >> ylabel('Electrical Power (MWh) ','color', 'b', 'fontsize', 12 )

66

>> xlabel('Time Duration Jan. 2005', 'color', 'b', 'fontsize', 12)

0 100 200 300 400 500 600 700 8001000

1500

2000

2500

3000

3500

4000

4500Consumption of Electrical Power Over Jan. 2005

Ele

ctr

ical P

ow

er

(MW

h)

Time Duration Jan. 2005

Figure 3.7: Consumption of Electrical Power Over Jan. 2005

For the test of stationarity, as it is described, the ADF test is performed in this

section. For the application of ADF test, C-based packet program MATLAB (MATrix

LABlatory) will be used to perform ADF test. However, there are many written codes for

ADF tests for the Matlab, the one written by James P. LeSage who is a professor at the

University of Toledo in the Department of Economics is the most efficient code to

represent the series93.

The usage of the Matlab code for ADF test is below:

% USAGE: results = adf(x,p,nlag) % where: x = a time-series vector

93 James P. LeSage,Written Matlab Modules For the Statistical Methods http://www.spatial-econometrics.com/html/jplv7.zip

67

% p = order of time polynomial in the null-hypothesis % p = -1, no deterministic part % p = 0, for constant term % p = 1, for constant plus time-trend % p > 1, for higher order polynomial % nlags = # of lagged changes of x included

adf function takes there parameters, first one is the series which is wanted to be tested for

this research, the electrical energy consumption data in January 2005 is used, it is named

powerJan2005. The second parameter is p, the order of time polynomial. Because the there

is no actual trend in the series of powerJan2005, p=0 selected. The last parameter is the

lag length of the ADF test, for the optimal lag length, m a xp p= is selected. The following

result is observed in Matlab for maximum lag length:

>> powerJan2005 = powerJFM2005(1:744); >> pmax=12*sqrt(sqrt(744/100))

pmax =

19.8187

Since we have 24*31=744 observed data, T is selected 744 and m a xp is calculated as

19.8187 and chosen 20 as an integer. Then the following result is observed in Matlab for

maximum lag length:

>> adf(powerJan2005, 0, 20)

ans = meth: 'adf' y: [722x1 double] nobs: 722 nvar: 22 beta: [22x1 double] yhat: [722x1 double] resid: [722x1 double] sige: 2.5390e+004 bstd: [22x1 double] bint: [22x2 double] tstat: [22x1 double] rsqr: 0.9589 rbar: 0.9577

68

dw: 2.0346 nlag: 20 alpha: 0.9798 adf: -1.6920 crit: [6x1 double]

From the ADF test result it is shown that adf: -1.6920, if we compare the values

in the tableau which are -3.43, -3.12, -2.86, -2.57 for the significance levels: 1%, 2,5%, 5%,

10% correspondingly. The absolute value of the ADF test is less than the values in the

tableau for all the significance level which means that we can not reject the null hypothesis

and say that the powerJan2005 is not stationary.

0H : te = 1 or 0H : the series is not stationary.

1H : te 1 or 1H : The series is stationary.

As it is described in the previous section, to make the series stationary, the series

needs to be differentiate for the next step then repeated the process for the observed first

order differentiated power series.

>> diffpowerJan2005 = powerJan2005(2:end)-powerJan2005(1:end-1); >> plot(diffpowerJan2005) >> title('First Difference of Consumption of Electrical Power Over Jan. 2005', 'color', 'b', 'fontsize', 12); >> ylabel('Electrical Power (MWh) ','color', 'b', 'fontsize', 12 ); >> xlabel('Time Duration Jan. 2005', 'color', 'b', 'fontsize', 12);

69

0 100 200 300 400 500 600 700 800-600

-400

-200

0

200

400

600

800

1000

1200First Difference of Consumption of Electrical Power Over Jan. 2005

Ele

ctrica

l Po

we

r (M

Wh

)

Time Duration Jan. 2005

Table 3.3: Seasonally Differentiated Time Series, Seasonal Index: 24

After getting the first order difference of the series powerJan2005 named as

diffpowerJan2005, we can repeat the process. The ADF test result is observed for the

differentiated series as below:

>> adf(diffpowerJan2005, 0, 20)

ans = meth: 'adf' y: [721x1 double] nobs: 721 nvar: 22 beta: [22x1 double] yhat: [721x1 double] resid: [721x1 double] sige: 2.5353e+004 bstd: [22x1 double]

70

bint: [22x2 double] tstat: [22x1 double] rsqr: 0.4967 rbar: 0.4816 dw: 1.9826 nlag: 20 alpha: -2.2642 adf: -14.7869 crit: [6x1 double]

From the ADF test result it is shown that adf: -14.7869, if we compare the

values in the Table 2.9 which are -3.43, -3.12, -2.86, -2.57 for the significance levels: 1%,

2,5%, 5%, 10% correspondingly. The absolute value of the ADF test is higher than the

values in the tableau for all the significance level which means that we can reject the null

hypothesis and say that the powerJan2005 is stationary.

0H : te = 1 or 0H : the series is not stationary.

1H : te 1 or 1H : The series is stationary.

As a result, taking one time differentiation for the electrical power consumption

series we get a stationary time series. We can understand from Figure 3.8 that the mean of

the series is constant and it is around 0 and variance is constant over the time. Now

sophisticated forecasting methods can be applied to the time series. In the next sections by

the application of the forecasting methods, the forecasting findings will be introduced with

the error terms.

71

7065605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Au

toco

rre

lati

on

Autocorrelation Function for powerJan2005(with 5% significance limits for the autocorrelations)

Figure 3.8: Autocorrelation Function for powerJan2005

7065605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Pa

rtia

l A

uto

co

rre

lati

on

Partial Autocorrelation Function for powerJan2005(with 5% significance limits for the partial autocorrelations)

Figure 3.9: Partial Autocorrelation Function for powerJan2005

72

As it defined before the sample autocorrelation should lies in the interval calculated

by the formula given by formula (2.31). Numbers of the lags outside of the boundary are

implying the parameters of AR and MA process.

2 /Nm à 1

0 2 0 2 ( 0 . 0 3 6 7 ) 0 0 . 0 7 3 37 4 4

= =m m m

3.3 Applications Of Autoregressive Moving Average Models For January 2005

ARMA(p, q) model is composed of AR(p) and MA(q) so the data is tested in terms

of autoregressive and moving averages together. Because the ARMA(p, q) model can be

applied to the stationary data, first it is essential to test the data if it is stationary. If the data

is found to be non-stationary, integration process is conducted to observe a stationary data.

To establish the parameters of the AR and MA, related autocorrelation and partial

autocorrelation function are obtained from the data:

7065605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Au

toco

rre

lati

on

Autocorrelation Function for powerJan2005_sDiff(with 5% significance limits for the autocorrelations)

Figure 3.10: Autocorrelation Function for powerJan2005_sDiff

73

7065605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Pa

rtia

l A

uto

co

rre

lati

on

Partial Autocorrelation Function for powerJan2005_sDiff(with 5% significance limits for the partial autocorrelations)

Figure 3.11: Partial Autocorrelation Function for powerJan2005_sDiff

From the autocorrelation and partial autocorrelation function of the seasonally

differentiated electrical power consumption data named powerJan2005_sDiff, it is not clear

to determine the parameters p and q for ARMA(p, q) process. From the ACF function, the

correlation is dying down extremely slowly under the critical value calculated as

0 0 . 0 7 3 3m so we can say that the autoregressive parameter AR(p) takes very high

parameter such as 35 but practically the AR(p) model can not handled such a high

parameter correctly. Therefore to set a limit of 3 for AR(p) practically helps to estimate the

autoregressive model. From the PACF function, there is a significant correlation in the first

4 lags. For the averaging model the MA(q), the parameter q should take 4 at maximum.

The ACF and the PACF of the series indicate that the series has some outliers which

mislead the model building step of forecasting. For short term forecasting, we actually

focus on the business days and holiday days separately because both situation has different

dynamics. Since there is a big change between business day and holidays, for example, as it

is seen from the Figure 3.13 the maximum values are 3151 MWh for holidays and 4253

74

MWh for business day. In addition to this the consumption in business day increases at

time lag 5 but the consumption in holiday still decreases until time lag 9.

Power Consumption

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Hours

Po

wer

(MW

h)

Holiday

Business

Figure 3.12: Power Consumption Business Days versus Holidays

After detection of the effect of the holidays, we should improve forecasting model

for the business days. For the values of the parameters of the ARMA process, new ACF

and PACF functions are observed for the consumption data of business days of January

2005. Related results are given below:

75

43038734430125821517212986431

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Index

po

we

r01

05

_B

us

Time Series Plot of power0105_Bus

Figure 3.13: Power Consumption of Business Day

65605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Au

toco

rre

lati

on

Autocorrelation Function for power0105_Bus(with 5% significance limits for the autocorrelations)

Figure 3.14: Autocorrelation Function for power0105_Bus

76

As seen from the Figure 3.14 and Figure 3.15, not surprisingly, time series has a

seasonality of 24 hours as it occurs in previous series. To eliminate the seasonality, a

differencing is taken on series by choosing the lag as 24. Therefore we lost 24 observations

by differencing. The related outputs for clarifying the situation are given below:

43038734430125821517212986431

800

600

400

200

0

-200

-400

-600

-800

Index

po

we

r01

05

_B

us_

Dif

Time Series Plot of power0105_Bus_Dif

Figure 3.15: Seasonally Differentiated Power Consumption of Business Day

77

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1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Au

toco

rre

lati

on

Autocorrelation Function for power0105_Bus_Dif(with 5% significance limits for the autocorrelations)

Figure 3.16: Autocorrelation Function for power0105_Bus_Dif

Even the time series plot (Figure 3.18) seems like the series is stationary but the

autocorrelation plot indicates that there is still a need for differencing. Because the

correlation is very large at the starting but it is gradually decreasing to zero and again it

starts to increase but the velocity is getting slower, this behavior indicates that there is a

need for one or two lag differencing (one or two non-seasonal integration). The series is

differentiated at lag 1 so the series again lost 1 observation. The related outputs are below:

78

43038734430125821517212986431

500

250

0

-250

-500

-750

Index

po

we

r01

05

_B

us_

Dif

1

Time Series Plot of power0105_Bus_Dif1

Figure 3.17: Seasonal+ Lag1 Differentiated Power Consumption

Seasonally differentiation plus lag 1 differentiation looks more stationary with mean

around zero and constant variance. After make the series ready for ARIMA process the

parameter estimation can build by the autocorrelation and the partial autocorrelation

function of the differentiated series. The ACF and PACF function are given below:

79

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1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Au

toco

rre

lati

on

Autocorrelation Function for power0105_Bus_Dif1(with 5% significance limits for the autocorrelations)

Figure 3.18: Autocorrelation Function for power0105_Bus_Dif1

65605550454035302520151051

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Pa

rtia

l A

uto

co

rre

lati

on

Partial Autocorrelation Function for power0105_Bus_Dif1(with 5% significance limits for the partial autocorrelations)

Figure 3.19: Partial Autocorrelation Function for power0105_Bus_Dif1

80

To verify the process is accurate, lag in the correlation and Q statistic must be

checked. At the beginning of the process, we have 432 observations. In the seasonal

differencing 24 observation and in the lag 1 differencing 1 observed data have lost,

eventually we have 407 valid observed data. For a white-noise time series, 95% confidence

interval for the autocorrelation coefficients or the critical value for the correlation function

is set to:

2 /Nm à 1

0 2 0 2 ( 0 . 0 4 9 6 ) 0 0 . 0 9 9 24 0 7

= =m m m

Table 3.4: Autocorrelation of power0105_Bus_Dif1

Lag ACF T LBQ Lag ACF T LBQ

1 -0,175332 -3,54 12,60 13 0,071277 1,34 34,07

2 -0,111752 -2,19 17,74 14 0,002509 0,05 34,07

3 0,062825 1,22 19,36 15 0,011546 0,22 34,13

4 0,046419 0,90 20,25 16 -0,088946 -1,66 37,50

5 -0,054165 -1,04 21,47 17 0,063390 1,18 39,21

6 -0,047602 -0,91 22,41 18 0,073900 1,37 41,55

7 -0,023132 -0,44 22,63 19 0,043474 0,80 42,36

8 -0,057099 -1,09 23,99 20 -0,076595 -1,41 44,89

9 0,012973 0,25 24,06 21 -0,006545 -0,12 44,90

10 -0,033866 -0,65 24,54 22 0,118013 2,16 50,93

11 -0,128328 -2,45 31,47 23 0,017398 0,31 51,06

12 0,033032 0,62 31,93 24 -0,439382 -7,95 134,97

Since the seasonality is 24, the autocorrelation function is very high at the lag 24 which

takes the highest value of -0.4392. The number of autocorrelations whose values are higher

than the calculated critical values by the Formula (2.31) which is 0.099 determine the

maximum number of moving average parameters MA(q). Hence, there are 5 significant

correlations in the table so the q should less than 4. Another statistic, the LBQ is 134.97 at

lag 24 however the chi-square value (the upper 0.05 point of a chi-square distribution with

81

24 degree of freedom) is 36.4151, which means that such a model should have a value less

than 36.4151 to be regarded as a fit model for the series. Therefore, the LBQ should be less

than chi-square value for the possible ARIMA models.

Table 3.5: Partial Autocorrelation of power0105_Bus_Dif1

Lag PACF T Lag PACF T

1 -0,175332 -3,54 13 0,029810 0,60

2 -0,147013 -2,97 14 0,028928 0,58

3 0,015369 0,31 15 0,032702 0,66

4 0,048015 0,97 16 -0,117308 -2,37

5 -0,026524 -0,54 17 -0,004830 -0,10

6 -0,056312 -1,14 18 0,052806 1,07

7 -0,060737 -1,23 19 0,085185 1,72

8 -0,089545 -1,81 20 -0,028402 -0,57

9 -0,017761 -0,36 21 -0,043214 -0,87

10 -0,047339 -0,96 22 0,072313 1,46

11 -0,150329 -3,03 23 0,082191 1,66

12 -0,039412 -0,80 24 -0,418670 -8,45

Again since the seasonality is 24, the partial autocorrelation function is very high at

the lag 24 which is -0.4187. The number of partial autocorrelations whose values are higher

than the calculated critical values by the Formula (2.31) which is 0.099 determine the

maximum number of moving average parameters AR(p). There are 3 significant

correlations in the table so the p should less than 3. Consecutively, however the possibility

of number of the ARIMA models are very large, an accurate model should has both one

seasonal and one non-seasonal integrations or differentiations so the model might be

ARIMA(p, 1, q)(p, 1, q)24 and the most probable models can be listed as:

ARIMA(1, 1, 0)(0, 1, 2)24

ARIMA(1, 1, 0)(0, 1, 1)24

ARIMA(1, 1, 0)(1, 1, 1)24

ARIMA(0, 1, 1)(0, 1, 1)24

82

ARIMA(0, 1, 2)(1, 1, 0)24

ARIMA(0, 1, 0)(2, 1, 0)24

To select the most adequate model among these models, the Goodness-of-fit test

should be first keep in mind to eliminate the models which are not adequate for the time

series, or which are not exactly fit to the data. For the application of the Goodness-of- fit

test, the p-value of the Ljung-Box Q test must be higher than the significance level of %5.

Then among the adequate models, the Akaike Information Criteria (AIC) or Bayesian

Information Criteria can be used for selecting the better model. Furthermore, descriptive

indicators, such as MAPE, MSE, MAD can also be helpful for selection of model. Since we

have 744 observed data, 24 data points are lost in seasonal differentiation, then 720 data

points are left for simulating. Simulations for each model are performed in SPSS Statistic

17.0 Release 17.0.0 (Aug 23, 2008) and Minitab® 15.1.0.0. Related results are given in the

below:

3.3.1 Model 1: ARIMA(1, 1, 0)(0, 1, 2)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(1,1,0)(0,1,2)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18) Number

of

Outliers

Stationary

R-squared R-squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,385 ,982 95,027 2,037 9,167 24,760 15 ,053 0

Forecast

Model=power0105_Buss-Model_1

83

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2858,84 2686,20 2594,00 2525,41 2485,30 2522,44 2722,68 2995,15 3852,25 4128,24 4316,62 4288,37

UCL 3037,90 2915,95 2868,81 2838,23 2832,09 2900,14 3128,95 3428,10 4310,34 4610,16 4821,24 4814,71

LCL 2679,77 2456,44 2319,19 2212,60 2138,51 2144,74 2316,41 2562,19 3394,16 3646,32 3811,99 3762,02

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

Beginning of the evaluation of the mode should be started from the Model Statistic

table, since the p-value of Ljung-Box Q test which is 0.053 is higher than the significant

value of 0.05 or, in another words, say that the Ljung-Box Q test is not significant so the

null hypothesis is not rejected and it concludes that the autocorrelations for all lags up to

lag k are equal to zero or the model is adequately fits to the time series.

84

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 24,760 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom) it is 26.2962 which means that the statistic value of Ljung-Box Q test is less then

the chi-square value. We can conclude that the residuals of ARIMA(1, 1, 0)(0, 1, 2)24 are

randomly distributed. From the residual plot, we can also see that the residuals are

distributed without autocorrelation on right and left hand side of the zero line. There are not

many residuals exceed the boundary of the critical value. The other descriptive statistics

such as MAPE, MSE, BIC will be used to compare the model with the other adequate

models.

3.3.2 Model 2: ARIMA(1, 1, 0)(1, 1, 1)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(1,1,0)(1,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,385 ,982 94,995 2,036 9,167 24,777 15 ,053 0

Forecast

85

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2859,10 2687,05 2594,05 2524,41 2485,23 2523,27 2723,57 2997,77 3858,58 4131,64 4320,40 4289,97

UCL 3037,86 2916,53 2868,53 2836,87 2831,65 2900,57 3129,41 3430,28 4316,20 4613,07 4824,52 4815,79

LCL 2680,34 2457,58 2319,56 2211,94 2138,82 2145,97 2317,72 2565,26 3400,95 3650,20 3816,28 3764,15

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.053 is

higher than the significant value of 0.05. It implies that the Ljung-Box Q test is not

significant so the null hypothesis is not rejected and it concludes that the autocorrelations

for all lags up to lag k are equal to zero or the model is adequately fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

86

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 24,777 with 15 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom) it is 24.9958 which means that the statistic value of Ljung-Box Q test is less then

the chi-square value. We can conclude that the residuals of ARIMA(1, 1, 0)(0, 1, 1)24 are

randomly distributed. From the residual plot, we can also see that the residuals are

distributed without autocorrelation on right and left hand side of the zero line. There are not

many residuals exceed the boundary of the critical value.

3.3.3 Model 3: ARIMA(1, 1, 0)(0, 1, 1)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(1,1,0)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18) Number

of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,383 ,982 95,062 2,044 9,153 24,778 16 ,074 0

Forecast

Model=power0105_Buss-Model_1

Date

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2861,59 2685,58 2598,93 2532,51 2489,91 2524,65 2726,14 2991,84 3829,21 4117,58 4302,54 4278,20

87

UCL 3041,35 2915,60 2873,97 2845,47 2836,79 2902,39 3132,41 3424,77 4287,24 4599,41 4807,05 4804,41

LCL 2681,82 2455,56 2323,90 2219,56 2143,04 2146,91 2319,87 2558,91 3371,17 3635,75 3798,02 3751,99

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.074 is higher

than the significant value of 0.05. It implies that the Ljung-Box Q test is not significant so

the null hypothesis is not rejected and it concludes that the autocorrelations for all lags up

to lag k are equal to zero or the model is adequately fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

88

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 24,778 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 16 degree of

freedom) it is 26.2962 which means that the statistic value of Ljung-Box Q test is less then

the chi-square value. We can conclude that the residuals of ARIMA(1, 1, 0)(0, 1, 1)24 are

randomly distributed. From the residual plot, we can also see that the residuals are

distributed without autocorrelation on right and left hand side of the zero line. There are not

many residuals exceed the boundary of the critical value.

3.3.4 Model 4: ARIMA(0, 1, 1)(0, 1, 1)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(0,1,1)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,386 ,982 94,836 2,046 9,149 24,254 16 ,084 0

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2859,81 2684,07 2597,62 2530,49 2487,98 2522,34 2723,49 2989,30 3827,18 4115,86 4301,31 4277,79

UCL 3039,27 2911,55 2864,60 2831,84 2820,17 2882,74 3110,04 3400,35 4261,33 4571,97 4778,34 4774,88

LCL 2680,35 2456,60 2330,64 2229,14 2155,79 2161,94 2336,94 2578,26 3393,02 3659,76 3824,27 3780,70

89

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2859,81 2684,07 2597,62 2530,49 2487,98 2522,34 2723,49 2989,30 3827,18 4115,86 4301,31 4277,79

UCL 3039,27 2911,55 2864,60 2831,84 2820,17 2882,74 3110,04 3400,35 4261,33 4571,97 4778,34 4774,88

LCL 2680,35 2456,60 2330,64 2229,14 2155,79 2161,94 2336,94 2578,26 3393,02 3659,76 3824,27 3780,70

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.084 is

higher than the significant value of 0.05. It implies that the Ljung-Box Q test is not

significant so the null hypothesis is not rejected and it concludes that the autocorrelations

for all lags up to lag k are equal to zero or the model is adequately fits to the time series.

90

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 24.254 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 16 degree of

freedom) it is 26.2962 which means that the statistic value of Ljung-Box Q test is less then

the chi-square value. We can conclude that the residuals of ARIMA(0, 1, 1)(0, 1, 1)24 are

randomly distributed. From the residual plot, we can also see that the residuals are

distributed without autocorrelation on right and left hand side of the zero line. There are not

many residuals exceed the boundary of the critical value.

3.3.5 Model 5: ARIMA(0, 1, 2)(1, 1, 0)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(0,1,2)(1,1,0)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,256 ,978 104,491 2,306 9,357 28,245 15 ,020 0

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

91

Forecast 2814,12 2637,89 2600,35 2399,76 2403,41 2430,18 2615,51 2911,87 3827,66 4115,75 4347,21 4319,03

UCL 3018,26 2893,63 2897,61 2733,41 2769,86 2826,72 3040,01 3362,60 4303,19 4614,83 4868,78 4862,17

LCL 2609,98 2382,15 2303,09 2066,11 2036,97 2033,64 2191,01 2461,13 3352,14 3616,66 3825,63 3775,89

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.020 is

less than the significant value of 0.05. It implies that the Ljung-Box Q test is significant so

the null hypothesis is rejected and it concludes that the autocorrelations for all lags up to

lag k are not equal to zero or the model is not adequately fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

92

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 28.245 with 15 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom), it is 24.9958, which means that the statistic value of Ljung-Box Q test is greater

than chi-square value. We can conclude that the residuals of ARIMA(0, 1, 2)(1, 1, 0)24 are

not randomly distributed. From the residual plot, we can also see that the residuals are

distributed seasonal like behavior, they are declining gradually on left hand side of the zero

line and there are also some residuals on the right hand side of the zero line. However there

are not many residuals exceed the boundary of the critical value.

3.3.6 Model 6: ARIMA(0, 1, 0)(2, 1, 0)24

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(0,1,0)(2,1,0)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,238 ,977 105,679 2,324 9,365 42,705 16 ,000 0

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2831,81 2668,21 2609,12 2445,64 2435,57 2454,32 2642,36 2921,94 3833,38 4115,54 4330,56 4326,19

UCL 3038,10 2959,95 2966,43 2858,22 2896,85 2959,63 3188,15 3505,42 4452,25 4767,89 5014,75 5040,80

LCL 2625,51 2376,47 2251,82 2033,06 1974,28 1949,01 2096,56 2338,46 3214,50 3463,19 3646,36 3611,57

93

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2831,81 2668,21 2609,12 2445,64 2435,57 2454,32 2642,36 2921,94 3833,38 4115,54 4330,56 4326,19

UCL 3038,10 2959,95 2966,43 2858,22 2896,85 2959,63 3188,15 3505,42 4452,25 4767,89 5014,75 5040,80

LCL 2625,51 2376,47 2251,82 2033,06 1974,28 1949,01 2096,56 2338,46 3214,50 3463,19 3646,36 3611,57

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.000 is

less than the significant value of 0.05. It implies that the Ljung-Box Q test is significant so

the null hypothesis is rejected and it concludes that the autocorrelations for all lags up to

lag k are not equal to zero or the model is not adequately fits to the time series.

94

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 42.705 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom), it is 24.9958, which means that the statistic value of Ljung-Box Q test is greater

than chi-square value. We can conclude that the residuals of ARIMA(0, 1, 2)(1, 1, 0)24 are

not randomly distributed. From the residual plot, we can also see that the residuals are

distributed seasonal like behavior, they are declining gradually on left hand side of the zero

line and there are also some residuals on the right hand side of the zero line. In addition to

this, there are many residuals exceed the boundary of the critical value. As a result, this

model could be accepted as the worst forecasting model for the electrical consumption data

of January 2005.

3.3.7 Model Selection For ARIMA Models

As it has been already explained any models whose significance values are less than

the significance level of 0.05 don’t fit to the time series. If we look at the p-value of the

Ljung-Box Q test, given as Sig. in the Table 3.6, Model 5 and Model 6 whose p-values are

0.020 and 0 respectively are regarded as inadequate models. Therefore the null hypothesis

is rejected and models are accepted as fit models for Model 5 and Model6. However, if we

look at the p-value of the Model 1, Model2, Model 3 and Model 4, they are 0.053, 0.053,

0.074 and 0.084 respectively. These models can be regarded as adequate models for the

electrical power consumption data of January 2005.

Table 3.6: Comparison of ARIMA Models

INDICATORS MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 MODEL 6

95

Sig. 0.053 0.053 0.074 0.084 0.020 0.000

Statistic 24.760 24.777 24.778 24.254 28.245 42.705

N. BIC 9.167 9.167 9.153 9.149 9.357 9.365

MAPE 2.037 2.036 2.044 2.046 2.306 2.324

RMSE 95.027 94.995 95.062 94.836 104.491 105.679

R-Squared 0.982 0.982 0.982 0.982 0.978 0.977

S. R-Squared 0.385 0.385 0.382 0.386 0.256 0.238

The result of the model checking we have four models which are ARIMA(1, 1,

0)(0, 1, 1)24, ARIMA(1, 1, 0)(1, 1, 1)24, ARIMA(0, 1, 1)(0, 1, 1)24, ARIMA(0, 1, 2)(1, 1,

0)24 respectively. The descriptive indicators are used to compare the adequate models.

Firstly the Bayesian Information Criteria is used to compare the adequate models. The

smaller the BIC is, the better the model is for the series. Depends on the Schwarz’s

Bayesian Criterion (BIC), if we look at the Table 3.6 again Model 4 has the smallest

Normalized BIC value as 9.149 and the BIC values of the other models are 9.167, 9.167,

9.153 for Model 1, Model 2 and Model 3 respectively. In addition to this, for test of time

series in terms of random distribution, the Statistic value of the Model 4 is the smallest.

This means that the Model 4 behave white noise most likely than other models.

Other criteria for selecting the most appropriate model are comparing the errors or

residuals. If we compare the MAPE, MSE of the model, the Model 4 has the largest MAPE

value as 94.836 with respect to the other model as 2.037, 2.036, 2.044 respectively Model 1

to 3. However, the Model 4 has the smallest RMSE value as 94.836 with respect to the

other models as 95.027, 94.995, 95.062 respectively Model 1 to Model 3. Both the MAPE

and the RMSE are used the test the predicted model how much fits to the series with the

difference of the MAPE is more successful of comparing series with different unit but the

RMSE is more successful when comparing the same unit as the dependent series94. Because

the all the ARIMA models are created for the purpose of the dependent series, electrical

94 SPSS User Manuel, Online Help

96

power consumption January 2005, we can ignore the MAPE and select the RMSE as error

indicator. The other indicators gave same results for all adequate ARIMA models.

As a result of the application of ARIMA models, ARIMA Model 4, which is

ARIMA(0, 1, 1)(0, 1, 1)24, can be selected as the best forecasting model with respect to the

values illustrated in the Table 3.6.

3.4 Applications Of Smoothing Methods For January 2005

For analysis of the power consumption data, another efficient method is exponential

smoothing technique. The base of smoothing techniques is to correct the residual of the

previous observation so that to make a better forecasting for the next period95. In this

section, the exponential smoothing methods, which are simple exponential smoothing,

Holt’s exponential smoothing, Holt-Winter’s exponential smoothing methods are applied to

the time series. The applications are performed by SPSS Statistic 17.0 Release 17.0.0 (Aug

23, 2008) and the related results of each method are given in tables.

3.4.1 Application Of Simple Exponential Smoothing For January 2005

The simple exponential smoothing method which has one smoothing parameter a

is applied to the data and the following result observed in MINITAB.

Model Description

Model Type

Model ID power0105_Buss Model_1 Simple Seasonal

Model Statistics

95 Hanke and Wichern, p.114

97

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,497 ,985 85,435 1,877 8,924 30,920 16 ,014 0

Exponential Smoothing Model Parameters

Model Estimate SE t Sig.

power0105_Buss-Model_1 No Transformation Alpha (Level) ,800 ,048 16,786 ,000

Delta (Season) 9,163E-5 ,074 ,001 ,999

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2842,65 2669,70 2579,42 2526,47 2484,08 2526,86 2735,69 3001,53 3831,42 4114,53 4291,92 4253,53

UCL 3010,57 2884,73 2832,96 2813,40 2800,90 2870,98 3105,10 3394,60 4246,81 4551,10 4748,68 4729,64

LCL 2674,73 2454,66 2325,87 2239,54 2167,27 2182,74 2366,29 2608,46 3416,03 3677,96 3835,15 3777,42

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

98

The smoothing constant a is an iterative procedure that minimizes the mean

squared error (MSE)96. SPSS calculated the optimal value of the a and it is found as 0.800.

From the Model Statistic table, the p-value of Ljung-Box Q test which is 0.014 is less than

the significant value of 0.05. It implies that the Ljung-Box Q test is significant so the null

hypothesis is rejected and it concludes that the autocorrelations for all lags up to lag k are

not equal to zero or the model is not adequately fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

96 Hanke and Wichern, p.116

99

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 30.920 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom), it is 24.9958, which means that the statistic value of Ljung-Box Q test is greater

than chi-square value. We can conclude that the residuals of the Simple Exponential

Smoothing are not randomly distributed. From the residual plot, we can also see that the

residuals are distributed seasonal like behavior, they are declining gradually on left hand

side of the zero line and there are also some residuals on the right hand side of the zero line.

3.4.2 Application Of Exponential Smoothing Adjusted For Trend: Holt’s Methods

For January 2005

Besides the simple exponential smoothing methods accepts as the time series is

fluctuating occasionally the methods requires estimated current level. However sometimes

time series has its currency information trend itself so the Holt’s technique uses this feature

to establish a better model of estimation. The Holt’s method is applied to the data and the

following results are obtained in SPSS:

Model Description

Model Type

Model ID power0105_Buss Model_1 Holt

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,115 ,887 237,539 5,413 10,969 57,973 16 ,000 0

100

Exponential Smoothing Model Parameters

Model Estimate SE t Sig.

power0105_Buss-Model_1 No Transformation Alpha (Level) 1,000 ,048 20,768 ,000

Gamma (Trend) ,600 ,073 8,236 ,000

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 3168,12 2981,23 2794,34 2607,45 2420,56 2233,67 2046,78 1859,89 1672,99 1486,10 1299,21 1112,32

UCL 3635,00 3862,04 4147,26 4488,55 4881,68 5322,83 5808,80 6336,90 6904,84 7510,67 8152,69 8829,38

LCL 2701,23 2100,41 1441,41 726,34 -40,57 -855,50 -

1715,25

-

2617,13

-

3558,85

-

4538,46

-

5554,26

-

6604,73

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

101

SPSS calculated the optimal value of the a and b and they are selected as 1.000

and 0.600 respectively. From the Model Statistic table, the p-value of Ljung-Box Q test

which is 0.000 is less than the significant value of 0.05. It implies that the Ljung-Box Q test

is significant so the null hypothesis is rejected and it concludes that the autocorrelations for

all lags up to lag k are not equal to zero or the model is not adequately fits to the time

series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 57.923 with 16 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 16 degree of

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freedom), it is 26.2962, which means that the statistic value of Ljung-Box Q test is greater

than chi-square value. We can conclude that the residuals of the Holt’s Method are not

randomly distributed. From the residual plot, we can also see that there are many residuals

which are exceed the confidence boundary of the model and they are also distributed

seasonal like behavior, they are declining gradually on left hand side of the zero line and

there are also some residuals on the right hand side of the zero line.

3.4.3 Application Of Exponential Smoothing Adjusted For Trend And Seasonal

Variation: Winter’s Methods For January 2005

In the Holt’s method, the trend is handled in addition to simple exponential

smoothing method. This time, by the Winter’s method, the seasonality is also handled so

the Winter’s method has three parameters which are a , b and g . The Winter’s method

also suggest two seasonality, first one is multiplicative and the second one is additive.

3.4.3.1 Application Of Winter’s Additive Method For January 2005

The Winter’s method is applied to the data in SPSS and the model selected as

Additive. The following results are obtained in SPSS:

Model Description

Model Type

Model ID power0105_Buss Model_1 Winters' Additive

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

103

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,497 ,985 85,484 1,874 8,939 30,881 15 ,009 0

Exponential Smoothing Model Parameters

Model Estimate SE t Sig.

power0105_Buss-Model_1 No Transformation Alpha (Level) ,801 ,048 16,734 ,000

Gamma (Trend) 2,282E-6 ,005 ,000 1,000

Delta (Season) ,001 ,080 ,013 ,990

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SPSS calculated the optimal value of the a , b and g , and they are selected as

0.801, 2.282x10-6 and 0.001 respectively. From the Model Statistics table, the p-value of

Ljung-Box Q test which is 0.009 is less than the significant value of 0.05. It implies that the

Ljung-Box Q test is significant so the null hypothesis is rejected and it concludes that the

autocorrelations for all lags up to lag k are not equal to zero or the model is not adequately

fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-

Box Q test. The test statistic value is 30.881 with 15 degrees of freedom. If we check the

chi-square value (the upper 0.05 point of a chi-square distribution with 15 degree of

freedom), it is 24.9958, which means that the statistic value of Ljung-Box Q test is greater

than chi-square value. We can conclude that the residuals of the Winter’s Additive Method

are not randomly distributed. From the residual plot, we can also see that there are some

residuals which are exceed the confidence boundary of the model and they are also

distributed seasonal like behavior, they are, again like in the Holt’s method, declining

gradually on left hand side of the zero line and there are also some residuals on the right

hand side of the zero line.

3.4.3.2 Application Of Winter’s Multiplicative Method For January 2005

For the multiplicative seasonality, the Winter’s method is performed again and the

method type is selected as Multiplicative. The related result is observed and given in the

below:

Model Description

105

Model Type

Model ID power0105_Buss Model_1 Winters' Multiplicative

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0105_Buss-

Model_1

0 ,386 ,982 94,691 2,048 9,143 42,593 15 ,000 0

Exponential Smoothing Model Parameters

Model Estimate SE t Sig.

power0105_Buss-Model_1 No Transformation Alpha (Level) ,884 ,048 18,535 ,000

Gamma (Trend) 5,809E-5 ,005 ,011 ,991

Delta (Season) ,298 ,166 1,792 ,074

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2821,67 2646,44 2552,97 2507,47 2480,03 2538,86 2774,99 3064,40 3936,27 4201,23 4351,51 4274,42

UCL 3007,79 2888,23 2839,35 2833,77 2842,52 2944,35 3246,21 3608,65 4651,05 4981,00 5175,42 5100,47

LCL 2635,56 2404,65 2266,58 2181,17 2117,54 2133,36 2303,77 2520,16 3221,49 3421,47 3527,59 3448,38

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

106

SPSS calculated the optimal value of the a , b and g , and they are selected as

0.884, 5.809x10-6 and 0.298 respectively. From the Model Statistics table, the p-value of

Ljung-Box Q test which is 0.000 is less than the significant value of 0.05. It implies that the

Ljung-Box Q test is significant so the null hypothesis is rejected and it concludes that the

autocorrelations for all lags up to lag k are not equal to zero or the model is not adequately

fits to the time series.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

To test whether the time series is random, we can use the statistic values of Ljung-Box Q

test. The test statistic value is 42.593 with 15 degrees of freedom. If we check the chi-

square value (the upper 0.05 point of a chi-square distribution with 15 degree of freedom),

107

it is 24.9958, which means that the statistic value of Ljung-Box Q test is greater than chi-

square value. We can conclude that the residuals of the Winter’s Multiplicative Method are

not randomly distributed. The residuals of the model are like to Winter’s Additive methods.

3.5 Exploring The Best Fitted Forecasting Model For January 2005

By applying the smoothing methods, we don’t get a improvement because if we

look at the Table 3.7, the p-values of the smoothing methods are 0.014, 0, 0.009 and 0 for

the smoothing methods; simple seasonal exponential smoothing, Holt’s method, Winter’s

additive methods and Winter’s multiplicative methods respectively.

Table 3.7: Comparing ARIMA(0, 1, 1)(0, 1, 1)24 and Smoothing Methods

INDICATORS ARIMA(0, 1, 1)(0, 1, 1)24 Simp. Exp.Sm. Holt's Method Winter's Add. Winter's Mul.

Sig. 0.084 0.014 0.000 0.009 0.000

Statistic 24.254 30.902 57.973 30.881 42.593

BIC 9.149 8.924 10.969 8.939 9.143

MAPE 2.046 1.877 5.143 1.874 2.048

RMSE 94.836 85.434 237.539 85.484 94.961

R-Squared 0.982 0.985 0.887 0.985 0.982

S. R-Squared 0.386 0.497 0.115 0.497 0.386

Since the smoothing models are not adequately fit the time series, the other

indicators are not important for model checking. However the statistics in the Table 3.7

give information for models. For example the Exponential smoothing method has the

smallest BIC even the model is not adequate, a kind of a spurious forecasting model. The

Holt’s method is the worst method for time series data because, in addition of being not

adequate, the residuals of the model are random and the RMSE of the model is very large

comparing to the other models. The reason for this could be explained by the number of

parameters of the model, it has two parameters which can handle the level and the trend but

the time series has a seasonal part. The RMSE value of the Winter’s additive method is

smallest but the model is not adequate and the residuals are not random. Therefore the

Winter’s additive method can be called as spurious forecasting model.

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As a result of the application of ARIMA models and the smoothing methods, the is

ARIMA(0, 1, 1)(0, 1, 1)24 model can be selected as the best forecasting model with respect

to the values illustrated in the Table 3.7. The R-square value shows the power of the model

for the prediction of future. Therefore the ARIMA model explains the time series with 98%

of confidence. Consecutively, the fitted value and the upper-bound and the lower-bound of

the forecasting are shown it the figure below.

Table 3.8: Forecasting Boundary of ARIMA(0, 1, 1)(0, 1, 1)24

3.6 Re-Modeling Of January 2005 By SPSS 17 “Time Series Modeler”

In this section, model building is performed by the help of SPSS 17 Time Series

Modeler. The forecasting models which are introduced in Section.2 are applied by SPSS

automatically in the system of “trial-and-error”. SPSS performs the modeler until all

possible models are applied to the data and then SPSS checks the statistics by itself when

109

the most fitted model is determined, finally the model applied to data and the pre-defined

statistics are illustrated in the output file of SPSS.

Result of Time Series Modeler is given below;

Model Description

Model Type

Model ID power0105_Buss Model_1 Simple Seasonal

Model Statistics

Model=power0105_Buss-Model_1

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

0 ,497 ,985 85,435 1,877 8,924 30,920 16 ,014 0

Table 3.9: Definition of Time Series Modeler Function

GET FILE='C:\Documents and Settings\Mesut\Desktop\TEZ\SPSS_17\power0105_Bus.sav'. PREDICT THRU DAY 19 HOUR 11. * Time Series Modeler. TSMODEL /MODELSUMMARY PRINT=[MODELFIT RESIDACF RESIDPACF] /MODELSTATISTICS DISPLAY=YES MODELFIT=[ SRSQUARE RSQUARE RMSE MAPE NORMBIC] /MODELDETAILS PRINT=[ FORECASTS] PLOT=[ RESIDACF RESIDPACF] /SERIESPLOT OBSERVED FORECAST FIT FORECASTCI FITCI /OUTPUTFILTER DISPLAY=ALLMODELS /AUXILIARY CILEVEL=95 MAXACFLAGS=24 /MISSING USERMISSING=EXCLUDE /MODEL DEPENDENT=power0105_Buss PREFIX='Model' /EXPERTMODELER TYPE=[ARIMA EXSMOOTH] TRYSEASONAL=YES /AUTOOUTLIER DETECT=OFF.

By performing the Time Series Modeler in SPSS 17 to data by specifying the

parameters shown as in the Table 3.6, SPSS suggests the Simple Seasonal forecasting

model. However, the Model Statistics shows that the selected model is not adequate for the

110

consumption of January 2005, because the p-value of Ljung-Box Q test is significant so we

have to reject the null hypothesis.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

The error of the Time Series Modeler function can be explained by this, SPSS

compare the possible model in light of the Normalized BIC. The model which has the

smallest Normalized BIC is suggested as the best model of forecasting. However the model

checking should be performed first then among the adequate models whose p-value have to

be higher than 0.0597 the Normalized BIC can be used to compare for the same series98.

However the SPSS Time Series Modeler is correct for the model whose p-value is higher

than the significance level. The definition of the Normalized BIC is given by the SPSS 17

Statistic in the online help menu;

“Normalized BIC: Normalized Bayesian Information Criterion. A general

measure of the overall fit of a model that attempts to account for model

complexity. It is a score based upon the mean square error and includes a

penalty for the number of parameters in the model and the length of the series.

The penalty removes the advantage of models with more parameters, making

the statistic easy to compare across different models for the same series.”

As it is seen in the Table 3.7, Time Series Modeler is performed by selecting the

detecting of outlier option off. If the outlier option is selected “on” and then the modeler is

applied to data again the following result is observed;

97 Palit and Popović, p.210 98 Tsay, p.61

111

Table 3.10: Definition of Time Series Modeler Function

PREDICT THRU DAY 19 HOUR 11. * Time Series Modeler. TSMODEL /MODELSUMMARY PRINT=[MODELFIT RESIDACF RESIDPACF] /MODELSTATISTICS DISPLAY=YES MODELFIT=[ SRSQUARE RSQUARE RMSE MAPE NORMBIC] /MODELDETAILS PRINT=[ FORECASTS] PLOT=[ RESIDACF RESIDPACF] /SERIESPLOT OBSERVED FORECAST FIT FORECASTCI FITCI /OUTPUTFILTER DISPLAY=ALLMODELS /AUXILIARY CILEVEL=95 MAXACFLAGS=24 /MISSING USERMISSING=EXCLUDE /MODEL DEPENDENT=power0105_Buss PREFIX='Model' /EXPERTMODELER TYPE=[ARIMA EXSMOOTH] TRYSEASONAL=YES /AUTOOUTLIER DETECT=ON TYPE=[ ADDITIVE LEVELSHIFT INNOVATIONAL TRANSIENT SEASONALADDITIVE LOCALTREND ADDITIVEPATCH].

Model Description

Model Type

Model ID power0105_Buss Model_1 ARIMA(0,1,1)(1,1,0)

Model Statistics

Model=power0105_Buss-Model_1

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

0 ,550 ,987 82,091 1,919 8,993 13,325 16 ,649 9

By performing the Time Series Modeler in SPSS 17 to the data by specifying the

parameters shown as in the Table 3.8, this time outliers detection is selected on, SPSS

suggests the ARIMA(0,1,1)(1,1,0)24 forecasting model. The Model Statistics shows that the

selected model adequately fits to the data for the consumption of January 2005, because the

p-value of Ljung-Box Q test which 0.649 is higher than 0.05 so there is not enough

evidence to reject the null hypothesis.

0H : p > 0.05 or 0H : model fits to the time series.

1H : p < 0.05 or 1H : model does not fit to the time series.

112

As we can see in Table.126, SPSS detects 9 outliers in the time series. The outliers

are classified as additive, innovational and transient. The outliers are listed in the Outliers

table below.

Outliers

Estimate SE t Sig.

power0105_Buss-Model_1 5 12 Additive -216,755 53,159 -4,077 ,000

6 0 Innovational -437,509 81,785 -5,350 ,000

8 11 Additive -273,928 52,625 -5,205 ,000

11 0 Additive -328,373 57,669 -5,694 ,000

11 1 Additive -258,421 56,898 -4,542 ,000

12 7 Transient Magnitude -309,056 63,717 -4,850 ,000

Decay factor ,950 ,067 14,105 ,000

13 0

Level Shift -681,937 65,226 -10,455 ,000

14 8

Innovational -316,539 82,528 -3,836 ,000

18 8

Innovational 478,297 82,076 5,827 ,000

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The residual ACF and PACF plot summarize the model; there is no significant

autocorrelation which exceeds the boundary of the 95% confidence interval for the

autocorrelation coefficients of the model. If we look at the Statistic value of the Ljung-Box

Q test which is 13.325, is in the upper and lower bound of the chi-square value (the upper

0.05 point of a chi-square distribution with 16 degree of freedom), which is 26.2960 and

the lower value is 7.9620. We can conclude that the residuals of the ARIMA(0,1,1)(1,1,0)24

model are randomly distributed.

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2848,59 2679,88 2629,21 2428,95 2434,57 2460,68 2638,89 2949,06 4099,05 4319,06 4565,07 4550,44

UCL 3008,86 2879,05 2860,84 2689,02 2720,26 2769,87 2969,92 3300,58 4469,92 4708,33 4971,90 4974,11

LCL 2688,31 2480,71 2397,57 2168,89 2148,89 2151,49 2307,86 2597,55 3728,18 3929,80 4158,24 4126,77

114

Forecast

Model=power0105_Buss-Model_1

19 0 19 1 19 2 19 3 19 4 19 5 19 6 19 7 19 8 19 9 19 10 19 11

Forecast 2848,59 2679,88 2629,21 2428,95 2434,57 2460,68 2638,89 2949,06 4099,05 4319,06 4565,07 4550,44

UCL 3008,86 2879,05 2860,84 2689,02 2720,26 2769,87 2969,92 3300,58 4469,92 4708,33 4971,90 4974,11

LCL 2688,31 2480,71 2397,57 2168,89 2148,89 2151,49 2307,86 2597,55 3728,18 3929,80 4158,24 4126,77

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

Figure 3.20: Forecasting Boundary of ARIMA(0,1,1)(1,1,0)24

115

SECTION 4

4 EXPLORATION AND APPLICATION OF THE BEST FITTED

FORECASTING MODEL FOR EACH MONTHS BY SPSS TIME

SERIES MODELER

In the previous sections, the definitions of electricity and time series component are

given. Later of these, in the light of these definitions, the forecasting models are improved

and applied to the data observed during January 2005. In this section, the best fitted models

are determined first and then these models are applied to the series of 22 moths separately.

Starting of the analysis begins with the exploring the best fitted models. The steps

of the forecasting can be rewritten here as listed below;

1. The Time Series Modeler is applied to the raw data which are named as

power0205 (February 2005), power0305 (March 2005), … , power0707 (July

2005)

2. Adequate models are determined and applied to the raw data

3. If there is any un-adequate model observed, the Time Series Modeler is applied

to these data but outlier detection sets on.

4. Adequate models are determined and applied to the rest of the raw data

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5. If there is still any un-adequate model observed, this mean that the seasonality

can not be handled. Therefore the days which are officially announced as

holiday, especially in week days, are deducted from the raw data and newly

observed data are named as; power0205_Bus (February 2005), power0305_Bus

(March 2005), … , power0707_Bus (July 2005), which we call business day.

6. The Time Series Modeler is applied to the data observed during business day.

7. Adequate models are determined and applied to the data observed during

business day.

8. If there are any un-adequate models observed, the Time Series Modeler is

applied to these data but outlier detection sets on.

9. Adequate models are determined and applied to the rest of the data.

10. If there are any un-adequate models still left, then descriptive statistic values

take the places of determination of fitted model.

Table 4.1: Model Description of Raw Data, Outlier Detection is off

Model Description

Model Type

Model ID power0105 Model_1 Winters' Multiplicative

power0205 Model_2 Simple Seasonal

power0305 Model_3 Winters' Multiplicative

power0405 Model_4 Winters' Multiplicative

power0505 Model_5 Winters' Multiplicative

power0605 Model_6 Winters' Multiplicative

power0705 Model_7 Winters' Multiplicative

power0805 Model_8 Winters' Multiplicative

power0905 Model_9 Winters' Multiplicative

power1005 Model_10 Simple Seasonal

power1105 Model_11 Winters' Multiplicative

power1205 Model_12 Winters' Multiplicative

power0806 Model_13 Winters' Multiplicative

117

power0906 Model_14 Winters' Multiplicative

power1006 Model_15 Winters' Multiplicative

power1106 Model_16 Winters' Multiplicative

power0107 Model_17 Winters' Multiplicative

power0207 Model_18 Winters' Multiplicative

power0307 Model_19 Winters' Multiplicative

power0407 Model_20 Winters' Multiplicative

power0507 Model_21 Winters' Multiplicative

power0607 Model_22 Winters' Multiplicative

power0707 Model_23 Winters' Multiplicative

Table 4.2: Model Statistics of Raw Data, Outlier Detection is off

Model Statistics

Model

Number of

Predictors

Model Fit

statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared Statistics DF Sig.

power0105-Model_1 0 ,481 36,325 15 ,002 0

power0205-Model_2 0 ,503 37,088 16 ,002 0

power0305-Model_3 0 ,522 33,262 15 ,004 0

power0405-Model_4 0 ,526 29,899 15 ,012 0

power0505-Model_5 0 ,569 22,358 15 ,099 0

power0605-Model_6 0 ,541 28,949 15 ,016 0

power0705-Model_7 0 ,540 46,317 15 ,000 0

power0805-Model_8 0 ,564 36,285 15 ,002 0

power0905-Model_9 0 ,505 28,127 15 ,021 0

power1005-Model_10 0 ,448 55,401 16 ,000 0

power1105-Model_11 0 ,456 50,485 15 ,000 0

power1205-Model_12 0 ,566 37,128 15 ,001 0

power0806-Model_13 0 ,577 42,611 15 ,000 0

power0906-Model_14 0 ,515 36,838 15 ,001 0

power1006-Model_15 0 ,513 31,178 15 ,008 0

power1106-Model_16 0 ,529 29,648 15 ,013 0

power0107-Model_17 0 ,490 50,908 15 ,000 0

power0207-Model_18 0 ,531 28,251 15 ,020 0

118

power0307-Model_19 0 ,569 35,633 15 ,002 0

power0407-Model_20 0 ,524 43,111 15 ,000 0

power0507-Model_21 0 ,527 17,798 15 ,273 0

power0607-Model_22 0 ,521 15,958 15 ,385 0

power0707-Model_23 0 ,544 38,333 15 ,001 0

As we can see from the Table 4.2, p-values of Model_5, Model_21 and Model_22

are, respectively, 0.099, 0.273, and 0.385, which means that theses models are adequate

because they are greater than the significance level of 0.05. Therefore we can determine the

forecasting models for the data from the Table 4.1, and then for the rest of the data, Time

Series Modeler is applied again with the outlier detection is enabled. The related results are

illustrated below;

Table 4.3: Model Description of Raw Data, Outlier Detection is on

Model Description

Model Type

Model ID power0205 Model_1 ARIMA(0,1,10)(0,1,1)

power0305 Model_2 ARIMA(0,1,0)(0,1,0)

power0405 Model_3 ARIMA(0,1,12)(2,1,0)

power0605 Model_4 ARIMA(0,1,0)(0,1,0)

power0705 Model_5 ARIMA(0,1,11)(0,1,1)

power0805 Model_6 ARIMA(0,1,13)(0,1,1)

power0905 Model_7 ARIMA(0,1,1)(1,1,1)

power1005 Model_8 ARIMA(0,1,0)(1,1,1)

power1105 Model_9 ARIMA(0,1,11)(1,1,1)

power1205 Model_10 ARIMA(1,1,1)(0,1,1)

power0806 Model_11 ARIMA(0,1,11)(0,1,0)

power0906 Model_12 ARIMA(0,1,0)(0,1,1)

power1006 Model_13 ARIMA(2,1,10)(1,1,1)

119

power1106 Model_14 ARIMA(0,1,2)(1,1,1)

power0107 Model_15 ARIMA(0,1,13)(0,1,1)

power0207 Model_16 ARIMA(0,1,11)(2,1,0)

power0307 Model_17 ARIMA(0,1,4)(1,1,0)

power0407 Model_18 ARIMA(0,1,11)(1,1,0)

power0707 Model_19 ARIMA(0,1,11)(1,1,1)

Table 4.4: Model Statistics of Raw Data, Outlier Detection is on

Model Statistics

Model Number of Predictors

Model Fit statistics Ljung-Box Q(18)

Number of Outliers Stationary R-squared Statistics DF Sig.

power0205-Model_1 0 ,629 27,436 15 ,025 11

power0305-Model_2 0 ,534 32,997 18 ,017 19

power0405-Model_3 0 ,558 20,048 15 ,170 10

power0605-Model_4 0 ,508 18,684 18 ,412 18

power0705-Model_5 0 ,671 40,933 15 ,000 12

power0805-Model_6 0 ,706 33,797 16 ,006 12

power0905-Model_7 0 ,636 13,255 15 ,583 13

power1005-Model_8 0 ,706 18,942 16 ,272 15

power1105-Model_9 0 ,572 25,017 15 ,050 13

power1205-Model_10 0 ,572 23,639 15 ,071 3

power0806-Model_11 0 ,459 30,737 17 ,021 17

power0906-Model_12 0 ,644 37,402 17 ,003 12

power1006-Model_13 0 ,858 54,521 14 ,000 14

power1106-Model_14 0 ,658 35,258 14 ,001 11

power0107-Model_15 0 ,665 21,963 16 ,144 14

power0207-Model_16 0 ,623 28,824 14 ,011 15

power0307-Model_17 0 ,571 31,628 16 ,011 15

power0407-Model_18 0 ,541 24,124 15 ,063 13

power0707-Model_19 0 ,684 43,393 15 ,000 21

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From the Table 4.4, p-values of Model_3, Model_4, Model_7, Model_8, Model_9,

Model_10, Model_15 and Model_18 are, respectively, 0.170, 0.412, 0.583, 0.272, 0.050,

0.071, 0.144, and 0.063, which means that these models are adequate because they are

greater than the significance level of 0.05. Therefore we can determine the forecasting

models for the data from the Table 4.3.

At this point we still have some data which could not be handled without

elimination the special cases such as holidays. Therefore the rest of data are eliminated

from holidays and Time Series Modeler is applied for the newly observed data with

detection of outlier is disabled. The related results are illustrated below;

Table 4.5: Model Description of Data of Business Day, Outlier Detection is off

Model Description

Model Type

Model ID power0205_Bus Model_1 Simple Seasonal

power0305_Bus Model_2 Simple Seasonal

power0705_Bus Model_3 Simple Seasonal

power0805_Bus Model_4 Simple Seasonal

power0806_Bus Model_5 Simple Seasonal

power0906_Bus Model_6 Simple Seasonal

power1006_Bus Model_7 Winters' Multiplicative

power1106_Bus Model_8 Simple Seasonal

power0207_Bus Model_9 Simple Seasonal

power0307_Bus Model_10 Simple Seasonal

power0407_Bus Model_11 Simple Seasonal

121

Table 4.6: Model Statistics of Data of Business Day, Outlier Detection is off

Model Statistics

Model Number of Predictors

Model Fit statistics Ljung-Box Q(18)

Number of Outliers Stationary R-squared Statistics DF Sig.

power0205_Bus-Model_1 0 ,537 20,881 16 ,183 0

power0305_Bus-Model_2 0 ,543 37,062 16 ,002 0

power0705_Bus-Model_3 0 ,574 41,893 16 ,000 0

power0805_Bus-Model_4 0 ,574 34,264 16 ,005 0

power0806_Bus-Model_5 0 ,543 57,559 16 ,000 0

power0906_Bus-Model_6 0 ,536 27,367 16 ,038 0

power1006_Bus-Model_7 0 ,372 22,486 15 ,096 0

power1106_Bus-Model_8 0 ,495 45,930 16 ,000 0

power0207_Bus-Model_9 0 ,512 62,636 16 ,000 0

power0307_Bus-Model_10 0 ,541 33,286 16 ,007 0

power0407_Bus-Model_11 0 ,542 40,412 16 ,001 0

From the Table 4.6, p-values of Model_1 and Model_7 are, respectively, 0.183,

and 0.096, which means that these models are adequate because they are greater than the

significance level of 0.05_Bus. Therefore we can determine the forecasting models for the

data from the Table 4.5. Since the all the model is not adequately fit to the data, for the next

of the procedure, Time Series Modeler is performed for the rest of data of business day but

the outlier detection is enabled. The related results are given below;

Table 4.7: Model Description of Data of Business Day, Outlier Detection is on

Model Description

Model Type

Model ID power0305_Bus Model_1 ARIMA(0,1,1)(0,1,1)

power0705_Bus Model_2 ARIMA(0,1,1)(0,1,1)

power0805_Bus Model_3 ARIMA(0,1,1)(0,1,1)

122

power0806_Bus Model_4 ARIMA(1,0,0)(0,1,1)

power0906_Bus Model_5 ARIMA(1,0,0)(0,1,1)

power1106_Bus Model_6 ARIMA(0,1,9)(2,1,0)

power0207_Bus Model_7 ARIMA(1,1,7)(1,1,0)

power0307_Bus Model_8 ARIMA(0,1,1)(0,1,0)

power0707_Bus Model_9 ARIMA(0,1,1)(0,1,1)

Table 4.8: Model Statistics of Data of Business Day, Outlier Detection is on

Model Statistics

Model Number of Predictors

Model Fit statistics Ljung-Box Q(18)

Number of Outliers Stationary R-squared Statistics DF Sig.

power0305_Bus-Model_1 0 ,715 26,388 16 ,049 10

power0705_Bus-Model_2 0 ,686 18,669 16 ,286 13

power0805_Bus-Model_3 0 ,753 17,518 16 ,353 9

power0806_Bus-Model_4 0 ,890 26,149 16 ,050 10

power0906_Bus-Model_5 0 ,881 22,677 16 ,123 10

power1106_Bus-Model_6 0 ,531 15,871 13 ,256 8

power0207_Bus-Model_7 0 ,647 17,930 14 ,210 14

power0307_Bus-Model_8 0 ,545 25,710 17 ,080 18

power0707_Bus-Model_9 0 ,631 25,863 16 ,056 9

From the Table 4.8, p-values of all the models except model 1 are higher than the

significance level of 0.05. However the p-value of the Model_1 is 0.049 which is slightly

different than the significance level so we could accept the null hypothesis and we can

conclude that the Molel_1 is adequate since there no other methods to apply the data.

Therefore we can determine the forecasting models for the data from the Table 4.7.

After the determination of the best fitted model, applications of the best fitted model for

each month can be performed separately. These applications are given in the appendix.

123

4.1 Application Of The Best Fitted Forecasting Model For February 2005

Model Description

Model Type

Model ID power0205_Bus Model_1 Simple Seasonal

Model Statistics

Model Number of

Predictors

Model Fit statistics Ljung-Box Q(18) Number of

Outliers Stationary R-

squared

R-

squared

RMSE MAPE Normalized

BIC

Statistics DF Sig.

power0205_Bus-

Model_1

0 ,537 ,981 93,290 2,009 9,097 20,881 16 ,183 0

Forecast

power0205_Bus-Model_1

Model 21 0 21 1 21 2 21 3 21 4 21 5 21 6 21 7 21 8 21 9 21 10 21 11

Forecast 2643,38 2494,28 2367,43 2303,38 2260,93 2308,48 2465,48 2732,28 3546,33 3811,63 4005,68 4018,93

UCL 2826,69 2729,03 2644,22 2616,62 2606,80 2684,16 2868,77 3161,41 3999,82 4288,25 4504,35 4538,71

LCL 2460,07 2259,52 2090,63 1990,13 1915,05 1932,80 2062,19 2303,15 3092,83 3335,01 3507,01 3499,14

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

124

125

4.2 Application Of The Best Fitted Forecasting Model For March 2005

Model Description

Model Type

Model ID power0305_Bus Model_1 ARIMA(0,1,1)(0,1,1)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0305_Bus-

Model_1

0 ,715 ,991 66,023 1,534 8,535 26,388 16 ,049 10

Forecast

power0305_Bus-Model_1

Model 24 0 24 1 24 2 24 3 24 4 24 5 24 6 24 7 24 8 24 9 24 10 24 11

Forecast 2761,41 2590,11 2481,78 2457,27 2427,31 2486,70 2615,43 2944,92 3788,39 4024,08 4134,84 4097,65

UCL 2887,94 2742,19 2655,70 2650,58 2638,24 2713,87 2857,77 3201,53 4058,52 4307,08 4430,15 4404,78

LCL 2634,89 2438,03 2307,85 2263,96 2216,39 2259,52 2373,09 2688,30 3518,26 3741,07 3839,52 3790,52

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

126

127

4.3 Application Of The Best Fitted Forecasting Model For April 2005

Model Description

Model Type

Model ID Power0405 Model_1 ARIMA(0,1,12)(2,1,0)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC

Statistic

s DF Sig.

power0405-

Model_1

0 ,558 ,978 89,105 2,441 9,140 20,048 15 ,170 10

Forecast

power0405-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecas

t

2497,32 2321,66 2282,20 2282,49 2288,03 2245,94 2330,99 2577,07 3276,44 3535,46 3646,73 3648,63

UCL 2670,86 2567,08 2582,77 2629,55 2676,06 2671,00 2790,12 3067,89 3797,04 4084,21 4222,28 4249,76

LCL 2323,79 2076,25 1981,63 1935,42 1900,00 1820,87 1871,87 2086,24 2755,84 2986,70 3071,19 3047,50

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

128

129

4.4 Application Of The Best Fitted Forecasting Model For May 2005

Model Description

Model Type

Model ID Power0505 Model_1 Winters' Multiplicative

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC

Statistic

s DF Sig.

power0505-

Model_1

0 ,569 ,977 87,971 2,356 8,981 22,358 15 ,099 0

Forecast

power0505-Model_1

Model 32 0 32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10 32 11

Forecast 2445,43 2286,64 2216,74 2178,82 2164,08 2130,20 2212,96 2461,78 3095,02 3363,70 3484,76 3445,78

UCL 2618,14 2521,24 2500,68 2505,57 2530,40 2528,83 2660,48 2987,60 3777,20 4124,25 4290,81 4260,80

LCL 2272,73 2052,04 1932,80 1852,08 1797,76 1731,57 1765,44 1935,96 2412,84 2603,15 2678,71 2630,76

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

130

131

4.5 Application Of The Best Fitted Forecasting Model For June 2005

Model Description

Model Type

Model ID Power0605 Model_1 ARIMA(0,1,0)(0,1,0)

Model Statistics

Model Number of

Predictors

Model Fit statistics Ljung-Box Q(18) Number of

Outliers Stationary R-

squared

R-

squared

RMSE MAPE Normalized

BIC

Statistics DF Sig.

power0605-

Model_1

0 ,508 ,976 92,378 2,625 9,231 18,684 18 ,412 18

Forecast

power0605-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecast 2539,00 2319,00 2257,00 2213,00 2152,00 2066,00 2214,00 2431,00 3243,00 3515,00 3680,00 3693,00

UCL 2720,38 2575,51 2571,16 2575,76 2557,58 2510,29 2693,89 2944,02 3787,14 4088,58 4281,57 4321,32

LCL 2357,62 2062,49 1942,84 1850,24 1746,42 1621,71 1734,11 1917,98 2698,86 2941,42 3078,43 3064,68

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

132

133

4.6 Application Of The Best Fitted Forecasting Model For July 2005

Model Description

Model Type

Model ID Power0705_Bus Model_1 ARIMA(0,1,1)(0,1,1)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0705_Bus-

Model_1

0 ,686 ,991 59,625 1,618 8,395 18,669 16 ,286 13

Forecast

power0705_Bus-Model_1

Model 22 0 22 1 22 2 22 3 22 4 22 5 22 6 22 7 22 8 22 9 22 10 22 11

Forecast 2570,50 2411,06 2316,74 2258,73 2267,83 2210,32 2262,44 2527,92 3381,20 3616,64 3739,99 3820,63

UCL 2684,94 2536,25 2451,83 2403,03 2420,80 2371,49 2431,42 2704,35 3564,79 3807,12 3937,11 4024,18

LCL 2456,07 2285,88 2181,66 2114,42 2114,86 2049,15 2093,47 2351,49 3197,61 3426,16 3542,86 3617,07

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

134

135

4.7 Application Of The Best Fitted Forecasting Model For August 2005

Model Description

Model Type

Model ID Power0805_Bus Model_1 ARIMA(0,1,1)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0805_Bus-

Model_1

0 ,753 ,987 73,251 1,854 8,754 17,518 16 ,353 9

Forecast

power0805_Bus-Model_1

Model 24 0 24 1 24 2 24 3 24 4 24 5 24 6 24 7 24 8 24 9 24 10 24 11

Forecast 2672,12 2528,04 2433,31 2407,98 2352,75 2387,61 2364,97 2627,64 3525,28 3800,70 3966,53 3967,70

UCL 2808,89 2693,42 2623,05 2619,27 2583,60 2636,49 2630,65 2909,13 3821,72 4111,39 4290,83 4305,07

LCL 2535,35 2362,65 2243,58 2196,68 2121,90 2138,74 2099,29 2346,16 3228,84 3490,02 3642,23 3630,33

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

136

137

4.8 Application Of The Best Fitted Forecasting Model For September 2005

Model Description

Model Type

Model ID Power0905 Model_1 ARIMA(0,1,1)(1,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC

Statistic

s DF Sig.

power0905-

Model_1

0 ,636 ,982 81,972 2,124 8,973 13,255 15 ,583 13

Forecast

power0905-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecast 2608,43 2463,77 2403,64 2343,36 2326,40 2359,17 2404,67 2602,91 3376,36 3633,50 3766,86 3752,30

UCL 2761,78 2665,39 2644,04 2617,10 2629,84 2689,64 2760,13 2981,71 3777,15 4055,13 4208,35 4212,79

LCL 2455,09 2262,14 2163,24 2069,62 2022,97 2028,69 2049,21 2224,11 2975,58 3211,88 3325,38 3291,82

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

138

139

4.9 Application Of The Best Fitted Forecasting Model For October 2005

Model Description

Model Type

Model ID Power1005 Model_1 ARIMA(0,1,0)(1,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC

Statistic

s DF Sig.

power1005-

Model_1

0 ,706 ,983 75,711 1,954 8,855 18,942 16 ,272 15

Forecast

power1005-Model_1

Model 32 0 32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10 32 11 32 12

Forecast 2732,20 2555,01 2491,35 2507,47 2584,27 2486,09 2458,67 2652,11 3394,48 3638,04 3797,54 3873,97 3815,91

UCL 2874,44 2756,16 2737,69 2791,92 2902,29 2834,47 2834,96 3054,37 3821,15 4087,79 4269,24 4366,64 4328,70

LCL 2589,96 2353,87 2245,00 2223,02 2266,25 2137,72 2082,39 2249,84 2967,81 3188,30 3325,84 3381,30 3303,12

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

140

141

4.10 Application Of The Best Fitted Forecasting Model For November 2005

Model Description

Model Type

Model ID power1105 Model_1 ARIMA(0,1,11)(1,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC

Statistic

s DF Sig.

power1105-

Model_1

0 ,572 ,986 97,170 2,495 9,322 25,017 15 ,050 13

Forecast

power1105-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecast 2830,86 2662,21 2531,83 2447,26 2414,69 2420,74 2596,29 2767,39 3626,26 3910,87 4027,57 3987,34

UCL 3015,25 2922,97 2851,19 2816,03 2826,99 2872,39 3084,13 3288,91 4179,41 4493,95 4639,10 4618,49

LCL 2646,47 2401,44 2212,46 2078,49 2002,40 1969,09 2108,46 2245,88 3073,10 3327,80 3416,04 3356,19

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

142

143

4.11 Application Of The Best Fitted Forecasting Model For December 2005

Model Description

Model Type

Model ID power1205 Model_1 ARIMA(1,1,1)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power1205-

Model_1

0 ,572 ,980 102,410 2,419 9,322 23,639 15 ,071 3

Forecast

power1205-Model_1

Model 32 0 32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10 32 11 32 12

Forecast 2025,31 1847,36 1713,55 1648,90 1613,30 1630,12 1854,03 2026,25 2797,91 3091,75 3282,75 3283,84 3114,06

UCL 2220,13 2128,04 2056,09 2045,97 2056,71 2116,56 2379,20 2588,06 3393,69 3719,99 3941,60 3972,13 3830,45

LCL 1830,50 1566,69 1371,00 1251,84 1169,90 1143,68 1328,86 1464,43 2202,12 2463,52 2623,89 2595,55 2397,68

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

144

145

4.12 Application Of The Best Fitted Forecasting Model For August 2006

Model Description

Model Type

Model ID Power0806_Bus Model_1 ARIMA(1,0,0)(0,1,1)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0806_Bus-

Model_1

0 ,890 ,991 67,323 1,591 8,573 26,149 16 ,052 10

Forecast

power0806_Bus-Model_1

Model 24 0 24 1 24 2 24 3 24 4 24 5 24 6 24 7 24 8 24 9 24 10 24 11

Forecast 3015,89 2817,39 2670,89 2565,09 2525,93 2504,24 2504,38 2785,53 3689,78 3986,57 4149,19 4187,09

UCL 3144,75 2986,88 2864,74 2774,95 2746,75 2732,72 2738,29 3023,34 3930,39 4229,21 4393,29 4432,26

LCL 2887,03 2647,90 2477,04 2355,24 2305,12 2275,76 2270,46 2547,72 3449,17 3743,94 3905,08 3941,92

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

146

147

4.13 Application Of The Best Fitted Forecasting Model For September 2006

Model Description

Model Type

Model ID power0906_Bus Model_1 ARIMA(1,0,0)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0906_Bus-

Model_1

0 ,881 ,989 66,166 1,561 8,577 22,677 16 ,123 10

Forecast

power0906_Bus-Model_1

Model 22 0 22 1 22 2 22 3 22 4 22 5 22 6 22 7 22 8 22 9 22 10 22 11

Forecast 2811,15 2632,96 2542,74 2570,51 2593,69 2540,92 2515,80 2675,10 3475,99 3762,46 3899,56 3899,69

UCL 2938,32 2779,50 2695,09 2724,72 2748,52 2695,94 2670,89 2830,21 3631,11 3917,58 4054,68 4054,81

LCL 2683,99 2486,42 2390,38 2416,29 2438,87 2385,90 2360,71 2519,99 3320,88 3607,35 3744,44 3744,57

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

148

149

4.14 Application Of The Best Fitted Forecasting Model For October 2006

Model Description

Model Type

Model ID Power1006_Bus Model_1 Winters' Multiplicative

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power1006_Bus-

Model_1

0 ,372 ,979 113,625 2,854 9,501 22,486 15 ,096 0

Forecast

power1006_Bus-Model_1

Model 23 0 23 1 23 2 23 3 23 4 23 5 23 6 23 7 23 8 23 9 23 10 23 11

Forecast 2845,58 2656,96 2556,32 2500,57 2602,29 2662,33 2673,48 2861,50 3481,37 3767,92 3984,94 4055,09

UCL 3068,80 2944,77 2896,09 2886,44 3047,51 3157,21 3207,23 3463,77 4235,97 4606,57 4892,57 4999,11

LCL 2622,37 2369,16 2216,54 2114,70 2157,08 2167,45 2139,73 2259,24 2726,78 2929,26 3077,32 3111,07

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

150

151

4.15 Application Of The Best Fitted Forecasting Model For November 2006

Model Description

Model Type

Model ID power1106_Bus Model_1 ARIMA(0,1,9)(2,1,0)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power1106_Bus-

Model_1

0 ,531 ,987 83,757 1,805 9,054 15,871 13 ,256 8

Forecast

power1106_Bus-Model_1

Model 23 0 23 1 23 2 23 3 23 4 23 5 23 6 23 7 23 8 23 9 23 10 23 11

Forecast 3194,68 3045,21 2855,47 2783,11 2768,76 2816,22 3028,01 3378,29 4193,72 4421,59 4563,78 4576,02

UCL 3357,80 3230,30 3060,20 3005,74 3007,96 3070,91 3288,63 3644,72 4465,82 4696,02 4840,51 4855,03

LCL 3031,57 2860,12 2650,75 2560,48 2529,57 2561,52 2767,38 3111,87 3921,61 4147,17 4287,06 4297,00

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

152

153

4.16 Application Of The Best Fitted Forecasting Model For January 2007

Model Description

Model Type

Model ID Power0107 Model_1 ARIMA(0,1,13)(0,1,1)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0107-

Model_1

0 ,665 ,987 93,510 2,103 9,268 21,963 16 ,144 14

Forecast

power0107-Model_1

Model 32 0 32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10 32 11 32 12

Forecast 3374,26 3136,53 2991,52 2914,04 2879,68 2927,45 3116,39 3360,53 4362,43 4690,31 4891,28 4919,96 4797,63

UCL 3554,67 3391,67 3304,01 3274,87 3283,10 3369,38 3593,72 3870,82 4903,67 5260,83 5489,65 5544,93 5448,12

LCL 3193,85 2881,38 2679,04 2553,21 2476,27 2485,53 2639,06 2850,24 3821,18 4119,79 4292,92 4294,99 4147,13

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

154

155

4.17 Application Of The Best Fitted Forecasting Model For February 2007

Model Description

Model Type

Model ID Power0207_Bus Model_1 ARIMA(1,1,7)(1,1,0)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalize

d BIC

Statisti

cs DF Sig.

power0207_Bus-

Model_1

0 ,647 ,990 80,317 1,697 9,068 17,930 14 ,210 14

Forecast

power0207_Bus-Model_1

Model 21 0 21 1 21 2 21 3 21 4 21 5 21 6 21 7 21 8 21 9 21 10 21 11

Forecast 3192,67 2994,75 2925,31 2874,54 2791,31 3029,88 3095,94 3446,88 4447,45 4730,82 4835,69 4822,05

UCL 3349,62 3186,58 3137,39 3107,47 3042,70 3298,66 3381,00 3735,42 4742,08 5030,58 5140,73 5132,20

LCL 3035,72 2802,91 2713,24 2641,61 2539,91 2761,10 2810,89 3158,34 4152,82 4431,06 4530,66 4511,89

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

156

157

4.18 Application Of The Best Fitted Forecasting Model For March 2007

Model Description

Model Type

Model ID power0307_Bus Model_1 ARIMA(0,1,1)(0,1,0)

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary

R-squared

R-

squared RMSE MAPE

Normalize

d BIC

Statisti

cs DF Sig.

power0307_Bus-

Model_1

0 ,545 ,986 94,011 1,984 9,384 25,710 17 ,080 18

Forecast

power0307_Bus-Model_1

Model 23 0 23 1 23 2 23 3 23 4 23 5 23 6 23 7 23 8 23 9 23 10 23 11

Forecast 3134,50 2994,36 2825,86 2748,50 2768,95 2775,93 2773,56 3264,46 4216,17 4541,63 4730,21 4628,76

UCL 3319,07 3202,79 3055,69 2997,89 3036,49 3060,46 3074,11 3580,23 4546,45 4885,82 5087,77 4999,20

LCL 2949,94 2785,93 2596,03 2499,10 2501,41 2491,41 2473,00 2948,69 3885,88 4197,45 4372,66 4258,33

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

158

159

4.19 Application Of The Best Fitted Forecasting Model For April 2007

Model Description

Model Type

Model ID power0407 Model_1 ARIMA(0,1,11)(1,1,0)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0407-

Model_1

0 ,541 ,978 102,191 2,404 9,461 24,124 15 ,063 13

Forecast

power0407-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecast 3146,79 2850,42 2777,36 2597,10 2565,43 2647,29 2657,20 3113,24 4140,19 4395,70 4560,99 4545,97

UCL 3346,58 3132,97 3138,95 3023,31 3047,67 3179,71 3235,45 3733,95 4800,64 5093,63 5294,49 5306,51

LCL 2946,99 2567,87 2415,78 2170,89 2083,18 2114,87 2078,94 2492,52 3479,74 3697,77 3827,50 3785,42

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

160

161

4.20 Application Of The Best Fitted Forecasting Model For May 2007

Model Description

Model Type

Model ID Power0507 Model_1 Winters' Multiplicative

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0507-

Model_1

0 ,527 ,976 102,518 2,310 9,287 17,798 15 ,273 0

Forecast

power0507-Model_1

Model 32 0 32 1 32 2 32 3 32 4 32 5 32 6 32 7 32 8 32 9 32 10 32 11

Forecast 2985,00 2833,37 2714,74 2629,54 2603,77 2590,89 2564,73 2896,24 3675,40 3971,83 4138,31 4113,76

UCL 3186,26 3108,40 3044,24 3004,98 3024,77 3054,05 3063,98 3493,28 4457,82 4840,00 5064,14 5055,10

LCL 2783,74 2558,34 2385,25 2254,10 2182,77 2127,73 2065,47 2299,19 2892,98 3103,66 3212,47 3172,41

162

163

4.21 Application Of The Best Fitted Forecasting Model For June 2007

Model Description

Model Type

Model ID power0607 Model_1 Winters' Multiplicative

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0607-

Model_1

0 ,521 ,979 104,555 2,267 9,327 15,958 15 ,385 0

Forecast

power0607-Model_1

Model 31 0 31 1 31 2 31 3 31 4 31 5 31 6 31 7 31 8 31 9 31 10 31 11

Forecast 2831,58 2638,80 2527,38 2444,84 2423,06 2336,89 2340,91 2618,48 3415,67 3699,51 3894,89 3913,91

UCL 3036,85 2917,55 2862,51 2827,07 2852,52 2797,91 2845,05 3217,27 4221,91 4595,64 4859,56 4904,02

LCL 2626,31 2360,06 2192,25 2062,61 1993,59 1875,87 1836,77 2019,68 2609,42 2803,39 2930,21 2923,80

For each model, forecasts start after the last non-missing in the range of the requested estimation period, and end at the last period for which non-missing values of all the predictors are available or at the end date of the requested forecast period, whichever is earlier.

164

165

4.22 Application Of The Best Fitted Forecasting Model For July 2005

Model Description

Model Type

Model ID power0707_Bus Model_1 ARIMA(0,1,1)(0,1,1)

Model Statistics

Model

N u m b e r o f

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared

R-

squared RMSE MAPE

Normalized

BIC Statistics DF Sig.

power0707_Bus-

Model_1

0 ,631 ,988 81,139 1,758 8,928 25,863 16 ,056 9

Forecast

power0707_Bus-Model_1

Model 23 0 23 1 23 2 23 3 23 4 23 5 23 6 23 7 23 8 23 9 23 10 23 11

Forecast 3098,05 2893,59 2800,57 2739,14 2720,37 2645,50 2622,25 3045,41 4068,42 4388,71 4592,77 4624,46

UCL 3246,88 3075,53 3010,47 2973,67 2977,19 2922,83 2918,67 3359,75 4399,73 4736,16 4955,63 5002,12

LCL 2949,21 2711,64 2590,68 2504,60 2463,54 2368,17 2325,84 2731,06 3737,11 4041,27 4229,90 4246,81

166

167

5 CONCLUSION

In conclusion, the research focuses on the short term electrical energy consumption

of the Trakya region in Turkey. For a better modeling of the situation, the components of

the time series model are given since the electrical energy data are observed by per hour.

The results of applications of the each forecasting methods for the January 2005 are given

in the Section 3 and also related discussions are made in this section too. In the later of the

research, by the help of the SPSS Time Series Modeler, best fitted forecasting methods are

determined and the results of the application of the methods are given in the Section 4 for

the data of 22 months.

Since the electrical energy can be used for people’s needs, which can be, some

times, using for running machines in industry, illumination, heating or running electrical

appliances or using for any part of the life, the electrical power consumption value changes

depends on the amount of these factors. It is obvious that the power consumed by industrial

machines is much bigger than the power consumed by electrical appliances. Trakya region

of Turkey has many industrial factories, so the biggest part of the consumption of the

power is used for the needs of the industry. Therefore, as we can see in the Section 3, the

difference of power needs between summer and winter time are not very high and the

pattern of the data is slightly different from each other, because the constant consumption

by the industry.

The Table 5.1 shows the best fitted forecasting model for each month, the majority

of the models are seasonal ARIMA with eliminating the outliers. This means that in every

data has double seasonality, which the first one can be handled by lag 1 differentiation and

the second one can be handled by seasonal differentiation which is 24 hours.

168

Table 4.9: Summary of Forecasting Models for All Months

ORDER DATA MODEL OUTLIERS

1 power0105_Bus ARIMA(0,1,1)(1,1,0) 9

2 power0205_Bus Simple Seasonal 0

3 power0305_Bus ARIMA(0,1,1)(0,1,1) 10

4 power0405 ARIMA(0,1,12)(2,1,0) 10

5 power0505 Winters' Multiplicative 0

6 power0605 ARIMA(0,1,0)(0,1,0) 18

7 power0705_Bus ARIMA(0,1,1)(0,1,1) 17

8 power0805_Bus ARIMA(0,1,1)(0,1,1) 9

9 power0905 ARIMA(0,1,1)(1,1,1) 13

10 power1005 ARIMA(0,1,0)(1,1,1) 15

11 power1105 ARIMA(0,1,11)(1,1,1) 13

12 power1205 ARIMA(1,1,1)(0,1,1) 3

13 power0806_Bus ARIMA(1,0,0)(0,1,1) 10

14 power0906_Bus ARIMA(1,0,0)(0,1,1) 10

15 power1006_Bus Winters' Multiplicative 0

16 power1106_Bus ARIMA(0,1,9)(2,1,0) 8

17 power0107 ARIMA(0,1,13)(0,1,1) 14

18 power0207_Bus ARIMA(1,1,7)(1,1,0) 14

19 power0307_Bus ARIMA(0,1,1)(0,1,0) 18

20 power0407 ARIMA(0,1,11)(1,1,0) 13

21 power0507 Winters' Multiplicative 0

22 power0607 Winters' Multiplicative 0

23 power0407_Bus ARIMA(0,1,1)(0,1,1) 9

The MAPEs for the first 5 forecasting model are, respectively, 1.919, 2.009, 1.534,

2.441, 2.356. The highest MAPE is 2.894 which is observed by the result of the Winter’s

Multiplicative for the data October 2006 and the lowest MAPE is 1.534 which is observed

by the result of the ARIMA(0,1,1)(0,1,1) for the data March 2005. Therefore, the performance of

the forecasting models can be said to be very high and the performance of the ARIMA

models are higher than smoothing methods because the ARIMA models can detect the

outliers.

169

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175

APPENDICES

1. Upper Critical Values Of Chi-Square Distribution With Degrees Of Freedom

2. Lowe Critical Values Of Chi-Square Distribution With Degrees Of Freedom

3. Program Suggestion For Data Formalization Written In Visual C

4. Consumption Data Per Months

176

Upper critical values of chi-square distribution with degrees of freedom 99

Probability of exceeding the critical value 0.10 0.05 0.025 0.01 0.001

1 2.706 3.841 5.024 6.635 10.828 2 4.605 5.991 7.378 9.210 13.816 3 6.251 7.815 9.348 11.345 16.266 4 7.779 9.488 11.143 13.277 18.467 5 9.236 11.070 12.833 15.086 20.515 6 10.645 12.592 14.449 16.812 22.458 7 12.017 14.067 16.013 18.475 24.322 8 13.362 15.507 17.535 20.090 26.125 9 14.684 16.919 19.023 21.666 27.877 10 15.987 18.307 20.483 23.209 29.588 11 17.275 19.675 21.920 24.725 31.264 12 18.549 21.026 23.337 26.217 32.910 13 19.812 22.362 24.736 27.688 34.528 14 21.064 23.685 26.119 29.141 36.123 15 22.307 24.996 27.488 30.578 37.697 16 23.542 26.296 28.845 32.000 39.252 17 24.769 27.587 30.191 33.409 40.790 18 25.989 28.869 31.526 34.805 42.312 19 27.204 30.144 32.852 36.191 43.820 20 28.412 31.410 34.170 37.566 45.315 21 29.615 32.671 35.479 38.932 46.797 22 30.813 33.924 36.781 40.289 48.268 23 32.007 35.172 38.076 41.638 49.728 24 33.196 36.415 39.364 42.980 51.179 25 34.382 37.652 40.646 44.314 52.620 26 35.563 38.885 41.923 45.642 54.052 27 36.741 40.113 43.195 46.963 55.476 28 37.916 41.337 44.461 48.278 56.892 29 39.087 42.557 45.722 49.588 58.301 30 40.256 43.773 46.979 50.892 59.703 31 41.422 44.985 48.232 52.191 61.098 32 42.585 46.194 49.480 53.486 62.487 33 43.745 47.400 50.725 54.776 63.870 34 44.903 48.602 51.966 56.061 65.247 35 46.059 49.802 53.203 57.342 66.619 36 47.212 50.998 54.437 58.619 67.985 37 48.363 52.192 55.668 59.893 69.347 38 49.513 53.384 56.896 61.162 70.703 39 50.660 54.572 58.120 62.428 72.055 40 51.805 55.758 59.342 63.691 73.402

99 Formed from: http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm

177

Lower critical values of chi-square distribution with degrees of freedom100

Probability of exceeding the critical value 0.90 0.95 0.975 0.99 0.999

1. .016 .004 .001 .000 .000 2. .211 .103 .051 .020 .002 3. .584 .352 .216 .115 .024 4. 1.064 .711 .484 .297 .091 5. 1.610 1.145 .831 .554 .210 6. 2.204 1.635 1.237 .872 .381 7. 2.833 2.167 1.690 1.239 .598 8. 3.490 2.733 2.180 1.646 .857 9. 4.168 3.325 2.700 2.088 1.152 10. 4.865 3.940 3.247 2.558 1.479 11. 5.578 4.575 3.816 3.053 1.834 12. 6.304 5.226 4.404 3.571 2.214 13. 7.042 5.892 5.009 4.107 2.617 14. 7.790 6.571 5.629 4.660 3.041 15. 8.547 7.261 6.262 5.229 3.483 16. 9.312 7.962 6.908 5.812 3.942 17. 10.085 8.672 7.564 6.408 4.416 18. 10.865 9.390 8.231 7.015 4.905 19. 11.651 10.117 8.907 7.633 5.407 20. 12.443 10.851 9.591 8.260 5.921 21. 13.240 11.591 10.283 8.897 6.447 22. 14.041 12.338 10.982 9.542 6.983 23. 14.848 13.091 11.689 10.196 7.529 24. 15.659 13.848 12.401 10.856 8.085 25. 16.473 14.611 13.120 11.524 8.649 26. 17.292 15.379 13.844 12.198 9.222 27. 18.114 16.151 14.573 12.879 9.803 28. 18.939 16.928 15.308 13.565 10.391 29. 19.768 17.708 16.047 14.256 10.986 30. 20.599 18.493 16.791 14.953 11.588 31. 21.434 19.281 17.539 15.655 12.196 32. 22.271 20.072 18.291 16.362 12.811 33. 23.110 20.867 19.047 17.074 13.431 34. 23.952 21.664 19.806 17.789 14.057 35. 24.797 22.465 20.569 18.509 14.688 36. 25.643 23.269 21.336 19.233 15.324 37. 26.492 24.075 22.106 19.960 15.965 38. 27.343 24.884 22.878 20.691 16.611 39. 28.196 25.695 23.654 21.426 17.262 40. 29.051 26.509 24.433 22.164 17.916

100 Formed from: http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm

178

PROGRAM SUGGESTION FOR DATA FORMATION #include <stdio.h> #include <string.h> // This program is written in C to convert the matrix which holds // the electrical energy consumption data as [hourXday] for every // month which is named as WholeData into one column and stores the // data hour by hour beginning from Jan. 1, 2005 at 1:00 through // Dec. 31, 2005 at 24:00. The listed matrix is named as ListedWholeData. // Be sure that the text file is present in the same directory with the // program before run it. The matrixes are shaped as below: // // // | DAY... | |DAY1:1 | // |H 1 2 3 ...24| | 2 | // |O 2 | | 3 | // WholeData = |U 3 | ListedWholeData = | . | // |R . | | . | // |. . | | . | // |. . | | 24| // |.24 | |DAY2:1 | // // // Written by Mesut Gunes for any comment please contact me: // gunesmes@yahoo.com int main() { FILE *file; FILE *destination; float power[288][31]; /* be sure that it is large enough to hold all the data! */ int i, j; int hour, month; hour = month =0; for (j=0; j<31; j++){ for (i=0; i<288; i++){ power[i][j] = 0; } } file = fopen("WholeData2007.txt", "r"); destination = fopen("ListedWholeData2007.txt", "w"); if(file==NULL) { printf("Error: can't open file.\n"); return 1; } else { printf("File opened successfully.\n");

179

for(month=0; month<12;){ for (i=24*month; i<24*(month+1); i++){ for (j=0; j<31; j++){ fscanf(file, "%f", &power[i][j]); } } month+=1; } for(month=0; month<12;){ for (j=0; j<31; j++){ for (i=24*month; i<24*(month+1); i++){ if(power[i][j] == 0) break; fprintf(destination, "%4.2f\n", power[i][j]); printf("%4.2f\n", power[i][j]); hour+=1; } } printf("--- %d. months finishes %d. days ---\n", month+1, hour/24); month+=1; } fprintf(destination, "\n----------------------------\n"); fprintf(destination, "Number of hours : %d \n\n", hour); fprintf(destination, "Number of days : %d \n\n", hour/24); fprintf(destination, "Number of months : %d \n\n", month); printf("\n----------------------------\n"); printf("Number of hours : %d \n\n", hour); printf("Number of days : %d \n\n", hour/24); printf("Number of months : %d \n\n", month); fclose(file); } return 0; }

180

POWER CONSUMPTION JANUARY 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2304 2184 2329 2808 2802 2733 2836 2832 2792 2384 2710 2740 2816 2854 2879 2860 2427 2870 2865 2244 1866 1876 2107 2172 2835 2881 2764 2841 2853 2829 2560

2 2153 1950 2025 2624 2729 2647 2668 2675 2591 2254 2510 2616 2618 2645 2754 2672 2230 2685 2505 1873 1692 1791 1944 1978 2730 2593 2649 2627 2738 2500 2421

3 1953 1820 2014 2496 2515 2502 2574 2536 2382 2106 2462 2561 2531 2572 2576 2494 2295 2500 2489 1738 1585 1739 1825 1874 2537 2593 2513 2670 2617 2399 2309

4 1856 1748 2016 2452 2452 2488 2493 2480 2301 2085 2421 2455 2543 2550 2514 2364 2243 2473 2334 1713 1534 1662 1743 1839 2504 2564 2513 2474 2549 2382 2106

5 1778 1747 1953 2447 2424 2430 2454 2507 2350 2061 2390 2497 2442 2455 2488 2414 2130 2441 2313 1505 1513 1603 1765 1823 2459 2471 2442 2473 2509 2217 2116

6 1745 1735 1978 2513 2488 2464 2519 2486 2338 2125 2460 2528 2511 2596 2487 2368 2136 2472 2354 1490 1498 1668 1687 1883 2473 2459 2428 2510 2439 2325 2135

7 1700 1734 2170 2740 2722 2677 2689 2572 2343 2308 2730 2851 2755 2750 2588 2537 2426 2599 2368 1804 1551 1684 1654 2125 2597 2640 2638 2742 2566 2317 2278

8 1644 1798 2582 2992 2983 3033 2987 2529 2251 2681 2823 3014 2916 3069 2778 2226 2609 2642 2395 1929 1532 1607 1781 2499 3038 2914 2829 2967 2632 2220 2644

9 1840 2074 3447 3743 3731 3678 3773 3406 2220 3611 3762 3831 3766 3791 3376 2611 3590 3586 2804 1990 1676 1821 1760 3507 3682 3566 3665 3619 3229 2371 3812

10 1982 2405 3775 3948 3961 3952 4020 3693 2558 3941 3961 4041 3966 4108 3940 2836 3953 3953 3258 2015 1870 2168 2274 3767 4012 3937 3946 4022 3571 2525 3993

11 2249 2633 3975 4142 4174 4111 4128 3865 2978 4038 3976 4123 4239 4282 4024 3005 4171 4143 3419 2049 2070 2286 2443 4078 4219 4101 4073 4178 3784 2807 4298

12 2475 2813 4033 4148 4096 4024 3904 3906 2965 3999 3882 3770 4114 4200 4083 3202 4296 4216 3295 2011 2063 2429 2546 4168 4236 4096 4158 4080 3941 2972 4338

13 2599 2880 3920 3955 3964 3944 3765 3749 2928 3896 3843 3910 4046 3973 4007 3218 4115 4126 3060 1950 2075 2374 2558 3994 4124 4031 4049 3816 3768 3012 4278

14 2585 2805 4071 4034 3954 3835 4086 3634 2959 3913 3889 4024 4003 4250 4023 3250 4277 4222 2846 1893 1874 2370 2489 4040 4201 4016 4120 4064 3799 3029 4388

15 2559 2848 3972 4066 3996 3828 4164 3463 2919 3980 3875 3993 3997 4139 3938 3237 4204 4133 2691 1855 1913 2318 2470 4103 4178 4064 4093 4024 3708 3139 4341

16 2555 2805 3958 3967 4011 3839 4097 3393 2855 3919 3935 3920 3985 4153 3851 3188 4275 4105 2610 1829 1920 2280 2382 4018 4076 3942 4025 3927 3692 3260 4269

17 2777 2867 4285 4128 4093 4095 4244 3619 2994 4133 4076 4126 4132 4297 3901 3378 4394 4151 2678 1930 1935 2415 2534 4181 4139 3916 4102 4123 3584 3127 4375

18 2896 3151 4184 4253 4174 4176 4288 3665 3257 4253 4190 4196 4278 4285 3904 3435 4323 4211 2820 2192 2240 2617 2751 4315 4246 4154 4224 4210 3695 3357 4412

19 2781 3068 3980 3994 3958 3942 3972 3567 3228 4003 3972 4038 4051 3984 3831 3372 4062 4102 2826 2242 2231 2580 2821 4040 3956 3876 4041 3934 3561 3261 4098

20 2747 3075 3773 3788 3817 3770 3752 3546 3191 3706 3772 3858 3883 3811 3603 3321 3840 3804 2841 2216 2235 2579 2741 3739 3810 3730 3825 3721 3456 3200 3894

21 2689 2968 3634 3728 3654 3663 3659 3422 3151 3596 3710 3728 3785 3755 3546 3292 3671 3599 2782 2204 2196 2492 2625 3661 3606 3603 3643 3631 3397 3160 3802

22 2624 2943 3531 3596 3617 3581 3557 3344 3070 3608 3490 3503 3609 3495 3498 3185 3660 3550 2746 2208 2208 2472 2710 3510 3511 3557 3519 3569 3336 3102 3694

23 2561 2891 3372 3391 3495 3508 3446 3310 3022 3352 3425 3438 3557 3498 3318 2994 3512 3407 2730 2220 2185 2401 2720 3301 3324 3420 3500 3430 3287 3077 3596

24 2441 2729 3145 3084 3158 3146 3204 3167 2733 3106 3119 3138 3197 3219 3173 2723 3263 3267 2585 2083 2177 2278 2465 3281 3214 3166 3302 3186 3041 2868 3355

TO

TA

L

55

.49

3

59

.66

9

78

.12

2

83

.03

4

82

.96

7

82

.06

6

83

.27

9

77

.36

3

66

.37

4

79

.05

7

81

.37

8

82

.90

0

83

.73

9

84

.72

9

81

.08

0

70

.18

1

82

.10

3

83

.25

7

65

.61

4

47

.18

2

45

.63

8

51

.50

9

54

.79

3

77

.89

5

83

.70

5

82

.28

9

83

.06

0

82

.83

4

77

.75

1

67

.45

7

83

.51

2

CU

MIL

AT

IV

E

55

.49

3

11

5.1

62

19

3.2

84

27

6.3

18

35

9.2

85

44

1.3

51

52

4.6

30

60

1.9

93

66

8.3

67

74

7.4

24

82

8.8

02

91

1.7

02

99

5.4

41

1.0

80.1

70

1.1

61.2

50

1.2

31.4

31

1.3

13.5

34

1.3

96.7

91

1.4

62.4

05

1.5

09.5

87

1.5

55.2

25

1.6

06.7

34

1.6

61.5

27

1.7

39.4

22

1.8

23.1

27

1.9

05.4

16

1.9

88.4

76

2.0

71.3

10

2.1

49.0

61

2.2

16.5

18

2.3

00.0

30

181

POWER CONSUMPTION FEBRUARY 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1 2763 2840 2909 2702 2700 2784 2481 2722 2906 2980 2991 3037 2932 2423 2741 2716 2803 2825 2838 2824 2416 2734 3041 2844 2671 2763 2655 2412

2 2589 2799 2742 2712 2579 2608 2367 2625 2816 2805 2795 2848 2676 2265 2635 2500 2617 2627 2745 2617 2245 2655 2861 2565 2423 2589 2587 2295

3 2463 2628 2642 2662 2362 2467 2138 2563 2714 2703 2679 2656 2521 2096 2483 2413 2527 2488 2586 2350 2134 2418 2753 2410 2344 2463 2365 2143

4 2373 2597 2364 2521 2323 2352 2131 2481 2661 2647 2622 2565 2499 2050 2451 2399 2519 2448 2528 2232 2149 2449 2391 2402 2400 2373 2257 2065

5 2349 2562 2441 2303 2302 2270 2103 2499 2566 2587 2565 2551 2347 2011 2359 2440 2485 2433 2398 2259 2007 2421 2394 2419 2318 2349 2200 2009

6 2409 2601 2422 2355 2285 2237 2164 2440 2634 2661 2645 2569 2265 2096 2477 2462 2537 2531 2490 2321 2039 2393 2374 2486 2423 2409 2269 2073

7 2478 2745 2533 2517 2397 2307 2315 2569 2724 2773 2719 2685 2364 2392 2672 2685 2728 2730 2519 2315 2223 2622 2574 2518 2557 2478 2304 2288

8 2698 2973 2765 2742 2525 2203 2531 2838 3054 3034 2978 2853 2216 2727 2816 2954 2822 2929 2712 2196 2566 2967 2791 2923 2899 2698 2017 2691

9 3324 3951 3590 3492 3119 2302 3260 3599 3783 3809 3869 3503 2452 3782 3699 3632 3633 3681 3327 2212 3477 3809 3745 3618 3651 3324 2390 3575

10 3590 4144 3914 3797 3401 2583 3743 3962 4013 4094 4125 3886 2750 3979 3944 3861 3892 3887 3586 2515 3942 3948 3887 3900 3774 3590 2698 3889

11 3824 4347 4125 3983 3555 2887 3994 4263 4282 4252 4266 3997 2910 4169 4144 4069 4159 4170 3798 2879 4073 4077 4015 3965 3892 3824 2841 4097

12 3793 4402 4216 4053 3810 2996 4042 4419 4321 4429 4337 4085 2976 4157 4143 3998 4087 4135 3842 2993 4068 4018 3911 3968 3860 3793 2943 4074

13 3700 4196 4204 3729 3766 3028 3995 4321 4319 4270 4084 4044 3097 4044 3965 3993 3947 3869 3668 2964 3917 3837 3740 3707 3496 3700 2861 3993

14 3649 4348 4100 4006 3882 3046 3944 4348 4403 4300 4294 3940 3031 4122 3941 4052 3981 4128 3640 2962 3962 3887 3824 3666 3666 3649 2741 4067

15 3497 4243 4083 3916 3684 3022 4136 4354 4381 4366 4201 3836 2993 4052 4009 4058 4005 4048 3570 2924 3950 3816 3889 3740 3733 3497 2699 4043

16 3493 4211 4149 3937 3630 3059 4105 4219 4395 4380 4118 3708 2942 3979 3975 3998 3952 3979 3365 2887 3846 3683 3888 3727 3696 3493 2611 4053

17 3442 4178 4273 3296 3551 3006 4008 4218 4374 4312 4172 3696 2995 3911 3890 4088 3905 4013 3363 2900 3942 3766 4011 3750 3770 3442 2657 4046

18 3596 4387 4278 3421 3619 3224 4098 4310 4308 4383 4265 3800 3191 4167 4038 4166 4100 4080 3577 3066 3980 3993 4074 3854 3853 3596 2869 4082

19 3590 4161 3978 3641 3582 3306 3869 4130 4168 4164 4039 3738 3218 3989 3934 3971 3963 3986 3514 3264 3976 3981 3931 3823 3833 3590 3017 4019

20 3415 4065 3912 3389 3553 3132 3643 3955 4009 4004 3834 3673 3324 3799 3811 3812 3807 3775 3454 3266 3715 3723 3700 3644 3643 3415 3051 3847

21 3334 3759 3505 3342 3474 3066 3539 3768 3766 3801 3641 3476 3166 3741 3505 3663 3716 3647 3439 3108 3736 3632 3636 3554 3513 3334 2959 3629

22 3251 3701 3450 3133 3354 3041 3479 3638 3641 3634 3625 3453 3135 3432 3425 3596 3575 3526 3342 3096 3437 3574 3470 3454 3428 3251 2906 3551

23 3133 3658 3314 3181 3213 2961 3300 3573 3588 3529 3594 3392 2885 3330 3307 3412 3376 3429 3292 3021 3380 3351 3375 3329 3348 3133 2906 3385

24 3007 3267 3082 2931 3097 2809 2809 3240 3323 3312 3400 3254 2854 3046 3089 3276 3208 3233 2982 2699 3082 3060 3050 3110 3141 3007 2701 3005

TO

TA

L

75

.75

8

86

.76

3

82

.98

8

77

.76

1

75

.76

2

66

.69

4

78

.19

3

85

.05

1

87

.14

6

87

.22

8

85

.86

0

81

.24

5

67

.73

9

79

.75

9

81

.45

2

82

.21

2

82

.34

1

82

.59

5

76

.57

4

65

.86

8

78

.26

0

80

.81

1

81

.32

4

79

.37

4

78

.32

9

75

.75

8

63

.50

1

79

.33

1

CU

MIL

AT

IV

E

75

.75

8

16

2.5

21

24

5.5

09

32

3.2

70

39

9.0

32

46

5.7

26

54

3.9

19

62

8.9

70

71

6.1

16

80

3.3

44

88

9.2

04

97

0.4

49

1.0

38.1

88

1.1

17.9

47

1.1

99.3

99

1.2

81.6

11

1.3

63.9

52

1.4

46.5

47

1.5

23.1

21

1.5

88

.98

9

1.6

67.2

49

1.7

48.0

60

1.8

29.3

84

1.9

08.7

58

1.9

87.0

87

2.0

62.8

45

2.1

26.3

46

2.2

05.6

77

182

POWER CONSUMPTION MARCH 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2681 2767 2802 2822 2815 2579 2298 2679 2746 2807 2820 2820 2743 2245 2790 2639 2654 2713 2498 2609 2322 2646 2670 2873 2743 2691 0 2231 2558 2619 2703

2 2648 2626 2642 2691 2617 2531 2123 2510 2594 2666 2719 2597 2479 2137 2565 2546 2525 2542 2504 2383 2120 2608 2638 2539 2588 2480 2622 1976 2395 2480 2517

3 2547 2555 2548 2591 2549 2330 1980 2418 2546 2492 2554 2568 2388 2050 2513 2320 2385 2441 2441 2286 2132 2470 2483 2440 2509 2465 2292 1900 2289 2362 2396

4 2478 2571 2476 2514 2478 2288 2001 2363 2493 2461 2522 2536 2299 1970 2352 2350 2364 2444 2305 2249 2017 2418 2467 2447 2438 2428 2196 1849 2231 2380 2410

5 2476 2542 2532 2478 2443 2181 1985 2359 2477 2478 2532 2483 2275 1956 2379 2416 2400 2435 2338 2183 2050 2441 2457 2468 2421 2397 2225 1809 2231 2263 2362

6 2508 2556 2657 2555 2455 2237 2075 2447 2491 2537 2532 2478 2240 2106 2416 2483 2469 2440 2328 2194 2063 2504 2551 2560 2525 2325 2156 1890 2234 2314 2430

7 2697 2741 2645 2762 2484 2124 2259 2621 2627 2701 2754 2577 2185 2238 2555 2580 2592 2566 2428 2113 2281 2637 2712 2596 2566 2381 2070 1745 2385 2495 2530

8 3006 3051 3104 3067 2757 2155 2684 3087 2969 2884 3082 2828 2199 2698 2952 2880 2942 2936 2619 2150 2734 3040 2942 3025 2943 2647 1998 2363 2680 2752 2867

9 3810 3965 3953 3949 3431 2364 3647 3803 3817 3783 3853 3561 2382 3761 3801 3677 3565 3595 3325 2427 3759 3844 3854 3844 3805 3311 2147 3315 3437 3638 3697

10 4067 4168 4173 4129 3733 2577 3909 4145 4090 3954 4153 3841 2682 4058 3817 3878 3887 3885 3571 2664 3977 4094 4089 3978 3910 3636 2254 3617 3717 3895 3937

11 4287 4312 4352 4199 3893 2700 3970 4278 4159 4131 4261 3904 2788 4137 4077 3962 4011 3955 3648 2810 4152 4083 4152 4124 4005 3721 2600 3775 3897 3944 4048

12 4325 4287 4331 4197 3798 2809 3996 4295 4117 4184 4249 3937 2819 4101 3985 3912 3948 3805 3583 3002 4056 4094 4066 4021 3936 3570 2704 3727 3876 3936 4045

13 4163 4166 4257 3829 3692 2812 3761 4209 3969 4018 4073 3830 2819 4006 3776 3723 3801 3578 3453 2973 3930 3887 3856 3786 3574 3465 2759 3671 3769 3835 3901

14 4231 4261 4211 4059 3573 2760 3825 4171 3967 4073 4183 3723 2788 3930 3818 3735 3763 3861 3300 2961 3981 3871 3950 3941 3741 3287 2735 3710 3827 3821 3998

15 4243 4309 4219 3978 3555 2657 3811 4098 3968 4063 4179 3555 2672 3976 3812 3732 3724 3843 3284 2803 4033 3953 3933 3902 3791 3198 2687 3699 3847 3870 4015

16 4227 4199 4214 3933 3505 2597 3787 4166 3860 4073 4153 3464 2671 3929 3760 3729 3715 3726 3134 2861 3937 3907 3906 3861 3772 3159 2640 3665 3826 3848 3972

17 4179 4288 4141 3917 3266 2569 3849 4240 3833 4087 4156 3363 2704 3916 3748 3738 3751 3697 3070 2770 3864 3888 3913 3847 3789 3003 2586 3570 3789 3794 3916

18 4156 4270 4226 3984 3382 2783 3923 4213 3889 4046 4133 3314 2744 3889 3848 3771 3781 3623 3071 2824 3881 3842 3919 3836 3793 3142 2586 3393 3727 3707 3889

19 4063 4287 4185 4065 3467 3023 3908 4045 4060 4069 4140 3627 3089 3988 3986 3935 3892 3876 3268 3105 3980 4051 3999 3974 3942 3393 2634 3294 3690 3700 3753

20 3861 3951 3966 3845 3446 3042 3697 3847 3863 4001 3925 3506 3086 3781 3825 3728 3747 3676 3265 3165 3828 3903 3905 3854 3718 3372 3039 3511 3737 3771 3781

21 3738 3706 3801 3775 3243 2972 3531 3746 3702 3847 3741 3400 3018 3622 3667 3618 3670 3442 3120 3069 3664 3761 3765 3724 3643 3200 2911 3419 3690 3647 3673

22 3598 3552 3678 3584 3254 3037 3496 3382 3624 3571 3561 3324 3051 3472 3491 3570 3467 3251 3180 3024 3574 3638 3565 3583 3468 3145 2903 3267 3472 3552 3561

23 3446 3473 3457 3432 3122 2936 3329 3396 3482 3449 3450 3298 2877 3435 3347 3464 3337 3252 3081 2872 3348 3479 3431 3339 3342 3164 2770 3107 3328 3346 3337

24 3150 3277 3284 3156 3007 2587 2993 3105 3103 3220 3287 2990 2630 3014 3013 2976 2951 2965 2955 2712 3093 3141 3219 3054 3243 2911 2633 2862 3094 3169 3180

TO

TA

L

84

.58

5

85

.87

8

85

.85

6

83

.51

0

75

.96

6

62

.64

9

76

.83

7

83

.62

3

82

.44

5

83

.59

3

85

.01

1

77

.52

4

63

.62

5

78

.41

3

80

.29

2

79

.36

3

79

.34

0

78

.54

6

69

.46

3

64

.20

6

78

.77

4

82

.20

0

82

.44

1

81

.61

6

80

.20

4

72

.48

8

58

.14

4

71

.36

3

CU

M.

84

.58

5

17

0.4

63

25

6.3

19

33

9.8

29

41

5.7

95

47

8.4

44

55

5.2

81

63

8.9

04

72

1.3

49

80

4.9

42

88

9.9

53

96

7.4

77

1.0

31.1

02

1.1

09.5

15

1.1

89.8

07

1.2

69.1

70

1.3

48.5

10

1.4

27.0

56

1.4

96.5

19

1.5

60.7

25

1.6

39.4

99

1.7

21.6

99

1.8

04.1

40

1.8

85.7

56

1.9

65.9

61

2.0

38.4

49

2.0

96.5

93

2.1

67.9

56

183

POWER CONSUMPTION APRIL 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2761 2759 2704 2292 2701 2699 2785 2754 2772 2618 2064 2389 2515 2611 2601 2605 2476 2077 2442 2482 2485 2572 2501 2467 2112 2508 2555 2448 2492 2639

2 2547 2587 2559 2133 2483 2525 2595 2612 2514 2286 1924 2305 2381 2405 2456 2389 2326 1866 2365 2391 2403 2366 2394 2227 1943 2396 2352 2396 2304 2339

3 2472 2473 2417 1976 2463 2422 2526 2446 2472 2149 1839 2256 2289 2340 2360 2380 2150 1825 2269 2400 2243 2243 2239 2006 1926 2322 2235 2345 2275 2288

4 2417 2355 2234 1949 2416 2343 2478 2407 2379 2102 1758 2210 2249 2332 2297 2288 2126 1822 2196 2196 2285 2296 2205 1980 1841 2235 2267 2311 2231 2310

5 2398 2360 2173 1927 2348 2379 2439 2455 2316 2205 1729 2215 2237 2301 2251 2267 2103 1837 2132 2209 2285 2302 2189 1969 1854 2239 2241 2301 2286 2295

6 2449 2419 2168 2052 2480 2433 2467 2509 2343 2160 1870 2251 2335 2348 2343 2287 2116 1828 2296 2231 2308 2247 2284 1949 1839 2312 2245 2282 2246 2218

7 2560 2439 2141 2285 2579 2579 2640 2623 2439 2052 1976 2389 2469 2381 2460 2324 1896 1923 2404 2395 2358 2278 2121 1879 2094 2353 2399 2356 2413 2301

8 2907 2604 2122 2692 2867 2883 2988 2969 2615 1989 2246 2656 2663 2716 2681 2388 1946 2389 2628 2571 2644 2631 2351 1999 2431 2769 2655 2682 2719 2497

9 3743 3277 2266 3570 3651 3687 3829 3774 3365 2174 3366 3304 3471 3436 3522 3205 2187 3365 3414 3486 3440 3365 2744 2115 3417 3486 3451 3450 3403 3138

10 4030 3656 2406 3962 3859 3885 3957 4008 3652 2392 3617 3584 3748 3766 3638 3452 2342 3547 3698 3640 3542 3604 3123 2449 3575 3651 3562 3661 3656 3436

11 4197 3917 2736 4115 3997 3963 4075 4126 3716 2592 3684 3740 3844 3753 3824 3513 2544 3689 3729 3648 3691 3740 3235 2575 3773 3740 3661 3734 3730 3626

12 4170 3905 2806 4031 3938 3976 3975 3966 3673 2661 3690 3668 3739 3771 3919 3573 2526 3657 3681 3718 3621 3599 3276 2609 3638 3666 3680 3742 3756 3635

13 4014 3747 2782 4002 3804 3809 3805 3743 3504 2539 3548 3553 3626 3622 3636 3428 2540 3446 3483 3530 3523 3480 3216 2601 3532 3467 3535 3525 3557 3494

14 3952 3661 2792 3963 3977 3698 3761 3625 3506 2493 3557 3625 3631 3651 3586 3353 2477 3581 3553 3468 3488 3351 3113 2525 3486 3536 3504 3613 3566 3340

15 4075 3638 2700 3995 3905 3849 3794 3860 3207 2486 3598 3671 3719 3699 3730 3106 2446 3525 3514 3604 3563 3596 3121 2481 3490 3627 3530 3571 3674 3330

16 4038 3484 2725 3924 3798 3742 3713 3747 2995 2316 3609 3611 3623 3679 3725 3077 2403 3540 3514 3526 3513 3504 2998 2458 3466 3522 3568 3487 3625 3207

17 4073 3424 2709 3881 3746 3691 3696 3589 2883 2323 3549 3577 3524 3680 3722 2932 2350 3559 3559 3487 3539 3498 2871 2330 3474 3526 3512 3473 3689 3189

18 3992 3263 2650 3834 3668 3753 3638 3487 2874 2220 3373 3484 3461 3512 3605 2767 2302 3413 3437 3365 3449 3436 2810 2354 3350 3385 3416 3477 3531 3022

19 3826 3268 2713 3678 3539 3716 3567 3456 2845 2302 3261 3377 3312 3479 3541 2881 2378 3218 3258 3175 3298 3289 2800 2315 3261 3208 3289 3298 3395 3002

20 3850 3428 3003 3807 3671 3812 3625 3575 3160 2542 3385 3377 3464 3545 3441 3011 2570 3342 3419 3184 3296 3203 3040 2631 3348 3334 3309 3226 3371 3122

21 3662 3410 3030 3718 3725 3795 3591 3593 3222 2716 3392 3499 3535 3582 3471 3113 2736 3351 3429 3402 3387 3382 3049 2855 3413 3434 3485 3405 3513 3218

22 3493 3312 3032 3523 3526 3650 3472 3466 2937 2776 3246 3505 3320 3319 3305 3020 2710 3240 3343 3224 3281 3235 2862 2835 3276 3302 3317 3374 3331 3078

23 3471 3210 2904 3445 3419 3530 3386 3308 3013 2680 3114 3151 3239 3255 3240 3012 2575 3087 3171 3145 3020 3119 2819 2724 3180 3159 3160 3191 3190 3048

24 3142 2987 2705 3119 3076 3167 3205 3198 2831 2319 2768 2933 2931 2931 2937 2768 2405 2906 2857 2859 2938 2856 2771 2472 2771 2881 2874 2753 2873 2804

TO

TA

L

82

.23

8

75

.58

2

62

.47

6

77

.87

2

79

.63

4

79

.98

6

80

.00

7

79

.29

7

71

.23

5

57

.08

9

70

.16

4

74

.33

1

75

.32

3

76

.11

1

76

.29

0

69

.13

8

56

.62

9

70

.02

9

73

.78

8

73

.33

5

73

.59

7

73

.19

0

66

.13

1

56

.80

4

70

.48

9

74

.05

4

73

.80

1

74

.09

8

74

.82

3

70

.57

6

0

CU

M.

82

.23

8

15

7.8

20

22

0.2

96

29

8.1

67

37

7.8

01

45

7.7

87

53

7.7

94

61

7.0

91

68

8.3

26

74

5.4

15

81

5.5

79

88

9.9

10

96

5.2

33

1.0

41.3

44

1.1

17.6

34

1.1

86.7

72

1.2

43

.40

1

1.3

13.4

30

1.3

87.2

18

1.4

60.5

53

1.5

34.1

50

1.6

07.3

40

1.6

73.4

72

1.7

30.2

76

1.8

00.7

65

1.8

74.8

19

1.9

48.6

20

2.0

22.7

18

2.0

97.5

41

2.1

68.1

17

2.1

68.1

17

184

POWER CONSUMPTION MAY 2005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2496 2156 2556 2427 2531 2539 2555 2321 2071 2342 2372 2489 2470 2468 2496 2119 2428 2459 2387 2165 2444 2381 1986 2414 2457 2452 2457 2468 2375 1977 2597

2 2312 2038 2317 2330 2380 2412 2276 2191 1885 2339 2361 2239 2302 2421 2243 1933 2322 2201 2261 2052 2280 2171 1867 2221 2277 2238 2266 2324 2180 1870 2248

3 2236 1951 2249 2271 2335 2263 2263 2101 1868 2218 2174 2169 2276 2320 2140 1850 2248 2247 2213 2008 2144 2012 1793 2174 2237 2112 2229 2198 2140 1777 2220

4 2155 1936 2201 2252 2287 2237 2245 2010 1729 2231 2239 2144 2212 2293 2053 1801 2168 2259 2177 1885 2171 2017 1794 2156 2217 2077 2196 2097 2144 1754 2178

5 2092 1901 2196 2219 2299 2266 2145 2001 1732 2218 2258 2145 2232 2244 2006 1794 2157 2215 2200 1980 2180 1904 1743 2186 2206 2118 2212 2096 1973 1703 2168

6 2041 1893 2188 2236 2277 2222 2118 1976 1778 2134 2170 2121 2205 2201 1835 1771 2155 2166 2129 1897 2048 1859 1708 2166 2108 2195 2151 2052 1818 1748 2108

7 2027 2020 2341 2377 2271 2219 2201 1934 1859 2236 2299 2280 2330 2221 1949 1921 2305 2373 2016 2075 2076 1803 1754 2284 2179 2249 2261 2093 1706 1875 2234

8 1961 2442 2606 2622 2723 2616 2389 1839 2359 2621 2608 2527 2547 2448 1972 2290 2601 2555 2230 2301 2284 1782 2176 2556 2459 2534 2534 2255 1763 2140 2466

9 2166 3335 3254 3366 3022 3386 3047 2027 3187 3244 3372 3232 3430 3112 2089 3192 3213 3390 2818 3231 2963 1909 2861 3321 3177 3314 3231 2949 1931 3154 3249

10 2501 3672 3657 3606 3638 3677 3281 2292 3431 3560 3507 3494 3554 3284 2383 3447 3495 3638 3056 3507 3149 2153 3228 3526 3316 3440 3526 3164 2185 3401 3421

11 2659 3700 3689 3619 3698 3760 3487 2513 3673 3581 3582 3593 3602 3401 2520 3490 3639 3680 3152 3620 3323 2334 3508 3621 3599 3618 3666 3330 2413 3501 3592

12 2679 3596 3675 3629 3602 3696 3341 2536 3539 3605 3671 3520 3603 3433 2554 3554 3609 3628 3138 3579 3362 2431 3565 3626 3584 3637 3616 3332 2413 3502 3610

13 2661 3456 3449 3456 3571 3478 3213 2484 3472 3418 3495 3414 3362 3275 2507 3453 3439 3424 3040 3388 3191 2398 3345 3493 3429 3475 3412 3265 2410 3477 3452

14 2496 3522 3504 3425 3578 3510 3120 2444 3522 3466 3511 3493 3410 3183 2381 3456 3522 3472 3028 3389 3103 2370 3375 3581 3383 3509 3329 3168 2352 3462 3519

15 2518 3633 3643 3499 3674 3613 3167 2386 3555 3435 3528 3529 3528 3159 2413 3484 3589 3565 3087 3485 3142 2282 3505 3597 3519 3641 3510 3122 2304 3522 3560

16 2373 3565 3542 3481 3535 3601 2959 2298 3543 3412 3448 3513 3489 3040 2340 3423 3509 3578 3029 3383 3008 2304 3454 3513 3505 3572 3533 2958 2215 3504 3480

17 2339 3567 3536 3592 3561 3492 2833 2283 3513 3433 3408 3554 3441 2921 2303 3344 3492 3552 2966 3452 2844 2274 3474 3413 3392 3474 3494 2911 2267 3383 3454

18 2390 3409 3468 3305 3392 3356 2799 2216 3252 3337 3397 3319 3412 2805 2251 3361 3425 3326 2944 3306 2821 2314 3360 3428 3310 3356 3331 2757 2234 3354 3286

19 2378 3265 3288 3211 3347 3310 2697 2288 3172 3141 3242 3329 3232 2735 2204 3207 3239 3196 2820 3057 2806 2392 3172 3207 3146 3133 3178 2772 2259 3135 3116

20 2577 3264 3277 3268 3248 3220 2828 2385 3144 3096 3257 3162 3129 2789 2459 3125 3181 3101 2807 3035 2781 2380 2990 3148 3062 3118 3127 2754 2245 3036 3040

21 2890 3435 3439 3431 3414 3320 3039 2788 3284 3320 3273 3355 3388 3094 2696 3266 3390 3327 2957 3233 2898 2529 3178 3256 3198 3322 3217 2908 2635 3154 3180

22 2901 3425 3368 3331 3278 3190 2910 2683 3212 3104 3204 3241 3276 3081 2781 3115 3308 3190 2820 3115 2807 2596 3092 3195 3145 3239 3099 2937 2658 3193 3128

23 2777 3188 3101 3200 3174 3111 2836 2551 3090 3014 3011 3067 3108 2893 2658 3108 3104 3104 2797 3022 2754 2549 3001 2996 3002 3099 2952 2846 2512 3042 3034

24 2523 2785 2881 2905 2956 2851 2638 2338 2878 2856 2714 2867 2796 2806 2388 2791 2927 2843 2599 2803 2528 2314 2758 2785 2739 2907 2822 2633 2361 2831 2807

TO

TA

L

58

.14

6

71

.15

4

73

.42

4

73

.05

8

73

.79

0

73

.34

4

66

.38

6

54

.88

6

68

.74

7

71

.36

0

72

.10

0

71

.79

6

72

.33

3

67

.62

7

55

.62

1

68

.29

2

72

.46

4

72

.48

9

64

.66

9

68

.96

6

65

.10

7

53

.45

8

66

.68

5

71

.86

2

70

.64

5

71

.82

9

71

.34

8

65

.38

7

53

.49

4

67

.49

2

71

.14

6

CU

M.

58

.14

6

12

9.3

00

20

2.7

24

27

5.7

82

34

9.5

72

42

2.9

16

48

9.3

02

54

4.1

88

61

2.9

35

68

4.2

95

75

6.3

95

82

8.1

91

90

0.5

24

96

8.1

51

1.0

23.7

72

1.0

92.0

64

1.1

64.5

28

1.2

37.0

17

1.3

01.6

86

1.3

70.6

52

1.4

35.7

59

1.4

89.2

17

1.5

55.9

02

1.6

27.7

64

1.6

98.4

09

1.7

70.2

38

1.8

41.5

86

1.9

06.9

73

1.9

60.4

67

2.0

27.9

59

2.0

99.1

05

185

POWER CONSUMPTION JUNE 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2480 2445 2462 2698 2221 1952 2460 2521 2519 2666 2624 2375 1973 2442 2473 2497 2559 2633 2502 1947 2510 2521 2549 2537 2578 2436 2065 2472 2476 2545

2 2260 2330 2418 2337 2161 1799 2310 2328 2376 2341 2401 2208 1935 2337 2326 2355 2383 2369 2302 1875 2322 2407 2364 2402 2393 2172 1897 2407 2331 2325

3 2213 2206 2301 2213 2089 1771 2295 2321 2239 2242 2297 2135 1886 2207 2251 2279 2288 2326 2199 1771 2231 2296 2345 2272 2284 2132 1778 2319 2209 2263

4 2197 2251 2244 2147 2025 1768 2228 2314 2269 2221 2244 2104 1760 2179 2192 2288 2245 2304 2179 1747 2209 2225 2203 2252 2230 2095 1762 2211 2174 2219

5 2272 2230 2264 2178 1948 1694 2186 2216 2183 2198 2235 2004 1759 2182 2252 2290 2290 2250 2137 1725 2217 2298 2231 2215 2134 1959 1825 2213 2222 2158

6 2158 2211 2231 2170 1900 1778 2248 2202 2244 2168 2238 2034 1769 2236 2251 2205 2234 2129 1989 1690 2137 2173 2215 2181 2167 1904 1732 2328 2218 2072

7 2168 2215 2338 2116 1855 1726 2138 2204 2245 2311 2069 1820 1825 2256 2267 2272 2133 2293,6 1947 1852 2263 2209 2220 2263 2168 1824 1697 2187 2140 2220

8 2558 2523 2559 2382 1857 2259 2461 2564 2605 2597 2278 1796 2176 2533 2541 2482 2537 2467 1910 2292 2531 2490 2476 2554 2289 1721 2139 2475 2458 2437

9 3294 3235 3343 2913 1987 3246 3281 3329 3364 3346 2922 2122 3112 3282 3327 3362 3227 3073 2066 3159 3353 3320 3388 3336 2912 1773 3130 3386 3320 3249

10 3539 3380 3514 3204 2256 3476 3486 3577 3609 3571 3188 2331 3476 3460 3579 3572 3620 3272 2185 3511 3423 3493 3516 3525 3134 1876 3590 3580 3544 3521

11 3624 3636 3702 3389 2406 3706 3691 3725 3841 3676 3423 2428 3604 3636 3694 3718 3772 3445 2335 3574 3702 3732 3651 3708 3306 2262 3671 3708 3688 3686

12 3618 3637 3675 3363 2459 3635 3687 3720 3679 3701 3369 2428 3625 3656 3648 3728 3661 3423 2439 3610 3677 3740 3729 3690 3343 2328 3737 3695 3702 3699

13 3476 3472 3411 3258 2433 3416 3484 3476 3612 3408 3313 2371 3502 3533 3488 3585 3433 3382 2400 3431 3426 3473 3521 3445 3172 2334 3615 3556 3547 3555

14 3569 3502 3488 3088 2441 3551 3591 3529 3659 3368 3174 2355 3610 3528 3511 3681 3503 3270 2425 3564 3527 3618 3590 3463 3204 2360 3669 3625 3548 3621

15 3631 3642 3606 3147 2418 3567 3651 3621 3716 3607 3065 2408 3556 3570 3573 3622 3693 3245 2513 3560 3559 3732 3667 3621 3098 2275 3718 3656 3621 3718

16 3549 3577 3491 3002 2290 3666 3614 3600 3728 3626 3020 2355 3567 3610 3565 3659 3669 3181 2317 3508 3591 3659 3686 3548 3013 2184 3646 3611 3547 3640

17 3406 3469 3528 2964 2232 3554 3552 3596 3708 3469 2910 2162 3513 3458 3584 3565 3527 2986 2335 3486 3451 3531 3599 3531 2975 2238 3555 3525 3490 3591

18 3339 3406 3364 2783 2253 3382 3476 3496 3507 3401 2763 2190 3404 3275 3433 3464 3332 2858 2258 3275 3237 3388 3458 3358 2832 2143 3413 3391 3355 3439

19 3155 3180 3245 2703 2229 3169 3176 3250 3311 3184 2749 2191 3187 3195 3174 3264 3107 2799 2138 3040 3076 3130 3171 3104 2769 2137 3184 3125 3112 3220

20 3060 2996 2928 2665 2244 3024 3027 3139 3116 3019 2665 2208 2995 2959 3076 3028 2999 2727 2216 2940 2937 2965 3042 2903 2668 2173 2987 2987 2939 2954

21 3195 3289 3180 2844 2458 3203 3200 3211 3294 3228 2787 2462 3179 3137 3158 3179 3112 2932 2437 3096 3009 3071 3007 2966 2829 2442 3016 3020 2980 3076

22 3077 3166 3182 2915 2593 3184 3282 3209 3232 3098 2917 2528 3116 3176 3104 3188 3077 2961 2456 3089 3103 3188 3166 3055 2966 2580 3068 3090 3124 3093

23 2996 3081 3124 2831 2556 3050 3140 3119 3061 3078 2879 2483 2953 3011 3055 3104 3095 2881 2500 3048 3087 3061 3114 3052 2815 2471 3056 3017 3031 3020

24 2775 2883 2842 2677 2309 2838 2848 2931 2830 2751 2734 2344 2790 2928 2809 2894 2923 2812 2322 2817 2885 2519 2874 2884 2612 2302 2835 2868 2826 2820

TO

TA

L

71

.61

0

71

.96

2

72

.43

9

65

.98

6

53

.61

6

68

.41

4

72

.51

3

73

.19

7

73

.94

4

72

.27

4

66

.26

3

53

.84

2

68

.27

1

71

.78

6

72

.33

3

73

.27

8

72

.42

0

68

.01

8

54

.50

5

67

.60

8

71

.46

1

72

.23

9

72

.78

0

71

.86

4

65

.88

9

52

.11

7

68

.78

3

72

.45

2

71

.60

1

72

.14

0

0

CU

M.

71

.61

0

14

3.5

72

21

6.0

11

28

1.9

97

33

5.6

13

40

4.0

27

47

6.5

40

54

9.7

37

62

3.6

81

69

5.9

55

76

2.2

18

81

6.0

60

88

4.3

31

95

6.1

17

1.0

28.4

50

1.1

01.7

28

1.1

74.1

48

1.2

42.1

66

1.2

96.6

71

1.3

64.2

79

1.4

35.7

40

1.5

07.9

79

1.5

80.7

59

1.6

52.6

23

1.7

18.5

12

1.7

70.6

29

1.8

39.4

12

1.9

11.8

64

1.9

83.4

65

2.0

55.6

05

2.0

55.6

05

186

POWER CONSUMPTION JULY 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2509 2581 2493 2043 2289 2438 2482 2559 2597 2388 2078 2596 2616 2591 2543 2616 2323 2099 2612 2654 2563 2643 2666 2522 2181 2513 2556 2646 2702 2641 2423

2 2331 2394 2145 1911 2181 2362 2305 2354 2551 2234 1918 2370 2437 2436 2406 2453 2305 1907 2371 2445 2442 2477 2511 2312 1970 2417 2410 2541 2498 2482 2308

3 2270 2332 2127 1797 2048 2247 2212 2300 2442 2115 1851 2388 2357 2301 2329 2323 2174 1945 2383 2425 2325 2404 2389 2212 1854 2372 2338 2482 2341 2356 2193

4 2197 2247 2079 1739 2031 2224 2181 2257 2286 2047 1813 2219 2259 2296 2303 2313 2278 1772 2324 2371 2352 2268 2266 2110 1875 2314 2275 2352 2325 2289 2194

5 2200 2247 2083 1693 2031 2214 2143 2243 2288 2050 1821 2281 2264 2333 2279 2258 1989 1759 2250 2351 2367 2309 2331 2169 1878 2337 2310 2328 2345 2295 2079

6 2166 2192 2033 1729 2030 2149 2135 2186 2142 2024 1816 2271 2255 2227 2285 2182 1931 1757 2221 2243 2191 2290 2209 2020 1743 2221 2204 2275 2351 2195 1975

7 2118 2303 1874 1727 2026 2198 2191 2326 2225 1903 1864 2282 2309 2376 2246 2213 1881 1814 2286 2329 2310 2334 2180 2002 1830 2357 2346 2319 2323 2197 1941

8,00 2488 2523 1764 1972 2237 2400 2475 2566 2353 1914 2145 2592 2626 2601 2517 2331 1909 2147 2588 2617 2545 2517 2455 1922 2304 2528 2646 2648 2591 2393 1915

9 3335 3076 1805 2933 3148 3010 3220 3346 2900 2072 3103 3371 3321 3342 3320 2918 2019 3211 3458 3534 3504 3342 3015 2050 3267 3487 3377 3474 3460 2966 2035

10 3558 3272 2116 3260 3339 3435 3466 3596 3208 2178 3542 3677 3649 3590 3627 3128 2201 3593 3660 3764 3661 3612 3195 2307 3571 3646 3655 3630 3738 3162 2254

11 3706 3470 2288 3492 3501 3580 3682 3784 3419 2309 3644 3785 3823 3788 3808 3364 2424 3789 3808 3937 3895 3825 3460 2390 3698 3822 3857 3752 3770 3412 2407

12 3736 3471 2297 3489 3537 3653 3712 3760 3369 2355 3790 3785 3853 3800 3783 3389 2427 3826 3801 3995 3893 3822 3408 2437 3787 3841 3814 3833 3965 3398 2432

13 3519 3373 2259 3369 3400 3445 3639 3576 3192 2337 3663 3762 3683 3715 3492 3239 2444 3749 3738 3808 3830 3653 3305 2522 3652 3631 3715 3740 3766 3272 2483

14 3516 3280 2293 3427 3477 3581 3648 3622 3132 2361 3741 3727 3829 3731 3558 3234 2374 3728 3851 3943 3820 3604 3339 2499 3778 3707 3791 3755 3734 3287 2437

15 3722 3243 2320 3520 3539 3610 3759 3770 3226 2398 3848 3931 3875 3744 3695 3071 2372 3775 3821 3947 3830 3778 3245 2473 3785 3781 3861 3873 3935 3158 2423

16 3694 3081 2317 3467 3523 3603 3683 3650 3115 2403 3818 3854 3777 3745 3616 3098 2363 3820 3829 3870 3839 3760 3095 2412 3750 3774 3786 3773 3688 3096 2387

17 3633 3024 2210 3412 3475 3513 3632 3677 3010 2262 3699 3821 3671 3673 3613 3029 2365 3792 3718 3826 3841 3658 3022 2361 3700 3702 3707 3700 3636 3025 2363

18 3442 2923 2230 3210 3374 3340 3453 3597 2871 2357 3509 3573 3570 3482 3438 2867 2282 3544 3573 3430 3620 3489 2908 2279 3469 3570 3641 3614 3464 2887 2280

19 3199 2838 2228 3054 3095 3166 3186 3229 2716 2345 3274 3357 3215 3322 3208 2787 2260 3211 3339 3454 3335 3290 2761 2273 3316 3334 3389 3289 3249 2774 2267

20 2982 2767 2238 2955 2877 2991 2998 3036 2770 2308 3124 3146 3096 3002 2984 2832 2288 3042 3205 3172 3161 3055 2784 2332 3012 3150 3197 3096 3020 2808 2310

21 3036 2863 2401 2936 2969 3102 3071 3225 2876 2543 3223 3300 3227 3248 3115 2831 2496 3099 3231 3259 3256 3179 2955 2565 3176 3286 3307 3275 3147 2893 2530

22 3097 2875 2507 2865 3096 3085 3149 3202 2825 2585 3231 3227 3178 3222 3109 2914 2529 3239 3210 3241 3226 3102 2896 2580 3229 3235 3231 3189 3106 2905 2554

23 3020 2812 2481 2893 3004 2978 3143 3089 2820 2559 3068 3131 3131 2986 3002 2835 2477 3120 3086 3103 3143 3046 2887 2485 3090 3144 3028 3170 3024 2861 2481

24 2898 2618 2311 2508 2758 2863 2922 2600 2667 2415 2868 2930 2956 2894 2846 2705 2339 2859 2920 2931 2984 2959 2724 2379 2927 2861 2872 2937 2903 2715 2359

TO

TA

L

72

.37

0

67

.80

6

52

.89

9

65

.40

1

68

.98

4

71

.18

6

72

.48

7

73

.54

8

66

.99

8

54

.45

9

70

.45

3

75

.37

6

74

.97

8

74

.44

3

73

.12

2

66

.93

0

54

.44

9

70

.59

4

75

.28

3

76

.64

9

75

.93

4

74

.41

4

68

.00

7

55

.61

3

70

.84

2

75

.03

1

75

.31

0

75

.69

1

75

.07

7

67

.46

8

55

.03

1

CU

M.

72

.37

0

14

0.1

76

19

3.0

75

25

8.4

76

32

7.4

60

39

8.6

46

47

1.1

33

54

4.6

81

61

1.6

79

66

6.1

38

73

6.5

91

81

1.9

67

88

6.9

45

96

1.3

89

1.0

34.5

10

1.1

01.4

40

1.1

55.8

89

1.2

26.4

82

1.3

01.7

65

1.3

78.4

14

1.4

54.3

48

1.5

28.7

62

1.5

96.7

69

1.6

52

.382

1.7

23.2

23

1.7

98.2

54

1.8

73.5

64

1.9

49.2

55

2.0

24.3

32

2.0

91.8

01

2.1

46.8

32

187

POWER CONSUMPTION AUGUST 2005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2174,9 2656,5 2673,3 2672,3 2642,8 2631 2416,2 2063,2 2583,1 2598,2 2596 2610 2568 2484 2185 2642 2658 2782 2663 2632 2436 2065 2630 2642 2694 2715 2623 2506 2131 2429 2364

2 2022,9 2504,6 2558 2472,7 2481,9 2558,3 2316,3 1967,3 2410,6 2598,2 2448 2494 2503 2375,3 2037 2466 2419 2533 2538 2544 2311 2020 2554 2437 2548 2521 2647 2375 2054 2447 2319

3 1947,8 2422,5 2472,6 2460,5 2353,7 2498,3 2234,7 1842,9 2430,5 2433,1 2369 2363 2471 2305,9 1993 2390 2440 2437 2455 2439 2228 1957 2364 2406 2393 2385 2458 2223 1947 2370 2162

4 1882,8 2371,1 2420,7 2440 2422,7 2426,3 2165,2 1834,2 2279,1 2433,1 2319 2299 2320 2164,2 1916 2368 2431 2391 2437 2382 2096 2068 2376 2436 2340 2377 2421 2127 1986 2360 2129

5 1801,6 2263,2 2329 2387,1 2431,7 2390,5 2102,3 1802,2 2298,1 2250,6 2270 2309 2233 2128,5 1866 2390 2384 2372 2449 2399 2118 1759 2296 2304 2329 2375 2276 2120 1855 2195 2155

6 1882,3 2376,8 2322,7 2353,7 2379,2 2268,9 1999,6 1913,7 2356,1 2250,6 2286 2270 2274 2133,8 1895 2418 2460 2400 2518 2253 2096 2034 2317 2328 2373 2436 2310 2052 1930 2155 2175

7 1907,5 2286,4 2379,7 2324,7 2447,1 2294,5 1983,3 1871,6 2269,8 2375,7 2352 2216 2298 2058 1878 2352 2352 2367 2419 2234 1889 1938 2304 2353 2415 2305 2192 2104 1920 2212 2187

8 2256,7 2471,2 2706 2617 2619,7 2444,4 1904,2 2183,2 2530,5 2375,7 2566 2502 2375 1882,5 2345 2648 2622 2673 2653 2414 1846 2216 2614 2629 2541 2613 2447 1965 2329 2331 2530

9 3097,6 3349,8 3561,2 3559 3580,6 3088,8 1848,6 3303,6 3368 2580 3369 3412 3000 2179,2 3364 3565 3394 3396 3506 3145 2023 3394 3409 3392 3447 3596 3035 1981 3302 3076 3497

10 3559,2 3643,4 3803,7 3862,2 3897,9 3333,3 2094,8 3559,7 3484,4 3383,5 3710 3644 3350 2311,4 3681 3827 3742 3707 3831 3318 2257 3588 3799 3523 3730 3872 3249 2268 3567 3303 3719

11 3743 3853 3955 4070 4037 3607 2350,8 3743 3700 3516 3830 3830 3580 2500,8 3820 3998 3866 3189 3995 3539 2400 3796 3877 3771 3993 3953 3525 2444 3711 3409 3958

12 3846,8 3896,6 3957,4 3965,9 4057,5 3532,6 2354,6 3765,9 3651,1 3812 3759 3851 3564 2578,4 3912 4015 3906 3769 3948 3541 2444 3834 3880 3665 3991 4006 3548 2498 3714 3509 3921

13 3844,3 3684,6 3890,8 3916,4 3800,6 3382,4 2406,1 3652,9 3505,8 3819 3705 3581 3354 2574,9 3830 3843 3764 3704 3752 3376 2424 3639 3737 3709 3866 3813 3404 2588 3620 3339 3785

14 3855,4 3779,6 3866 3960,6 3740,9 3310 2383,3 3731,2 3592,8 3649,2 3762 3599 3393 2674 3860 3990 3885 3865 3757 3258 2433 3820 3811 3694 3826 3758 3319 2563 3694 3428 3889

15 3958,7 3796,9 3892,5 4026,4 4004,1 3323,1 2370,9 3793,8 3687,4 3655 3737 3842 3276 2646,4 3930 4007 3865 3877 3893 3065 2521 3819 3870 3864 3844 3967 3233 2500 3733 3491 3977

16 3983,6 3773,7 3977,5 3984,7 3913,6 3196,4 2333,5 3794,8 3710,7 3752,3 3724 3750 3288 2557,4 3914 3893 3898 3852 3887 3009 2546 3837 3938 3796 3827 3907 3140 2455 3684 3359 3944

17 3811 3774,5 3842 3889,9 3905,9 2944,5 2310,3 3715,5 3541,7 3578,5 3683 3732 3100 2480,6 3894 3829 3930 3859 3827 2925 2393 3745 3819 3761 3760 3825 3164 2450 3683 3350 3820

18 3633,6 3593,9 3599,4 3692,9 3657,4 2869,2 2174,2 3599 3504,6 3578,5 3470 3558 2943 2436,1 3655 3610 3774 3762 3562 2920 2420 3645 3593 3546 3649 3674 2935 2366 3567 3198 3666

19 3455,3 3395,5 3451,3 3511,7 3366,5 2830,5 2198,3 3355 3221,2 3308,9 3247 3279 2868 2462,1 3384 3437 3440 3483 3356 2810 2434 3339 3400 3467 3433 3429 2879 2449 3227 3051 3434

20 3226,5 3165,4 3217 3315 3228 2835,6 2334,5 3218,1 3056,7 3308,9 3121 3180 2855 2460,5 3235 3322 3332 3336 3232 2841 2495 3312 3311 3348 3365 3286 2919 2535 3124 3019 3423

21 3384,4 3278,9 3297,3 3452,2 3433 2940,2 2586 3302,4 3243,3 3301,1 3309 3336 3047 2692 3399 3402 3514 3427 3339 3023 2753 3360 3433 3479 3490 3331 3038 2717 3229 3213 3441

22 3269,4 3260,2 3343,9 3306,3 3282,1 2864,8 2497,8 3193,5 3135,8 3301,1 3238 3132 2937 2681,7 3271 3314 3338 3286 3244 2956 2662 3323 3304 3346 3347 3234 2959 2622 3059 3052 3273

23 3191,6 3097,4 3262 3233 3207,8 2879,6 2449,2 3019,2 3084,8 3083,5 3114 3127 2847 2727,9 3166 3108 3216 3246 3104 2828 2609 3230 3122 3209 3179 3133 2889 2610 2752 2833 3131

24 2987,1 2984,3 2961,2 2984,8 2955,3 2669,8 2353,3 2790,2 2796,9 3083,5 2943 2912 2742 2484,4 2968 2964 3094 3013 2994 2779 2411 2847 2820 2942 2994 2940 2654 2412 2698 2729 2984

TO

TA

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72

72

4

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68

0

77

74

1

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9

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72

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49

87

39

77

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31

60

10

01

14

0

10

74

53

9

11

52

33

8

12

30

06

3

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13

84

14

7

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77

5

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09

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81

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5

16

58

17

9

17

34

22

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18

11

59

7

18

89

04

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19

58

30

7

20

15

23

5,2

20

85

75

0,2

21

55

60

6,2

22

31

48

7,9

188

POWER CONSUMPTION SEPTEMBER 2005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2620,6 2710,3 2641,5 2400 2023,6 2504,4 2479,2 2581,6 2610,3 2529,3 2485,6 2125,3 2568 2578,4 2621,6 2566,6 2563,7 2506 2163 2576 2566 2553 2535 2615 2423 2146 2451 2589 2549 2629

2 2423,9 2576,2 2411,7 2247,5 2089,3 2374,8 2382,6 2365,8 2449,5 2483,2 2256,8 1962,1 2396 2424,7 2457,7 2480,7 2358,2 2311,9 2040 2458 2418 2465 2460 2436 2292 1956 2397 2428 2415 2464

3 2484,8 2376,7 2405,9 2228,2 1882,2 2399,1 2310,5 2356 2335,2 2364,2 2200 1907,6 2424 2427,2 2393,4 2351,9 2382,1 2228,8 1946 2430 2369 2407 2408 2311 2171 1896 2357 2332 2322 2415

4 2401 2387,8 2352,1 2132,8 1842,5 2284,2 2294,4 2254 2291,2 2330,1 2054,6 1717,5 2323 2345,5 2327,6 2160,2 2261 2153,4 1934 2394 2350 2357 2322 2336 2160 1832 2239 2317 2263 2401

5 2298,9 2378,1 2296,1 2055,4 1765 2256,1 2251,1 2314,2 2329,4 2386,9 2066,6 1899,6 2268 2205,4 2357,5 2211,8 2280 2167,7 1905 2346 2316 2380 2306 2336 2082 1826 2219 2306 2269 2360

6 2414,5 2411,9 2336 2042,5 1865,5 2272,1 2339,8 2322,7 2392,2 2339,6 2135,2 1829,5 2333 2319,1 2442,5 2281,1 2305 2182,8 1953 2413 2431 2474 2317 2336 2041 1867 2331 2417 2270 2322

7 2466,1 2458,4 2268,7 1981 1849,6 2323,7 2345,1 2402,8 2372,2 2309,4 2128,5 1944,8 2385 2221,3 2443 2355,9 2295,5 2014,3 2070 2456 2467 2528 2440 2351 2103 2005 2484 2438 2466 2434

8 2645,8 2571,7 2451,8 1725,2 2140,7 2551,5 2481,9 2602,6 2623,7 2366 1786,8 2473,4 2655 2677,1 2619,4 2608,5 2481,7 1905,9 2220 2725 2683 2589 2710 2445 2106 2339 2540 2654 2642 2651

9 3589,3 3514,8 3034,9 2046,8 3311,9 3384 3551,4 3482,6 3481,6 3056,7 2045,3 3230,3 3418 3491,1 3411,4 3293,2 3041,9 2219,8 3406 3444 3492 3395 3401 3078 2098 3177 3339 3369 3470 3400

10 3871,8 3828,3 3249 2191,7 3538,5 3638 3643,7 3722,5 3715,1 3228,5 2399,2 3564,4 3708 3765 3677,5 3594,1 3448,2 2403,9 3679 3809 3650 3655 3683 3372 2353 3379 3582 3621 3671 3649

11 3967 3915 3436 2338,6 3671 3838 3769 3789 3794 3540 2534,1 3669 3841 3863 3796 3743 3631 2546,8 3913 3895 3835 3751 3827 3646 2531 3695 3756 3780 3762 3695

12 3946,6 3905,8 3361,2 2430,5 3769,9 3828 3786,7 3844,3 3858,3 3554 2596,2 3768,6 3760 3805,1 3789,6 3787,7 3657,9 2530,5 3953 3849 3764 3833 3770 3402 2562 3665 3606 3677 3759 3664

13 3853,2 3637,3 3269 2407,2 3570,1 3677,2 3690,8 3731,6 3578,2 3324 2623,3 3580,8 3588 3670,7 3661,1 3540,1 3463,9 2678 3762 3766 3714 3559 3483 3380 2616 3461 3520 3532 3672 3361

14 3968,7 3780 3255,3 2420,1 3618,2 3708,9 3709,5 3692,2 3675,4 3324,1 2583,8 3576,7 3682 3816,3 3713,3 3518,7 3458,6 2625,4 3654 3754 3812 3699 3543 3344 2487 3468 3668 3632 3669 3533

15 3985 3831,5 3104,5 2373,6 3787,1 3830,4 3859 3731,8 3791 3198,6 2577,4 3785,6 3809 3813,2 3812,2 3778,9 3375,3 2603,1 3780 3788 3836 3802 3708 3257 2557 3601 3648 3711 3663 3692

16 3943,1 3598,3 3086,6 2344,6 3660,1 3795,6 3874,9 3723,8 3793 3237,6 2463,7 3768,6 3815 3816,9 3791,7 3654,2 3295,6 2539,5 3867 3806 3767 3664 3691 3144 2576 3579 3639 3678 3694 3570

17 3864,5 3723,4 3029,6 2319,8 3620,8 3724,7 3804,7 3673 3690,2 3026,6 2412 3608 3749 3641,9 3723,4 3625,5 3127,9 2517,2 3883 3752 3757 3692 3723 3055 2386 3616 3653 3650 3641 3674

18 3725,9 3506,8 2905,6 2343 3501,2 3518,7 3571,5 3505,8 3490,2 2892,7 2356,4 3523,2 3624 3552,7 3636,6 3556,2 3124,5 2500,9 3756 3702 3647 3624 3550 2945 2488 3441 3525 3595 3566 3553

19 3557,8 3283,2 2850,8 2315,39 3281,8 3348,1 3390,8 3432,7 3356,6 2916,8 2446,6 3335,2 3485 3486,8 3518,9 3369,8 2996,2 2568 3667 3573 3578 3432 3400 2985 2495 3473 3458 3511 3557 3385

20 3429,6 3359,8 3053,2 2493,6 3319,6 3405,7 3405,4 3490,7 3454 3038,6 2679,6 3409,1 3596 3596,6 3527,6 3496,2 3238,9 2851 3602 3504 3496 3533 3543 3156 2760 3504 3566 3536 3554 3519

21 3455,3 3397,1 3002,5 2571 3368,9 3375,1 3387,7 3414,6 3333 3109 2733 3360,6 3425 3439,9 3454,4 3425,4 3192,2 2758,9 3561 3648 3510 3446 3387 3057 2784 3367 3473 3335 3429 3406

22 3434 3178,4 2884,2 2532,2 3192 3311,7 3255,1 3213,9 3234,3 2985,8 2665,7 3184,3 3231 3324 3335,9 3272,5 3069,9 2743,9 3275 3228 3229 3207 3242 3002 2696 3253 3267 3221 3266 3257

23 3229,8 3148,9 2706,8 2462,4 3080,5 3106,9 3165,3 3182,9 3115,9 2914,1 2541,8 3071,2 3155 3210,2 3150,5 3151 3155,3 2654,2 3147 3064 3140 3176 3098 2947 2547 3105 3092 3009 3082 3124

24 2970,8 2901,3 2698 2320,91 2789 2907,1 2913,9 2961,9 2817,5 2730,2 2304,8 2844,6 2992 3001,9 2893,2 2896,8 2766,5 2523,1 2876 2870 2878 2901 2917 2719 2374 2812 2873 2825 2877 2907

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1

68

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78

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20

08

99

2,2

20

84

52

0,2

21

59

58

4,8

21

59

58

4,8

189

POWER CONSUMPTION OCTOBER 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2659 2447 2105 2444 2486 2468 2501 2540 2456 2047 2532 2605 2626 2597 2619 2516 2187 2684 2735 2739 2799 2765 2712 2220 2493 2761 2685 2718 2621 2564 2429

2 2451 2290 1868 2161 2271 2270 2346 2363 2290 1914 2329 2417 2448 2461 2450 2384 2019 2517 2602 2640 2564 2679 2469 2071 2484 2502 2567 2523 2457 2389 2221

3 2381 2197 1850 2117 2239 2297 2339 2335 2207 1928 2333 2379 2379 2407 2403 2250 1948 2418 2515 2464 2511 2515 2348 1965 2434 2455 2488 2419 2414 2214 2235

4 2305 2110 1854 2064 2437 2306 2365 2357 2211 1987 2375 2406 2373 2473 2425 2314 1998 2434 2580 2449 2505 2571 2393 1958 2410 2455 2496 2473 2395 2304 2236

5 2272 2079 1781 2153 2426 2436 2416 2437 2233 2035 2442 2428 2483 2540 2518 2337 2067 2606 2600 2650 2592 2599 2457 2123 2556 2614 2609 2555 2484 2370 2300

6 2240 2058 1799 2133 2320 2341 2370 2251 2039 1960 2359 2367 2373 2397 2327 2218 1943 2573 2561 2556 2577 2586 2455 2017 2503 2516 2551 2308 2425 2351 2136

7 2304 2030 1931 2256 2314 2292 2294 2180 2070 1980 2323 2349 2374 2430 2360 2014 1953 2467 2559 2490 2558 2424 2189 2041 2464 2518 2533 2370 2248 2237 2186

8 2339 1905 2265 2496 2456 2460 2472 2255 1762 2175 2536 2552 2553 2571 2335 1861 2230 2515 2658 2660 2755 2463 2020 2280 2685 2657 2682 2602 2400 2047 2532

9 3147 2036 3163 3258 3154 3086 3154 2829 1716 2939 3184 3164 3160 3249 2936 1867 3017 3325 3385 3272 3335 3062 2016 3092 3403 3366 3234 3374 2710 2029 3460

10 3364 2094 3438 3512 3436 3418 3417 3145 1999 3340 3425 3473 3467 3460 3197 2088 3422 3579 3628 3630 3669 3371 2291 3425 3522 3544 3523 3571 3026 2391 3644

11 3558 2424 3608 3564 3542 3552 3570 3232 2180 3516 3565 3635 3616 3598 3444 2329 3590 3745 3783 3793 3792 3561 2503 3567 3701 3791 3666 3765 3277 2570 3787

12 3561 2511 3600 3564 3442 3529 3531 3322 2291 3497 3627 3666 3662 3613 3481 2520 3695 3814 3819 3865 3867 3568 2626 3679 3857 3744 3715 3790 3384 2817 3952

13 3405 2530 3420 3407 3455 3495 3269 3312 2369 3489 3545 3566 3565 3285 3462 2630 3664 3718 3814 3779 3532 3533 2609 3544 3686 3687 3616 3478 3367 2975 3966

14 3333 2493 3393 3504 3463 3545 3347 3234 2350 3514 3574 3578 3598 3515 3313 2547 3713 3823 3882 3818 3749 3393 2609 3614 3747 3671 3650 3543 3351 2981 4022

15 3295 2446 3586 3540 3567 3540 3505 3127 2365 3526 3591 3602 3624 3587 3299 2619 3739 3858 3873 3787 3797 3359 2602 3631 3762 3744 3690 3609 3326 3014 4090

16 3112 2506 3536 3504 3533 3557 3526 3087 2309 3536 3619 3634 3616 3575 3226 2538 3754 3839 3956 3797 3747 3304 2563 3627 3807 3691 3662 3606 3202 3061 4090

17 3048 2372 3501 3525 3501 3493 3454 3016 2337 3534 3651 3612 3572 3527 3234 2598 3731 3801 3933 3736 3739 3220 2626 3634 3765 3664 3650 3647 3207 3080 3879

18 3035 2395 3478 3485 3361 3358 3317 2955 2470 3420 3504 3410 3495 3394 3118 2685 3564 3764 3813 3649 3622 3234 2679 3582 3662 3629 3584 3555 3208 3166 3825

19 3160 2639 3479 3510 2916 3002 3014 2754 2396 3038 3087 3080 3124 3058 2920 2611 3274 3370 3432 3386 3376 3157 2711 3392 3550 3505 3576 3550 3194 3140 3939

20 3202 2843 3451 3483 3328 3354 3355 3095 2750 3412 3310 3278 3477 3416 3143 2821 3622 3728 3733 3720 3669 3358 2881 3577 3671 3675 3605 3525 3212 3113 3811

21 3127 2789 3345 3338 3226 3239 3221 3035 2690 3208 3330 3341 3358 3321 3109 2731 3521 3526 3561 3586 3507 3229 2800 3443 3517 3508 3517 3414 3122 3070 3579

22 3022 2677 3113 3396 3157 3169 3180 2956 2636 3123 3217 3201 3284 3198 3031 2728 3432 3485 3458 3444 3446 3186 2816 3365 3500 3400 3446 3351 3105 3087 3450

23 2930 2537 3064 3079 2997 3006 2992 2828 2546 3024 3053 3113 3156 3184 2954 2706 3259 3329 3355 3371 3386 3147 2767 3229 3246 3266 3375 3203 3011 2996 3347

24 2782 2372 2739 2893 2820 2746 2813 2716 2355 2837 2817 2891 2964 2982 2876 2440 2959 3052 3120 3136 3054 3154 2590 2996 3123 3077 3043 2962 2875 2955 3110

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2

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7

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2

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16

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4,5

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8,0

5

20

69

78

9,0

5

21

34

71

2,5

5

22

12

93

7,5

5

190

POWER CONSUMPTION NOVEMBER 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2785 2710 2195 1737 1847 2001 2140 2709 2810 2760 2781 2852 2731 2365 2806 2778 2804 2769 2878 2815 2509 2967 2941 2979 2916 2900 2902 2495 2806 2886

2 2557 2525 1860 1615 1629 1813 1985 2636 2697 2622 2621 2619 2559 2268 2759 2761 2686 2663 2657 2703 2248 2780 2863 2809 2712 2779 2614 2151 2587 2773

3 2549 2487 1689 1552 1522 1721 1843 2477 2464 2609 2508 2533 2423 2088 2541 2637 2608 2518 2625 2453 2316 2730 2641 2759 2609 2584 2437 2120 2629 2572

4 2646 2484 1650 1525 1484 1648 1784 2373 2472 2368 2404 2497 2308 2106 2482 2488 2580 2510 2585 2386 2138 2626 2635 2683 2558 2569 2411 2231 2505 2475

5 2617 2425 1569 1431 1511 1641 1761 2450 2550 2502 2419 2421 2267 2042 2466 2521 2519 2476 2539 2384 2074 2575 2620 2596 2566 2539 2287 2047 2473 2486

6 2430 2354 1605 1446 1470 1598 1842 2487 2458 2396 2463 2450 2393 2097 2445 2507 2513 2556 2708 2321 2171 2594 2610 2636 2560 2449 2176 2036 2482 2485

7 2537 2166 1851 1490 1479 1633 2086 2509 2596 2604 2638 2485 2261 2265 2534 2600 2742 2566 2772 2409 2195 2746 2829 2879 2877 2588 2283 2229 2704 2730

8 2698 2158 1936 1394 1544 1707 2512 2892 2847 2795 2843 2659 2200 2565 2913 3022 2952 2949 2533 2293 2783 3012 3116 3103 3013 2743 2140 2625 2873 2791

9 3619 2667 1988 1655 1765 1930 3365 3575 3757 3732 3767 3374 2441 3711 3769 3825 3761 3755 3418 2325 3845 4021 4023 3987 3858 3481 2331 3642 3679 3660

10 3821 3042 2098 1953 2072 2135 3696 3949 4050 3959 3951 3731 2579 3962 3946 4058 4040 3950 3714 2773 4176 4214 4336 4186 4175 3764 2664 3815 4116 3965

11 3935 3165 2097 2047 2293 2423 3938 4142 4055 4153 4106 3927 2865 4088 4122 4121 4089 4152 3841 3016 4426 4372 4506 4379 4399 3880 2801 3993 4105 4051

12 3935 3138 2098 2211 2355 2651 3991 4076 4002 4141 3917 3894 2904 4065 4085 4165 4165 4034 3749 3090 4423 4336 4432 4426 4185 3932 2854 3990 4074 3981

13 3897 3044 2000 2189 2309 2619 3976 3886 3859 3895 3797 3741 3124 3962 3976 3990 4010 3934 3850 3150 4259 4189 4364 4181 4158 3737 2895 3856 3953 3863

14 3975 2772 1843 2102 2295 2602 4044 3932 3933 3905 3965 3624 3044 4102 4028 4016 4037 4135 3755 3145 4407 4268 4459 4255 4240 3656 2851 3974 3920 3867

15 4015 2707 1826 2045 2232 2566 4104 4077 4018 4034 4016 3622 2961 4077 4089 4103 4127 4143 3779 3166 4320 4243 4495 4316 4317 3639 2857 3895 3919 3925

16 3985 2690 1813 2100 2190 2595 4117 4053 3951 4060 4043 3619 2992 4109 4053 4119 4148 4191 3726 3132 4302 4265 4534 4391 4316 3621 2817 3976 3937 3884

17 3829 2883 1900 2159 2372 2683 4170 4208 4215 4265 4229 3755 3155 4366 4331 4402 4221 4287 3867 3342 4435 4514 4664 4530 4456 3819 2962 4263 4162 4188

18 3806 2812 2078 2131 2536 2772 4160 4211 4342 4331 4239 3825 3253 4325 4348 4393 4336 4316 3784 3310 4489 4508 4636 4549 4454 3776 3189 4293 4207 4244

19 3840 2870 2081 2249 2494 2899 3960 4099 4205 4199 4021 3684 3311 4165 4044 4138 4061 4075 3619 3354 4275 4333 4372 4302 4282 3643 3174 4037 3996 4024

20 3589 2864 2053 2259 2489 2817 3825 3810 3849 3867 3797 3611 3241 3869 4036 3870 3840 3819 3544 3222 3977 4023 4094 4088 3995 3597 3102 3791 3800 3850

21 3518 2884 2092 2238 2480 2714 3641 3754 3750 3736 3628 3444 3128 3819 3744 3709 3795 3731 3367 3153 3888 3969 3947 3956 3775 3458 2967 3770 3739 3667

22 3436 2862 2036 2192 2446 2757 3543 3596 3657 3623 3487 3403 3133 3696 3656 3513 3518 3613 3381 3220 3812 3767 3826 3764 3633 3458 3015 3544 3612 3578

23 3314 2747 2037 2137 2360 2620 3299 3403 3536 3447 3517 3265 2998 3486 3450 3539 3442 3519 3338 3061 3647 3581 3682 3643 3635 3286 2995 3477 3419 3403

24 3150 2558 1944 2118 2203 2441 3084 3204 3133 3273 3188 3181 2875 3321 3492 3290 3284 3409 3281 2854 3343 3407 3440 3427 3517 3229 2708 3219 3275 3241

TO

TA

L

80

47

9

65

01

5

46

34

0

45

97

6

49

37

7

54

98

5

76

86

5

82

50

9

83

20

6

83

27

6

82

34

5

78

21

3

67

14

4

80

91

7

84

11

6

84

56

4,7

84

27

7

84

06

8

79

31

0

69

07

6

84

45

7

88

03

8

90

06

1

88

82

3

87

20

7

79

12

5

65

43

3

79

46

8

82

97

1

82

58

7

CU

M.

80

47

9

14

54

94

19

18

34

23

78

10

28

71

87

34

21

72

41

90

37

50

15

46

58

47

52

66

80

28

75

03

73

82

85

86

89

57

30

97

66

47

10

60

76

3

11

45

32

7,7

12

29

60

4,7

13

13

67

2,7

13

92

98

2,7

14

62

05

8,7

15

46

51

5,7

16

34

55

3,7

17

24

61

4,7

18

13

43

7,7

19

00

64

4,7

19

79

76

9,7

20

45

20

2,7

21

24

67

0,7

22

07

64

1,7

22

90

22

8,7

191

POWER CONSUMPTION DECEMBER 2005

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2799 2771 2741 2752 2292 2703 2684 2813 2755 2876 2855 2497 3056 2879 2888 2959 2860 3022 2440 2977 2959 3074 3082 3018 2937 2515 2997 3003 2941 2834 2849

2 2591 2669 2668 2515 2310 2647 2707 2692 2769 2677 2620 2180 2898 2787 2845 2728 2750 2540 2395 2764 2805 2793 2781 2862 2584 2336 2768 2702 2718 2740 2677

3 2715 2574 2619 2394 1999 2491 2484 2449 2564 2581 2531 2184 2521 2635 2576 2678 2624 2490 2113 2674 2749 2706 2668 2657 2542 2221 2660 2599 2612 2575 2584

4 2510 2478 2468 2290 1868 2396 2506 2428 2437 2527 2356 2137 2450 2616 2586 2584 2605 2394 1954 2692 2593 2589 2678 2641 2478 2256 2537 2559 2545 2556 2447

5 2404 2435 2443 2241 1934 2423 2462 2500 2440 2519 2278 2024 2466 2514 2537 2540 2552 2299 1923 2625 2675 2618 2655 2628 2412 2171 2479 2501 2507 2488 2513

6 2512 2469 2523 2266 2023 2454 2482 2442 2573 2421 2328 2102 2562 2580 2564 2577 2510 2260 2017 2578 2690 2608 2705 2541 2438 2019 2555 2524 2521 2558 2463

7 2647 2706 2541 2231 2288 2637 2687 2722 2803 2534 2520 2327 2636 2731 2783 2792 2684 2389 2345 2902 2940 2996 2953 2771 2419 2528 2881 2842 2819 2832 2543

8 2739 2886 2534 2236 2534 2921 2945 2862 3025 2717 2218 2731 2849 3067 3052 3062 2808 2228 2620 3250 3238 3223 3219 2806 2341 2909 3007 3095 3010 3001 2578

9 3699 3634 3334 2151 3554 3739 3752 3657 3760 3503 2349 3742 3884 3900 3844 3608 3554 2381 3658 3925 4051 4092 4154 3578 2434 3945 3861 3782 3583 3807 3225

10 4027 3881 3659 2466 3887 3928 3895 3798 4144 3784 2732 4110 4101 4152 4163 4108 3824 2677 4103 4217 4346 4336 4361 4005 2746 4241 4190 4024 4034 3998 3530

11 4055 4059 3846 2779 4042 4090 4074 3939 4186 3973 2993 4244 4268 4380 4342 4381 3999 2991 4366 4457 4481 4433 4519 4252 3105 4440 4392 4191 4236 4139 3741

12 4105 3926 3827 2786 3985 3956 4048 3989 3994 4082 3101 4305 4239 4387 4319 4131 4083 3251 4375 4419 4433 4553 4284 4368 3289 4475 4412 4174 4201 4004 3839

13 3868 3746 3581 2748 3804 3747 3797 3854 3727 3896 3149 4213 4030 4193 4173 4055 3920 3194 4302 4164 4300 4439 4141 4269 3282 4312 4269 3973 3943 3748 3526

14 3921 3939 3530 2814 3837 3836 3882 3921 3980 3896 3116 4273 4140 4180 4285 4273 3705 3301 4429 4267 4414 4395 4502 4160 3309 4450 4349 4197 4053 4036 3530

15 4031 3903 3530 2806 3903 3966 3942 3972 4042 3819 3085 4358 4167 4256 4258 4313 3672 3264 4427 4416 4391 4531 4377 4024 3288 4412 4325 4090 4058 4041 3362

16 4134 3872 3462 2759 3910 3981 3984 4011 4034 3777 3059 4312 4213 4191 4257 4285 3632 3211 4304 4327 4362 4481 4396 3992 3242 4367 4307 4151 4109 4045 3217

17 4342 4174 3723 3118 4211 4309 4191 4264 4352 3862 3242 4538 4441 4409 4503 4433 3814 3381 4573 4649 4589 4720 4554 4094 3444 4586 4387 4403 4282 4303 3333

18 4344 4238 3669 3201 4308 4242 4299 4254 4329 3867 3328 4472 4407 4441 4454 4486 3781 3417 4528 4645 4702 4621 4641 4118 3494 4621 4577 4455 4245 4285 3463

19 4056 3987 3503 3154 3983 4071 4011 4011 4097 3629 3285 4243 4177 4215 4147 4250 3759 3305 4288 4415 4413 4412 4368 3996 3539 4339 4310 4148 4086 4039 3333

20 3845 3805 3448 3111 3837 3869 3881 3843 3892 3550 3204 3974 4092 3978 3964 4000 3668 3230 4052 4204 4133 4276 4148 3846 3451 4035 4073 3805 3919 3863 3048

21 3619 3535 3386 3047 3695 3715 3667 3832 3680 3407 3163 3785 3912 3907 3831 3808 3451 2992 4014 4039 3948 4042 4031 3728 3352 3868 3954 3831 3734 3631 3075

22 3583 3472 3317 3052 3474 3508 3610 3629 3638 3400 3175 3622 3721 3732 3743 3641 3405 2937 3769 3880 3854 3854 3856 3568 3373 3857 3766 3689 3641 3560 2746

23 3462 3458 3136 2894 3394 3421 3436 3455 3433 3310 3068 3619 3536 3580 3625 3594 3394 2941 3704 3662 3843 3767 3712 3428 3192 3601 3582 3509 3463 3554 2677

24 3384 3310 3165 2706 3193 3250 3326 3327 3238 3176 2742 3344 3330 3295 3423 3400 3317 2805 3593 3509 3392 3587 3443 3367 3050 3396 3481 3360 3319 3413 2494

TO

TA

L

83

39

1

81

92

7

76

65

2

64

51

6

78

26

4

82

29

9

82

75

0

82

66

2

83

89

1

79

78

1

68

49

6

83

33

4

86

09

4

87

00

4

87

16

3

86

68

2

80

37

0

68

90

0

84

28

9

89

65

9

90

30

0,6

91

14

4

90

22

4

84

71

5

71

74

1

85

89

9

88

12

1

85

60

3

84

57

9

84

04

9

72

79

2

CU

M.

83

39

1

16

53

18

24

19

70

30

64

86

38

47

50

46

70

49

54

97

99

63

24

61

71

63

52

79

61

33

86

46

29

94

79

63

10

34

05

7

11

21

06

1

12

08

22

4

12

94

90

6

13

75

27

6

14

44

17

6

15

28

46

5

16

18

12

4

17

08

42

4,6

17

99

56

8,6

18

89

79

2,6

19

74

50

7,6

20

46

24

8,6

21

32

14

7,6

22

20

26

8,6

23

05

87

1,6

23

90

45

0,6

24

74

49

9,6

25

47

29

1,6

192

POWER CONSUMPTION AUGUST 2006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2884 2907 2910 2870 3008 2752 2403 2924 2936 2868 2891 3022 2762 2590 2861 2875 2896 2976 3056 2880 2453 2960 2888 2956 2945 3028 2927 2503 2845 2846 2712

2 2733 2706 2704 2798 2738 2779 2252 2680 2780 2776 2751 2791 2580 2298 2784 2702 2844 2839 2803 2563 2136 2782 2768 2763 2678 2751 2632 2395 2658 2727 2639

3 2616 2601 2611 2569 2663 2541 2120 2662 2683 2613 2670 2692 2462 2118 2715 2609 2725 2735 2723 2357 1965 2660 2623 2758 2605 2604 2522 2264 2549 2636 2510

4 2561 2567 2600 2546 2601 2469 2109 2549 2618 2604 2661 2653 2335 2154 2583 2639 2645 2641 2601 2345 2060 2614 2583 2658 2535 2512 2438 2143 2480 2466 2424

5 2516 2471 2570 2565 2577 2454 2030 2463 2555 2581 2617 2617 2359 2021 2626 2603 2635 2596 2572 2278 2118 2630 2505 2632 2548 2547 2406 2074 2548 2426 2466

6 2471 2507 2604 2551 2510 2392 2005 2547 2528 2655 2537 2626 2469 2102 2534 2692 2568 2672 2376 2595 2092 2625 2617 2619 2749 2634 2496 2124 2449 2508 2400

7 2425 2404 2504 2521 2452 2101 2057 2663 2506 2525 2515 2532 2137 2117 2503 2573 2635 2566 2465 2167 2136 2603 2640 2737 2553 2555 2129 2233 2516 2486 2467

8 2786 2866 2868 2905 2673 2110 2552 2786 2867 2848 2894 2704 2144 2480 2866 2864 2979 2979 2615 2174 2503 2924 2964 2919 2895 2742 2148 2573 2756 2637 2761

9 3792 3759 3652 3780 3375 2284 3683 3727 3780 3936 3918 3320 2220 3660 3780 3926 3867 3937 3378 2357 3729 3906 3903 3817 3791 3407 2287 3710 3647 3328 3521

10 3802 4003 4013 4086 3680 2460 4002 4005 4101 4088 4200 3735 2466 3975 4173 4263 4223 4236 3769 2459 4084 4308 4166 4135 4100 3709 2629 4042 3965 3603 3810

11 4099 4226 4135 4254 3954 2645 4140 4115 4305 4254 4387 3787 2811 4291 4352 4380 4374 4399 3900 2754 4318 4437 4381 4373 4250 3905 2787 4302 4156 3664 3982

12 4180 4271 4233 4336 3920 2768 4249 4144 4272 4317 4386 3922 2862 4396 4300 4396 4424 4433 3963 2845 4405 4426 4402 4373 4259 4002 2927 4356 4166 3838 4028

13 4033 4070 4020 4016 3796 2829 4115 3920 4093 4159 4059 3783 2852 4230 4203 4284 4290 4212 3826 2847 4183 4268 4236 4149 4150 3859 2910 4296 4001 3764 3843

14 4109 4162 4190 4165 3752 2851 4286 4003 4295 4186 4118 3714 2860 4373 4321 4358 4400 4092 3810 2858 4361 4329 4253 4323 4211 3811 2973 4340 4110 3825 4036

15 4232 4277 4288 4318 3657 2726 4334 4026 4278 4294 4292 3700 2749 4365 4329 4324 4440 4378 3719 2830 4417 4389 4381 4412 4410 3799 2920 4350 4211 3896 4053

16 4224 4123 4194 4268 3600 2761 4301 4125 4226 4240 4323 3628 2784 4325 4325 4266 4419 4314 3684 2800 4384 4292 4380 4333 4364 3767 2867 4251 4198 3819 4029

17 4178 4099 4105 4213 3373 2695 4168 4082 4210 4241 4345 3478 2649 4232 4253 4258 4361 4313 3539 2803 4272 4299 4232 4289 4235 3580 2863 4032 4176 3759 3933

18 4025 3918 4013 4054 3273 2707 4049 3998 4104 3942 4072 3303 2636 4038 4015 3946 4174 4219 3363 2695 4091 4034 4032 4181 4135 3431 2805 3781 4035 3651 3818

19 3730 3725 3742 3775 3193 2681 3756 3710 3821 3731 3755 3288 2650 3793 3739 3823 3891 3891 3313 2669 3840 3841 3793 3877 3752 3318 2733 3458 3769 3537 3693

20 3409 3496 3504 3521 3168 2701 3499 3385 3541 3555 3579 3207 2606 3516 3625 3651 3709 3598 3258 2801 3695 3638 3696 3721 3637 3326 2869 3162 3601 3458 3589

21 3685 3664 3649 3686 3348 2960 3668 3633 3717 3794 3696 3478 2883 3695 3752 3809 3914 3743 3449 2970 3772 3840 3848 3859 3735 3503 3105 3474 3753 3600 3641

22 3632 3514 3630 3590 3331 2880 3617 3529 3584 3675 3602 3317 2888 3508 3636 3715 3657 3664 3311 2927 3587 3675 3635 3643 3548 3414 3087 3310 3546 3430 3444

23 3450 3399 3469 3443 3190 2892 3423 3406 3415 3489 3454 3192 2810 3477 3442 3519 3511 3565 3204 2795 3527 3429 3562 3515 3427 3306 2994 3208 3412 3335 3320

24 3301 3279 3278 3153 3073 2713 3252 3358 3364 3429 3484 3133 2732 3189 3287 3383 3395 3416 3180 2709 3458 3315 3383 3330 3367 3160 2795 3028 3299 3237 3260

TO

TA

L

82

.87

2

83

.01

2

83

.48

4

83

.98

0

76

.90

4

63

.15

0

80

.06

9

82

.43

8

84

.57

8

84

.80

0

85

.20

4

77

.62

0

62

.70

6

80

.94

2

85

.00

6

85

.85

6

86

.97

5

86

.41

4

77

.87

5

63

.47

8

81

.58

7

86

.22

1

85

.87

1

86

.37

4

84

.88

0

78

.67

1

65

.24

5

79

.40

7

82

.84

3

78

.47

2

80

.37

8

CU

M.

82

.87

2

16

5.8

84

24

9.3

68

33

3.3

48

41

0.2

52

47

3.4

02

55

3.4

72

63

5.9

10

72

0.4

88

80

5.2

88

89

0.4

92

96

8.1

12

1.0

30.8

18

1.1

11.7

60

1.1

96.7

66

1.2

82.6

22

1.3

69.5

97

1.4

56.0

11

1.5

33.8

86

1.5

97.3

64

1.6

78.9

51

1.7

65.1

72

1.8

51.0

42

1.9

37

.416

2.0

22.2

96

2.1

00.9

67

2.1

66.2

12

2.2

45.6

19

2.3

28.4

62

2.4

06.9

34

2.4

87.3

12

193

POWER CONSUMPTION SEPTEMBER 2006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2782 2775 2612 2282 2800 2917 2860 2928 2811 2710 2292 2750 2843 2785 2880 2923 2679 2362 2785 2752 2759 2792 2787 2767 2901 2837 2704 2777 2810 2846

2 2702 2627 2491 2105 2667 2753 2750 2764 2727 2558 2160 2583 2665 2644 2679 2678 2588 2106 2569 2576 2617 2627 2642 2536 2544 2658 2604 2674 2632 2726

3 2587 2504 2337 2032 2546 2667 2632 2753 2605 2350 2082 2521 2581 2640 2660 2682 2454 2106 2602 2505 2600 2544 2520 2401 2396 2407 2601 2592 2576 2668

4 2538 2447 2253 1925 2455 2560 2511 2636 2522 2295 2040 2420 2526 2540 2427 2539 2493 1939 2466 2446 2486 2444 2447 2494 2697 2435 2660 2611 2661 2677

5 2543 2442 2164 1976 2490 2560 2497 2528 2528 2272 2035 2461 2493 2468 2499 2574 2265 2048 2446 2481 2474 2458 2521 2516 2738 2627 2616 2652 2661 2674

6 2553 2421 2293 2023 2524 2564 2553 2608 2580 2282 2139 2499 2463 2571 2554 2496 2221 1990 2554 2489 2552 2504 2474 2419 2608 2653 2512 2619 2537 2634

7 2543 2408 2221 2061 2499 2617 2609 2486 2448 2043 2101 2507 2527 2528 2530 2474 2204 2017 2564 2546 2593 2530 2537 2157 2432 2454 2565 2528 2601 2475

8 2764 2498 1873 2295 2782 2955 2747 2865 2641 2153 2454 2809 2792 2877 2854 2593 2113 2473 2784 2807 2808 2843 2515 1884 2271 2682 2639 2766 2711 2553

9 3548 3268 1991 3433 3678 3710 3736 3752 3354 2203 3366 3666 3670 3744 3699 3382 2241 3511 3633 3657 3731 3657 3332 1898 3262 3353 3496 3478 3483 3165

10 3878 3546 2225 3812 3885 4060 3892 3965 3624 2465 3707 3820 3911 3947 3864 3620 2573 3877 3889 3993 3928 3932 3655 2167 3688 3774 3726 3794 3708 3470

11 4064 3594 2591 4041 4176 4278 4049 4131 3772 2569 3919 4040 3964 4110 4127 3818 2738 4040 4071 4084 4124 4090 3793 2456 3907 3911 3874 3849 3852 3695

12 4009 3623 2743 4038 4167 4198 4156 4209 3824 2698 3881 4049 4094 4107 4176 3816 2833 4016 4032 4154 4107 4080 3780 2552 3943 3887 3892 3873 3821 3683

13 3779 3548 2704 3898 4012 4078 3923 3920 3733 2670 3836 3829 3915 3929 3793 3702 2872 3859 3837 3950 3862 3773 3698 2647 3771 3759 3808 3757 3509 3625

14 3781 3447 2705 4023 4260 4302 3989 3917 3712 2751 3848 3927 3973 4048 3929 3624 2841 3944 3976 3978 3909 3763 3667 2751 3839 3843 3845 3876 3684 3520

15 3990 3432 2701 4114 4226 4236 4102 4152 3560 2591 4003 4003 4027 4098 4055 3586 2801 4027 4053 4130 3998 3964 3587 2645 3866 3793 3931 3980 3866 3540

16 3981 3368 2583 4042 4126 4120 4044 4141 3420 2586 3925 3969 4092 4087 4058 3545 2777 4027 4039 4122 4024 3935 3567 2703 3888 3837 3879 3936 3900 3425

17 3886 3123 2723 3909 4106 4078 4077 4055 3372 2562 3974 4148 3943 3990 4021 3308 2727 4068 4055 4026 3994 3983 3324 2617 3839 3858 3861 3881 3843 3298

18 3772 3133 2428 3796 4043 3953 3882 3905 3222 2541 3763 3819 3861 3912 3772 3222 2779 3824 3825 3785 3833 3737 3302 2662 3653 3638 3696 3796 3703 3285

19 3534 3083 2449 3561 3752 3647 3617 3691 3153 2593 3714 3548 3664 3734 3706 3192 2744 3849 3744 3714 3705 3836 3323 2896 3539 3572 3643 3601 3510 3268

20 3593 3221 2735 3652 3975 3714 3630 3714 3429 2870 3715 3766 3831 3830 3790 3438 3125 3867 3868 3712 3817 3777 3564 2992 3385 3633 3663 3701 3627 3420

21 3582 3272 2836 3574 3675 3688 3677 3679 3347 2929 3601 3624 3798 3707 3752 3347 3046 3741 3767 3640 3687 3685 3375 2951 3568 3612 3626 3675 3515 3307

22 3401 3183 2836 3519 3573 3538 3558 3533 3299 2834 3461 3506 3658 3594 3600 3271 2927 3538 3586 3440 3470 3490 3320 2745 3355 3415 3512 3497 3396 3227

23 3312 2998 2704 3300 3426 3407 3389 3318 3160 2760 3292 3385 3513 3435 3410 3219 2980 3355 3330 3322 3361 3336 3257 2791 3271 3365 3368 3276 3338 3151

24 3257 2961 2614 3225 3294 3290 3177 3365 3047 2624 3225 3240 3335 3287 3315 3095 2713 2979 3261 3145 3128 3301 3130 2628 3167 3209 3252 3165 3256 3140

TO

TA

L

80

.37

6

72

.91

9

59

.81

2

76

.63

4

83

.13

5

83

.88

9

82

.05

7

83

.01

4

75

.88

9

60

.90

8

76

.53

3

80

.88

5

82

.13

9

82

.61

3

82

.14

9

76

.14

3

63

.73

1

77

.56

1

81

.73

4

81

.45

4

81

.56

5

81

.08

1

76

.11

7

61

.27

4

78

.52

5

79

.21

1

79

.97

1

80

.35

3

79

.19

9

75

.47

0

0

CU

M.

80

.37

6

15

3.2

95

21

3.1

07

28

9.7

41

37

2.8

76

45

6.7

65

53

8.8

22

62

1.8

36

69

7.7

25

75

8.6

33

83

5.1

66

91

6.0

51

99

8.1

90

1.0

80.8

03

1.1

62.9

52

1.2

39.0

95

1.3

02.8

26

1.3

80.3

87

1.4

62.1

21

1.5

43.5

75

1.6

25.1

40

1.7

06.2

21

1.7

82.3

38

1.8

43.6

12

1.9

22.1

37

2.0

01.3

48

2.0

81.3

19

2.1

61.6

72

2.2

40.8

71

2.3

16.3

41

2.3

16.3

41

194

POWER CONSUMPTION OCTOBER 2006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2759 2278 2801 2768 2748 2877 2798 2623 2433 2822 2831 2845 2909 2993 2800 2417 2905 3000 3141 3063 3130 2901 2292 1785 1838 1957 2705 2732 5408 2393 2736

2 2608 2263 2622 2671 2606 2689 2733 2633 2313 2639 2592 2671 2761 2763 2581 2327 2704 2800 2918 2833 2885 2594 1956 1587 1731 1870 2517 2603 2467 2148 2589

3 2461 2089 2640 2561 2518 2624 2554 2499 2156 2622 2529 2691 2585 2679 2497 2209 2683 2733 2767 2775 2753 2405 1739 1509 1601 1716 2531 2463 2112 2039 2428

4 2457 2112 2681 2605 2645 2620 2614 2511 2165 2640 2516 2688 2677 2652 2423 2244 2620 2751 2766 2632 2823 2391 1602 1329 1490 1743 2345 2391 2244 2054 2248

5 2551 2199 2826 2672 2655 2745 2637 2533 2218 2693 2662 2715 2765 2720 2578 2360 2727 2836 2940 2799 2797 2458 1501 1313 1530 1685 2355 2435 2151 2072 2351

6 2329 2102 2587 2645 2602 2609 2625 2380 2131 2628 2634 2600 2535 2600 2424 2307 2689 2787 2881 2844 2673 2324 1542 1394 1498 1798 2350 2348 2326 2140 2376

7 2118 2087 2553 2589 2536 2559 2528 2247 2281 2606 2579 2654 2672 2500 2271 2276 2652 2783 2756 2714 2611 2267 1597 1397 1551 1672 2423 2364 2100 2251 2596

8 2063 2390 2780 2704 2630 2779 2496 2000 2383 2834 2692 2857 2842 2617 2126 2496 2905 3012 2964 2843 2427 1936 1743 1404 1506 2129 2682 2596 2137 2720 2872

9 2096 3342 3448 3488 3484 3460 3192 2007 3314 3415 3435 3521 3473 3132 2168 3408 3629 3672 3639 3585 3089 1883 1839 1631 1690 2962 3370 3117 2340 3622 3645

10 2180 3642 3709 3731 3733 3775 3490 1946 3631 3713 3671 3761 3736 3514 2313 3772 3898 4024 3896 3870 3293 2091 1864 1789 2018 3405 3603 3356 2641 3912 3868

11 2489 3815 3820 3809 4000 4027 3652 2513 3793 3849 3870 3967 3921 3719 2700 3883 3975 4222 4060 4076 3583 2361 1905 1920 2159 3539 3709 3501 2758 4120 4121

12 2570 3859 3831 3822 3936 4044 3684 2629 3879 3891 3883 4020 4023 3800 2860 3981 4008 4261 4149 4138 3622 2466 1852 2126 2330 3646 3723 3526 2819 4063 4084

13 2704 3797 3760 3851 3854 3713 3633 2753 3826 3839 3787 3857 3690 3705 2912 3848 3991 4180 4023 3777 3595 2476 1748 2172 2312 3361 3471 3482 2740 3996 3991

14 2709 3864 3839 3912 3887 3930 3610 2800 3981 3915 3885 3962 3856 3709 2866 3914 4090 4261 4047 4009 3423 2474 1709 1869 2222 3611 3620 3378 2720 4047 4076

15 2718 3873 3913 3909 4010 3930 3517 2772 3981 3940 3919 3990 4062 3644 2880 4025 4148 4298 4126 4066 3375 2459 1655 2187 2186 3637 3641 3314 2629 4169 4214

16 2779 3882 3886 3919 3971 3983 3438 2747 3975 3894 3928 4075 4055 3509 2840 4000 4109 4231 4150 4005 3253 2429 1627 1985 2142 3547 3611 3235 2676 4194 4307

17 2743 3832 3922 3939 3981 3891 3367 2804 3835 3934 3920 4046 4045 3469 2872 3928 4155 4367 4111 4021 3179 2491 1631 1924 2211 3612 3633 3170 2817 4396 4486

18 2689 3575 3722 3709 3818 3832 3328 2864 3772 3827 3753 3826 3888 3399 2983 3908 4025 4239 3885 3861 3295 2624 1651 1990 2221 3606 3605 3085 3086 4343 4470

19 2810 3392 3511 3434 3673 3481 3135 2722 3444 3430 3361 3420 3408 3147 2867 3613 3592 3855 3640 3611 3160 2500 2011 2348 2595 3756 3767 3365 3106 4236 4259

20 3010 3662 3709 3668 3742 3694 3335 2985 3648 3712 3681 3771 3685 3544 3098 3861 3967 4085 3949 3931 3470 2768 1956 2359 2588 3580 3685 3383 3069 3938 3973

21 2928 3554 3622 3511 3635 3605 3278 2935 3578 3547 3672 3646 3592 3396 3056 3777 3832 4013 3797 3769 3336 2733 1957 2313 2522 3445 3522 3245 3002 3663 3783

22 2866 3354 3484 3505 3464 3452 3292 2928 3467 3488 3477 3459 3490 3366 3021 3641 3772 3845 3601 3700 3174 2715 1942 2267 2534 3374 3422 3178 2911 3530 3675

23 2828 3313 3387 3336 3370 3364 3210 2840 3351 3344 3427 3399 3402 3261 3005 3497 3652 3753 3509 3687 3231 2666 1923 2180 2472 3238 3263 3129 2768 3343 3555

24 2729 3093 3199 3175 3272 3376 3122 2748 3246 3205 3165 3292 3358 3296 2905 3290 3472 3546 3488 3542 3099 2739 1898 2159 2320 3032 3138 2980 2651 3153 3363

TO

TA

L

62

.19

2

75

.36

8

80

.25

0

79

.93

1

80

.76

7

81

.06

1

75

.26

6

62

.41

9

76

.80

0

80

.42

5

79

.86

7

81

.73

2

81

.42

8

77

.13

4

65

.04

7

78

.97

9

84

.19

9

87

.55

2

85

.20

3

84

.15

0

75

.27

7

59

.14

8

43

.13

9

44

.93

7

49

.26

7

69

.92

0

76

.69

1

72

.37

5

65

.67

5

80

.54

0

84

.06

7

CU

M.

62

.19

2

13

7.5

60

21

7.8

10

29

7.7

41

37

8.5

08

45

9.5

69

53

4.8

35

59

7.2

54

67

4.0

54

75

4.4

79

83

4.3

46

91

6.0

78

99

7.5

06

1.0

74.6

40

1.1

39.6

87

1.2

18.6

66

1.3

02.8

65

1.3

90.4

17

1.4

75.6

20

1.5

59.7

70

1.6

35.0

47

1.6

94.1

95

1.7

37.3

34

1.7

82.2

71

1.8

31.5

38

1.9

01.4

58

1.9

78.1

49

2.0

50.5

24

2.1

16.1

99

2.1

96.7

39

2.2

80.8

06

195

POWER CONSUMPTION NOVEMBER 2006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2888 3035 2960 3280 3001 2709 3010 3070 3009 3083 3067 3053 2766 3091 3169 3080 3058 3058 2950 2585 3019 2964 3005 2977 3016 3033 2602 3084 3037 3136

2 2736 2830 2746 2988 2822 2417 2878 2881 2866 2726 2957 2853 2326 2904 2866 2919 2889 2945 2778 2456 2961 2916 2834 2848 2871 2688 2378 2858 2915 3033

3 2665 2621 2698 2851 2597 2211 2694 2773 2819 2779 2733 2779 2305 2831 2792 2833 2772 2805 2636 2176 2802 2917 2732 2803 2760 2579 2378 2702 2696 2837

4 2566 2532 2545 2714 2529 2220 2690 2770 2723 2635 2721 2593 2235 2752 2788 2647 2739 2688 2493 2269 2753 2715 2729 2712 2671 2506 2210 2668 2672 2757

5 2562 2559 2548 2643 2493 2173 2659 2740 2577 2633 2594 2523 2238 2770 2784 2652 2670 2698 2450 2168 2713 2726 2670 2631 2661 2454 2187 2647 2721 2737

6 2610 2569 2575 2662 2440 2275 2700 2795 2834 2812 2628 2539 2369 2817 2779 2779 2727 2685 2505 2155 2598 2665 2763 2743 2598 2412 2202 2730 2749 2791

7 2654 2709 2526 2716 2468 2220 2677 2948 2745 2905 2608 2386 2524 2985 3061 2999 2786 2750 2375 2414 2934 2913 2858 2930 2665 2410 2506 2892 2945 3047

8 3079 2966 3061 2913 2295 2902 3157 3221 3215 3207 3001 2410 2884 3271 3284 3228 3263 2850 2349 2730 3162 3184 3257 3331 3075 2318 3011 3199 3345 3417

9 3946 3793 3983 3789 2585 4045 4188 4080 4042 4003 3764 2438 3878 4234 4161 4025 4051 3760 2443 3875 4167 3963 3995 4036 3637 2522 3953 4161 4183 4142

10 4157 4141 4369 4179 2863 4270 4478 4284 4259 4218 4054 2946 4270 4422 4280 4278 4260 4039 2674 4232 4363 4293 4280 4195 3997 2782 4347 4399 4347 4392

11 4376 4205 4470 4467 3170 4535 4545 4370 4378 4340 4285 3084 4145 4600 4461 4296 4425 4119 3127 4366 4401 4404 4419 4390 4190 3048 4435 4544 4511 4527

12 4199 4146 4325 4476 3241 4535 4574 4381 4372 4164 4292 3046 4288 4497 4426 4331 3998 4044 3101 4342 4354 4257 4231 4085 3973 3182 4408 4504 4573 4558

13 4096 3935 4303 4402 3292 4478 4467 4193 4198 4111 4228 3119 4369 4297 4091 4226 3995 4039 3137 4179 4099 4170 4010 3899 3994 3084 4228 4377 4385 4370

14 4166 4093 4502 4297 3283 4572 4487 4244 4216 4339 4097 3161 4434 4463 4266 4267 4183 4051 2971 4376 4236 4303 4230 4146 3879 3005 4313 4492 4446 4425

15 4215 4164 4555 4313 3271 4536 4465 4278 4254 4299 4112 3025 4556 4507 4270 4305 4165 3910 3135 4316 4344 4227 4186 4129 3802 3079 4348 4502 4484 4450

16 4207 4081 4576 4108 3176 4528 4418 4192 4230 4274 3936 3034 4603 4448 4294 4305 4191 3843 3021 4365 4294 4213 4226 4114 3628 2953 4381 4518 4528 4486

17 4391 4328 4604 4125 3355 4506 4542 4445 4315 4529 4030 3356 4791 4630 4650 4541 4479 4057 3458 4777 4514 4369 4398 4408 3877 3224 4689 4713 4693 4725

18 4417 4375 4643 4150 3535 4640 4575 4603 4558 4565 4059 3505 4793 4690 4693 4659 4540 4024 3495 4734 4571 4519 4426 4489 3929 3439 4666 4704 4764 4749

19 4301 4180 4396 3959 3578 4336 4331 4382 4350 4199 3947 3441 4482 4403 4383 4386 4317 3816 3458 4280 4271 4255 4222 4257 3798 3349 4395 4418 4342 4515

20 4001 3893 4175 3799 3439 4118 4164 4168 4165 4002 3789 3434 4238 4216 4118 4146 4054 3763 3410 4141 4116 4040 4039 3907 3589 3297 4092 4205 4207 4253

21 3836 3766 4047 3748 3307 3965 4010 4016 3962 3887 3654 3335 4110 4108 3988 4052 3856 3895 3269 4059 3906 3970 3901 3846 3618 3355 3968 4083 4104 4137

22 3760 3676 3820 3593 3329 3867 3900 3819 3876 3755 3641 3310 3831 3927 3903 3834 3791 3557 3237 3856 3890 3768 3754 3698 3501 3311 3833 3953 3934 3993

23 3588 3548 3804 3573 3281 3710 3745 3729 3737 3616 3464 3198 3684 3894 3712 3730 3690 3543 3205 3649 3723 3747 3640 3664 3399 3262 3717 3750 3766 3856

24 3384 3388 3489 3480 3130 3616 3575 3596 3327 3504 3501 2947 3627 3538 3503 3560 3484 3367 2785 3478 3463 3545 3563 3570 3330 2968 3547 3574 3602 3720

TO

TA

L

86

.80

1

85

.53

4

89

.72

0

87

.22

1

72

.47

9

87

.38

1

90

.92

7

89

.97

6

89

.02

5

88

.58

5

85

.16

1

71

.51

6

87

.74

7

92

.29

3

90

.72

1

90

.07

6

88

.38

4

84

.30

5

70

.45

9

85

.97

8

89

.65

4

89

.04

1

88

.36

8

87

.80

5

82

.45

6

70

.26

0

86

.79

0

91

.67

7

91

.94

9

93

.05

1

CU

M.

86

.80

1

17

2.3

35

26

2.0

55

34

9.2

76

42

1.7

55

50

9.1

36

60

0.0

63

69

0.0

39

77

9.0

64

86

7.6

49

95

2.8

10

1.0

24.3

26

1.1

12.0

73

1.2

04.3

66

1.2

95.0

87

1.3

85.1

63

1.4

73

.547

1.5

57.8

52

1.6

28.3

11

1.7

14.2

89

1.8

03.9

43

1.8

92.9

84

1.9

81.3

52

2.0

69.1

57

2.1

51.6

13

2.2

21.8

73

2.3

08.6

63

2.4

00.3

40

2.4

92.2

89

2.5

85.3

40

196

POWER CONSUMPTION JANUARY 2007 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2144 2001 2355 2327 2849 3034 2861 2683 3047 2964 3173 3187 3155 2980 2385 3081 3126 3090 3115 3163 3028 2633 2800 2983 3009 3052 3063 3246 2890 3194 3239

2 1958 1972 2011 2288 2724 2884 2702 2452 2912 2885 2903 2967 2817 2824 2461 2896 2905 2874 2914 2975 2810 2380 2762 2838 2882 2864 2907 2833 2555 3032 2976

3 1878 1896 1926 2184 2626 2659 2511 2356 2819 2815 2807 2833 2786 2657 2160 2876 2901 2844 2899 2762 2625 2226 2718 2698 2814 2712 2764 2698 2339 2896 2849

4 1719 1814 1884 2054 2557 2622 2451 2266 2768 2762 2771 2781 2742 2576 2104 2729 2799 2716 2788 2698 2508 2191 2610 2595 2673 2636 2654 2598 2355 2812 2833

5 1671 1781 1810 1942 2493 2604 2370 2274 2707 2697 2764 2763 2738 2430 2153 2734 2736 2744 2769 2696 2509 2189 2530 2510 2654 2630 2674 2553 2357 2831 2730

6 1570 1799 1847 1974 2589 2575 2434 2379 2778 2802 2836 2769 2760 2421 2373 2773 2938 2793 2824 2730 2471 2177 2660 2673 2687 2618 2682 2522 2329 2796 2893

7 1722 1784 1897 2334 2779 2665 2437 2626 2936 3046 3077 3080 2844 2357 2582 3069 3100 3067 2945 2800 2590 2590 2885 2937 2925 2970 2645 2588 2617 2992 3056

8 1657 1779 1869 2548 3041 2739 2372 2872 3288 3222 3278 3387 2959 2311 2991 3335 3293 3324 3293 2952 2355 2859 3137 3190 3088 3199 2909 2432 2858 3209 3353

9 1856 2022 2145 3571 3872 3409 2626 4101 4147 3894 4116 4203 3840 2503 4067 4177 4220 4035 4150 3741 2571 3965 3975 4005 4028 4111 3710 2523 4255 4380 4254

10 2095 2329 2385 4012 4147 3882 2897 4307 4332 4449 4557 4474 4115 2798 4442 4513 4549 4498 4420 4123 2824 4207 4259 4350 4301 4398 3980 2986 4578 4702 4658

11 2265 2542 2747 4252 4502 4053 3160 4658 4581 4546 4754 4575 4356 2973 4585 4670 4653 4644 4601 4173 3094 4410 4435 4466 4419 4493 4277 3106 4903 4886 4919

12 2377 2592 2883 4289 4358 4176 3164 4595 4535 4576 4607 4470 4302 3195 4625 4619 4499 4524 4368 4263 3190 4371 4374 4416 4324 4363 4363 3309 4989 4937 4935

13 2435 2655 2909 4244 4183 4015 3236 4499 4429 4316 4575 4101 4243 3182 4483 4450 4353 4447 4135 4120 3132 4211 4150 4229 4246 4008 4312 3390 4839 4757 4825

14 2381 2541 2739 4280 4345 3997 3249 4488 4514 4420 4480 4479 4189 3161 4433 4532 4506 4437 4503 4031 3114 4232 4218 4186 4266 4299 4228 3308 4793 4772 4838

15 2246 2548 2718 4306 4304 3827 3159 4542 4566 4422 4484 4413 4074 3089 4449 4528 4436 4495 4409 3937 2942 4233 4268 4217 4355 4328 4065 3254 4707 4820 4885

16 2313 2500 2729 4242 4252 3750 3056 4481 4505 4439 4417 4368 3934 3018 4434 4548 4414 4451 4389 3903 2922 4173 4271 4094 4310 4228 4024 3168 4777 4686 4834

17 2588 2701 2964 4358 4405 3821 3201 4656 4631 4704 4589 4525 3919 3189 4572 4683 4627 4617 4507 3929 3116 4329 4384 4259 4440 4265 4062 3278 4870 4734 4811

18 2658 2825 3080 4408 4403 3878 3503 4771 4738 4723 4759 4653 4119 3387 4775 4786 4751 4726 4647 4030 3431 4479 4537 4465 4547 4559 4093 3481 4724 4881 4884

19 2695 2727 3054 4131 4284 3738 3474 4473 4445 4404 4515 4371 3967 3419 4458 4520 4541 4509 4332 3918 3425 4285 4300 4292 4312 4286 3941 3461 4684 4635 4612

20 2608 2678 2948 3787 3950 3701 3523 4028 4099 4149 4264 4144 3869 3401 4206 4207 4266 4201 4109 3861 3394 4034 4130 4088 4091 4055 3839 3505 4298 4419 4368

21 2578 2767 2972 3733 3857 3536 3451 3993 3965 4021 4099 3989 3659 3356 4068 4070 4115 4209 3941 3667 3381 3904 3920 3894 3958 3902 3680 3362 4121 4237 4225

22 2603 2708 2994 3671 3751 3452 3403 3931 3934 3893 3895 3763 3638 3321 3896 3993 3991 3981 3773 3554 3170 3803 3777 3770 3823 3754 3550 3287 3911 4020 4057

23 2549 2592 2913 3499 3626 3405 3271 3781 3744 3756 3834 3669 3617 3283 3782 3805 3889 3795 3754 3530 3188 3835 3640 3673 3704 3571 3433 3321 3744 3966 3902

24 2465 2569 2736 3414 3484 3313 3040 3489 3511 3547 3665 3600 3468 3152 3669 3664 3589 3708 3606 3384 2988 3237 3489 3433 3603 3430 3406 3178 3587 3788 3790

TO

TA

L

53

.03

0

56

.12

1

60

.51

5

81

.84

9

87

.38

0

81

.73

3

71

.54

9

88

.70

2

91

.92

9

91

.45

1

93

.21

7

91

.56

3

86

.10

8

70

.98

2

88

.15

0

93

.25

3

93

.19

6

92

.72

9

91

.19

2

84

.93

9

70

.77

8

84

.95

4

88

.23

0

88

.25

9

89

.45

7

88

.73

0

85

.26

1

73

.38

9

92

.08

0

96

.37

9

96

.72

5

CU

M.

53

.03

0

10

9.1

51

16

9.6

66

25

1.5

15

33

8.8

95

42

0.6

28

49

2.1

77

58

0.8

79

67

2.8

08

76

4.2

59

85

7.4

76

94

9.0

39

1.0

35.1

47

1.1

06.1

29

1.1

94.2

79

1.2

87.5

32

1.3

80.7

28

1.4

73.4

57

1.5

64.6

49

1.6

49.5

88

1.7

20.3

66

1.8

05.3

20

1.8

93.5

50

1.9

81.8

09

2.0

71.2

66

2.1

59.9

96

2.2

45.2

57

2.3

18.6

46

2.4

10.7

26

2.5

07.1

05

2.6

03.8

30

197

POWER CONSUMPTION FEBRUARY 2007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1 3234 3096 3265 3144 2799 3220 3300 3188 3171 3329 3072 2492 3079 3080 3198 3144 3147 3221 2741 3213 3134 3109 3065 3240 3222 2754 3105 3139

2 3013 2958 3051 2922 2581 3063 3086 3241 3072 2942 2821 2438 3181 2888 2923 3144 3057 2892 2474 3016 2968 3032 2916 3030 3058 2494 2983 2919

3 2931 2912 3026 2786 2416 2999 2961 2804 2922 2890 2685 2433 2771 2680 2747 2747 2818 2741 2334 2908 2889 2878 2876 2887 2800 2421 2884 2887

4 2853 2708 2903 2628 2355 2886 2851 2826 2680 2719 2455 2174 2719 2697 2716 2739 2714 2591 2258 2796 2801 2793 2730 2716 2598 2316 2724 2849

5 2812 2686 2753 2617 2308 2864 2862 2749 2770 2557 2413 2034 2679 2666 2690 2681 2629 2523 2321 2726 2780 2776 2768 2757 2547 2250 2673 2772

6 2844 2789 2829 2633 2381 2892 2734 2816 2855 2579 2414 2232 2565 2540 2760 2740 2555 2546 2371 2708 2717 2801 2773 2859 2597 2426 2924 2985

7 3013 2938 2995 2605 2549 3034 3042 2980 2949 2665 2476 2502 2945 2956 2918 2946 2700 2524 2540 2964 2863 2955 2867 2914 2615 2664 3041 3031

8 3320 3308 3081 2458 2910 3340 3295 3277 3159 2891 2282 2640 3162 3184 2970 3122 2930 2428 2823 3278 3284 3316 3243 2880 2499 3096 3369 3394

9 4303 4214 3864 2502 4193 4446 4334 4152 4115 3626 2302 4002 4128 4068 4099 4143 3815 2591 4060 4244 4112 4211 4273 3785 2650 4201 4400 4377

10 4783 4554 4291 2937 4579 4673 4660 4512 4376 3952 2789 4225 4322 4350 4413 4435 4192 2772 4539 4541 4384 4385 4478 4148 2829 4579 4650 4682

11 4818 4811 4419 3230 4913 4758 4897 4732 4612 4166 3122 4589 4386 4461 4571 4621 4389 3267 4741 4560 4542 4493 4734 4491 3448 4819 4757 4787

12 4873 4774 4530 3363 4964 4770 4881 4744 4582 4160 3186 4560 4443 4418 4636 4532 4451 3441 4781 4627 4535 4372 4645 4571 3399 4869 4701 4801

13 4691 4384 4397 3468 4825 4639 4689 4432 4138 3991 3114 4367 4231 4242 4472 4133 4314 3292 4553 4457 4344 4253 4254 4533 3434 4753 4483 4695

14 4589 4761 4313 3443 4986 4695 4760 4595 4370 3852 3068 4381 4273 4260 4510 4514 4268 3488 4682 4403 4324 4329 4592 4466 3365 4830 4532 4787

15 4575 4749 4161 3426 4908 4782 4720 4556 4369 3753 3000 4448 4165 4398 4518 4516 4195 3386 4741 4407 4357 4328 4554 4352 3334 4752 4549 4827

16 4636 4727 4041 3329 4791 4693 4673 4574 4214 3664 2927 4408 4183 4384 4571 4472 4092 3367 4688 4383 4315 4294 4525 4263 3218 4736 4513 4752

17 4690 4653 4002 3410 4834 4829 4856 4746 4444 3769 3060 4475 4284 4426 4588 4490 4082 3371 4749 4516 4352 4392 4644 4211 3255 4688 4461 4824

18 4814 4843 4262 3605 4873 4888 4862 4747 4493 3921 3393 4595 4441 4544 4621 4614 4170 3557 4781 4600 4423 4436 4717 4297 3544 4733 4575 4786

19 4554 4589 4075 3621 4613 4657 4543 4612 4324 3893 3391 4352 4237 4464 4487 4506 4091 3660 4630 4510 4472 4434 4494 4151 3732 4638 4467 4669

20 4298 4266 3936 3590 4269 4331 4344 4302 4247 3713 3370 4239 4145 4136 4210 4212 3943 3578 4344 4327 4287 4215 4265 4120 3698 4400 4210 4452

21 4143 4055 3813 3464 4150 4191 4235 4105 3973 3619 3373 4028 3989 3994 4070 4071 3839 3482 4150 4157 4059 4007 4128 3877 3603 4190 4142 4204

22 3995 3916 3729 3338 4037 4035 4066 3910 3879 3559 3302 3830 3874 3798 3995 3840 3647 3446 3935 4037 3941 3903 3977 3777 3528 4040 3956 4039

23 3874 3843 3639 3294 3955 4006 4012 3844 3784 3544 3074 3747 3679 3700 3771 3732 3621 3381 3884 3896 3901 3783 3857 3697 3449 3857 3884 3935

24 3678 3741 3483 3102 3727 3797 3739 3630 3539 3433 2865 3461 3541 3569 3556 3643 3444 3232 3697 3642 3722 3714 3744 3603 3183 3705 3685 3713

TO

TA

L

95

.33

4

94

.27

6

88

.85

7

74

.91

4

92

.91

5

96

.48

7

96

.40

0

94

.07

3

91

.03

7

83

.18

7

69

.95

4

86

.65

1

89

.42

0

89

.90

2

92

.01

0

91

.73

8

87

.10

1

74

.77

4

90

.81

7

92

.91

3

91

.50

6

91

.20

7

93

.11

8

89

.62

4

75

.60

5

92

.20

9

93

.66

3

96

.30

4

CU

M.

95

.33

4

18

9.6

10

27

8.4

67

35

3.3

81

44

6.2

96

54

2.7

83

63

9.1

83

73

3.2

56

82

4.2

93

90

7.4

80

97

7.4

34

1.0

64.0

85

1.1

53

.505

1.2

43.4

07

1.3

35.4

17

1.4

27.1

55

1.5

14.2

56

1.5

89.0

30

1.6

79.8

47

1.7

72.7

60

1.8

64.2

66

1.9

55.4

73

2.0

48.5

91

2.1

38.2

15

2.2

13.8

20

2.3

06.0

29

2.3

99.6

92

2.4

95.9

96

198

POWER CONSUMPTION MARCH 2007 hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 3305 3244 3252 3182 2779 3303 3313 3276 3158 3356 3193 2900 3091 3203 3158 3066 3200 3013 2733 2893 2932 3089 3030 3152 3001 2671 3091 3203 3276 3158 3252

2 3018 3134 2904 2896 2442 2943 2990 2994 3026 3036 2995 2593 2987 3113 2997 3017 3071 2914 2401 2830 2807 2735 2978 2977 2780 2433 2987 3113 2994 3026 2904

3 2903 2764 2780 2680 2404 2738 2892 2895 2863 2867 2610 2401 2893 2883 2835 2860 2949 2809 2241 2663 2676 2639 2961 2802 0 2525 2893 2883 2895 2863 2780

4 2800 2781 2744 2585 2236 2639 2810 2696 2791 2725 2618 2384 2810 2805 2776 2819 2760 2676 2233 2666 2642 2488 2746 2651 2728 2219 2810 2805 2696 2791 2744

5 2669 2761 2755 2523 2298 2745 2756 2765 2817 2727 2580 2326 2765 2829 2780 2739 2726 2558 2246 2691 2625 2602 2696 2667 2506 2220 2765 2829 2765 2817 2755

6 2839 2862 2818 2519 2209 2794 2783 2776 2828 2767 2465 2300 2814 2827 2830 2830 2680 2557 2232 2714 2716 2642 2787 2607 2415 2300 2814 2827 2776 2828 2818

7 2941 2967 2748 2451 2545 2738 3011 3033 2829 2776 2473 2453 2875 2945 2944 3034 2802 2477 2418 2615 2891 2723 2796 2628 2439 2274 2875 2945 3033 2829 2748

8 3220 3138 2846 2233 2876 3347 3165 3316 3323 2981 2621 2983 3367 3268 3259 3353 3118 2357 2827 3175 3125 3221 3218 2818 2263 2865 3367 3268 3316 3323 2846

9 4393 4321 3706 2534 4063 4231 4205 4241 4277 3951 2612 4244 4151 4296 4025 4000 3949 2671 4067 4020 3976 3984 3949 3668 2345 3896 4151 4296 4241 4277 3706

10 4565 4542 4063 2751 4468 4427 4434 4472 4605 4287 2898 4590 4559 4680 4533 4508 4300 2925 4296 4215 4173 4338 4139 4121 2606 4247 4559 4680 4472 4605 4063

11 4771 4683 4342 3070 4726 4568 4498 4682 4796 4511 3205 4674 4763 4864 4779 4731 4444 3021 4422 4321 4200 4511 4444 4145 2800 4434 4763 4864 4682 4796 4342

12 4713 4524 4312 3260 4747 4626 4554 4691 4696 4530 3368 4598 4787 4871 4772 4642 4392 3250 4286 4341 4193 4525 4434 4141 3056 4504 4787 4871 4691 4696 4312

13 4619 4084 4140 3221 4626 4419 4358 4505 4342 4402 3335 4363 4689 4728 4615 4257 4187 3206 4206 4099 4030 4321 4118 3985 3147 4308 4689 4728 4505 4342 4140

14 4663 4439 3978 3246 4694 4473 4479 4463 4676 4247 3340 4419 4715 4763 4617 4551 4048 3144 4276 4135 4021 4371 4468 3863 3184 4276 4715 4763 4463 4676 3978

15 4663 4371 3816 3180 4634 4458 4430 4402 4699 4100 3311 4445 4821 4861 4668 4532 3922 3069 4298 4190 4052 4391 4482 3827 2974 4298 4821 4861 4402 4699 3816

16 4527 4349 3678 3143 4670 4393 4324 4385 4648 4066 3276 4363 4729 4762 4631 4383 3861 2957 4134 4084 4025 4450 4433 3751 2941 4134 4729 4762 4385 4648 3678

17 4563 4454 3600 3324 4644 4505 4369 4438 4774 3988 3328 4388 4693 4806 4536 4455 3743 3007 4192 4213 4077 4440 4342 3566 2943 4192 4693 4806 4438 4774 3600

18 4639 4511 3802 3288 4631 4524 4378 4531 4531 3951 3500 4408 4766 4792 4511 4440 3767 3060 4201 4204 4161 4401 4219 3594 2936 4201 4766 4792 4531 4531 3802

19 4609 4452 3897 3457 4634 4557 4524 4512 4583 4260 3581 4521 4748 4795 4588 4547 4085 3470 4282 4348 4259 4496 4360 3896 3026 4282 4748 4795 4512 4583 3897

20 4360 4170 3855 3547 4247 4367 4338 4357 4381 3875 3617 4211 4469 4462 4369 4341 3984 3490 4180 4131 4013 4186 4132 3713 3499 4180 4469 4462 4357 4381 3855

21 4214 3954 3708 3416 4145 4118 4185 4160 4208 3829 3558 4067 4225 4191 4170 4168 3788 3448 3978 3990 3901 4026 4004 3665 3511 3978 4225 4191 4160 4208 3708

22 4009 3814 3526 3356 3969 3953 3931 4015 4030 3755 3510 3913 4029 4175 4112 4053 3708 3414 3883 3760 3764 3896 3920 3583 3394 3883 4029 4175 4015 4030 3526

23 3933 3805 3510 3268 3804 3855 3799 3990 3900 3683 3401 3739 3889 3913 3863 3917 3668 3294 3736 3681 3599 3709 3655 3505 3280 3736 3889 3913 3990 3900 3510

24 3635 3502 3370 3082 3673 3624 3645 3650 3668 3516 3181 3618 3870 3728 3865 3700 3589 3021 3517 3459 3385 3688 3550 3415 3134 3517 3870 3728 3650 3668 3370

TO

TA

L

94

.56

7

91

.62

4

84

.14

8

72

.20

8

90

.16

3

92

.34

5

92

.17

1

93

.24

4

94

.44

7

88

.18

5

74

.57

4

88

.89

9

95

.50

5

96

.56

0

94

.23

2

92

.94

0

86

.73

9

71

.80

8

85

.28

3

87

.43

7

86

.24

2

89

.87

0

89

.85

9

82

.74

1

66

.90

6

85

.57

2

95

.50

5

96

.56

0

93

.24

4

94

.44

7

84

.14

8

CU

M.

94

.56

7

18

6.1

91

27

0.3

39

34

2.5

47

43

2.7

10

52

5.0

55

61

7.2

26

71

0.4

70

80

4.9

17

89

3.1

02

96

7.6

76

1.0

56.5

75

1.1

52.0

80

1.2

48.6

40

1.3

42.8

72

1.4

35.8

12

1.5

22.5

51

1.5

94.3

59

1.6

79.6

42

1.7

67.0

79

1.8

53.3

21

1.9

43.1

91

2.0

33.0

50

2.1

15.7

91

2.1

82.6

97

2.2

68.2

69

2.3

63.7

74

2.4

60.3

34

2.5

53.5

78

2.6

48.0

25

2.7

32.1

73

199

POWER CONSUMPTION APRIL 2007 hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 3106 2668 3081 3084 3009 3038 3097 2923 2539 3041 3005 3112 3088 3213 2909 2615 3057 3035 3097 3119 3128 2836 2375 2684 2964 2974 3036 3061 2982 2643

2 2921 2472 2899 2928 2902 2958 2857 2768 2552 2972 2798 2898 2869 2889 2775 2314 2877 2808 2959 2877 2865 2626 2151 2494 2814 2827 2886 2904 2764 2304

3 2671 2379 2828 2861 2791 2907 2857 2572 2208 2789 2798 2795 2737 2740 2588 2217 2754 2785 2818 2814 2728 2447 2088 2488 2685 2731 2647 2750 2650 2258

4 2554 2281 2788 2804 2713 2800 2613 2495 2203 2781 2650 2695 2595 2735 2349 2263 2686 2751 2810 2788 2651 2335 2047 2456 2671 2705 2692 2687 2405 2144

5 2545 2193 2709 2730 2715 2737 2639 2446 2258 2654 2638 2731 2654 2703 2468 2202 2713 2751 2807 2698 2598 2331 2087 2378 2640 2689 2679 2705 2345 2145

6 2538 2403 2832 2769 2719 2716 2600 2366 2373 2846 2680 2775 2749 2732 2466 2342 2797 2802 2797 2908 2662 2296 2169 2426 2714 2792 2744 2694 2483 2172

7 2461 2523 2912 2974 2916 3035 2692 2339 2287 2808 2846 2813 2891 2790 2396 2468 2883 2965 2947 2887 2656 2199 2239 2507 2841 2826 2911 2674 2368 2221

8 2411 2936 3315 3275 3214 3152 2831 2219 2838 3210 3215 3192 3254 2823 2185 2899 3178 3188 3340 3217 2896 2089 2397 2907 3038 3163 3197 3221 2262 2723

9 2631 3896 4176 4083 4125 4226 3549 2379 4051 4051 3929 4077 4058 3694 2422 3925 4053 4211 4167 4153 3525 2416 3219 3933 4083 3980 4049 3636 2418 3812

10 2951 4304 4323 4330 4399 4448 3971 2835 4323 4193 4247 4301 4356 3887 2785 4276 4281 4359 4382 4344 3887 2587 3448 4171 4226 4233 4193 3913 2727 4064

11 3202 4509 4560 4472 4601 4556 4117 3046 4443 4349 4474 4438 4522 4053 3011 4475 4555 4523 4598 4404 4009 2815 3612 4296 4312 4390 4350 4071 2949 4250

12 3266 4447 4520 4444 4597 4570 4120 3092 4463 4327 4475 4397 4527 4017 3092 4454 4470 4393 4526 4352 4054 2853 3570 4174 4302 4413 4354 4040 2963 4250

13 3286 4209 4299 4234 4501 4173 3865 3021 4244 3936 4258 4256 4058 3818 3073 4278 4264 4283 4247 3961 3885 2825 3518 4015 4088 4153 4003 3856 2996 4088

14 3192 4240 4334 4237 4473 4094 3738 2861 4320 4110 4373 4221 3998 3732 3001 4315 4340 4380 4315 3984 3745 2798 3528 4001 4154 4230 3968 3731 2802 4180

15 3155 4262 4378 4292 4492 4323 3617 2876 4268 4126 4397 4184 4197 3692 2862 4290 4304 4451 4423 4107 3637 2705 3537 4176 4103 4230 4105 3660 2823 4190

16 3108 4160 4305 4188 4412 4227 3556 2775 4222 4100 4404 4201 4140 3627 2848 4307 4275 4509 4401 4116 3483 2696 3521 4043 4123 4166 4142 3595 2776 4110

17 2944 4145 4193 4129 4378 4189 3274 2796 4113 4053 4385 4142 4142 3421 2715 4231 4234 4372 4334 4028 3291 2659 3496 4028 4050 4099 4125 3416 2722 4110

18 2946 4017 4202 4037 4266 4029 3238 2699 4065 3936 4307 4005 3981 3311 2914 4003 4126 4192 4235 3911 3228 2705 3368 3872 3982 4010 3930 3348 2669 4049

19 2993 3950 4024 3903 4092 3930 3272 2840 3919 3842 4248 3871 3825 3307 2834 3972 3994 4002 4023 3699 3141 2709 3330 3745 3814 3883 3805 3297 2667 3847

20 3372 4061 4193 4073 4152 4016 3571 3244 4095 3965 4200 4024 3942 3492 3262 4003 4063 4121 4176 3893 3324 2949 3326 3836 3964 3882 3827 3409 3005 3851

21 3366 4018 4128 4012 4151 4102 3635 3364 4040 4083 4078 4131 4008 3680 3336 4092 4194 4226 4199 3972 3546 3142 3564 4029 4073 3961 4032 3711 3305 4015

22 3450 3827 3929 3877 3950 3794 3512 3309 3883 3928 3853 3979 3893 3607 3436 3943 3952 3962 3962 3838 3461 3082 3388 3992 3955 3908 3876 3571 3223 3761

23 3358 3719 3854 3757 3852 3688 3447 3181 3757 3695 3690 3885 3747 3483 3203 3708 3827 3850 3869 3672 3360 2929 3334 3772 3784 3767 3741 3458 3138 3590

24 3152 3497 3604 3535 3586 3595 3339 2945 3450 3498 3531 3539 3527 3304 2950 3517 3540 3507 3628 3526 3154 2813 2956 3406 3425 3604 3691 3311 2891 3472

TO

TA

L

71

.58

0

85

.11

5

90

.38

4

89

.02

8

91

.00

5

89

.30

1

80

.00

4

67

.39

1

84

.91

4

87

.29

1

89

.47

9

88

.66

1

87

.75

5

80

.75

0

67

.87

6

85

.10

9

89

.41

4

90

.42

4

91

.05

9

87

.27

0

78

.91

2

63

.84

0

72

.26

8

83

.82

6

86

.80

5

87

.61

6

86

.98

3

80

.71

6

66

.33

3

82

.25

0

CU

M.

71

.58

0

15

6.6

95

24

7.0

79

33

6.1

07

42

7.1

12

51

6.4

13

59

6.4

17

66

3.8

08

74

8.7

22

83

6.0

13

92

5.4

92

1.0

14.1

53

1.1

01.9

08

1.1

82.6

58

1.2

50.5

34

1.3

35.6

43

1.4

25.0

57

1.5

15.4

81

1.6

06.5

40

1.6

93.8

10

1.7

72.7

22

1.8

36.5

62

1.9

08.8

30

1.9

92.6

56

2.0

79.4

61

2.1

67.0

77

2.2

54.0

60

2.3

34.7

76

2.4

01.1

09

2.4

83.3

59

200

POWER CONSUMPTION MAY 2007 hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 2922 2932 2941 2999 3094 2898 2442 2895 2885 2922 2965 3016 2833 2585 2855 2937 3028 2962 2846 2651 2301 2823 2931 2926 2862 2917 2778 2436 2912 2939 2973

2 2804 2854 2829 2831 2857 2656 2295 2733 2802 2834 2857 2743 2709 2201 2790 2837 2822 2805 2674 2307 2214 2819 2854 2774 2720 2795 2655 2267 2771 2714 2870

3 2698 2638 2754 2750 2735 2532 2171 2672 2774 2680 2679 2681 2541 2092 2583 2695 2695 2713 2546 2230 2239 2642 2635 2661 2735 2644 2458 2227 2628 2624 2728

4 2637 2656 2653 2698 2725 2396 2167 2589 2675 2595 2624 2541 2347 2052 2513 2622 2596 2590 2423 2179 2002 2583 2497 2556 2583 2652 2459 2026 2597 2563 2680

5 2570 2637 2679 2653 2629 2379 2121 2513 2583 2528 2593 2494 2332 2019 2518 2610 2594 2579 2464 1990 2000 2591 2540 2629 2601 2584 2315 2025 2600 2657 2703

6 2642 2630 2774 2693 2667 2308 2141 2481 2553 2549 2544 2512 2285 2039 2416 2578 2535 2545 2358 2058 2006 2543 2533 2599 2543 2456 2254 2140 2513 2563 2696

7 2623 2612 2819 2714 2549 2114 2151 2582 2549 2544 2634 2523 2137 1959 2563 2530 2550 2463 2297 1952 1972 2415 2498 2562 2422 2427 2151 2124 2591 2711 2598

8 2951 3099 3219 3127 2646 2118 2550 2865 2990 2942 2835 2672 2119 2610 2871 2961 3005 3016 2412 2003 2435 2930 2841 2725 2969 2718 2179 2639 2958 3345 3012

9 3835 3858 4016 3875 3556 2271 3587 3792 3853 3818 3807 3380 2316 3624 3665 3828 3869 3890 3160 2264 3536 3829 3748 3799 3860 3543 2242 3670 3687 3998 3802

10 4031 4113 4226 4049 3857 2675 3921 3992 4121 4087 4116 3790 2664 4046 3970 4035 4096 4151 3368 2505 3936 3987 4055 4037 4123 3772 2564 4021 4095 4171 4172

11 4221 4286 4314 4279 3988 2784 4124 4217 4297 4156 4213 3899 2858 4137 4166 4164 4260 4429 3587 2775 4075 4242 4205 4244 4312 3978 2780 4223 4263 4394 4292

12 4142 4376 4234 4205 4033 2891 4126 4164 4287 4180 4197 3910 2890 4057 4101 4162 4279 4094 3577 2859 4102 4172 4243 4190 4259 3962 2916 4237 4306 4355 4178

13 3973 4265 4159 3931 3779 2883 3975 4010 4059 4031 3856 3751 2799 3926 3925 4018 4093 3956 3437 2869 3917 4011 3981 4033 3975 3771 2921 4089 4145 4193 4028

14 4035 4341 4174 3887 3759 2848 4054 4101 4123 4038 3922 3648 2866 3932 3814 4049 4303 4058 3384 2889 4033 4135 4094 4107 4062 3694 2943 4167 4024 4215 4125

15 4063 4377 4230 4128 3595 2729 4110 4089 4071 4148 4085 3640 2735 4005 4102 4158 4206 4241 3342 2765 4129 4157 4176 4139 4185 3693 2845 4326 4195 4373 4228

16 3964 4368 4141 4383 3461 2671 4021 4074 4116 4110 4092 3439 2715 4006 4092 4175 4172 4184 3300 2812 4035 4145 4133 4074 4100 3519 2714 4261 4189 4256 4280

17 3849 4201 4151 3705 3373 2694 3957 4016 4045 3969 4042 3375 2678 3883 4052 4067 4127 4013 3111 2707 4010 4049 4193 4043 4078 3503 2721 3824 4074 4283 4194

18 3863 4190 3923 3866 3227 2725 3775 3780 3898 3886 3840 3201 2641 3840 3962 3879 3960 3902 3054 2725 3775 3944 4085 3913 3999 3324 2653 3692 3940 4099 3996

19 3725 3992 3781 3800 3156 2554 3651 3629 3659 3771 3746 3189 2668 3725 3710 3711 3751 3758 3100 2680 3829 3777 3757 3723 3728 3220 2692 3571 3718 3880 3790

20 3866 4031 3723 3717 3462 2809 3727 3506 3656 3634 3632 3130 2670 3620 3559 3592 3719 3643 3143 2876 3596 3594 3637 3525 3642 3194 2705 3613 3611 3676 3577

21 3844 3974 3930 3821 3674 3130 3865 3744 3727 3855 3792 3412 3106 3762 3812 3790 3817 3718 3107 3015 3716 3824 3776 3705 3795 3411 3085 3802 3719 3850 3790

22 3714 3915 3822 3728 3451 3162 3609 3544 3583 3773 3630 3347 3074 3620 3732 3743 3758 3589 3126 2979 3654 3695 3668 3714 3657 3428 3101 3631 3647 3741 3579

23 3610 3770 3713 3675 3271 3091 3463 3428 3458 3607 3538 3299 2982 3533 3548 3550 3626 3429 3034 2835 3569 3485 3576 3591 3702 3311 2929 3530 3462 3554 3500

24 3317 3400 3424 3455 3035 2840 3248 3199 3367 3305 3276 3150 2799 3229 3261 3294 3342 3244 2860 2614 3201 3237 3294 3314 3364 3075 2748 3368 3402 3393 3347

TO

TA

L

83

.89

9

87

.51

6

86

.63

0

84

.97

0

78

.57

9

64

.15

5

79

.25

2

82

.61

2

84

.13

0

83

.96

0

83

.51

5

76

.73

9

63

.76

1

78

.50

2

82

.57

8

83

.98

3

85

.20

2

83

.96

9

71

.70

8

61

.53

7

78

.28

0

83

.62

9

83

.94

8

83

.58

1

84

.27

4

77

.59

0

63

.80

7

79

.90

9

84

.04

8

86

.54

6

85

.13

8

CU

M.

83

.89

9

17

1.4

15

25

8.0

45

34

3.0

15

42

1.5

94

48

5.7

49

56

5.0

01

64

7.6

13

73

1.7

43

81

5.7

03

89

9.2

18

97

5.9

57

1.0

39.7

18

1.1

18.2

20

1.2

00.7

98

1.2

84.7

81

1.3

69.9

83

1.4

53.9

52

1.5

25.6

60

1.5

87.1

97

1.6

65.4

77

1.7

49.1

06

1.8

33.0

54

1.9

16.6

35

2.0

00.9

09

2.0

78.4

99

2.1

42.3

06

2.2

22.2

15

2.3

06.2

63

2.3

92.8

09

2.4

77.9

47

201

POWER CONSUMPTION JUNE 2007 hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1 2942 3066 2838 2482 3009 2856 2937 3086 3105 3069 2606 3023 3047 2928 2983 3010 2760 2417 3030 3090 3065 3014 3211 3138 2696 3247 3368 3397 3326 3166

2 2771 2802 2699 2314 2925 2844 2814 2796 2879 2769 2260 2756 2731 2805 2802 2760 2578 2281 2849 2885 2909 2889 2979 2901 2485 3047 3137 3149 3180 2983

3 2663 2758 2532 2148 2689 2634 2836 2660 2657 2660 2180 2592 2737 2684 2674 2686 2728 2246 2829 2802 2832 2837 2835 2707 2407 2908 2934 3015 2948 3036

4 2598 2705 2424 2108 2661 2675 2615 2568 2608 2513 2100 2543 2652 2602 2598 2600 2451 2151 2678 2723 2808 2754 2804 2587 2377 2837 2944 2945 2999 2936

5 2638 2631 2378 2104 2624 2584 2614 2562 2617 2320 2115 2544 2633 2575 2702 2571 2444 2138 2674 2718 2729 2683 2767 2568 2284 2775 2926 2950 3070 2781

6 2569 2473 2315 2048 2590 2544 2610 2541 2533 2193 2043 2467 2540 2553 2469 2445 2042 2028 2480 2578 2573 2552 2606 2471 2275 2708 2747 2832 2780 2740

7 2674 2356 2166 1967 2529 2609 2715 2663 2410 2206 2171 2485 2584 2554 2457 2451 2148 2005 2494 2560 2659 2634 2657 2348 2109 2790 2700 2802 2779 2638

8 3015 2726 2196 2743 2871 2791 2796 2771 2731 2147 2383 2828 2897 2960 3005 2639 2084 2649 2931 2972 3063 2889 2861 2260 2824 3218 3211 3350 3211 2866

9 3973 3494 2251 3730 3914 3871 3767 3932 3279 2374 3794 3883 3845 3859 3889 3502 2353 3820 3812 4033 4066 3900 3647 2594 3956 4286 4226 4355 4273 3530

10 4099 3737 2566 4117 4204 4238 4150 4120 3732 2571 4026 4115 4130 4165 4166 3734 2596 4137 4231 4299 4333 4222 4018 2718 4424 4541 4494 4671 4661 3835

11 4305 3949 2838 4315 4420 4279 4206 4323 3883 2831 4254 4299 4411 4446 4374 3939 2819 4407 4430 4433 4480 4461 4157 3079 4598 4650 4827 4789 4722 4102

12 4322 3961 2900 4368 4414 4271 4248 4297 3848 2905 4280 4318 4449 4443 4366 4009 2914 4447 4450 4486 4615 4492 4228 3120 4623 4746 4811 4784 4725 4089

13 4070 3810 2922 4151 4147 4051 4118 3930 3701 2880 4096 4121 4278 4221 4056 3836 2881 4300 4259 4403 4442 4291 4063 3049 4598 4618 4813 4661 4509 3965

14 4075 3757 2886 4217 4331 4171 4214 4097 3703 2821 4177 4133 4272 4381 4062 3789 2890 4345 4411 4439 4503 4340 4064 3167 4692 4739 4747 4702 4479 3786

15 4281 3671 2877 4298 4297 4272 4227 4169 3601 2777 4221 4246 4442 4349 4304 3729 2854 4458 4466 4553 4579 4542 3972 3162 4711 4752 4665 4752 4635 3905

16 4330 3549 2818 4270 4345 4265 4220 4170 3568 2787 4208 4197 4210 4299 4303 3585 2740 4396 4415 4512 4575 4456 3931 3076 4643 4673 4642 4707 4533 3793

17 4222 3428 2757 4217 4216 4239 4192 4116 3494 2773 4193 4147 4254 4208 4086 3329 2727 4368 4274 4448 4487 4460 3853 3038 4546 4577 4560 4648 4501 3570

18 4077 3267 2657 4134 4033 4073 4075 3968 3301 2751 3975 4016 4135 4056 4012 3277 2733 4180 4098 4239 4297 4232 3565 2933 4390 4443 4352 4468 4332 3431

19 3797 3266 2668 3763 3874 3850 3820 3727 3247 2647 3753 3737 3847 3835 3774 3176 2694 3834 3832 3983 4003 3927 3535 2831 4055 4181 4086 4199 3997 3318

20 3539 3183 2715 3503 3799 3682 3671 3525 3174 2682 3505 3584 3701 3550 3560 3188 2653 3636 3634 3678 3715 3697 3402 2825 3817 3911 3939 3922 3736 3269

21 3677 3448 3008 3840 3864 3794 3845 3704 3373 2934 3629 3722 3682 3687 3701 3348 2877 3717 3787 3773 3739 3843 3620 2984 3939 3989 4001 3988 3868 3400

22 3603 3354 2898 3692 3661 3772 3859 3680 3450 3024 3638 3710 3593 3758 3599 3330 2962 3712 3821 3798 3773 3847 3606 3148 3916 4039 3959 3965 3790 3468

23 3511 3293 2889 3575 3495 3610 3541 3520 3326 2877 3466 3514 3565 3700 3502 3277 2920 3496 3676 3694 3692 3698 3499 3125 3798 3865 3832 3889 3665 3431

24 3328 3248 2790 3324 3341 3405 3329 3455 3141 2700 3217 3299 3359 3412 3658 3192 2744 3280 3503 3482 3447 3556 3488 2977 3582 3744 3634 3667 3616 3160

TO

TA

L

85

.07

9

77

.93

2

63

.98

8

81

.42

6

86

.25

1

85

.38

0

85

.41

8

84

.37

9

77

.36

2

64

.21

0

80

.28

9

84

.27

7

85

.99

4

86

.03

0

85

.10

2

77

.40

1

63

.59

0

82

.44

8

87

.06

4

88

.58

0

89

.38

1

88

.21

7

83

.36

6

68

.80

4

87

.74

3

93

.28

3

93

.55

3

94

.60

3

92

.33

2

81

.19

7

CU

M.

85

.07

9

16

3.0

11

22

6.9

99

30

8.4

25

39

4.6

76

48

0.0

56

56

5.4

74

64

9.8

53

72

7.2

15

79

1.4

25

87

1.7

14

95

5.9

91

1.0

41.9

85

1.1

28.0

15

1.2

13.1

17

1.2

90.5

18

1.3

54.1

08

1.4

36.5

55

1.5

23.6

19

1.6

12.1

99

1.7

01.5

80

1.7

89.7

97

1.8

73.1

63

1.9

41.9

67

2.0

29.7

10

2.1

22.9

93

2.2

16.5

46

2.3

11.1

49

2.4

03.4

81

2.4

84.6

78

202

POWER CONSUMPTION JULY 2007 hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

1 3111 2760 3051 3150 3125 3211 3148 2916 2490 3117 3102 3154 3097 3154 2813 2578 3139 3108 3148 3160 3237 3090 2715 3158 3259 3269 3182 3123 2938 2624 3004

2 2676 2218 2878 2966 2985 3066 2986 2723 2346 2847 2984 2998 2969 2900 2795 2390 3023 2907 2980 2952 3008 2850 2516 2901 2981 3046 3021 2899 2804 2399 2912

3 2682 2172 2774 2920 2846 3316 2817 2703 2316 2778 2880 2928 2772 2758 2547 2257 2819 2791 2862 2918 2875 2686 2443 2927 2896 2966 2898 2811 2611 2332 2805

4 2520 2179 2685 2864 2803 2806 2696 2549 2166 2739 2860 2792 2784 2679 2526 2190 2689 2760 2813 2819 2834 2423 2406 2740 2890 2919 2847 2743 2554 2329 2757

5 2457 2123 2671 2897 2794 2867 2885 2570 2232 2777 2686 2828 2729 2654 2408 2198 2648 2731 2795 2894 2815 2452 2245 2687 2875 2933 2817 2704 2629 2267 2764

6 2319 2011 2644 2643 2829 2753 2613 2301 2075 2603 2711 2613 2671 2610 2238 2209 2656 2767 2773 2646 2750 2323 2078 2724 2775 2821 2833 2736 2401 2232 2689

7 2327 2008 2618 2556 2642 2657 2656 2187 2068 2694 2646 2719 2552 2487 2306 2299 2578 2620 2606 2687 2644 2276 2146 2734 2821 2742 2701 2593 2323 2288 2786

8 2145 2541 2969 3003 3208 3112 2795 2243 2665 3021 3050 3122 3060 2621 2226 2555 2803 2990 3128 3156 2924 1943 2460 3040 3177 3224 3165 2881 2236 2770 3263

9 2391 3839 3986 4039 4024 3980 3354 2409 3777 3983 3962 4011 4017 3460 2218 3676 4020 4121 4127 4108 3435 1940 3870 4161 4210 4424 4198 3714 2518 4069 4098

10 2796 4134 4347 4305 4281 4184 3696 2573 4157 4329 4267 4269 4082 3744 2603 4191 4359 4373 4473 4399 3982 2439 4349 4516 4565 4570 4525 3961 2746 4362 4431

11 2773 4323 4436 4498 4541 4300 3923 2763 4445 4588 4548 4467 4296 3937 2772 4434 4432 4590 4633 4633 4165 2649 4635 4728 4810 4772 4738 4222 2899 4557 4563

12 2890 4432 4487 4477 4602 4292 3986 2938 4450 4623 4511 4528 4274 3953 2921 4446 4522 4590 4693 4714 4203 2736 4697 4760 4783 4791 4761 4174 3024 4577 4644

13 2874 4336 4321 4351 4408 3980 3862 2998 4193 4527 4415 4412 4162 3755 2879 4254 4377 4506 4575 4453 4107 2945 4633 4668 4613 4651 4575 4062 3151 4541 4456

14 2881 4408 4476 4548 4576 3938 3742 2978 4309 4540 4493 4448 4052 3743 2907 4328 4426 4579 4587 4331 4073 2859 4767 4714 4738 4807 4657 3979 2928 4548 4476

15 2897 4509 4530 4627 4680 4240 3618 2951 4484 4672 4577 4550 4337 3708 2898 4484 4537 4587 4660 4625 4016 2902 4753 4666 4671 4799 4766 3965 2955 4649 4578

16 2863 4418 4488 4588 4593 4252 3590 2891 4397 4536 4542 4476 4298 3645 2900 4447 4477 4590 4587 4617 3926 2827 4667 4688 4603 4679 4659 3839 3012 4588 4567

17 2686 4356 4423 4404 4612 4181 3557 2824 4358 4474 4383 4457 4229 3439 2877 4409 4350 4561 4556 4496 3732 2803 4589 4583 4316 4597 4554 3628 2993 4596 4528

18 2691 4183 4167 4356 4328 3999 3429 2747 4080 4327 4177 4137 4063 3326 2805 4210 4272 4303 4307 4275 3619 2805 4481 4470 4355 4472 4295 3687 2987 4328 4283

19 2654 3869 4100 4128 4085 3611 3378 2811 3786 3903 4021 3820 3724 3297 2781 3894 3933 3980 4147 4009 3561 2854 4126 4194 4088 4095 3989 3421 2878 3972 3950

20 2771 3613 3783 3801 3781 3446 3261 2771 3541 3709 3728 3747 3512 3148 2792 3660 3744 3759 3802 3762 3582 2904 3811 3885 3955 3900 3811 3331 2940 3768 3742

21 2960 3735 3822 3844 3864 3626 3406 2969 3656 3808 3794 3847 3590 3351 2981 3722 3766 3901 3884 3928 3639 3107 4000 3991 3973 3991 3896 3547 3133 3877 3908

22 2982 3781 3918 3915 3854 3643 3397 3038 3710 3784 3750 3761 3593 3371 3045 3725 3820 3826 3898 3782 3544 3184 3922 3874 3884 3853 3787 3476 3057 3706 3884

23 2924 3568 3735 3782 3702 3606 3334 2952 3600 3659 3631 3676 3552 3168 2938 3606 3629 3688 3652 3644 3530 3062 3771 3861 3849 3730 3728 3339 3040 3612 3674

24 2778 3319 3515 3518 3520 3304 3109 2781 3444 3525 3495 3463 3495 3090 2821 3355 3511 3478 3603 3548 3399 2874 3586 3628 3539 3649 3680 3231 2955 3494 3485

TO

TA

L

65

.04

9

82

.83

3

88

.82

2

90

.17

7

90

.68

1

86

.37

0

79

.23

9

65

.58

3

82

.74

4

89

.56

2

89

.20

9

89

.22

1

85

.91

0

77

.99

7

64

.99

5

83

.51

8

88

.53

0

90

.10

6

91

.29

0

90

.55

6

83

.59

9

64

.93

0

87

.66

6

92

.29

8

92

.62

6

93

.69

9

92

.08

1

82

.06

3

67

.71

0

86

.48

5

90

.24

6

CU

M.

65

.04

9

14

7.8

82

23

6.7

04

32

6.8

81

41

7.5

62

50

3.9

32

58

3.1

71

64

8.7

54

73

1.4

98

82

1.0

60

91

0.2

69

99

9.4

90

1.0

85.4

00

1.1

63.3

97

1.2

28.3

92

1.3

11.9

10

1.4

00.4

40

1.4

90.5

46

1.5

81.8

36

1.6

72.3

92

1.7

55.9

91

1.8

20.9

21

1.9

08.5

87

2.0

00.8

85

2.0

93.5

11

2.1

87.2

10

2.2

79.2

91

2.3

61.3

54

2.4

29.0

64

2.5

15.5

49

2.6

05.7

95

3 spaces before and after figures/tables and their caption