t3 load forecasting

8/12/2019 T3 Load Forecasting

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Load Forecasting

Load demand forecasting is essentially important for the electric companies. It has many

applications including energy purchasing and generation planning, load switching, contract

evaluation, and infrastructure development. A large variety of mathematical methods have been

developed for load forecasting. Many variables and factors could affect the load forecasting. The

most important factor is load peak for the given regions for at least for the last 5 years.

Forecasting refers to predict how greatly power will be expected to supply where and when the

power must be delivered. Electric load forecasting can be divided into three categories, namely:

Short-term load forecasting, Medium-term load forecasting and, Long-term load forecasting.

The short-term load forecasting predicts load demand in time interval from one day to several

weeks. It can be used to approximate load flows to make decision that can avoid overloading.

Therefore, this will help in developing network reliability and decreases occurrences of equipmentfailures and blackouts.

The medium-term load forecasting predicts the load demand from a month to several years. This

will provides essential information for future planning operation.

The long-term load forecasting predicts the load demand in time interval from a year up to twenty

years, it is essentially for power system planning, utility development, and employees hiring.

Forecasting Techniques

Forecasting techniques relays only on the extrapolation of past observation of the load using

mathematical procedure to extrapolate them into the future. One of the forecasting techniques is the

time-series models. These models depend on the fitting of a time series to original data. The load,

PL(t), is expressed as a function of time t,f(t). Some of the models are:

Straight Line PL(t) =a + b.t

Time Polynomial PL(t) =i

i

itb

Exponential PL= a.ebt

The parameters of the above models can be estimated using the least-square technique.

Method of Least Squares

Example 1- Linear Model

Based on the annual peak load data given in Table 1

a. Find the function of the form

y= c1+ c2x

that is the best least-squares fit to the data points.

b. Hence estimate the annual peak load and growth for five more years (6-10).

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Table 1 Substation annual peak loads

Solution:

The least squares solution that minimizes the least-square error is given by

( )

.4520

17920.

1

1

1

....

2

1

2

12

1

2

1

1

=

=

=== +

C

C

C

C

x

x

x

y

y

y

YXXXYXCCXY

nn

TT

MMM

kWxy 452017920+=

Based on this model the annual peak load for the subsequent five (6-10) years can be estimated. The

results are shown in Table 2

Table 2: Estimated annual peak loads for years 6 to 10

kWxy 452017920+=

y = 4520x + 17920

R2= 0.9377

0

10000

20000

30000

40000

50000

60000

70000

0 2 4 6 8 10Year

AnnualPeakLoad,k

12

Given Data Forecas ted Linear (Given Data)

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Example 2- Exponential Model

Based on the annual peak load data given in Table 1

a. Find the function of the form

y=c1exp(c

2x) kW

that is the best least-squares fit to the data points.

b. Hence estimate the annual peak load and growth for five more years (6-10).

Based on this model the annual peak load for the subsequent five (6-10) years can be estimated. The

results are shown in Table 3

Table 3 Estimated annual peak loads for years 6 to 10

Year Peal Load, kW

6 48174

7 55947

8 64976

9 75461

10 87638

y=19633*exp(0.1496*t) kW

y = 19633e0.1496x

R2= 0.9355

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 2 4 6 8 10

Year

AnnualPeakLoad,k

12

Given Data Forecasted Expon. (Given Data)

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t3 load forecasting

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