a hybrid intelligent algorithm based short-term load forecasting approach

Electrical Power and Energy Systems 45 (2013) 313–324

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Electrical Power and Energy Systems

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A hybrid intelligent algorithm based short-term load forecasting approach

Rahmat-Allah Hooshmand ⇑, Habib Amooshahi, Moein ParastegariDepartment of Electrical Engineering, University of Isfahan, Hezar-Jerib St., 8174673441 Isfahan, Iran

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

Article history:Received 14 April 2012Received in revised form 25 August 2012Accepted 6 September 2012Available online 24 October 2012

Keywords:Short-term load forecastingArtificial neural networkAdaptive neuralFuzzy inference systemWavelet transformSimilar-hour

0142-0615/$ - see front matter Crown Copyright � 2http://dx.doi.org/10.1016/j.ijepes.2012.09.002

⇑ Corresponding author. Tel.: +98 311 7934073; faxE-mail addresses: [email protected] (R.-A. H

gmail.com (H. Amooshahi), [email protected] (M.

In this paper, a new two-step algorithm is proposed for short-term load forecasting (STLF). In the firststep of the method, a wavelet transform (WT) and an artificial neural network (ANN) are used for the pri-mary forecasting of the load over the next 24 h. Inputs of this step are weather features (include the dailymean temperature, maximum temperature, mean humidity, and mean wind speed) and previous dayload data. In the second step, a WT, the similar-hour method and adaptive neural fuzzy inference system(ANFIS) are used to improve the results of primary load forecasting. In this study, a WT is employed toextract low-order components of the load and weather data. Furthermore, the number of weather datainputs has been reduced by investigating the weather conditions of different cities. To evaluate the per-formance of the proposed method, it is applied to forecast Iran’s load and New South Wales ofAustralian’s load. Simulation results in four different cases show that the proposed method increases loadforecasting accuracy.

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1. Introduction

The STLF plays an important role in power system operation.STLF results are applied in the unit commitment problem, eco-nomic load dispatch, power system security, and in determiningthe generation reserve of the system. Currently, STLF is effectivelyused for price forecasting in deregulated power markets. In addi-tion, the error between the actual and forecasted load affects thereliability of the power system. Therefore, it is important to im-prove the accuracy of load forecasting to improve the operationalperformance of the power system [1].

To date, many STLF methods have been developed, and themethods can be divided into two categories. The first category con-sists of conventional methods such as multiple linear regression,time series, the state space model, general exponential smoothing,and knowledge-based approaches [2]. In these methods, it is as-sumed that the system load is related to the load of previous daysand weather data. However, it is difficult to determine an appropri-ate non-linear, mathematical relation between the load and otherdata (such as weather features and the type of day). The secondforecasting category consists of intelligent algorithms. Intelligentmethods such as evolutionary programming [3,4], expert systems[5], ANN [6–8], and fuzzy inference [9] are included in this cate-gory. Among the intelligent methods, the ANN method is especiallyattractive because it has clear model, easy to implement, and itprovides good performance [1]. The main reason for the success

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of ANN in load forecasting is its ability to determine non-linearrelationships between loads and the data that affect them.

The ANFIS approach uses a fuzzy inference system for trainingthe ANN. Although it has better performance relative to the ANN,the large amount of training data limits its performance. Thisweakness leads to using a combination of ANFIS with other meth-ods to construct hybrid method [10–12]. In Ref. [10], the ANFIS ap-proach is employed to adjust primary forecasting based on thereal-time price environment. Additionally, in Refs. [11,12], a com-bination of the fuzzy method and the ANN method is used for loadforecasting.

The WT can be used to extract low and high frequency compo-nent of the load data. If actual load without extracting low or highfrequency components is used to train the ANN, the high frequencycomponent disturbs the forecasted load pattern. In order to im-prove the accuracy of the STLF, low frequency component [12–14] or high and low frequency component [15–18] of load patternshould be used for training of the neural network. High frequencycomponent of load data contains important information of loadbehavior; therefore, these data should be used in the load forecastmethod. In the cases which only low frequency component of loadpattern is used, high frequency component of load pattern will beconsidered indirectly by considering actual load without decompo-sition as the target of the forecast problem.

The selection of appropriate input variables is one of the mostimportant aspects of load forecasting. Therefore, the factors affect-ing the load pattern should be taken into account as the input vari-ables. Weather information from different cities is one of the inputparameters that affect the load pattern. In Ref. [14], temperature,humidity, and wind speed are employed for load forecasting. In

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314 R.-A. Hooshmand et al. / Electrical Power and Energy Systems 45 (2013) 313–324

large-scale power systems, effective weather information shouldbe selected from all the points covered by the network [19]. Forthis purpose, the properties of each regional load should also be ta-ken into account. For instance, in cold climate areas where naturalgas heating systems are used, temperature variation has no signif-icant effect on electricity consumption. An analysis of historicaldata shows that if these data have factors similar to the forecastedload, the historical data can be used to improve load forecastingaccuracy [18,20]. This analysis shows that the load on a specificday has characteristics that are similar to a load in a day with sim-ilar weather temperature. Therefore, a similar hour or similar dayin the previous year can be considered as similarity. This similarityhas not been investigated in previous studies.

In this paper, a new algorithm is proposed to improve the accu-racy of the STLF. The proposed algorithm consists of two steps. Inthe first step, the exogenous variables are initially selected with re-gard to geographical areas and the condition of the consumers. Pri-mary forecasting for the next 24 h is then performed using the ANNapproach. In the second step, the ANFIS method is used to improvethe results of the first step. For this purpose, similar hour data areused as the input in the second step. It should be noted that the in-put data in each step are decomposed by the WT. The simulationresults confirm the capability of the proposed method to improveaccuracy of STLF in Iran. In order to verify the effectiveness ofthe proposed forecasting method, its results on the New SouthWales of Australian are compared with those of four differentmethods with the same historical data.

2. The proposed STLF method

There is a nonlinear relationship between the input and outputvariables in the STLF. Therefore, the ANN method can be employedto determine the nonlinear relationship between large quantitiesof input and output (forecasted load) data. Of course, the major de-fect of the ANN is its lack of inference. Although inference is used inthe ANFIS approach, this system is not useful with a large quantityof training data. Therefore, a two-step algorithm can be used toachieve the advantages of both approaches.

Furthermore, the WT can be employed to remove the effects ofhigh-order components of input data on the forecasted load. Be-cause inputs contain various order components, and the load pat-terns are nonlinear and complex, the output of the ANN alsocontains various order components. Therefore, the ANN outputshould also be decomposed. In the following section, the proposedSTLF algorithm is presented and discussed.

2.1. The proposed structure

The proposed algorithm consists of two steps: the primary fore-cast and the secondary forecast. The primary forecast determines a24-h load pattern. In the second step, the primary forecast resultsare improved. Fig. 1 shows the data chart of the proposed forecast-ing method. As shown in this figure, in the primary forecastingstep, the weather information (mean temperature, maximumtemperature, mean humidity, and mean wind speed of Ahwazand Tehran) and low component of the 24 h pervious load are usedas inputs of ANN. Output of ANN is 24 h next day primary forecast.In the complete forecasting step, low frequency component of sim-ilar day and output of primary forecasting have been extractedfirst. Then, the value of the load of ith hour of the low frequencycomponent of similar hour load and ith hour of the low frequencycomponent of similar hour load are used as the inputs of ANFIS.This process should be performed for all 24 h of a day to completethe forecast of next day.

In the next sections, details of the proposed load forecast pro-cess will be described. The effects of using different mother wave-lets on the input data are then investigated. In addition, the effectof the similar hour factor on the load forecasting is studied.

2.2. Data processing using the WT

Through the use of mathematical transforms and filter theory,specifications and features of the data can be extracted. The WTcan be used to extract the features and specifications of a signalin time and frequency domains. The basic equations of this trans-form for time series input signal x(t) are as follows:

XWTðs; sÞ ¼1ffiffiffiffiffijsj

pZ þ1

�1xðtÞ � w� t � s

s

� �dt ð1Þ

xðtÞ ¼ 1c2W

Z þ1

�1

Z þ1

�1XWTðs; sÞ

1s2 w

t � ss

� �ds � ds ð2Þ

where w is the mother wavelet and x(t) is the input signal. XWT(s, s)is the output of the WT. s and s are the parameters related to themother wavelet.

There are different mother wavelets for different applicationssuch as Haar, Daubechies, Coiflet, Symlet and Mexican Hat. Theselection of the optimal mother wavelet has a significant effecton the obtained results. Thus, in Section 4.1, different motherwavelets are analyzed, and the optimal wavelet is selected.

The discrete WT is based on the filter theory. It can be used toextract different components of the input signal, as shown inFig. 2a for one stage of the WT. At each stage, the signal is decom-posed into two parts to generate approximations and detail com-ponents. In fact, the convolution of the initial signal with themother wavelet determines these components. By repeating thisdecomposition process, the high-order and low-order componentsare extracted. This process is known as the wavelet decompositiontree and is depicted in Fig. 2b.

In order to use WT grouping similar data should be performedsuch that similar data points are in the same group. Traditionaldata clustering, also called crisp clustering, uses hard thresholdsto group data points into separate groups while fuzzy clusteringuses fuzzy logic (soft thresholds) to create overlapped groups ofdata. In fuzzy clustering, each data object can belong to more thanone cluster at the same time with a different possibility degree ormembership function value. In this paper, universal threshold rule,and soft thresholding method is used in the WT. Level-dependentestimation of level noise is used for threshold rescaling and then28 level of Wavelet decomposition is performed.

2.3. The ANN employed for load forecasting

As shown in Fig. 1, the proposed algorithm uses ANN in its firststep. The ANN method is used to determine the nonlinear relation-ship between input and output. Thus, it can be used to solve spe-cific problems such as pattern recognition and data classificationproblems. The simplest existing ANN is multi-layer perceptron(MLP), the structure of which is presented in Fig. 3. The MLP neuralnetwork consists of three layers: input, hidden and output layers.Each layer consists of a number of neurons. Neurons of each layerare connected to the neurons of the next layer by synaptic weights.These synaptic weights are determined by training the network sothat, for each training set, the following performance function (E) isminimized:

E ¼ 1N

XN

i¼1

ðtargeti � outputiÞ2 ð3Þ

start

Weatherdata

24 hours pervious Load

data from IGMC

ANN

Wavelet(extract low frequency

component)

ANFIS

Save forcasted i-th hour

end

Wavelet (extract low frequency

component)

Wavelet(extract low frequency

component)

i=1

i-th

Hour

primary forecasting

com

plet

e fo

reca

stin

g

i-th Similar hour

SimilarDayfrom

IGMC

i-th Hour of primery forecast

primery forecas

If i<24Yes

No

i=i+1

Fig. 1. Block diagram for the proposed STLF algorithm.

S

FiltersLow-pass High-pass

A D

(a)

S

CA1 CD1

CA 2 CD2

CA 3 CD 3

(b)Fig. 2. (a) Filtering process in the WT and (b) wavelet decomposition tree.

R.-A. Hooshmand et al. / Electrical Power and Energy Systems 45 (2013) 313–324 315

where targeti and outputi are the actual and predicted output of thenetwork at ith pattern, respectively, and N represents the number ofsamples employed for training.

In this study, the back-propagation algorithm is used for train-ing the understudy feed-forward ANN. For this purpose, the

Levenberg–Marquardt optimization algorithm is employed for itstraining. This network has one hidden layer with five neurons.The hyperbolic tangent sigmoid transfer function is used in thehidden layer of this ANN. The presented ANN structure has 32neurons in the input layer and 24 neurons in the output layer,

Inputlayer

Hiddenlayer

Outputlayer

ni

1i

2i

1O

nO

2O

Fig. 3. Multi-layer perceptron neural network.

Fig. 5. Adaptive neural-fuzzy inference system structure.


where the linear transfer function is used in the input and outputneurons. Fig. 4 is shown sample results of the best validation per-formance for the ANN training.

The number of the hidden layers is determined based on theKolmogorov Theorem [21]. The number of neurons in the hiddenlayer should be carefully determined. If the number is too small,the network cannot find the complex relationship between inputand output and may have difficulty in convergence during training.If the number is too large, the training process will take longer andcould harm the capability of ANN [1]. The number of hidden layersand other parameters of the understudy ANN are determined bytrial and error method.

2.4. The ANFIS employed to STLF improvement

According to the proposed algorithm presented in Fig. 1, theANFIS approach is employed in the second step of load forecasting.The structure of this network combines the advantages of the twoapproaches: neural networks and a fuzzy system. The marriage ofthese two intelligent approaches combines the good reasoning offuzzy system and the calculation capability of ANN.

The ANFIS structure is constructed of two parts: the antecedentand the conclusion. They are connected to each other by a set ofrules. ANFIS is a multilayer network that consists of five layers.Fig. 5 shows a block diagram of this five layer network with two in-puts. The first layer performs the fuzzification process. The secondlayer executes the fuzzy AND of the antecedent part of fuzzy rules.The third layer performs the normalization of the membershipfunctions. The fourth layer performs the consequent part of the fuz-zy rules, and finally the fifth layer calculates the output of network.

Fig. 4. Sample results of the best validatio

In this structure, a hybrid Sugeno training algorithm is used todetermine parameters of the fuzzy inference system. This trainingalgorithm combines the least-squares technique and backpropaga-tion (BP) gradient descent algorithms to generate and train a set ofparameters of membership functions of the fuzzy inferencesystem.

2.4.1. Specifications of the first layerIn this layer, every node i is a square node with a node function

that is defined as follows:

O1;i ¼ lAiðxÞ for i ¼ 1;2lBi�2

ðyÞ for i ¼ 3;4�

ð4Þ

where x or y is the ith node input and Ai or Bi�2 is a fuzzy set relatedto this node. Therefore, this O1,i is the membership degree of the (A1,A2, B1, B2) fuzzy sets.

2.4.2. Specifications of the second layerIn this layer, each node is a circle node labeled as ‘‘Prod’’. The

output of the node is also the product of all the incoming signalsto that layer. So,

O2;i ¼ wi ¼ lAiðxÞ � lBi

ðyÞ i ¼ 1;2 ð5Þ

In this layer, each T-norm operator (minimum-multiplication,and etc.) that can perform the fuzzy AND operation is applicable.

2.4.3. Specifications of the third layerIn this layer, every node is labeled as ‘‘Norm’’. The output of the

node in this layer (O3,i or wi) is calculated as follows:

O3;i ¼ wi ¼wi

w1 þw2¼ 1;2 ð6Þ

n performance for the ANN training.


In other words, the output of every node of this layer is the nor-malized outputs of the pervious layer.

2.4.4. Specifications of the fourth layerIn this layer, every node i is adapted to the O4,i node function.

So,

O4;i ¼ wi � fi ¼ wi � ðpixþ qiyþ riÞ ð7Þ

where,

fi ¼ Pixþ qiyþ ri ð8Þ

and (pi, qi, ri) is the set of the ith node parameters, known as conse-quent parameters.

2.4.5. Specifications of the fifth layerIn this layer, the node is labeled as ‘‘Sum’’. The output of the sin-

gle node in this layer is equal to the ANFIS output. This output isthe sum of all the incoming signals, as shown below:

overall output ¼ O5;1 ¼ f ¼X

i

wi � fi ¼P

iwi � fiPiwi

ð9Þ

The membership functions and fuzzy rules of ANFIS are ac-quired from a large lot of existing data instead of experience. Thisnetwork consists of a bell-shape membership function for every in-put variable. 78 nodes, 108 linear parameters, 27 nonlinear param-eters, 552 training data pairs and 27 fuzzy rules are the otherinformation about understudied ANFIS system.

The network has three inputs including the primary decom-posed forecasting, the decomposed similar-hour load, and ‘‘time’’.The ‘‘time’’ input is used to define the hour at which the load isforecasted. Also, the primary forecasting is output of the ANN.

2.5. The similar-hour application in the proposed algorithm

In the second step of the proposed algorithm, the performanceof similar conditions is used to reduce the forecast error betweenthe primary forecast and the actual load. In general, similar condi-tions can be a similar hour or day from the view of time or weatherconditions. In this study, the similar-hour load is used as one of theinputs of the system. An analysis of the similarities of successive-year loads shows that the load of the previous year can be consid-ered as a similar load. Thus, in the proposed structure, one input ofANFIS is used to define similar-hour load. The difference betweenthe forecasted load and similar-hour load results from the differ-ence in the type of the weekday, weather condition, and annualload growth. It should be noted that the similar-hour load consistsof undesirable components. These components can be filtered byusing the WT to increase load forecasting accuracy.

3. Investigation of load and weather characteristics

In order to evaluate the performance of the proposed algorithm,the presented STLF method is used for forecasting Iran’s load. Theinput data for this system include Iran’s load and weather informa-tion for two successive years (2008 and 2009). Iran’s load informa-tion is available at http://sccisrep.igmc.ir/RptParam.aspx and Iran’sweather information is available at http://www.wunder-ground.com/history/. It should be noted that large industries’ loadsin the network are not considered in the proposed STLF mechanismbecause there are small variations between industries’ forecastedloads and their actual load.

There are many input features that affect load forecasting accu-racy. Because there are a large amount of features, the effective fea-tures should be selected. Temperature is one of these effective

features. The weather features include the daily mean temperature,maximum temperature, mean humidity, and mean wind speed.

Iran is a large country with diverse weather conditions. There-fore, the weather conditions of cities where their weather condi-tions particularly affect the load should be selected as the inputof proposed STLF method. These cities should be selected to coverthe entire country. Total load of Isfahan, Tehran, Shiraz and Ahwazis close to 50% of total load of Iran. Therefore, the weather condi-tion of these cities should be considered as the input data of theproposed load forecasting problem. As shown in Fig. 6, these citieshave approximately the same temperature (http://www.wunder-ground.com/history). Also, value of mean absolute error betweenvariable part of the temperature of Tehran and Isfahan is 1.81.The error between variable part of the temperature of Tehranand Shiraz is 2.18 �C. Among Isfahan, Tehran, Shiraz, Tehran hasthe highest load. These statements confirm that Tehran’s tempera-ture can be used as the indicator of the temperature of Isfahan andShiraz (and other mild isothermal cities). Weather conditions ofAhwaz are also selected as the indicator of hot isothermal cities.Meanwhile, in the cold regions of Iran, consumers usually use nat-ural gas for heating systems. Thus, these consumers have little ef-fect on the load pattern, and the effect of these consumers can bemodeled in a way similar to temperate cities such as Tehran.Therefore, the effective exogenous inputs of cold and temperatecities are determined.

In order to illustrate dependency between the load and climatecondition during training days, the graphs for each quantity areprovided. These graphs are shown in Fig. 7. As shown in the graphsof this figure, the peak load of the Iran usually increases by an in-crease in the temperature of the Ahwaz and Tehran (Fig. 7a and b)and also, the peak load of the Iran usually decreases by an increasein the average humidity and mean wind speed of the Ahwaz andTehran in the specified temperatures (Fig. 7c–f).

In the proposed method presented in Fig. 1, the 32 inputs of thefirst step of the algorithm are the previous 24-h load and weatherinformation (mean temperature, maximum temperature, meanhumidity, and mean wind speed of the two cities of Tehran andAhvaz). The output of this step is the primary forecasted load ofthe next day.

4. Simulation results

In this section, the simulation results of different parts of theproposed STLF method are presented for load forecasting in Iran.

4.1. Data modification by the WT

4.1.1. Modification of the input dataTo increase the accuracy of load forecasting, low-order compo-

nents of the input data should be extracted using the WT. Accord-ing to Fig. 1, this transform is used at three locations. It can beobserved that the WT has decomposed the high-order componentsof the input data. In addition, to select the best mother wavelet, theeffect of different mother wavelets should be studied. The effect ofthe best version of mother wavelet on next-day load forecasting isshown in Table 1.

In this table, the mean absolute error (MAE) criterion is used tocompare and evaluate the performance of different mother wave-lets. This criterion is defined as follows:

MAE ¼ 1N

XN

i¼1

jti � Oij ð10Þ

where ti and Oi are the actual load and the forecasted load at the ithhour, respectively, and N is the number of hours in the forecastedperiod.

http://sccisrep.igmc.ir/RptParam.aspx

http://www.wunderground.com/history/

http://www.wunderground.com/history/

http://www.wunderground.com/history

http://www.wunderground.com/history

Fig. 6. Annual temperature changes for three cities: (a) Tehran, (b) Isfahan, and (c) Shiraz.


The results of Table 1 show that the best results are related tothe DMeyer mother wavelet. In other words, when the DMeyermother wavelet is used, the value of the MAE criterion reducesto 10.053 MW. Fig. 8 shows the performance of the two Symletsand DMeyer mother wavelets. Based on this figure, the DMeyerwavelet provides more accurate load forecasting. A suitablemother wavelet is a wave that has a better decomposing effect

on the data. Fig. 8 shows the validity of the results of Table 1.Therefore, the DMeyer wavelet is employed in the proposed STLFproblem.

4.1.2. Modification of similar hoursFig. 9 represents the load curve for 1 day and its similar-hour

load. The difference between these two curves results from the

25 30 35 40

2.8

3

3.2

3.4x 104

Mean Temperature of Ahwaz (°C)

Peak

Loa

d (M

W)

(a)

10 20 30 40

2.8

3

3.2

3.4x 104

Average Humidity of Ahwaz (%)

Peak

Loa

d (M

W)

(c)

0 5 10 15

30

40

50

Mean Wind Speed of Ahwaz (km/h)

Max

Tem

pera

ture

of

Ahw

az (°

C)

(e)

15 20 25 30

2.8

3

3.2

3.4x 104

Mean Temperature of Tehran (°C)

Peak

Loa

d (M

W)

(b)

20 40 60 80

2.8

3

3.2

3.4x 104

Average Humidity of Tehran (%)

Peak

Loa

d (M

W)

(d)

0 5 10 15

20

30

40

Mean Wind Speed of Tehran (km/h)

Max

Tem

pera

ture

of

Tehr

an (°

C)

(f)

Fig. 7. Dependency between the load and climate condition.

Table 1The algorithm input data specifications at thefirst step.

Mother wavelet MAE value (MW)

Haar 66.820Daubechies 2 103.066Symlets 5 510.201Coiflets 5 109.504BiorSplines 2.6 53.713ReverseBior 3.7 43.297DMeyer 10.053

5 10 15 202

2.2

2.4

2.6

2.8

3x 104

Hours (hr)

Load

(MW

)

DMeyerSymletswithout wavelet

Fig. 8. Daily load curve determined by DMeyer and Symlets mother wavelets.

0 5 10 15 202

2.2

2.4

2.6

2.8

3

3.2x 104

Hours (hr)

Load

(MW

)

forecasted hourssimilar hours

Fig. 9. Load curve for the forecasted hours and the similar-hours for 1 day beforeusing the WT.


difference between the type of weekdays, weather conditions, theannual load growth. The WT will reduce differences betweenforecasted load and similar-hour load, as shown in Fig. 10.Furthermore, by investigation on these figures it can be concludedthat low frequency component of similar-hours load has similarpattern with low frequency component of forecasted load,therefore it can be used to determine low frequency componentof forecasted load.

5 10 15 202.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3x 104

Hours (hr)

Load

(MW

)

forecasted hourssimilar hours

Fig. 10. Load curve for the forecasted hours and the similar-hours for 1 day afterusing the WT.


4.2. The STLF results

In this subsection, the proposed method presented in Fig. 1 isused to determine the STLF results. The effectiveness of the pro-posed method is demonstrated on forecasting load for five cases.These five cases are selected from different years (2004, 2009,and 2012), different power systems (Iran and New South Walesof Australia) and different months (March, May and August) toshow overall performance of the proposed method.

Case 1: Day-ahead load forecasts in May 14, 2009 (Thursday). Inthis regard, the first step of the proposed mechanism is trainedby load and weather information from April 21, 2009 to May 13,2009. The second step of the mechanism is trained by similar-hour data (load and weather information from April 21, 2008to May 13, 2008).

Table 2Testing of the 24-h load in the first day using the proposed algorithm for May 14, 2009 (T

Hour (h) Actual load � 104 MW Step one: primary forecasting

Forecast load � 104 MW

1 2.462 2.4609072 2.3302 2.3285173 2.2498 2.2494184 2.2042 2.2039775 2.182 2.1817116 2.1626 2.1624397 2.1123 2.1122298 2.1756 2.1621329 2.3404 2.34035

10 2.4486 2.4484411 2.5251 2.52500612 2.5916 2.59155413 2.6351 2.63355714 2.6308 2.63006515 2.6494 2.64959816 2.6396 2.63877217 2.6049 2.60479318 2.5443 2.54414419 2.4768 2.47663920 2.544 2.54393321 2.8466 2.8465222 2.8851 2.88507723 2.8097 2.80956624 2.6724 2.670028MAE 10.0527

Case 2: Weekly load forecasts during May 14–20, 2009. Friday(May 15, 2009) which is weekend in Iran, is eliminated fromunder studied days. The training data for this case is the sameas the case ‘1’. The weather information of May 14–20,2009 days have large similarity with those of the similar days.Case 3: Weekly load forecasts during May 21–27, 2009. Friday(May 22, 2009) which is weekend in Iran, is eliminated fromunder studied days. The first step of the proposed mechanismis trained by load and weather information from April 28,2009 to May 20, 2009. The second step of the mechanism istrained by similar-hour data (load and weather informationfrom April 28, 2008 to May 20, 2008). It should be noted thatthe weather information of these testing days have largechanges in comparison with the similar days.Case 4: Holidays load forecast during March 20–23, 2012 whichare New Year holydays. The first step of the proposed mecha-nism is trained by load and weather information from February27, 2012 to March 19, 2012. The second step of the mechanismis trained by similar-hour data (load and weather informationfrom February 27, 2011 to March 19, 2011).Case 5: In order to verify the effectiveness of the proposed fore-casting method, its results on the New South Wales ofAustralian are compared with those of four different methodswith the same historical data introduced in Ref. [10] for day-ahead load forecasts of the New South Wales of Australian onlyin August 1, 2004. In this regard, the first step of the proposedmechanism is trained by the load and weather informationfrom July 12, 2004 to July 31, 2004. The second step of themechanism is trained by similar-hour data (load and weatherinformation from July 12, 2004 to July 31, 2003).

4.2.1. Case 1Table 2 shows the results of the load forecasting for the case 1.

This table shows the primary and complete forecasting results ofthe next day. In order to compare these results, values of the errorof each hour are calculated by the following relations.

error ¼ Loadforecast � Loadactual ð11Þ

hursday).

Step two: proposed complete forecasting

Error (MW) Forecast Load � 104 MW Error (MW)

10.9348 2.462703 �7.030616.8341 2.331051 �8.5094

3.8234 2.249774 0.25842.2318 2.204315 �1.14842.895 2.182031 �0.30751.6087 2.162488 1.11660.7132 2.112025 2.7508

134.6776 2.174239 13.60520.5015 2.340226 1.73631.5975 2.448596 0.04110.942 2.525133 �0.33130.4568 2.591132 4.6829

15.4264 2.634995 1.0547.3538 2.631269 �4.686�1.9842 2.649676 �2.7588

8.2833 2.640031 �4.31251.0705 2.605214 �3.13851.5585 2.544513 �2.12941.6137 2.475778 10.2170.6682 2.543942 0.5850.7988 2.84636 2.40290.2301 2.88477 3.2971.3426 2.809387 3.1274

23.7173 2.67264 �2.39533.4009

0 20 40 60 80 100 120 140-20

0

20

40

60

80

100

120

140

160

Hours (hr)

erro

r (M

W)

Fig. 11. Error generated between the real load and the forecasted load for theprimary forecasting of case 2 (between 14 and 20 May).

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

60

70

80

Hours (hr)

erro

r (M

W)

Fig. 12. Error generated between the real load and the forecasted load for the wholetrend of forecasting of case 2.


where Loadforecast and Loadactual denote the forecasted and actualload, respectively. With regard to Table 2, it is observed that the AN-FIS system (the second step of load forecasting) increases the accu-racy of load forecasting. As shown in the table, the maximum erroroccurred at hour 08:00 of the first day. This error is about134.6776 MW in the primary forecasting and about 13.6052 MWin a proposed complete forecasting. Therefore, the maximum errorof the forecasting process has improved about 89.89%. In the firstday, the primary forecasting error by the MAE criteria was10.0527 MW, and for the complete forecasting, it was 3.4009 MW.The MAE value for this case is improved about 66.17%. These resultsdemonstrate the effect of the second step of the proposed algorithmfor the improvement of load forecasting.

4.2.2. Case 2In this subsection, the effectiveness of the proposed method is

demonstrated on case 2. Table 3 represents the performance ofproposed STLF algorithm for each step (primary and complete fore-casting steps) separately, which shows the results of six successivedays. Furthermore, in this table, the performance of primary loadforecasting is compared with the performance of complete loadforecasting by the use of MAE and maximum error criteria.

As shown in Table 3, The MAE value for six successive days im-proved about 57.38%. Therefore, it can be concluded that the sec-ond step of the proposed two-step forecasting method improvesprimary forecasting results.

In Fig. 11, the error between the real load and the forecastedload by the first step (primary forecasting) is shown for six succes-sive days (during May 14–20, 2009). In Fig. 12, the error of the pro-posed STLF method is also shown. By comparing these figures, itcan be concluded that, applying the second step of the proposedalgorithm reduces error spikes. In addition, all the errors are gen-erally positive in the primary forecasting, showing that the fore-casted load is larger than the real load.

In these conditions, the mean of the maximum temperature inAhwaz during the training days was 36.55, but there was a changebetween 39 �C and 44 �C during the six testing days, producing po-sitive error. In this case, the data related to low temperature days isused to train proposed method. Therefore, if it is tested by the datarelated to high temperature days, the proposed method might haveerror. As shown in Fig. 7a, increases in the temperature of Ahwazleads to increase in the peak load. Consequently, the above men-tioned error might be positive. Therefore, this intense increase intemperature caused the forecasted load to become larger thanthe real load, but the second step of the proposed method correctsthis problem.

According to Fig. 11, the maximum forecasting error occurseach morning at 08:00. The lowest load on the network is at07:00. Therefore, the maximum error takes place at 08:00 becauseit follows the lowest daily load. As shown in Table 3, the completealgorithm improves the primary forecast results about 22% in thefifth day. In addition, at 104th h (08:00 on the fifth day (19May)) a glaring error is observed in Fig. 12. In this case, although

Table 3Test results for the first six successive days of case 2 (between 14 and 20 May).

Day Step one: primary forecasting Step two

WNN (MAE) Max. error (MW) WNN and

1(14 May 2009) 10.0527 134.6776 3.40102(16 May 2009) 9.9332 122.2402 4.15753(17 May 2009) 10.4910 125.0608 4.09534(18 May 2009) 12.2463 156.0775 4.25555(19 May 2009) 9.0001 69.9671 7.01756(20 May 2009) 12.3643 148.7637 4.3848Total MAE (MW) 10.6813 4.5519

the fifth day is not a holiday, a special event takes place and affectsthe load pattern. Therefore, the error at the beginning of the work-ing hour is justifiable.

In this case, because the weather information of the under-study week is look like weather conditions of the similar-hour,so the load forecasting in this week has a high accuracy.

4.2.3. Case 3In order to study the performance of the proposed method in

conditions with great changes of temperature, new six successive

: proposed complete forecasting Improvement percentage (%)

ANFIS (MAE) Max. error (MW)

13.6052 66.1724.1305 58.1517.0110 60.9611.7504 65.2573.7421 2212.7762 64.54

57.38%

28 April 20 May 27 May15

20

25

30

35

40

Days

Mea

n T

empe

ratu

re (

C )

AhwazTehran

forecasteddaystrain days

°

Fig. 13. Mean temperature of train days and forecasted days of case 3 (between 28April and 27 May).

28 Aprill 20 May 27 May15

20

25

30

35

40

45

50

Days

Max

.Tem

pera

ture

( C

)

AhwazTehran

Train days Forecast days

°

Fig. 14. Max. temperature of train days and forecasted days of the case 3 (between28 April and 27 May).


days (case 3) are used. The weather information in these days haslarge changes in comparison with training days (2 April–20 May,2009) and similar-hour’s weather information. The mean and max-imum temperatures of the training and testing days of this case areshown in Figs. 13 and 14, respectively. As shown in these figures,the temperature of the under-study days (May 21–27, 2009) iseffectively increased.

Table 4 represents the performance of the proposed STLF algo-rithm for each step (primary and complete load forecasting steps).In this table, the performance of primary and complete load fore-casting steps are compared with each other by the use of MAEand maximum error criteria. As shown in this table, the MAE valuefor May 21–27, 2009 days is improved about 33.53%. Therefore, itcan be concluded that when the weather conditions of theunder-study week are effectively changed (in comparison withweather conditions of the training days and similar-hour’s weatherinformation), the next week primary load forecasting error is in-creased. In this condition, proposed similar-hour method increasesthe forecasting accuracy.

Table 4Test results for the new six successive days of case 3 (between 21 and 27 May).

Day Step one: primary forecasting Step two

WNN (MAE) Max. error (MW) WNN an

1(21 May 2009) 94.1407 581.5689 68.68452(23 May 2009) 86.5720 422.7623 51.52653(24 May 2009) 84.8516 525.3381 48.78424(25 May 2009) 77.3816 356.7641 55.15645(26 May 2009) 95.8104 369.9452 63.72866(27 May 2009) 124.1258 648.3854 86.2734Total MAE (MW) 93.8137 62.3589

4.2.4. Case 4According to dates presented in cases 2 and 3, Friday (May 15,

2009 and May 22, 2009) which is weekend in Iran, is eliminatedfrom under studied days. In order to study the performance ofthe proposed method for holydays, new four successive days (case4) are used. Table 5 represents the performance of the proposedSTLF algorithm for each step (primary and complete load forecast-ing steps). In this table, the performance of primary and completeload forecasting steps are compared with each other by the use ofMAE and maximum error criteria. As shown in this table, the MAEvalue for March 20–23, 2012 days is improved about 40.27%.

4.2.5. Case 5In this case, in order to verify the effectiveness of the proposed

forecasting method, its results on the New South Wales ofAustralian only in August 1, 2004 are compared with those of fourother methods from Ref. [10].

For this purpose, the first step of the proposed mechanism istrained by load and weather information from July 12, 2004 to July31, 2004. In this system, weather conditions of Sydney are selectedas the exogenous variable.

For the easy comparison of the methods, the load is forecastedfor each half hour. Therefore, 52 inputs should be used in the firststep of the algorithm. They are the previous 24-h (48 half hours)load and weather information (mean temperature, maximum tem-perature, mean humidity, and mean wind speed of the Sydney).The output of this step is the primary forecasted load of the nextday. The second step of the mechanism is trained by the low ordercomponents of the primary forecasting, ‘‘time’’ and low order com-ponents of the similar-hour data (load and weather informationfrom July 12, 2003 to July 31, 2003). The output of this step isthe complete forecasted load of the next day.

In order to compare these results, values of absolute percentageerror (APE or error%) and mean absolute percentage error (MAPE/average error%) are calculated by the following relations.

APE ¼ error% ¼ jLoadforecast � LoadactualjLoadactual

� 100 ð12Þ

MAPE ¼ average error% ¼ 1N

XN

i¼1

APEi ð13Þ

where Loadforecast and Loadactual denote the forecasted and actualload and APEi is absolute percentage error at ith hour and N is thenumber of the hours in the forecasted period.

The four methods investigated in Ref. [10] are the following:

(1) Method I (RBFNN method with historical demand data andwithout price change).

(2) Method II (RBFNN method with historical demand data andprice change).

(3) Method III (ANFIS method with historical demand data andprice change).

: proposed complete forecasting Improvement percentage (%)

d ANFIS (MAE) Max. error (MW)

426.2047 27.04486.9486 40.48319.7388 42.51365.1305 28.72205.2205 33.48537.1964 30.49

33.53%

Table 5Test results for the new four successive holidays of case 4 (20–23 March 2012).

Day Step one: primary forecasting Step two: proposed complete forecasting Improvement percentage (%)

WNN (MAE) Max. error (MW) WNN and ANFIS (MAE) Max. error (MW)

1 (20 March 2012) 128.67 726.14 93.65 691.58 27.21692(21 March 2012) 357.36 934.11 171.67 752.25 51.96163(22 March 2012) 286.58 491.47 199.22 409.93 30.48364(23 March 2012) 177.93 336.92 103.21 215.34 41.9940Total MAE (MW) 237.6350 141.9375 40.2708%

Table 6Comparison results of different forecasting methods for case 5 (August 1, 2004).

Time Real load (MW) Method I Method II Method III Method IV Proposed methodAPE (error %) APE (error %) APE (error %) APE (error %) APE (error %)

0:00 8353.2 1.316 �0.379 �1.289 0.496 0.2650:30 8094.7 3.546 �1.144 �1.487 2.657 �2.3881:00 7887.5 3.744 �0.77 �1.991 2.422 �0.2611:30 7620.9 6.027 3.671 �0.239 2.756 �0.0802:00 7251.2 6.632 4.784 1.131 3.013 �0.0112:30 6962.3 2.482 �1.359 �1.982 2.186 �0.4123:00 6732.8 �6.125 1.857 �2.265 0.359 �0.0633:30 6628.9 �1.213 �0.14 �0.053 1.632 �1.4954:00 6506.4 3.858 �2.96 �0.862 �0.578 �2.1004:30 6500.9 �1.392 �1.829 �2.367 �0.418 �0.7095:00 6537.8 �1.348 �0.477 0.102 �1.548 �1.6705:30 6683.0 �2.126 �0.711 2.303 �0.95 0.2096:00 6885.7 �3.725 �0.741 0.639 �2.427 1.0856:30 7144.6 0.564 �1.166 1.253 �1.922 �4.4017:00 7483.7 1.876 �1.601 1.044 �1.63 �2.0757:30 8037.9 �2.215 �1.373 0.137 0.842 0.3598:00 8553.7 0.573 �1.498 �1.211 1.328 �0.2738:30 8936.4 1.123 �1.789 �1.778 0.96 0.2629:00 9146.7 3.081 �1.137 �2.71 1.754 1.2549:30 9165.5 7.311 0.013 �1.085 �4.549 �0.39810:00 9091.7 1.315 �1.344 �1.056 1.209 �2.76410:30 8936.1 �4.527 0.225 1.235 2.315 �3.17711:00 8737.9 1.432 4.184 1.569 1.516 �0.28711:30 8507.7 5.011 0.8 0.596 �3.147 1.32412:00 8396.5 4.115 6.556 0.369 2.082 �3.44812:30 8300.8 0.834 1.414 �1.137 0.42 �0.81013:00 8156.0 5.158 �0.467 �1.243 3.834 �7.33213:30 8082.2 �2.471 0.762 �1.803 �1.592 �3.40014:00 7996.2 1.628 0.96 �3.914 �1.706 0.20314:30 8038.5 �4.115 1.729 �2.106 �2.132 �0.54115:00 8065.2 0.531 0.068 �4.568 0.827 �6.47015:30 8166.1 �2.093 1.462 �5.12 �1.905 �4.04016:00 8361.7 3.176 0.239 �2.29 �1.874 �1.57016:30 8748.3 0.734 6.734 2.987 �1.141 �2.86617:00 9255.1 2.825 2.559 5.706 2.161 �0.59317:30 10061.9 1.315 1.656 3.904 0.765 1.13218:00 10471.5 �1.936 3.462 4.288 �1.573 �1.12218:30 10419.2 �3.75 �0.113 1.977 �2.098 1.14419:00 10098.7 2.453 �3.984 0.416 �1.235 �0.77619:30 9883.2 2.623 �2.912 1.105 �0.73 �2.52820:00 9912.8 �4.361 �0.531 3.389 2.316 �0.86920:30 9774.9 1.052 �1.143 2.207 1.803 �0.80921:00 9555.6 0.943 �2.951 0.177 �0.526 0.36221:30 9136.8 �1.29 �5.028 �2.8 �1.159 �3.61422:00 9061.5 3.125 �0.754 1.18 1.948 �0.82322:30 8766.8 5.081 �2.134 �0.865 2.479 �2.72823:00 8532.2 0.658 2.706 �0.868 0.629 �0.32623:30 8263.4 1.691 �1.833 2.062 �0.58 �2.101MAPE (average error %) 2.719% 1.836% 1.810% 1.669% 1.603%


(4) Method IV (RBFNN associated with ANFIS method with his-torical demand data and price change).

Tables 6 shows the comparative results related to case 5. Asshown in this table, the MAPE of the proposed method is 1.603%,which has a significant reduction in comparison with methods Ito IV which they are 2.719%, 1.836%, 1.810% and 1.669%, respec-tively. Therefore, it can be concluded that the results of proposed

method are more accurate forecast in comparison with the resultsof the methods I to IV.

5. Conclusion

In this paper, a new algorithm was presented for short-timeload forecasting. This algorithm consists of two steps. The first step


uses the ANN and the WT in its structure. To increase the accuracyof the forecasting, the Dmeyer mother wavelet is used in this pa-per. In the second step of the proposed algorithm, the ANFIS ap-proach, similar-hour load, and the WT were used to improve theprimary forecast. Under these conditions, the output of the ANFISshows the complete forecast results. In these conditions, if thetemperature changes a little (or large) in test day temperature, pri-mary load forecasting has small (or high) error. The simulation re-sults show that the second step of the proposed two-stepforecasting method improves primary forecasting results for bothlittle and large changes in test day temperature. Furthermore, itcan be concluded that when the weather conditions are effectivelychanged (in comparison with those of the previous week), primaryload forecasting error is increased. But, proposed similar-hourmethod increases the forecasting accuracy. The results of the pro-posed forecasting method in comparison with those of four differ-ent methods are represented the capability of the proposedforecasting method.

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a hybrid intelligent algorithm based short-term load forecasting approach

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