Research ArticleA Novel Hybrid Method for Short-Term Power Load Forecasting

Huang Yuansheng Huang Shenhai and Song Jiayin

Department of Economic Management North China Electric Power University Baoding China

Correspondence should be addressed to Huang Shenhai hshncepu163com

Received 20 March 2016 Revised 21 June 2016 Accepted 11 July 2016

Academic Editor Jit S Mandeep

Copyright copy 2016 Huang Yuansheng et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Influenced bymany uncertain and random factors nonstationary nonlinearity and time-variety appear in power load series whichis difficult to forecast accurately Aiming at locating these issues of power load forecasting an innovative hybridmethod is proposedto forecast power load in this paper Firstly ensemble empirical mode decomposition (EEMD) is used to decompose the powerload series into a series of independent intrinsic mode functions (IMFs) and a residual term Secondly genetic algorithm (GA) isthen applied to determine the best weights of each IMF and the residual term named ensemble empirical mode decompositionbased on weight (WEEMD)Thirdly least square support vector machine (LSSVM) and nonparametric generalized autoregressiveconditional heteroscedasticity (NPGARCH) are employed to forecast the subseries respectively based on the characteristics ofpower load series Finally the forecasted power load of each component is summed as the final forecasted result of power loadCompared with other methods the forecasting results of this proposed model applied to the electricity market of Pennsylvania-New Jersey-Maryland (PJM) indicate that the proposed model outperforms other models

1 Introduction

In the operation of power system power load forecasting isnot only an important part of power system planning but alsoone of the most influential factors for the improvement ofsocial economy developing which has a significant impacton generation transmission and distribution Therefore itis crucial to design an efficient method to forecasting powerload accurately by improving both economic efficiency andpower supply quality and enhancing reliability of powersystem operation [1 2]

However the power load forecasting results are influ-enced by many uncertain random factors including changesof nature environment and electricity price and factorsinfluencing power load [3 4] causing the complex volatilitycharacteristics of power load which lead the time-series ofpower load series to inherent nonstationary and discrete inpractice even in the short-term dynamics Notably due tothe factors influencing the short-term power load previousstudies [5ndash7] mainly focus on the establishment of scientificforecastingmethod to enhance the adaptability for thesemul-tifactors Therefore the time-varying components of powerload are hardly separated to extract the information in them

Under this circumstance a novel hybrid method forpower load forecasting has been proposed in this paper Basedon artificial algorithm the advantages of econometric mod-els and signal processing are emphasized by this researchSpecifically this hybrid method for load power forecastingincludes ensemble empirical mode decomposition based onvariable weights (WEEMD) genetic algorithm (GA) leastsquare support vector machine (LSSVM) and nonparamet-ric generalized autoregressive conditional heteroscedasticity(NPGARCH) Notably in order to test the validity andfeasibility of the model amount of historical data of powerload in American Electric Power (AEP) has been adopted toapply this new hybridmethod and compare it with previouslywell-knownmethods for the power load forecasting accuracyResults indicate that this hybrid method outperforms thecompared methods with the forecasting accuracy

The rest of the paper is organized as follows Section 2summaries previous literature over methodology for powerload forecasting Section 3 briefly describes EEMD GAnonparametric GARCH and LSSVM and proposes theimproved WEEMD as well as presenting the procedure ofthe newly hybrid method Section 4 evaluates the forecastingaccuracy and tests the robustness of the proposedmethod by

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2016 Article ID 2165324 10 pageshttpdxdoiorg10115520162165324

2 Journal of Electrical and Computer Engineering

comparing with other forecasting methods Section 5 drawsconclusions

2 Related Literature Review

Current power load forecasting methods can be broadlydivided into two categories statistical analysis method [8ndash11] and artificial algorithm [12ndash15] The traditional statisticalanalysis methods are always under the framework of time-series analysis [16] By usingARMAandARMAwithweatherinputs Bolzern and Fronza [8] propose two short-term pre-dictors of the winter power load Respectively the power loadforecast results are satisfied with both predictors and similarin these two cases In order to model certain behavior ofenergy consumption Wang [9] employs conventional fuzzysystems based on the integrated algorithm and results showthat the monthly electricity consumption of Iran is accuratelyforecasted with this proposed method In [10] consideringthe nonlinearity and volatility of power load series analyzingthe threshold characteristics Wang et al adopt a noveldouble-threshold generalized autoregressive conditional het-eroscedasticity (DT-GARCH) model for short-term powerload forecasting To forecast the power load efficiently andscientifically Liu [11] synthesizes the time-series modelingwith the regressionmodeling According to the residual errorfrom regression forecasting the accuracy of power load fore-casting can be improved by correcting the error of GARCHmodel

As the artificial algorithm applied in the power load fore-casting is prevalent in recent decades there are plenty ofresearches related to that Taking the characteristics of ran-domness tendency and periodicity of short-term power loadinto account Sun and Ye [12] propose a model based onLSSVM and fruit fly algorithm (FOA) for short-term loadforecasting In order to reduce the nonlinear power loadsequence and improve the accuracy of forecasting resultHu and Chang [13] decompose the time-series into severalcomponents by local wave method and use optimal param-eters to establish the DEMD-LSSVM model for componentforecasting Lauret et al [14] utilize Bayesian techniques todesign an optimal neural network (NN) based model forpower load forecasting where Bayesian technique offers greatadvantages on traditional neural network learning methodsBased on an artificial neural network (ANN) Shao et al [15]proposed an approach combined with a fuzzy system forshort-term power load forecastingThe load error is obtainedfrom the historical information and past forecasted loaderrors are caused by fuzzy systems and the final forecastedload can be obtained by adding the load error to preliminaryload forecasted by ANN In [16] to improve the forecastingperformance by searching a suitable parameters combinationthe paper presents an SVR-based electric load forecastingmodel by applying a novel algorithm named chaotic antswarm optimization (CAS) Combined with the chaoticbehavior of single ant and self-organization behavior of antcolony in the foraging process the CAS is proposed to over-come premature local optimum In [17] a combination of thewavelet transform (WT) and gray model is proposed for

short-termpower load forecasting which is improved by par-ticle swarm optimization (PSO) With this proposed methodtaking mean temperature mean relative humidity meanwind speed and previous days load data into considerationand eliminating the high frequency of historical data built bythe WT the accuracy can be largely improved

With the improvement of the forecasting accuracy Ghe-lardoni et al [18] decompose time power load series withempirical mode decomposition (EMD) into two sets ofcomponents respectively describing the trend of energyconsumption values LSSVM is built to forecast these twocomponents The hybrid method proposed in [19] enhancesthe capability for forecasting This proposed method is mod-eled based on supporting vector regression (SVR) EMD andregression (AR) which can simultaneously provide forecast-ing with high accuracy and interpretability In order to solvethe problem of mode mixing and high frequency randomcomponents Liu et al [19] proposed an optimized methodbased on ensemble empirical mode decomposition (EEMD)and subsection particle swarm optimization (SS-PSO) Byextracting and reconstructing intrinsicmode function (IMF)the power load series movement is well forecasted In [20]the proposed method based on complementary ensembleempirical mode decomposition (CEEMD) fuzzy entropy andecho state network (ESN) with leaky integrator neurons(LiESN) enhances the forecasting accuracy of power load

In summary although the characteristics of power loadseries are complex such as being richmultidimensional non-linear time-varying and nonstationary the previous litera-ture has accumulated a great deal of experience about powerload forecasting Particularly the forecasting methods havebeen constantly proposed and the forecasting performancehas been continuously improved all of which provide asignificant foundation for the present study However we canstill find that the method of power load forecasting can beproblematical based on the analysis and research of previousliterature while there are also some uncertain factors ofpower load forecasting For example both EEMD and EMDdecompose the original power load series into several compo-nents and other forecasting methods are directly built basedon the decomposed components in most of the literaturewithout analysis of the weights of each component in originalpower load series Besides as the power load is affected bygreat uncertainties the power load series movement is diffi-cult to capture and there will be nonlinear and time-varyingfeature in power load series caused by no matter the externalfactors or the internal factors But the existing methods forpower load forecasting are usually not effective to separatenonlinear and time-varying components of power load andunable to extract their inherent moving mechanisms whichconsequently affects the forecasting accuracy

Based on the potential faultiness mentioned above ahybrid method for power load forecasting is developed andapplied to PJM by this study Specially the ensemble empiri-cal mode decomposition (EEMD) model decomposes powerload into series of intrinsic mode functions (IMFs) and resi-dual And genetic algorithm (GA) is used to determine theweights of each component which is based on deviation

Journal of Electrical and Computer Engineering 3

between fitted values and actual values For weighted compo-nents with the heteroscedasticity character GARCH is morefavorable for forecasting However the LSSVM method isused in the forecasting of the subseries with the character-istics of nonstationary and nonlinearity subseries On theone hand power load forecasting can be more convenientand accurate after the decomposition of the power loadcomponents because of the separation of other influentialfactors On the other hand with other neural networkmodels which cannot fundamentally solve problems of thelocal minimum the difficulty in determination of hiddenlayer and the slow training rate the LSSVM can not only getover these disadvantages but also can improve the accuracyof forecasting Therefore based on the components weightedby GAmethod LSSVMmethod can be more in line with thepower load study in this research

3 Power Load Forecasting Methodology

31 Genetic Algorithms (GA) Genetic algorithms code thecandidate solutions of an optimization algorithmas a string ofcharacters which are usually binary digits [21] In accordancewith the terminology that is borrowed from the field ofgenetics this bit string is usually named as chromosomeThesolution represented by its chromosome is considered as anindividual The algorithm starts with the initial generationof the population The fitness of the individuals within thepopulation is assessed and new individuals are generatedfor the further generation A number of genetic operatorscontaining selector operator crossover and mutation areavailable for this purpose By a number of fixed generationswhich is the termination condition the best individual willbe obtained with the max fitness which is the global optimalsolution of the issues

32 The WEEMD Method EMD an effective method forsignal processing is gradually replaced by EEMD whichovercomes themixingmodel problem [22ndash25]The essence ofEEMD is to decompose a time-series into a set of independentintrinsic mode functions (IMFs) and the residue obtained byadding a random Gaussian white noise sequence which isdifferent from EMD While the time-series is decomposedby EEMD the IMF is a function satisfying the following twoconditions

(1) In the whole data set the number of extreme and thenumber of zero crossings must either differ or differat most by one

(2) At any point mean values of the envelope defined byboth the local maxima and minima are zero

For an arbitrary time-series 119883(119905) procedures of EEMDmethod can be described as follows

(1) Add the white noise to power load series 119883(119905) with119894 = 1 and set the number of ensemble (119872)

119883119894 (119905) = 119883 (119905) + 119899119894 (119905) (1)

where 119899119894(119905) denotes the 119894th added white noises series

and 119883119894(119905) represents the noise-added power load of

the 119894th trial

(2) Decompose the noise-added series 119883119894(119905) into 119869 IMFs

119888119894119895(119895 = 1 2 119869) by using EMD where 119888

119894119895is the 119895th

IMF of the 119894th trial and 119869 is the number of IMFs

(3) Repeat Steps (1) and (2) until 119894 = 119872

(4) Calculate the ensemble mean 119888119895(119905) of119873 trails for each

IMF then 119888119895(119905) = (1119872)sum

119872

119894=1119888119894119895(119905) where 119888

119895(119905) (119895 =

1 119869) is the 119895th IMF component by using EEMD

In this paper weights assignment for each IMF isproposed based on EEMD and the rationality of this weightsassignment proved by this study is as follows for an arbitrarytime-series 119883(119905) setting any value of each IMF satisfies thefunction 119891(119905) and by the conditions mentioned above thenumber of extreme and zero crossings of each IMF is 119902 whichare obtained by the following equations

119891119895 (119905) = 0

119889119891119895 (119905)

119889119905= 0

(2)

Assigning weight to each IMF then

120596119895119891119895 (119905) = 0

120596119895119889119891119895 (119905)

119889119905= 0

(3)

where 120596119895 a constant is the weights of 119895th IMF

Obviously the weights have no effect on the values whichsatisfies the first conditions Specially mean values of theenvelope will not be changed by weight assignment and thededuction can be expressed as follows

119898max + 119898min = 0 (4)

Assigning weight to it

120596119895(119898max + 119898min) = 0 (5)

where 119898max is the mean value of the envelope of the localmaxima and 119898min is the mean values of the envelope of thelocal minima

GA method is built to determine the weights of eachIMF and individuals119882 = (120596

1 1205962 120596

119869) are first randomly

generated as initial population 1198820 By using the genetic

operators selector operator crossover andmutation the bestindividual 119882 = (120596

1 1205962 120596

119869) can be obtained Specially

4 Journal of Electrical and Computer Engineering

in the selector operator the fitness function is defined asfollows

120576119896 (119905) =

1003816100381610038161003816119882119896 sdot 119862 minus 119883 (119905)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1205961198961 1205961198962 120596

119896119869 120596119903) sdot(

1198881

1198882

119888119869

)minus119883(119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816

119869

sum

119895=1

120596119896119895119888119895 (119905) minus 119883 (119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119896 = 1 2 119898)

(6)

where 120576119896(119905) is error and119898 is the size of initial population

As the GA operator is designed to maximize the fitnessfunction the above minimization problem can be solved byusing the following transformation

119891119896=

1

120576119896 (119905)

(7)

where 119891119896is the fitness of 119896th individual

The election probability of each individual is 119901119896

119901119896=

119891119896

sum119898

119896=1119891119896

(8)

As described above the process of EEMD is indeed likesifting which has an effect to eliminate riding waves TheIMFs are extracted from the power load series and containldquoinformationrdquo about the time-series This paper uses weightsas the contribution of IMF to 119883(119905) the greater the weight isthe larger the amount of ldquoinformationrdquo IMF contains

33 The Nonparametric GARCH (1 1) Method Nonparamet-ric GARCH (1 1) model for the error fluctuation [26] whichrequires less assumptions is defined as

119905= 120590119905120593119905

1205902

119905= 119892 (120590

2

119905minus1 119905minus1)

(9)

where 119905is estimation of random processes 120593

119905is specific

transformation sequence of zero mean and unit variance 1205902119905

is the conditional variance 120590119905is the volatility

Nonparametric model can be used to estimate the condi-tional variance and (9) can be rewritten as follows

2

119905= 119892 (120590

2

119905minus1 119905minus1) + 119881119905

119881119905= 119892 (120590

2

119905minus1 119905minus1) (1205932

119905minus 1)

(10)

where 119881119905is the martingale difference sequence

According to the equations above the function 2

119905is

regressed between lagged variables 119905minus1

and 1205902119905minus1119892 can be esti-

mated by using nonparametric smoothing method and theautoregression function The calculation of nonparametricGARCH [27ndash30] is as follows

(1) Using parameters GARCH (1 1) model fits the volatil-ity 1199050 with estimation using maximum likelihood

estimate parameter being employed as parameterestimation where 119886 = 1

(2) 1205902119905119898

is as weight and 2119905is estimated by using 119911

119905minus1and

2

119905minus1119898minus1 Smooth nonparametric estimation method

is applied to obtain the estimation 119886of autoregres-

sion function 119892(3) Standard deviation is obtained by using

2

119905119886= 119892119886(2

119905minus1119898minus1 119905minus1) 2 le 119905 le 119899 (11)

(4) Increment119898 and return to step (2) if 119886 gt 119860 where119872is a prespecified maximum number of iterations

The nonparametric estimation is an improvement overthe parametric GARCH estimation of volatility By means ofstep (1)ndash(4) continuous iteration there is little to pick andchoose between volatility estimates 2

119905119886for various values

of 119886 However the algorithm can often be improved byaveraging over the final 119896 estimates to obtain

119905lowast

=

119860

sum

119886=119860minus119896+1

119905119886

119896 (12)

34The LSSVMMethod LSSVM is proposed as an improvedalgorithm based on support vector machine (SVM) [31ndash35]with the given training data set 119911

119894 119910119894 (119894 = 1 2 119873) with

the input 119911119894isin 119877119899 and the output 119910

119894isin 119877119899 The following

regression model is constructed by using nonlinear mappingfunction 120601(119911

119894)

119891 (119911119894) = 119882

119879120601 (119911119894) + 119887 (13)

With the given training data set 119911119894 119910119894 (119894 = 1 2 119873)

the optimization problem of LSSVM is defined as follows

min 119869 (119882 120585119894) =

1

2119882119879119882+

119862

2

119872

sum

119894=1

120585119894

st 119910119894= 119882119879120593 (119911119894) + 119887 + 120585

119894 119894 = 1 2 119899

(14)

According to the Kuhn-Tucker conditions the LSSVMregression model can be expressed as

119910 (119911119894) =

119899

sum

119894=1

119886119894119896 (119911 119911

119894) + 119887 (15)

119896(119911 119911119894) is the kernel function which can map variables

to the feature space and avoid high dimensional complexdifficulties This paper applies RBF as the kernel functionwhich is defined as

119896 (119909 119909119894) = exp[minus

1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817

2

(21205902)] (16)

where 120590 is the kernel function parameter The LSSVMmethod can be used by establishing the parameters 120590 and 119888

Journal of Electrical and Computer Engineering 5

Power load series

EEMD

WIMF(1) WIMF(2) WIMF(i) WIMF(n)

Yes NoARCH effect

Nonparametric GARCH LSSVM

Sum

Forecasted results

GA

R(n)

Figure 1 The procedures of power load forecasting using the novelhybrid model

35 The Hybrid Method for Power Load Forecasting Con-sidering the complex volatility characteristics of power loadseries much more scientific forecasting models are requiredto address the nonlinearity and time variations Under thiscircumstance the WEEMD based on EEMD is proposedto extract different components of power load series andassign weights to each component (IMF) according to itsstandard deviation where the LSSVM is presented to fore-cast the subseries with the characteristics of nonstationaryand nonlinearity and the nonparametric GARCH (1 1) isused to forecast the subseries with heteroscedasticity Withthis hybrid model the power load movement can be wellforecasted The procedures of the improved model can bedescribed as Figure 1 and the concrete steps are given asfollows

(1) The power load series is first decomposed by EEMDinto 119899 intrinsic mode functions (IMFs) and oneresidual series and then

119883 (119905) =

119869minus1

sum

119895=1

119862119895 (119905) + 119877 (119905) (17)

where119883(119905) is the original power load series and 119862119895(119905)

and 119877(119905) are decomposed from the series

(2) Each IMF series and the residual series are assignedto be weighted by GA which can be represented asfollows

119883(119905) =

119869minus1

sum

119895=1

120596119895119862119895 (119905) + 120596119903119877 (119905) (18)

(3) To verify the existence of ARCH effect and het-eroscedasticity ARCH-LM is used to test the sub-series which is related to the stochastic error and then

119883 (119905) =

119898

sum

119895=1

120596119895119873119895 (119905) +

119869

sum

119894=119898+1

120596119894119878119894 (119905) (19)

where 119873119895(119905) is the subseries with heteroscedastic-

ity and 119878119894(119905) represents the subseries without het-

eroscedasticity(4) The LSSVM is built to forecast the future values of

119878119894(119905) meanwhile the nonparametric GARCH model

is presented to forecast the future values of119873119895(119905) and

their forecasted results are 119894(119905) and

119895(119905) respec-

tively which can be represented as follows

(119905) =

119898

sum

119895=1

120596119895119895 (119905) +

119869

sum

119894=119898+1

120596119894119894 (119905) (20)

where (119905) is the forecasted value of power loadseries

To examine the proposed hybrid method performancethree criteriamdashmean absolute error (MAE) mean absolutepercentage error (MAPE) and root mean square error(RMSE)mdashare represented as follows

MAE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

MAPE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

119874119905

RMSE = radic 1

119873

119873

sum

119905=1

(119874119905minus 119905)2

(21)

where 119874119905and

119905represent the real and forecasted values

respectively and 119873 is the number of the forecasting perfor-mance evaluations

4 Case Studies

Pennsylvania-New Jersey-Maryland (PJM) reliable opera-tions and efficient wholesale market is a fair and efficientelectricity market which provides information on electricalfield For our simulation the short-term load power datafrom American Electric Power (AEP) are obtained hourlyfrom 152015 to 1082015 Data points from 152015 to3172015 are selected as training samples and the data from182015 to 1082015 are selected as the test sample Figure 2presents the power load of the training sample which showsthat the power load severely fluctuates periodically

41 Data Processing for IMF According to procedure pro-posed above first the original power load series is decom-posed by the EEMD into seven independent intrinsic modefunctions and one residual which are shown in Figure 3

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

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International Journal of

2 Journal of Electrical and Computer Engineering

comparing with other forecasting methods Section 5 drawsconclusions

2 Related Literature Review

Current power load forecasting methods can be broadlydivided into two categories statistical analysis method [8ndash11] and artificial algorithm [12ndash15] The traditional statisticalanalysis methods are always under the framework of time-series analysis [16] By usingARMAandARMAwithweatherinputs Bolzern and Fronza [8] propose two short-term pre-dictors of the winter power load Respectively the power loadforecast results are satisfied with both predictors and similarin these two cases In order to model certain behavior ofenergy consumption Wang [9] employs conventional fuzzysystems based on the integrated algorithm and results showthat the monthly electricity consumption of Iran is accuratelyforecasted with this proposed method In [10] consideringthe nonlinearity and volatility of power load series analyzingthe threshold characteristics Wang et al adopt a noveldouble-threshold generalized autoregressive conditional het-eroscedasticity (DT-GARCH) model for short-term powerload forecasting To forecast the power load efficiently andscientifically Liu [11] synthesizes the time-series modelingwith the regressionmodeling According to the residual errorfrom regression forecasting the accuracy of power load fore-casting can be improved by correcting the error of GARCHmodel

As the artificial algorithm applied in the power load fore-casting is prevalent in recent decades there are plenty ofresearches related to that Taking the characteristics of ran-domness tendency and periodicity of short-term power loadinto account Sun and Ye [12] propose a model based onLSSVM and fruit fly algorithm (FOA) for short-term loadforecasting In order to reduce the nonlinear power loadsequence and improve the accuracy of forecasting resultHu and Chang [13] decompose the time-series into severalcomponents by local wave method and use optimal param-eters to establish the DEMD-LSSVM model for componentforecasting Lauret et al [14] utilize Bayesian techniques todesign an optimal neural network (NN) based model forpower load forecasting where Bayesian technique offers greatadvantages on traditional neural network learning methodsBased on an artificial neural network (ANN) Shao et al [15]proposed an approach combined with a fuzzy system forshort-term power load forecastingThe load error is obtainedfrom the historical information and past forecasted loaderrors are caused by fuzzy systems and the final forecastedload can be obtained by adding the load error to preliminaryload forecasted by ANN In [16] to improve the forecastingperformance by searching a suitable parameters combinationthe paper presents an SVR-based electric load forecastingmodel by applying a novel algorithm named chaotic antswarm optimization (CAS) Combined with the chaoticbehavior of single ant and self-organization behavior of antcolony in the foraging process the CAS is proposed to over-come premature local optimum In [17] a combination of thewavelet transform (WT) and gray model is proposed for

short-termpower load forecasting which is improved by par-ticle swarm optimization (PSO) With this proposed methodtaking mean temperature mean relative humidity meanwind speed and previous days load data into considerationand eliminating the high frequency of historical data built bythe WT the accuracy can be largely improved

With the improvement of the forecasting accuracy Ghe-lardoni et al [18] decompose time power load series withempirical mode decomposition (EMD) into two sets ofcomponents respectively describing the trend of energyconsumption values LSSVM is built to forecast these twocomponents The hybrid method proposed in [19] enhancesthe capability for forecasting This proposed method is mod-eled based on supporting vector regression (SVR) EMD andregression (AR) which can simultaneously provide forecast-ing with high accuracy and interpretability In order to solvethe problem of mode mixing and high frequency randomcomponents Liu et al [19] proposed an optimized methodbased on ensemble empirical mode decomposition (EEMD)and subsection particle swarm optimization (SS-PSO) Byextracting and reconstructing intrinsicmode function (IMF)the power load series movement is well forecasted In [20]the proposed method based on complementary ensembleempirical mode decomposition (CEEMD) fuzzy entropy andecho state network (ESN) with leaky integrator neurons(LiESN) enhances the forecasting accuracy of power load

In summary although the characteristics of power loadseries are complex such as being richmultidimensional non-linear time-varying and nonstationary the previous litera-ture has accumulated a great deal of experience about powerload forecasting Particularly the forecasting methods havebeen constantly proposed and the forecasting performancehas been continuously improved all of which provide asignificant foundation for the present study However we canstill find that the method of power load forecasting can beproblematical based on the analysis and research of previousliterature while there are also some uncertain factors ofpower load forecasting For example both EEMD and EMDdecompose the original power load series into several compo-nents and other forecasting methods are directly built basedon the decomposed components in most of the literaturewithout analysis of the weights of each component in originalpower load series Besides as the power load is affected bygreat uncertainties the power load series movement is diffi-cult to capture and there will be nonlinear and time-varyingfeature in power load series caused by no matter the externalfactors or the internal factors But the existing methods forpower load forecasting are usually not effective to separatenonlinear and time-varying components of power load andunable to extract their inherent moving mechanisms whichconsequently affects the forecasting accuracy

Based on the potential faultiness mentioned above ahybrid method for power load forecasting is developed andapplied to PJM by this study Specially the ensemble empiri-cal mode decomposition (EEMD) model decomposes powerload into series of intrinsic mode functions (IMFs) and resi-dual And genetic algorithm (GA) is used to determine theweights of each component which is based on deviation

Journal of Electrical and Computer Engineering 3

between fitted values and actual values For weighted compo-nents with the heteroscedasticity character GARCH is morefavorable for forecasting However the LSSVM method isused in the forecasting of the subseries with the character-istics of nonstationary and nonlinearity subseries On theone hand power load forecasting can be more convenientand accurate after the decomposition of the power loadcomponents because of the separation of other influentialfactors On the other hand with other neural networkmodels which cannot fundamentally solve problems of thelocal minimum the difficulty in determination of hiddenlayer and the slow training rate the LSSVM can not only getover these disadvantages but also can improve the accuracyof forecasting Therefore based on the components weightedby GAmethod LSSVMmethod can be more in line with thepower load study in this research

3 Power Load Forecasting Methodology

31 Genetic Algorithms (GA) Genetic algorithms code thecandidate solutions of an optimization algorithmas a string ofcharacters which are usually binary digits [21] In accordancewith the terminology that is borrowed from the field ofgenetics this bit string is usually named as chromosomeThesolution represented by its chromosome is considered as anindividual The algorithm starts with the initial generationof the population The fitness of the individuals within thepopulation is assessed and new individuals are generatedfor the further generation A number of genetic operatorscontaining selector operator crossover and mutation areavailable for this purpose By a number of fixed generationswhich is the termination condition the best individual willbe obtained with the max fitness which is the global optimalsolution of the issues

32 The WEEMD Method EMD an effective method forsignal processing is gradually replaced by EEMD whichovercomes themixingmodel problem [22ndash25]The essence ofEEMD is to decompose a time-series into a set of independentintrinsic mode functions (IMFs) and the residue obtained byadding a random Gaussian white noise sequence which isdifferent from EMD While the time-series is decomposedby EEMD the IMF is a function satisfying the following twoconditions

(1) In the whole data set the number of extreme and thenumber of zero crossings must either differ or differat most by one

(2) At any point mean values of the envelope defined byboth the local maxima and minima are zero

For an arbitrary time-series 119883(119905) procedures of EEMDmethod can be described as follows

(1) Add the white noise to power load series 119883(119905) with119894 = 1 and set the number of ensemble (119872)

119883119894 (119905) = 119883 (119905) + 119899119894 (119905) (1)

where 119899119894(119905) denotes the 119894th added white noises series

and 119883119894(119905) represents the noise-added power load of

the 119894th trial

(2) Decompose the noise-added series 119883119894(119905) into 119869 IMFs

119888119894119895(119895 = 1 2 119869) by using EMD where 119888

119894119895is the 119895th

IMF of the 119894th trial and 119869 is the number of IMFs

(3) Repeat Steps (1) and (2) until 119894 = 119872

(4) Calculate the ensemble mean 119888119895(119905) of119873 trails for each

IMF then 119888119895(119905) = (1119872)sum

119872

119894=1119888119894119895(119905) where 119888

119895(119905) (119895 =

1 119869) is the 119895th IMF component by using EEMD

In this paper weights assignment for each IMF isproposed based on EEMD and the rationality of this weightsassignment proved by this study is as follows for an arbitrarytime-series 119883(119905) setting any value of each IMF satisfies thefunction 119891(119905) and by the conditions mentioned above thenumber of extreme and zero crossings of each IMF is 119902 whichare obtained by the following equations

119891119895 (119905) = 0

119889119891119895 (119905)

119889119905= 0

(2)

Assigning weight to each IMF then

120596119895119891119895 (119905) = 0

120596119895119889119891119895 (119905)

119889119905= 0

(3)

where 120596119895 a constant is the weights of 119895th IMF

Obviously the weights have no effect on the values whichsatisfies the first conditions Specially mean values of theenvelope will not be changed by weight assignment and thededuction can be expressed as follows

119898max + 119898min = 0 (4)

Assigning weight to it

120596119895(119898max + 119898min) = 0 (5)

where 119898max is the mean value of the envelope of the localmaxima and 119898min is the mean values of the envelope of thelocal minima

GA method is built to determine the weights of eachIMF and individuals119882 = (120596

1 1205962 120596

119869) are first randomly

generated as initial population 1198820 By using the genetic

operators selector operator crossover andmutation the bestindividual 119882 = (120596

1 1205962 120596

119869) can be obtained Specially

4 Journal of Electrical and Computer Engineering

in the selector operator the fitness function is defined asfollows

120576119896 (119905) =

1003816100381610038161003816119882119896 sdot 119862 minus 119883 (119905)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1205961198961 1205961198962 120596

119896119869 120596119903) sdot(

1198881

1198882

119888119869

)minus119883(119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816

119869

sum

119895=1

120596119896119895119888119895 (119905) minus 119883 (119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119896 = 1 2 119898)

(6)

where 120576119896(119905) is error and119898 is the size of initial population

As the GA operator is designed to maximize the fitnessfunction the above minimization problem can be solved byusing the following transformation

119891119896=

1

120576119896 (119905)

(7)

where 119891119896is the fitness of 119896th individual

The election probability of each individual is 119901119896

119901119896=

119891119896

sum119898

119896=1119891119896

(8)

As described above the process of EEMD is indeed likesifting which has an effect to eliminate riding waves TheIMFs are extracted from the power load series and containldquoinformationrdquo about the time-series This paper uses weightsas the contribution of IMF to 119883(119905) the greater the weight isthe larger the amount of ldquoinformationrdquo IMF contains

33 The Nonparametric GARCH (1 1) Method Nonparamet-ric GARCH (1 1) model for the error fluctuation [26] whichrequires less assumptions is defined as

119905= 120590119905120593119905

1205902

119905= 119892 (120590

2

119905minus1 119905minus1)

(9)

where 119905is estimation of random processes 120593

119905is specific

transformation sequence of zero mean and unit variance 1205902119905

is the conditional variance 120590119905is the volatility

Nonparametric model can be used to estimate the condi-tional variance and (9) can be rewritten as follows

2

119905= 119892 (120590

2

119905minus1 119905minus1) + 119881119905

119881119905= 119892 (120590

2

119905minus1 119905minus1) (1205932

119905minus 1)

(10)

where 119881119905is the martingale difference sequence

According to the equations above the function 2

119905is

regressed between lagged variables 119905minus1

and 1205902119905minus1119892 can be esti-

mated by using nonparametric smoothing method and theautoregression function The calculation of nonparametricGARCH [27ndash30] is as follows

(1) Using parameters GARCH (1 1) model fits the volatil-ity 1199050 with estimation using maximum likelihood

estimate parameter being employed as parameterestimation where 119886 = 1

(2) 1205902119905119898

is as weight and 2119905is estimated by using 119911

119905minus1and

2

119905minus1119898minus1 Smooth nonparametric estimation method

is applied to obtain the estimation 119886of autoregres-

sion function 119892(3) Standard deviation is obtained by using

2

119905119886= 119892119886(2

119905minus1119898minus1 119905minus1) 2 le 119905 le 119899 (11)

(4) Increment119898 and return to step (2) if 119886 gt 119860 where119872is a prespecified maximum number of iterations

The nonparametric estimation is an improvement overthe parametric GARCH estimation of volatility By means ofstep (1)ndash(4) continuous iteration there is little to pick andchoose between volatility estimates 2

119905119886for various values

of 119886 However the algorithm can often be improved byaveraging over the final 119896 estimates to obtain

119905lowast

=

119860

sum

119886=119860minus119896+1

119905119886

119896 (12)

34The LSSVMMethod LSSVM is proposed as an improvedalgorithm based on support vector machine (SVM) [31ndash35]with the given training data set 119911

119894 119910119894 (119894 = 1 2 119873) with

the input 119911119894isin 119877119899 and the output 119910

119894isin 119877119899 The following

regression model is constructed by using nonlinear mappingfunction 120601(119911

119894)

119891 (119911119894) = 119882

119879120601 (119911119894) + 119887 (13)

With the given training data set 119911119894 119910119894 (119894 = 1 2 119873)

the optimization problem of LSSVM is defined as follows

min 119869 (119882 120585119894) =

1

2119882119879119882+

119862

2

119872

sum

119894=1

120585119894

st 119910119894= 119882119879120593 (119911119894) + 119887 + 120585

119894 119894 = 1 2 119899

(14)

According to the Kuhn-Tucker conditions the LSSVMregression model can be expressed as

119910 (119911119894) =

119899

sum

119894=1

119886119894119896 (119911 119911

119894) + 119887 (15)

119896(119911 119911119894) is the kernel function which can map variables

to the feature space and avoid high dimensional complexdifficulties This paper applies RBF as the kernel functionwhich is defined as

119896 (119909 119909119894) = exp[minus

1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817

2

(21205902)] (16)

where 120590 is the kernel function parameter The LSSVMmethod can be used by establishing the parameters 120590 and 119888

Journal of Electrical and Computer Engineering 5

Power load series

EEMD

WIMF(1) WIMF(2) WIMF(i) WIMF(n)

Yes NoARCH effect

Nonparametric GARCH LSSVM

Sum

Forecasted results

GA

R(n)

Figure 1 The procedures of power load forecasting using the novelhybrid model

35 The Hybrid Method for Power Load Forecasting Con-sidering the complex volatility characteristics of power loadseries much more scientific forecasting models are requiredto address the nonlinearity and time variations Under thiscircumstance the WEEMD based on EEMD is proposedto extract different components of power load series andassign weights to each component (IMF) according to itsstandard deviation where the LSSVM is presented to fore-cast the subseries with the characteristics of nonstationaryand nonlinearity and the nonparametric GARCH (1 1) isused to forecast the subseries with heteroscedasticity Withthis hybrid model the power load movement can be wellforecasted The procedures of the improved model can bedescribed as Figure 1 and the concrete steps are given asfollows

(1) The power load series is first decomposed by EEMDinto 119899 intrinsic mode functions (IMFs) and oneresidual series and then

119883 (119905) =

119869minus1

sum

119895=1

119862119895 (119905) + 119877 (119905) (17)

where119883(119905) is the original power load series and 119862119895(119905)

and 119877(119905) are decomposed from the series

(2) Each IMF series and the residual series are assignedto be weighted by GA which can be represented asfollows

119883(119905) =

119869minus1

sum

119895=1

120596119895119862119895 (119905) + 120596119903119877 (119905) (18)

(3) To verify the existence of ARCH effect and het-eroscedasticity ARCH-LM is used to test the sub-series which is related to the stochastic error and then

119883 (119905) =

119898

sum

119895=1

120596119895119873119895 (119905) +

119869

sum

119894=119898+1

120596119894119878119894 (119905) (19)

where 119873119895(119905) is the subseries with heteroscedastic-

ity and 119878119894(119905) represents the subseries without het-

eroscedasticity(4) The LSSVM is built to forecast the future values of

119878119894(119905) meanwhile the nonparametric GARCH model

is presented to forecast the future values of119873119895(119905) and

their forecasted results are 119894(119905) and

119895(119905) respec-

tively which can be represented as follows

(119905) =

119898

sum

119895=1

120596119895119895 (119905) +

119869

sum

119894=119898+1

120596119894119894 (119905) (20)

where (119905) is the forecasted value of power loadseries

To examine the proposed hybrid method performancethree criteriamdashmean absolute error (MAE) mean absolutepercentage error (MAPE) and root mean square error(RMSE)mdashare represented as follows

MAE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

MAPE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

119874119905

RMSE = radic 1

119873

119873

sum

119905=1

(119874119905minus 119905)2

(21)

where 119874119905and

119905represent the real and forecasted values

respectively and 119873 is the number of the forecasting perfor-mance evaluations

4 Case Studies

Pennsylvania-New Jersey-Maryland (PJM) reliable opera-tions and efficient wholesale market is a fair and efficientelectricity market which provides information on electricalfield For our simulation the short-term load power datafrom American Electric Power (AEP) are obtained hourlyfrom 152015 to 1082015 Data points from 152015 to3172015 are selected as training samples and the data from182015 to 1082015 are selected as the test sample Figure 2presents the power load of the training sample which showsthat the power load severely fluctuates periodically

41 Data Processing for IMF According to procedure pro-posed above first the original power load series is decom-posed by the EEMD into seven independent intrinsic modefunctions and one residual which are shown in Figure 3

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

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Journal of Electrical and Computer Engineering 3

between fitted values and actual values For weighted compo-nents with the heteroscedasticity character GARCH is morefavorable for forecasting However the LSSVM method isused in the forecasting of the subseries with the character-istics of nonstationary and nonlinearity subseries On theone hand power load forecasting can be more convenientand accurate after the decomposition of the power loadcomponents because of the separation of other influentialfactors On the other hand with other neural networkmodels which cannot fundamentally solve problems of thelocal minimum the difficulty in determination of hiddenlayer and the slow training rate the LSSVM can not only getover these disadvantages but also can improve the accuracyof forecasting Therefore based on the components weightedby GAmethod LSSVMmethod can be more in line with thepower load study in this research

3 Power Load Forecasting Methodology

31 Genetic Algorithms (GA) Genetic algorithms code thecandidate solutions of an optimization algorithmas a string ofcharacters which are usually binary digits [21] In accordancewith the terminology that is borrowed from the field ofgenetics this bit string is usually named as chromosomeThesolution represented by its chromosome is considered as anindividual The algorithm starts with the initial generationof the population The fitness of the individuals within thepopulation is assessed and new individuals are generatedfor the further generation A number of genetic operatorscontaining selector operator crossover and mutation areavailable for this purpose By a number of fixed generationswhich is the termination condition the best individual willbe obtained with the max fitness which is the global optimalsolution of the issues

32 The WEEMD Method EMD an effective method forsignal processing is gradually replaced by EEMD whichovercomes themixingmodel problem [22ndash25]The essence ofEEMD is to decompose a time-series into a set of independentintrinsic mode functions (IMFs) and the residue obtained byadding a random Gaussian white noise sequence which isdifferent from EMD While the time-series is decomposedby EEMD the IMF is a function satisfying the following twoconditions

(1) In the whole data set the number of extreme and thenumber of zero crossings must either differ or differat most by one

(2) At any point mean values of the envelope defined byboth the local maxima and minima are zero

For an arbitrary time-series 119883(119905) procedures of EEMDmethod can be described as follows

(1) Add the white noise to power load series 119883(119905) with119894 = 1 and set the number of ensemble (119872)

119883119894 (119905) = 119883 (119905) + 119899119894 (119905) (1)

where 119899119894(119905) denotes the 119894th added white noises series

and 119883119894(119905) represents the noise-added power load of

the 119894th trial

(2) Decompose the noise-added series 119883119894(119905) into 119869 IMFs

119888119894119895(119895 = 1 2 119869) by using EMD where 119888

119894119895is the 119895th

IMF of the 119894th trial and 119869 is the number of IMFs

(3) Repeat Steps (1) and (2) until 119894 = 119872

(4) Calculate the ensemble mean 119888119895(119905) of119873 trails for each

IMF then 119888119895(119905) = (1119872)sum

119872

119894=1119888119894119895(119905) where 119888

119895(119905) (119895 =

1 119869) is the 119895th IMF component by using EEMD

In this paper weights assignment for each IMF isproposed based on EEMD and the rationality of this weightsassignment proved by this study is as follows for an arbitrarytime-series 119883(119905) setting any value of each IMF satisfies thefunction 119891(119905) and by the conditions mentioned above thenumber of extreme and zero crossings of each IMF is 119902 whichare obtained by the following equations

119891119895 (119905) = 0

119889119891119895 (119905)

119889119905= 0

(2)

Assigning weight to each IMF then

120596119895119891119895 (119905) = 0

120596119895119889119891119895 (119905)

119889119905= 0

(3)

where 120596119895 a constant is the weights of 119895th IMF

Obviously the weights have no effect on the values whichsatisfies the first conditions Specially mean values of theenvelope will not be changed by weight assignment and thededuction can be expressed as follows

119898max + 119898min = 0 (4)

Assigning weight to it

120596119895(119898max + 119898min) = 0 (5)

where 119898max is the mean value of the envelope of the localmaxima and 119898min is the mean values of the envelope of thelocal minima

GA method is built to determine the weights of eachIMF and individuals119882 = (120596

1 1205962 120596

119869) are first randomly

generated as initial population 1198820 By using the genetic

operators selector operator crossover andmutation the bestindividual 119882 = (120596

1 1205962 120596

119869) can be obtained Specially

4 Journal of Electrical and Computer Engineering

in the selector operator the fitness function is defined asfollows

120576119896 (119905) =

1003816100381610038161003816119882119896 sdot 119862 minus 119883 (119905)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1205961198961 1205961198962 120596

119896119869 120596119903) sdot(

1198881

1198882

119888119869

)minus119883(119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816

119869

sum

119895=1

120596119896119895119888119895 (119905) minus 119883 (119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119896 = 1 2 119898)

(6)

where 120576119896(119905) is error and119898 is the size of initial population

As the GA operator is designed to maximize the fitnessfunction the above minimization problem can be solved byusing the following transformation

119891119896=

1

120576119896 (119905)

(7)

where 119891119896is the fitness of 119896th individual

The election probability of each individual is 119901119896

119901119896=

119891119896

sum119898

119896=1119891119896

(8)

As described above the process of EEMD is indeed likesifting which has an effect to eliminate riding waves TheIMFs are extracted from the power load series and containldquoinformationrdquo about the time-series This paper uses weightsas the contribution of IMF to 119883(119905) the greater the weight isthe larger the amount of ldquoinformationrdquo IMF contains

33 The Nonparametric GARCH (1 1) Method Nonparamet-ric GARCH (1 1) model for the error fluctuation [26] whichrequires less assumptions is defined as

119905= 120590119905120593119905

1205902

119905= 119892 (120590

2

119905minus1 119905minus1)

(9)

where 119905is estimation of random processes 120593

119905is specific

transformation sequence of zero mean and unit variance 1205902119905

is the conditional variance 120590119905is the volatility

Nonparametric model can be used to estimate the condi-tional variance and (9) can be rewritten as follows

2

119905= 119892 (120590

2

119905minus1 119905minus1) + 119881119905

119881119905= 119892 (120590

2

119905minus1 119905minus1) (1205932

119905minus 1)

(10)

where 119881119905is the martingale difference sequence

According to the equations above the function 2

119905is

regressed between lagged variables 119905minus1

and 1205902119905minus1119892 can be esti-

mated by using nonparametric smoothing method and theautoregression function The calculation of nonparametricGARCH [27ndash30] is as follows

(1) Using parameters GARCH (1 1) model fits the volatil-ity 1199050 with estimation using maximum likelihood

estimate parameter being employed as parameterestimation where 119886 = 1

(2) 1205902119905119898

is as weight and 2119905is estimated by using 119911

119905minus1and

2

119905minus1119898minus1 Smooth nonparametric estimation method

is applied to obtain the estimation 119886of autoregres-

sion function 119892(3) Standard deviation is obtained by using

2

119905119886= 119892119886(2

119905minus1119898minus1 119905minus1) 2 le 119905 le 119899 (11)

(4) Increment119898 and return to step (2) if 119886 gt 119860 where119872is a prespecified maximum number of iterations

The nonparametric estimation is an improvement overthe parametric GARCH estimation of volatility By means ofstep (1)ndash(4) continuous iteration there is little to pick andchoose between volatility estimates 2

119905119886for various values

of 119886 However the algorithm can often be improved byaveraging over the final 119896 estimates to obtain

119905lowast

=

119860

sum

119886=119860minus119896+1

119905119886

119896 (12)

34The LSSVMMethod LSSVM is proposed as an improvedalgorithm based on support vector machine (SVM) [31ndash35]with the given training data set 119911

119894 119910119894 (119894 = 1 2 119873) with

the input 119911119894isin 119877119899 and the output 119910

119894isin 119877119899 The following

regression model is constructed by using nonlinear mappingfunction 120601(119911

119894)

119891 (119911119894) = 119882

119879120601 (119911119894) + 119887 (13)

With the given training data set 119911119894 119910119894 (119894 = 1 2 119873)

the optimization problem of LSSVM is defined as follows

min 119869 (119882 120585119894) =

1

2119882119879119882+

119862

2

119872

sum

119894=1

120585119894

st 119910119894= 119882119879120593 (119911119894) + 119887 + 120585

119894 119894 = 1 2 119899

(14)

According to the Kuhn-Tucker conditions the LSSVMregression model can be expressed as

119910 (119911119894) =

119899

sum

119894=1

119886119894119896 (119911 119911

119894) + 119887 (15)

119896(119911 119911119894) is the kernel function which can map variables

to the feature space and avoid high dimensional complexdifficulties This paper applies RBF as the kernel functionwhich is defined as

119896 (119909 119909119894) = exp[minus

1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817

2

(21205902)] (16)

where 120590 is the kernel function parameter The LSSVMmethod can be used by establishing the parameters 120590 and 119888

Journal of Electrical and Computer Engineering 5

Power load series

EEMD

WIMF(1) WIMF(2) WIMF(i) WIMF(n)

Yes NoARCH effect

Nonparametric GARCH LSSVM

Sum

Forecasted results

GA

R(n)

Figure 1 The procedures of power load forecasting using the novelhybrid model

35 The Hybrid Method for Power Load Forecasting Con-sidering the complex volatility characteristics of power loadseries much more scientific forecasting models are requiredto address the nonlinearity and time variations Under thiscircumstance the WEEMD based on EEMD is proposedto extract different components of power load series andassign weights to each component (IMF) according to itsstandard deviation where the LSSVM is presented to fore-cast the subseries with the characteristics of nonstationaryand nonlinearity and the nonparametric GARCH (1 1) isused to forecast the subseries with heteroscedasticity Withthis hybrid model the power load movement can be wellforecasted The procedures of the improved model can bedescribed as Figure 1 and the concrete steps are given asfollows

(1) The power load series is first decomposed by EEMDinto 119899 intrinsic mode functions (IMFs) and oneresidual series and then

119883 (119905) =

119869minus1

sum

119895=1

119862119895 (119905) + 119877 (119905) (17)

where119883(119905) is the original power load series and 119862119895(119905)

and 119877(119905) are decomposed from the series

(2) Each IMF series and the residual series are assignedto be weighted by GA which can be represented asfollows

119883(119905) =

119869minus1

sum

119895=1

120596119895119862119895 (119905) + 120596119903119877 (119905) (18)

(3) To verify the existence of ARCH effect and het-eroscedasticity ARCH-LM is used to test the sub-series which is related to the stochastic error and then

119883 (119905) =

119898

sum

119895=1

120596119895119873119895 (119905) +

119869

sum

119894=119898+1

120596119894119878119894 (119905) (19)

where 119873119895(119905) is the subseries with heteroscedastic-

ity and 119878119894(119905) represents the subseries without het-

eroscedasticity(4) The LSSVM is built to forecast the future values of

119878119894(119905) meanwhile the nonparametric GARCH model

is presented to forecast the future values of119873119895(119905) and

their forecasted results are 119894(119905) and

119895(119905) respec-

tively which can be represented as follows

(119905) =

119898

sum

119895=1

120596119895119895 (119905) +

119869

sum

119894=119898+1

120596119894119894 (119905) (20)

where (119905) is the forecasted value of power loadseries

To examine the proposed hybrid method performancethree criteriamdashmean absolute error (MAE) mean absolutepercentage error (MAPE) and root mean square error(RMSE)mdashare represented as follows

MAE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

MAPE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

119874119905

RMSE = radic 1

119873

119873

sum

119905=1

(119874119905minus 119905)2

(21)

where 119874119905and

119905represent the real and forecasted values

respectively and 119873 is the number of the forecasting perfor-mance evaluations

4 Case Studies

Pennsylvania-New Jersey-Maryland (PJM) reliable opera-tions and efficient wholesale market is a fair and efficientelectricity market which provides information on electricalfield For our simulation the short-term load power datafrom American Electric Power (AEP) are obtained hourlyfrom 152015 to 1082015 Data points from 152015 to3172015 are selected as training samples and the data from182015 to 1082015 are selected as the test sample Figure 2presents the power load of the training sample which showsthat the power load severely fluctuates periodically

41 Data Processing for IMF According to procedure pro-posed above first the original power load series is decom-posed by the EEMD into seven independent intrinsic modefunctions and one residual which are shown in Figure 3

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

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International Journal of

4 Journal of Electrical and Computer Engineering

in the selector operator the fitness function is defined asfollows

120576119896 (119905) =

1003816100381610038161003816119882119896 sdot 119862 minus 119883 (119905)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1205961198961 1205961198962 120596

119896119869 120596119903) sdot(

1198881

1198882

119888119869

)minus119883(119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816100381610038161003816

119869

sum

119895=1

120596119896119895119888119895 (119905) minus 119883 (119905)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119896 = 1 2 119898)

(6)

where 120576119896(119905) is error and119898 is the size of initial population

As the GA operator is designed to maximize the fitnessfunction the above minimization problem can be solved byusing the following transformation

119891119896=

1

120576119896 (119905)

(7)

where 119891119896is the fitness of 119896th individual

The election probability of each individual is 119901119896

119901119896=

119891119896

sum119898

119896=1119891119896

(8)

As described above the process of EEMD is indeed likesifting which has an effect to eliminate riding waves TheIMFs are extracted from the power load series and containldquoinformationrdquo about the time-series This paper uses weightsas the contribution of IMF to 119883(119905) the greater the weight isthe larger the amount of ldquoinformationrdquo IMF contains

33 The Nonparametric GARCH (1 1) Method Nonparamet-ric GARCH (1 1) model for the error fluctuation [26] whichrequires less assumptions is defined as

119905= 120590119905120593119905

1205902

119905= 119892 (120590

2

119905minus1 119905minus1)

(9)

where 119905is estimation of random processes 120593

119905is specific

transformation sequence of zero mean and unit variance 1205902119905

is the conditional variance 120590119905is the volatility

Nonparametric model can be used to estimate the condi-tional variance and (9) can be rewritten as follows

2

119905= 119892 (120590

2

119905minus1 119905minus1) + 119881119905

119881119905= 119892 (120590

2

119905minus1 119905minus1) (1205932

119905minus 1)

(10)

where 119881119905is the martingale difference sequence

According to the equations above the function 2

119905is

regressed between lagged variables 119905minus1

and 1205902119905minus1119892 can be esti-

mated by using nonparametric smoothing method and theautoregression function The calculation of nonparametricGARCH [27ndash30] is as follows

(1) Using parameters GARCH (1 1) model fits the volatil-ity 1199050 with estimation using maximum likelihood

estimate parameter being employed as parameterestimation where 119886 = 1

(2) 1205902119905119898

is as weight and 2119905is estimated by using 119911

119905minus1and

2

119905minus1119898minus1 Smooth nonparametric estimation method

is applied to obtain the estimation 119886of autoregres-

sion function 119892(3) Standard deviation is obtained by using

2

119905119886= 119892119886(2

119905minus1119898minus1 119905minus1) 2 le 119905 le 119899 (11)

(4) Increment119898 and return to step (2) if 119886 gt 119860 where119872is a prespecified maximum number of iterations

The nonparametric estimation is an improvement overthe parametric GARCH estimation of volatility By means ofstep (1)ndash(4) continuous iteration there is little to pick andchoose between volatility estimates 2

119905119886for various values

of 119886 However the algorithm can often be improved byaveraging over the final 119896 estimates to obtain

119905lowast

=

119860

sum

119886=119860minus119896+1

119905119886

119896 (12)

34The LSSVMMethod LSSVM is proposed as an improvedalgorithm based on support vector machine (SVM) [31ndash35]with the given training data set 119911

119894 119910119894 (119894 = 1 2 119873) with

the input 119911119894isin 119877119899 and the output 119910

119894isin 119877119899 The following

regression model is constructed by using nonlinear mappingfunction 120601(119911

119894)

119891 (119911119894) = 119882

119879120601 (119911119894) + 119887 (13)

With the given training data set 119911119894 119910119894 (119894 = 1 2 119873)

the optimization problem of LSSVM is defined as follows

min 119869 (119882 120585119894) =

1

2119882119879119882+

119862

2

119872

sum

119894=1

120585119894

st 119910119894= 119882119879120593 (119911119894) + 119887 + 120585

119894 119894 = 1 2 119899

(14)

According to the Kuhn-Tucker conditions the LSSVMregression model can be expressed as

119910 (119911119894) =

119899

sum

119894=1

119886119894119896 (119911 119911

119894) + 119887 (15)

119896(119911 119911119894) is the kernel function which can map variables

to the feature space and avoid high dimensional complexdifficulties This paper applies RBF as the kernel functionwhich is defined as

119896 (119909 119909119894) = exp[minus

1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817

2

(21205902)] (16)

where 120590 is the kernel function parameter The LSSVMmethod can be used by establishing the parameters 120590 and 119888

Journal of Electrical and Computer Engineering 5

Power load series

EEMD

WIMF(1) WIMF(2) WIMF(i) WIMF(n)

Yes NoARCH effect

Nonparametric GARCH LSSVM

Sum

Forecasted results

GA

R(n)

Figure 1 The procedures of power load forecasting using the novelhybrid model

35 The Hybrid Method for Power Load Forecasting Con-sidering the complex volatility characteristics of power loadseries much more scientific forecasting models are requiredto address the nonlinearity and time variations Under thiscircumstance the WEEMD based on EEMD is proposedto extract different components of power load series andassign weights to each component (IMF) according to itsstandard deviation where the LSSVM is presented to fore-cast the subseries with the characteristics of nonstationaryand nonlinearity and the nonparametric GARCH (1 1) isused to forecast the subseries with heteroscedasticity Withthis hybrid model the power load movement can be wellforecasted The procedures of the improved model can bedescribed as Figure 1 and the concrete steps are given asfollows

(1) The power load series is first decomposed by EEMDinto 119899 intrinsic mode functions (IMFs) and oneresidual series and then

119883 (119905) =

119869minus1

sum

119895=1

119862119895 (119905) + 119877 (119905) (17)

where119883(119905) is the original power load series and 119862119895(119905)

and 119877(119905) are decomposed from the series

(2) Each IMF series and the residual series are assignedto be weighted by GA which can be represented asfollows

119883(119905) =

119869minus1

sum

119895=1

120596119895119862119895 (119905) + 120596119903119877 (119905) (18)

(3) To verify the existence of ARCH effect and het-eroscedasticity ARCH-LM is used to test the sub-series which is related to the stochastic error and then

119883 (119905) =

119898

sum

119895=1

120596119895119873119895 (119905) +

119869

sum

119894=119898+1

120596119894119878119894 (119905) (19)

where 119873119895(119905) is the subseries with heteroscedastic-

ity and 119878119894(119905) represents the subseries without het-

eroscedasticity(4) The LSSVM is built to forecast the future values of

119878119894(119905) meanwhile the nonparametric GARCH model

is presented to forecast the future values of119873119895(119905) and

their forecasted results are 119894(119905) and

119895(119905) respec-

tively which can be represented as follows

(119905) =

119898

sum

119895=1

120596119895119895 (119905) +

119869

sum

119894=119898+1

120596119894119894 (119905) (20)

where (119905) is the forecasted value of power loadseries

To examine the proposed hybrid method performancethree criteriamdashmean absolute error (MAE) mean absolutepercentage error (MAPE) and root mean square error(RMSE)mdashare represented as follows

MAE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

MAPE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

119874119905

RMSE = radic 1

119873

119873

sum

119905=1

(119874119905minus 119905)2

(21)

where 119874119905and

119905represent the real and forecasted values

respectively and 119873 is the number of the forecasting perfor-mance evaluations

4 Case Studies

Pennsylvania-New Jersey-Maryland (PJM) reliable opera-tions and efficient wholesale market is a fair and efficientelectricity market which provides information on electricalfield For our simulation the short-term load power datafrom American Electric Power (AEP) are obtained hourlyfrom 152015 to 1082015 Data points from 152015 to3172015 are selected as training samples and the data from182015 to 1082015 are selected as the test sample Figure 2presents the power load of the training sample which showsthat the power load severely fluctuates periodically

41 Data Processing for IMF According to procedure pro-posed above first the original power load series is decom-posed by the EEMD into seven independent intrinsic modefunctions and one residual which are shown in Figure 3

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

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International Journal of

Journal of Electrical and Computer Engineering 5

Power load series

EEMD

WIMF(1) WIMF(2) WIMF(i) WIMF(n)

Yes NoARCH effect

Nonparametric GARCH LSSVM

Sum

Forecasted results

GA

R(n)

Figure 1 The procedures of power load forecasting using the novelhybrid model

35 The Hybrid Method for Power Load Forecasting Con-sidering the complex volatility characteristics of power loadseries much more scientific forecasting models are requiredto address the nonlinearity and time variations Under thiscircumstance the WEEMD based on EEMD is proposedto extract different components of power load series andassign weights to each component (IMF) according to itsstandard deviation where the LSSVM is presented to fore-cast the subseries with the characteristics of nonstationaryand nonlinearity and the nonparametric GARCH (1 1) isused to forecast the subseries with heteroscedasticity Withthis hybrid model the power load movement can be wellforecasted The procedures of the improved model can bedescribed as Figure 1 and the concrete steps are given asfollows

(1) The power load series is first decomposed by EEMDinto 119899 intrinsic mode functions (IMFs) and oneresidual series and then

119883 (119905) =

119869minus1

sum

119895=1

119862119895 (119905) + 119877 (119905) (17)

where119883(119905) is the original power load series and 119862119895(119905)

and 119877(119905) are decomposed from the series

(2) Each IMF series and the residual series are assignedto be weighted by GA which can be represented asfollows

119883(119905) =

119869minus1

sum

119895=1

120596119895119862119895 (119905) + 120596119903119877 (119905) (18)

(3) To verify the existence of ARCH effect and het-eroscedasticity ARCH-LM is used to test the sub-series which is related to the stochastic error and then

119883 (119905) =

119898

sum

119895=1

120596119895119873119895 (119905) +

119869

sum

119894=119898+1

120596119894119878119894 (119905) (19)

where 119873119895(119905) is the subseries with heteroscedastic-

ity and 119878119894(119905) represents the subseries without het-

eroscedasticity(4) The LSSVM is built to forecast the future values of

119878119894(119905) meanwhile the nonparametric GARCH model

is presented to forecast the future values of119873119895(119905) and

their forecasted results are 119894(119905) and

119895(119905) respec-

tively which can be represented as follows

(119905) =

119898

sum

119895=1

120596119895119895 (119905) +

119869

sum

119894=119898+1

120596119894119894 (119905) (20)

where (119905) is the forecasted value of power loadseries

To examine the proposed hybrid method performancethree criteriamdashmean absolute error (MAE) mean absolutepercentage error (MAPE) and root mean square error(RMSE)mdashare represented as follows

MAE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

MAPE = 1

119873

119873

sum

119905=1

10038161003816100381610038161003816119874119905minus 119905

10038161003816100381610038161003816

119874119905

RMSE = radic 1

119873

119873

sum

119905=1

(119874119905minus 119905)2

(21)

where 119874119905and

119905represent the real and forecasted values

respectively and 119873 is the number of the forecasting perfor-mance evaluations

4 Case Studies

Pennsylvania-New Jersey-Maryland (PJM) reliable opera-tions and efficient wholesale market is a fair and efficientelectricity market which provides information on electricalfield For our simulation the short-term load power datafrom American Electric Power (AEP) are obtained hourlyfrom 152015 to 1082015 Data points from 152015 to3172015 are selected as training samples and the data from182015 to 1082015 are selected as the test sample Figure 2presents the power load of the training sample which showsthat the power load severely fluctuates periodically

41 Data Processing for IMF According to procedure pro-posed above first the original power load series is decom-posed by the EEMD into seven independent intrinsic modefunctions and one residual which are shown in Figure 3

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 Journal of Electrical and Computer Engineering

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Input signal22

2

18

16

14

12

1

08

times104

Pow

er lo

ad (M

W)

Times (h)

Figure 2 Power load changes from 152015 to 3172015

In order to assign weights for each IMF GA method isused to select the best individual In Figure 4 the results showthat the average fitness is 0545 while the algorithm iteratesto 745 times which do not change in later iterations andthis individual is the best one Besides the decompositionof the power load series with assigned weights is shown inFigure 5 Obviously the assigned weights will not change themovement of the power load series but the domainwhichwillbe significant to the predicted values

Considering the impact caused by the closer prices on thefurther data three training samples near the forecasting pointare selected as input variable

119883 = (

119909 (119889 119905 minus 3)

119909 (119889 119905 minus 2)

119909 (119889 119905 minus 1)

) (22)

where 119909(119889 119905) is the price on 119889th at time 119905th Actually thepower load series is generally nonstationary which willaffect the forecasting results of LSSVM without handling SoARCH-LM test is proposed to resolve this problem 1-hourreturn of the power load is calculated as 119877 = ln(119909

119905119909119905minus1)

Figure 6 provides the distribution of 1-hour return series from152015 to 3172015 Obviously volatility cluster appeared inthe residual and the variance in the area of a is larger than b

ARCH-LM test based on AR (3) is used to quantitativelytest the heteroscedasticity andWIMF1 is taken as an exampleto test the heteroscedasticity

In Table 1 obviously the significance of coefficients isclose to zero which indicates that significant autocorrelationappears in WIMF1 with Lag1 Lag2 and Lag3 and displaysautocorrelation characteristic of WIMF1 Therefore ARCH-LM test is applied to exam the conditional heteroscedasticityof returns series and the result of test is shown in Table 2

The 119865-statistic and the Lag1 of residual in Table 2 isunder the significance level of 0005 So the assumption ofARCH is not accepted It is the WIMF1 which illustrates theheteroscedasticity

Each WIMF is tested by the same method generallythe subseries of WIMF1 WIMF2 and WIMF5 have het-eroscedasticity characteristic and without the notable het-eroscedasticity there areWIMF3WIMF4WIMF6WIMF7and WIMF8 Then nonparametric GARCH model is estab-lished to forecast the power load A large number of domes-tic and international demonstration analyses have shownthat GARCH (1 1) can accurately describe the fluctuation

Table 1 Autocorrelation test

119905-statistic ProbLag1 minus2261395 00000Lag2 minus3069547 00000Lag3 minus1865080 00000

Table 2 Test of conditional heteroscedasticity of returns series

119865-statistic 4571244 Prob 00034119905-statistic Prob

Lag1 3281471 00010Lag2 0723646 04694Lag3 minus1499284 01339

Table 3 Parameter of GA

Main parameter ValueInitial population size 10Evolution iteration 1000Crossover probability 04Mutation probability 005

characteristics of the model and therefore this paper adoptsnonparametric GARCH (1 1) to imitate the power loadseries

42 Result Analysis of the Hybrid Forecasting Method Theperformance of LSSVM relays on the parameters of 120574 and 1205902which respectively represent the regulation parameter andkernel parameter A large number of domestic and interna-tional demonstration analyses indicate that two parametersare experientially determined Based on a number of teststhis paper adopts 100 for 120574 and 01 for 120590

2 The mainparameters in GA are listed in Table 3

In Figure 7 the error caused by the hybrid forecastingmethod is clearly shownThe errormovement stably changesthe maximum of relative error should be no more than 10and meanwhile the MAE MAPE and RMSE are 244469156 and 40738 respectively whichmean that the forecastingresults are acceptable

43 Comparative Analysis

431 Hourly Power Load Forecasting Analysis To demon-strate the forecasting performance of the novel hybridmethod LSSVM BPNN EEMD plus LSSVM EEMD plusBPNN and GA-LSSVM are employed as the comparativemethods which are shown in Figure 8 Table 4 summarizesthe values of the three error criteria including MAE RMSEand MAPE and the forecasted results of the six methodsshow that using the proposed hybrid method the powerload series forecasted errors can be accepted Notably theMAE is less than 2 and meanwhile it is evident thatMAE and RMSE are lower than the other methods whichimplies that the forecasting accuracy of the proposedmethod

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Electrical and Computer Engineering 7

Table 4 The error of power load forecasting using different methods based on hourly observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 244469 13137 18122 622200 10834 909020MAPE () 156 844 1181 405 712 608RMSE (MW) 407308 15525 20894 720567 12207 10313

0 500 1000 1500 2000 2500minus500

0500

IMF1

0 500 1000 1500 2000 2500minus2000

02000

IMF5

minus50000

5000

IMF2

minus10000

1000

IMF6

minus10000

1000

IMF3

minus20000

2000

IMF7

minus10000

1000

IMF4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 3 The decomposition of the power load series

0 200 400 600 800 1000 120002468

101214

Generation iteration

Fitn

ess

times106

Figure 4 Fitness curve

appears better than the comparative methods Comparedwith the MAPE of the hybrid method 156 the subop-timum with the MAE 405 is worse than the proposedmethod and the result indicates that the hybrid method byusing nonparametric GARCH (1 1) to forecast the subserieswith heteroscedasticity has well captured the time-varyingvolatility features of the power load series Meanwhile by theresults of EEMD-LSSVM andWEEMD-LSSVM it is obviousthat assigning weights to each IMF improves the forecastingaccuracy Besides it verifies that EEMDmethod decomposespower load series to constitutive subseries forecasted moreaccurately than original series by directly comparing LSSVM

with EEMD Generally the forecasted results of the proposedmethod are reasonable and much more accurate than theother method based on the hourly observations

432 Daily Power Load Forecasting Analysis As the datafrequency is a significant factor for the sensitivity of the time-series forecasting to examine the robustness of the hybridmethod this study adopts a daily observation method toforecast the power load And the forecasted power load isdecomposed to ten parts shown in Figure 9

Table 5 shows the errors of forecasted results amongdifferent methods and the MAE MAPE and RMSE of thehybridmethod can be accepted with smallerMAE and RSMEvalues and theMAPE is less than 1 comparingwith the othermethods which indicates that the hybridmethod has a betterperformance than other five methods Besides due to thedifferences in their characteristics the forecasting accuracycan be improved and clustered by using WEEMD methodHence this newly proposed hybrid method for power loadforecasting in this paper has relatively reliable robustnesswithrespect to the data frequency

5 Conclusions

To address the problem of power load forecasting withthe characteristic of nonstationary nonlinearity and time-varying this paper proposes a novel hybridmethod for power

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Electrical and Computer Engineering

Table 5 The error of power load forecasting using different methods based on daily observation

Hybrid method LSSVM BPNN WEEMD-LSSVM GA-LSSVM EEMD-LSSVMMAE (MW) 1441263 13343236 16027205 5023101 10623505 10729767MAPE () 0389 3488 4146 1313 2749 2854RMSE (MW) 1845988 17460604 22325684 6561656 14855986 13914859

0 500 1000 1500 2000 2500minus100

0100

WIM

F1

0 500 1000 1500 2000 2500minus2000

02000

WIM

F

minus50000

5000

WIM

F2

minus10000

1000

WIM

Fminus1000

01000

WIM

F3

minus20000

2000

WIM

F

minus10000

1000

WIM

F4

115

2

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

r

times104

Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

0 500 1000 1500 2000 2500Time (h)

Figure 5 The decomposition of the power load series with assigned weights

0 500 1000 1500 2000minus15

minus10

minus5

0

5

10

15

Resid

Time (h)

ab

Figure 6 The residual of the power load series with assignedweights

0 50 100 150 200 250minus2000

minus1500

minus1000

minus500

0

500

1000

Erro

r (M

W)

Time (h)

Figure 7 The error of the hybrid method

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1

Pow

er lo

ad (M

W)

Figure 8 The comparison between the prediction results based onhourly observation

load forecasting The data frequency has been changed totest the robustness of the proposed method Besides otherfive methods presented by this study are compared withthe proposed one to verify the accuracy of hybrid methodby different criteria presented above In the end severalconclusions are drawn as follows

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Electrical and Computer Engineering 9

0 50 100 150 200 250

LSSVMActual valueEEMD-LSSVMGA-LSSVM

The new hybrid methodBPNNWEEMD-LSSVM

times104

Time (h)

22

2

18

16

14

12

1Pow

er lo

ad (M

W)

Figure 9 The comparison between the prediction results based ondaily observation

(a)The newly proposed decomposition algorithm namedWEEMD has a better performance than EEMD method (b)Due to the differences in their characteristics improvementof the forecasting accuracy the components are clustered(c) Regardless of the influence of data frequency or thefluctuation of time-series the proposed hybrid method hasexcellent forecasting performance for power load

Competing Interests

The authors declare that they have no competing interests

References

[1] H A Malki N B Karayiannis and M BalasubramanianldquoShort-term electric power load forecasting using feedforwardneural networksrdquo Expert Systems vol 21 no 3 pp 157ndash1672004

[2] W-J Lee and J Hong ldquoA hybrid dynamic and fuzzy time seriesmodel for mid-term power load forecastingrdquo InternationalJournal of Electrical Power amp Energy Systems vol 64 pp 1057ndash1062 2015

[3] H C Huang R C Hwang and J G Hsieh ldquoShort-term powerload forecasting by non-fixed neural network model with fuzzyBP learning algorithmrdquo International Journal of Power andEnergy Systems vol 22 no 1 pp 50ndash57 2002

[4] A K Topalli I Erkmen and I Topalli ldquoIntelligent short-termload forecasting in Turkeyrdquo International Journal of ElectricalPower and Energy Systems vol 28 no 7 pp 437ndash447 2006

[5] T Yalcinoz and U Eminoglu ldquoShort term and medium termpower distribution load forecasting by neural networksrdquo EnergyConversion and Management vol 46 no 9-10 pp 1393ndash14052005

[6] A H Sanstad S McMenamin A Sukenik G L Barbose andC A Goldman ldquoModeling an aggressive energy-efficiency sce-nario in long-range load forecasting for electric power trans-mission planningrdquo Applied Energy vol 128 pp 265ndash276 2014

[7] N Amjady and F Keynia ldquoMid-term load forecasting of powersystems by a new prediction methodrdquo Energy Conversion andManagement vol 49 no 10 pp 2678ndash2687 2008

[8] P Bolzern and G Fronza ldquoRole of weather inputs in short-termforecasting of electric loadrdquo International Journal of ElectricalPower and Energy Systems vol 8 no 1 pp 42ndash46 1986

[9] RWang ldquoShort-term electricity price forecasting based on greysystem theory and time series analysisrdquo in Proceedings of theAsia-Pacific Power andEnergy EngineeringConference (APPEECrsquo10) pp 28ndash31 SichuanChina March 2010

[10] Y R Wang Q L Wan and H Chen ldquoShort term load fore-casting based on double-threshold GARCHmodelsrdquo Journal ofSoutheast University (Natural Science Edition) vol 41 no 6 pp1182ndash1187 2011

[11] D Liu ldquoA model for medium- and long-term power loadforecasting based on error correctionrdquo Dianwang JishuPowerSystem Technology vol 36 no 8 pp 243ndash247 2012

[12] W Sun and M Ye ldquoShort-term load forecasting based onwavelet transform and least squares support vector machineoptimized by fruit fly optimization algorithmrdquo Journal of Elec-trical and Computer Engineering vol 2015 Article ID 862185 9pages 2015

[13] Y Hu and X R Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[14] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Management vol 49no 5 pp 1156ndash1166 2008

[15] Z Shao FGao S-L Yang andB-G Yu ldquoAnew semiparametricand EEMD based framework for mid-term electricity demandforecasting inChina hidden characteristic extraction and prob-ability density predictionrdquo Renewable and Sustainable EnergyReviews vol 52 pp 876ndash889 2015

[16] W-C Hong ldquoApplication of chaotic ant swarm optimization inelectric load forecastingrdquoEnergy Policy vol 38 no 10 pp 5830ndash5839 2010

[17] S Bahrami R-A Hooshmand andM Parastegari ldquoShort termelectric load forecasting by wavelet transform and grey modelimproved by PSO (particle swarm optimization) algorithmrdquoEnergy vol 72 pp 434ndash442 2014

[18] L Ghelardoni A Ghio and D Anguita ldquoEnergy load forecast-ing using empirical mode decomposition and support vectorregressionrdquo IEEE Transactions on Smart Grid vol 4 no 1 pp549ndash556 2013

[19] Z Liu W Sun and J Zeng ldquoA new short-term load forecastingmethod of power system based on EEMD and SS-PSOrdquo NeuralComputing and Applications vol 24 no 3-4 pp 973ndash983 2014

[20] Q Li J Li and H Ma ldquoShort-term electricity load forecast-ing based on complementary ensemble empirical mode decom-position-fuzzy permutation and echo state networkrdquo Journal ofComputer Applications vol 34 no 12 pp 3651ndash3655 2014

[21] L A Gallego M J Rider M Lavorato and A Paldilha-Feltrin ldquoAn enhanced genetic algorithm to solve the static andmultistage transmission network expansion planningrdquo Journalof Electrical and Computer Engineering vol 2012 Article ID781041 12 pages 2012

[22] X L An D X Jiang S H Li and M H Zhao ldquoApplicationof the ensemble empirical mode decomposition and Hilberttransform to pedestal looseness study of direct-drive windturbinerdquo Energy vol 36 no 9 pp 5508ndash5520 2011

[23] X Zhu J Zhang and S Fu ldquoShort-term wind speed predictionmodel based on EEMD and SVMrdquo Journal of North ChinaElectric Power University vol 40 no 5 pp 60ndash64 2013

[24] M Mao W Gong L Chang Y Cao and H Xu ldquoShort-termphotovoltaic generation forecasting based on EEMD-SVMcombined methodrdquo Proceedings of the Chinese Society of Elec-trical Engineering vol 33 no 34 pp 17ndash24 2013

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Electrical and Computer Engineering

[25] Y Li D Niu and D Li ldquoNovel hybrid power load forecastingmethod based on ensemble empirical mode decompositionrdquoPower System Technology vol 32 no 8 pp 58ndash62 2008

[26] A Hou and S Suardi ldquoA nonparametric GARCH model ofcrude oil price return volatilityrdquo Energy Economics vol 34 no2 pp 618ndash626 2012

[27] C Schittenkopf G Dorffner and E J Dockner ldquoForecastingtime-dependent conditional densities a semi-non-parametricneural network approachrdquo Journal of Forecasting vol 19 no 4pp 355ndash374 2000

[28] YWang F Li QWan andH Chen ldquoHybridmomentumTAR-GARCHmodels for short term load forecastingrdquo in Proceedingsof the 2011 IEEE PES General Meeting The Electrification ofTransportation and the Grid of the Future pp 24ndash29 DetroitMich USA July 2011

[29] H Chen Q Wan F Li and Y Wang ldquoShort term load fore-casting based on improved ESTARGARCHmodelrdquo in Proceed-ings of the IEEE Power and Energy Society General Meeting pp1ndash6 San Diego Calif USA July 2012

[30] Y Huang and J Li ldquoA LS-SVM approach based on GA andNPGARCH for short-term traffic forecastingrdquo Energy Educa-tion Science andTechnology Part A Energy Science andResearchvol 32 no 6 pp 8607ndash8614 2014

[31] C J Yang H W Lu H Y Ma et al ldquoLoad forecasting byconsidering wind power based on sequential time classificationLSSVM modelrdquo Advanced Materials Research vol 712ndash715 pp2437ndash2440 2013

[32] H Yang and X Chang ldquoShort-term load forecasting based onlocal wave method and LSSVMrdquo Electrical Measurement andInstrumentation vol 52 no 7 pp 5ndash9 2015

[33] Q Gong W Lu W Gong and X Wang ldquoShort-term loadforecasting of LSSVM based on improved PSO algorithmrdquoCommunications in Computer and Information Science vol 483pp 63ndash71 2014

[34] H Zhang T Yao and T Ma ldquoForecasting of steam load basedon phase space reconstruction and improved LSSVM algo-rithmrdquo Energy Education Science and Technology Part A EnergyScience and Research vol 32 no 3 pp 1939ndash1952 2014

[35] M M Hadow A N Abd Allah and S P Abdul KarimldquoReliability evaluation of distribution power systems based onartificial neural network techniquesrdquo Journal of Electrical andComputer Engineering vol 2012 Article ID 560541 5 pages2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of