Short-term Electric Load Forecasting Based on CEEMDAN and LSSVMOptimized by Cuckoo Search AlgorithmFeng Jiang',Yunfei Zhang?1.School of Automation.Huazhong University of Science and Technology.Wuhan 430073.China2.School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,ChinaE-mail:zyf:2960511894@outlook.comAbstract:The article takes Irish short-term electric load forecasting (STLF)as the research object.Firstly,it uses the adaptivewhite noise (CEEMDAN)to integrate the empirical mode decomposition to decompose the short-term electric load data,anduses Lempel-Ziv complexity analysis to divide the Intrinsic Mode Function (IMF)obtained after decomposition into threecategories:high frequency sequence (HF),the low frequency sequence (LF)and the trend term (T).Then,the least squaressupport vector machine model (LSSVM)optimized by the cuckoo search algorithm (CS)is utilized to predict it.Finally,thefinal prediction value is obtained by the add integration method.At the same time,the other five benchmark models are addedas the comparison model,and the validity of the model is illustrated by two dimensions:error analysis and model test.Theresults show that the hybrid integrated model proposed has higher horizontal precision and direction accuracy than otherbenchmark models,and passes the DM test with the benchmark model.It also demonstrates that the accuracy of the modelafter adding the decomposition is higher than that of the model without decomposition.Key Words:Short-term Load Forecasting,Complete Ensemble Empirical Mode Decomposition with Adaptive Noise,CuckooSearch Algorithm,Least Squares Support Vector Machinehigh-frequency modes are considered as different input1Introductionfeatures for constructing individual predictors[].In the STLF,due to various factors such as climate andSTLF is the basis for realizing the safety and economicholidays,the short-term electric load is always in a state ofoperation of power systems.For a power system,drastic changes and has a nonlinear characteristicimproving the safety and economy of power grid operationTherefore,scholars have proposed more predictionand improving power quality all depend on accurate loadtechniques in STLF.Specific forecasting techniques can beforecasting.And STLF plays an increasingly indispensabledivided into three categories:econometric models,artificialrole in smart grids[1].STLF is divided into ultra-short-termintelligence models,and hybrid integration models.First,forecasting,short-term forecasting,medium-and long-termtraditional statistical and econometric models are widelyforecasting,and long-term forecasting.Short-termused in STLF.The ARIMA model is used in STLF,and theforecasting is obviously variability and non-static,so it isresults show that the ARIMA model can represent the mostmore difficult to predict[2].And STLF plays a major roleappropriate forecast period every quarter,month,and weekin the modern power system engineering discipline.The[7].Some scholars have used the GARCH model toaccuracy of its prediction accuracy directly affects theestimate the hourly spot price data for the five regions ofsafety,economy and power quality of power systemthe Indian electricity market.The results demonstrate thatoperation.Therefore,whether this paper can actuallythe combination with the ARIMA model has betterimprove the prediction accuracy of power load is verypredictive performance [8].Although these models basedon stationary data and linear assumptions can achieveThe power network is essentially a nonlinearhigher prediction accuracy,they cannot effectively capturetime-varying system,so many decomposition methods arethe nonlinearity of power load changes.In order to copeapplied to the pre-processing of short-term power load datawith this limitation,artificial intelligence models such asto achieve the effect of noise reduction and processing ofartificial neural network (ANN),support vector machineoutliers[3].Among them,some prediction methods can be(SVM),random forest(RF),and extreme leaming machinecombined with wavelet transform to achieve better(ELM)are used to predict short-term electric loadprediction results.Wavelet transform can extract noise withdata[9,10,11,12].These artificial intelligence models arehigh-frequency and has excellent noise reduction effect[4]better than the traditional measurement models in theIn addition,EMD is employed in short-term power loadcapture performance of nonlinear modes,so that betterdata decomposition,and in some cases it is better thanprediction results can be obtained.At the same time,inwavelet transform,but it is difficult to remove the tail endorder to overcome the shortcomings of the single modeleffect generated during the decomposition process[5].and further improve the accuracy of STLF,more scholarsSome scholars have applied the singular valueuse the decomposition-integrated hybrid model fordecomposition to short-term power load dataprediction [13,14,15.161.decompositionThe extractedlow-frequencyandTherefore,this paper applies the improved CEEMDANdecomposition to short-term power load.The remainder ofthis paper is organized as below.Section 2 introduces therelevant methodologies utilized in this paper.Section 3Similarly,for x,the residual of the kth IMF componentpresents the empirical analysis outcomes and theis calculated,and then the k+1th IMF is obtained:comparative results of the hybrid forecasting model.The1short-term power load data is decomposed into multiple(4IMFs and residual sequences by CEEMDANdecomposition method.The IMF is further divided intohigh-frequency sequences and low frequency sequences byE()represents a function that extracts the i-th IMFLempel-Ziv complexity calculation,and the CS-optimizedLSSVM hybrid model is used to predict the abovecomponent by EMD decomposition.Repeat steps until thesequences,then compared with SVM,RF,BPNN,ELM,residual is no more than two extremes.The residual iscalculated as follows:CS-LSSVM,and two dimensions from error analysis andmodel checking.(5)2 MethodologyFinally,theoriginal signal x(t)is expressed asFour main methods that we used in this paper aredescribed briefly in this section.They are a decompositionx(t)=(6)technique CEEMDAN,a key forecasting algorithmLSSVM,a swarm intelligent optimization algorithm CSand a hybrid model CEEMDAN-CS-LSSVM which2.2Least Squares Support Vector Machinecombined those three methods.2.1The least square support vector machine (LSSVM)hasComplete Ensemble Empirical Modedifferent processing on the hyperplane based on the SVMDecomposition with Adaptive Noisemodel classification principle.LSSVM transforms theSVM's inequality constraint problem into an equalityThe empirical mode decomposition (EMD)methodconstraint problem,which greatly reduces theproposed by Huang et al.is a processing method forcomputational complexity by changing the structure of thenon-stationary signals,which can decompose the originalloss function 20].Given a trainingsetsequence into several Intrinsic Mode Function (IMF)andone residual sequence (Res)[17].The integrated empirical,,i=1,...,N,where x is the input vector andmode decomposition (EEMD)method effectively removesye is the associated output vector,the LSSVM resultthe modal aliasing effect of EMD by adding different whiteoptimization problem can be expressed in the followingnoise to the original signal multiple times [18].Torres MEform:et al.proposed a complete aggregation experience with1adaptive white noise.Mode decomposition (CEEMDAN),which uses the characteristics of Gaussian white noise2(7)zero-mean to add adaptive white noise to eachdecomposition,further shortening the calculation time andreducing the experimental error based on the removal ofWhere y and eg represent relative weights andthe EMD mode aliasing effect[19].The adaptive whiteregression errors,respectively,N is the number of samples,noise complete aggregation empirical mode decompositionmodel (CEEMDAN)decomposition steps are as follows:and function(@,e)represents the structural riskFirst,the first EMD decomposition signal IMF isconsisting of empirical risk and confidence intervals.Toobtained by decomposing the signal:solve the above problems,the Lagrangian multiplier isconstructed as follows:(1)1Wherex(t)represents the original signal,wo represents the increased white noise amplitude,Where a is the Lagrange Multiplier.According to theKarush-Kuhn-Tucker (KKT)condition,it can be converted(t)represents the unit variance white noise,into the following constraints:and c represents the IMF obtained by empirical modedecomposition.Then calculate the difference signal:5(t)=x(t)-G(t)(2)Decompose(t)+wE ('(t))to get the second IMF:(3)Pa.If r>Pa,the bird's nest position is randomly updated,otherwise the position of the nest is unchanged.2.4 CEEMDAN-CS-LSSVM(9)arIn this paper,a novel hybrid integrated prediction modelCEEMDAN-CS-LSSVM for short-term electric load datais proposed.Firstly,the CEEMDAN decompositionOr-0[o()+b]-1+e=0.k=1...Nmethod is used to decompose the short-term electric loaddata,and then IMFs with high frequency to low frequencyDeriving and arranging the constraints further translatesand residual (Res)are obtained.After that,they are furtherinto:divided into a high frequency sequence HF,a lowfrequency sequence LF,and a trend term T by Lempel-Ziv0complexity calculation.The three-segment sequence is(10)predicted by the CS-optimized LSSVM model,and theprediction results are linearly added to obtain the finalWhere a =[a,...,a],Y=[y,...,yN ]I are theprediction result.Among them,because the training data isdifferent,the parameters of the LSSVM model after eachunit matrix,and =K(xg,x;)x,j=1,...,NCS optimization are different,which can better adapt to theK(x,x,)is the kernel function of the SVM thatcharacteristics of each segment of data.Therefore,it isequivalent to using different models to predict the sequencesatisfies the Mercer theorem (the radial basis function isof each segment after decomposition,so that the predictiongenerally chosen).The expression of the final regressionresults are more Precision.function is as follows:f(x)=>aK(x.x)+b3 Experiment analysisThis section is an empirical analysis chapter to2.3 Cuckoo Search Algorithmdemonstrate the performance of the proposed model andthe other five comparative models in the predictionaccuracy and testing of the data set.The standard Cuckoo Search algorithm (CS)is inspiredFirst,the Irish original power load data curve is dividedby the brooding behavior of cuckoos.It is a globalinto two groups:a training set and a test set.There are aintelligent optimization algorithm by introducing the Levytotal of 2880 observations for the training model,96flight mechanism of birds to simulate the process of cuckooobservations for each model's test performance,and thensearching for nests and spawning in nature.Yang and Debproposed the following three ideal states set by thespecific evaluation indicators are given.Fig.I shows theCEEMDAN decomposition results,with frequencies fromalgorithm:low to high.The IMF is then divided into low frequency(1)The cuckoo only has one bird's egg in eachhigh frequency and trend terms by Lempel-Ziv complexitygeneration's reproduction process,and randomly chooses aanalysis.The results are given in Table 1 and Fig.2.Thebird's nest to hatch.model prediction results presented in this paper are shown(2)Before finding a better bird's nest,the current bestbird's nest as the next generation's host will enter the nextin Fig.3,and the results of comparison with the other fivebenchmark models are given in Fig.4.The final DM testbreeding.results are shown in Table 2.(3)The total number of nests available for eachgeneration is fixed.The probability that the bird eggs underthe cuckoo are found by the host is 0,1.If the bird's egg is3.1 Data Description and Evaluation Criteriaperceived by the host,the host will give up the egg,or giveup the entire nest and find a suitable location to build a newThe article uses the short-term electrical load data ofnest [211.Ireland in December 2018.with a data interval of 15Based on the above three ideal states,the update formulaminutes,a total of 2976.From December 1st to Decemberfor the position and path of the cuckoo looking for the host30th,a total of 2,880 data points were used as training data.nest is as follows:On December 31,a total of 96 data points were used as test(12)data to make a reasonable prediction of Ireland's short-termpower load.L)=(A)sin(/2)1(13)In this paper,the root mean square error (RMSE),theπmean absolute error (MAE),and the mean absolutex represents the position of the i-th nest at the t-thpercentage error (MAPE)are selected as the horizontalaccuracy test standards.The horizontal accuracy is onlyiteration,and the step factor a>0 is used to control thepart of the prediction accuracy test.Therefore,the DSstep size,and its value obeys a normal distribution.index is used to test the direction accuracy,and then theAfter the position update by formula (1),the randommodel accuracy is fully reflected.The smaller the RMSE,number r (r e[0,1])is generated,and r is compared withMAE and MAPE,the higher the horizontal accuracy of the