A Hybrid Forecasting Model Based on Empirical Mode Decomposition and the Cuckoo Search Algorithm : A Case Study for Power Load

Power load forecasting always plays a considerable role in the management of a power system, as accurate forecasting provides a guarantee for the daily operation of the power grid. It has beenwidely demonstrated in forecasting that hybrid forecasts can improve forecast performance compared with individual forecasts. In this paper, a hybrid forecasting approach, comprising Empirical Mode Decomposition, CSA (Cuckoo Search Algorithm), and WNN (Wavelet Neural Network), is proposed. This approach constructs a more valid forecasting structure and more stable results than traditional ANN (Artificial Neural Network) models such as BPNN (Back Propagation Neural Network), GABPNN (Back Propagation Neural Network Optimized by Genetic Algorithm), andWNN. To evaluate the forecasting performance of the proposed model, a half-hourly power load in New South Wales of Australia is used as a case study in this paper. The experimental results demonstrate that the proposed hybrid model is not only simple but also able to satisfactorily approximate the actual power load and can be an effective tool in planning and dispatch for smart grids.


Introduction
In a power system, the short-term power load forecasting is very important for the stable operation of the system.Accurate forecasting is a guarantee in the development of preventive maintenance plans, which include generator safeguards, power system reliability estimation, and scheduling dispatch [1,2].High-accuracy power load forecasts improve the economic and social benefits of power grid management, which reduce generation costs, improve the security of power systems, and help administrators develop optimal plans.Moreover, accurate load forecasting is crucial in forecasts of the power price in power markets [3].Therefore, developing power load forecasting techniques to achieve accurate, simple, and fast load forecasts is necessary.Thus far, many shortterm power load forecasting methods have been proposed, and these methods can be mainly divided into three categories: conventional methods, modern forecasting methods, and hybrid forecasting methods.Conventional methods include multiple linear regression analysis [4,5], time series [6,7], state space models [8], general exponential smoothing [9], and knowledge-based methods.However, these methods cannot provide appropriate nonlinear mathematical relationships to express actual power loads.The primary modern forecasting methods are intelligent evolutionary algorithms [10,11], expert systems [12,13], neural networks [14][15][16][17], and fuzzy inference [18].Intelligent algorithms and neural networks obtain good performance because of their clear patterns, easy implementation, and strong ability to address the problem.Hybrid forecasting methods, proposed to avoid the shortcomings that exist in individual forecasting methods, have become increasingly prevalent [19,20].A detailed introduction of the three categories is given below.
The deduction processes of traditional forecasting methods are rigorous, and most of them are based on traditional mathematics theories such as statistics, calculus, and modeling by subjective data analysis [21].The main idea of trend extrapolation technology is to look for the trend of data changes, according to the trend equation, to forecast future data.The method is simple, and, especially for smooth power 2 Mathematical Problems in Engineering load changes, it can achieve a good prediction effect.Its deficiency is that its precision is greatly influenced by the random load component [22].The regression analysis method is often applied to short-term load forecasting [23].This method has many advantages such as a simple principle and better quality of data which leads to better precision; however, the selection of the main factors affecting power load in the model is difficult as many factors that affect the forecasting accuracy are hard to quantify.This model is lacking any self-study capability, and the input variable and output variable cannot be revised automatically [24].With years of development, the time series forecasting method has become a mature theory method and has been applied to power load forecasting [25].The basic time series prediction models mainly include AR, MA, and ARMA [26].Although the time series forecasting method has advantages such as only requiring a small volume of historical data and a small amount of calculation and the fast speed of its calculation, this method has certain limitations such as its inability to reflect the influence of meteorological factors and how its forecasting accuracy will decrease with the increase of the prediction step [27].ANN [17] is a type of nonlinear simulation of the human brain information processing system with an intelligent processing process; for an inaccurate variation trend, this method also has a good ability to adapt, is able to grasp information and keep on learning, and has good knowledge reasoning and self-optimization [28].An expert system is a computer system based on the knowledge of the programming approach, mainly a software system, and the main components of an expert system include the inference engine of the system, the expert knowledge base, the explain interface, and the knowledge acquisition module.An expert system is a program that has decisionmaking capabilities based on reasoned knowledge; however, this method is limited by whether the expert knowledge is complete [29].The grey forecasting method is an important technique in grey theory, and it uses approximate differential equations to describe future tendencies for a time series [30].The limitation of this method is that the greater the dispersion degree of data, the worse the forecasting accuracy.Although traditional forecasting methods and forecasting methods based on intelligent computing have their respective applications, it is difficult to achieve better results when using one of them by itself [31].In the literature related to forecasting [31][32][33][34], the forecasting results are not quite as good with any single forecasting model.The primary reason is that single forecasting models cannot extract the complicated factors encountered in reality.
Due to the limitations of the forecasting capacity of a single model, it cannot always be optimal in all cases.In this paper, a novel hybrid model was developed with the hope of obtaining more accurate power load forecasting results.The proposed hybrid wind speed forecasting model can be grouped into four steps.Firstly, we used the empirical model decomposition technique, which represents a nonstationary data analysis technique, to reconstruct the original wind speed series.Secondly, a WNN model was employed to create the power load forecasting, and the parameters in the WNN model were tuned by the CSA.The simulation results illustrate that the hybrid model is an effective method in power load forecasting.The main contributions of this paper are summarized as follows: (1) The CSA algorithm is applied to choose the optimal initial weight in the WNN model, which always leads to unstable forecasting error.
(2) In the field of power load forecasting, the proposed hybrid model is manifested as a valid method with efficient computation and satisfactory forecasting accuracy.
(3) Considering the skewness and kurtosis of the forecasting accuracy distribution, the developed forecasting availability is proposed as an effective evaluation criterion for model selection in the power load forecasting field.
This paper is organized as follows.First, we outline the concept of models used in this paper, including empirical model decomposition, WNN, CSA, BPNN, GABPNN, and EMD-CSAWNN.Second, the modeling processes of the methods mentioned above are introduced.Simulation results are presented and analyzed.Finally, the overall conclusion is included.

Methodology
In this section, the required individual tools will be presented concisely, including the empirical model decomposition technique, BPNN, the WNN model, and the CSA and GA algorithms.Moreover, the proposed hybrid approach will be described in detail.In addition, the structure of the feedforward neural network will be confirmed.

Empirical Mode Decomposition.
Empirical model decomposition was proposed by Karthikeyan and Kumar as an adaptive method for nonstationary time series analysis, and it is now widely used.It can be applied to any type of signal decomposition [35].Thus, it has obvious advantages in processing nonstationary and nonlinear series.The foundation of this technique is to decompose a time series into a finite set of several IMFs and a residue [36].Definition 1.All IMFs are defined to satisfy the following conditions: (1) the number of local extreme points and the number of zero crossings must be equal or at least differ by only one; (2) the mean value of the upper envelope and lower envelope is zero.Definition 2. The stoppage criterion determined is defined as The sifting process stops when SD  is smaller than a pregiven value.The process of decomposition is over when the value of SD  is between 0.2 and 0. The process of denoising Reconstruct data E M D p a r a m e t e r o f S e t t h e i n i t i a l Empirical mode decomposition empirical model decomposition technique are illustrated in Figure 1.

Artificial Neural Network (ANN)
2.2.1.Confirmation of the Structure of the Network.The ANN has received considerable attention as a powerful computational tool for forecasting in many fields since 1980.ANN models always outperform statistical models because of their ability to map the inputs onto outputs via simple computation [37].We discuss the feed-forward neural network in this paper because of its strong learning ability and simple structure.The determination of the network structure is as follows [38]., . . .,   )| < .Note that, ∀ > 0, ∃ a three-layer network structure, and the output function of the hidden layer is (), the output function of the input and output layer is linear, and the total relationship of /0 is( 1 , . . .,   ), such that max | f( 1 , . . .,   ) − ( 1 , . . .,   )| < .
Definition 5. ∀ > 0 and  : [0, 1]  →   , there exists a three-layer structure that can approximate  in any square error precision of .
The definition above proves that, ∀ : [0, 1]  →   , we can use a feed-forward neural network with a three-layer structure  × (2 + 1) ×  to approximate it accurately.Thus, this part not only proves the existence of the mapping network but also demonstrates the network structure of the mapping.In summary, this paper adopts the three-layer neural network as the basis neural network.

BPNN.
BPNN is a type of multilayer feed-forward neural network with an error back propagation learning process.The structure of BPNN is illustrated in Figure 2. Details of BPNN are introduced in [40].

WNN.
WNN, a feed-forward network, is generally multilayer [41].It is widely applied in signal processing because of its advantages of the localization property and generalization ability [42].The structure of WNN is shown in Figure 2.

Neural Network Optimized by an Intelligence Algorithm.
The intelligent optimization algorithm provides an efficient and powerful mathematical tool for optimizing the initial weights and thresholds of the ANN [43].

CSA.
Cuckoo search is a heuristic swarm intelligence algorithm inspired by the behavior of the obligating brood parasitism of cuckoo species [44].CSA is utilized in this paper for its stronger capability of global optimization [43].Definition 6.To simulate the mode of cuckoo breeding, three idealized assumptions are presented, as follows: (1) each cuckoo selects nest randomly and dumps only one egg at a time, (2) the eggs with high quality will be carried over to the next generation, and (3) the available nest number  is fixed, and the probability of the host bird discovering the exotic egg is   .Definition 7. The Lévy flight model simulates the process of the nest-seeking characteristic of cuckoo, and the update formula of the path and location is as follows:  Here  =  − , 1 <  < 3,  and V obey the normal distribution,  ∼ (0,  2  ), V ∼ (0, 1),   = [Γ() sin(0.5(− 1))/ 2 (−2)/2 Γ(0.5)( − 1)] 1/(−1) ,  iter * denotes the location of the best nest at generation iter, and Γ is the standard gamma function with unbounded variance and mean of the probability distribution.

GA.
GA is a population-based optimization algorithm that simulates natural genetic mechanisms and biological evolutionism.It possesses a capacity for powerful global optimization [45].The principle of GA relies on a random process, which is constituted by the processes of selection, crossover, and mutation [46].The implementation process is shown in Figure 2.

GABPNN.
The primary mechanism of GABPNN is composed of three parts: GA optimization, determination of the BPNN structure, and forecasting covered by BPNN [47].The pseudo-code for GABPNN is as shown in Algorithm 1.

EMD-CSAWNN.
In this paper, the proposed model, which incorporates the empirical model decomposition technique into the WNN model based on CSA, is adopted for short-term power load forecasts.Empirical model decomposition represents a self-adaptive decomposition technique to decompose short-term power load series into several IMFs and one residual item.WNN is adopted as a forecasting engine in the proposed approach because of its powerful approximation and high computation speed.Additionally, to avoid the deficiencies of WNN such as its unstable structure, CSA is used to initialize and determine the weights and thresholds of WNN, thereby imparting an outreach capacity to WNN. Figure 3 illustrates the general structure of the hybrid power load forecasting method.The pseudo-code for the algorithm of the EMD-CSAWNN model is as shown in Algorithm 2.

Experiments and Evaluations
Applications of the proposed hybrid approach and five comparison models are shown in this subsection.All algorithms are operated on the given platform: 3.20 GHz CPU, 8.00 GB RAM, Windows 7, and MATLAB R2012a.Meanwhile, taking into account the randomness factors and to make sure the final results are reliable and independent from the initial weights, we carry out each ANN experiment 50 times and then take the average value.

Evaluation Metrics.
Forecasting accuracy is an important criterion for evaluating a forecasting model.In this paper, the basic error calculation method is as follows: Here,  is the number of data points; the formula AE represents the absolute error between the observed value and the forecasting value at time ,  is the observed value, and x is the forecasting value at time .To avoid a positive or negative offset in forecasting error, solve the problem for which positive and negative forecasting error cannot be added, adding to the absolute value of the error, and take the average in the end.This error belongs to the comprehensive index in error analysis: RMSE is the square root of the mean square error.It also belongs to the comprehensive index in error analysis.Take the square of the absolute error AE; thus, the role of great values in the error will be strengthened, improving the sensitivity of the indicators, which is the prevailing reason in the error analysis: where the symbolic meaning is as above.The indicator is the average of the absolute error.The index is one of the comprehensive indexes in error analysis that usually occupies a very important position in the analysis and forecasting performance of the model. ( 3 DO / * Find all local maxima and minima of ℎ −1 () by cubic spline.* / (4) / * Produce the upper and lower envelopes expressed as  max () and  min ().* / (5) END WHILE (7) IMF  (27) iter= iter + 1 To determine the degree of correlation between different forecasting model results with observed values, GRA [48] is employed in this paper.
Definition 9 (grey relational degree).By focusing the degree of   () at utter points, the algorithm on the grey relational degree is Considering the generation capacity of the proposed hybrid model, four statistical indices are employed as evaluation metrics to measure the forecasting accuracy, MAE, RMSE, MAPE, and GRA.MAPE, MAE, and RMSE measure the mean performance, and GRA illustrates how well the forecasted data points fit the trend.

Results and Analysis
The experiments were divided into three parts, Experiment 1, Experiment 2, Experiment 3, Experiment 4, and Mathematical Problems in Engineering     1 and 2, Figures 5, 6, and 7.Each individual model exhibits its best performance at a special time.For example, Figure 6 shows that BPNN provides the lowest MAPE value at 3:00 among all of the individual models, and CSAWNN yields the highest accuracy forecasting value from 1:00 to 3:00 among all of the individual models, whereas the maximum error is with the BPNN forecasting model on February 2, with a MAPE value of 10.12%.This result is due to the unstable initialization of the ANN.The result of the original data of empirical model decomposition is shown in Figure 3(a).The noise in the data is eliminated by using the empirical model decomposition technique; in this paper, the IMF1 is a high-frequency sequence with small values, which can be regarded as interference factors.As a result, the rest of the IMFs and the remainder term can be constructed as the training input of the CSAWNN model.This indicates that the hybrid model is an effective power load forecasting approach.The GRA result is shown in Table 5.In addition, on March 1, the GRA of GABPNN is higher than that of the hybrid model; on the remaining 27 days, the values of GRA offered by the hybrid model are higher than those of the other five models.
According to the average value of GRA over the 28 days, the forecasting effects of all six forecasting models are increasing in the following order: ARIMA, BPNN, which is the WNN, CSAWNN, GABPNN, and EMD-CSAWNN, which concludes that the effect of the hybrid forecasting model is the best model among the six forecasting models.
The higher the power load forecasting accuracy, the lower the economic cost, which has actual economic significance [49].As is illustrated in this case, the ANN optimized by the intelligence algorithm after denoising provides a better power load forecasting effect.

Discussion
In this section, we discuss two important evaluation metrics, convergence speed and degree of certainty [50], offered by the GABPNN and CSAWNN models to determine a more practical forecasting model by considering reality factors such as forecasting stability and calculation time.The results illustrate that the CSAWNN model is more practical than the GABPNN model in forecasting power load.In addition, we propose forecasting availability to analyze and evaluate the quality of power load forecasting.

Convergence Speed.
The computational complexity of evolutionary algorithms and swarm intelligence still remains a challenging issue; here, we use convergence speed as one of the evaluation metrics to examine the forecasting performance of GABPNN and CSAWNN.We obtain the computation time of the best fitness by analyzing the convergence speed of GA and CSA for use in comparative evaluation of optimization algorithm performance.However, the exploration and development are always two competing goals, and the conflict would exist between the convergence speed and forecasting accuracy.We define performance less than 10 −5 as the convergence criteria.We take the data from January 12, January 19, and January 26 as an example to illustrate the convergence speed of GA and CSA; Figure 12 shows the results of the comparison of evolutions among GA and CSA with different population sizes.We observed that the fitness values monotonically decrease as the iterations increase.In addition, when the iterations are less than 100, the larger the population size, the faster the convergence speed.We also observed that CSA has better convergence speed than GA.At iteration 20, the further consideration; on that basis, this section will give a general discrete form of forecasting availability [51].Step 1. EMD method is applied to preprocess the original power load data initially Step 2. WNN is employed to carry out the forecasting by using the data processed by EMD method Step   Especially if the priori information of the discrete probability distribution of  types of methods is unknown, we define   = 1/,  = 1, 2, . . ., .

Definition 13. 𝑚 𝑘
is called the -order forecasting availability unit of th forecasting method, and  is a continuous function of a certain  unit.( Definition 14 illustrates that the 1st-order forecasting availability is the expectation forecasting accuracy sequence.The 2nd-order forecasting availability is the difference between the expectation and standard deviation of the forecasting accuracy sequence.We use the forecasting availability to evaluate the power load forecasting results in this paper.Through Figure 14, we obtain that the 1st-order and 2nd-order forecasting availability offered by the hybrid model are 0.9222 and 0.8366, respectively, which outperform those of the others; this evaluation result corresponds to the previous evaluation criterion.Thus, the hybrid model is a more valid model than the others.

Conclusion
The one-day-ahead power load forecasting is an extremely important problem in power load planning, secure operation, and energy expenditure economy.Assessment of the power load as accurately and quickly as possible is the primary objective in power load forecasting.However, power load is affected by various uncertain factors such as climate change and the social environment, which may lead to difficulty in obtaining accurate power load forecasts.The accuracy of traditional individual forecasting methods, which lack denoising, is not satisfactory for power load forecasting.Herein, a hybrid EMD-CSAWNN model for short-term power load forecasting is developed.The empirical model decomposition technique is applied to reduce the high-frequency items.On the basis that WNN can handle the data with nonlinear features, the ensemble forecasting method is adopted to overcome the uncertainty of the outcomes that can be attributed to the randomness of the initialization of the single WNN.Moreover, we use the CSA to optimize the parameter in the ensemble forecasting model.Experimental studies of power load forecasting in NSW demonstrate that the hybrid model has higher precision than conventional forecasting models.
The proposed EMD-CSAWNN model can provide efficient computation and satisfactory forecasting accuracy for this type of data.Therefore, the developed hybrid approach is suggested for broad application in power load forecasts or even other fields such as wind speed and traffic flow forecasts.Mean absolute percentage error GRA:

Abbreviations
Grey relational analysis : The number of sample data points used to build the NN model

Figure 1 :
Figure 1: The construction of empirical model decomposition.

Figure 4 (
Figure 4(b) exhibits 1008 power load data points from January 12, 2009, to February 1, 2009, divided into three groups, with 336 data points in every group.Because the power load data of NSW are collected once every half hour, each day includes 48 data points.On different days of the week, daily life and human economic production usually have different behaviors; thus, the characteristics of the load are different on different days.To minimize forecasting error as much as possible, we forecast the load of different days in the week separately.In this paper, the cycles of data division are seven days; the first three weeks of Monday data, January 12, January 19, and January 26, are employed to forecast the next Monday load on February 2, 2009.Accordingly, the data on January 13, January 20, and January 27 are employed to forecast the power load on February 3, 2009.The rest can be conducted in the same manner.The structures of the training and testing sets are illustrated in Figure 3(b).

Figure 3 :
Figure 3: The construction of EMD-CSAWNN.(a) IMFs and the residual decomposed by empirical model decomposition.(b) The structure of the training and testing sets of the neural network.(c) The procedure of WNN combined with CSA.(d) The procedure of CSA.(e) The structure of WNN.(f) The forecasting sequence and error by using the EMD-CSAWNN model.

Figure 4 :
Figure 4: Description of observations in New South Wales of China.(a) Location of the study site.(b) The original power load series from January 12 to February 1, 2009.(c) The statistical measures for the power load.

Experiment 4 .
The power load on Thursday,April 24, 2008,  and Tuesday, April 29, 2008, from New South Wales of Australia is used to globally testing the proposed hybrid model.The results are shown as in Tables6 and 7. To forecast the power load on Thursday, April 24, 2008, the historical values from the Thursdays of the first three weeks, April 3, April 10, and April 17, are chosen, respectively.To forecast the power load on Tuesday,April 29, 2008, the historical values from the Thursdays of the first three weeks, April 8, April 15, and April 22, are chosen, respectively.Test results (AE, MAE, RMSE, and MAPE) are presented in Tables6 and 7and part (a) of Figure11.
to the figure shown above, in Feb. 2, 2009, among the correlation coefficients of BPNN, GABPNN, WNN, CSAWNN, EMD-CSAWNN, and ARIMA, EMD-CSAWNN obtain the maximum correlation coefficient.As described in Section 4.2, the greater the correlation, the more excellent the corresponding forecasting models.Thus, the results illustrate in Feb. 2, 2009, six models in the following order of increasing: ARIMA, WNN, BPNN, GABPNN, CSAWNN, and EMD-

Figure 7 :
Figure 7: The comprehensive evaluation of forecasting models for February 2. (a) The comparison of GRA by using six different models.(b) The comparison of MAE, RMSE, and MAPE by using six different models.(c) The scatterplot of forecasting versus actual levels by using six different models.(d) The evaluation results of six different models.The value in bold is the best value of each evaluation index.

Figure 9 :
Figure 9: The forecasting results and actual values from February 2 to March 1.

3 .Figure 10 :
Figure 10: The comprehensive evaluation of forecasting models from February 2 to March 1.(a) The radar diagram of MAPE by using six different models.(b) Comparison of forecasting MAPE by using the EMD-CSAWNN and ARIMA models.The red line is the polynomial regression line.(c) The comparison of GRA and MAPE by using six different models.(d) The comparison of MAE and RMSE by using six different models.(e) The scatterplot of forecasting versus actual levels by using six different models.The solid line represents the perfect fit: that is,  = .(f) Evaluation results of six different models.The red font is the best value of every evaluation index; the green font is the worst.(g) The comparison of the box plot by using six different models.The whiskers in the box plot indicate the primary range for the data, in which the lowest data are 1.5 times the interquartile range of the lower quartile and the highest data are 1.5 times the interquartile range of the upper quartile.The outliers, which are not included between the whiskers, are represented by the red crosshair.

Figure 11 :Figure 12 :Figure 13 :
Figure 11: The comprehensive evaluation of forecasting models in Experiments 4 and 5. (a) Comparison of forecasting results by eight models on Thursday, April 24, 2008, and Tuesday, April 29, 2008, from New South Wales of Australia.(b) Comparison of forecasting results by eight models on Saturday, June 28, 2008, and Monday, June 30, 2008, from Victoria of Australia.
3. Additional details of the →   ,  can be accurately approximated using a three-layer forward neural network realization.The first layer of the network is the input layer, containing  neurons.The middle layer is the hidden layer, containing 2 + 1 neurons.

Table 1
shows the experimental results for Monday of six types of forecasting models.The average values of MAPE for six models on February 2, 1.6% are 1.54%, 1.97%, 1.37%, 1.02%, and 1.94%, respectively; as shown in Table2,

Table 1 :
Comparison of power load forecasting result by using different methods in Feb. 2. Experiment 2. Figure 8 and Table 3 describe the comparison of six models with values on weekdays and weekends on dif- addition, it is shown that the value of MAPE offered by the hybrid model is more stable than that of the other proposed models, and the maximum value of MAPE is 2.54%.By comparing the hybrid model with the other models, it is shown that the hybrid model can provide high and stable forecasting accuracy.ferent evaluation metrics.On weekdays, the best performance model is the hybrid model and the value of MAPE is 0.82%; on the contrary, the worst is the ARIMA model, whose value of MAPE is 1.48%.The MAPE offered by the hybrid model is 44.59% lower than that offered by the ARIMA model.On weekends, the value of MAPE offered by the hybrid model

Table 2 :
Comparison of power load forecasting result by using different methods in Feb. 2.
78%, and 1.44%, respectively.The maximum value of MAPE offered by the ARIMA model is 4.4% over 28 days.Meanwhile, on all days of the test, the average values of MAE, MAPE, and RMSE offered by the hybrid model are all smaller than those of the other models.The average value of MAPE offered by the hybrid model over four weeks is 0.78%, and the highest decrease is 39.06% compared with the other ANN models.
Table 6 indicates that EMD-CSAWNN has the highest accuracy forecasting results on Thursday, April 24, 2008; the maximum, minimum, and average MAPE values are 1.2355% at 2:00, 1.1836 at 14:00, and 1.2025%, respectively.The second-highest to sixth-highest accurate models are GABPNN, BPNN, RBFNN, CSAWNN, WNN, ENN, and ARIMA with average MAPE values of 1.6436%, 1.7795%, 1.8314%, 2.3373%, 2.4141%, 3.1381%, and 5.5872%, respectively.Table 7 indicates that EMD-CSAWNN still yields the highest accuracy forecasting value from among all of other models mentioned in this paper when forecasting power load on Tuesday, April 29, 2008; the maximum, minimum, and average MAPE values are 1.9844% at 14:00, 1.6033% at 12:00, and 1.7811%, respectively.According to the average MAPE value, CSANN is the second most accurate model, GABPNN is the third most accurate model, RBFNN is the fourth most accurate model, WNN is the fifth most accurate model, BPNN is the sixth most accurate model, ENN is the fifth most accurate model, and ARIMA is the sixth most accurate model with average MAPE values of 2.5827%, 2.8472%, 2.8473%, 3.1717%, 3.2725%, 3.5151%, and 3.7549%, respectively.As shown in Table 6, the average MAPE afforded by the hybrid model decreased by 78.48% compared with the maximum average MAPE value.In Table 7, the average MAPE afforded by the hybrid model decreased by 52.57% compared with the maximum average MAPE value.In addition, it is shown that the value of MAPE offered by the hybrid model is more stable than that of the other proposed models.By comparing

Table 3 :
Comparison of power load forecasting evaluation by using different methods between weekdays and weekends.

Table 4 :
Comparison of power load forecasting evaluation by using different methods from Feb. 2 to Mar. 1.

Table 6 :
Comparison of power load forecasting result by using different methods on Thursday, Apr. 24, 2008, from New South Wales.

Table 7 :
Comparison of power load forecasting result by using different methods on Tuesday, Apr. 29, 2008, from New South Wales.

Table 8 :
Comparison of power load forecasting result by using different methods on Saturday, Jun. 28, 2008, from Victoria.

Table 9 :
Comparison of power load forecasting result by using different methods on Monday, Jun. 30, 2008, from Victoria.The BPNN, GABPNN, WNN, CSAWNN, EMD-CSAWNN, and ARIMA forecasting results between weekdays and weekends.