Energy 49 (2013) 279e288. Contents lists available at SciVerse ScienceDirect. Energy. journal homepage:

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1 Energy 49 (203) 279e288 Contents lists available at SciVerse ScienceDirect Energy journal homepage: Using multi-output feedforward neural network with empirical mode decomposition based signal filtering for electricity demand forecasting Ning An a, Weigang Zhao b, *, Jianzhou Wang b, Duo Shang c, Erdong Zhao d a Anhui Province Key Laboratory of Affective Computing and Advanced Intelligent Machine, School of Computer and Information, Hefei University of Technology, Hefei , China b School of Mathematics and Statistics, Lanzhou University, Lanzhou , China c College of Engineering and Applied Science, Stony Brook University, Stony Brook, NY 794, USA d School of Business Management, North China Electric Power University, Beijing 02206, China article info abstract Article history: Received 8 April 202 Received in revised form 29 August 202 Accepted 2 October 202 Available online 27 November 202 Keywords: EMD-based signal filtering Seasonal adjustment Feedforward neural network Electricity demand forecasting Multi-output forecasting For accurate electricity demand forecasting, this paper proposes a novel approach, MFES, that combines a multi-output FFNN (feedforward neural network) with EMD (empirical mode decomposition)-based signal filtering and seasonal adjustment. In electricity demand forecasting, noise signals, caused by various unstable factors, often corrupt demand series. To reduce these noise signals, MFES first uses an EMD-based signal filtering method which is fully data-driven. Secondly, MFES removes the seasonal component from the denoised demand series and models the resultant series using FFNN model with a multi-output strategy. This multi-output strategy can overcome the limitations of common multi-stepahead forecasting approaches, including error amplification and the neglect of dependency between inputs and outputs. At last, MFES obtains the final prediction by restoring the season indexes back to the FFNN forecasts. Using the half-hour electricity demand series of New South Wales in Australia, this paper demonstrates that the proposed MFES model improves the forecasting accuracy noticeably comparing with existing models. Ó 202 Elsevier Ltd. All rights reserved.. Introduction People around the world have become increasingly dependent on electricity supply. Since electricity is hard to store, planning for electricity supply to satisfy its consumer demand with minimal waste is important for any power utility. In addition, an increased number of countries strive to achieve a wide range of applications of renewable energies in the sake of saving environment and depleted fossil fuels. These renewable energies including wind energy, solar energy and wave energy are often unstable due to their intermittent energy sources. This issue highlights the need for power utilities to plan and manage their electricity supply in a proactive manner. To plan electricity supply requires that electricity demand forecasting plays a crucial role since it can help power utilities make correct scheduling decisions to maintain the balance between supply and demand. * Corresponding author. Tel.: þ ; fax: þ addresses: ning.an@hfut.edu.cn (N. An), zwgstd@gmail.com (W. Zhao), wjz@lzu.edu.cn (J. Wang), shd8786@gmail.com (D. Shang), erdongzh@26.com (E. Zhao). Since electricity demand always suffers from various unstable factors including unpredictable weather conditions, sudden social changes, holidays, dynamic electricity prices and more, the demand series often shows a highly nonlinear characteristic along with seasonality that makes it very difficult to develop an accurate electricity demand forecasting model []. To tackle this challenge, researchers in the past decades have proposed a wide variety of models including: regression-based approaches [2], Grey-based models [3,4], fuzzy regression algorithm [5], singular spectral analysis [6], various neural network models [7e9], support vector regression [0]; hybrid models including hybrid fuzzy neural approaches [], Grey-fuzzy-based electricity management system [2] and Grey-Markov model [3]; combination models including adaptive particle swarm optimizationbased combined method [4], wavelet transform combination model based on neural network and evolutionary algorithm [5], wavelet transforms and adaptive models [6], and adaptive fuzzy combination model based on the self-organizing map and support vector regression [7]. While these methods improve the forecasting accuracy for different cases, they chose to model the original electricity demand series directly without considering inherent characteristics of the /$ e see front matter Ó 202 Elsevier Ltd. All rights reserved.

2 280 N. An et al. / Energy 49 (203) 279e288 Table Operational summary of the empirical mode decomposition. Give x(t) which is the signal for empirical mode decomposition Initialize I Set i ¼ I Notate x as r 0 for description convenience Decompose N Repeat { I Set k ¼ 0 I Notate r i as h i,k for description convenience Sift N Repeat {, Compute the envelope mean of h i,k m ik (t) ¼ [U ik (t) þ L ik (t)]/2, Compute in the following sequence h ik (t) ¼ h i,k (t) m ik (t) k ¼ k þ } until (SD k < ε ), Designate h i,k as the ith IMF c i c i (t) ¼ h i,k (t), Separate IMF from the rest of the data r i (t) ¼ r i (t) c i (t), Let r n ¼ r i, c n ¼ c i and then i ¼ i þ } until (max(c n, r n ) < ε 2 or r n is monotonic) data. As discussed earlier, noise signals caused by unstable factors increase the convergence difficulty and forecasting accuracy. Guo [8] and Dong [9] consider the first IMF (intrinsic mode function) obtained by EMD (empirical mode decomposition) as noise, and demonstrate that eliminating the first IMF improves the forecasting accuracy in their experiments. In addition, the EMD-based signal filtering proposed in Ref. [20] indicates that noise potentially contains the first IMF or the first several IMFs. With this insight, this paper considers eliminating the noise interference to improve forecasting accuracy using the EMD-based signal filtering. This method is a fully data-driven approach without any predetermined filter or wavelet function, which means it is more efficient than the traditional noise reduction methods such as wavelet analysis. This paper then applies season index method, a common seasonal adjustment technology, on the processed data series to eliminate the seasonal component that influences the modeling procedure. Next, we model the intermediate data series by FFNN (feedforward neural network) using a multi-output forecasting strategy that overcomes the limitations of common multi-step-ahead forecasting approaches, including error amplification and the neglect of dependency between inputs and outputs. Finally, we restore the season indexes back to the FFNN forecasts to obtain the final electricity demand data series prediction. This paper is organized as follows: Section 2 specifies the EMDbased signal filtering and the seasonal adjustment method is described in Section 3. Feedforward neural network and its multioutput forecasting strategy are illustrated in Section 4. In Section 5 the proposed model is shown and the experimental results with their discussion are displayed in Section 6. Finally, Section 7 concludes this paper with the discussion on the contribution of this paper. 2. EMD-based signal filtering 2.. Empirical mode decomposition Huang et al. [2] proposed EMD (empirical mode decomposition) to decompose complicated signals into a series of IMFs (intrinsic mode functions) through the sifting process [22]. Each IMF component represents only one mode of oscillation imbedded in the signal at a certain scale or frequency band and it is quite distinct from others [2]. In the decomposition process, EMD picks out the highest frequency oscillation as the first IMF, and the frequency of the following IMFs decreases on each step. All of these IMFs satisfy two conditions [2]: ) the difference between the number of extrema and the number of zero-crossings is less than or equal to in the whole data series; 2) the mean value of the upper and lower envelopes is equal to zero at any point. Here the extrema includes maxima and minima, and the upper and lower envelopes are obtained respectively by connecting the local maxima and local minima using two cubic spline lines. For a signal x(t), the EMD process is shown in Table, where ε is often equal to 0.2 or 0.3, ε 2 is a very small predetermined value, U ik and L ik are the upper and lower envelopes of h i,k and SD k is defined by Eq. (). SD k ¼ XT t ¼ hi;k ðtþ h ik ðtþ 2 h 2 i;k ðtþ () Signal IMF Detailed illustration of the repeated sifting process Left minus Right h i0 h i h ik r IMF 2 Left minus Right m i0 m i m ik r i IMF i- Left minus Right Left minus Right Operation of subtraction IMF i The ith IMF, that is c i r n- Left minus Right IMF n r n The residue of EMD r n Fig.. The process of empirical mode decomposition.

3 N. An et al. / Energy 49 (203) 279e Since this process does not use any predetermined filter or wavelet function, it is a fully data-driven approach [20,22]. In addition, we can reconstruct the original signal using the following equation: xðtþ ¼ Xn i ¼ c i ðtþþr n ðtþ (2) where n is the number of IMFs. For better illustration, Fig. depicts this EMD decomposition process Filtering approach Using aforementioned EMD method, Boudraa and Cexus [20] introduced an EMD-based signal filtering to reduce the noise from a given signal. Because this method is a fully data-driven method and does not require any threshold setting and wavelet basis function selection, it is far more efficient than the traditional wavelet analysis. However, its effectiveness of noise removal in their experiments is similar to or even outperforms the wavelet method. The key assumption of this method is that the low frequencies have higher signal-to-noise ratio than the high ones for many signal classes corrupted by white noises [20]. Given a signal x(t) that is a deterministic signal y(t) corrupted by a noise z(t), our objective is to extract y(t) from x(t), that is, to find an approximation byðtþ to y(t) that minimizes the equation MSE y; by ¼ T t ¼ yðtþ byðtþ 2 (3) which is the MSE (mean square error) between the two signals where T is the length of y(t). Following the above key assumption that lower frequency corresponds to higher signal-to-noise ratio and assuming x(t) is decomposed into n IMFs and a residue r n by EMD, byðtþ can be reconstructed by the kth w nth IMFs and r n as follows by k ðtþ ¼ Pn i ¼ k IMF i ðtþþr n ðtþ; k ¼ 2;.; n (4) Since y(t) is unknown, CMSE (consecutive mean square error) is proposed to substitute the measure in Eq. (3). Just as its name implies, this quantity measures the squared Euclidean distance between two consecutive reconstructions of the signal which is defined in Ref. [20] as follows: CMSE by k ;by kþ ¼ T t¼ where k ¼,., n. If 2 by k ðtþ by kþ ðtþ ¼ T t¼ IMF 2 kðtþ (5) j ¼ argmin CMSE by k ; by kþ (6) <k<n then we estimate byðtþ as byðtþ ¼by j ðtþ ¼ Xn i ¼ j 3. Seasonal adjustment IMF i ðtþþr n ðtþ (7) From our practical experiences, for a time series containing seasonal components, it is usually more accurate to model the trend component than the original series. We hence consider the trend and seasonal components respectively to improve the modeling performance. This leads to a key problem that how to find the underlying trend, i.e. how to estimate seasonal components and remove them from the given series. The season index method is very effective at addressing this key problem, and has drawn significant attention. We briefly describe this method as discussed in Ref. [23]. For a time series x t (t ¼, 2,., T) with a seasonal component whose cycle length is s and cycle number is m, we notate it as {x, x 2,., x s ; x 2, x 22,., x 2s ;.; x m, x m2,., x ms } and let x k ¼ðx k þ x k2 þ / þ x ks Þ=s (k ¼, 2,., m ). Then the jth season index is defined as follows I j ¼ I j þ I 2j þ / þ I mj ; j ¼ ; 2;.; s (8) m where I kj ¼ x kj =x k (k ¼, 2,., m; j ¼, 2,., s). Using the above season indexes, we can eliminate the seasonal effect according to Eq. (9). x 0 kj ¼ x kj I j ; k ¼ ; 2;.; m; j ¼ ; 2;.; s (9) Then fx 0 ; x0 2 ;.; x0 s ; x0 2 ; x0 22 ;.; x0 2s ;.; x0 m ; x0 m2 ;.; x0 ms g which can also been notated as x 0 tðt ¼ ; 2;.; TÞ is the trend component. Assuming the fitness and prediction of x 0 t is bx0 t (t ¼, 2,., T,.), the modeling results of x t can be constructed as Eq. (0) bx t ¼ bx 0 t I (0) where I ¼ I j when t ¼ j, s þ j, 2s þ j,., (m )s þ j. 4. Multi-output forecasting of feedforward neural network 4.. Feedforward neural network An FFNN (feedforward neural network) is commonly referred to as MLPs (multilayer perceptrons) that consist of a set of sensory units called neurons. Neurons in turn groups into an input layer, one or more hidden layers, and an output layer. The neurons of adjacent layers are connected by directed weighted edges [24]. Neuron layers compute in a strictly feedforward fashion: signals pass from one neuron in one layer to another neuron in the next layer, but cannot pass to the previous layer or another neuron in the current layer because there are no feedback connections and no interactions between neurons in the same layer. In other words, signals can only pass from the input layer to the first hidden layer, then to the second hidden layer and so on, finally flow out the output layer. Furthermore, if signals from n neurons of the previous layer flow into one neuron i, it will flow out as an ensemble according to Eq. () 0 y i ¼ Xn w ij x ij w i0 A () j ¼ where w ij is the weight of the link from neuron j of the previous layer to the current neuron i, x ij is the corresponding signal, and w i0 is the inherent threshold of neuron i which is treated as a normal weight with the input signal being. In addition, f is called activation function or transfer function where linear function (purelin) f(x) ¼ x, logistic sigmoid function (logsig) f(x) ¼ /( þ exp( x)) and hyperbolic tangent sigmoid function (tansig) f(x) ¼ 2/ ( þ exp( 2x)) are usually used. Clearly, if there are N and K neurons in the input layer and output layer respectively, this feedforward network can map

4 282 N. An et al. / Energy 49 (203) 279e288 a point in R N (the input space) to a point in R K (the output space), which is similar to how a nonlinear regression performs [25]. Since the weight parameters are unknown, it is necessary to obtain weights which accurately reflect the relationship of input and output variables. Given a training data set with P inputeoutput pairs of vectors, the most powerful method to resolve this problem is BP (back-propagation) algorithm which targets to minimize the performance function Eq. (2). E ¼ 2P X P X K p ¼ k ¼ d ðpþ k o ðpþ 2 (2) k This performance function is the global mean sum squared error between calculated outputs o (p) and targeted outputs d (p) where p and k are indexes for the pth training sample and for the kth component of the output vector respectively. BP algorithm is based on the principle of gradient descent in which the network weights are moved along the negative of the gradient of Eq. (2) [26]. More specifically, the weight adjustment of w ji which is the weight from neuron i in layer m to neuron j in layer m þ is as follows: Dw ji ¼ hd ðpþ o ðpþ (3) j i where h is called learning rate which should be appropriately chosen to speed up the rate of convergence without oscillation, o ðpþ i is the pth output of neuron i in layer m, and d ðpþ is the pth d error j term which is back-propagated from the neuron j in layer m þ defined by Mohandes [27]: h i h i d ðpþ ¼ d ðpþ o ðpþ o ðpþ o ðpþ ; if neuron j is in the output layer j j j j j d ðpþ j h ¼ y ðpþ y ðpþ j j i P where k is index of neurons in layer m þ Multi-output forecasting k d ðpþ k w kj; if neuron j is in a hidden layer Given a time series {x t : t ¼, 2,., T}, we intend to forecast the next H, H, values by an autoregressive model as x tþ ¼ f ðx t d ; x t d ;.; x t d mþ Þþε tþ ¼ f ðx t d Þþε tþ (4) where d is the lag time, m is the number how many previous values are considered, ε is a white noise and X t d ¼ (x t d, x t d,., x t d mþ ) denotes the input vector of this model. Furthermore, we notate the H forecasts as Y ¼ðbx Tþ ; bx Tþ2 ;.; bx TþH Þ¼ðy ; y 2 ;.; y H Þ. To obtain these forecasts, there are two common multi-stepahead strategies: the iterated approach and the direct approach [28]. For the former one, the model is trained using one set of inputeoutput pairs fðx t d ; x tþ Þrt < Tg on a one-step-ahead basis, and then to forecast the next H values step by step as follows: ðx t d ; x t d ;.; x t d mþ Þbx tþ ; bx t d ;.; bx Tþ ; x T ;.; x t d mþ bx tþ ; bxt d ; bx t d ;.; bx t d mþ bx tþ ; T t T þ d T þ d < t < T þ d þ m t T þ d þ m For the latter one, H models are respectively trained using H sets of inputeoutput pairs fðx t d ; x tþh Þrt T hg, h ¼, 2,., H; then the next H values are forecasted as follows: Model : d bx Tþ Model 2 : d bx Tþ2.. Model H : d bx TþH Essentially, the iterated method is one-step-ahead strategy where the predicted values replace the unknown values to continue the one-step-ahead forecasting. While this method might have accurate predictions at times, the prediction error in each step cannot completely equal to 0 and it will propagate and amplify each step forward. As a result, this method is commonly used for shortterm forecast horizon instead of longer-term horizon tasks [29]. On the other hand, the direct method neglects the dependency between input variables and output variables. If H is sufficiently large, this model cannot even capture any relationship between inputs and outputs, let alone provide good prediction. In order to overcome the above shortcomings, this paper adopts a multi-input-multi-output strategy that targets the multi-output mapping instead of the single-output mapping of Eq. (4): F : R m R H X t d X tþ ¼ FðX t d Þ þ E (5) where X tþ ¼ (x tþ, x tþ2,., x tþh ) and E is the noise vector [29]. This method uses only one model with the number of outputs equal to the length of the horizon to be forecasted [28]. After training the model by one set of inputeoutput pairs fðx t d ; X tþ Þrt T Hg,we can predict those H values directly as follows Y ¼ Fð d Þ (6) Since all inputs are actual values, this method avoids the amplification of prediction errors. One obvious limitation of this robust method is that it only works with models that allow multiple outputs. Fortunately, FFNN model is one of such models. Fig. 2 depicts the multi-output forecasting process: the entire shaded region represents the trained FFNN model which preserves the inputeoutput relationship in its weight parameters and can be regarded as a black box requiring no detailed information [25]. If we input d into this black box, the predicted values Y can be obtained directly. 5. The proposed model Forecasting electricity demand accurately depends on the reliability and accuracy of historical data. In the real operation of power systems, a number of uncertain factors, most of which are beyond the control, may influence the data acquisition process including measurement, recording, conversion and transmission. Any of these factors can introduce noises and uncertainties in the electricity demand data series. Many existing models cannot handle this kind of data series well because they impose a number of pseudo-variation requirements on models and this affects the correct understanding of data variations. This would lead to poor generalization and undesirable forecasting performance, even though the training data are fitted perfectly. To address this problem, this paper proposes to use the EMD-based signal filtering approach, which has many benefits discussed in Section 2, to reduce the noise in the data series. In addition to a trend component, an electricity demand data series has one or more seasonal components because it is often affected by seasonal factors including weather, time, holidays and more. To further improve the forecasting accuracy, this paper proposes to use aforementioned season index method to complement the noise reduction method. After these processing steps,

5 N. An et al. / Energy 49 (203) 279e x T-d x T-d- y x T-d-m+ y H Input Layer Hidden Layers Output Layer Fig. 2. The illustration of multi-output forecasting using a feedforward neural network. FFNN with multi-output training and forecasting will be used on the data series to get the final forecasting results by Eq. (0). In a nutshell, the proposed model combines a multi-output feedforward neural network with empirical mode decomposition based signal filtering and seasonal adjustment. The name of this model is shortened as MFES (Multi-output FFNN with EMD-based signal filtering and Seasonal adjustment). As shown in Fig. 3, the MFES model consists of the following four steps: Step. Noise reduction: uses EMD-based signal filtering to reduce the noise term of the original signal; Step 2. Seasonal adjustment: removes the seasonal component from the resultant signal from Step and obtain the trend component; Step 3. Multi-output forecasting: predicts the future values of the trend using FFNN with a multi-output strategy; Step 4. Achieving final forecasts: restores the seasonal factor back to above predicted values and achieves final forecasts. 6. Simulation 6.. Problem description This study collects the electricity demand data (load pattern) of New South Wales in Australia covering the period from 2nd May 20 to 26th June 20 (eight weeks in total) in order to forecast the demand values in the following week (from 27th June 20 to 3rd July 20). Collected from these data are on a half-hour basis starting from 00:30 to 24:00, i.e. there are 48 observations per day. More specially, the original series has 2688 values which are shown in Fig. 4 and this study aims to forecast the next 336 values. Start Signal xt () Empirical mode decomposition as Table. EMD-based signal filtering Obtain n IMFs c, c2,..., c n, and one residue rn j arg min[ CMSE( yˆ, y ˆ )], where k k n n yˆ k c i k i rn n k y ˆ c r j i j i n is the noise-reduced signal of xt () Seasonal adjustment Notate yˆ j () t as xt (), i.e., xt There is a seasonal component in x t with seasonal length s Yes Compute the s season indexes I j, j,2,, s using Eq. (8) Remove the seasonal factor as xt x t I j, when t j, s j,2 s j, No Let I j, j, 2,, s Notate x t as x t Construct the training set as t {( X, X ) t T H} t d Multi-output forecasting by FFNN Train the feedforward neural network using BP algorithm With FFNN inputs being X T d, obtain the FFNN outputs ˆx, ˆx 2,, xˆh Obtain the final forecasts by taking back the seasonal factor as xt ˆ xi ˆ, t j, s j,2 s j, () t j End Fig. 3. The overall flowchart of the proposed model.

6 284 N. An et al. / Energy 49 (203) 279e288 Fig. 4 shows that the shape of data series in the same day of different weeks especially weekends (Saturday and Sunday) is more similar compared with the shape of data series in different days of one week. Considering this cyclic behavior, this study divides the original data series into seven groups based on the day of the week, i.e. Monday group, Tuesday group, and so on. This study then analyzes each of these day groups, and forecasts the corresponding day of the week, i.e. using Monday group to forecast following Monday. This refinement can improve the forecasting performance in two ways: this process only requires seven short 48-step-ahead forecasting instead of one long 336-step-ahead forecasting, and this breakdown decreases the forecasting difficulty; the uncertainties associated with each series are much less than the original series, and this makes it easier to model these series Statistics measures of forecasting performance There are three common criteria to evaluate the forecasting performance. They are RMSE (root mean square error), MAE (mean absolute error) and MAPE (mean absolute percentage error). For a time series x t (t ¼, 2,., T) with the corresponding forecast bx t, these measures can be calculated as follows vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u RMSE ¼ t xt bx 2 t (7) T t ¼ MAE ¼ T MAPE ¼ T t ¼ xt bx t (8) t ¼ x t bx t 00% (9) x t Clearly, the above criteria represent three kinds of deviation between the forecasts and the actual values: the smaller they are, the better the forecasting accuracy is Multi-output forecasting To address aforementioned forecasting problem, this section discusses four models, i.e. MFNN (Multi-output Feedforward Neural Network), MFE (Multi-output FFNN with EMD-based signal filtering), MFS (Multi-output FFNN with Seasonal adjustment) and MFES. The detailed modeling process of the MFES, which is proposed in this paper, is described as follows. First of all, MFES uses EMD-based signal filtering to denoise the seven original series in order to eliminate the noise interference. Fig. 5 displays this noise reduction process for the Monday original series. We can clearly observe its pre- and post-denoising series. Obviously, the resultant denoised series becomes smooth and it will be used to model instead of the original series. The situation of the rest six original series is similar to the Monday series and we omit their figures here. From our observation, these seven resultant series exhibit strong seasonality. Due to habitual behaviors of human being, where one half-hour session falls during the day will impact how the electricity demand changes during this particular half-hour session. To verify the existence of this seasonality in these seven series, we group the data by half-hour of the day, and get 48 groups in each series. Fig. 6 depicts box plots of these 48 groups for the seven denoised electricity demand series, and it clearly shows the half-hour of the day seasonality for all seven series. To improve the forecasting accuracy, MEFS takes this seasonality into consideration and employs the season index method on the denoised series where the period s ¼ 48. Next, MEFS uses FFNN model with a multi-output forecasting strategy to extrapolate from past behavior of seven intermediate series. Here, each series is normalized and the training set of each normalized series consists of inputeoutput pairs where input variables are 48 consecutive values of this series and output variables are the next 48 values. In other words, the multi-output forecasting expression Eq. (5) takes following parameter assignments: d ¼ 0, m ¼ 48 and H ¼ 48. In addition, since a feedforward neural network with three layers can approximate any continuous function in a reasonable way [30] and a hidden layer of 2n þ nodes is sufficient to map any function for n inputs according to Kolmogorovs theorem [3], we select three-layer FFNNs with 97 nodes in the hidden layer, where the activation function tansig and purelin are used in the hidden layer and output layer respectively. After FFNNs predict 48 values ahead and re-scale them for these seven series respectively, MEFS restores their corresponding season indexes back to these forecasts using Eq. (0), and achieves the final electricity demand forecasts. For impartial forecasting performance evaluation, this study uses the same FFNN parameter settings for MFNN, MFE and MFS models as those for MFES model. To reiterate differences between these models and MFES: while MFNN simulates the original series directly, MFE simulates the denoised series with inherent seasonal factors untouched and MFS simulates the seasonal-factor-removed series with inherent noise untouched. Fig. 7 shows the final predicted values by these four models, and it has one sub-graph showing results for each day: Monday, Tuesday and so on. Particularly, Table 2 lists the actual and predicted electricity demand The total electricity demand (MW) The day of each week Fig. 4. The electricity demand of New South Wales from 2nd May to 26th June, 20.

7 N. An et al. / Energy 49 (203) 279e Total demand (MW) Noise signal Denoised demand Fig. 5. Eliminate the noise signal from the electricity demand series on Monday. Denoised demand series values (MW) 2000 Monday Tuesday Wednesday Thursday 2000 Friday Saturday Sunday Half hour of the day Fig. 6. Box plots of the half-hour of the day seasonal pattern for the seven denoised electricity demand series. values along with the season indexes of MFS and MFES (season index and season index2 respectively) on Monday in detail. Here, season index and season index2 stand for season indexes of the original and denoised series respectively. They are located in various half-hour of the day. From this table, we can clearly observe the experimental process Comparative analysis Table 3 has various performance measures of four forecasting models discussed so far, and it reveals many details. When comparing MFE and MFS models with MFNN model, we have following observations: MFNN vs. MFE: In terms of important parameters RMSE, MAE and MAPE, MFE has desired lower values than MFNN for five days including Mon, Wed, Thur, Sat and Sun. Considering the aggregate values for the whole week, while RMSE of MFE is slightly higher than that of MFNN, MFE has reduced MAE by.40% and MAPE by 3.23%. MFNN vs. MFS: In terms of important parameters RMSE, MAE and MAPE, MFS has desired lower values than MFNN for five days including Mon, Tue, Wed, Thur and Fri. In addition, MFS has lower RMSE than MFNN on Sat. Considering the aggregate values for the whole week, MFS has reduced RMSE by 5.7%, MAE by 8.89% and MAPE by 9.4%. Above all, MFE and MFS are both better than MFNN for most days of the week, which leads to forecasting accuracy improvement for different cases for the whole week. While MFS gains a larger improvement than MFE in some cases, MFE has a better performance on several days especially weekends when MFS is not superior to MFNN. Combining merits of both MFE and MFS, MFES could obtain even better results. From Table 3, we can find there are two cases: On Tue, Wed, Thur and Fri: According to these three criteria, compared with MFS, MFES has slightly higher RMSE on Tue and Wed, and slightly higher MAE on Wed. In general, however, MFES performs better than MFS, which in turn performs better than MFE. On Mon, Sat and Sun: According to these three criteria, MFS has worse forecasting performance than MFE. At the same time, MFES greatly reduces three errors compared with MFS, and its performance is comparable to that of MFE. As a matter of fact, RMSE of MFES on Sat and Sun is even lower than that of MFE. In summary, among three investigated models (MFE, MFS and MFES), MFES has the best performance for four days in a week and is close to have the best performance for the rest three days in a week. Considering the aggregate values for the whole week, compared with MFE and MFS, MFES has reduced RMSE by 2.49% and 6.73% respectively, MAE by 28.5% and 3.09% respectively, and MAPE by 27.05% and 2.70% respectively.

8 286 N. An et al. / Energy 49 (203) 279e288 2 x x 04 Monday Monday Tuesday Wednesday Thursday Friday Saturday Sunday x 04 Tuesday x 04 Wednesday x 04 Thursday x 04 Friday x 04 Saturday Actual demand values Forecasted demand by MFNN Forecasted demand by MFE Forecasted demand by MFS Forecasted demand by MFES x 04 Sunday Fig. 7. Forecasting results of the four models for the electricity demand during the period from 27th June to 3rd July 20 for New South Wales. Table 2 The actual values, forecasts of the four models and season indexes on Monday (27th June 20). Time Actual value (MW) Predicted value (MW) of Season index Season index2 MFNN MFE MFS MFES 00: : : : : : : : : : : : : :00 0, :30 0, :00, :30, , , , :00, , , , , :30 0, , , , , :00 0, , , , :30 0, , , , :00 0, , , :30 0, , :00 0, : :

9 N. An et al. / Energy 49 (203) 279e Table 2 (continued ) Time Actual value (MW) Predicted value (MW) of Season index Season index2 MFNN MFE MFS MFES 3: : : : : : : , , :00 0, , , , , :30, , , , , :00,873.53, , , , :30,937.50,254.99, ,209.09, :00,87.77,443.96,308.65,0974, :30,59.45, , , , :00, , , , , :30, , , , , :00 0, , , :30 0, , :00 0, :30 0, : : : Table 3 Compare the forecasting performance of the four models for the electricity demand during the period from 27th June to 3rd July 20 for New South Wales. Date RMSE of MAE of MAPE (%) of MFNN MFE MFS MFES MFNN MFE MFS MFES MFNN MFE MFS MFES Monday Tuesday Wednesday Thursday Friday Saturday Sunday Whole week The aforementioned facts confirm that MFES is much better than MFNN. According to the three criteria, MFES outperforms MFNN significantly for every day. In total, for the whole week, compared with MFNN, MFES has reduced RMSE by 2.38%, MAE by 29.5% and MAPE by 29.4%. In a nutshell, both Table 3 and Fig. 7 demonstrate that while MFES clearly outperforms the other three models, these four models all have an acceptable performance for each day of the week. Their prediction curves almost coincide with the original data curves in Fig. 7. This fully illustrates the advantage of the multioutput forecasting strategy. In addition, for the whole week, since MFE and MFES outperform MFNN and MFS respectively, the advantage of EMD-based filtering is also apparent. 7. Conclusions This paper proposes a new electricity demand forecasting model called MFES. MFES first uses EMD-based signal filtering and seasonal adjustment to process the original electricity demand series in order to minimize the interference of noise signals and seasonal components. Here, the EMD-based signal filtering is a fully data-driven technology which is more efficient than traditional noise reduction methods since it does not require any threshold setting and wavelet basis function selection. Secondly, MFES employs FFNN to model the intermediate series with a multioutput strategy and overcomes the limitations of common multistep-ahead forecasting. Experiments with different criteria (RMSE, MAE and MAPE) clearly demonstrate that MFES significantly improves the electricity demand forecasting accuracy and provides great values for power utilities to control and plan for electricity supply. Acknowledgments This research was supported by the National Natural Science Foundation of China (Grant No. 7702, Grant No , and Grant No ), and the National High-Tech Research & Development Program of China (863 Program, Grant No. 202AA003). References [] Zhu S, Wang J, Zhao W, Wang J. A seasonal hybrid procedure for electricity demand forecasting in China. Applied Energy 20;88():3807e5. [2] Papalexopoulos AD, Hesterberg TC. A regression-based approach to shortterm system load forecasting. IEEE Transactions on Power Systems 990; 5(4):535e47. [3] Zhou P, Ang BW, Poh KL. A trigonometric Grey prediction approach to forecasting electricity demand. Energy 2006;3(4):2839e47. [4] Akay D, Atak M. Grey prediction with rolling mechanism for electricity demand forecasting of Turkey. Energy 2007;32(9):670e5. [5] Azadeh A, Saberi M, Seraj O. An integrated fuzzy regression algorithm for energy consumption estimation with non-stationary data: a case study of Iran. Energy 200;35(6):235e66. [6] Afshar K, Bigdeli N. Data analysis and short term load forecasting in Iran electricity market using singular spectral analysis (SSA). Energy 20;36(5): 2620e7.

10 288 N. An et al. / Energy 49 (203) 279e288 [7] Srinivasan D. Energy demand prediction using GMDH networks. Neurocomputing 2008;72(e3):625e9. [8] Azadeh A, Ghaderi SF, Sohrabkhani S. A simulated-based neural network algorithm for forecasting electrical energy consumption in Iran. Energy Policy 2008;36(7):2637e44. [9] Cai Y,Wang J-Z,Tang Y,Yang Y-C.An efficient approach for electric load forecasting using distributed ART (adaptive resonance theory) & HS-ARTMAP (Hyperspherical ARTMAP network) neural network. Energy 20;36(2):340e50. [0] Wang S, Yu L, Tang L, Wang S. A novel seasonal decomposition based least squares support vector regression ensemble learning approach for hydropower consumption forecasting in China. Energy 20;36():6542e54. [] Srinivasan D, Lee MA. Survey of hybrid fuzzy neural approaches to electric load forecasting. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. vol. 5. Vancouver, BC, Canada; 995, p. 4004e8. [2] Yao AWL, Chi SC, Chen CK. Development of an integrated Grey-fuzzy-based electricity management system for enterprises. Energy 2005;30(5):2759e7. [3] Kumara U, Jain VK. Time series models (Grey-Markov, Grey model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India. Energy 200;35(4):709e6. [4] Wang J, Zhu S, Zhang W, Lu H. Combined modeling for electric load forecasting with adaptive particle swarm optimization. Energy 200;35(4):67e8. [5] Amjady N, Keynia F. Short-term load forecasting of power systems by combination of wavelet transform and neuro-evolutionary algorithm. Energy 2009;34():46e57. [6] Nguyen HT, Nabney IT. Short-term electricity demand and gas price forecasts using wavelet transforms and adaptive models. Energy 200;35(9):3674e85. [7] Che J, Wang J, Wang G. An adaptive fuzzy combination model based on selforganizing map and support vector regression for electric load forecasting. Energy 202;37():657e64. [8] Guo Z, Zhao W, Lu H, Wang J. Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model. Renewable Energy 202;37():24e9. [9] Dong Y, Wang J, Jiang H, Wu J. Short-term electricity price forecast based on the improved hybrid model. Energy Conversion and Management 20;52(8e9): 2987e95. [20] Boudraa A-O, Cexus J-C. EMD-based signal filtering. IEEE Transactions on Instrumentation and Measurement 2007;56(6):296e202. [2] Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society A: Mathematical. Physical & Engineering Sciences 998;454(97):903e95. [22] An X, Jiang D, Li S, Zhao M. Application of the ensemble empirical mode decomposition and Hilbert transform to pedestal looseness study of directdrive wind turbine. Energy 20;36(9):5508e20. [23] Niu D, Cao S, Zhao L, Zhang W. Power load forecasting technology and its applications [in Chinese]. Beijing: China Electric Power Press; 998. [24] Ekonomou L. Greek long-term energy consumption prediction using artificial neural networks. Energy 200;35(2):52e7. [25] Kalogirou SA, Bojic M. Artificial neural networks for the prediction of the energy consumption of a passive solar building. Energy 2000;25(5):479e 9. [26] Kiani MKD, Ghobadian B, Tavakoli T, Nikbakht AM, Najafi G. Application of artificial neural networks for the prediction of performance and exhaust emissions in SI engine using ethanol-gasoline blends. Energy 200;35(): 65e9. [27] Mohandes MA, Rehman S, Halawani TO. A neural networks approach for wind speed prediction. Renewable Energy 998;3(3):345e54. [28] Andrawis RR, Atiya AF, El-Shishiny H. Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition. International Journal of Forecasting 20;27(3):672e88. [29] Bontempi G, Taieb SB. Conditionally dependent strategies for multiple-stepahead prediction in local learning. International Journal of Forecasting 20; 27(3):689e99. [30] Cadenas E, Rivera W. Short term wind speed forecasting in La Venta, Oaxaca, México, using artificial neural networks. Renewable Energy 2009;34(): 274e8. [3] Plumb AP, Rowe RC, York P, Brown M. Optimisation of the predictive ability of artificial neural network (ANN) models: a comparison of three ANN programs and four classes of training algorithm. European Journal of Pharmaceutical Sciences 2005;25(4e5):395e405.

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