Forecasting electricity load demand using hybrid exponential smoothing-artificial neural network model

Electric power as source of energy is very important for human life, for industrial activities as well as in the daily life of the household. The distribution of electricity in Indonesia is handled by PLN (state-owned electric company). PLN supplies electricity needs of customers. There are four groups of customers: residential, industrial, commercial and public. The growth in population and industrialization means increasing number of customers and it should be translated into the growth in electricity demand. Since the electricity cannot be easily stored in large quantities to fulfill national demand, the electricity must be produced as much as is needed at all times. When the electricity supply is less than the demand, the consumer needs are not be served well. This can lead economic loss to the state. Otherwise, excess of the quantity of electrical energy supplied over its demanded resulting in wastage costs. Therefore, accurate model forecasting for electricity power load would be needed in development planning process of electric power system.


I. Introduction
Electric power as source of energy is very important for human life, for industrial activities as well as in the daily life of the household.The distribution of electricity in Indonesia is handled by PLN (state-owned electric company).PLN supplies electricity needs of customers.There are four groups of customers: residential, industrial, commercial and public.The growth in population and industrialization means increasing number of customers and it should be translated into the growth in electricity demand.Since the electricity cannot be easily stored in large quantities to fulfill national demand, the electricity must be produced as much as is needed at all times.When the electricity supply is less than the demand, the consumer needs are not be served well.This can lead economic loss to the state.Otherwise, excess of the quantity of electrical energy supplied over its demanded resulting in wastage costs.Therefore, accurate model forecasting for electricity power load would be needed in development planning process of electric power system.In this paper, univariate time series models are chosen by assuming that other variables can be captured in the load demand series itself.A time series of electricity load contains multiple seasonal cycles like daily, weekly and monthly seasonal cycles (see [1], [2], [3], [4], [5], and [6]).Over the years, several different forecasting techniques have been proposed to model the multiple seasonal electricity load.Some of them are based on the concept of exponential smoothing.Because of its simplicity, robustness and accuracy, Holt-Winter exponential smoothing became well known and was widely used to model single seasonal time series.Taylor [6] developed traditional ) to accommodate a second seasonal component.This method, called by double seasonal Holt-Winter (DSHW), corrects for residual using a simple autoregressive model.It assumes that the cycle of the intra-day is the same for all days of the week so that updates are the same for each day of the week.Gould et al. [4] improved DSHW by allowing the seasonal terms of one sub-cycle to be updated during the time for another sub-cycles.This approach is done by using the same sub-cycles for the days displaying similar patterns, such that it is possible with the model to have different smoothing parameters for different sub-cycles.
Several exponential smoothing methods are equivalent to point forecasts of special cases of linear innovation state space model ( [8]).Exponential smoothing methods are optimal for a class of innovation state space models (see [9] and [10]).De Livera et al. [2] introduced an innovations state space modelling framework based on trigonometric formulation for exponential smoothing.This state space exponential smoothing model allowed for any autocorrelation in the residuals to be taken into account.
In the recent study, some researchers hybridized two models to improve load forecasting performance.Sadaei et al. [23] and [24] implemented fuzzy as a part of hybrid models and [25] combined wavelet and ANN to forecast Australia electricity market load data.Shukur et al. [4] hybridized DSHW with ANN where components of DSHW are updated by substituting the original data with the output of ANN.In this paper, a hybrid approach based on exponential smoothing modified by [2] and neural network based on feed-forward back-propagation is proposed in order to enhance the forecasting accuracy.The strategy of building hybrid model used in this paper is different from those in [4].In this study, state space exponential smoothing is proposed to determine the level, trend, seasonal and irregular components which then become the inputs of ANN.

A. Exponential Smoothing Model
Forecasting methods based on the concept of exponential smoothing obtain the forecasts by combining the exponentially decreasing weighted past observations.In 1957, Holt introduced additive and multiplicative seasonal exponential smoothing ( [26]).In the following year, [7] provided empirical test for Holt's methods and it then became more popular, known as Holt-Winters' method.Taylor [6] introduced DSHW as the extension of Holt-Winters method.This method is suitable for double seasonal time series with nested seasonal patterns and integer seasonality.
De Livera et al. [2] proposed exponential smoothing state space model with Box-Cox transformation, ARMA error, trend and trigonometric representation of seasonal components, named by TBATS.In this model, trigonometric functions based on Fourier series [27] is used to represent seasonal component.Thus, TBATS is more flexible approach to accommodate integer and non-integer seasonality, multiple nested and non-nested seasonal patterns.

B. Artificial Neural Network
ANN can be used for modelling and forecasting nonlinear time series ( [29], [30]).ANN learns from past behavior and finds subtle functional relationships among data in the past and then obtains forecast values via prediction future behavior.The structure of ANN consists of input nodes, hidden layers and output nodes.One or two hidden layers are enough for most forecasting problems [31].The best network is obtained from the right combination of the number of input nodes, hidden layers and output nodes.This is also influenced by the weights that connecting every two nodes.Backpropagation is the most popular learning algorithm in selecting the weights.In its implementation, there are several optimization algorithm that can be included into the back-propagation algorithm, such as conjugate gradient, Gauss-Newton, and Levenberg-Marquardt.These algorithms can be used to train the network, finding the weights by minimizing the sum of square error function ( [32]).
In this study, the network involves some inputs and one output.The input nodes are the past observations and the output is the forecast value.ANN model is focused on the feed forward neural network with Levenberg-Marquardt back-propagation algorithm.

III. Proposed Hybrid Model and Algorithm
Based on (1), the forecast values of TBATS are obtained from the summation of level, trend and seasonal components.Since there may be linearity and nonlinearity in load data series together, hybrid TBATS-ANN is proposed to improve forecasting performance.In this paper, TBATS is used to decompose load time series data into level, trend, seasonal and irregular components and ANN is applied to capture nonlinearity in the data.The idea is finding forecast value by using ANN where the past m time period level, trend, seasonal and irregular obtained from TBATS be inputs of ANN.Framework of this study is shown in Fig. 1.Algorithm of the proposed method is presented below.
Step 1: Divide the data into in-sample and out-sample data.
Step 2: Apply TBATS model to decompose load time series which has complex seasonal into level, trend, seasonal and irregular components.The following steps show how TBATS model is constructed and how the model extract the datasets [ , and define the initial seasonal state estimates as ̂ () = ∑  ̂(i)  (   (i) ) +  ̂(i)  (   (1) ) where  ̂(i) and  ̂(i) are estimated by regressing   against the trigonometric terms.The number of harmonics   in the trigonometric models is selected based on the value of Akaike Information Criterion (AIC).e. Approximate the initial level and trend components by computing a linear regression on the first  * deseasonalized values, against a time variable  = 1, . .,  * .The intercept and the slope of this regression are then set as the initial level and the initial trend respectively.f.Optimize the initial state values along with the Box-Cox parameter and the smoothing parameters by maximizing the likelihood.g.Select the best model based on the value of AIC.In this case, ARMA (, ) error component is only retained if the resulting model has lower AIC than the model with no ARMA component.h.Obtain the level component by   , trend component by   , and the first and the second seasonal components by   (1) and   (2) respectively.Irregular component,   , is obtained from   −   −   −   (1) −   (2) .

IV. Illustration
This research uses two load time series data for showing the forecasting performance of the proposed hybrid approach.A half-hourly load of Bawen, Salatiga, which is recorded from 1 February to April 2013 is used as the first illustration and an hourly load of Java-Bali from January until July 2010 be the second illustration.The forecast accuracy of proposed hybrid model is compared with TBATS, ANN, and DSHW.In this study, TBATS and DSHW are implemented using R.3.3.0 and ANN model is obtained through Matlab R2015a.

A. Application to A Half Hourly Load Data
A half-hourly load of Bawen substation measured in Megawatt (MW) taken from PT PLN P3B Java Bali Region Salatiga is used in this research.The three months data recorded from 1 February to 30 April 2010 is divided into training data set (in-sample) and testing data set (out-sample).The first two months is considered as an in-sample data and the rest month be out-sample data.The load series contains a daily and weekly seasonal patterns with period 48 and 336, respectively.Based on the selection procedure, TBATS does not need Box-Cox transformation and ARMA (3,2) process is appropriate to describe the irregular component.Since there is no damping parameter, the growth rate   was omitted from the model.Thus, the inputs of ANN are level, seasonal 1, seasonal 2 and irregular components of TBATS.In this case, the number of nodes in hidden layer is set to 10 and  is chosen between 1 and min ( 1 ,  2 ) = 48 so that the model produces the smallest MSE.The comparisons of forecast accuracy among the models are shown in Table 1 and Fig. 2. It can be seen from Table 1 that among the three single models, TBATS yields the highest RMSE and MAPE both in in-sample and out-sample and DSHW produces the smallest one.This probably because DSHW is designed to model integer and nested seasonal pattern which coincides in the given illustration while TBATS is more powerful in non-integer and non-nested seasonal pattern.By combining with ANN, the better performance of forecasting is achieved.Fig. 2 shows that hybrid TBATS(1,{3,2},−,{<48,5>,<336,5>})-ANN(48-10-1) yields the smallest MAPE and RMSE for the load of Bawen.It reduces MAPE of TBATS 77% and ANN 45% at out-sample.

B. Application to An Hourly Load Data
Java Bali load data used in the second illustration was taken from PT PLN P3B Java Bali for period 1 January 2010 to 31 July 2010.The data from January until June 2010 is used as in-sample and July 2010 as out-sample.Different from the first case, Java Bali load exhibits daily seasonal pattern with period 24 and weekly seasonal pattern with period 168.TBATS decomposed the series into level, trend, seasonal 1, seasonal 2, and irregular components.Though the irregular component of the series is not uncorrelated, it cannot be described by ARMA model.This may have caused the MAPE and RMSE of TBATS relatively large.Comparisons of forecast accuracy between the selected TBATS, ANN, DSHW and proposed hybrid approach is presented in Table 2.There is no guarantee that ARMA process appropriate to describe the irregular component of the series.This is probably caused by the existence of the nonlinearity pattern in the data that cannot handle by TBATS.ANN model is superior in handling nonlinear pattern.The hybrid TBATS-ANN is proposed to capture multiple seasonality, high frequency seasonality and nonlinearity pattern of the series therefore the forecast performance can be improved.Algorithm of the proposed hybrid approach is started by decomposing the load series into level, trend, seasonal and irregular components and continuing using the decomposed components as inputs of ANN.Thus the forecast can be obtained from ANN model with the inputs are the level, trend, seasonal and irregular components of the series.Based on the results for load data of Bawen and Java Bali substations which have integer and nested seasonal pattern, the proposed hybrid model generally yields smaller MAPE and RMSE than TBATS, ANN and DSHW.

1 −
−2 1+ −2 , and activation function in output layer is linear function, () = .Back-propagation learning algorithm based on Levenberg Marquardt algorithm is used to estimate the weight w and the bias b.
2]. a. Estimate an initial value for Box-Cox parameter and transform the data.b

Table 1 .
Comparison of MAPEs and RMSEs of The Proposed Hybrid Approach with TBATS, ANN and DSHW for Load of Bawen

Table 2 .
Comparison of MAPEs and RMSEs of The Proposed Hybrid Approach with TBATS, ANN and DSHW for Load of Java Bali