Review Article | Open Access
Long-term load forecasting using neural network approach for Jordan’s power system
EA. Feilat1*, D. Talal Al-Sha’abi2 and MA. Momani2
1Electrical Engineering Department, University of Jordan, Amman- Jordan
2Electrical Power Engineering Department, Yarmouk University, Irbid- Jordan
*Corresponding author: Eyad A. Feilat
Electrical Engineering Department, University of Jordan, Amman- Jordan; E-mail: E.Feilat@ju.edu.jo
Received: November 8th, 2017; Accepted: November 28th, 2017; Published: December 4th, 2017
Eng Press. 2017; 1(1): 43-50. doi: 10.28964/EngPress-1-108
Ⓒ 2017 Copyright by Feilat EA. Creative Commons Attribution 4.0 International License (CC BY 4.0).
This paper presents a neural network (NN) based approach for long-term load forecasting (LTLF) of the Jordanian power system from 2015 to 2029. Two types of feed forward neural networks (FFNN) are examined, namely, the back-propagation and the radial basis function neural networks; (BPNN) and (RBFNN), respectively. Historical data obtained from the National Electric Power Company (NEPCO) have been used in training and testing the proposed neural networks. The simulation results show that both neural networks show quite good performance over a long forecasting period. The performance accuracy of both NNs is assessed in terms of the mean square error (MSE) and mean absolute error (MAE). Moreover, the forecasting results of the proposed NN approach have been compared with the forecasting results obtained by NEPCO. It was found that the results are comparable and satisfactory. The case study reveals that the proposed NN approach can be effectively applied for forecasting the annual peak loads of the Jordan’s system.
KEYWORDS: Load forecasting; Neural networks; Radial basis function; Back propagation.
Power system restructuring yielded to generation, transmission and distribution corporate entities. These entities are confronted with increasing demand on reliable operation of power system networks. The major worry for every electric utility is the ability to supply reliable and uninterrupted service to their customers, both large and light loads. The challenge becomes more difficult with the fast and sharp increasing on the energy demand in growing countries.1,2
Load forecasting plays a crucial role in developing and enhancing the efficiency of the power system, since it guarantees economic and reliable planning, control and operation of the power system. It helps an electric utility to make important decisions including decisions on purchase and generation of electric power, and development of transmission and distribution systems infrastructure. It is considered as a key of success for the development of electrical power systems. Therefore, developing accurate mathematical models for electric load forecasting became essential to the operation and planning of power transmission and distribution utilities.1,2
Load forecasting can be divided into three categories: short-term load forecasting (STLF) which is usually from one hour to one week, medium-term load forecasting (MTLF) which is usually from a week to a year, and long-term load forecasting (LTLF) which is required to be valid from 5 to 25 years. A LTLF is generally known as an annual peak load forecasting.2
Several forecasting methods have been developed for STLF, MTLF and LTLF. These methods can be classified in to two broad categories: parametric and nonparametric methods. Parametric methods that are used for load forecasting include mathematical such as statistical regression techniques3-6 and time series methods including mathematical models such as Autoregressive (AR), Moving Average (MA), ARMA and Autoregressive Integrated Moving Average (ARIMA).7-9 On the other hand, nonparametric methods are primarily artificial intelligence based algorithms; such as artificial neural networks (ANNs),10-16 fuzzy logic (FL),17,18 and expert systems (ES),19 genetic algorithms (GAs),20 support vector machines (SVM)21,22 and wavelets.23,24
For STLF and MTLF several factors are considered such as historical load, time factors and weather data.8-12 Likewise, LTLF is affected by the socio-economic and demographic data and their forecast such as gross domestic product (GDP) and population (POP), and other factors that depend on the electric power system in the country like power losses in the power system (in MW) and load factor (LF). Several case studies have been conducted for LTLF using different regression, neural network and combined neural-network fuzzy logic techniques.25-34
Artificial neural networks (ANNs) have been applied successfully to solve some complex practical problems such as function approximation, pattern classification, and nonlinear mapping for which conventional approaches have proven ineffective.35-37 The essential purpose of the development of the ANNs is to make the computers do what a human being cannot do. Due to the availability of the fast and inexpensive personal computers, the attention in ANNs has been prospered in the current digital world. ANNs can be considered as adaptive tools which can save information through the learning process; the network is trained using actual electrical peak load data from the past. ANNs can discover and learn correlated factors between input data sets and matching target values. After training, the network can be used to forecast the outcome of new independent input data.
In this paper, two types of multi-layer FFNNs; namely backpropagation neural network (BPNN) and radial basis function neural network (RBFNN) are developed to forecast the peak load of Jordan’s power system for the period 2015-2029. Input variables including the peak load (PL), gross domestic product (GDP) and population (POP) are used for developing the proposed ANN. Several ANN models with different structures, learning algorithms and transfer functions have been used in order to achieve the best generalization ability. The forecasting results of the two proposed ANNs are compared with the forecasting results obtained by NEPCO using Gompertz extrapolation technique.38
The interconnected system in Jordan consists of the main generating power stations, 132 kV and 400 kV transmission grid, which interconnects the power plants with the load centers and different areas in Jordan is illustrated in Figure 1. The system also includes the 230 kV, 400 kV tie lines with Syria and the 400 kV tie line with Egypt. Moreover, the Jordan’s power system incorporates three power distribution networks. The annual peak load reached a value of 2900 MW in the year 2014 and 3300 MW in the year 2015.39
The variations of PL of the Jordan’s system in MW, GDP in millions of JOD and POP in 1000 inhabitants from 2000-2013, are illustrated in (Figure 2).
The correlation between the input variables PL, GDP and POP is estimated using the MATLAB corrcoef function. The correlation results are presented in Table 1. It can be seen that the annual PL highly depends on the GDP, POP and GDP2.
ARTIFICIAL NEURAL NETWORKS
ANNs are data processing systems consist of highly interconnected elements, called neurons, are connected together in layers and work in parallel. In its basic form a FFNN consists of an input layer, an output layer, and one or more hidden layers. Each layer consists of a set of neurons or nodes that are fully connected to the neurons in the next layer. The neurons are linked by synaptic weights, which are allowed to adjust through a learning procedure. A neuron output of the hidden layer can be described as
where are inputs of the pth input pattern; wh1,wh2 ,L ,wk are the weights of the hth hidden neuron; wo is a threshold; and is the activation function. The number of neurons and hidden layers is problem dependent. FFNNs are divided into two groups depending on the type of activation functions and learning methods; namely BPNNs and RBNNs network.35,39
The process of determining the weights is called training process. In the training process, sets of input-output patterns are associated by properly adjusting the weights in the network such that an error measure (the difference between the target and the predicted outputs of the network) is minimized. A sum of squared error function is commonly used. Various training algorithms have been developed to adapt the weights in ANNs to reduce the error defined
where tk is the target output, and Ok is the predicted output of the neural network.
Backpropagation Neural Network (BPNN)
BPNNs have been applied to nonlinear system modelling and function approximation problems. It has been proven that a network with one hidden layer can perform any nonlinear mapping and no more than two hidden layers are needed for most applications.35,36 A one-hidden layer BPNN is shown in Figure 3. Normally, the transfer function for the hidden layers can be one of different differentiable transfer functions such as the logsigmoid given by Eq (3), and for the output layer is the linear given by Eq (4) as shown in (Figure 4).
The BPNN is usually trained in supervised learning using a gradient descent rule to adapt the weights, and the error is calculated and propagated backwards from the output to the hidden layer to the input. The weights are adjusted so as to make the error between the actual response and the desired response smaller than a target value.
Radial Basis Function Neural Network (RBFNN)
RBFNNs are powerful techniques for interpolation in multidimensional space. They can be used very efficiently for interpolation and for smoothing of data. The RBFNN has a topology of input layer with input nodes equal to the size of the input pattern. It has also one hidden layer with nonlinear radial basis neurons that are connected directly to all of the nodes in the input layer. The output layer consists of neurons, with linear activation functions, fully connected to the hidden layer as shown in Figure 5. The neuron output in the output layer is chosen to be a linear sum of all inputs coming from the neurons of the hidden layer, that is
where fj (xp) is a radially symmetric function. The most common basis function is the Gaussian
where σj and cj are the width and center of the radial basis function, respectively. The weights wkj can be determined by using the least-squares (LS) method after selecting suitable values for the width and center of the function. The main advantage of the RBFNN over the BPNNNN is the fast learning.
ANN Model Development
The MATLAB neural network toolbox33,34 can be used to design both of the proposed BBNN and RBFNN. The BPNN model can be constructed using the MATLAB newff function which determines the specific architecture of the proposed BPNN. In this function, the number of hidden layers, number of hidden neurons, the number of output variables, the type of activation functions in the hidden and output layers, the training algorithm and a target error are specified. Several training algorithms have been developed in MATLAB to speed up the training process such as traingdm, traingdx, trainrp or trainlm, etc.40
Likewise, the RBFNN model can be constructed using the MATLAB newrb command function. Initially the first layer has no neurons, after simulating the network input vector with the largest error is set up, and then a neuron with a linear function and weights equal to that vector is added. As training goes on, more hidden neurons are added until a specific target error is achieved. The hidden neurons are processing units that execute the Gaussian basis function. The output unit is a summing neuron which renders weighted sum of the hidden layer neurons output.
INPUT-OUTPUT DATA PROCESSING
ANNs training and testing can be more efficient, learn more quickly and give better performance if the inputs and targets are pre-processed before being used to train the ANN to equalise the importance of input variables. In this way, the ANN output always falls into a normalized range. The ANN output can then be reversed transformed back into the units of the original target data. There are several functions in MATLAB for data pre-processing such as mapstd and mapminmax. The function mapstd normalizes inputs/targets to have a 0 mean and a 1 variance, whereas the function mapminmax normalizes inputs/targets to fall in the range [−1, 1]. Similarly, inputs/targets can be normalized to fall in the range [0,1] using the minmax function given by Eq (7).
where xn is the normalized data, xmin is the minimum value of x and xmax is the maximum value of x.
ANN’s PERFORMANCE INDEX
Generally, the performance of proposed ANNs can be assessed in terms of the mean square error (MSE) and mean absolute error (MAE) where,
where N is the number of output samples.
Both of the proposed BPNN and RBFNN have been trained using the historical data of the annual PL, GDP and POP over the period 2000 to 2014 years. These values will also be used to forecast the PL for the years 2015 to 2029. Accordingly, the historical data comprising input-target patterns have been divided in two sets; training and testing sets. The training set comprising 70% of the historical data while the testing set comprising 30%. The training and testing input-output patterns are presented in Table 2 and Table 3, respectively.
Training and Testing Performance of the BPNN
In this work, the architecture of the proposed BPNN consists of input layer with four inputs (year, POP, GDP and GDP2) and an output layer with one output (PL). Moreover, architectures with one, two or three hidden layers with several numbers of hidden neurons have been examined for the best performance of forecasting. The logsigmoid and purelin activation functions have been used for the hidden and output layers, respectively. Moreover, the effects of the training algorithms such as trainlm, trainrp and traingdx and the normalization function such as mapminmax and mapstd on the performance of the BPNN have also been investigated. In this work, it was found that the mapminmax normalization function gives better performance compared to mapstd. The results of training and testing simulations are presented in Table 4. The performance of the BPNN has been assessed in terms of the MSE and MAE indices.
Examining the results of Table 4, it can be seen that an architecture of four inputs, one hidden layer with 10 neurons and one output (4×10×1) is the most suitable architecture of the proposed BPNN in terms of the least MSE and MAE error convergence between the target and actual ANN output. The training and testing performance of the proposed BPNN peak load forecaster is depicted in (Figure 6 and Figure 7), respectively.
Examining the training and testing results, it can be seen that the BPNN load forecaster shows excellent performance. Both targets and actual BPNN outputs match each other with high degree of accuracy.
Training and Testing Performance of the RBFNN
In MATLAB, a RBFNN can be constructed using either newrb or newrbe function. In this work the newrbe function has been used as it leads to faster convergence and lease MSE and MAE errors. (Figure 8) and (Figure 9) show the training and testing performance of the proposed RBFNN with an architecture of four inputs, one hidden layer with 15 neurons and one output (4×15×1) and a 0.5 width constant.
Load Forecasting using the Proposed BPNN and RBFNN
The results of peak load forecasting of both the BPNN and RBFNN for the years 2015-2029 together with the forecasting results obtained by NEPCO are presented in (Table 5). The growth rates are also presented.
A comparison between the proposed BPNN, RBFNN and NEPCO forecasting results over the years (2015-2029) are depicted in (Figure 10). Figure 10 reveals that the forecasting results of the peak loads and growth rates are comparable. This is considered acceptable for long-term load forecasting study.
A neural network approach for long term peak load forecasting of the Jordan’s power system is proposed in this paper. A BPNN and RBFNN have been developed. The peak load is related to the GDP and population. Several architectures of the proposed BPNN and RBFNN have been examined. It was found that the best architectures is a 4×10×1 for the BPNN and a 4×15×1 for the RBFNN. The forecasting results of the BPNN and the RBFNN have been compared to that obtained by NEPCO for the years 2015-2029. It was found that the results are comparable and satisfactory. The results of the case study show that both BPNN and RBFNN provide reliable and efficient technique for long term annual peak load forecasting.
CONFLICTS OF INTEREST
The authors declare that they have no conflicts of interest.
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