Application of a hybrid quantized Elman neural network in short-term load forecasting

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Highlights

  • A hybrid quantized Elman neural network with quantized training is proposed for STLF.

  • The GA algorithm is used to optimize the structures of the proposed neural model.

  • The comparisons for STLF are carried out among the ENN, MFNN and our neural models.

Abstract

This paper investigates the short-term load forecasting (STLF) problem via a hybrid quantized Elman neural network (HQENN) with the least number of quantized inputs, hourly historical load, hourly predicted target temperature and time index. The purpose is to show the capabilities of HQENN to learn the complex dynamics of hourly power load time series and forecast the near future loads with high accuracies. The HQENN model is comprised of the qubit neurons and the classic neurons. The laws of quantum physics are employed to describe the interactions of the qubit neurons and the classic neurons. The extended quantum learning algorithm makes the context-layer weights being extended into the hidden-layer weights matrix such that they can be updated along with hidden-layer weights to extract more information about the load series. To improve the forecasting accuracy, the genetic algorithm (GA) is introduced to obtain the optimal or suboptimal structure of the HQENN model. The results indicate that the forecasting method based on HQENN has an acceptable high accuracy.

Introduction

Short term load forecasting (STLF) of power systems has significant impact on the electric network’s reliability and market demands. The accurate load forecasting, referring to hourly power load prediction of ranging from one to several days ahead, can provide sufficient information for the market operators determining day-ahead market prices and the relational participants preparing bids. The inaccurate forecasting will result in a great deal of loss for power companies. The relevant literature suggests that a 1% increase in forecasting error implied a 10 million increase in operating costs [27]. For over-load forecasts, the sub-optimal scheduling of power unit commitments will lead to the start-up and fixed costs. For under-load forecasts, the optimal electricity-generation could be required to guarantee supply which causes purchases of expensive peaking power [10].

As indicated above, the forecasting of short-term-load is crucially important for the efficiency of electrical utilities operation. The SLTF problem is investigated, in both of the practice and the academia, by many techniques that have been developed, such as support vector machine [26], neural networks [4], [13], and statistical analysis [5], [23], [29], to mention but a few. Owing to the real-time, controllable, random, dynamic and nonlinear relationships of the loads, the neural networks, among these methods mentioned above, are recognized as one of powerful computational tools with strong robustness and fault tolerance to solve the STLorder to improve the prediction accuracy and stabilityF problem influenced by several factors including seasonal factors, past usage patterns, climatic conditions, social activities [15], [36].

During the last decades there have been lots of research work focusing on the neural network to find nonlinear relationship between the load and the affecting factors only using the historical data set without any structural model. The work in [36], using the rough set to avoid the influence of noise data and weak interdependency data, decreases the training time of back propagation (BP) network and improves the accuracy of STLF. In [3], the weights of BP neural network are adjusted by the particle swarm optimization (PSO) algorithm. Exploiting the wavelet transformation, the redundant information is extracted from the load curve which offers a high forecasting precision. Ref. [28] presents a hybrid STLF approach based on the wavelet decomposition and the fuzzy neural network, which shows superiority over the non-wavelet methods for the same set of data of the same utility. The authors in [6] present a similar day-based approach applying a wavelet neural network (WNN) to forecast the power load. In [12], the authors propose a method of WNN with data pre-filtering to predict the loads 1 h into the future in 5-min steps in a moving window manner based on real-time data collected.

Although the aforementioned methods are reported to be proper and helpful for the power load forecasting, the following issues should be considered:

  • In fact, the load forecasting can be essentially regarded as a processing of time series employing extrapolation of historical data for the estimation of future hourly loads. The aforementioned methods, using the static artificial neural network (ANN) with the likes of BP neural network, radial basis function (RBF) neural network, WNN, focus on the statistical property of the power loads. However, even from an intuitive perspective, it is evident that the nature of the load is dynamic, rather than static. The change in the load is not only influenced by the external weather and time variables, but also highly dependent on the past and current load state. Thus, in this sense, static neural networks are suboptimal load forecasting models, and previous load state information has to be incorporated by presenting the network with the appropriate past load values [33].

  • To some extent, the predictive ability of the network, depending on its own topological structure and learning algorithm, is crucially important for the accuracy of STLF. The neural networks mentioned above, from the perspective of topological structure, essentially belonging to feed-forward networks, have accomplished the weights-fixed mapping from input space to output space. The states of any neurons of these networks are only determined by the corresponding unit-inputs, rather than the initial states and past states of the neurons. The dynamic nature of these networks is limited since the initial states and the past states are independent of each other. In order to make the initial states and the past states of the neurons can be involved in a series of processing, recurrent neural network (RNN) uses feedback connections to model spatial as well as temporal dependencies between input and output series [32]. In this sense, RNN, exhibiting inherent dynamic behavior of the neural network, is used to construct empirical models for the load as a dynamic system. Because of the nonlinear nature of these models, the behavior of the load prediction system is captured in a compact, robust and more natural representation [33].

  • So far, there are only few studies having been reported to address STLF problem using the RNN, such as the three-layer RNN [33], the Jordan RNN [17], the real-time RNN [14], the Elman neural network (ENN) [16], the echo state network (ESN) [7]. For example, the authors in [16] propose a method using the combination of wavelet transform (WT) and ENN to predict 1-day-ahead electrical power load. The ENN they designed is trained by the standard back-propagation (BP) algorithm, known as Elman BP (EBP). However, the ENN using the EBP training often suffers from low convergence speed and poor generalization performance [19], [20], [31]. In order to improve the prediction accuracy and stability, the ENN used in [16] is inevitably combined with other techniques such as WT to set a hybrid model. Actually, besides the ENN being used as a part of hybrid methods, improving its own performance of ENN can also reach the expected accuracy of STLF. In recent years, some relevant literatures [34], [21], [11], [25] report that the quantum neural computation (QNC), being generated by the combination of quantum computing and neural computing, is introduced into the RNN for improving its convergence speed and generalization performance. Therefore, the ENN with quantum techniques may be an effective approach to address the STLF problem due to the quantum parallelism and entanglement of QNC.

This paper focuses on the scenario of hourly load prediction using a hybrid quantized Elman neural network (HQENN). Both the qubit neurons and the classic neurons are taken as the basic elements of the proposed network. The laws of quantum physics are employed to describe the interactions of the qubit neurons and the classic neurons. Unlike the well-known EBP learning, the corresponding training algorithm contains the updating law of the quantum parameters. The weights of the context layer are updated along with the weights of hidden layer for extracting more gradient information about load series. Based on GA, the optimal or suboptimal structure of our model is appropriately selected for enhancing the load forecasting ability. For the sake of completeness, several approaches including the ENN based on EBP learning [16], the multilayer feed-forward neural network (MFNN) based on BP learning [3], and our proposed neural network based on quantized EBP training, are compared and discussed in this paper. The performance of each presented method is evaluated by means of an extensive simulation study, using actual hourly load data from the power system in Chongqing.

Section snippets

A hybrid quantized Elman neural model

As a subclass of recurrent neural networks, ENN [8], [9] is conceived to operate on time series represented by internal states of neural activation. It has been proved remarkably useful for prediction of discrete-time series due to the promising abilities of modeling nonlinear dynamic systems and learning time-varying patterns [1], [24]. In this section, the quantum techniques are introduced into ENN for improving its convergence speed and generalization performance, thereby producing a HQENN

Application of the proposed neural model

In this section, some practical issues are investigated to construct the HQENN model for the application of STLF. The forecaster using the proposed neural model is desired to be a hourly system with the outputs integrating 24 h load values into the future.

Numerical experiments

The numerical simulations are run on a laptop PC (Intel (R) Core (TM) i3-2350M, 2.30 GHz, 2 GB RAM). The simulation models and design of experiment are implemented in “MATLAB 7.0”. To verify the forecasting accuracy of the HQENN model based on qeEBP training, the simulation results are compared to the current utility practices such as the MFNN model based on BP training [3] and the ENN model based on EBP training [16].

As mentioned in Section 3, the dataset containing the loads and their

Conclusion

This paper focuses on studying the capability of the HQENN model for STLF. The main contribution is that a novel HQENN model and its qeEBP training algorithm are proposed to learn complex dynamics of hourly power load time series and forecast the near future loads. For the structure, the quantum map layer is employed to address the quantized load pattern mismatch between the input layer and the hidden layer. For the learning algorithm, unlike the EBP training with fixed context-layer weights,

Acknowledgement

This work is jointly supported by the Youth Science and Technology Innovation Talents Project of Chongqing Science & Technology Commission under Grant No. cstc2013kjrc-qnrc40005 and the Scientific Research Foundation for the Introduced Talent of Chongqing University of Posts & Telecommunications under Grant No. 2013-07.

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