Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 7910971, 8 pages

http://dx.doi.org/10.1155/2016/7910971

## Short-Term Load Forecasting Model Based on Quantum Elman Neural Networks

^{1}College of Automation and Electrical Engineering, Qingdao University, Qingdao 266071, China^{2}Qingdao Electric Power Company, Qingdao 266002, China

Received 27 March 2016; Revised 18 June 2016; Accepted 11 July 2016

Academic Editor: Antonino Laudani

Copyright © 2016 Zhisheng Zhang and Wenjie Gong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Short-term load forecasting model based on quantum Elman neural networks was constructed in this paper. The quantum computation and Elman feedback mechanism were integrated into quantum Elman neural networks. Quantum computation can effectively improve the approximation capability and the information processing ability of the neural networks. Quantum Elman neural networks have not only the feedforward connection but also the feedback connection. The feedback connection between the hidden nodes and the context nodes belongs to the state feedback in the internal system, which has formed specific dynamic memory performance. Phase space reconstruction theory is the theoretical basis of constructing the forecasting model. The training samples are formed by means of -nearest neighbor approach. Through the example simulation, the testing results show that the model based on quantum Elman neural networks is better than the model based on the quantum feedforward neural network, the model based on the conventional Elman neural network, and the model based on the conventional feedforward neural network. So the proposed model can effectively improve the prediction accuracy. The research in the paper makes a theoretical foundation for the practical engineering application of the short-term load forecasting model based on quantum Elman neural networks.

#### 1. Introduction

Short-term load forecasting (STLF) is the basis for the normal and safe operation of power system. Since the introduction of competition mechanism in power market, the power company has put forward higher requirements on the accuracy and rapidity for load forecasting [1–3]. Many classical methods were applied to the study of STLF model, such as ARIMA model and ARMAX model [4, 5]. However, the ability of these classical methods to deal with the nonlinear time series is poor. With the introduction of artificial intelligence technology to the study of STLF model, it has opened up many new research methods such as neural network and expert system [6, 7]. Because of the strong nonlinear time series processing ability, neural network is widely used in the study of STLF.

The process of human brain information processing may be related to the quantum phenomenon, and quantum mechanical effects may exist in the brain, which had been shown by some research results [8]. The quantum systems have the similar dynamic characteristics with the biological neural networks. The fusion of artificial neural network and quantum theory can better simulate the process of human brain information processing. Quantum neural network can improve the approximation ability and information processing efficiency of artificial neural network, which had been used for many applications [9–13].

The STLF model based on quantum Elman neural networks (QENN) is constructed in this paper. QENN is composed of the quantum neurons. The quantum neuron model consists of the weighting part, the aggregating part, the activating part, and the excitation part. Different from the traditional multilayer feedforward neural network, QENN has not only the feedforward connection but also the Elman feedback connection. The Elman feedback connection between the hidden nodes and the context nodes belongs to the state feedback in the internal system, which has formed specific dynamic memory performance [14].

Some studies had shown that the load time series is nonlinear and chaotic [15]. Phase space reconstruction theory (PSRT) is the important analysis method for research on chaotic time series. The training samples are formed by means of -nearest neighbor approach (KNNA) based on PSRT.

Through the actual example simulation, it is proved that the proposed model can effectively improve the prediction accuracy and has adaptability to different load time series.

#### 2. Quantum Elman Neural Networks

QENN is composed of quantum neurons, and quantum neurons are the basic elements of building QENN.

##### 2.1. Quantum Neuron Model

###### 2.1.1. Qubit

In the classical computation, the binary numbers “0” and “1” are used to represent the information, and they are usually called bits. In the quantum computation, and are used to represent the two basic states of microscopic particles, and they are usually called qubits. The difference between qubits and bits is that, in addition to the state of and , the state of qubits can be a linear combination of states, which is usually called the superposition.

In quantum computation, a qubit state can be expressed aswhere and express the basic states of microscopic particles. and are the probability amplitudes, and they should meet the following relations:

In order to further understand the superposition of the qubits, an electron is used to illustrate. An electron can be in the ground state of low energy level, and it can also be in the excitation state of high energy level. According to the superposition principle, the electron can be in the state of linear combination of these two states, that is, the superposition state . It is shown in Figure 1.