Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 268470, 6 pages

http://dx.doi.org/10.1155/2015/268470

## A Fundamental Wave Amplitude Prediction Algorithm Based on Fuzzy Neural Network for Harmonic Elimination of Electric Arc Furnace Current

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 11 April 2015; Accepted 25 May 2015

Academic Editor: William Guo

Copyright © 2015 Wanjun Lei et al. 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

Electric arc furnace (EAF) causes the harmonics to impact on the supply network greatly and harmonic elimination is a very important research work for the power quality associated with EAF. In the paper, a fundamental wave amplitude prediction algorithm based on fuzzy neural network for harmonic elimination of EAF current is proposed. The proposed algorithm uses the learning ability of the neural network to refine Takagi-Sugeno type fuzzy rules and the inputs are the average of the current measured value in different time intervals. To verify the effectiveness of the proposed algorithm, some experiments are performed to compare the proposed algorithm with the back-propagation neural networks, and the field data collected at an EAF are used in the experiments. Moreover, the measured amplitudes of fundamental waves of field data are obtained by the sliding-window-based discrete Fourier transform on the field data. The experiments results show that the proposed algorithm has higher precision. The real curves also verify that the amplitude of fundamental wave current could be predicted accurately and the harmonic elimination of EAF would be realized based on the proposed algorithm.

#### 1. Introduction

Electric arc furnace (EAF) smelts the raw metal by generating arcs and has been widely used in the steel industry. For the characteristics of electric arc and meltdown processes, EAF causes some undesirable disturbing effects, such as harmonics and flicker, which would have high impact on the supply network [1]. Therefore, harmonic elimination is of important theoretical significance and practical motivation for the power quality associated with EAF.

Traditionally, most researches focus on the steady-state modeling for harmonic elimination and some improved models of EAF are presented recently. The cubic spline interpolation is proposed to model the voltage-current characteristic of EAF [2], and a new EAF-specific model based on field measurements of instantaneous furnace voltages and currents is presented [3]. Moreover, a mathematical model of the 3-phase AC of EAF is proposed in a more macroscopic level of modeling [4]. However, due to the instability of smelting process and the randomness of the arc generation, establishing a precise model of the EAF is extremely difficult. Moreover, because some physical responses of EAF cannot be obtained from the theoretical study easily, the assumptions of parameters would simplify the EAF model and the analysis results would be affected. Artificial neural network (ANN) learns the relationship between output and input by adjusting the interconnections of neurons and has been adopted for harmonic elimination [5–11]. In particular, an ANN-based inductances on-line estimation of the swinging power cables is discussed for efficient power control of EAF [12]. Nevertheless, opaqueness is major shortcoming of ANN. Hence, to deal with this problem, the fuzzy neural network (FNN) is proposed [13]. FNN is a combined system with ANN and fuzzy logic technique. The fuzzy concepts could improve the transparency for understanding the inner working of ANN, and for fuzzy logic technique, the fuzzy rules have clear semantic meanings; namely, FNN has the advantages of learning optimization ability of ANN and the human-like thinking of fuzzy logic technique. In addition, the parameter of FNN could be determined easily. Adaptive neurofuzzy inference system (ANFIS) is one kind of FNN and a first-order Takagi-Sugeno fuzzy system. Since ANFIS could excellently estimate a system with uncertainty, a new method based on ANFIS is proposed to evaluate the slag quality in EAF using power quality indices [14].

This paper proposes a fundamental wave amplitude prediction algorithm based on FNN for harmonic elimination of EAF current. For the proposed algorithm, ANFIS is used to predict the real-time amplitude of fundamental wave current of EAF, which could provide a guarantee for the realization of harmonic elimination. The inputs are the average of the current measured value in different time intervals. To verify the effectiveness of the proposed algorithm, some experiments are performed on the field data collected at an EAF. In the experiments, the proposed algorithm is compared with the back-propagation neural networks (BPNN) for estimating the fundamental wave amplitude. Moreover, the measured values of fundamental wave amplitude of field data are obtained by the sliding-window-based discrete Fourier transform (SW-DFT) on the field data. The paper is organized as follows. The power supply system model and the equivalent circuit of EAF are described in Section 2. In Section 3, the proposed algorithm is presented in detail. In Section 4, the experiments results are discussed to verify the effectiveness of the proposed algorithm. Finally, Section 5 concludes the paper.

#### 2. Electric Arc Furnace

The EAF power supply system model is shown in Figure 1. is a supply transformer and is a furnace transformer. is the grid impedance and is the busbar impedance of EAF. According to the state variables of EAF, such as the arc length, the current value, and the temperature, the controller could regulate the stalls of output voltage of the furnace transformer and the electrode position. The equivalent circuit is shown in Figure 2. and are equivalent to the grid impedance. The transformer with a ratio of :1 is equivalent to and . and are equivalent to the busbar impedance. is the power source. Time-varying resistance and are the arc equivalent model.