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A radial basis function (RBF) neural network adaptive sliding mode control system is developed for the current compensation control of three-phase active power filter (APF). The advantages of the adaptive control, neural network control, and sliding mode control are combined together to achieve the control task; that is, the harmonic current of nonlinear load can be eliminated and the quality of power system can be well improved. Sliding surface coordinate function and sliding mode controller are used as input and output of the RBF neural network, respectively. The neural network control parameters are online adjusted through gradient method and Lyapunov theory. Simulation results demonstrate that the adaptive RBF sliding mode control can compensate harmonic current effectively and has strong robustness to disturbance signals.

Active power filters are commonly used to deal with the increasing harmonic current in electrical system nowadays, which can degrade the quality of power system. Since APF is a complicated nonlinear system, advanced controller can be utilized to control the APF. In order to improve the performance of APF, adaptive control, neural network control, fuzzy control, and sliding mode control have been proposed to control the APF. Kömürcügil and Kükrer [

Since neural network has the capability to approximate any nonlinear function, the tracking control using neural network for nonlinear dynamic system has become a promising research topic. Man et al. [

Neural network does not depend on mathematical models; sliding mode control has strong robustness. The motivation of this paper is to investigate the combination of adaptive control, neural network control and sliding mode control applied to APF based on Lyapunov analytical method. So it is necessary to combine the advantages of adaptive control, neural network control, and sliding mode control to improve the control performance of APF. In this paper, a Lyapunov adaptive sliding mode control method based on RBF neural network is presented to overcome the shortcomings of traditional methods. The key property of this method is that the weights of neural network can be online adjusted, and the asymptotical stability of the system can be guaranteed by Lyapunov stability theory. The contribution of this paper can be emphasized as follows.

The sliding mode technique has been combined with the adaptive control and neural network control to achieve the desired elimination of harmonic current in APF system. The performance of current tracking and total harmonic distortion (THD) can be improved effectively.

The adaptive RBF sliding mode controller does not rely on accurate mathematical model since it has the ability to approximate the nonlinear function of APF. The adaptive neural controller is used to model the relationship between the sliding surface and the control law.

The adaptive neural network sliding mode control is proposed to deal with nonlinear load in APF system and to improve the performance of current tracking. This is a successful example of using adaptive control, RBF neural network control, and sliding mode control with application to three-phase APF.

The schematic diagram of the three-phase three-wire shunt active power filter is shown in Figure

Schematic structure of shunt APF.

The principle of shunt APF is as follows. First, the harmonic current

Based on Kirchhoff’s current law, we can get the circuit expressions as follows:

In this section, an adaptive RBF neural network sliding mode controller is proposed. The sliding surface is the input of the RBF neural network, the sliding mode controller is the output of RBF neural network. A single input and a single output neural sliding mode control can be achieved by using the neural network learning function to approximate the sliding surface coordinate function

Block diagram of adaptive RBF sliding mode control system.

Functions of (

Define compensation current and its derivative as follows:

The structure of RBF neural network is shown in Figure

Structure of RBF neural network.

Here an RBF neural network is used to model the relationship between the sliding surface and the control law. The output of RBF neural network can be expressed as follows:

Based on Lyapunov stability theory, the reaching condition of the sliding surface is

The adjustment indexes of the RBF is as follows:

From the chain rule, the following property can be obtained:

The update equation of the weights can be expressed as follows:

If the perfect control law exists, which makes the RBF sliding mode controller reach the best performance, at this moment APF system reaches the sliding surface; then the system gets to sliding mode motion.

If the time-varying function

In this paper, the RBF neural network is used to approximate the relationship between the sliding variable and the control law. The control law may have certain difference with the perfect control law

From (

Then

Substituting (

In this section, simulation is implemented to investigate the proposed adaptive RBF sliding mode control towards shunt APF using Matlab/Simulink package with SimPower Toolbox. In the simulation, the controller starts to work from 0.05 second, and disturbance signal is introduced into the APF system at 0.12 second. The simulation parameters of the APF system are selected as follows.

Parameters in RBF neural network: The number of hidden layer neuron

Figure

A phase current.

Current harmonic analysis from 0 to 0.04 second.

Current harmonic analysis from 0.06 to 0.1 second.

Current harmonic analysis from 0.13 to 0.17 second.

Command current and compensation current.

Voltage wave of the DC side.

Figure

Three phase sliding surface.

An adaptive RBF neural sliding mode control method is proposed for three-phase active power filter. An RBF neural network control is used to adaptively approximate the nonlinear function of APF. The weights of the RBF neural network are adjusted according to gradient method. The sliding mode control is used to improve the robustness of the APF system. Simulation results demonstrate the good compensating performance of the harmonic current with the proposed adaptive RBF sliding mode controller.

The authors thank the anonymous reviewers for useful comments that improved the quality of the paper. This work is partially supported by National Science Foundation of China under Grant no. 61074056, the Fundamental Research Funds for the Central Universities under Grant no. 2612012B06714 and the Scientific Research Foundation of High-Level Innovation and Entrepreneurship Plan of Jiangsu Province.