Journal of Control Science and Engineering

Volume 2019, Article ID 5032694, 23 pages

https://doi.org/10.1155/2019/5032694

## A Simple Flexible and Robust Control Strategy for Wind Energy Conversion Systems Connected to a Utility Grid

^{1}Unité de Recherche d’Automatique et d’Informatique Appliquée (LAIA), Département de Génie Électrique, IUT FOTSO Victor Bandjoun, Université de Dschang, BP 134 Bandjoun, Cameroon^{2}Unité de Recherche de Matière Condensée d’Électronique et de Traitement du Signal (LAMACETS), Département de Physique, Université de Dschang, BP 69 Dschang, Cameroon

Correspondence should be addressed to Armel Simo Fotso; rf.oohay@ommistof

Received 10 January 2019; Revised 11 April 2019; Accepted 17 April 2019; Published 14 May 2019

Academic Editor: Haiping Du

Copyright © 2019 Armel Simo Fotso 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

This paper presents a simple and robust control strategy for a variable speed wind turbine conversion system using a squirrel-cage induction generator and a three-phase voltage source (AC/DC/AC) Pulse Width Modulation (PWM) converter connected to the utility grid through an LCL filter. The control strategy integrates for the generator side an adaptive radial basis function (RBF) neurosliding mode controller associated with the rotor flux oriented vector control which is used to regulate the turbine rotation speed, rotor flux, and the DC bus voltage. For the grid side, the inverter current and voltage regulation as well as the current injected into the grid are regulated by PI controllers for two modes of operation, namely, the stand-alone mode and grid connected mode. The main contribution of this article is the introduction of a new and simple control algorithm allowing automatic mode switching method based on wind speed. The proposed scheme is very efficient and can be easily implemented in practice. Simulation results illustrate the effectiveness and feasibility of the proposed algorithm.

#### 1. Introduction

##### 1.1. Antecedents and Motivations

Wind energy conversion systems connected to the utility grid are becoming more rampant in recent years as the world’s electricity power demand is growing. Several studies have demonstrated that the installed wind power generation capacity in the world has been increasing at more than per year for the last 10 years [1]. The major advantage of these systems is the abundant availability of the wind power source as compared to conventional energy sources such as natural gas, oil, etc. To improve their efficiency, an adequate choice of electrical generator together with an advanced and reliable control strategy is needed.

Among the different variants of electrical generators, the squirrel-cage induction machine is one of the best candidates for the implementation of the variable wind speed conversion system in both isolated and grid connected production due to its numerous advantages such as its robustness and reduced price which considerably decreases the cost of installation of the wind conversion system as well as the price of the energy produced. The disadvantages of this machine are, among others, the very high coupling which exists between its parameters and which induces a poor regulation of voltage and frequency as well as the necessity for an external excitation source.

Variable speed operation of wind turbines has many advantages that are well known in the literature, but simple and reliable control methods under wind speed variation need to be developed in order to improve the performances of the wind energy conversion system in both grid connected and stand-alone operating modes. For the grid connected mode, the power produced by the wind turbine needs to be regulated in order to be injected into the grid. Furthermore, the injected voltage has to be synchronized with the grid voltage. Thus to achieve these objectives, a power converter which enables a certain controllability of electrical power in the grid is needed. To achieve grid synchronization, different methods to extract the phase angle have been studied in the literature such as zero crossing method, filtering of grid voltage method, and PLL technique [2]. However, the PLL technique is the most used method for grid synchronization due to its numerous advantages such as better rejection of grid harmonics and others kind of disturbances.

In recent years, some advanced control strategies have been proposed for wind energy conversion systems [3–11]. In [3], the authors examined the voltage regulation at the load terminal through the control of a single-phase PWM inverter. The proposed algorithm ensures a perfect switching between the two operation modes and provides an uninterrupted power supply to the load. However, the study concerns only a single-phase system. A distributed generation unit connected to the grid using a variable speed permanent magnet synchronous generator is examined in [4]. The proposed control scheme ensures good DC-link regulation, low distortion, and high quality power flows into the grid. However, time-varying parameter estimation and flexible control between grid connected and stand-alone operation modes have not been investigated. In [5], a control algorithm for a wind conversion system based on a permanent magnet synchronous generator for an isolated site is presented. A first-order sliding mode control technique is developed for the control of the generator side quantities as well as the extraction of the maximum available power on the wind turbine. Nevertheless, the grid connected mode has not been investigated. A grid connected wind conversion system based on a squirrel-cage induction generator is examined in [6]. In this paper, an adaptive control algorithm based on PI controllers for a three-phase rectifier ensures the regulation of the generator side quantities. A three-phase PWM controlled inverter connected to the grid through an LCL filter regulates the voltage across the load and the grid current. However, the authors did not address the problem of power drop detection. In [10], the authors designed a RBF neurosliding mode controller for a stand-alone variable wind speed conversion system. But the grid connected mode operation has not been investigated. A robust control algorithm for a three-phase voltage source inverter directly connected to the grid through an LCL filter is presented in [7]. But only the current injected to the network is regulated to stabilize the system. Reference [9] presents the modelling of a PV module and a new control topology for a single stage three-phase grid connected photovoltaic system. The controls aims include simultaneously grid synchronization, reactive power compensation, output current harmonic reduction, and maximum power point tracking. Nevertheless flexible control between stand-alone mode operation and grid connected mode operation has not been investigated. In [12], the authors examined a variable speed generation system which contains a voltage source inverter connected to the grid through an LCL filter with the MPPT algorithm and unity power factor. However, the configuration offers a weak harmonic performance at lower switching frequencies in higher power applications. In addition, the uninterruptible supply of the AC load during the transition between grid connected and stand-alone modes has not been investigated. A flexible algorithm for the control of a small wind conversion system with grid failure detection and automatic switching between the grid connected and stand-alone operating modes based on a PLL controller is proposed in [8]. But details on the generator side control such as flux and generator speed regulation have not been provided. Furthermore the variation of electrical parameters has not been investigated.

From this review it can be noticed that concerning the wind energy conversion systems authors have not yet investigated the method which consists in effectively transferring the maximum power captured by the wind turbine to the grid. It is also noteworthy that a flexible control of wind energy conversion system, with power detection, operating in stand-alone and grid connected mode has not yet been investigated.

##### 1.2. Main Contribution

From the above drawbacks, we propose in this paper, a complete wind turbine conversion system based on a squirrel-cage induction machine connected to the utility grid through an LCL filter. A rotor flux oriented vector control strategy associated with a RBF neurosliding mode control technique is used to regulate the DC bus voltage, the rotor flux, and the rotating speed of the generator under a large variation of the wind turbine speed. The control of the grid side PWM converter is ensured by a simple, flexible, and robust algorithm enabling:(i)The automatic switch between two functioning mode based on wind speed.(ii)The voltage regulation across the load.(iii)The grid current regulation.

In order to ensure an optimal operation of the proposed conversion system, a control method based on the MPPT technique is proposed. It consists in effectively transferring the maximum power extracted by the wind turbine for each wind speed to the grid. A three-phase voltage source AC/DC/AC converter associated with a flux oriented vector control of the self-excited induction generator (SEIG) is used. The algorithm integrates the regulation of the rotor flux and generator rotor speed as well as the DC bus voltage control to improve the efficiency of the overall system. The low speed operation of the system implies that it can be operated in isolated areas with weak wind profile.

##### 1.3. Structure of the Paper

The paper is organized as follows: In Section 2, the RBF neural network controller is designed. In Section 3, the nonlinear dynamics of induction generator and control objectives are introduced and the RBF neurosliding mode control technique is designed to achieve the regulation of DC bus voltage, rotor flux, and generator speed with adaptation of rotor time constant. In Section 4, the PI control strategy is developed for grid side inverter. In Section 5, computing results using the proposed RBF neurosliding mode technique and PI controllers, respectively, for generator and grid side are reported. Some concluding remarks are given in Section 6.

#### 2. Design of RBF Neural Network Controller

In this section, a direct method for robust adaptive control using RBF neural network for a class of nonlinear systems is propose.

Let us consider the nonlinear system in the following form: where , , and , are, respectively, state variables, system input, and output; and are unknown smooth functions; is the nominal part of the system; it does not depend upon the control input while the uncertainties and external disturbance are concentrated in the term d(t) assumed to be bounded by an unknown constant . Since all physical plants operate in bounded regions, we study the control problem of system (1) whose state belongs to a compact subset .

*Assumption 1. *The sign of is known and . Since the sign of is assumed to be known, without losing generality, we may assume that in the following development. The case where is discussed in Remark.

*Assumption 2. *It is also assume that .

*Remark 3. *Assumption 1 seems to be a restriction for the proposed control scheme. It should be noticed that many physical electromechanical systems [13–16] possess such a property.

Assumption 2 is not a restriction for the proposed control scheme. It has been used to simplify the study in this section. The case when the sign of is not constant will be discussed later.

Define the desired smooth signal , the tracking error , and augmented item , aswhere is a design parameter. From (2), we have

Proposition 4. *Consider system (1). If the desired controller is chosen as where is a design parameter, then converges exponentially to .*

*Proof. *Substituting into (3) yields

*Remark 5. *The above desired controller is not implementable since the functions and the terms and are assumed to be unknown. In the following, RBF neural network combined with the sliding mode technique will be applied to approximate the unknown controller .

From (4), the desired controller can be rewritten aswhere the first term , function of , , and , is the nominal continuous bounded part, the second term is the uncertain part assumed to be bounded by unknown constant, and compact set is defined asThe nominal part of the above controller is continuous and can be approximated by a radial basis function (RBF) neural network [17, 18]. Thus, can be described as follows [19]:where denotes a nonlinear function; and , are the center and the width of the th hidden unit, respectively; is the number of the hidden nodes or radial basis function units (RBF); is the optimal weight vector and satisfies ; is the input vector of the RBF network; is the optimal approximation error, which is unknown and bounded

Note that the term is time-varying and cannot be approximated by a static neural network. In the following analysis, sliding robust terms will be used in the identification scheme to compensate the effect of this uncertainty time-varying term. The controller will be approximated assuming that the terms and are bounded by unknown positive constants.

For this purpose, the following neural controller is proposed in order to approximate the control signal where the term is introduced in order to improve the convergence rate of the neural network in the presence of the uncertainties terms.

Substituting (9) in (3) yields From (4), we haveSubstituting (11) in (10) yields From the fact that the neural network is a linear function of and using Taylor series expansion, (12) can be rewritten aswhere and are assumed to be bounded as followsand is unknown positive constant.

Proposition 6. *Consider the class of nonlinear systems described by (1), the sliding-neural network controller (9), and Assumptions 1 and 2. If the bias term , the learning rule of the weight , and the adaptation law for the unknown bound are chosen as with , , and being the well-known projection function [20] on the compact set , then the neural network controller error will converge in finite time to the origin.*

*Proof. *In order to prove the finite time convergence to the origin of neural network controller error , the following Lyapunov candidate function is considered:Computing its time-derivative yieldsConsidering (13) yields If the terms , the learning rule of the weight , and the adaptive law for the unknown bound are given by (15)-(17), the following inequalities hold:The above inequality (21) can also be rewritten asFrom the fact that are bounded by construction, one can conclude that all the terms are bounded.

From (17), it is clear thatConsequently, there exists a finite time such that satisfies the inequalityand by taking into account Assumption 2, the neural network controller error will converge in finite time to the origin.

*Remark 7. *In the case where , the Lyapunov candidate function (18), Assumption 2 are replaced by, respectively, and the term is substituted by

*Remark 8. *In the case where the sign of is not constant, the tracking error converges to the ball with radius proportional to .

*Remark 9. *Under realistic operation conditions, the neural network controller error converges to the neighborhoods of zero and will always increase. Therefore, the following choice for is used instead of (17):where is the optimum neural network controller error under realistic operation conditions.

The block-diagram of the RBF neural network controller is depicted in Figure 1.