Integral-type terminal sliding mode control approach for wind energy conversion system with uncertainties

Highlights

• Integral-type terminal sliding mode control (ITTSMC) is proposed for the PMSG-WT.

• Finite-time control of the WECS based on PMSG are obtained using the ITTSMC.

• Parametric uncertainties and random noise effect are handled by the ITTSMC.

• Simulation results are given to verify the effectiveness of proposed ITTSMC approach.

Abstract

This paper investigates a robust controller for the wind energy conversion system (WECS) based on permanent magnet synchronous generator (PMSG) with parametric uncertainties. A robust nonlinear controller is developed for PMSG wind turbine (PMSG-WT) using integral-type terminal sliding mode control (ITTSMC) to ensure maximum aerodynamic power for the system and enhance its performance. The proposed control technique: (i) ensures the convergence of the state variables of the system in finite-time; (ii) reduces the chattering problem in the sliding mode control (SMC); (iii) increases the robustness of the PMSG-WT in the presence of uncertainties. The simulation results for the proposed controller efficiency are performed using the MATLAB/Simulink environment. Besides, a comparative study considers the performance of the suggested control technique with backstepping and SMC techniques. The performance of the ITTSMC method is checked using different situations such as varying wind conditions, parametric uncertainties, and random noise.

Introduction

Currently, global warming is considered one of the most critical environmental problems, because with population growth and industrialization, greenhouse gas emissions, especially carbon dioxide (${\text{CO}}_2$), have increased. Simultaneously, millions of people still do not have access to electricity, which remains a big challenge for the electricity supply [1]. These issues have led to great interest in electricity production from green energy sources, especially wind energy. It has developed rapidly and may account for 20% of global energy providing real advantages of ecological aspects, easy maintenance and low running cost, all with a huge and inexhaustible electricity generation scope [2].

The wind turbine (WT) technologies found on the global market include the fixed speed WT, semi-variable speed WT and variable speed WT (VSWT). Amongst those technologies, the most predominant in wind farms is the VSWT, due to its ability to enhance energy capture and its aptitude to achieve a controlled maximum power point tracking (MPPT) approach to get maximum power at different wind velocities [2]. Many machine categories are employed in VSWT such as the double field induction generator, the cage asynchronous generator, and permanent magnet synchronous generator (PMSG). Compared to other aero-generators,

the PMSGs are widely used both in the navy and on shore, for their main properties, such as simplicity of structure, self-excitation, high power factor, high reliability, great power density, better compatibility with the grid, and no losses in the rotor or gearbox. These features enable the machine to increase operating speed and reduce maintenance requirements [3]. The quality of the power interjected into the electric network mainly hangs on the behavior of the wind at the site and the regulator approach used for the VSWT. Moreover, in wind energy conversion system (WECS), the control task is still very complicated, because of the coupling between the state variables of the PMSG during the change of its physical parameters. In order to deal with these challenges, several control approaches have been established in the literature. Amongst those controllers, linear controllers have been widely used in WECS, as the proportional integral (PI) in terms of their simplicity and low-cost [4]. Fuzzy logic and intelligent approaches are more efficient with robustness, using a training database to deduce the different rules for a fuzzy control or use it to drive artificial neural networks [5]. However, these intelligent controllers are significantly impacted by learning and training conditions during training. A list of nonlinear controllers has nevertheless been designed to solve these issues, for instance fractional order fuzzy PID [6], backstepping control [7], sliding mode control (SMC) [8], etc.

In the control that must be preformatted, the method adopted by WECS is the SMC [8], [9]. This technique gives an excellent level of robustness against uncertainties. The SMC achieves only asymptotic convergence and has some problems in the control system such as the chattering phenomena, which represents the major drawback of this method. To solve these problems in SMC, improve the tracking control performances, and to attain the finite-time convergence of all state variables in PMSG-WT, a finite-time controller is proposed known as fast terminal SMC [10], [11]. This technique is proposed to control various nonlinear systems such as quadrotor UAV [10], [12], the steer-by-wire systems [13], [14], [15], and the electronic throttle [16], [17], [18].

Based on this controller, a robust controller terminal SMC is suggested to resolve the problem of controlling the PMSG-WT in the presence of parametric uncertainties and random noises effect.

In this subsection, some related works are given. For example, the authors in [7] intended to explore the involvement of a backstepping control in PMSG-WT using the Lyapunov stability technique. Then, the wind profile derived from Dakhla-Morocco city is employed to assess the efficiency of the complete system by applying the backstepping nonlinear control. In [9], a SMC and second-order SMC (SO-SMC) are developed to regulate the PMSG-based WECS. For this reason, a voltage mode SO-SMC is first designed to obtain the maximum power, for which the mechanism senseless is used to generate the reference voltage. Then, SO surface of SMC is constructed using a proportional integral derivative type sliding surface with independent gains. The SO-SMC voltage mode structure was not applied before a voltage control for PMSG-WT composite of a booster converter and rectifier. Finally, the suggested approach improves performance through higher voltage control.

In [19], a passivity-based controller (PBC) is used for PMSG based tidal turbine in order to follow both the rotational speed and the trajectories of the torque from the generator. To surmount the issues of the basic PI controller, the PBC adopts a fuzzy logic approach enabling the development of the desired torque for rapid convergence and robustness against the parameter variations. In [20], the state space dynamic of the PMSG-WT is derived. Furthermore, this paper elaborates on the high gain observer (HGO) that provides an estimation of the position/speed rotor and the torque. The HGO also offers estimates of the voltage and the grid frequency. Moreover, the parameters at the generator side and the power network side are only estimated through current and voltage measurements. Eventually, the performance of the HGO is proven with simulation results.

Paper [21] presents a controller combining adaptive sliding mode (ASM) controller with active disturbance rejection control (ADRC) for direct-drive of the WECS based on PMSG. The ASM observer is reserved to estimate the position and rotational speed. On the other hand, the ADRC is a means of enhancing the anti-disturbance ability. The simulation results show that the ASM technique gives high robustness and more precise monitoring. The authors in [22] have developed a sensorless MPPT approach to estimate the wind speed with the absence of the wind speed sensors, yet increase the overall system resilience and reliability. In addition, the model predictive controller (MPC) is developed to conduct the states of the five-phase PMSG based WECS to track their reference values. A comparative analysis of speed rotor regulator is discussed over MPC and basic PI controllers. The efficiency analysis indicates the outstanding performance of the MPC versus PI.

The [23] proposes a SMC for WECS based on two five-phase PMSGs using a fifteen-switch rectifier. The SMC is used to regulate both generator-side and electrical network-side converters. Comparative simulation results based on PI and SMC controllers under changing wind velocity prove that SMC guarantees good efficiency in permanent as well as in transient states. In [24], a super-twisting SMC (STSMC) is featured for gearless PMSG-WT. The goal of the established regulator is to guarantee robustness against external disturbances and the grid fault condition. When compared to the PI and first-order SMC, the STSMC method, under various conditions, is robust and performs better according to the simulation results.

The aims of the present paper is to design a robust controller integral-type terminal sliding mode control (ITTSMC) to adjust converters on both generator and grid sides. This approach is proposed to stabilize and track the optimum reference of the PMSG-WT in a finite-time, as well as to reinforce its robustness against system parameter variations. The Lyapunov stability theory is used to verify the ITTSMC stability. The proposed ITTSMC method is compared with other nonlinear control strategies, while considering various scenarios. Moreover, the simulation results of the suggested approach show high precision tracking performances, high stabilization precision, also reduce the chattering problem while maintaining the performance in terms of the state variables tracking and robustness against uncertainties. The foremost contributions of the present paper are summarized as follows:

• A ITTSM controller is proposed for WT based on PMSG, which is characterized by higher robustness against parametric uncertainties and random noise effect.

• Finite-time control, fast convergence, and accurate tracking of the WECS based on PMSG are obtained using the proposed control technique.

• Compared with the backstepping technique proposed by the authors of [7] and the SMC presented in [8], the ITTSMC approach proposed in this work achieves some performances such as high precision tracking, faster convergence, high level of robustness, and the chattering problem in SMC [8] is reduced.

The present paper is structured as follows: The Section 2 details the model of PMSG-WT. The ITTSMC approach designed in the present paper for monitoring the PMSG-WT at parametric uncertainties and random noise, is the focus of Section 3. Compared with other approaches, the numerical simulation confirms the robustness of the ITTSMC technique in Section 4. Finally, the paper closes with a detailed conclusion in Section 5.