Modeling of a Variable Speed

Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved International Review of Automatic Control, Vol. 8, N. 4 316 Changes in wind speed affect the PMSG output power and system performance. A control system is required to improve the efficiency and performance by ensuring that the generator operates at the maximum power point. By controlling the PMSG rotor speed, this maximum power point can be achieved. Several speed control strategies have been developed. Proportional integral PI controller has been widely used in industrial processes, because it is simple and easy to implement. PI controllers have shown good performance for PMSG speed control [12]. However, the determination of the PI control parameter is very difficult, so the necessary tuning parameters PI. This can be done by several methods, including neural networks, fuzzy logic, B-spline networks, genetic algorithms, heuristic optimization methods, and particle swarm optimization PSO [13]- [20], [28]-[30]. Aissaoui et al [13] tuned PI controllers using a fuzzy logic method to control the speed of a PMSG. Based on simulation results, a PI controller tuned by fuzzy logic can determine the maximum power with better performance than the PI controller alone. However, the success of the fuzzy logic method is highly dependent on the determination rule and membership function used. Tuning PI controller parameters with a heuristic method for PMSG speed control has shown to have better performance with fewer errors [17]. However, the use of a heuristic method is a long process and is difficult to implement in practice. To improve performance PI controller , in this paper, the parameters of PI controller tuned by using PSO. PSO is a multiobjective optimization that can tune the parameters PI for the PMSG speed control based on error steady state, maximum overshoot, rise time and settling time. Compared with genetic algorithms and the linear quadratic regulator LQR method, PSO produces better dynamic performance for linear brushless DC motors [21]. PSO is also a very simple method that is easy to implement and code using a computer, and for these reasons has been widely studied [14]-[20]. This paper presents the use of PSO for tuning a PI controller for the speed control of a PMSG-driven wind turbine. Speed control using the PSO-PI system is compared to using the PI controller with pole assignment. This paper is organized as follows: in Section 2 the variable speed wind turbine and the PMSG models are described. In Section 3, an overview of particle swarm optimization is presented. In Section 4, the control strategy is described how PSO is used to optimally tune the PI controller for speed control of the PMSG. In Section 5, we compare the performance of the PSO-PI controller and PI controller via simulation results. In Section 6 we show our final conclusions of the paper.

II. Modeling of a Variable Speed

Wind Turbine The wind energy conversion system of interest here consists of a wind turbine, permanent magnet synchronous generator PMSG, control rectifiers, a pulse width modulation PWM system and electronic filters. Kinetic energy from the wind is converted into rotational energy using the turbine, which is then converted into electrical energy by the attached three- phase generator. Three-phase electric energy is rectified by a circuit controlled by PWM. Here, modeling of the wind conversion systems will be undertaken using dq models and description of the control systems to obtain optimum power. II.1. Wind Turbine Model The power and torque produced by a wind turbine are dependent on the wind speed. Wind power P w and torque T w are expressed as follows [13], [22], [23]: P w = 0.5 πρCpλ,βR 2 v w 3 1 = = 0,5 , 2 where ρ is air density, Cp is the coefficient of turbine power conversion, λ is the tip speed ratio, R is the blade radius, and v w is the wind speed. Cp can be expressed as follows where β is the pitch angle: = 0.5176 116 − 0.4 − 5 + 0.0068 3 1 = 1 + 0.08 − 0.035 + 1 4 The tip speed ratio compares the turbine angular speed ω r and the wind speed, expressed as follows: = 5 The dynamic equation of the wind turbine can be expressed by: = 1 [ − − ] 6 where J is the inertia moment, F is the friction coefficient, T m is the torque that is produced by the turbine, and T L is generator torque. Fig. 1 shows the characteristics of turbine output power as a function of turbine speed for different wind speeds with a pitch angle of 0 o . It is clear that different wind speeds produce very different maximum output power values. II.2. Permanent Magnet Synchronous Generator Model PMSG can be modeled using a dq equivalent circuit as shown in Figs. 2 [9], [22]-[24]. Based on this equivalent circuit a mathematical model in a synchronous reference frame can be expressed as follows: Copyright © 2015 Praise Worthy Prize S.r.l. - All rights reserved International Review of Automatic Control, Vol. 8, N. 4 317 = − + + 1 7 = − − − 1 + 1 8 where i d is the d-axis stator currents, i q is the q-axis stator current, v d is d -axis stator voltage, v q is the q-axis stator voltage, Rs is the winding resistance Ω, L d is winding inductance on the d-axis H, L q is the winding inductance on the axis q H, ψr is permanent magnetic flux Wb, and ω r is the electrical rotating speed of the PMSG rads. The angular speed of the electric generator is dependent on the number of pole pairs P and the angular velocity of the generator ω g which can be expressed by Eq. 9: ω r = P ∙ ω g 9 Electromagnetic torque produced by the PMSG in terms of the dq model can be expressed as follows: T e = 1.5PL d - L q ∙ i d t ∙ i q t + i q t ψ r 10

III. Overview of Particle Swarm Optimization PSO