Investigating Linear Matrix Inequality Constraints in a 2.5MW DFIG Wind Turbine

Abstract

The use of renewable energies has become widespread due to bioenvironmental concerns and a shortage of fossil fuels. In designing a robust controller for wind turbine system, variable speed is amongst one of the challenges to today's engineering. The wind energy transformation system includes complex aerodynamic and electrical components along with the unpredictable performance of wind speed and the other turbulence factors that render the existence of a robust controller necessary. In the present article, a robust controller has been proposed based on LMI method for variable-speed wind turbines with DFIG. To do so, the linear matrix inequality theories have been seminally explicated and the wind turbines and their nonlinear modeling have been subsequently introduced. Next, the linear model of the wind turbine system has been extracted based on the nonlinear model and offered within the format of M-Δ structure. Then, the linear matrix constraints have been defined for it and solved using MATLAB following which the feedback law is extracted and enforced on the system. The simulation results indicated that the controller has a good response. Keywords: Wind turbine, Robust control, Linear matrix inequality 1. INTRODUCTION During the past centuries, humankind has made use of wind as a source of energy. During the 17 th and 18 th centuries, the wind was considered as useful energy. During the late 19 th century, the first experiments were carried out for producing electricity by the use of wind but later on, little attention was paid to wind energy for generating power. It was with the expensiveness of the fossil fuels and oil that the attentions were once again directed towards renewable energies like the wind. Nowadays, wind energy is one of the important arms in generating power. However, in manufacturing and installing a wind turbine for generating power, energy generation, and such scales as output, cost, the effect on the power grid and so forth are of great importance. Control system plays an important role in improving the output and performance of the wind energy conversion systems (WECS). The use of proper wind turbine controllers contributes to the maximization of the controlled power of the available wind energy and supports the machine and the structure in the course of extreme wind conditions. The complicacy of designing optimum controllers for wind energy conversion system is increased with the increase in the size of their power. To reach the maximum performance, the majority of wind turbines work in the variable speed (Vs) mode and variable pitch (Vp) angle. In 2007, Bianchi used black-box method and model fitting technique based on system response data for identifying the wind energy conversion system's model [1]. There are many reasons for the use of DFIG wind turbines amongst which the possibility of the turbine energy's storage, reduction of stress in the mechanical structure, reduction in the acoustic noise, active and reactive power controllability and some others can be pointed out. In case of ...