A Homotopy-Function-Based Method For Analyzing Frequency Stability Of Power System With Wind Farm

Wind energy is clean and abundant, it becomes the fast developing renewable energy. As the wind power in power system is increasing, the research on stability of power system becomes more and more important. When the wind power suffers a big disturbance, it will affect frequency dynamics of power system as active power balance is disturbed. This paper is focused on a method to analyze the frequency stability of power system with wind farm.Eigenvalue analysis is a method for analyzing stability of complicated non-linear system, Homotopy function characterized the coupling relationship in topological spaces, and it can identify relationship between eigenvalues and state variables of wind power.This paper introduces homotopy function into frequency stability analysis of power system with wind farm. Firstly, the principle and features of squirrel cage induction generators (SCIG) and doubly fed induction generators (DFIG) are discussed respectively. On this basis, a unified mathematical model of power system including wind farms is established for frequency stability. Some methods for frequency stability are discussed later in this paper, especially eigenvalue analysis developed from Lyapunov theory. Then, this paper detailedly researches the principle of homotopy function and application in eigenvalue analysis of wind power system. In order to accurately analyze eigenvalue of frequency stability in power system with wind farm, homotopy function is used to distinguish the relationship between eigenvalues and state variables (especially frequency variables). At last, through eigenvalue analysis and the relationship which homotopy function is determined, frequency stability for wind farms equipped with SCIG and DFIG are compared respectively.It is show that wind farms equipped by doubly fed induction machines can contribute to improve the frequency dynamics. Simulation results are presented which verify the theoretics.