Optimal supplementary frequency controller design using the wind farm frequency model and controller parameters stability region

In most of the existing studies, the frequency response in the variable speed wind turbines (VSWTs) is simply realized by changing the torque set-point via appropriate inputs such as frequency deviations signal. However, effective dynamics and systematic process design have not been comprehensively discussed yet. Accordingly, this paper proposes a proportional-derivative frequency controller and investigates its performance in a wind farm consisting of several VSWTs. A band-pass filter is deployed before the proposed controller to avoid responding to either steady state frequency deviations or high rate of change of frequency. To design the controller, the frequency model of the wind farm is first characterized. The proposed controller is then designed based on the obtained open loop system. The stability region associated with the controller parameters is analytically determined by decomposing the closed-loop system's characteristic polynomial into the odd and even parts. The performance of the proposed controller is evaluated through extensive simulations in MATLAB/Simulink environment in a power system comprising a high penetration of VSWTs equipped with the proposed controller. Finally, based on the obtained feasible area and appropriate objective function, the optimal values associated with the controller parameters are determined using the genetic algorithm (GA).