Load frequency control for power system considering parameters variation using parallel distributed compensator based on Takagi-Sugino fuzzy

Due to the dependence of large sectors of industrial, commercial, and residential consumers on electricity, the necessity of a reliable and economic generation system that has a regulated frequency is a crucial task. Frequency regulation within permissible standard limits is called load frequency control (LFC). The LFC based on PID controller has proven its effectiveness due to its simple structure and clear concept. However, a fixed gains PID controller can be designed to provide an optimal response at a particular operating condition, but it may exhibit unsatisfactory performance with change in the system's working conditions due to system nonlinearities and parameters variation. To cope with this issue, this article proposes a polytope representation of the system and designs a set of optimal PID controllers at the vertices of the polytope model. After that, Takagi-Sugino fuzzy controller is utilized to blend these optimal controllers to provide the necessary control action based on the actual operating condition. The resultant controller ensures optimal operation at the operation of polytope vertices. To ensure the system's stability over the space of parameter variation, the stability condition as a set of linear matrix inequalities (LMIs) is deduced. Because the number of LMI conditions grows dramatically with the number of system vertices, the paper employs a tensor product transformation technique to represent the system with the minimum number of vertices. The local controllers are optimized using the Grey Wolf Optimizer (GWO) considering a customized objective function that considers the system's integral time absolute error (ITAE), the frequency nadir, and the oscillation. To validate the proposed methodology, the system closed loop poles are determined at a large number of operating conditions. Eventually, the system response is evaluated at different operating conditions with varying load and generation capacity. The proposed control provides a supreme response compared to fixed optimal PID and fixed gain robust PID controller based on H∞ design criteria controllers.