Robust pole placement for power systems using two-dimensional membership fuzzy constrained controllers

This study presents a design method of power system stabilisers (PSSs) to damp system oscillations. The design is based on fuzzy logic and linear matrix inequality (LMI) techniques. The design guarantees a robust pole placement in a desired region in the complex plane for different loading conditions. Due to system non-linearity and load dependency, the whole wide range of operating condition is divided into three subregions. For each subregion, a norm-bounded uncertainty linear model is developed and a robust LMI-based pole placer is designed considering controller constraint. Takagi-Sugeno fuzzy model is used to guarantee smoothly switching between the LMI-based controllers of the three subregions. The proposed technique avoids solving many LMIs as in the polytypic approach and avoids the infeasibility problem that might arise from solving the LMIs for the complete region of operation. In addition, the proposed fuzzy logic switching controller has reduced drastically the fuzzy rules due to the use of two-dimensional (2D) membership functions. Particle swarm optimisation is used to tune the proposed 2D membership functions to guarantee smooth switching of the controllers while maintaining the desired constraints. The simulation results of both single-machine and multi-machine power systems confirm the effectiveness of the proposed PSS design.