Robust control of electrical power systems using PSSs and Bilinear Matrix Inequalities

•We propose a methodology for robust pole placement in power systems.•The power system model used is the small signal stability model.•The controller design is based on the linearization of Bilinear Matrix Inequalities.•It also guarantees adequate damping for oscillations at various operating points.•Decentralized and PSS structured controllers are used.

This work presents the application of Bilinear Matrix Inequalities to the robust adjustment of Power System Stabilizers with pre-defined structure. Results of some tests show that gain and zeros adjustments are sufficient to guarantee robust stability and performance with respect to various operating points. Making use of the flexible structure of BMIs, we propose an algorithm that guarantees a minimum damping factor specified for the closed loop system, always using a controller with flexible structure. The technique used here is the pole placement, whose objective is to place the poles of the closed loop system in a specific region of the complex plane. The BMIs are linearized using the homotopic method. Results of tests with a nine-machine system are presented and discussed, in order to validate the algorithm proposed.