Robust multi-objective PSSs design via complex Kharitonov's theorem

Abstract

This paper represents a step toward shooting an optimal robust three-parameter power system stabilizer (PSS) with the common form of (x1+x2s)/(1+x3s). The whole set of stabilizing PSSs is graphically characterized using d-decomposition with which the controller-parameter space is subdivided into root-invariant regions. Design is accomplished using the bench mark model of single machine-infinite bus system (SMIB). Rather than Hurwitz stability, d-decomposition is extended to consider d-stability where D refers to a pre-specified damping cone in the open left half of the complex s-plane to enhance time-domain specifications. Pole clustering in damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such cone. Parametric uncertainties of the model imposed by continuous variation in load patterns is captured by an interval polynomial. As a result, computing the set of all robust d-stabilizing PSSs calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by a complex version of Kharitonov's theorem. A less-conservative and computationally effective approach based on only two extreme plants is concluded from the geometry of the stability region in the controller parameter plane. Simulation results affirm the robust stability and performance with the proposed PSSs over wide range of operating points.