Robust pole-placer power system stabilisers design via complex Kharitonov's theorem

In this paper, the synthesis of robust three-parameter power system stabilisers (PSSs) is presented. Graphical characterisation of the set of stabilising PSSs is carried out using D-decomposition. Dynamic model of single-machine infinite-bus system (SMIB) is considered to accomplish the design. 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 plane to enhance time-domain specifications. Pole clustering in a damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such cone. Parametric uncertainties of the model are captured by an interval polynomial. Hence, performance enhancement calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by the complex version of Kharitonov's theorem. A less-conservative and computationally effective approach is concluded from the geometry of the stability region. Simulation results affirm robust stability and performance over a wide range of operating points.