Decentralised design of robust multi‐objective PSSs: D ‐decomposition approach

Abstract

This study addresses the problem of determining the set of all robust three-parameter power system stabilisers having the form . Graphical characterisation of stabilising power system stabilisers (PSSs) is carried out using D-decomposition, whereas the controller–parameter space is subdivided into root-invariant regions. Rather than Hurwitz stability, D-decomposition can parameterise D-stabilising PSSs that enforce pole-clustering in a pre-specified region D to ensure better time-domain specifications. The convex region of D-stabilising PSSs is sketched by mapping the contours from the s-plane onto the controller–parameter plane by two parametric functions and with fixed . The frequency range considered for mapping is initially computed to avoid sweeping over unnecessary frequencies. Based on the geometry of the D-stability region, analytical expressions are derived to compute optimal σ − ζ PSSs for an arbitrary operating point. Parametric uncertainties are captured by an image-set polynomial where the region guarantying robust D-stability of the family is investigated. A computationally effective approach based on stabilising two vertex plants is concluded from the D-stability region. Extension to multi-machine systems is treated where decentralised PSSs are synthesised. An iterative algorithm is suggested to modify a set of initial feasible PSSs sequentially while maximising damping indices. Simulation results confirm the efficacy of the suggested method.