Open AccessDecentralised design of robust multi‐objective PSSs: D ‐decomposition approach
Author(s) -
Ayman Mohamed,
Soliman Mahmoud
Publication year - 2020
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2019.1415
Subject(s) - parametric statistics , parameter space , stability (learning theory) , robust control , mathematical optimization , robustness (evolution) , mathematics , polynomial , control theory (sociology) , computer science , control system , engineering , artificial intelligence , mathematical analysis , geometry , chemistry , biochemistry , statistics , control (management) , machine learning , electrical engineering , gene
This study addresses the problem of determining the set of all robust three‐parameter power system stabilisers having the form ( x 1 + x 2 s ) / ( 1 + x 3 s ) . 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 σ − ζ contours from the s ‐plane onto the controller–parameter plane by two parametric functions x 1ω , σ , ζand x 2ω , σ , ζwith fixed x 3 . 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.