Uncertain LPV Modeling of Power Systems using PCA-Based Parameter Set Mapping for Robust PSS Designing

This paper presents a new methodology for uncertain polytopic linear parameter-varying (LPV) modeling of power systems based on parameter set mapping (PSM) with principle component analysis (PCA). At first, an LPV representation of the system dynamics is generated by linearization of its usual differential-algebraic equations about the transient operating points. Then, the PCA-based PSM algorithm is used to reduce the number of models and generate a reduced polytopic LPV model. Because of the system nonlinearity and approximations of model reduction, some uncertainties are considered for each model. A robust pole placement controller is designed to assign the poles of polytopic model in a linear matrix inequality (LMI) region such that the response of the system has a proper damping ratio. A sufficient condition is also proposed to guarantee the asymptotic stability of the closed loop model against the uncertainties. Finally, the proposed controller is synthesized as a power system stabilizer (PSS). It is considered for a single-machine power system and then it is simulated in multi-machine case and compared its performance with a tuned standard conventional PSS and other cases of the controller. The results show the robust performance of the proposed controller especially in different operation conditions and faults.