A new LPV modeling approach using PCA-based parameter set mapping to design a PSS

This paper presents a new methodology for the modeling and control of power systems based on an uncertain polytopic linear parameter-varying (LPV) approach using parameter set mapping with principle component analysis (PCA). An LPV representation of the power system dynamics is generated by linearization of its differential-algebraic equations about the transient operating points for some given specific faults containing the system nonlinear properties. The time response of the output signal in the transient state plays the role of the scheduling signal that is used to construct the LPV model. A set of sample points of the dynamic response is formed to generate an initial LPV model. PCA-based parameter set mapping is used to reduce the number of models and generate a reduced LPV model. This model is used to design a robust pole placement controller to assign the poles of the power system in a linear matrix inequality (LMI) region, such that the response of the power system has a proper damping ratio for all of the different oscillation modes. The proposed scheme is applied to controller synthesis of a power system stabilizer, and its performance is compared with a tuned standard conventional PSS using nonlinear simulation of a multi-machine power network. The results under various conditions show the robust performance of the proposed controller.