A Polynomial Chaos-based Approach to Sizing of Virtual Synchronous Generators

This paper proposes a Generalized Polynomial Chaos (gPC)-based approach to determine sizes of Virtual Synchronous Generator (VSG) units to enhance the dynamic performance of power systems. With the high integration of renewable energy sources, distributed generators, and energy storage units, the overall system inertial level has reduced. VSGs have the potential to compensate for the reduced inertia and enhance stability margins of electric power systems. On the other hand, determining the minimum sizes of VSGs units under several system uncertainties is challenging and requires advanced stochastic approaches. Monte Carlo simulation and Perturbation techniques have been used for a long time to quantify impacts of stochastic variables on power systems. These approaches are computationally involved especially for large systems. The gPC-based method provides a faster and efficient method to quantify uncertainties in various power system problems where the behavior of random variables is represented as a series of orthogonal polynomials that can be easily evaluated. In the proposed approach, the time domain simulation approach for multi-machine systems is integrated with the gPC to estimate the sizes of VSG units under various failure conditions. The proposed method is demonstrated on the reduced WECC-9 bus system. The results are compared with Monte Carlo simulation to validate the accuracy and efficiency of gPC.