Data-Driven Optimal PMU Placement for Power System Nonlinear Dynamics Using Koopman Approach

Abstract

A phasor measurement unit (PMU) serves as a superior tool to monitor the dynamics of the power system, but its high cost remains a practical concern that requires the optimal placement of the PMU (OPP). Traditionally, researchers relied on model-based approaches to analyze this problem. However, these methods not only suffer from inevitable parameter uncertainties but can also be computationally expensive for complicated power system dynamic models. Faced with these issues, this article proposes a data-driven OPP approach utilizing an augmented Koopman operator. This operator lifts the original nonlinear state space to a high-dimensional linear Koopman space in a data-driven manner, which fully eliminates the model discrepancy while achieving high computing efficiency. Theoretically, we prove that the observability matrix in the augmented Koopman canonical coordinates preserves the whole dynamic evolution of both the system model and its associated measurement model. Finally, we propose a modified genetic algorithm to solve the established OPP problem, which is enhanced to further accelerate the search speed. The simulation results reveal the excellent performance of our proposed method.