Estimation of the location of inter-area oscillations and their interactions in electrical power systems using Lyapunov modal analysis

Abstract

Modern large-scale electrical power systems face serious stability threats in the form of low-frequency oscillations. Based on the recently proposed Lyapunov modal analysis framework, this study proposes a method for estimating the location and structure of inter-area oscillations as well as their interactions on the graph of an electrical power system. This method combines the known approaches of modal analysis and spectral decomposition of Lyapunov functions. In contrast to conventional modal analysis, modal indicators that consider the energy of voltage disturbances accumulated over time are proposed rather than the instantaneous dynamics of an individual perturbation. These indicators help analyze not only the location and structure of individual inter-area oscillations but also the geometry and structure of their pair-wise interactions in terms of the mutual action of modes, which is produced in the nodes over time. Motivational examples that illustrate the benefits of the proposed energy-based indicators are discussed. In test experiments using the New England IEEE 68 bus system, the proposed method is compared with the network modeshapes method to assess the locations of the nodes and ties that are critical for the selected inter-area oscillations. In a scenario experiment, the locations of the most sensitive nodes at the resonant modal interaction are examined. The proposed method can be used to analyze the resonance phenomena that arise in modern EPSs, especially in connection with the growth of renewable energy sources and the active use of thyristor converters. Novel approach can improve various control methods used for damping inter-area oscillations, optimal placement of sensors and stabilizers, and the analysis of voltage stability.