An analytical approach for the stability analysis of power networks through Kuramoto oscillators model

Abstract

In recent years, ensuring stability in power networks has posed a significant challenge for network control engineers, primarily due to the substantial growth in power demand and the complexities involved in integrating renewable energy sources. This study endeavours to augment the existing research by presenting theoretical findings in a practical manner through the introduction of a novel Lyapunov function and the application of LaSalle’s invariance principle to establish an unequivocal and accurate synchronization condition in power networks. The study’s salient contributions include (I) the Fresh approach of utilizing a second-order configuration of asymmetrically networked, dissimilar oscillators; (II) the incorporation of lossy power networks, culminating in non-identical phase delays in the analytical model of the oscillating network; and (III) the introduction of an entirely original Lyapunov function to provide a precise and unambiguous estimation for the region of attraction in power networks. Analytical findings substantiate that network synchronization is assured by the algebraic connectivity of the network graph exceeding a particular threshold value. The study’s transient stability conditions have been authenticated via numerical simulations of the IEEE 39-bus system.