Coherent Swing Instability of Power Grids

We interpret and explain a phenomenon in short-term swing dynamics of multi-machine power grids that we term the Coherent Swing Instability (CSI). This is an undesirable and emergent phenomenon of synchronous machines in a power grid, in which most of the machines in a sub-grid coherently lose synchronism with the rest of the grid after being subjected to a finite disturbance. We develop a minimal mathematical model of CSI for synchronous machines that are strongly coupled in a loop transmission network and weakly connected to the infinite bus. This model provides a dynamical origin of CSI: it is related to the escape from a potential well, or, more precisely, to exit across a separatrix in the dynamical system for the amplitude of the weak nonlinear mode that governs the collective motion of the machines. The linear oscillations between strongly coupled machines then act as perturbations on the nonlinear mode. Thus we reveal how the three different mode oscillations—local plant, inter-machine, and inter-area modes—interact to destabilize a power grid. Furthermore, we present a phenomenon of short-term swing dynamics in the New England (NE) 39-bus test system, which is a well-known benchmark model for power grid staCommunicated by V. Rom-Kedar. Y. Susuki ( ) · I. Mezić Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070, USA e-mail: [email protected] Present address: Y. Susuki Department of Electrical Engineering, Kyoto University, Katsura, Nishikyo, Kyoto 615-8510, Japan T. Hikihara Department of Electrical Engineering, Kyoto University, Katsura, Nishikyo, Kyoto 615-8510, Japan 404 J Nonlinear Sci (2011) 21: 403–439 bility studies. Using a partial linearization of the nonlinear swing equations and the proper orthonormal decomposition, we show that CSI occurs in the NE test system, because it is a dynamical system with a nonlinear mode that is weak relative to the linear oscillatory modes.