Yoshihiko Susuki

Nonlinear Koopman Modes and Coherency Identification of Coupled Swing Dynamics

We perform modal analysis of short-term swing dynamics in multi-machine power systems. The analysis is based on the so-called Koopman operator, a linear, infinite-dimensional operator that is defined for any nonlinear dynamical system and captures full information of the system. Modes derived through spectral analysis of the Koopman operator, called Koopman modes, provide a nonlinear extension of linear oscillatory modes. Computation of the Koopman modes extracts single-frequency, spatial modes embedded in non-stationary data of short-term, nonlinear swing dynamics, and it provides a novel technique for identification of coherent swings and machines.

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 stability 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.

Global swing instability in the New England power grid model

Global swing instability is an undesirable and emergent phenomenon of synchronous machines in a power grid, implying that most of the machines in the system simultaneously lose synchronism with the rest of the grid after being subjected to a finite and local disturbance. Recently we reported that global instability occurred in the classical model of swing dynamics in the New England power grid model. This paper analyzes the global instability in the New England power grid model. We show that the proper orthonormal decomposition and the Galerkin method for model reduction can determine a dynamical mechanism responsible for the global instability. These methods applied in this paper make it possible to find the occurrence of global instability in real power grids.

Nonlinear Koopman modes of coupled swing dynamics and coherency identification

We report modal analysis of coupled swing dynamics of a multi-machine power system. The analysis is based on the so-called Koopman operator, a linear, infinite-dimensional operator that is defined for any nonlinear dynamical system and captures full information of the system. The modal analysis makes it possible to extract single-frequency modes, which are called Koopman modes, embedded in the coupled swing dynamics and to identify a coherent group of generators in which they swing together in frequency and phase.

Ergodic partition of phase space in continuous dynamical systems

The theory of ergodic partition of phase space in discrete dynamical systems is extended to continuous dynamical systems or flows. This makes it possible to identify invariant sets of measure-preserving flows such as Hamiltonian flows. The extended theory is applied to an analysis of transient stability of multi-machine power systems.

Coherent Swing Instability of power systems and cascading failures

We describe short-term swing dynamics leading to cascading failure in an interconnected power system. The notion of Coherent Swing Instability (CSI) was recently proposed in which most of synchronous machines in a power system coherently lose synchronism with the rest of the system after being subjected to a local and finite disturbance. CSI is an escape phenomenon from resonance in the nonlinear mode that governs the collective motion of machines. For a network of weakly interconnected power systems, we show that CSI happens for all of the systems in a cascade manner and gives the mechanism of cascading failure in the network, that is, the sequence of escape phenomena that can occur in a class of high-dimensional dynamical systems.