Spectral Analysis of Network Coupling on Power System Synchronization with Varying Phases and Voltages

Synchronization is the basis for any functional AC power systems which requires all voltage phasors in the network to rotate at the same frequency with steady magnitudes. In contrast to the traditional phase-only model by omitting voltage dynamics (usually as a Kuramoto model), this paper considers coupled phase and voltage dynamics. Specifically, we aim to uncover under what condition a negative eigenvalue of the coupling matrix occurs, which could cause desynchronization. To this end, we generalize the classical Schur complement formula to the case where sub-matrices are singular with special nullspace. Based on it, a necessary and sufficient condition is first obtained by exploiting the underlying structural properties in sub-matrices. Furthermore, the basic relation between the power system susceptance and the spectrum is also revealed, building the connection between network parameters and synchronization and highlighting the role of network shunts. Simulations on a rudimentary 3-bus power system well verify our results. This work reveals the inherent discrepancy between the phase-only and phase-amplitude oscillator models, shedding new light on better understanding and analyzing broader complicated oscillator networks beyond power systems.