The Effect of Transmission-Line Dynamics on Grid-Forming Dispatchable Virtual Oscillator Control

In this paper, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based ac power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, that is, if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of ac power inverters with respect to a prespecified solution of the ac power-flow equations. While this approximation is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system. In this paper, we establish explicit bounds on the controller set-points, branch powers, and control gains that guarantee almost global asymptotic stability of dVOC in combination with a dynamic model of the transmission network.