Virtual Oscillator Control subsumes droop control

In this paper we examine the amplitude and phase dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of a class of weakly nonlinear Liénard-type oscillators. The general strategy of controlling inverters to emulate the behavior of Liénard-type oscillators is termed Virtual Oscillator Control (VOC), and it presents a compelling time-domain alternative to ubiquitous droop control methods which linearly trade off voltage frequencies and magnitudes with active and reactive power injections. In comparison to droop control, which assumes a priori that the network operates in a quasi-stationary sinusoidal steady state, VOC is a time-domain control strategy that globally stabilizes a desired sinusoidal steady state. The main, and somewhat surprising, result of this paper is that - when reduced to the sinusoidal steady state - the VOC dynamics correspond to those of droop control. Hence, VOC is a globally stabilizing control strategy that can deal with higher-order harmonics and includes droop control in the harmonic steady state. The results are intriguing, in that they suggest that droop control laws can be recovered from averaging the complex dynamics of a class of weakly nonlinear limit-cycle oscillators.