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We consider the problem of frequency synchronization and power sharing in a lossy droop-controlled autonomous microgrid with distributed rotational and electronic generation (MDREG). At first, we establish equivalence of the dynamics of a regulated synchronous generator and a droop-controlled inverter with low pass filter. We then give a necessary and sufficient condition for local synchronization of the microgrid by using ideas from graph theory and second order consensus algorithms. In addition, we show that sources in an MDREG can achieve a desired active power distribution via frequency droop control and provide synchronization conditions for a lossless microgrid as a special case. Our analysis is further validated via a simulation example of a lossy microgrid based on the CIGRE benchmark medium voltage distribution network.
Schiffer et al. (2013) studied this question.