  Distributed consensus-based controllers for optimal secondary frequency
regulation of microgrids and power systems have received substantial attention
in recent years. This paper provides a Lyapunov-based proof that, under a
time-scale separation, these control schemes are stabilizing for a wide class
of nonlinear power system models, and under weak assumptions on (i) the
objective functions used for resource allocation, and (ii) the graph topology
describing communication between agents in the consensus protocol. The results
are illustrated via simulation on a detailed test system.

Optimization and Control