This paper focuses on the optimal utilization of grid-connected microgrids for providing frequency regulation services to the bulk system they are connected to. We consider microgrids comprised of several distributed energy resources (DER) interconnected via an electrical network. We then formulate a joint DER scheduling and power flow optimization problem in order to determine the DER set-points so that the cost of failing to follow some regulation signal is minimized in each regulation contract; this problem is non-convex. We propose a convex relaxation for this problem, and propose a family of continuous-time control laws, the trajectories of which can be computed in a distributed way. We prove that these converge to an optimal solution of the relaxed problem, and that they result in feasible power flows for the system at each time instant. The proposed continuous-time control laws have to be implemented in a discrete-time fashion over some communication network. We propose a discrete-time approximation of our control laws, and show that the resulting discrete-time control laws converge to an optimal solution of the relaxed problem.

%B IEEE Transactions on Control of Network Systems %8 11/2017 %G eng %! IEEE Trans. Control Netw. Syst. %R 10.1109/TCNS.2017.2773019