A Convex Approximation for the Tertiary Control of Unbalanced Microgrids

•An OPF algorithm taylored for tertiary control in microgrids is proposed.•This model considers 24h operation and includes renewable energy sources, energy storage devices, and grid code limitations.•Power flow equations are simplified using a recently developed approximation based on Wirtinger’s calculus•Simulation results demonstrate the algorithm is suitable for tertiary control. This article presents an optimization model for tertiary control in three-phase unbalanced microgrids. This model considers 24h operation and includes renewable energy sources, energy storage devices, and grid code limitations. Power flow equations are simplified using a recently developed approximation based on Wirtinger’s calculus. The proposed model is evaluated both theoretically and practically. From the theoretical point of view, the model is suitable for tertiary control since it is convex; hence, global optimum, uniqueness of the solution, and convergence of the interior point method are guaranteed. From the practical point of view, the model is simple enough to be implemented in a small single-board computer with low time calculation. The latter is evaluated by implementing the model in a Raspberry-Pi board with the CIGRE low voltage benchmark; the model is also evaluated in the IEEE 123-nodes test system for power distribution networks.