Risk-constrained microgrid reconfiguration using group sparsity

The system reconfiguration task is considered for existing power distribution systems and microgrids, in the presence of renewable-based generation and load foresting errors. The system topology is obtained by solving a chance-constrained optimization problem, where loss-of-load (LOL) constraints and ampacity limits of the distribution lines are enforced. Similar to various distribution system reconfiguration renditions, solving the resultant problem is computationally prohibitive due to the presence of binary line selection variables. Further, lack of closed-form expressions for the joint probability distribution of forecasting errors hinders tractability of LOL constraints. Nevertheless, a convex problem reformulation is developed here by resorting to a scenario approximation technique, and by leveraging the underlying group-sparsity attribute of currents flowing on distribution lines equipped with tie and sectionalizing switches. The novel convex LOL-constrained reconfiguration scheme can also afford a distributed solution using the alternating direction method of multipliers, to address the case where multifacilities are managed autonomously from the rest of the system.