This paper presents an energy management system (EMS) for single-phase or balanced three-phase microgrids via robust convex optimization. Along a finite planning horizon, the solution provided by the proposed microgrids EMS remains feasible under adverse conditions of random demands and renewable energy resources. The proposed model is represented as a convex mixed-integer second-order cone programming model. Two operation modes are considered: grid-connected and isolated modes. In grid-connected mode, the proposed EMS minimizes the costs of energy imports, dispatches of distributed generation (DG) units, and the operation of the energy storage systems. In isolated mode, the proposed EMS minimizes the unsupplied demand, considering consumer priorities. Global robustness of the proposed mathematical model is adjusted using a single parameter ζ. The robustness of the solutions provided by the robust EMS is assessed using the Monte Carlo simulation method. In this case, DG units are set to operate in frequency and voltage droop control to support network fluctuations. Simulations are deployed using a microgrid with 136-nodes and several distributed energy resources. Results showed that the proposed model is suitable for the short-term microgrids energy management system. The robustness of the final solution was directly proportional to the operational costs, and it can be effectively controlled by the proposed parameter ζ for both operation modes. When compared to stochastic approaches, the proposed formulation showed to be more flexible and less time-consuming.

The proliferation of distributed energy assets necessitates the provision of flexibility to efficiently operate modern distribution systems. In this article, we propose a flexibility market through which the DSO may acquire flexibility services from asset aggregators in order to maintain network voltages and currents within safe limits. A max-min fair formulation is proposed for the allocation of flexibility. Since the DSO is not aware of each aggregator's local flexibility costs, we show that strategic misreporting can lead to severe loss of efficiency. Using mechanism design theory, we provide a mechanism that makes it a payoff-maximizing strategy for each aggregator to make truthful bids to the flexibility market. While typical truthful mechanisms only work when the objective is the maximization of Social Welfare, the proposed mechanism lets the DSO achieve incentive compatibility and optimality for the max-min fairness objective.