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 phasor measurement technology has made it possible the monitoring and control of wide‐area power systems. In this study, a new genetic algorithm based method for optimal placement of phasor measurement units (PMUs) considering observability and security issues is proposed. The idea is to allocate the least number of PMUs while providing the most redundant set of measurements. This allocation philosophy ensures reliability in the state estimation process. Moreover, the allocation method also takes into account security issues, by preserving the system's observability in case of loss of PMUs. In particular, the loss of a single PMU [( n − 1) criterion] is considered. The proposed method was tested on IEEE standard test systems and the results are discussed and evaluated.

This paper proposes a probabilistic optimal power flow (POPF) for unbalanced three-phase electrical distribution systems considering robust constraints. Wind velocity, solar irradiation, and demands are considered as exogenous random variables with dissimilar probability distribution functions. The proposed two-stage POPF model determines the optimal generation dispatch that minimizes the average production cost while satisfying probabilistically robust constraints. The robustness of the solution is adjusted through a parameter involving the first two moments of the random state variables. The 2m + 1 point estimate method (PEM) provides the scenarios for the proposed POPF model, which can be solved using commercial solvers. The model's accuracy is evaluated by comparing the results obtained with the PEM and with a classical scenario generator technique. The model is validated through two IEEE distribution feeders with 13 and 123 nodes, comprising dispatchable and renewable generation. Results show that the model can accurately estimate the mean and standard deviation of the state random variables when compared with results obtained through Monte Carlo simulations. Various levels of conservatism are assessed, demonstrating the model's flexibility and applicability.