Joint optimization of day-ahead and uncertain near real-time operation of microgrids

Due to the feature of a distribution-free model of uncertainties, robust optimization has become an attractive and efficient way to the energy management systems. In microgrids, regardless of the real-time conditions, this approach is used only to model the day-ahead energy management in the presence of renewables uncertainties. However, energy management can be done more efficiently by joint optimization of day-ahead and near real time conditions. In this case, in addition to the renewable uncertainty, the uncertainty of the real time market price is added to the problem. Furthermore, in the existing joint optimization models, which are mostly formulated with stochastic methods, the operational constraints such as exact power flow equations are discarded. This paper proposes a two-stage full robust model for joint optimization of day-head and uncertain real-time operation of microgrids considering exact modeling of the operational constraints. According to the forecasted value of renewable generations, the day-ahead problem is formulated as a MILP at the first stage. The uncertain real-time operation is formulated in the second stage by completely robust modeling of the uncertainties. In order to maintain the convex structure of the real-time problem, nonlinear constraints of the power flow equations are formulated based on the second-order cone relaxation of the branch flow equations, which is necessary for solving the problem using the cutting plan methods in a polynomial time. For solving the two-stage model, the dual Bender's decomposition algorithm is used. The proposed model is implemented on the modified IEEE 33 bus network, and the results including sensitivity analysis on the price and renewable budgets are presented. In addition, the efficiency and effectiveness of the proposed model are shown by comparing the results with two other methods in joint optimization and traditional robust day-ahead management method to determine the effect of considering real-time operation. At the end, the effect of the network structure and operational limitations on the results has been studied.