Development of a robust optimization method for optimal operation of microgrids with electric vehicles and renewable energy resources - Zandrazavi, Seyed Farhad (2023)
Microgrids can pave the way for the decarbonization of power systems by providing excellent infrastructure for the proliferation of distributed energy resources and electric vehicles. Nevertheless, in the presence of renewable energy generation and electric vehicles, the energy management of microgrids seems inseparable from uncertainties. On one hand, imperfect forecasts of intermittent renewable energy generation, electric load demand, and electricity price impose a high level of uncertainties in the daily optimal operation of microgrids. On the other hand, neglecting uncertainties by microgrids’ operators may lead to non-optimal solutions or even infeasible operational points. In order to mathematically model the optimal energy management of microgrids, firstly some fundamental concepts linked to mathematical optimization are briefly introduced, including local optimality, feasibility, convexity, linear programming, integer programming, mixed-integer linear programming, nonlinear nonconvex programming, and nonlinear convex programming. In addition, the power flow formulation in microgrids is extracted step by step, and then it is used to model deterministic energy management of microgrids as a nonlinear nonconvex programming problem. Then, relaxation and linearization are used to transform the aforementioned model into a convex model so as to guarantee the global optimality of the solutions. Secondly, to embrace uncertainty, the most well-known methods deployed widely in the literature for modeling uncertainty in the operation of microgrids are introduced and their characteristics are explained and compared. In order to model uncertainty in practice, a two-stage stochastic mixed-integer conic programming model is presented. Uncertainties linked to photovoltaic generation, wind power generation, electric demand, and electricity prices are included in the model via scenarios. It is noteworthy that the optimization models are developed in AMPL and solved via the CPLEX solver and tests are carried out on IEEE 33-bus and 69-bus test systems, to evaluate the effectiveness of the proposed models. The results show how considering the reconfigurability of microgrids can positively affect the operation by contributing to cost, voltage deviation and power loss reduction. Moreover, the results show considering scenarios can contribute to uncertainty modeling, yet it will affect the optimal solution compared to deterministic methods, as the constraints must be satisfied for every scenario, simultaneously.