A single and multiobjective robust optimization of a microgrid in distribution network considering uncertainty risk

In this paper, single and multi-objective robust optimization of a microgrid (MG) including photovoltaic (PV) and wind turbine (WT) sources with battery storage has been performed in a radial 33-bus distribution network considering uncertainty risk for minimizing the cost of energy losses, cost of electricity purchase from the post as well as power purchase from the MG. The problem is implemented in two approaches without uncertainty (deterministic) and with uncertainty (robust) via a flow direct algorithm (FDA). In the deterministic approach, the variables such as the site and the optimal size of the equipments in the short-term study horizon of 24 h, as well as the total cost, have been determined that the results of the MG deterministic optimization in the network indicate the reduction of network losses with the total cost minimization. The superior capability of the recommended deterministic approach based on the FDA is also confirmed in comparison with GA and PSO algorithms. In addition, the MG optimization problem with the robust approach with the information gap decision theory (IGDT) with risk-averse strategy is implemented to achieve the maximum radius of uncertainty (MRU) of renewable production and also network demand in three single and multi-objective cases. Based on the proposed robust approach, the level of system robustness has been determined in the condition of the worst uncertainty scenario against forecasting errors by considering different uncertainty budgets. It is also determined which uncertain parameter is more sensitive to the changes of the uncertainty budget. The findings demonstrated that in the multi-objective robust optimization, the constraints of the problem are not satisfied for budgets more than 40%, and in for sample the system uncertainty budget of 5%, there is a 27.51% decrease in resource production and a 0.87% increase in network load. The 40% uncertainty budget of the system is robust with a 16.80% decrease in resource generation and a 19.10% increase in network load. Therefore, one of the benefits of multi-objective optimization in comparison with single-objective optimization is balancing the sensitivity of uncertain parameters.