Optimizing Energy Management in LVDC Microgrids: A Comparative Study of Linear and Non-Linear EMS Formulations

This paper presents an Energy Management System (EMS) for a grid-tied Low-Voltage Direct Current (LVDC) Microgrid (MG) equipped with Photovoltaic (PV) units, Battery Energy Storage Systems (BESSs), and AC and DC loads. The objective of this EMS is to minimize the facility's operational costs associated with the energy exchange with the external network. Optimal Power Flow (OPF) equations are included in the EMS model in non-linear and linear forms. In the former case, the optimization problem is defined as a MixedInteger Quadratically Constrained Programming (MIQCP) problem, while the latter is a Mixed-Integer Linear Programming (MILP) problem. The case study is a 3-bus MG, for which the deviation between the results obtained with the two formulations of OPF equations is evaluated. In this way, the impact of the linearized approach on electrical, economic, and computational performances is assessed. A sensitivity analysis carried out by varying the parameters of the lines shows the limits and the validity domain of the approximation introduced by linear OPF equations, also focusing on computational aspects. When considering the base length of the lines, the results prove a negligible impact on Mean Absolute Percentage Error (MAPE) in voltages (0.01%) and power (1.71%) between the non-linear and linear implementations. On the other hand, the findings show a growing trend in terms of MAPE when increasing the length of the lines and higher differences in the OPF results. However, the computation time of the linear implementation (0.79 s) is significantly lower in comparison to the non-linear approach (632.4 s).