Robust Next-Day Scheduling of PV Generation Sources Supplying a Standalone DC Microgrid via a Semi-Definite Programming Model

This study focuses on optimizing the efficient operation of standalone direct-current (DC) microgrids with photovoltaic (PV) sources using semi-definite programming (SDP) optimization. The PV source operation model is formulated as a nonlinear programming (NLP) problem with the objective of minimizing daily energy losses and reducing CO2 emissions compared to diesel generators. Transforming the NLP model into convex optimization involves a linear matrix model that combines positive semi-definite matrices with an affine space. This approach enhances robustness by incorporating uncertainties in demand and PV source power. The robust SDP model employs a min–max strategy for worst-case scenario energy management dispatch (EMD). Evaluating a 27-bus standalone DC microgrid, the SDP model outperforms random-based algorithms by achieving global optima in both objectives. Under uncertainties, the energy loss objective increases by 21.6706% with demand uncertainty, 0.3997% with PV source uncertainty, and 22.2009% with both. Meanwhile, the CO2 emissions objective increases by 11.9184%, 1.8237%, and 14.0045%, respectively. Additional simulations on an 85-node DC network confirm the efficacy of SDP in worst-case scenario EMD. All simulations utilized MATLAB’s Yalmip tool with the Mosek solver.