An affine arithmetic approach for microgrid dispatch with variable generation and load

A self-validated computing (SVC) method, based on affine arithmetic (AA) is proposed in this paper to solve the optimal power flow (OPF) problem for microgrids with renewable sources of variable generation. In the AA-based OPF formulation, all the state and control variables are presented in affine form, to represent the variable load, and wind and solar generation. Hence, the OPF model becomes an interval-based model with upper and lower bounds to represent the uncertain variables. To check the accuracy of the AA-based method, the resulted intervals are compared against those obtained from Monte-Carlo Simulation (MCS), in a 13-bus microgrid test system. The obtained real power generation intervals for thermal generators are used to determine the reserves required in dispatchable generators in the short-term to properly supply for the variability of load and intermittent renewable generation sources.