A Bounding Method for Day-Ahead Economic Dispatch with a Dynamic Uncertainty Set of PV Power Output

Abstract

In this paper, we propose a bounding method for the optimal demand-dispatch schedules in the form of time-series intervals for battery-aided electrical grids with solar photovoltaic systems (PV) when the confidence intervals of both PV output and its temporal change are known. The result corresponds to the minimal regulating capacity for generators and batteries to meet most economically power demand induced by any PV output scenario. We model a set of predicted demand scenarios as a class of convex polytope, and formulate a day-ahead economic dispatch problem as parametric quadratic programming (pQP). Then, our problem reduces to finding the interval hull of minimizers of the pQP over the convex polytope. To solve it, we prove that a minimizer of the pQP for any feasible active set of constraints can be maximized/minimized at a fixed vertex on the convex polytope, from which it can be shown that the optimal generation at any time slot reaches its maximum/minimum if power demand is maximum/minimum at any time slot, and that the optimal discharging power at each time slot does so if power demand is maximum/minimum at the same time slot and as low/high as possible at the other time slots. This means the time-series intervals of dispatch solutions can be obtained by solving the day-ahead economic dispatch problem only for a finite number of such power demand scenarios. Numerical simulations demonstrate the effectiveness of the proposed method.

Keywords

• day-ahead economic dispatch
• dynamic uncertainty set
• parametric quadratic programming