Two-Timescale Stochastic Dispatch of Power Distribution Networks

Smart distribution grids should optimally integrate stochastic renewable resources while effecting voltage regulation. Since some decisions have to be designed in advance, energy management is a multistage problem. For early stages, finding the optimal energy procurement accounting for the variability during real-time operation is a challenging task. The joint dispatch of slowand fast-timescale controls in a distribution grid is considered here. The substation voltage, the energy exchanged with a main grid, and the generation schedules for small diesel generators have to be decided on a slow timescale; whereas optimal photovoltaic inverter setpoints are found on a more frequent basis. While inverter and looser voltage regulation limits are imposed at all times, tighter bus voltage constraints are enforced on the average or in probability, thus enabling more efficient renewable integration. Upon reformulating the two-stage grid dispatch as a stochastic convex-concave problem, two distribution-free schemes are put forth. An average dispatch algorithm converges provably to the optimal two-stage decisions via a sequence of convex quadratic programs. Its non-convex probabilistic alternative entails solving two slightly different convex problems and is numerically shown to converge. Numerical tests on a real-world distribution feeder verify that both novel schemes yield lower costs over competing alternatives.