  Smart distribution grids should efficiently integrate stochastic renewable
resources while effecting voltage regulation. The design of energy management
schemes is challenging, one of the reasons being that energy management is a
multistage problem where decisions are not all made at the same timescale and
must account for the variability during real-time operation. The joint dispatch
of slow- and fast-timescale controls in a smart 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 data-driven schemes yield lower costs over competing alternatives.
