  Contemporary electricity distribution systems are being challenged by the
variability of renewable energy sources. Slow response times and long energy
management periods cannot efficiently integrate intermittent renewable
generation and demand. Yet stochasticity can be judiciously coupled with system
flexibilities to enhance grid operation efficiency. Voltage magnitudes for
instance can transiently exceed regulation limits, while smart inverters can be
overloaded over short time intervals. To implement such a mode of operation, an
ergodic energy management framework is developed here. Considering a
distribution grid with distributed energy sources and a feed-in tariff program,
active power curtailment and reactive power compensation are formulated as a
stochastic optimization problem. Tighter operational constraints are enforced
in an average sense, while looser margins are enforced to be satisfied at all
times. Stochastic dual subgradient solvers are developed based on exact and
approximate grid models of varying complexity. Numerical tests on a real-world
56-bus distribution grid and the IEEE 123-bus test feeder relying on both grid
models corroborate the advantages of the novel schemes over their deterministic
alternatives.
