  Distribution microgrids are being challenged by reverse power flows and
voltage fluctuations due to renewable generation, demand response, and electric
vehicles. Advances in photovoltaic (PV) inverters offer new opportunities for
reactive power management provided PV owners have the right investment
incentives. In this context, reactive power compensation is considered here as
an ancillary service. Accounting for the increasing time-variability of
distributed generation and demand, a stochastic reactive power compensation
scheme is developed. Given uncertain active power injections, an online
reactive control scheme is devised. This scheme is distribution-free and relies
solely on power injection data. Reactive injections are updated using the
Lagrange multipliers of a second-order cone program. Numerical tests on an
industrial 47-bus microgrid and the residential IEEE 123-bus feeder corroborate
the reactive power management efficiency of the novel stochastic scheme over
its deterministic alternative, as well as its capability to track variations in
solar generation and household demand.
