  Low-voltage distribution feeders were designed to sustain unidirectional
power flows to residential neighborhoods. The increased penetration of roof-top
photovoltaic (PV) systems has highlighted pressing needs to address power
quality and reliability concerns, especially when PV generation exceeds the
household demand. A systematic method for determining the active- and
reactive-power set points for PV inverters in residential systems is proposed
in this paper, with the objective of optimizing the operation of the
distribution feeder and ensuring voltage regulation. Binary PV-inverter
selection variables and nonlinear power-flow relations render the novel optimal
inverter dispatch problem nonconvex and NP-hard. Nevertheless,
sparsity-promoting regularization approaches and semidefinite relaxation
techniques are leveraged to obtain a computationally feasible convex
reformulation. The merits of the proposed approach are demonstrated using
real-world PV-generation and load-profile data for an illustrative low-voltage
residential distribution system.
