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 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 PVgeneration
and load-profile data for an illustrative low-voltage
residential distribution system.