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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, sparsitypromoting 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.

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