We consider the decentralized reactive power control of photovoltaic (PV) inverters spread throughout a radial distribution network. Our objective is to minimize the expected voltage regulation error, while guaranteeing the robust satisfaction of distribution system voltage magnitude and PV inverter capacity constraints. Our approach entails the offline design and the online implementation of the decentralized controller. In the offline control design, we compute the decentralized controller through the solution of a robust convex program. Under the restriction that the decentralized controller have an affine disturbance feedback form, the optimal solution of the decentralized control design problem can be computed via the solution of a finite-dimensional conic program. In the online implementation, we provide a method to implement the decentralized controller at a time-scale that is fast enough to counteract the fluctuations in the system disturbance process. The resulting trajectories of PV inverter reactive power injections and nodal voltage magnitudes are guaranteed to be feasible for any realization of the system disturbance under the proposed controller. We demonstrate the ability of the proposed decentralized controller to effectively regulate voltage over a fast time-scale with a case study of the IEEE 123-node test feeder.
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