Time-varying renewable energy generation can result in seriousunder-/over-voltage conditions in future distribution grids. Augmentingconventional utility-owned voltage regulating equipment with the reactive powercapabilities of distributed generation units is a viable solution. Localcontrol options attaining global voltage regulation optimality at fastconvergence rates is the goal here. In this context, novel reactive powercontrol rules are analyzed under a unifying linearized grid model. Forsingle-phase grids, our proximal gradient scheme has computational complexitycomparable to that of the rule suggested by the IEEE 1547.8 standard, but itenjoys well-characterized convergence guarantees. Adding memory to the schemeresults in accelerated convergence. For three-phase grids, it is shown thatreactive injections have a counter-intuitive effect on bus voltage magnitudesacross phases. Nevertheless, when our control scheme is applied to unbalancedconditions, it is shown to reach an equilibrium point. Yet this point may notcorrespond to the minimizer of a voltage regulation problem. Numerical testsusing the IEEE 13-bus, the IEEE 123-bus, and a Southern California Edison47-bus feeder with increased renewable penetration verify the convergenceproperties of the schemes and their resiliency to grid topologyreconfigurations.
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