Voltage Regulation Algorithms for Multiphase Power Distribution Grids

Time-varying renewable energy generation can result in serious under-/over-voltage conditions in future distribution grids. Augmenting conventional utility-owned voltage regulating equipment with the reactive power capabilities of distributed generation units is a viable solution. Local control options attaining global voltage regulation optimality at fast convergence rates is the goal here. In this context, novel reactive power control rules are analyzed under a unifying linearized grid model. For single-phase grids, our proximal gradient scheme has computational complexity comparable to that of the rule suggested by the IEEE 1547.8 standard, but it enjoys well-characterized convergence guarantees. Adding memory to the scheme results in accelerated convergence. For three-phase grids, it is shown that reactive injections have a counter-intuitive effect on bus voltage magnitudes across phases. Nevertheless, when our control scheme is applied to unbalanced conditions, it is shown to reach an equilibrium point. Yet this point may not correspond to the minimizer of a voltage regulation problem. Numerical tests using the IEEE 13-bus, the IEEE 123-bus, and a Southern California Edison 47-bus feeder with increased renewable penetration verify the convergence properties of the schemes and their resiliency to grid topology reconfigurations.