Fast localized voltage regulation in single-phase distribution grids

Distribution grids undergo a transformative change with the emergence of renewables, demand-response programs, and electric vehicles. Fluctuations in active power injections can dramatically affect voltage magnitudes across the grid. The power electronics of distributed generation (DG) units can provide an effective means of the much needed voltage regulation. On the other hand, the scalability and time-variability of DGs call for localized and fast-responding control schemes. In this context, a reactive power control rule is introduced here after applying a proximal gradient algorithm on a judiciously defined voltage regulation cost. An accelerated control scheme is further developed. The latter scheme not only affords localized processing, but it also enjoys a notable speedup advantage with only a slight modification of the original control rule. Numerical tests on the IEEE 13-bus and 34-bus systems with high solar penetration corroborate its superior convergence rates.