Affinely Adjustable Robust Volt/VAr Control Without Centralized Computations

This paper proposes a completely non-centralized Volt/VAr control (VVC) algorithm for active distribution networks which are faced with voltage magnitude violations due to the high penetration of solar photovoltaics (PVs). The proposed VVC algorithm employs a two-stage architecture where the settings of the classical voltage control devices (VCDs) are decided in the first stage through a distributed optimization engine powered by the alternating direction method of multipliers (ADMM). In contrast, the PV smart inverters are instructed in the second stage through linear Q(P) decision rules - which are computed in a decentralized manner by leveraging robust optimization theory. The key to this non-centralized VVC routine is a proposed network partition methodology (NPM) which uses an electrical distance metric based on node $Q-|V|^{2}$ sensitivities for computing an intermediate reduced graph of the network, which is subsequently divided into the final partitions using the spectral clustering technique. As a result, the final network partitions are connected, stable, close in cardinality, contain at least one PV inverter for zonal reactive power support, and are sufficiently decoupled from each other. Numerical results on the UKGDS-95 and IEEE-123 bus systems show that the non-centralized solutions match closely with the centralized robust VVC schemes, thereby significantly reducing the voltage violations compared to the traditional deterministic VVC routines.