Data-driven adjustable robust solution to voltage-regulation problem in PV-rich distribution systems

Abstract

Adjustable robust counterpart (ARC) methodology has been recently utilised in distribution system operation to allow fast-acting devices, such as PV inverters, to take live recourse actions in response to operating point deviations. Available ARC models are used to obtain the controller parameters based on the worst-case realisations. However, we show that such a strategy might lead to over-conservative results when uncertainty realises away from the worst-case. To close this gap, this paper extends ARC to allow exploiting probabilistic information of uncertainty within the optimisation problem. This results in controller parameters that not only secure the worst-case but also work better in expectation. We formulate our approach as a linear program that minimises the real power curtailment (RPC) and reactive power usage of PV inverters while maintaining network voltages in an acceptable range. In contrast to the conventional ARC, our approach considers a segmented uncertainty set, and assigns a probability to each segment based on historical data. It then optimises to find inverter controller parameters in the form of piecewise affine functions, with each piece associated with one segment in the segmented uncertainty set. In live operation, the controllers use the real-time local measurements and assigned piecewise affine functions to generate real and reactive power set-points for the inverters. The performance of the proposed approach is validated using Monte-Carlo simulations on IEEE 37-bus and 906-bus networks. The simulations show that the proposed approach improves the performance of ARC by 30% to 60% over a variety of experiments.