Fair operating envelopes under uncertainty using chance constrained optimal power flow

Abstract

The significant penetration of rooftop solar photovoltaics (PV) is pushing low-voltage distribution networks to the brink of their technical limits, which increasingly requires distribution system operators (DSO) to limit power exports. The easiest but also the bluntest instrument is to impose a blanket constraint, which is suboptimal and not in the best interest of PV owners. Alternatively, the DSO can compute PV export limits, also called operating envelopes, using AC optimal power flow (OPF) in real-time. However, this assumes full observability of customer demand, which is unrealistic in practice. To address this gap, we propose a bi-level framework under uncertainty to compute operating envelopes that are robust against uncertainty. At the upper level, the DSO solves a deterministic OPF using day-ahead prediction of customer demand and PV generation. The linearised OPF solution is then used in a chance-constrained OPF problem, resulting in a second-order cone model, which could be solved efficiently. At the lower level, prosumers optimise battery operation against the operating envelopes submitted by the DSO day-ahead. The proposed operating envelopes are fair in the sense that all prosumers are subject to the same export limit irrespective of their location in the network.