Day-ahead dynamic operating envelopes using stochastic unbalanced optimal power flow

Driven by the energy transition, distribution networks are dealing with increasing uptake of distributed energy resources, including solar photovoltaic generation. Residential rooftop solar allows customers to minimize exposure to price increases in the market, which has led to high penetration of PV in regions with high amounts of solar hours such as Australia. Eventually, this leads to congestion in the network, either due to voltage rise, or due to overcurrent in lines or transformers. Distribution utilities are now moving on from static export limits for customers in congested networks, to dynamic limits that are based on the state of the network. It is considered thoughtful to give customers advance warning, e.g. day-ahead, of the moments and degrees of export limitation, despite uncertainty surrounding the future state of the network. Therefore, in this paper, we consider the application of general polynomial chaos expansion based stochastic unbalanced optimal power flow to the day-ahead determination of dynamic export limits. We perform a numerical study on a European style low voltage feeder and illustrate the impact of fairness principles on chance-constrained stochastic nonlinear optimization without the need of sampling, linearizing the power flow equations, or applying relaxations. Case studies show the necessity of considering unbalanced study of distribution system. It was observed that equality measures reduce the overall output of the system in an attempt to achieve equal relative injection, while alpha fairness with a higher value of alpha is a compromise between the efficiency and fairness in DOEs.