  This paper presents a novel distributed optimal power flow (DOPF) method for
fair distributed energy resource (DER) coordination in the context of mandated
rooftop PV inverter control modes. In practice, inverter reactive power control
is increasingly required by grid connection codes, which often unfairly curtail
PV generation of prosumers towards the end of low-voltage feeders. Similarly,
optimization-based DER coordination methods that aim solely for
technically-efficient DER coordination do not consider the distribution of PV
curtailment across customers. To address these concerns, we develop a tractable
multi-objective DOPF method for optimal DER coordination that (i) curtails PV
generation fairly across prosumers, and (ii) incorporates a standard
piecewise-linear volt-var control reactive power control function without using
integer variables. Three equity principles representing different
interpretations of fairness are implemented in our coordination method; namely,
egalitarian, proportional and uniform dynamic PV curtailment redistribution.
The performance of our approach is demonstrated on low-voltage distribution
feeders of different sizes (5, 10, 25, 50 and 100 prosumers) using two network
topologies: line topology without lateral spurs and tree topology with lateral
spurs. Each network considers three levels of PV penetration, giving 30 test
systems in total. The results demonstrate the effectiveness of the proposed
DOPF method for fair DER coordination: PV curtailment is equitably distributed
among prosumers with a computational burden on par with conventional DOPF
approaches. Moreover, different fairness methods result in different patterns
of curtailment, which a regulator may choose between.
