Certificate-based Synthesis of Coordinated Droop Control for Heterogeneous Radial Distribution Networks

Abstract

Voltage certificates for droop-controlled low voltage feeders are often constructed from global worst-case quantities. In heterogeneous feeders, such bounds can hide where voltage risk arises and become increasingly conservative downstream as feeder sensitivities accumulate. This paper shows that voltage certificates can be used not only to assess a given controller, but also to design it. Specifically, we derive deterministic all-time, bus-wise voltage envelopes that retain local disturbance bounds, droop slopes, inverter limits, and feeder dependent sensitivities, while recovering the worst-case certificate as a special case. To overcome the deterioration of these bounds induced by the network topology, we introduce a droop architecture with virtual coordination and affine feedforward compensation that reshapes the effective voltage sensitivity. A scaling transformation converts the joint controller and certificate design into a linear program which ensures forward invariance and the satisfaction of reactive power reserve constraints. The controller uses only selected communication links and guarantees the certified voltage and inverter bounds for all admissible disturbances. Our certificates and methodology are evaluated on two radial low voltage network benchmarks: a five-customer residential feeder and a 26-customer rural network comprising four feeders. The studies demonstrate tighter and more spatially informative certificates, while respecting inverter limits.