Fast Probabilistic Hosting Capacity Analysis for Active Distribution Systems

Interconnection studies for distributed energy resources (DERs) can currently take months since they entail simulating a large number of power flow scenarios. If DERs are to be actively controlled, probabilistic hosting capacity analysis (PHCA) studies become more time-consuming since they require solving multiple optimal power flow (OPF) tasks. PHCA is expedited here by leveraging the powerful tool of multiparametric programming (MPP). Using an approximate grid model, optimal DER setpoints are decided by a quadratic program, which depends on analysis and uncertain parameters in a possibly nonlinear fashion. By reformulating this program, feasible and infeasible OPF instances alike are handled in a unified way to uniquely reveal the location, frequency, and severity of feeder constraint violations. The effect of voltage regulators is also captured by novel approximate models. Upon properly extending MPP to PHCA, we were able to find the exact minimizers for 518,400 OPF instances on the IEEE 123-bus feeder by solving only 6,905 of them, and 86,400 instances on a 1,160-bus feeder by solving only 2,111 instances. This accelerated PHCA by a factor of 10. Thus, a utility can promptly infer grid statistics using real-world data without a probabilistic characterization of uncertain parameters.