Aggregated Feasible Active Power Region for Distributed Energy Resources With a Distributionally Robust Joint Probabilistic Guarantee

Distributed Energy Resources (DERs) have valuable flexibility to provide grid services. The Aggregated Feasible Active Power Region (AFAPR) is useful for aggregating DERs and reducing the computational burden in system-wide DER scheduling. However, the uncertainty of DERs calls for a reliable AFAPR. This paper proposes a novel surrogate polytope method for deriving the inner approximation of the AFAPR that is jointly reliable for all DER constraints and linear network constraints across the scheduling period. Instead of directly applying the chance constraints to the low-level DER constraints and network constraints, the proposed method applies the Wasserstein Distributionally Robust Joint Chance Constraint (WDRJCC) to the surrogate polytope approximation of the AFAPR, which is reformulated into a tractable set of Mixed Integer Linear Programming (MILP) constraints. Our derived inner approximation to the reliable AFAPR is less conservative while still being reliable, as demonstrated by comparisons with four benchmarks in extensive case studies, and with the nonlinear Z-Bus power flow simulation applied to validate the satisfaction of network constraints. The historical data size required is small, making the proposed method easier to deploy. The scale of MILP constraints is small and does not increase with the network size nor with the number of DERs.