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The rapid development of distributed energy resources (DERs) has brought manychallenges to the operation of distribution networks in recent years, whereoperating envelopes (OEs), as a key enabler to facilitate DER integration viavirtual power plants, have attracted increasing attention. Geometrically, OEsare inherently linked to the feasible region (FR) concept, which depicts anarea that quantifies the permissible operational ranges for all DERs. Thispaper studies how to calculate FR for DERs based on a linear unbalancedthree-phase power flow model while considering uncertainties frommeasured/estimated network impedances, leading to the robust feasible region(RFR). With an initialised FR, the proposed solution algorithm aims to seek theRFR by solving a non-convex bilinear problem, formulated based on MotzkinTransposition Theorem, and updating the RFR alternatively until reachingconvergence. Two cases, including a 2-bus illustrative network and arepresentative Australian network, have been tested to demonstrate theeffectiveness of the proposed approach.

Feasible Region for DERs in Unbalanced Distribution Networks with Uncertain Line Impedances