  The rapid development of distributed energy resources (DERs) has brought many
challenges to the operation of distribution networks in recent years, where
operating envelopes (OEs), as a key enabler to facilitate DER integration via
virtual power plants, have attracted increasing attention. Geometrically, OEs
are inherently linked to the feasible region (FR) concept, which depicts an
area that quantifies the permissible operational ranges for all DERs. This
paper studies how to calculate FR for DERs based on a linear unbalanced
three-phase power flow model while considering uncertainties from
measured/estimated network impedances, leading to the robust feasible region
(RFR). With an initialised FR, the proposed solution algorithm aims to seek the
RFR by solving a non-convex bilinear problem, formulated based on Motzkin
Transposition Theorem, and updating the RFR alternatively until reaching
convergence. Two cases, including a 2-bus illustrative network and a
representative Australian network, have been tested to demonstrate the
effectiveness of the proposed approach.
