  Dynamic operating envelopes (DOEs) have been introduced in recent years as a
means to manage the operation of distributed energy resources (DERs) within the
network operational constraints. DOEs can be used by network operators to
communicate DER dispatchable capacity to aggregators without further
consideration of network constraints and are thus viewed as a key enabler for
demand-side participation in future electricity markets and for ensuring the
integrity of distribution networks. While a number of approaches have been
developed to calculate OEs, uncertainties in system data are typically ignored,
which can lead to unreliable results and introduce security risks in network
operations. This paper presents a deterministic procedure to calculate robust
DOEs (RDOEs) explicitly hedged against uncertainty and variability in
customers' loads and generations. The approach is based on a geometric
construction strictly included within the feasible region of a linear
unbalanced three-phase optimal power flow problem that specifies the network
operational constraints. The paper analyses and rigorously shows that the
proposed approach also delivers proportional fairness in capacity allocations,
and demonstrates how the RDOEs can be enlarged by (i) exploiting the knowledge
of customer operational statuses, and (ii) by optimising customers'
controllable reactive powers. Two case studies based on an illustrative
distribution network and an Australian representative low-voltage distribution
network illustrate the efficiency and compliance of the proposed approach.
