Robust Dynamic Operating Envelopes via Superellipsoid-based Convex Optimisation in Unbalanced Distribution Networks

TL;DR

This work addresses robust dynamic operating envelopes (DOEs) for distributed energy resource (DER) integration in unbalanced distribution networks under utilisation uncertainties. It introduces a one-step convex optimisation based on a superellipsoid to embed the DOE feasible region, formulating a robust counterpart by maximizing $\\log(\\det(L))$ under $y_1 \in \mathcal{E}_h$ constraints with $p = L w + u_c$ and $\\| w \\|_n^n \le 1$. The key contributions are (1) a convex superellipsoid-based method that bypasses the previous three-step procedure, (2) a strategy to select the superellipsoid’s squareness to reach near-optimality, and (3) extensive case studies demonstrating near-global-optimal performance on small to large networks with practical computation times. The findings indicate substantial DOE gains over deterministic and multi-step methods, with updates feasible day-ahead or hourly given adequate computing resources.

Abstract

Dynamic operating envelopes (DOEs) have been introduced to integrate distributed energy resources (DER) in distribution networks via real-time management of network capacity limits. Recent research demonstrates that uncertainties in DOE calculations should be carefully considered to ensure network integrity while minimising curtailment of consumer DERs. This letter proposes a novel approach to calculating DOEs that is robust against uncertainties in the utilisation of allocated capacity limits and demonstrates that the reported solution can attain close to global optimality performance compared with existing approaches.

Figures (5)

• Figure 1: (a) Conceptual example in calculating RDOEs via three steps; (b) Superellipsoid with $u_c=[0,0]^T$ and $L=[2,0;0,1]$.
• Figure 3: Topology of the AusNetwork (Information for customers' locations is available in LVFT_data (Network J). Especially, customers 30, 21, 16, 29, 2, 18, 22, 19 and 17, which are constrained in Fig.\ref{['fig_aus_J_hybrid_K_2_9_withQtrue_Mosek_SOCPtrue_LOBJtrue15']}, are connected to buses 64, 40, 45, 65, 65, 41, 40, 46 and 42, respectively).
• Figure 4: FRs and RDOEs compared with SO-based method under various approaches for TwbNetwork (boundaries for identified hyperellipsoid and superellipsoid are marked in red), where a): Dmtd; b): Three-step; c): sESD($K=2$); d): sESD($K=7$).
• Figure 5: DOEs calculated by various approaches for the AusNetwork, where customers in sub-figure (a)/(b) are exporting/importing powers and their upper/lower limits are 0 kW.
• Figure 6: DOE assessment based on exact UTPF for the AusNetwork.