Decision-Oriented Dynamic Operating Envelopes for Distributed Energy Resources via End-to-End Learning With Simulation-in-the-Loop

The large-scale exploitation of distributed energy resources (DERs) has significantly enhanced the sustainability, flexibility, and cost efficiency of distribution networks. Dynamic operating envelopes (DOEs) provide a technically reliable and practical solution to ensure operational security and facilitate DER utilization. This paper proposes an end-to-end learning-based approach with simulation-in-the-loop (E2E-SiL) for optimizing the DOEs for DERs, which merits a decision-oriented training framework with excellent reliability and computational efficiency. An input convex neural network (ICNN) model is applied to estimate the mapping relationship from bus power injection to constraint violation while ensuring the convexity of analytical expressions for critical physical quantities in DOE optimization. Based on the ICNN model, the DOE optimization problem is transformed into a fully linear form solvable within seconds. To bridge the gap between theoretical DOE formulation and practical applications, simulation software is utilized to evaluate the actual loss and guide the ICNN parameter updates, formulating a simulation-in-the-loop structure and enhancing the practicality of DOE results. A backpropagation algorithm is proposed to derive parameter gradients theoretically, which achieves efficient training and better physical interpretability. Numerical experiments validate the superiority of the proposed E2E-SiL framework, which enhances the practicality of DOE results and ensures better utilization of DERs.