A Privacy-Preserving Distributed Congestion Management Framework Via Implicit Differentiation Bilevel Optimization

The growing integration of flexible distributed energy resources (DERs), such as hybrid heat pumps (HHPs), provides distribution system operators (DSOs) with valuable tools to manage grid congestion. Traditional approaches typically model the interaction between DSOs and prosumers with flexibility resources as a bilevel optimization problem. In this framework, the overall problem is typically reformulated through the Karush–Kuhn–Tucker (KKT) conditions into a single-level optimization problem, under the assumption that the DSO has complete knowledge of the prosumers’ lower-level optimization models. This assumption, however, violates realistic privacy and communication constraints, making KKT-based approaches impractical in real-world applications. To address this issue, this paper introduces a privacy-preserving framework, namely implicit differentiation bilevel optimization (IDBO), which leverages implicit differentiation to construct a differentiable convex optimization model. In this setting, each prosumer in the lower-level only transmits non-sensitive intermediate gradients to the DSO in the upper level, thus maintaining data confidentiality while still enabling end-to-end gradient-based optimization. A case study based on real measurements from a pilot project demonstrates the effectiveness of the proposed method. The approach shows high accuracy and notable improvement in computational efficiency compared to the traditional KKT-based approach, particularly in large-scale settings with more than one hundred prosumers in a distributed structure.