Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

Electrical Engineering and Systems Science > Systems and Control
[Submitted on 25 Aug 2026]
Title:Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration
View PDF HTML (experimental)Abstract:The proliferation of distributed energy resources (DERs) in distribution grids enables the active coordination of these assets to reduce costs and enable cleaner operations. Realizing this potential requires solving multiphase AC optimal power flow (AC-OPF) quickly across varying loads, DER availabilities, and topology reconfigurations, at much greater speed and scale than conventional nonlinear solvers. Learning-based surrogates can offer millisecond inference, yet existing methods target largely balanced transmission systems and do not scale to the multiphase, unbalanced, and reconfigurable nature of distribution feeders at utility scale. We present the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes. Penalty+SLFS requires no labeled optimal solutions and trains directly from the AC-OPF objective and constraints through a differentiable fixed-point power flow solver, avoiding expensive label generation and admitting robust training procedures. Topology changes are handled efficiently using Sherman-Morrison-Woodbury updates of the admittance-matrix inverse, while an M-step Jacobian approximation accelerates differentiation through the power flow solver. At inference, SLFS repairs any infeasible predictions, providing feasibility guarantees with low computational overhead. On IEEE feeders ranging from 13 to 8,500 nodes, Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations, delivers up to three orders of magnitude speedups over IPOPT, and remains robust under large distributional shifts, demonstrating a viable path toward real-time, topology-aware AC-OPF for large-scale distribution grids.
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* The method presented is Penalty + Sequential Linearized Feasibility Seeking (SLFS).
* SLFS is a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes.
* Penalty+SLFS trains directly from the AC-OPF objective and constraints using a differentiable fixed-point power flow solver.
* Topology changes are handled via Sherman-Morrison-Woodbury updates of the admittance-matrix inverse.
* An M-step Jacobian approximation accelerates differentiation through the power flow solver.
* Inference involves SLFS repairing infeasible predictions, providing feasibility guarantees with low computational overhead.
* Testing was performed on IEEE feeders ranging from 13 to 8,500 nodes.
* The results showed negligible optimality gaps and near-zero constraint violations.
* The method delivered speedups of up to three orders of magnitude over IPOPT.
* The framework remained robust under large distributional shifts.

The research introduces the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework designed to solve multiphase AC Optimal Power Flow (AC-OPF) in distribution systems, specifically accounting for switch-induced topology changes. The method trains directly from the AC-OPF objective and constraints without requiring labeled optimal solutions. It achieves efficiency by utilizing a differentiable fixed-point power flow solver, which allows training via an M-step Jacobian approximation for differentiation through the power flow solution. Topology changes are managed using Sherman-Morrison-Woodbury updates on the admittance-matrix inverse. During inference, the SLFS method repairs any infeasible predictions while maintaining feasibility guarantees with low computational overhead. Testing on IEEE feeders ranging from 13 to 8,500 nodes demonstrated that Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations. The approach yielded speedups of up to three orders of magnitude compared to IPOPT and proved robust under large distributional shifts.

The research addresses a critical gap in applying complex optimization techniques like AC-OPF to real-time, dynamic distribution grids, specifically focusing on the scalability and handling of non-linear topology changes inherent in distributed energy resource environments. The novelty lies in embedding self-supervised learning directly into the feasibility seeking process, bypassing the bottleneck of generating expensive optimal labels. This methodology suggests a shift away from relying solely on traditional iterative solvers for highly dynamic systems toward differentiable surrogate models that learn the underlying physical relationships while enforcing hard constraints. The performance metrics—speedup and constraint adherence across a wide range of system sizes—suggest that this approach moves optimization closer to the millisecond inference required by real-time grid operation. A key implication is the potential for deploying high-fidelity, topology-aware control systems in distribution networks where computational speed currently limits deployment. However, the reliance on differentiable solvers and Jacobian approximations raises questions about whether these differentiations perfectly capture all physical non-linearities under extreme contingency scenarios not fully explored in the training set. Further investigation into generalization across varied network configurations, especially concerning fault isolation and protection schemes integrated into the learning objective, would be necessary to solidify its operational viability outside the tested IEEE feeder benchmarks.

Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

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Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

Facts Only

Executive Summary

Full Take