DiffOPF: Diffusion Solver for Optimal Power Flow

TL;DR

DiffOPF addresses the inherently multi-valued and non-convex AC-OPF by learning a joint distribution of loads and dispatch from historical data and enabling conditional sampling of dispatch plans given loads. By treating OPF as a conditional diffusion problem, it produces a diverse set of statistically credible warm starts that can be selectively used to balance cost and constraint satisfaction. The approach provides a theoretical sample-complexity bound and demonstrates superior performance to single-valued deep learning OPF solvers on multiple benchmarks, with clear practical benefits for risk-aware operational decision-making. Future work targets runtime acceleration through diffusion distillation and integrating constraints directly into the diffusion process for end-to-end constrained optimization.

Abstract

The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a given load. Existing deep learning OPF solvers are single-valued and thus fail to capture the variability of system parameters unless fully represented in the feature space, which is prohibitive. To solve this problem, we introduce a diffusion-based OPF solver, termed \textit{DiffOPF}, that treats OPF as a conditional sampling problem. The solver learns the joint distribution of loads and dispatch setpoints from operational history, and returns the marginal dispatch distributions conditioned on loads. Unlike single-valued solvers, DiffOPF enables sampling statistically credible warm starts with favorable cost and constraint satisfaction trade-offs. We explore the sample complexity of DiffOPF to ensure the OPF solution within a prescribed distance from the optimization-based solution, and verify this experimentally on power system benchmarks.

Figures (4)

• Figure 1: Multi-valued load-to-dispatch mapping in OPF. The multiplicity of dispatch setpoints in OPF arises from several sources: the inherent non-convexity of power flow equations, uncontrolled disturbances affecting OPF parameters, and controlled disturbances, such as transformer tap changes, shunt switching, and network topology switching. As a result, for a given load input $d$, the history of operations yields a distribution of dispatch setpoints. Trained on historical observations, single-valued deep learning OPF solvers return a deterministic prediction for $d$, typically the conditional expectation. DiffOPF, instead, learns the full distribution of dispatch setpoints, returning a credible population of setpoints consistent with the historical observations.
• Figure 2: Schematic of the proposed DiffOPF framework. Historical OPF records in $\mathcal{D}$ are used to learn the joint distribution $p_{\text{real}}(\mathbf{p}_d, \mathbf{q}_d,\mathbf{p}_g, \mathbf{q}_g)$. At the next stage, given a new demand observation $(\mathbf{p}_d, \mathbf{q}_d)$, the model generates OPF solutions $(\mathbf{p}_g, \mathbf{q}_g)$ by sampling the conditional distribution $p_{\theta}(\mathbf{p}_g, \mathbf{q}_g|\mathbf{p}_d, \mathbf{q}_d)$. In the interest of illustration, we only show a two-dimensional joint distribution between $\mathbf{p}_d$ and $\mathbf{p}_g$.
• Figure 3: Comparison of DiffOPF and DeepOPF for the selected dispatch setpoints in the PJM test case. DiffOPF captures the modality and support of the underlying distribution of dispatch setpoints, while single-valued DeepOPF only provides point predictions.
• Figure 4: Trade-off between optimality gap and voltage constraint violations for DiffOPF warm starts on a single load instance in the PJM test case.