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Learning Interior Point Method Central Path Projection for Optimal Power Flow

Farshad Amani, Amin Kargarian, Ramachandran Vaidyanathan

TL;DR

This framework, referred to as Learning-IPM (L-IPM), significantly reduces both the number of IPM iterations and overall solution time and introduces a grid-informed mechanism into the LSTM that enforces key operational constraints on generation, voltage magnitudes, and line flows.

Abstract

This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional learning models that attempt to predict the OPF solution directly, our approach learns the structure of the IPM trajectory itself, since even accurate predictions may not reliably reduce IPM iterations. The IPM follows a central path that iteratively progresses toward the optimal solution. While this trajectory encodes critical information about the optimization landscape, the later iterations become increasingly expensive due to ill-conditioned linear systems. Our analysis of the IPM central path reveals that its initial segments contain the most informative features for guiding the trajectory toward optimality. Leveraging this insight, we model the central path as a time series and use a Long Short-Term Memory (LSTM) network to project the path using only the first few stable iterations. To ensure that the learned trajectory remains within the feasible region--especially near the optimal point--we introduce a grid-informed mechanism into the LSTM that enforces key operational constraints on generation, voltage magnitudes, and line flows. This framework, referred to as Learning-IPM (L-IPM), significantly reduces both the number of IPM iterations and overall solution time. To improve generalization, we use a sampling-based strategy to generate a diverse set of load conditions that effectively span the operational space. Simulation results across a range of test systems--including a 2869-bus European transmission network--demonstrate that L-IPM achieves up to a 94% reduction in solution time and an 85.5% reduction in iterations, without compromising feasibility or accuracy.

Learning Interior Point Method Central Path Projection for Optimal Power Flow

TL;DR

This framework, referred to as Learning-IPM (L-IPM), significantly reduces both the number of IPM iterations and overall solution time and introduces a grid-informed mechanism into the LSTM that enforces key operational constraints on generation, voltage magnitudes, and line flows.

Abstract

This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional learning models that attempt to predict the OPF solution directly, our approach learns the structure of the IPM trajectory itself, since even accurate predictions may not reliably reduce IPM iterations. The IPM follows a central path that iteratively progresses toward the optimal solution. While this trajectory encodes critical information about the optimization landscape, the later iterations become increasingly expensive due to ill-conditioned linear systems. Our analysis of the IPM central path reveals that its initial segments contain the most informative features for guiding the trajectory toward optimality. Leveraging this insight, we model the central path as a time series and use a Long Short-Term Memory (LSTM) network to project the path using only the first few stable iterations. To ensure that the learned trajectory remains within the feasible region--especially near the optimal point--we introduce a grid-informed mechanism into the LSTM that enforces key operational constraints on generation, voltage magnitudes, and line flows. This framework, referred to as Learning-IPM (L-IPM), significantly reduces both the number of IPM iterations and overall solution time. To improve generalization, we use a sampling-based strategy to generate a diverse set of load conditions that effectively span the operational space. Simulation results across a range of test systems--including a 2869-bus European transmission network--demonstrate that L-IPM achieves up to a 94% reduction in solution time and an 85.5% reduction in iterations, without compromising feasibility or accuracy.

Paper Structure

This paper contains 30 sections, 18 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Motivation and Research Gap
  4. Contributions
  5. Preliminaries
  6. OPF Formulation
  7. Classic IPM
  8. Proposed Grid-Informed L-IPM
  9. Learning Model Architecture
  10. LSTM Training Mapping Strategy
  11. Grid-Informed LSTM for OPF Feasibility
  12. GI-LSTM Tuning
  13. Number of GI-LSTM Layers
  14. Regularization Techniques
  15. L-IPM for OPF Solution
  16. ...and 15 more sections

Figures (17)

  • Figure 1: IPM and the proposed L-IPM paths to the optimal solution.
  • Figure 2: Condition number and solution time of IPM's iterations in DCOPF.
  • Figure 3: L-IPM framework.
  • Figure 4: GI-LSTM projection of IPM central path.
  • Figure 5: Comparison of R2 scores for different look-back values.
  • ...and 12 more figures