Learning Interior Point Method Central Path Projection for Optimal Power Flow

Power system optimization has evolved from classical linear and quadratic programming to sophisticated nonlinear methods like IPM, which efficiently handle large-scale OPF problems. Recent advances incorporate machine learning for load forecasting, state estimation, and approximate solutions, but integrating these with classical optimization remains challenging. Existing algorithms often face high computational costs, especially in real-time scenarios with dynamic loads and renewable integration. The need for faster, scalable, and reliable OPF solutions drives research into hybrid approaches that combine data-driven models with traditional methods. Prior works include neural network approximations, heuristic warm-starts, and parallel computing, yet none fully exploit the trajectory structure of IPM to accelerate convergence.

Despite IPM's robustness, its iterative process becomes computationally prohibitive in large systems due to the ill-conditioning of linear systems in later iterations. Warm-start strategies improve initial guesses but do not reliably reduce total iteration count or runtime, as convergence depends on the entire path, including dual and slack variables. Existing learning-based methods often predict solutions directly, risking infeasibility or suboptimality. The core challenge is to leverage early iteration information to predict the entire central path, thus reducing the number of expensive linear solves while maintaining feasibility and accuracy. Achieving this requires modeling the trajectory's temporal dependencies and ensuring the predicted path adheres to system constraints.

This work introduces a novel framework that models the IPM central path as a time series, using LSTM networks trained on early stable iterations. The key innovations include: 1) leveraging the temporal structure of the path to predict subsequent steps; 2) incorporating grid-informed loss functions that penalize constraint violations, ensuring feasible trajectories; 3) using diverse load scenario sampling to enhance model robustness; and 4) combining path prediction with final IPM verification to guarantee solution quality. This approach significantly reduces the number of iterations and computational effort, especially in large, complex systems, while maintaining high solution fidelity.

• �� Collect early IPM iterations data, focusing on stable segments with well-conditioned matrices. • Train an LSTM network to learn the mapping from initial iteration states to subsequent path segments, capturing temporal dependencies. • Incorporate grid physics constraints into the loss function, penalizing violations of generator limits, voltage bounds, and line flows. • Generate diverse load scenarios via Latin Hypercube Sampling to ensure model robustness across operational conditions. • During optimization, use the trained LSTM to predict the central path, reducing the need for solving large linear systems in later iterations. • Refine the predicted solution with a final IPM step to verify optimality and feasibility. • Tune model hyperparameters, such as layer depth and regularization, to balance accuracy and generalization.

The framework was tested on systems ranging from small 3-bus networks to large 2869-bus European grids. Data was generated via multiple load scenarios, and models were trained using TensorFlow. Performance metrics included solution time, iteration count, and feasibility errors. Baseline comparisons involved classical IPM and warm-start strategies. Hyperparameter tuning identified optimal LSTM depth and regularization. The experiments demonstrated that L-IPM reduces total solution time by up to 94%, with iteration reductions exceeding 85%, while maintaining solution accuracy. Cross-scenario tests confirmed robustness under diverse load conditions, validating the approach's scalability and practical relevance.

In the largest tested system, L-IPM achieved a 94% reduction in total solution time (from ~120s to ~7.2s) and an 85.5% decrease in iteration count (from 85 to 13). The predicted paths maintained feasibility within operational constraints, with constraint violations below 0.1%. The model's generalization was confirmed across different load scenarios, including high-demand and low-demand cases. Ablation studies showed early iteration features are critical for accurate path prediction. Overall, the approach outperformed traditional warm-starts and heuristic methods, especially in complex, large-scale systems, demonstrating its potential for real-time applications.

This method can be directly applied to real-time grid dispatch, fast contingency analysis, and dynamic load management. It requires pre-training on historical data, enabling rapid prediction of optimal paths during operation. The approach is particularly suitable for large, complex networks with high renewable penetration, where computational speed is critical. Future integration with online learning and adaptive sampling could further enhance responsiveness, supporting autonomous grid control and resilience in smart grid environments.

The model's robustness under extreme disturbances or unforeseen contingencies remains to be validated. Its performance depends heavily on the diversity and representativeness of training data, which can be challenging for highly dynamic systems. High-dimensional models incur significant training costs, limiting real-time deployment without further optimization. Additionally, the approach assumes system parameters are known and stable, which may not hold during severe faults or topology changes. Future work should address these issues to improve reliability and adaptability.