# A Feasible Reduced Space Method for Real-Time Optimal Power Flow

arXiv: https://arxiv.org/abs/2110.02590 · HTML: https://mlsanity.com/paper/2110.02590/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)

## Abstract (arXiv)

We propose a novel feasible-path algorithm to solve the optimal power flow (OPF) problem for real-time use cases. The method augments the seminal work of Dommel and Tinney with second-order derivatives to work directly in the reduced space induced by the power flow equations. In the reduced space, the optimization problem includes only inequality constraints corresponding to the operational constraints. While the reduced formulation directly enforces the physical constraints, the operational constraints are softly enforced through Augmented Lagrangian penalty terms. In contrast to interior-point algorithms (state-of-the art for solving OPF), our algorithm maintains feasibility at each iteration, which makes it suitable for real-time application. By exploiting accelerator hardware (Graphic Processing Units) to compute the reduced Hessian, we show that the second-order method is numerically tractable and is effective to solve both static and real-time OPF problems.