# Transient Stability-Constrained OPF: Neural Network Surrogate Models and Pricing Stability

arXiv: https://arxiv.org/abs/2502.01844 · HTML: https://mlsanity.com/paper/2502.01844/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2025.

## Built on by (most cited first, 2 of 2)

- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)
- [Multi-Objective Deep Reinforcement Learning for Secure and Stable Power System Operation](https://mlsanity.com/paper/2608.20914/) (2026)

## Abstract (arXiv)

A Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem is proposed that enforces frequency stability constraints using Neural Network (NN) surrogate models. NNs are trained using a novel model-driven active sampling algorithm that iteratively generates NN training data located near the stability boundary and contained within the feasible set of the Alternating Current Optimal Power Flow (AC-OPF) problem. In the context of wholesale electricity markets, pricing structures are analyzed along with their dependencies on the selected input features to the NN surrogate model. An important insight identifies a trade-off between the accuracy of the NN surrogate model and sensible locational pricing structures. NN surrogate models for frequency stability are validated by ensuring the resulting TSC-OPF solution is stable over randomly generated load samples using a small Hawaii test case. The proposed TSC-OPF problem is shown to significantly enhance frequency stability at low computational cost and low financial cost to the system. For certain selections of NN inputs, the TSC-OPF problem is able to stabilize all load scenarios for which the solution to the AC-OPF problem resulted in instability.