# A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

arXiv: https://arxiv.org/abs/2306.04350 · HTML: https://mlsanity.com/paper/2306.04350/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2023.

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

- [A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback](https://mlsanity.com/paper/2502.15306/) (2025)

## Abstract (arXiv)

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to the solutions at which the power networks may be exposed to the risk of voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on a three-phase unbalanced nonlinear distribution power flow model to mitigate the errors arising from model linearization. The resultant gradients feature a blocked structure that enables us to further develop an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance the overall voltage safety while achieving comparable computational efficiency with the linearized algorithm.