# Data-Driven Power Flow Linearization: A Regression Approach

arXiv: https://arxiv.org/abs/1710.10621 · HTML: https://mlsanity.com/paper/1710.10621/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2017.

## Built on by (most cited first, 11 of 11)

- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [KCLNet: Physics-Informed Power Flow Prediction via Constraints Projections](https://mlsanity.com/paper/2506.12902/) (2025)
- [Federated Coordinate Descent for Privacy-Preserving Multiparty Linear Regression](https://mlsanity.com/paper/2209.07702/) (2022)
- [Data-driven Power Flow Linearization: Theory](https://mlsanity.com/paper/2407.02501/) (2024)
- [Synthetic Power Flow Data Generation Using Physics-Informed Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2504.17210/) (2025)
- [Rebuild AC Power Flow Models with Graph Attention Networks](https://mlsanity.com/paper/2509.22733/) (2025)
- [Test Time Training for AC Power Flow Surrogates via Physics and Operational Constraint Refinement](https://mlsanity.com/paper/2511.22343/) (2025)
- [Attention-Enhanced Graph Filtering for False Data Injection Attack Detection and Localization](https://mlsanity.com/paper/2601.18981/) (2026)
- [BOOST-RPF: Boosted Sequential Trees for Radial Power Flow](https://mlsanity.com/paper/2603.21977/) (2026)
- [Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening](https://mlsanity.com/paper/2607.12241/) (2026)
- [A Human-AI Teaming Framework for Deep Reinforcement Learning-Based Voltage Regulation in Distribution Networks](https://mlsanity.com/paper/2607.19667/) (2026)

## Abstract (arXiv)

The linearization of a power flow (PF) model is an important approach for simplifying and accelerating the calculation of a power system's control, operation, and optimization. Traditional model-based methods derive linearized PF models by making approximations in the analytical PF model according to the physical characteristics of the power system. Today, more measurements of the power system are available and thus facilitate data-driven approaches beyond model-driven approaches. This work studies a linearized PF model through a data-driven approach. Both a forward regression model ((P, Q) as a function of (theta, V)) and an inverse regression model ((theta, V) as a function of (P, Q)) are proposed. Partial least square (PLS)- and Bayesian linear regression (BLR)-based algorithms are designed to address data collinearity and avoid overfitting. The proposed approach is tested on a series of IEEE standard cases, which include both meshed transmission grids and radial distribution grids, with both Monte Carlo simulated data and public testing data. The results show that the proposed approach can realize a higher calculation accuracy than model-based approaches can. The results also demonstrate that the obtained regression parameter matrices of data-driven models reflect power system physics by demonstrating similar patterns with some power system matrices (e.g., the admittance matrix).