# Linear Single- and Three-Phase Voltage Forecasting and Bayesian State Estimation with Limited Sensing

arXiv: https://arxiv.org/abs/1806.06024 · HTML: https://mlsanity.com/paper/1806.06024/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2018.

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

- [Data-driven Models to Anticipate Critical Voltage Events in Power Systems](https://mlsanity.com/paper/2207.11803/) (2022)

## Abstract (arXiv)

Implementing state estimation in low and medium voltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty in forecasts can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post-hoc analysis. The method outperforms conventional WLS and is applied to different test feeders and validated on a real test feeder with the utility Alliander in The Netherlands.