Implementing state estimation in low and mediumvoltage 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.

中文翻译：

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有限感知的线性单相和三相电压预测和贝叶斯状态估计

鉴于许多网络的规模和传统方法对大量测量的依赖，在中低压配电中实施状态估计仍然具有挑战性。本文提出了一种通过利用一组有限的实时测量来改进实时电压预测的方法。该方法依赖于被表述为线性最小二乘估计问题的贝叶斯估计，它类似于经典的加权最小二乘 (WLS) 方法，适用于全网络可观察性不可用的场景。我们基于最近开发的不平衡三相潮流的线性近似来构建电压预测，作为使用高斯过程构建的负载预测的线性映射。实时更新电压预测的估计步骤是允许快速高分辨率状态估计更新的线性计算。预测中的不确定性可以先验确定并在后验平滑，使该方法可用于规划、操作和事后分析。该方法优于传统的 WLS，并应用于不同的测试馈线，并在荷兰公用事业公司 Alliander 的真实测试馈线上进行了验证。