The increasing integration of renewable energy requires a good model of the existing power distribution infrastructure, represented by its admittance matrix. However, a reliable estimate may either be missing or quickly become obsolete, as distribution grids are continuously modified. In this work, we propose a method for estimating the admittance matrix from voltage and current measurements. By focusing on μ\mu PMU measurements and partially observed networks, we show that voltage collinearity and noisy samples of all electric variables are the main challenges for accurate identification. Moreover, the accuracy of maximum likelihood estimation is often insufficient in real-world scenarios. To overcome this problem, we develop a flexible Bayesian framework that allows one to exploit different forms of prior knowledge about individual line parameters, as well as network-wide characteristics such as the sparsity of the interconnections. Most importantly, we show how to use maximum likelihood estimates for tuning relevant hyperparameters, hence making the identification procedure self-contained. We also discuss numerical aspects of the maximum a posteriori estimate computation. Realistic simulations conducted on benchmark electrical systems demonstrate that, compared to other algorithms, our method can achieve significantly greater accuracy than previously developed methods.

中文翻译：

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用于识别配电网的贝叶斯变量误差模型


可再生能源的日益一体化需要现有配电基础设施的良好模型，以其导纳矩阵为代表。然而，随着配电网的不断修改，可靠的估计可能会丢失或很快就会过时。在这项工作中，我们提出了一种根据电压和电流测量来估计导纳矩阵的方法。通过关注 μ\mu PMU 测量和部分观察的网络，我们表明所有电变量的电压共线性和噪声样本是准确识别的主要挑战。此外，在现实场景中，最大似然估计的准确性通常不足。为了克服这个问题，我们开发了一种灵活的贝叶斯框架，允许人们利用有关各个线路参数的不同形式的先验知识，以及网络范围的特征，例如互连的稀疏性。最重要的是，我们展示了如何使用最大似然估计来调整相关的超参数，从而使识别过程变得独立。我们还讨论了最大后验估计计算的数值方面。对基准电气系统进行的真实模拟表明，与其他算法相比，我们的方法可以比以前开发的方法实现更高的精度。