基于图盲声源分离的电力系统拓扑与状态估计
Power Systems Topology and State Estimation by Graph Blind Source Separation
摘要：
本文研究了电力系统状态和拓扑的盲估计问题。我们使用的线性化直流模型的实际功率测量与未知的电压相位（即状态）和一个未知的导纳矩阵（即拓扑结构），并表明最佳的问题，可以制定为一个盲声源分离（BSS）问题与加权拉普拉斯混合矩阵。我们开发的约束最大似然（ML）估计的拉普拉斯矩阵的这个图BSS（GBSS）问题的高斯分布状态。的ML-BEST被证明是唯一的状态二阶统计量的函数。由于ML-BEST方法的拓扑恢复阶段导致高复杂度的优化问题，因此我们提出了两种低复杂度的方法来实现它：1）两阶段拓扑恢复，其基于求解松弛凸优化，然后找到最接近的拉普拉斯矩阵，以及2）增强拉格朗日拓扑恢复。我们推导出一个封闭形式的表达相关的Cramer-Rao界（CRB）的拓扑矩阵估计。IEEE-14总线测试用例系统和随机网络的性能评估所提出的方法。结果表明，所提出的ML-BEST方法的状态估计性能与Oracle最小均方误差（MSE）状态估计器性能渐近一致，拓扑估计的MSE达到了所提出的CRB.
英文摘要：
In this paper, we consider the problem of blind estimation of states and topology (BEST) in power systems. We use the linearized DC model of real power measurements with unknown voltage phases (i.e. states) and an unknown admittance matrix (i.e. topology) and show that the BEST problem can be formulated as a blind source separation (BSS) problem with a weighted Laplacian mixing matrix. We develop the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS (GBSS) problem with Gaussian-distributed states. The ML-BEST is shown to be only a function of the states second-order statistics. Since the topology recovery stage of the ML-BEST approach results in a high-complexity optimization problem, we propose two low-complexity methods to implement it 1) Two- phase topology recovery, which is based on solving the relaxed convex optimization and then finding the closest Laplacian matrix, and 2) Augmented Lagrangian topology recovery. We derive a closed-form expression for the associated Cramer-Rao bound (CRB) on the topology matrix estimation. The performance of the proposed methods is evaluated for the IEEE-14 bus test-case system and for a random network. It is shown that, asymptotically, the state estimation performance of the proposed ML-BEST methods coincides with the oracles minimum mean-squared-error (MSE) state estimator, and the MSE of the topology estimation achieves the proposed CRB.
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