基于低秩规范多元分解的无模型状态估计
Model-Free State Estimation Using Low-Rank Canonical Polyadic Decomposition
摘要：
由于电网经历了可再生能源发电的高渗透水平，需要进行根本性的变革，以解决实时态势感知问题。本文利用张量的独特特性，设计了一个无模型的配电网态势感知和能量预测框架。这项工作将网络在多个时刻的状态表示为三向张量;因此，恢复网络的全部状态信息相当于估计张量的所有值。给定从$μ$相量测量单元和/或智能电表接收的测量值，使用状态张量的低秩规范多矢分解来进行未观测量的恢复-也就是说，状态估计任务被构成为利用测量量中的观测模式的张量插补问题。考虑了两种结构化抽样方案：平板抽样和纤维抽样。对于这两种方案，我们提出了充分的条件，保证可识别的状态张量的因素的采样板和纤维的数量。数值结果表明，所提出的框架，以实现高的估计精度在多个采样方案的能力。
英文摘要：
As electric grids experience high penetration levels of renewable generation, fundamental changes are required to address real-time situational awareness. This paper uses unique traits of tensors to devise a model-free situational awareness and energy forecasting framework for distribution networks. This work formulates the state of the network at multiple time instants as a three-way tensor; hence, recovering full state information of the network is tantamount to estimating all the values of the tensor. Given measurements received from $μ$phasor measurement units and/or smart meters, the recovery of unobserved quantities is carried out using the low-rank canonical polyadic decomposition of the state tensor---that is, the state estimation task is posed as a tensor imputation problem utilizing observed patterns in measured quantities. Two structured sampling schemes are considered: slab sampling and fiber sampling. For both schemes, we present sufficient conditions on the number of sampled slabs and fibers that guarantee identifiability of the factors of the state tensor. Numerical results demonstrate the ability of the proposed framework to achieve high estimation accuracy in multiple sampling scenarios.
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