This paper proposes a novel network-embedding based method to recover the missing measurements in power systems. In particular, we first construct the spatial and temporal graphs to describe both the spatial correlation among the buses in a power flow network and the temporal correlation of the bus states over different time. Secondly, we propose a Softwork algorithm to map the spatial and temporal graphs to low-dimensional spatiotemporal features. Then, we train a regression neural network using the pairs of spatiotemporal features and observed matrix entries. The trained network can then predict the missing measurements. Furthermore, the proposed missing data recovery algorithm can be extended to an online version to recover the missing measurements from streaming data collected in power systems in real time. Numerical experiments on real-world power systems verify the effectiveness of the proposed method. In particular, the proposed method achieves (on average) −55.36 dB, −42.06 dB, −53.26 dB and −45.32 dB relative recovery errors (RREs) for random, row, column and block missing patterns of the voltage magnitude matrix, respectively, which are much smaller than those achieved by the existing methods.

中文翻译：

---

使用网络嵌入的大型电力系统中丢失数据的恢复

本文提出了一种新颖的基于网络嵌入的方法来恢复电力系统中丢失的测量值。特别是，我们首先构造空间和时间图，以描述潮流网络中总线之间的空间相关性和不同时间的总线状态的时间相关性。其次，我们提出了一种Softwork算法，将时空图映射到低维时空特征。然后，我们使用时空特征对和观察到的矩阵项来训练回归神经网络。然后，训练有素的网络可以预测丢失的测量值。此外，所提出的丢失数据恢复算法可以扩展到在线版本，以实时从电力系统中收集的流数据中恢复丢失的测量值。在实际的电力系统上进行的数值实验证明了该方法的有效性。特别地，对于电压幅度矩阵的随机，行，列和块丢失模式，所提出的方法分别（平均）达到-55.36 dB，-42.06 dB，-53.26 dB和-45.32 dB相对恢复误差（RRE），与现有方法相比要小得多。