Hd-Deep-EM: Deep Expectation Maximization for Dynamic Hidden State Recovery Using Heterogeneous Data

Uncertain power generations and loads are continually integrated into the power system, causing high risks of dynamic events. To better monitor systems, advanced meters like Phasor Measurement Units (PMUs) can record high-resolution system dynamic states in real time. However, due to the high cost, the placement of PMUs is limited in a system. Thus, it's hard to obtain all the dynamic system states via PMUs. On the other hand, traditional sensors in a Supervisory Control and Data Acquisition (SCADA) system can broadly cover the system, though they only provide low-resolution measurements. In this article, we propose to utilize PMU and SCADA sensor data to recover the missing dynamic states in the power generation system. The problem has the following challenges based on unique properties of data: (1) Spatially, PMU and SCADA sensors have different locations. Thus, it's a must to approximate the data correlations to estimate the missing data accurately. (2) Temporally, the dynamic transitions in SCADA samples are scarce, urging efficient utilization of the SCADA data to approximate the dynamics. For challenge (1), we employ Deep Neural Networks (DNNs) with high capacities to capture spatial-temporal information to predict dynamic states. For challenge (2), we develop a new mechanism to utilize SCADA data efficiently. Specifically, we iteratively reuse the predicted dynamic states in the SCADA data to retrain the DNN model, gradually increasing the performance. The effectiveness of the proposed training procedure is theoretically verified via the framework of Expectation-Maximization (EM). Thus, our model to fuse heterogeneous data is termed Heterogeneous data Deep EM (Hd-Deep-EM). Finally, we demonstrate the high performance of the Hd-Deep-EM in diversified synthetic and realistic power systems.