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The increasing uncertainty of distributed energy resources promotes the risks of transient events for power systems. To capture event dynamics, Phasor Measurement Unit (PMU) data is widely utilized due to its high resolutions. Notably, Machine Learning (ML) methods can process PMU data with feature learning techniques to identify events. However, existing ML-based methods face the following challenges due to salient characteristics from both the measurement and the label sides: (1) PMU streams have a large size with redundancy and correlations across temporal, spatial, and measurement type dimensions. Nevertheless, existing work cannot effectively uncover the structural correlations to remove redundancy and learn useful features. (2) The number of event labels is limited, but most models focus on learning with labeled data, suffering risks of non-robustness to different system conditions. To overcome the above issues, we propose an approach called Kernelized Tensor Decomposition and Classification with Semi-supervision (KTDC-Se). Firstly, we show that the key is to tensorize data storage, information filtering via decomposition, and discriminative feature learning via classification. This leads to an efficient exploration of structural correlations via high-dimensional tensors. Secondly, the proposed KTDC-Se can incorporate rich unlabeled data to seek decomposed tensors invariant to varying operational conditions. Thirdly, we make KTDC-Se a joint model of decomposition and classification so that there are no biased selections of the two steps. Finally, to boost the model accuracy, we add kernels for non-linear feature learning. We demonstrate the KTDC-Se superiority over the state-of-the-art methods for event identification using PMU data. 

Nowadays, the data collected in physical/engineering systems allows various machine learning methods to conduct system monitoring and control, when the physical knowledge on the system edge is limited and challenging to recover completely. Solving such problems typically requires identifying forward system mapping rules, from system states to the output measurements. However, the forward system identification based on digital twin can hardly provide complete monitoring functions, such as state estimation, e.g., to infer the states from measurements. While one can directly learn the inverse mapping rule, it is more desirable to re-utilize the forward digital twin since it is relatively easy to embed physical law there to regularize the inverse process and avoid overfitting. For this purpose, this paper proposes an invertible learning structure based on designing parallel paths in structural neural networks with basis functionals and embedding virtual storage variables for information preservation. For such a two-way digital twin modeling, there is an additional challenge of multiple solutions for system inverse, which contradict the reality of one feasible solution for the current system. To avoid ambiguous inverse, the proposed model maximizes the physical likelihood to contract the original solution space, leading to the unique system operation status of interest. We validate the proposed method on various physical system monitoring tasks and scenarios, such as inverse kinematics problems, power system state estimation, etc. Furthermore, by building a perfect match of a forward-inverse pair, the proposed method obtains accurate and computation-efficient inverse predictions, given observations. Finally, the forward physical interpretation and small prediction errors guarantee the explainability of the invertible structure, compared to standard learning methods. 

Power system equipment presents special signatures at the incipient stage of faults. As more renewables are integrated into the systems, these signatures are harder to detect. If faults are detected at an early stage, economical losses and power outages can be avoided in modern power grids. Many researchers and power engineers have proposed a series of signature-specific methods for one type of equipment's waveform abnormality. However, conventional methods are not designed to identify multiple types of incipient faults (IFs) signatures at the same time. Therefore, we develop a general-purpose IF detection method that detects waveform abnormality stemming from multiple types of devices. To avoid the computational burden of the general-purpose IF detection method, we embed the abnormality signatures into a vector and develop a pre-training model (PTM) for machine understanding. In the PTM, signal "words," "sentences," and "dictionaries" are designed and proposed. Through the comparison with a machine learning classifier and a simple probabilistic language model, the results show a superior detection performance and reveal that the training radius is highly related to the size of abnormal waveforms.