{'fraction_non_alphanumeric': 0.0256563245823389, 'fraction_numerical': 0.0017899761336515514, 'mean_word_length': 5.628458498023716, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Real-Time Power System State Estimation and Forecasting via Deep Unrolled Neural Networks

Contemporary power grids are being challenged by rapid and sizeable voltage fluctuations that are caused by large-scale deployment of renewable generators, electric vehicles, and demand response programs. In this context, monitoring the grid's operating conditions in real time becomes increasingly critical. With the emergent large scale and nonconvexity, existing power system state estimation (PSSE) schemes become computationally expensive or often yield suboptimal performance. To bypass these hurdles, this paper advocates physics-inspired deep neural networks (DNNs) for real-time power system monitoring. By unrolling an iterative solver that was originally developed using the exact ac model, a novel model-specific DNN is developed for real-time PSSE requiring only offline training and minimal tuning effort. To further enable system awareness, even ahead of the time horizon, as well as to endow the DNN-based estimator with resilience, deep recurrent neural networks (RNNs) are also pursued for power system state forecasting. Deep RNNs leverage the long-term nonlinear dependencies present in the historical voltage time series to enable forecasting, and they are easy to implement. Numerical tests showcase improved performance of the proposed DNN-based estimation and forecasting approaches compared with existing alternatives. In real load data experiments on the IEEE 118-bus benchmark system, the novel model-specific DNN-based PSSE scheme outperforms nearly by an order-of-magnitude its competing alternatives, including the widely adopted Gauss–Newton PSSE solver.