Probabilistic power-supply reliability assessment for thermoelectric energy storage systems based on physics-guided intelligent estimation model of storage charge

Fluctuations in thermal input, ambient conditions, and intermittent load demand can significantly affect storage-state evolution and continuous power supply in a thermoelectric energy storage system. This study develops a probabilistic power-supply reliability assessment framework based on physics-guided storage-state estimation. A long short-term memory (LSTM)-based physics-guided neural network, denoted as PGNN-LSTM, is constructed to predict supercapacitor-voltage evolution under time-varying operating conditions. The proposed dual-output recursive estimator jointly predicts the storage-voltage transition and equivalent charging power, and couples the two outputs through an energy-consistency loss and a voltage-boundary penalty. The trained estimator is then combined with empirical Monte Carlo scenario generation to produce multiple future storage-voltage trajectories while preserving local temporal dependence and multivariable coupling in the measured operating data. Power-supply reliability is quantified using voltage quantiles, risk-level probabilities, and failure probability. Under the same chronological data partition and held-out evaluation sequence, PGNN-LSTM achieved lower prediction errors than the physics-only, plain LSTM, and physics-informed temporal convolutional network (PI-TCN) baselines, with an RMSE of 0.00742 V, an MAE of 0.00498 V, and R 2 of 0.97809. Formal probabilistic validation over a 3000 s horizon yielded a mean empirical CRPS of 0.1393 V and a PICP of 91.99% for the nominal 90% P05–P95 prediction interval. The maximum absolute deviation between the predicted and measured risk-state proportions was 4.29 percentage points, which is below the adopted practical engineering tolerance of 10 percentage points. These results demonstrate that the proposed framework can provide accurate storage-voltage estimation and probabilistic supply-risk information within the investigated operating envelope. Application to other hardware configurations requires system-specific data collection, recalibration, and validation.