As a type of magnetic sensor known for its high reliability and long lifespan, the reliability issues of Hall current sensors have attracted attention in fields such as electromagnetic compatibility. However, there is still a lack of sufficient failure data for reliability prediction. Therefore, a small-sample reliability prediction method based on the improved Bayes method is proposed. Firstly, the pseudo-failure lifespan data are acquired through the accelerated degradation testing of Hall current sensors subjected to temperature and humidity stressors, and the life is examined by the Weibull distribution; then, the data expanded using the BP neural network model are used as the a priori information, and the parameter estimation of the Weibull distribution is obtained by the Bootstrap method and Gibbs sampling; finally, the Peck accelerated model is implemented to achieve the normal temperature-humidity reliability prediction of Hall current sensors under stress, and the utility of the enhanced Bayes technique is confirmed through the application of the Wiener stochastic process model.

This study enhances regional integrated energy systems by proposing a Stackelberg planning–operation model with seasonal hydrogen storage, addressing source–network separation. An equilibrium algorithm is developed that integrates a competitive search routine with mixed-integer optimization. In the price–energy game framework, the hydrogen storage operator is designated as the leader, while energy producers, load aggregators, and storage providers act as followers, facilitating a distributed collaborative optimization strategy within the Stackelberg game. Using an industrial park in northern China as a case study, the findings reveal that the operator’s initiative results in a revenue increase of 38.60%, while producer profits rise by 6.10%, and storage-provider profits surge by 108.75%. Additionally, renewable accommodation reaches 93.86%, reflecting an absolute improvement of 20.60 percentage points. Total net energy imbalance decreases by 55.70%, and heat-loss load is reduced by 31.74%. Overall, the proposed approach effectively achieves cross-seasonal energy balancing and multi-party gains, providing an engineering-oriented reference for addressing energy imbalances in regional integrated energy systems.

In medium-voltage distribution systems, switch states determine how sections are grouped and supplied by feeders, defining the sectionalized operating configuration. Changes in load demand and distributed generation output can increase losses and cause voltage violations, making an existing configuration unsuitable for the new conditions. Switching corrections can redistribute power flows to reduce losses and voltage violations, but their benefits must be balanced against switching costs. Variations in loss costs also change return scales, which can impair reinforcement learning (RL) methods that use a fixed value-learning scale. To address these challenges, we propose an adaptive soft actor-critic (A-SAC) algorithm to correct sectionalized operating configurations and minimize cumulative operating cost. The dynamic adaptation mechanism adjusts the value-learning scale as operating conditions change, guiding the agent to learn lower-cost configuration correction policies while preserving the original cost objective. A masked softmax output layer excludes infeasible switching actions. Tests on a 37-bus test system under normal, high photovoltaic (PV) output, and changing source/load conditions show cost reductions of 3.2–6.2% relative to retaining the initial configuration and lower costs than other advanced RL algorithms. In the changing source/load scenario, the mean cost is 3.2% lower than that of soft actor-critic (SAC).