Electromagnetic coil is the key component of rotating equipment, and its reliability is very important for the normal operation of the equipment. In order to accurately evaluate the health status of electromagnetic coil, a health evaluation and anomaly detection method based on Mahalanobis distance (MD) and Box-Cox transformations is proposed. With the help of accelerated fatigue experiment, the whole life electrical data of high, medium and low frequency spectrum of electromagnetic coil is collected, and the low and medium frequency spectrum data are constructed as the initial feature set. And then, the initial feature set is mahalanized, and Mahalanobis distance is taken as the feature to evaluate the health state of the electromagnetic coil. With the help of Box-Cox transformations, MD is transformed into normal distribution form, and the electromagnetic coil fault early warning is realized according to 3 σ criterion. The results show that MD can accurately evaluate the degradation state of the electromagnetic coil and realize early warning.

To enhance the market-oriented operation capability of integrated energy retailers and improve the synergy and economic efficiency of complex microgrids, this paper constructs a bi-level optimization model of “upper-level price optimization, lower-level multi-energy flow scheduling” under the background of multi-energy coupling of electricity, heat, gas, and hydrogen. The upper level optimizes electricity and heat price signals using the APSO and IGWO algorithms, while the lower level realizes coordinated multi-energy flow scheduling based on these signals. The operational performance of the two algorithms is compared across four scenarios. The results show that the scenario with multi-energy storage (Scenario 3) is the optimal adaptive scenario: the charge–discharge regulation of energy storage interacts with price guidance, and the peak-shaving and valley-filling characteristics significantly improve the system’s energy utilization efficiency. This scenario can fully unlock the value of bi-level optimization and meet the operational requirements of complex multi-energy coupling. In the algorithm comparison, the APSO algorithm presents distinct advantages, outperforming the IGWO algorithm in the precise regulation of upper-level electricity and heat prices, lower-level multi-energy flow balance, total operation cost control, and convergence stability. It provides an effective technical solution for the economic and stable operation of integrated energy systems.