###### Abstract  
As one of the most critical components of the power grid system, transformer maintenance strategy planning significantly influences the safe, economical, and sustainable operation of the power system. Periodic imperfect maintenance strategies have become a research focus in preventive maintenance strategies for large power equipment due to their ease of implementation and better alignment with engineering realities. However, power transformers are characterized by long lifespans, high reliability, and limited defect samples. Existing maintenance methods have not accounted for the dynamic changes in maintenance costs over a transformer's operational lifetime. Therefore, we propose a maintenance interval optimization method that considers imperfect maintenance and dynamic maintenance costs. Utilizing defect and maintenance cost data from 400 220 KV oil-immersed transformers in northern China, we employed Bayesian estimation for the first time to address the distribution fitting of defect data under small sample conditions. Subsequently, we introduced imperfect maintenance improvement factors to influence the number of defects occurring in each maintenance cycle, resulting in more realistic maintenance cost estimations. Finally, we established an optimization model for transformer maintenance cycles, aiming to minimize maintenance costs throughout the transformer's entire lifespan while maintaining reliability constraints. Taking a transformer's strong oil circulation cooling system as an example, our method demonstrates that while meeting the reliability threshold recognized by the power grid company, the system's maintenance cost can be reduced by 41.443% over the transformer's entire life cycle. Through parameter analysis of the optimization model, we conclude that as the maintenance cycle increases, the factors dominating maintenance costs shift from corrective maintenance to preventive maintenance. m 2024 2  
corrective maintenance, which can be comparable to the cost of replacing the entire unit, many power transformers currently adopt a preventive maintenance strategy. Maintenance can be categorized into minimal maintenance, imperfect maintenance, and complete maintenance/replacement based on the extent of repair. Due to the technical complexity and high cost of major repairs/replacements, power transformers often undergo imperfect maintenance as their primary maintenance approach [2]. Imperfect maintenance can be further divided into sequential maintenance, fault control maintenance, maintenance restriction strategies, and periodic maintenance with fixed intervals. Due to the high cost and complexity of organizing maintenance inspections, periodic imperfect maintenance strategies are widely adopted for power transformers [3]. Compared to other maintenance strategies, periodic imperfect maintenance is closer to engineering practice and offers simplicity in operation and maintenance management, making it a popular choice in both research and practical applications [4]. Consequently, scholars and industry professionals have focused on the research of periodic imperfect maintenance strategies. In the context of wind turbine units under periodic maintenance, [PERSON] proposed a multi-objective fixed-cycle dynamic imperfect maintenance decision to address the issues of over-maintenance and under-maintenance [5]. [PERSON] et al. introduced an extended mixed-integer linear programming model that utilized information gap decision theory to optimize power grid maintenance costs and enhance network reliability. They applied this model to an actual distribution network in Iran [6]. [PERSON] et al. developed a more accurate meta-action unit periodic preventive maintenance strategy using the generalized geometric process method [7]. [PERSON] et al. established a transformer condition-based maintenance strategy by incorporating the proportional intensity model, which considered both operating time and maintenance activities [8]. [PERSON] et al.