Research on Estimators for Sampling Survey of Transformer Fault Conditions in Inner Mongolia Power Grid

Due to the vast territory of Inner Mongolia, full-coverage inspection of transformers within the jurisdiction consumes substantial manpower and material resources, making it difficult to efficiently assess the overall fault status of regional transformers through traditional monitoring methods. To address the insufficient accuracy of conventional sampling estimation methods, this study proposes two novel sampling estimators, \(\hat{\overline{Y}}_{PR1}\) and \(\hat{\overline{Y}}_{PR2}\), based on double auxiliary variables. These estimators integrate ratio, difference, exponential, and product estimation methods, enhancing the synergistic correlation between bivariate auxiliary variables and expanding the parameter-optimization space. Five auxiliary variables—total hydrocarbon, top-oil temperature, hydrogen, carbon monoxide, and carbon dioxide—are selected and grouped according to their correlation strength with fault prevalence. Using fault records and monitoring data from substations in the Inner Mongolia Power Grid spanning 2021 to 2025, the performance differences between the proposed estimators and traditional estimators are systematically analyzed through mean square error comparisons. The results demonstrate that the proposed estimators yield prominent accuracy gains under strong correlation between auxiliary variables and fault prevalence; under moderate- or weak-correlation conditions, they deliver comparable or slightly improved performance relative to conventional estimators across investigated sample sizes. They are particularly well-suited for transformer fault diagnosis scenarios, with substantially improved estimation accuracy. Monte Carlo simulation results confirm that the proposed estimators show good robustness within the studied strong-correlation scenario, while numerical comparisons across three correlation groups further illustrate how estimation performance varies with the correlation strength between auxiliary variables and the study variable. This study provides a new tool for efficient monitoring of transformer fault conditions in the Inner Mongolia Power Grid, offers a reference for the application of sampling estimation theory in the field of power equipment fault diagnosis, and contributes to enhancing the scientific rigor and precision of statistical work in power grid operation and maintenance.