# Transformer Fault Diagnosis Method Based on Incomplete Data and TPE-XGBoost
## 1 Introduction  
Transformers are one of the key equipment in the power system, and their operating status will directly affect the safety and stability of the system. The number of transformers in a power system is related to the size of the system, and the service life of different transformers varies widely. With the extension of service life, problems such as insulation aging or internal defects will inevitably appear. Therefore, real-time monitoring of transformer operation status and fault warning is extremely important to enhance the safety and stability of the power system [1]. Dissolved gas analysis (DGA) is one of the most important methods for understanding the health of transformers. Without affecting the normal operation of the transformer, internal defects of the transformer can be identified according to changes in components and the content of dissolved gas in transformer oil [2]. At the same time, the current transformer condition management based on digital methods has enriched application scenarios of monitoring data such as DGA. It is an advantage for data- and experience-based transformer fault diagnosis. However, it also introduces a new set of problems [3]. Based on operational experience, poor data quality due to missing data is one of the main problems currently faced. Due to the operating environment, reliability of monitoring equipment, or other accidental factors, data transmission interruptions or errors mayoccur, resulting in abnormal or missing data that can affect the accuracy and credibility of monitoring results [4]. For missing data problems, methods such as discarding data, single value filling method and linear filling method are widely used [5]. However, the generation and variation in dissolved gas in oil are directly determined by the fault energy. Traditional methods ignore the correlation between these gases when dealing with missing data, resulting in insufficient information on the recovered data. Bayesian probability matrix decomposition is used to fill in the missing DGA data to improve the quality of monitoring data. However, this method requires a complex sampling process, which will result in a long convergence time when dealing with high-dimensional data [6]. The rough set method in [7] achieves the subordinate approximation of transformer fault types and characteristics, which can solve the processing of incomplete transformer data to a certain extent, while the information on dissolved gas in transformer oil is not discussed. Therefore, efficient and accurate processing of the missing data of dissolved gas in oil is essential for predicting the transformer's condition. In addition, traditional methods such as the IEC Ratios, Rogers, Dornenburg, and Duval triangle and pentagon methods based on dissolved gas in oil are widely used in the diagnosis of transformer faults [8; 9; 10; 11; 12]. The accuracy of the diagnostic results of these methods depends on the experience of the operations and maintenance personnel, and the accuracy of diagnostic results still needs to be improved [13]. In recent years, artificial intelligence algorithms have been widely used for the condition assessment and fault diagnosis of electric equipment due to their self-organization and self-adaptability. These algorithms include association rules [14], support vector machines (SVM) [15], neural networks [16], random forest (RF) [17] and extreme gradient boosting (XGBoost) [18]. The multi-layer SVM is implemented for the faults diagnosis of transformers in [15], and the application results show that the accuracy of SVM is higher than fuzzy logic, multi-layer perceptron and radial basis function methods. The density-based clustering algorithm (DBSCAN) is used to eliminate the rigid fault boundaries of the conventional Duval pentagon method in [17], and investigations show that the accuracy of random forest is higher than k-nearest neighbor (kNN), Gaussian naive Bayes (GNB) and SVM methods.