Power transformers are complex and extremely important piece of electrical equipment in a power system, playing an important role in changing voltage and transmitting electricity. Its operational status directly affects the stability and safety of power grids, and once a fault occurs, it may lead to significant economic losses and social impacts. The traditional detection methods rely on the technical level of power system operation and maintenance personnel, and are based on Dissolved Gas Analysis (DGA) technology, which analyzes the components of dissolved gases in transformer oil for preliminary fault diagnosis. However, with the increasing accuracy and intelligence requirements for transformer fault diagnosis in power grids, the DGA analysis method is no longer able to meet the requirements. Therefore, this article proposes an improved transformer fault diagnosis method based on a residual BP neural network. This method deepens the BP neural network by stacking multiple residual network modules, and fuses and expands gas feature information through an improved BP neural network. In the improved residual BP neural network, SVM is introduced to judge the extracted feature vectors at each layer, screen out feature vectors with high accuracy, and increase their weights. The feature vector with the highest cumulative weight is selected as an input for transformer fault diagnosis. This method utilizes multi-layer neural network mapping to extract gas feature information with more significant feature differences after fusion expansion, thereby effectively improving diagnostic accuracy. The experimental results show that, compared with traditional BP neural network methods, the proposed algorithm has higher accuracy in transformer fault diagnosis, with an accuracy rate of 92%, which can ensure the sustainable, normal, and safe operation of power grids.