## 1 Introduction  
With a high proportion of new energy access [1; 2], the strong uncertainty and volatility of the power grid will lead to more extreme and drastic operating conditions for power equipment, and higher requirements are put forward for the safe and reliable operation of power equipment [3; 4; 5]. However, the power transformer is one of the key pieces of equipment in the power grid. How to accurately and effectively evaluate its risk grade not only provides a basis for the selection of equipment maintenance strategy but also has important significance for maintaining the stable operation of the system. At present, the research on risk assessment methods for power transformers mainly focuses on certain decision-making methods, with the equipment fault probability as the main index. For example, based on fault tree analysis, a risk assessment model of the power transformer was constructed, and the overall risk of the equipment is obtained mainly from the probability of occurrence of each component. However, the risk factors considered are too individual, and cannot fully reflect the actual risk influence condition of the equipment [6; 7]. A risk assessment model based on a health index was established and the influence of transformer fault on power grid economy and reliability is considered, but ignoring the influence of uncertain factors on the calculation of cutting load loss may lead to a high final quantified risk result [8]. A proportional risk model of aging load and healthy weather was proposed, which reflects the influence of different risk factors on the probability of equipment fault, but only judges the risk based on a single fault probability index, ignoring the loss of equipment fault [9]. Considering the problems existing in the traditional evaluation of the transformer risk index (TRI), a practical risk assessment method for power transformer groups was proposed, but the result factor is only calculated quantitatively according to relevant standards, which cannot reflect the influence of uncertain factors on the consequences caused by transformer fault [10]. The impact of the correlation between wind power and photovoltaic power generation on the operation risk of the outgoing transformer is considered and the risk is reduced by adjusting the correlation coefficient, but only the impact on the risk of equipment operation is considered and its consequences are ignored [11]. According to the guidelines, each risk index is calculated quantitatively and then the risk value of the transformer is obtained, but the influence of the power grid operation loss caused by equipment fault on the risk judgment is not considered [12]. The comprehensive risk assessment model of transformers was established to improve the accuracy and efficiency of evaluation, but the quantitative risk assessment is carried out only from the indexes of defect severity and fault probability, ignoring the deviation of equipment risk judgment caused by the influence of uncertain factors on operation loss and the value of the equipment itself [13]. A three-grade risk assessment model was constructed, but only the overall defect grade of the transformer is obtained according to the health index quantified by each grade model to represent the equipment risk condition [14]. The application of cloud theory to the transformer risk assessment method makes full use of the cloud model and can transform qualitative concepts into quantitative performance, but it is quantified to obtain the risk value represented by a certain value and then evaluate its grade [15; 16; 17]. The above methods rarely consider the influence of power grid operation loss caused by equipment fault on risk judgment and use a highly subjective certain decision-making method to evaluate the risk of power transformers. However, the loss of power grid operation is affected by uncertain factors, and the research on loss quantification is not deep enough.