## 1 Introduction  
As the main device of power systems, the power transformer is essential to the safe and reliable operation of the whole electrical network [1].The insulation structure determines the electric field distribution; thus, the optimization of the main insulation structure is of great importance to ensure the safe and stable operation of the power transformer [2, 3].With the increase of voltage levels, more and more attention has been paid to the electrical insulation problem of the power transformer. However, the insulation structure of a transformer is particularly complex, which makes the electric field distribution non-uniform. Therefore, to confirm the rationality and reliability of the main insulation structure of the transformer, it is necessary to test, calculate, and analyze the electric field distribution [4]. In engineering applications, electric field analysis methods can be divided into two types, the analytical methods and the numerical methods. A few simple problems may be solved by the analytic method; but in the majority of cases, an analytical method simply does not exist or it is extremely difficult to obtain.As a numerical method, the FEM (finite element method) has been applied in theelectric field calculation [5; 6; 7]. In the electrostatic ring structure optimization [8], the traditional finite element method (FEM was used to analyze the influence of each variable on the electric field intensity and summarize its changing rule through several specific points. The FEM generally adopted the inference method [8; 9], and the optimal values of the parameters were obtained by summarizing the changing law of each variable. Although it is possible to get the result, it cannot prove that the final result is the optimal solution, and it needs to constantly modify the model parameters for modeling analysis, which increases the calculation time. In addition to the FEM, the structure optimization methods roughly fall into two types. One is to establish the function expression between the optimization objective and the variables by using sensitivity analysis methods [10].Sometimes the selection of step length is involved in the sensitivity analysis methods and the accuracy cannot be guaranteed. Moreover, the sensitivity formulas are difficult to derive, and the process is rather complicated [11]. When the analytical expression for the relationship between the optimization variables and optimization objectives cannot be found, the other type of methods, the global optimization methods, or the response surface methodology(RSM)combined with FEM can be used for the optimization design. Global optimization methods such as the genetic algorithm [12; 13; 14; 15; 16] and the particle swarm optimization algorithm [8; 17; 18; 19] need to call a large number of modeling and optimization programs repeatedly, which significantly affect the efficiency of optimization. Most importantly, without appropriate fitness functions the local search ability may become worse and the search efficiency may be reduced. The RSM constructs an approximate function expression between the objective function and variables, and visualizes the objective function that is originally implicit. The repeated modeling and simulation can be avoided; thereby, the efficiency of the optimization can be significantly improved [20]. As a mathematical and statistical optimization method [21; 22], the RSM has been applied in many aspects. References [23] and [24] combined the RSM with the genetic algorithm and indicated that this method could reduce the number of experiments and solve the problem of fitness function selection. Reference [25] used the RSM to optimize the armature structure, and proved that this method had high feasibility, which provided an effective method for armature structure improvement. References [26; 27; 28] posed the methods for the optimization of an oil-immersed transformer cooling system and improved the design of the permanent magnet motor using RSM.