To accurately analyze the temperature rising and locate the hot-spot of oil-immersed transformer windings, a hybrid method based on the dimensionless least-squares finite element method (DLSFEM) and upwind finite element method (UFEM) is proposed in this paper. To solve the fluid-thermal coupling problem, the sequential iteration method was utilized. After that, the two-side equilibration method and the Jacobi preconditioned conjugate gradient method were used to solve the equations. Moreover, a product-level experimental platform for oil-immersed transformer windings was built. The influence of the turn-to-turn insulation and gravity on the temperature was discussed, and the results show that the influence is significant. To verify the effectiveness of the proposed method, a comparison between the simulation results of the proposed method and experimental results were made, which shows a good agreement. Aiming at verifying the efficiency of the proposed method, the convergence of the proposed method was compared with that of the commercial computational fluid dynamic (CFD) software Fluent. The results indicate that the convergence speed of the proposed method is much faster than that of Fluent, which means a better performance of the new method.

In order to study the characteristics of the temperature variation in oil-immersed power transformer windings during operation, a two-dimensional transient fluid-thermal coupling calculation method for the transient temperature rising of transformer windings is proposed. Based on the dimensionless least-square finite element method (DLSFEM), the two-dimensional transient fluid-thermal coupling calculation method calculates the velocity distribution of the transformer flow field at different time instants, and based on the upwind finite element method, the temperature distribution at each moment is calculated. Considering the influence of the nonlinear material properties and winding Joule loss on the calculation results, the sequential iteration method is applied to solve the fluid-thermal coupling problem, and finally, the characteristics of the field temperature change are obtained. Compared with the traditional least-square finite element method, the DLSFEM has smaller stiffness matrix number conditions, and the corresponding discrete equations have better convergence. An oil-immersed power transformer winding model is taken as an instance, and the temperature distribution is calculated by the proposed method and the commercial computational fluid dynamic software Fluent. The calculation results of the proposed method are basically consistent with those of Fluent, and its iterative number is much less than that of Fluent, which greatly improves the calculation efficiency.

In order to study the coupling fluid and thermal problems of the local winding in oil-immersed power transformers, the least-squares finite element method (LSFEM) and upwind finite element method (UFEM) are adopted, respectively, to calculate the fluid and thermal field in the oil duct. When solving the coupling problem by sequential iterations, the effect of temperature on the material property and the loss density of the windings should be taken into account. In order to improve the computation efficiency for the coupling fields, an algorithm, which adopts two techniques, the dimensionless LSFEM and the combination of Jacobi preconditioned conjugate gradient method (JPCGM) and the two-side equilibration method (TSEM), is proposed in this paper. To validate the efficiency of the proposed algorithm, a local winding model of a transformer is built and the fluid field is computed by the conventional LSFEM, dimensionless LSFEM, and the Fluent software. While the fluid and thermal computation results of the local winding model of a transformer obtained by the two LSFEMs are basically consistent with those of the Fluent software, the stiffness matrix, which is formed by the dimensionless scheme of LSFEM and preconditioned by the JPCGM and TSEM, has a smaller condition number and a faster convergence rate of the equations. Thus, it demonstrates a broader applicability.

In this paper, in view of the low efficiency of the traditional finite element method (FEM), which has been widely used in the insulation design of power transformers, the response surface methodology (RSM) is proposed to optimize the insulation structure of a power transformer electrostatic ring. Firstly, the power transformer model was built using the ANSYS parametric design language (APDL) to realize the automatic pre-processing of numerical calculation. Then with the objective of reducing the maximum electric field intensity, the Taguchi method was used to select the parameters that have a greater impact on the maximum electric field intensity, by which the subsequent optimization process could be effectively simplified. The test points were constructed by the central composite design (CCD) and a response surface model was established by the mutual calls of MATLAB and ANSYS. Finally, the variance analysis, diagnostic analysis, and significance test of regression were carried out to obtain the final response surface model. By comparing the result of RSM with that of FEM, we can find that the results obtained by the two methods are consistent and the maximum electric field strength is obviously reduced. The RSM is more systematic and convincing, which improves the optimization efficiency and provides a reliable and fast way for the optimization of power transformers.