Calculation of Nonlinear Electromagnetic Fields in the Steel Wall Vicinity of Transformer Bushings

Successful analytical formulas have been previously proposed to calculate the losses in tank regions of transformers assuming linear permeabilities in the analyzed boundary-valued problem. This has resulted in easy-to-implement and low-cost computational design procedures from a transformer factory economical point of view. However, designers and analysts of transformers are constantly seeking new ways of reducing transformer losses in actual power networks with thousands of transformers. As a result, this paper has focused on proposing new analytical formulas to determine the electromagnetic field in bushing regions of transformers, taking account of the true nature of the nonlinear permeability behavior of the tank wall. This way, the nonlinear Maxwell´s equations in the regions surrounding the bushings are solved using an integral equation formulation that properly includes boundary conditions. A practical iterative procedure is thus proposed to solve the resulting nonlinear equation. The iterative scheme shows excellent numerical convergence properties with a very low computational demand as compared with finite-element (FE) nonlinear models. A comparison between our analytical results and those of 3-D FE simulations reveals a close match for a wide range of conductor currents. Hence, our new formulas can be used to improve the design of transformers, increasing their efficiency.