New Analytical Formulas for Electromagnetic Field and Eddy Current Losses in Bushing Regions of Transformers

This paper presents a new and rigorous analytical calculation of electromagnetic field and eddy current losses in the zones of transformer tanks where bushings are mounted. This is done by solving Maxwell's equations in the regions surrounding bushings, with the corresponding boundary conditions and considering linear permeability. Then, by solving the modified Bessel's equation, the analytical formulas to calculate the magnetic field and eddy current losses in these regions are obtained and several cases are studied. The results are compared with 3-D finite element simulations and show very close correspondence. The obtained formulas allow straightforward calculations that can help designers to select proper parameters to optimize the design of transformers. This paper can be taken as the basis for the analysis of the nonlinear permeability case.