Calculation of the short-circuit reactance of transformers by a line integral based on surface magnetic charges

An efficient approach for calculating the short-circuit reactance of transformers is presented in this paper. This approach is based an the surface magnetic charge method and the band-ring mesh elements. The area integral in the calculation of the magnetic flux is transformed to a line integral, which can save on computing time and increase the calculation accuracy. The integral transformation results from the idea of the flux decomposition. Furthermore, based on the nux decomposition, a unified formula of calculating the short-circuit reactance of transformers is derived. The calculation of the formula is simplified by employing the band-ring boundary elements in the particular geometrical situation that the cylindrical windings and the elements are coaxial. Calculation examples illustrate that the approach presented in this paper is both efficient and accurate.