Design formulas for the leakage inductance of toroidal distribution transformers

In this paper, design formulas for the calculation of the leakage inductance of toroidal transformers are presented. The formulas are obtained from the analytical integration of the stored energy. The formulas are sufficiently simple and accurate to be introduced in the loop of a design program avoiding expensive finite element simulations. It is found that toroidal transformers naturally produce the minimum leakage inductance possible for medium-voltage power transformers. To limit the short-circuit currents in power and distribution systems, a larger than the minimum leakage inductance is often required. This paper presents two methodologies to increase the leakage inductance of toroidal distribution transformers: selectively enlarging the inter-winding spacing and inserting a piece of ferromagnetic material in the leakage flux region between the windings. Extensive validation with 2D and 3D finite element simulations is performed. Additionally, experimental verification of both formulas and numerical simulations was carried out comparing the calculations against measurements on prototypes.