Transformers are widely distributed and extremely important energy conversion equipment in the power system. However

the high altitude electromagnetic pulse (HEMP) can induce a steep pulse voltage with a peak value of up to thousands of kilovolts on the overhead line

and the frequency is up to 100 MHz

which is easy to damage the transformer and seriously threaten the safe and stable operation of the power system. Therefore

to protect the safety of the power system

analysing the transformer wave process under the action of HEMP is necessary. Accordingly

there is a need for an ultra-wide band model of the transformer. In this paper

the skin effect of winding is analysed

the dielectric response of oil-paper is fitted with the double relaxation Cole–Cole model

and the frequency dependent models of distribution parameters are established. Fractional order terms are introduced into the traditional multi-conductor transmission line (MTL) integer order model to describe the characteristics of these distribution parameters so that the frequency application range of the MTL model is extended to 100 MHz. The proposed MTL model is solved by the finite-difference time-domain algorithm and verified by the finite element method and experiment. The error is less than 5%

which verifies its accuracy and effectiveness.