Modelling a transformer
For a power transformer at minimum you would probably want to simulate saturation (as that is commonly used for saftey in the event of a fault) 

A circuit is a graphical mathematical description, if you want the math, you or someone else will need to convert this circuit to a state space description. Spice programs such as LT spice do this automatically. 

There are also commercially available physics simulators like comsol, CST or ansys that can do a 3d Finite Element Model (FEM). Or this


Source: https://hvdc.ca/webhelp/EMTDC/Transformers/The_Classical_Approach/the_classical_approach.htm

If you want the physical parameters, you model the circuit, and then figure out how much heat is produced from the components, then size the rest of the system around that.