A fundamental approach to transformer thermal modeling. I. Theory and equivalent circuit

A simple equivalent circuit to represent the thermal heat flow equations for power transformers is presented. Key features are the use of a current source analogy to represent heat input due to losses, and a nonlinear resistor analogy to represent the effect of air or oil cooling convection currents. An interesting historical note concerns the fact that the foregoing effect was first quantified in 1817. It is shown that the idea of “exponential response” is not the best way to think of the dynamics of the situation. It is also shown that one can consider ambient temperature to be a variable input to the system, and that it is properly represented as an ideal voltage source. Physical experimental verification, on an in-service 250 MVA transformer, is described in a companion paper.