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

TLDR

The thermal effect in transformers was first quantified in 1817. The study presents a simple equivalent circuit to model thermal heat flow in power transformers. The model uses a current‑source analogy for heat input from losses and a nonlinear‑resistor analogy for convection cooling. The analysis demonstrates that an exponential response model is inadequate and that ambient temperature should be treated as a variable input represented by an ideal voltage source.

Abstract

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. The 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.