Average temperature of oil-filled transformer windings with partial cooling ducts

An effective one-dimensional model is presented that describes the temperature profile of a winding of an oil-filled distribution transformer with an arbitrary number of partial cooling ducts. An analytical solution of the model is applied to a specific example — a low voltage winding of a 400 kVA distribution transformer with one or two partial cooling ducts. Starting from the exact solution, a simple and practical formula for the temperature rise of similar windings has been derived that is suitable for transformer designers.