## [JAC146] Analysis of Stray Loss in a Transformer

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### Overview

Transformers are made to be used long-term, so it has become an important design policy to control running costs from losses. These losses include copper loss in the coil and iron loss in the core. In high-capacity transformers, however, there is also stray loss in the tank from flux leakage from the core. From a safety standpoint, companies want to contain the heat produced from stray losses in the tank to well below the standards required for heat resistant design because they anticipate injuries from people touching the tank itself.
Predicting these losses and the heat that they generate is a vital component of transformer design, but it is difficult to estimate them from desktop calculations, so evaluations and detailed analyses using the finite element method (FEM) are indispensible.
This Application Note explains how to obtain losses in a transformer tank and use them to evaluate the temperature distribution in each part.

### Joule Loss Density Distribution

Fig. 1 shows the magnetic flux density distribution, fig. 2 shows the current density distribution, and fig. 3 shows the joule loss density distribution in the tank. From fig. 1, it is apparent that magnetic flux is leaking from the transformer to the tank. This leakage flux generates eddy currents in the tank, as shown in fig. 2. Fig. 3 shows that joule losses get bigger in places with high current density.

### Iron Loss Density Distribution

Fig. 4 shows the iron loss density distribution in the core. From fig. 4, it is apparent that iron losses increase in the inside corners. This is caused by the flow of magnet flux concentrating on the shortest path through the magnetic circuit.

### Losses

Fig. 5 and Fig. 6 shows the losses in each part. Use these loss values as heat sources to run the thermal analysis.

### Temperature Distribution

Fig. 7 shows the core’s temperature distribution, fig. 8 shows the winding’s temperature distribution, and fig. 9 shows the tank’s temperature distribution. From fig. 7, it is apparent that the temperature in the outside of the core is lower than in the inside of the core. This is because the core is cooled by insulating oil. In the same way, from fig. 8 it is apparent that the primary winding on the outside has a lower temperature than the secondary coil on the inside. From fig. 9, it is apparent that the temperature of the tank has not risen higher than the temperature of the insulating oil.