## [JAC032] Analysis of a Transformer

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### Overview

A transformer is an electrical device that uses electromagnetic induction to convert the voltage level of alternating current power. In an ideal transformer the secondary voltage is constant regardless of the load, but in reality it tends to vary with the size of the load and the power factor. The size of a transformer’s voltage variations is a vital output characteristic when considering constant voltage reception. It is also important to maintain a balanced state because an imbalance in the voltage and current in each phase can bring about a rise in the transformer’s temperature or a fault in the device using the transformer.
A transformer’s output characteristics depend on the leakage flux from the iron core. Leakage flux passes through the air instead of the iron core, so it is hard to predict accurately during the design phase. It is possible to handle magnetic flux passing through the air in a magnetic field analysis, meaning that it is also possible to evaluate a transformer’s output characteristics, including the effects of leakage flux.
In this example, the use of a magnetic field analysis to evaluate changes in the secondary voltage caused by load variations in a low frequency transformer.

### Secondary Voltage for the Load

Fig. 1 shows changes in the secondary voltage for the load. The ideal secondary voltage of the transformer used for this analysis is 14.1 V. When the load resistance decreases, the secondary current increases. Accordingly, the secondary voltage falls because the voltage drop increases due to the resistance of the secondary coil and the leakage reactance.

### Induced Voltage in the Secondary Coil

Secondary coil’s induced voltage amplitude and its phase are indicated in Table 1. Fig. 2 shows the vector plot for the induced voltage in the secondary coil, when the load resistance is large and small. The amplitude is shown by the vector length, and the phase is shown by the slope of the vector. When the load resistance is large the amplitude is almost the same and a phase difference of 120 deg is maintained, so the transformer is in a balanced state. On the other hand, when the load resistance is small there is a gap in amplitude between each phase, so the transformer is in an unbalanced state because the phase difference does not reach 120 deg.

### Magnetic Flux Density – RMS Distribution

Fig. 3 shows the magnetic flux density – RMS distribution of the transformer when the load resistance large and small. When the load resistance is large the magnetic flux density is distributed almost symmetrically, but when it is small the current in each phase is unbalanced, which makes the magnetic flux density asymmetric.