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Response Under Load

When a transformer is loaded, a current flows through its secondary coil. This current attenuates the magnetic field by producing an opposing magnetic field according to Lenz's law. As a result, part of the field is shifted out of the iron core so that the two coils are not subjected to the full magnetic field any more. The displaced field lines are termed stray field lines. This leakage leads to a drop in voltage, so that the secondary voltage is lower than what the winding ratio would suggest.

The current flowing through the secondary coil also causes the input current to rise. Both currents produce voltage drops across the coils due to their resistance. Consequently, a loaded transformer behaves like a generator with an internal resistance comprising ohmic and inductive components. Shown below is a simplified equivalent circuit diagram of a transformer incorporating an ohmic resistance RL. I is the load current.

Electrical Transformer Design !

The output voltage U2 is lower than the input voltage U1 by an amount equal to the transformer's internal voltage drop. The phase shift j between the two voltages depends on the type of load. The diagram below displays the relationships applicable to an ohmic load. The output voltage and load current are in phase in this case.

Electrical Transformer Design !

The transformer's internal voltage drop is composed of the partial drops I x R and I x XL, represented by the grey triangle (or Kapp triangle) in the vector diagram.

The vector diagram below shows the relationships applicable to a pure inductive load. The load current in this case lags behind the output voltage by 90°, as does the ohmic voltage drop I x R. Because the voltage across the load is in phase with the inductive voltage drop I x XL, the internal voltage drop caused by this kind of loading is quite large.

Electrical Transformer Design !

The next vector diagram shows the relationships applicable to a capacitive load. In this case, the load current leads the output voltage by 90°. The output voltage is higher than the input voltage, because the internal inductance and load capacitance form a series oscillating circuit. For this reason, large capacitors must not be connected unattenuated to the mains power grid.

Electrical Transformer Design !

The next vector diagram displays the relationships applicable to ohmic-inductive loads. The phase displacement between the load current and output voltage lies between 0 and 90° depending on the load resistance and inductance. This kind of loading results in the largest voltage drop, because the load's active resistance and reactance behave like a transformer's internal resistance. 

Electrical Transformer Design !

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