Tertiary Winding of Transformer

Tertiary Winding of Transformers

A transformer mainly consists of two windings; primary and secondary windings. But in addition, with a regular primary and secondary winding, the transformer is constructed with an extra third winding called tertiary winding.

The transformer consists of tertiary winding, a three-winding transformer or a triple wound transformer.

Typically, the tertiary winding is delta-connected. It is used in a transformer to protect against fault or short-circuit conditions. And it is also used to add a small load at a different voltage.

When the tertiary winding is used to protect the transformer against short-circuit and fault conditions, the tertiary winding is known as stabilizing winding. And when the tertiary winding is used to add a small load with the transformer, it is known as auxiliary winding.

When a fault or short circuit occurs in the transformer, considerable unbalance is produced in phase voltages. It can be compensated by the circulating current flowing in closed delta tertiary winding.

The reactance of tertiary winding is large enough to limit the circulating current to avoid the heating effect of winding.

Applications of Tertiary Winding

The tertiary winding is used in the below applications.

  • It is used to supply substation auxiliaries at different voltage levels from the primary and secondary windings.
  • To interconnect three supply systems operating at different voltage levels.
  • It is used to supply compensating devices operated at different voltage levels.
  • To load large split-winding generators.
  • To measure the voltage of an HV testing transformer.
  • In star-star connected transformer, the tertiary winding will allow sufficient earth fault current to flow for the operation of protective equipment. It is used to suppress harmonic voltage, and limit voltage unbalance when the main load is unsymmetrical.

Principle of Operation

The operating principle of a three-winding transformer is the same as the typical two-winding transformer.

The primary winding acts as magnetizing winding, and its current produces the main magnetic flux. This flux links the secondary and tertiary winding and induces EMF proportional to the number of turns in the windings.

When loads are connected with secondary and tertiary winding, the current that passes through these windings are I2 and I3.

The geometrical summation of magnetizing forces of secondary and tertiary windings can determine the demagnetising effect of these currents.

Therefore, the magnetizing force of primary and secondary winding must balance the combined secondary magnetizing force and have a magnetizing component.

    \[ I_1N_1=(-I_2N_2)+(-I_3N_3)+I_0N_1 \]

    \[ I_1=I_2'+I_3'+I_0 \]

Where, I_2'=-I_2\frac{N_2}{N_1} and I_3'=-I_3\frac{N_3}{N_1}

Secondary and tertiary windings will be fully loaded simultaneously, and the currents I2’ and I3’ will be in phase simultaneously. Hence, for this reason, the primary winding is designed for a lower load condition than the sum of the rated powers of the secondary and tertiary windings.

Construction of Tertiary Winding

A three-winding transformer consists of three sets of windings; Primary, secondary, and tertiary windings.

Three-winding transformers are operated at three different voltage levels; hence, it is termed low voltage (LV), medium voltage (MV), and high voltage (HV).

There are two alternative arrangements for three windings. HV winding is always away from the core for insulation coordination. LV and MV can be placed near to core. According to that, the schematic diagram of the two arrangements is shown in the figure below.


In two winding transformers, the kVA rating of primary and secondary is the same. But this is not happening in the case of a three-winding transformer. The kVA rating of a three-winding transformer is equal to the most significant kVA rating of any winding.

The rating of tertiary windings depends on which purpose it is used. For example, if used to supply additional load, the tertiary winding is designed and calculated on the same basis as the primary and secondary winding.

And if it is used for balancing load and controlling short circuit current, it carries current only during short-circuit period. In this condition, the rating of tertiary windings depends on the heat capacity.

In practice, the cross-section of tertiary winding is determined by the fault conditions irrespective of the fact for what purpose it is used.

Equivalent Circuit of Three-winding Transformer

The equivalent circuit of a three-winding transformer is represented by the resistance and leakage reactance of each winding. The equivalent circuit is shown in the figure below.

Equivalent Circuit of Three-winding Transformer
Equivalent Circuit of Three-winding Transformer

The above figure, 1-2-3, indicates the primary, secondary, and tertiary windings.

Here, we neglect the effect of exciting current in an equivalent circuit for simplicity.

A three-winding transformer’s load division between secondary and tertiary circuits is utterly arbitrary.

Three external circuits are connected between terminals 1, 2, and 3, respectively, and the common terminal is noted as O.

As we have neglected excitation current I0;

    \[ I_1 + I_2 + I_3 = 0 \]

Short-circuit impedance of winding 1 and 2 with winding 3 open;

    \[ Z_{12} = Z_1 + Z_2 \]

SC impedance of winding 2 and 3 with winding 2 open;

    \[ Z_{13} = Z_1 + Z_3 \]

SC impedance of winding 2 and 3 with winding 1 open;

    \[ Z_{23} =Z_2 + Z_3 \]

All impedances are referred to common base. Therefore, by solving above equations, we can write;

    \[ Z_1 = \frac{1}{2}(Z_{12}+Z_{13}-Z_{23}) \]

    \[ Z_2 = \frac{1}{2}(Z_{23}+Z_{12}-Z_{13}) \]

    \[ Z_3 = \frac{1}{2}(Z_{13}+Z_{23}-Z_{12}) \]

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