# Three-winding Transformer

**Definition:** Sometimes in high rating transformer, the third winding is constructed in addition to the primary and the secondary windings. The third winding is called the tertiary winding, and because of the three windings, the transformer is called the three-winding transformer.

The voltage ratings of all the three windings of the transformer are usually unequal.The primary winding has the highest voltage rating; the tertiary has the lowest voltage rating, and the secondary has the intermediate voltage rating.

The chief advantages of the three winding transformer is an economy of construction and their great efficiency. The schematic diagram of a three-phase transformer is shown in the figure below.

For an ideal transformer,

The tertiary winding is connected in delta. The main advantage of the using tertiary winding is that the delta connection suppresses harmonic voltage generated in the primary and secondary windings of the transformer. The tertiary winding is also used for the following purposes.

- Tertiary winding is used to supply substation auxiliaries (for example, lights, fans, and pumps) at a voltage different from those of the primary and secondary windings.
- The synchronous capacitor or static high voltage capacitor is connected across the delta-connected output of the tertiary winding for reactive power injection into the system for either power factor connection or voltage regulation.
- It is used to interconnect the three supply system operating at different voltages.
- The delta connected tertiary reduces the impedances offered to the zero sequence currents to allow sufficient earth fault current for proper operation of protective devices.
- Tertiary can be used for measuring the voltage of the high voltage testing transformer.

The unbalanced and third harmonic problem does not arise when one or both sets of windings are connected in delta. Usually, the rating of the three winding transformer is up to 35 percent of the total VA ratings of the transformer.

## Equivalent Circuit of a Three Winding Transformer

The equivalent circuit of a three winding transformer is shown in the figure below.Each winding is represented by its equivalent resistance and reactance. R_{1}, R_{2}, R_{3} are the resistances and the X_{1}, X_{2}, and X_{3} are the impedance of the primary, secondary and tertiary windings of the transformer.

If the excitation current is considered then, the R_{0} and X_{0} can be connected as shown in the figure above. The V_{1}, V_{2}, V_{3} are the voltages and the I_{1}, I_{2}, I_{3} are the currents of primary, secondary, and tertiary windings.

### Determination of Parameters of Three-Windings Transformers

The parameters of the equivalent circuit can be determined from the open circuit and the three short circuit tests.

### Short Circuit Test

The equivalent leakage impedances Z_{1}, Z_{2} and Z_{3}, referred to a common base can be determined by performing the three short circuits. In the first test, the winding two is short-circuited, winding three is kept open circuited, and a low voltage is applied to winding one so that the fault loads current flows in windings 2

The voltage, current and power input to winding one are measured. Let the V_{1}, I_{1} and P_{1} be the voltmeter, ammeter and wattmeter reading respectively.The Z_{12} indicates the short-circuit impedances of windings 1 and 2 with winding three open. Then ,

Equivalent resistance,

Equivalent leakage reactance,

The Z_{12} is the series combination of Z_{1} and Z_{2} respectively,

In the second short circuit test the winding three is a short-circuited and winding two is kept open. The low voltage is applied to winding 1 to circulate the full load current in winding 3. If Z_{13} represents the short circuit impedance of winding one and three with winding two left open.

In the third short circuit test, the winding three is short-circuited, and the winding one is kept open. The low voltage is applied to winding 2 to circulate the full load current in the short circuit winding 3. The Z_{23} represents the short circuit impedance to winding 2 and 3 with winding one open.

Solving equation (1), (2) and (3) we get the leakage impedance Z_{1}, Z_{2} and Z_{3} all referred to as primary,

### Open-Circuit Test

The open circuit test is carried out to determine the core loss, magnetising impedance and turn ratios. In open circuit test the voltmeter, ammeter and wattmeter are connected in low voltage winding. The secondary side is kept open, and the voltmeter is connected.

Since the high voltage side is opened the current drawn by the primary is no load current and I_{0} measured by the ammeter A. The magnetising impedance may be found by exciting current winding 1 with both winding 2 and 3 be open circuit. Then we have,

The voltage regulation of a three-winding transformer is defined as the ratio of the magnitude of the actual kVA loading of the winding to the base kVA used in determining the network parameters.