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### Three-phase transformers

When it is desired to raise or lower the voltage on three-phase lines, three-phase transformers or single-phase transformers are used.

For a given power, the three-phase transformer is less expensive and smaller than three single-phase transformers. In some cases it is preferred to use three single-phase transformers plus a spare unit rather than two three-phase transformers.

With three-phase transformers we can achieve four types of coupling

· the triangle-star;

· the triangle - triangle;

the star - triangle;

the star - star.

The most frequently used couplings are: triangle-star and triangle-triangle.

### Triangle - star coupling

delta-star coupling (Figure 2-6) is widely used in low-voltage distribution. This configuration gives the advantage of having, at the secondary, a line voltage allowing the connection of three-phase loads as well as a phase-neutral voltage for single-phase loads.

· ELp = primary line voltage;
· ILp = primary line current;
Ip = primary winding current;
· ELs = secondary line voltage;
Es = secondary winding voltage (phase voltage);
· They = secondary line current.
The nominal power of the transformers is given in KVA, and the relation of the voltages and currents in the case of a delta - star assembly is as follows:
At primary:
S = ELP ´ ILP ´ √3
ILP = Ip ´ √3
EP = ELP
In secondary:
S = ELS ´ ILS ´ √3
ES = SLS / √3
IS = THEY
Example 2.4
A 100KVA three-phase transformer is connected to the primary in delta and the secondary in star. It is powered by a 12KV three-phase source and the line voltage at the secondary is 380V. If the transformer is operating at its rated power. Determine the following values:
a) the phase voltage at the secondary;
b) the secondary line current;
c) the line current at the primary.
Solution:
a) ES = ELS / √3 = 380V / √3 = 220V
b) ILS = S /(ELS ´ √3) = 100KVA / (380 ´ √3) = 152.11 Amps
c) ILP = S / (ELP ´ √3) = 100KVA ´ 12KV ´ √3 = 4.81 Amps

### Triangle-triangle coupling

The delta-delta connection (Figure 2-7) is used in electrical installations when the use of single-phase voltage is not necessary.

This assembly causes no phase shift between the primary and secondary line current, while in a delta-star assembly, there is a phase shift of 30° between these two currents.

At primary:
S = EP ´ ILP ´ √3
EP = ELP
ILP = IP ´ √3
In secondary:
S = ELS ´ ILS ´ √3
SLS = EP
IS = ILS ´ √3

### Three-phase transformers

When it is desired to raise or lower the voltage on three-phase lines, three-phase transformers or single-phase transformers are used.

For a given power, the three-phase transformer is less expensive and smaller than three single-phase transformers. In some cases it is preferred to use three single-phase transformers plus a spare unit rather than two three-phase transformers.

With three-phase transformers we can achieve four types of coupling

· the triangle-star;

· the triangle - triangle;

the star - triangle;

the star - star.

The most frequently used couplings are: triangle-star and triangle-triangle.

### Triangle - star coupling

delta-star coupling (Figure 2-6) is widely used in low-voltage distribution. This configuration gives the advantage of having, at the secondary, a line voltage allowing the connection of three-phase loads as well as a phase-neutral voltage for single-phase loads.

· ELp = primary line voltage;
· ILp = primary line current;
Ip = primary winding current;
· ELs = secondary line voltage;
Es = secondary winding voltage (phase voltage);
· They = secondary line current.
The nominal power of the transformers is given in KVA, and the relation of the voltages and currents in the case of a delta - star assembly is as follows:
At primary:
S = ELP ´ ILP ´ √3
ILP = Ip ´ √3
EP = ELP
In secondary:
S = ELS ´ ILS ´ √3
ES = SLS / √3
IS = THEY
Example 2.4
A 100KVA three-phase transformer is connected to the primary in delta and the secondary in star. It is powered by a 12KV three-phase source and the line voltage at the secondary is 380V. If the transformer is operating at its rated power. Determine the following values:
a) the phase voltage at the secondary;
b) the secondary line current;
c) the line current at the primary.
Solution:
a) ES = ELS / √3 = 380V / √3 = 220V
b) ILS = S /(ELS ´ √3) = 100KVA / (380 ´ √3) = 152.11 Amps
c) ILP = S / (ELP ´ √3) = 100KVA ´ 12KV ´ √3 = 4.81 Amps

### Triangle-triangle coupling

The delta-delta connection (Figure 2-7) is used in electrical installations when the use of single-phase voltage is not necessary.

This assembly causes no phase shift between the primary and secondary line current, while in a delta-star assembly, there is a phase shift of 30° between these two currents.

At primary:
S = EP ´ ILP ´ √3
EP = ELP
ILP = IP ´ √3
In secondary:
S = ELS ´ ILS ´ √3
SLS = EP
IS = ILS ´ √3