Three-phase transformers [star - triangle]

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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