## Wednesday, February 17, 2021

Three-phase transformers
When it is desired to increase or decrease 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.

Three-phase transformers
When it is desired to increase or decrease 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 star triangle;
· The triangle - triangle;
· The star - triangle;
The star - star.
The most frequently used couplings are: delta-star and delta-delta.
Delta - 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 for connecting three-phase loads as well as a phase-to-neutral voltage for single-phase loads.

.

· ELp = primary line voltage;
· ILp = primary line current;
· Ip = current of the primary winding;
· ELs = secondary line voltage;
· Es = voltage of the secondary winding (phase voltage);
· They = secondary line current.
The nominal power of transformers is given in KVA, and the relationship of voltages and currents in the case of a delta - star connection is as follows:
At primary:
S = ELP ´ ILP ´ √3
ILP = Ip ´ √3
EP = ELP
In secondary:
S = ELS ´ ILS ´ √3
ES = ELS / √3
IS = ILS
Example
A three-phase 100KVA transformer is connected to the primary in delta and the secondary in star. It is powered by a three-phase 12KV source and the line voltage at the secondary is 380 V. If the transformer is operating at its rated power. Determine the following values:
a) the phase voltage at the secondary;
b) the line current at the secondary;
c) primary line current.
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 does not cause any 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
ELS = EP
IS = ILS ´ √3

Three-phase transformers
When it is desired to increase or decrease 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.

Three-phase transformers
When it is desired to increase or decrease 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 star triangle;
· The triangle - triangle;
· The star - triangle;
The star - star.
The most frequently used couplings are: delta-star and delta-delta.
Delta - 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 for connecting three-phase loads as well as a phase-to-neutral voltage for single-phase loads.

.

· ELp = primary line voltage;
· ILp = primary line current;
· Ip = current of the primary winding;
· ELs = secondary line voltage;
· Es = voltage of the secondary winding (phase voltage);
· They = secondary line current.
The nominal power of transformers is given in KVA, and the relationship of voltages and currents in the case of a delta - star connection is as follows:
At primary:
S = ELP ´ ILP ´ √3
ILP = Ip ´ √3
EP = ELP
In secondary:
S = ELS ´ ILS ´ √3
ES = ELS / √3
IS = ILS
Example
A three-phase 100KVA transformer is connected to the primary in delta and the secondary in star. It is powered by a three-phase 12KV source and the line voltage at the secondary is 380 V. If the transformer is operating at its rated power. Determine the following values:
a) the phase voltage at the secondary;
b) the line current at the secondary;
c) primary line current.
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 does not cause any 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
ELS = EP
IS = ILS ´ √3