In the three phase transformers, the phase voltage ratio is same as the turns ratio. But due to the different types of connections the ratio of line voltages is different. The relationship between voltages and currents for various types of connections is given in the table1.

While deriving these relationships, the following assumptions have been made :

- The primary line voltage is V
_{L }volts - The primary line current is I
_{L }amperes - Phase transformation ratio is K, where K = V
_{2}/V_{1}= N_{2}/N_{2}where v and v are phase voltages. - Loads are balanced.
- Loads are purely resistive i.e. having unity power factor.
- There is no losses and the transformer are ideal in behaviour.

**Choice of transformers**A three phase transformer has delta connected primary and a star connected secondary working on 50 Hz three phase supply. The line voltages of primary and secondary are 3300 V and 400 V respectively. The line current on the primary side is 12 A and secondary has unbalanced load at 0.8 lagging p.f. Determine the secondary phase voltage, line current and output.

V

_{L1}= 3300 V , I_{L1}= 12 ASecondary side star connected with p.f. 0.8.

Primary side : V

_{ph1}= V_{L1}= 3300 VSecondary side : V

_{ph2}= V_{L2}/√3= 400/√3 = 230.94 VTransformation ratio, K = V

_{ph2}/ V_{ph1}= 230.94/3300 = 0.0699Primary side, I

_{L1}= 12 A I

_{ph1}= I_{L1}/√3 = 12/√3 = 6.928 ASecondary side, K= I

_{ph1}/I_{ph2}**.**I

^{.}._{ph2}= I

_{ph1}/K= 6.928/0.0699= 99.11 A

Since secondary is connected in star

I

_{ph2 }= I_{L2}= 99.11 A Output = √3 V

_{L2}I_{L2}cosĪ¦ = √3 x 400 x 99.11 x 0.8

= 54935.62 W = 54.94 W

__Related articles :__**Three Phase Transformer****Three Phase Transformer Connection****Star-Star Connection of 3Phase Transformer****Delta-Delta Connection of 3-Phase Transformer****Star-Delta Connection of 3-Phase Transformer****Delta-Star Connection of 3-Phase Transfomer**

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