### Voltage and Current Relationships for Different Types of Connection

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 :
1. The primary line voltage is VL volts
2. The primary line current is IL amperes
3. Phase transformation ratio is K, where K = V2/V1= N2/N2  where v and v are phase voltages.
5. Loads are purely resistive i.e. having unity power factor.
6. There is no losses and the transformer are ideal in behaviour.
Choice of transformers

Example :
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.
Solution : Primary side connected wit delta
 Fig.  1
VL1 = 3300 V  , IL1 = 12 A
Secondary side star connected with p.f. 0.8.
Primary side :                    Vph1 = VL1 = 3300 V
Secondary side :                Vph2 = VL2/√3= 400/√3 = 230.94 V
Transformation ratio,          K = Vph2 / Vph1 = 230.94/3300 = 0.0699
Primary side,                       IL1 = 12 A
Iph1 = IL1/√3 = 12/√3 = 6.928 A
Secondary side,                   K= Iph1/Iph2
...                                         Iph2= Iph1/K= 6.928/0.0699= 99.11 A
Since secondary is connected in star
Iph2 = IL2 = 99.11 A
Output = √3  VL2 IL2 cosΦ
= √3 x 400 x 99.11 x 0.8
= 54935.62 W = 54.94 W
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