Voltage and Current Relationships for Different Types of Connections

Voltage and Current Relationships for Different Types of Connections  

AU: Dec.-05, 11, 14, May -11, 19

• 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 relationships between voltages and currents for various types of connections is given in the Table 7.5.1.

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

1. The primary line voltage is V_L volts

2. The primary line current is I_L amperes.

3. Phase Transformation Ratio is K,

K= V₂ / V₁= N₂ / N₁ where V₂ and V₁ are phase voltages.

4. Loads are balanced.

5. Loads are purely reisitive i.e. having unity power factor.

6. There are no losses and the transformers are ideal in behaviour.

1. Choice of Transformer Connections

Ex. 7.5.1 A 3-phase, 500 kVA, 6000 V/400 V, 50 Hz, delta-star connected transformer is delivering 300 kW at 0.8 pf lagging to a balanced 3-phase load connected to the LV side with HV side supplied from 6000 V, 3-phase supply. Calculate the line and winding currents in both the side. Assume the transformer to be ideal. AU : Dec.-05, May-19, Marks 15

Sol. :

Ex. 7.5.2 A 3 phase step down transsformer is connected to 6600 volts mains and it takes 10 A. Calculate the secondary line voltage, line current, and output for the following connections a) Delta - Delta b) Star – Star c) Star - Delta d) Delta - Star

Turns ratio/phase is 12. Draw connection diagrams.

Sol. :

Ex. 7.5.3 A 120 kVA, 6000/400 V, star/star, 3 phase, 50 Hz transformer has a iron loss of 1800 W. The maximum efficiency occur at 3/4 full load. Find the efficiency of the transformer at

1) Full load and 0.8 p.f. and

2) The maximum efficiency at unity p.f.  AU : Dec.-05 Marks 8

Sol. :

Ex. 7.5.4 A 3 phase, 100 kVA, 6600/1100 V transformer is delta connected on the primary ans star connected on the secondary. The primary resistance per phase is 1.8 Ω and secondary resistance per phase is 0.025 Ω. Determine the efficiency when the secondary is supplying full load at 0.08 p.f. and the iron loss is 15 k W.

Sol. :

Review Questions

1. State the voltage and current relations for various three phase transformer connections.

2. A transformer has a ∆ connected primary and a star connected secondary, working on 50 Hz supply. The line voltages on primary and secondary sides are 6.6 kV and 400 V respectively. The line current on the primary side is 8 A and the secondary side has a balanced load of 0.6 p.f. lagging. Find a) Output of the transformer b) The line current on the secondary side. (Ans.: a) 54.857 kW b) 132 A)

3. 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 a balanced load at 0.8 lagging p.f. Determine the secondary phase voltage line current and the output. [Ans. 230.94 V, 99.11 A, 54.94 kW]