Parallel Operation of Transformers with Unequal Voltage Ratios

Parallel Operation of Transformers with Unequal Voltage Ratios

AU: Dec.-05, 06

• Now we will consider the case of two transformers working in parallel and having unequal voltage ratio. This is shown in the Fig. 6.26.1.

• The voltage ratios of the two transformers are not equal. The parallel operation under this case is still possible. But as seen previously there would be a circulating current under no load condition.

• Let us consider voltage ratio of transformer 1 is slightly more than 2. So that induced e..m.f. E₁ is greater than E₂. Thus the resultant terminal voltage will be E₁ - E₂ which will cause a circulating current under no load condition.

I_c  =E₁-E₂ / Z₁+Z₂

From the circuit diagram we have,

Key Point: This circulating current I_C adds to I₁, but subtracts from I₂. Hence transformer 1 gets overloaded. The transformers will not share the load according to their ratings.

• The phasor diagram is shown in the Fig. 6.26.2.

• The two transformers will operate at different power factors ϕ₁ and ϕ₂ are the power factor angles of these two transformers whereas is the combined p.f. angle.

• Here E_A and E_B have the same phase but there may be some phase difference between the two due to some difference of internal connection as for the connection in parallel of a Star/Star and a Star/Delta 3 phase transformers.

Key Point: While solving the problems on parallel operation of transformers it is convenient to work with numerical values of impedances instead of percentage values.

Ex. 6.26.1 Two transformers A and B are connected in parallel to a load of (2 + j1.5)Ω. Their impedances in secondary terms are Z_A (0.15+j0.5) Ω and Z_B = (0.1+j0.6) Ω. Their no load terminal voltages are E_A = 207 ∠0^° V and EB = 205 40° volts. Find the power output and power factor of each transformer.

Sol. Two transformers A and B are supplying a load of impedance given by,

Ex. 6.26.2 Two transformers each of 800 kVA are connected in parallel. One has a resistance and reactance of 1% and 4 % respectively and the other has resistance and reactance of 1.5 % and 6 % respectively. Calculate the load shared by each transformer and corresponding power factor when the total load shared is 100 kVA at 0.8 power factor lagging.

Sol.:

kVA of transformer 1 = 800 and kVA of transformer 2 = 800

Ex. 6.26.3 Two single phase transformers, one of 100 kVA and the other of 60 kVA are connected in parallel to the same bus bars on the primary side their no load secondary voltage being 1000 V and 900 V respectively. Their resistances are 2.0 and 2.5 percent respectively and their reactances are 8 and 6 percent respectively. Calculate no load circulating current in the secondaries.

Sol. : Transformer 1 :

Review Questions

1. Deduce expressions for the load shared by the two transformers with unequal voltage ratios. AU: Dec.-05, 06, Marks 12

2. Two 100 kW single phase transformers are connected in parallel both on the primary and secondary. One transformer has an ohmic drop of 0.5 % at full load and an inductive drop of 8 % at full load current. The other has an ohmic drop of 0.75 % and inductive drop of 2 %. Show how will they share a load of 180 kW at 0.9 power factor. [Ans.: kW₁, 57.9, kW₂ = 121.5]

 3. A load of 200 kW at 0.85 power factor lagging is to be shared by two transformers A and B having the same rating and same transformation ratio. For transformer A the full load resistive drop is 1 % and reactance drop 5 % of the nominal terminal voltage for transformer B the corresponding values are 2 % and 6 %. Calculate the load kVA supplied by each transformer. [Ans.: KVA_A =  131; kVA_B = 105]

 4. A load of 450 kVA at 0.8 power factor lagging is to be shared by two three phase transformers A and B of equal ratings. If the equivalent delta Tow impedances as referred to secondary are (1.5 + j 5) Ω for A and (1.5 + j 4.5) Ω for B, calculate the load supplied by each transformer. [Ans.: Q_A=214.25 ∠-37.77° KVA, Q_B = 235.7865 ∠-36.03°KVA]

5. A 500 kVA transformer with 0.01 pu resistance and 0.05 pu reactance is connected in parallel with a 250 kVA transformer with 0.015 pu resistance and 0.04 pu reactance. The secondary voltage of each transformer is 400 V on no load. Find how they share a load of 750 kVA at power factor 0.8 lagging.

[Ans. : 471.16 ∠- 40.31° kVA, 280.90 ∠- 31.06° KVA]

6. Two 250 kVA transformers suppling a network are connected in parallel on both primary and secondary sides. Their voltage ratios are the same. The resistance drops are 1.5 % and 0.9 % and the reactance drops are 3.33 % and 4 % respectively. Calculate the kVA loading on each transformer and its power factor when the total load on the balls transformers is 500 kVA and at 0.707 lagging p.f. [Ans.: 265.8 kVA, 0.7709 (lag), 236.8 kVA, 0.6276 (lag]