Transformers-parallel operation

Requirements for parallel operation of transformers:

a)the same voltage-ratio
b)the same per-unit impedance
c)the same polarity
d)the same phase sequence and zero relative phase displacement.
(c) and (d) are absolutely essential, (a) must satisfy to a close degree, in (b), more latitude. it decides load sharing

The currents carried by two transformers are proportional to their ratings if their ohmic impedance are inversely proportional to those ratings and their per-unit impedance are identical.

A difference in the per-unit impedance results in a divergence of phase angle of the two currents, i.e. two transformers will work at different power factors

Transformers can be operated in parallel:

Transformer 1: Yy Yd Yd
Transformer 2: Dd Dy Yz

Practice Objectives:
1. If all other requirements for parallel operation of transformer are fulfilled, which one of following pairs of three phase transformers, with given VECTOR GROUPS, can be operated in parallel?
a. Y d 1 and Yy 0
b. Y d 1 and Dy 11
c. Dd 6 and Dy 1
d. Dd 0 and Dy 11

2.Two transformers operating in parallel will share the load depending upon their
a. Ratings
b. Leakage reactance
c. Efficiency
d. Per unit impedance

3.If per unit impedance of two transformers connected in parallel are not equal, then which one of the following statements is correct?
a. The power factor of the two transformers will be different from that of the connected load
b. Transformers will get overloaded
c. Dead short circuit occurs
d. The transformer with higher per unit impedance will share more load

4.Two single phase transformers A and B are connected in parallel, observing all requirements of a parallel operation, except that the induced voltage Ea is slightly greater than Eb; Zea and Zeb being the equivalent impedances of A and B, both referred to the secondary side.



Under this operating condition with the primary bus-bars being energized, a circulating current will flow:
a. Only in the secondary windings of A and B
b. In both the primary and the secondary windings of A and B
c. In both the primary and the secondary windings of A and B, as well as in the primary side network
d. In the primary and the secondary windings of A and B, and boost the voltages on the secondary side of both A and B

Solved Problems
1. A 500 kVA. transformer with 0.01pu resistance and 0.05 pu reactance is connected in parallel with a 250 kVA transformer with 0.015pu resistance and 0.04 pu reactance. Find how they share a load of 750 kVA, at a power factor 0.8 lagging.
Solution:
choose base kVA as 250 kVA.
Z₁ = 0.01+j0.05 = 0.051/78.7⁰ Ω
and Z₂ = 2(0.015+j0.04 = 0.03+j0.08 = 0.085/69.4⁰ Ω.
Z₁+Z₂ = 0.04+j0.13 = 0.136/72.9⁰ Ω.

total load kVA is S = 750/-36.9⁰ kVA;
S₁ = 750/-36.9⁰ . 0.085/69.4⁰ / 0.136/72.9⁰ = 471/-40.4⁰ kVA
S₁ = 471 kVA at power factor 0.762 lagging.

S₂ = 750/-36.9⁰ . 0.051/78.7⁰ / 0.136/72.9⁰ = 281/-31.1⁰ kVA
S₁ = 281 kVA at power factor 0.856 lagging.