Tutorial Problems on Transformer

Tutorial Problems

1. A 1000-kVA and a 500-kVA, 1-phase transformers are connected to the same bus-bars on the primary side. The secondary e.m.fs. at no-load are 500 and 510 V respectively. The impedance voltage of the first transformer is 3.4% and of the second 5%. What cross-current will pass between them when the secondaries are connected together in parallel ? Assuming that the ratio of resistance to reactance is the same in each, what currents will flow in the windings of the two transformers when supplying a total load of 1200 kVA.

[(i) 290 A (ii) 1577 and 900 A] (City & Guilds, London)

2. Two transformers A and B are connected in parallel to supply a load having an impedance of (2 + j 1.5W). The equivalent impedances referred to the secondary windings are 0.15 + j 0.5 W and 0.1 + j 0.6 W respectively. The open-circuit e.m.f. of A is 207 V and of B is 205 V. Calculate (i) the voltage at the load (ii) the power supplied to the load (iii) the power output of each transformer and

(iv) the kVA input to each transformer.

[(i) 189 Ð- 3.8°V (ii) 11.5 kW (iii) 6.5 kW, 4.95 kW (iv) 8.7 kVA, 6.87 kVA]

QUESTIONS AND ANSWERS ON TRANSFORMERS

How is magnetic leakage reduced to a minimum in commerical transformers ? Ans. By interleaving the primary and secondary windings.

Mention the factors on which hysteresis loss depends ?

Ans. (i) Quality and amount of iron in the core (ii) Flux density and (iii) Frequency.

How can eddy current loss be minimised ? Ans. By laminating the core.

In practice, what determines the thickness of the laminae or stampings ? Ans. Frequency.

Does the transformer draw any current when its secondary is open ?

Ans. Yes, no-load primary current.

Why ?

Ans. For supplying no-load iron and copper losses in primary.

Is Cu loss affected by power factor ?

Ans. Yes, Cu loss varies inversely with power factor.

Why ?

Ans. Cu loss depends on current in the primary and secondary windings. It is well-known that current required is higher when power factor is lower.

What effects are produced by change in voltage ? Ans. 1. Iron loss………varies approximately as V 2.

2. Cu loss………it also varies as V 2 but decreases with an increase in voltage if constant kVA output is assumed.

3. Efficiency………for distribution transformers, efficiency at fractional loads decreases with in- crease in voltage while at full load or overload it increases with increase in voltage and vice- versa.

4. Regulation………it varies as V2 but decreases with increase in voltage if constant kVA output is assumed.

5. Heating………for constant kVA output, iron temperatures increase whereas Cu temperatures decrease with increase in voltages and vice-versa.

Q. 10. How does change in frequency affect the operation of a given transformer ?

Ans. 1. Iron loss ………increases with a decrease in frequency. A 60-Hz transformer will have nearly 11% higher losses when worked on 50Hz instead of 60 Hz. However, when a 25-Hz trans- former is worked on 60 Hz, iron losses are reduced by 25%.

2. Cu loss………in distribution transformers, it is independent of frequecy.

3. Efficiency………since Cu loss is unaffected by change in frequency, a given transformer effi- ciency is less at a lower frequency than at a higher one.

4. Regulation………regulation at unity power factor is not affected because IR drop is independent of frequency. Since reactive drop is affected, regulation at low power factors decreases with a decrease in frequency and vice-versa. For example, the regulation of a 25-Hz transformer when operated at 50-Hz and low power factor is much poorer.

5. Heating………since total loss is greater at a lower frequency, the temperature is increased with decrease in frequency.

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