Problems solved about Real Transformer

Problem 92-1 Source: Problem developed by the site author.

Consider a 10 kVA transformer with a rated voltage of 2,300 / 230 volts and that was subjected to a short-circuit test showing, in this condition, V_cc = 80 volts (already referred to the secondary) and the power measured by the wattmeter was 400 watts. Calculate:

a) The transformation relation a.

b) The resistors and leakage reactances of the transformer's primary and secondary.

c) Calculate the power factor of the short-circuited transformer.

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Problem 92-2 Source: Problem developed by the site author.

Consider a single-phase 50 kVA transformer with a rated voltage of 13,200 / 220 volts and that underwent a test where the measuring instruments were located in the primary and were obtained the following readings:

Test Type	Voltage (V)	Current (A)	Real Power (W)
Open Circuit	13,200	0.32	900
Short Circuit	850	3.79	380

a) Determine the transformer resistances and reactances referred to the primary.

b) Draw a diagram with the values obtained.

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Problem 92-3 Source: Problem developed by the site author.

Based on the previous problem (problem 92-2), suppose we have connected to the secondary of the transformer a load of 40 kVA with FP = 0.85. Find:

a) Joule losses, or copper losses.

b) In this condition, what is the efficiency of the transformer.

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Problem 92-4 Source: Problem developed by the site author.

A single-phase 25 KVA transformer, with a primary voltage of 13,200 V and a secondary voltage of 220 V, it has a primary winding resistance of 0.3 Ω and a secondary winding resistance of 0.005 Ω. A load of 20 KVA with a FP = 0.75 is connected to the secondary. Iron losses are 120 W.

a) In this condition, find the efficiency of the transformer.

b) If you change the load to 25 KVA with FP = 0.9, what is the new efficiency?

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Problem 92-5 Source: Problem developed by the site author.

A single-phase transformer of 250 KVA, with a primary voltage of 13,200 V and a secondary voltage of 440 V is put to the test, and the results are shown in the table below.

Test Type	Voltage (V)	Current (A)	Real Power (W)
Open Circuit	13,200	1.20	2,000
Short Circuit	620	18.94	5,000

a) In this condition, find the efficiency of the transformer.

b) Determine the equivalent parameters of the transformer electrical circuit referred to the primary.

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Problem 92-6 Source: Problem developed by the site author.

In relation to the previous problem find:

a) If you change the load to 150 KVA with FP = 0.85, what is the new efficiency?

b) Determine the apparent power of the transformer so that maximum efficiency occurs and calculate the value of this efficiency, considering FP = 1.

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Problem 92-7 Source: Example 2-2 - page 64 - FITZGERALD, A. E. , KINGSLEY, Charles Jr. , UMANS, Stephen D. - Book: Electric Machinery - 5th ed. - McGraw-Hill - 1990.

A 50 kVA, 2,400:240 V , 60 Hz distribuition transformer has a leakage impedance of 0.72 + j 0.92 Ω in the high-voltage winding and 0.0070 + j 0.0090 Ω in the low-voltage winding. At rated voltage and frequency, the admittance Y_φ of the shunt branch accounting for the exciting currents (0.324 - j 2.24) x 10^-2 mhos when viewed from the low-voltage side. Draw the equivalent circuit referred to:

a) the high-voltage side.

b) the low-voltage side.

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Problem 92-8 Source: Example 2-3 - page 66 - FITZGERALD, A. E. , KINGSLEY, Charles Jr. , UMANS, Stephen D. - Book: Electric Machinery - 5th ed. - McGraw-Hill - 1990.

The 50 kVA, 2,400:240 V transformer whose constants are given in the previous problem is used to step down the voltage at the load end of a feeder whose impedance is 0.30 + j 1.60 Ω. The voltage V₁ at the sending end of the feeder is 2,400 V.

Find the voltage at the secondary terminals of the transformer when the load connected to its secondary draws rated current from the transformer and the power factor of the load is 0.80 lagging. Neglect the voltage drops in the transformer and feeder caused by the exciting current.

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