TUTORIAL 3- Transformers
1. How many turns must the primary and the secondary windings of a 220V-110V,
60Hz ideal transformer has if the core flux is not allowed to exceed 5mWb?
2. Consider a single phase 2400/240V transformer in Figure 1. The primary is connected to
a 2200∠0° V source and the secondary is connected to a load impedance of 2∠36.9° Ω.
Ω
Figure 1
Determine the following
a) The secondary output current and voltage
b) The load impedance as seen from the primary side
c) The input and output apparent powers.
3. A 250 kVA, 11 000V/400V, 50Hz single-phase transformer has 80 turns on the
secondary. Assume the transformer is ideal. Calculate:
a) The values of the primary and secondary currents
b) The number of primary turns
c) The maximum value of flux, Фm.
4. A 10 kVA 2400/240V 60Hz transformer was tested with the following results: Power
input during short circuit test is 340W, power input during open circuit test is 168 W.
Determine the efficiency of the transformer at full load. Given the load power factor is
0.8.
5. A 1: 10 step-up transformer is placed at the generator end of the transmission line and a
10:1 step-down transformer is placed at the load end of the line as shown in Figure 2.
Determine the load voltage and the transmission line losses.
Figure 2
6. A 1000-VA, 230/115-V, transformer has been tested to determine its equivalent
circuit. The results of the tests are taken from the primary side as in table 1.
Table1.
Open-circuit test
Voc = 230 V
Ioc = 0.45A
Poc = 30W
Short circuit test
Vsc = 19.1 V
Isc = 8.7 A
Psc = 42.3 W
(i) Find and sketch the equivalent circuit of the transformer referred to
low-voltage side.
(ii) The transformer’s efficiency at rated conditions and 0.8 PF lagging.
Given Pcu= 10.6 W and Pcore = 32.0 W.
7. The secondary winding of a transformer has a terminal voltage of v s (t ) = 282.8 sin 377t
V. The turn’s ratio of the transformer is 100:200. If the secondary current of the
transformer is i s (t ) = 7.07 sin (377t - 36.87 0 )A . Given the impedances of this
transformer referred to the primary side are;
Determine the following:
i. The primary current of this transformer.
ii. The transformer’s voltage regulation and efficiency
8. A single phase transformer has the following specifications
20 kVA, 2400/240, 60Hz, load power factor=0.8 lagging, Rp= 0.8Ω, Xp=3Ω,
Rs=0.008Ω and Xs=0.03Ω.
a) Find the equivalent circuit parameters referred to primary. Draw the
equivalent circuit diagram and phasor diagram referred to primary
b) Find Vp
c) Find the voltage regulation of the transformer
9. A transformer 50Hz, 440/220V, the primary current, power and voltage are
1.25A, 50W and 440V under no load condition. Ignore the primary winding
resistance and reactance. Calculate:
a) Core current and resistance (Ic and Rc)
b) Magnetizing current and reactance (Im and Xm)
c) Power factor under no load condition
10. Tests are performed on a 1ф, 48 kVA, 2400/240V, 60Hz transformer and the
following results are obtained:
Open Circuit Test (HV side open)
Voc = 240V
Ioc = 3A
Poc = 120W
Short Circuit Test (LV side shorted)
Vsc = 150V
Isc = 10A
Psc = 400 A
a) Derive the parameters for the approximate equivalent circuits referred to the
Low Voltage and High Voltage Side. Then, sketch the equivalent circuit
diagram for both sides.
b) Express the excitation current as percentage of the rated current.
c) Determine the power factor for the no load and short circuit test.