University of Tehran
Electrical Machines II
Homework#7 (3phase Transformers)
Due: Monday 8 Dec.
1- A 3-phase transformer has a star-connected primary and a delta-connected secondary.
The primary/secondary turns ratio is 2/1. It supplies a balanced, star-connected load,
each phase consisting of a resistance of 4 ohm in series with an inductive reactance of
3 ohm.
a) If the transformer was perfect, what would be the value of the load impedance per
phase viewed from the primary terminals?
From a practical test, the following primary input-readings were taken:
Total power Line voltage Line current
Secondary short circuited 12W
7.75V
2A
Secondary load connected 745 W
220V
2.35 A
b) Deduce, from the readings, the equivalent circuit of the load viewed from the primary
winding and explain why it differs from (a).
2- The following are the light-load test readings on a 3-phase, 100-kVA, 400/6600-V,
star/delta transformer:
Open circuit: supply to low-voltage side 400V, 1250W
Short circuit: supply to high-voltage side 314V, 1600 W, full-load current
Calculate the efficiencies at full load, 0.8 PF and at half full load, U.P.F. Calculate
also the maximum efficiency. What is the percentage leakage impedance based on
100% = rated- V/rated I?
3- A 3-phase, 50-Hz transformer is to have primary, secondary and tertiary windings for
each phase. The specification is as follows: Primary to be 6600V and delta connected.
Secondary to be 1000 V and delta connected. Tertiary to be 440V and star connected.
Determine suitable numbers of turns to ensure that the peak flux does not exceed
0.03Wb.
If the secondary is to supply a balanced load of 100kVA at 0.8 P.F. lagging and the
tertiary is to supply a balanced load of 50 kW at U.P.F, determine the primary linecurrent and power factor for this condition. Neglect all transformer imperfections.
4- The following light-load, line-input readings were taken on a 3-phase, 150-kVA,
6600/440V, delta/star-connected transformer:
Open-circuit test: 1900W, 440V, 16.5 A
Short-circuit test: 2700 W, 315V, 12.5 A.
a) Calculate the equivalent-circuit parameters per phase, referred to the H.V. side.
b) Determine the secondary terminal voltages when operating at rated and half-rated
current if the load power-factor is 0.8 lagging. Calculate also the efficiencies for these
loads.
c) Determine the secondary terminal voltage when operating at rated current with a load
power-factor of 0.8 leading and calculate the efficiency for this condition.
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University of Tehran
Electrical Machines II
Homework#7 (3phase Transformers)
Due: Monday 8 Dec.
Project 7(Bonus)
Do research about one of following topics:
1- What are Tap-Changers and their applications for transformers?
2- Why are the tertiary windings being used in the 3-phase transformers?
3- Explain the different applications of the variety of 3-phase transformers
(D-Y, D-Z, Y-Y, D-D, Y-Z and Z-Z).
Be ready for the Midterm exam!
Good Luck.
H.Ahmadi (h.ahmmadi@ece.ut.ac.ir)
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