Homework 7

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
Secondary load connected 745 W
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
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
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.
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 ([email protected])