Download Homework Set 3

Department of Electrical Engineering and Computer Science
EEL4205 Electric Machinery
Homework Set No. 3
Names: ____________________; _____________________; ____________________;
Problem 1.
The secondary winding of a transformer has a terminal voltage of vs (t )  282.8cos(377t )
V. The turns ratio of the transformer is 100:200 (n = 0.5) . The secondary current of the
transformer is is (t )  7.07cos(377t  36.87o ) . The impedances of this transformer
referred to the primary side are
Req  0.20 
RC  300 
X eq  0.750  X M  80 
(1) What’s the primary current of this transformer?
(2) What are its voltage regulation and efficiency'?
Answer:
(1)
(2)
MatLab code:
Problem 2.
A 20-kVA 8000/480-V distribution transformer has the following resistances and
reactances:
RP  32 
RS  0.05 
X P  45 
X S  0.06 
RC  250 k
X M  30 k
The excitation branch impedances are given to the high-voltage side of the transformer.
(1) Find the equivalent circuit of this transformer referred to the high-voltage side;
(2) Find the per-unit equivalent circuit of this transformer;
(3) Assume that this transformer is supplying rated load at 480 V and 0.8 PF lagging.
What is this transformer's input voltage? What is its voltage regulation?
(4) What is the transformer's efficiency under the conditions of part (3)?
Answer:
(1)
(2)
(3)
(4)
MatLab code:
Problem 3.
A 1000VA, 230/115V transformer has been tested to determine its equivalent circuit. The
results of the tests are shown below.
Open-circuit Test
VOC  230 V
Short-circuit Test
VSC  19.1 V
I OC  0.45 A
I SC  8.7 A
POC  30 W
PSC  42.3 W
All data given were taken from the primary side of the transformer.
(1) Find the equivalent circuit of this transformer referred to the low-voltage side of the
transformer.
(2) Find the transformer's voltage regulation at rated conditions and (a) 0.8 PF lagging,
(b) 1.0 PF, and (c) 0.8 PF leading.
(3) Determine the transformer’s efficiency at rated conditions and 0.8 PF lagging.
Answer:
(1)
(2) (a)
(b)
(c)
(3)
MatLab code:
Problem 4.
A 15kVA, 8000/230V distribution transformer has an impedance referred to the primary
of 80  j 300  . The components of the excitation branch referred to the primary side are
RC  350 k and X M  70 k .
(1) If the primary voltage is 7967 V and the load impedance is Z L  3.2  j1.5  , what
is the secondary voltage of the transformer? What is the voltage regulation of the
transformer?
(2) If the load is disconnected and a capacitor of  j 3.5  is connected in its place what
is the secondary voltage of the transformer? What is the voltage regulation of the
transformer?
Answer:
(1)
(2)
MatLab code:
Problem 5.
A 200 MVA, 15/200 kV, single-phase power transformer has a per-unit resistance of 1.2
percent and a per unit reactance of 5 percent (data taken from the transformer's
nameplate). The magnetizing impedance is j80 per unit.
(1) Find the equivalent circuit referred to the low-voltage side of this transformer;
(2) Calculate the voltage regulation of this transformer for a full-load current at power
factor of 0.8 lagging;
(3) Assume that the primary voltage of this transformer is a constant 15 kV, and plot the
secondary voltage as a function of load current for currents from no-load to full-load.
Repeat this process for power factors of 0.8 lagging, 1.0, and 0.8 leading.
Answer:
(1)
(2)
(3)
MatLab code:
Problem 6.
A 13,800/480 V, three-phase, Y- connected transformer bank consists of three identical
100-kVA 7967/480-V transformer. It is supplied with power directly from a large
constant-voltage bus. In the short-circuit test, the recorded values on the high-voltage side
for one or these transformers are
VSC  560 V
I SC  12.6 A PSC  3300 W
(1) If this bank delivers a rated load at 0.85 PF lagging and rated voltage, what is the
line-to-line voltage on the primary of the transformer bank?
(2) What is the voltage regulation under these conditions?
(3) Assume that the primary voltage of this transformer bank is a constant 13.8 kV, plot
the secondary voltage as a function or load current for currents from no-load to fullload. Repeat this process for power factors of 0.85 lagging, 1.0, and 0.85 leading.
(4) Plot the voltage regulation of this transformer as a function of load current for
currents from no-load to full-load. Repeat this process for power factors 0.85 lagging,
1.0, and 0.85 leading.
Answer:
(1)
(2)
(3)
(4)
MatLab code:
Problem 7.
A 100,000 kVA, 230/115 kV,    three-phase power transformer has a per-unit
resistance of 0.02 pu and a per-unit reactance of 0.055 pu. The excitation branch elements
are RC  110 pu and X M  20 pu .
(1) If this transformer supplies a load of 80 MVA at 0.85 PF lagging, draw the phasor
diagram for one phase of the transformer;
(2) What is the voltage regulation of the transformer bank under these conditions?
(3) Sketch the equivalent circuit referred to the low-voltage side of one phase of this
transformer. (Please scan and paste into this word file.)
(4) Calculate all of the transformer impedances referred to the low-voltage side.
Answer:
(1)
(2)
(3)
(4)
MatLab code: