ECE 524:
Transients in Power Systems
Session 35; Page 1/10
Spring 2014
ECE 524: Lecture 35 - Transformer Examples
MVA  1000kW
Given a three phase, 24kV:230kV, 150 MVA delta to Y-grounded transformer. The
24kV winding has an X/R ratio of 10, and a leakage reactance of 5.5%. The 230kV
winding has an X/R ratio of 12 and a leakage reactance of 7%. The core loss term is
equivalent to 50kW per phase on the wye side with rated voltage across the core loss
resistor. The magnetizing inductance is 20k at rated voltage referred to the HV side.
VLV  24kV
ω  2 π 60Hz
VHV  230kV
Srated  150MVA
2
ZBLV 
VLV
Srated
ZBHV 
VHV
2
Srated
LV winding resistance and leakage reactance:
XLV  5.5%
XLVohm  XLV ZBLV
LLV 
RLV 
XLVohm
ω
XLVohm
10
XLVohm  0.21 Ω
LLV  0.56 mH
RLV  0.021 Ω
However, these values are for a Y equivalent winding, now get delta equivalent values:
LLVΔ  3 LLV
LLVΔ  1.681 mH
RLVΔ  3 RLV
RLVΔ  0.063 Ω
HV winding resistance and leakage reactance:
XHV  7%
XHVohm  XHV ZBHV
LHV 
XHVohm
ω
XHVohm  24.69 Ω
LHV  65.483 mH
ECE 524:
Transients in Power Systems
RHV 
Session 35; Page 2/10
Spring 2014
XHVohm
RHV  2.057 Ω
12
Shunt branches:
Pcore  3 50kW
VHV
Rcore 
Multiply by three since given per phase.
2
Pcore
Rcore  352.67 kΩ
Alternate way:
 VHV 


3 

Rcore_alt 
2
Rcore_alt  352.67 kΩ
50kW
Xm  20kΩ
Lm 
Xm
ω
Lm  53.05 H
But we don't enter Lm directly. If we are entering V vs I for the characteristic:
Vrms1 
Irms1 
VHV
3
Vrms1
Xm
Vrms1  132.79 kV
Irms1  6.6395 A
Or for peak flux versus peak current
Φmag 
Vrms1
2 π 60Hz
Imag_pk 
Φpk 
2 Irms1
2 Φmag
Φmag  352.24 Wb
Imag_pk  9.39 A
Φpk  498.14 Wb
Since the transformer model puts the magnetizing branch and core loss term on the
primary winding, we will need to put the primary winding on the HV side when entering data.
ECE 524:
Transients in Power Systems
Session 35; Page 3/10
Spring 2014
ATPDraw Implementation:
Using the saturable transformer:
MAG
LV
HV
Y
SAT
ECE 524:
Transients in Power Systems

Session 35; Page 4/10
Spring 2014
Note that the 0,0 point was added to get the appropriate plot, but the program will add it
internally when running the case.
132.8
U [kV]rms
99.6
66.4
33.2
I [A]rms
0.0
0.0
1.7
3.3
5.0
6.6
ECE 524:
Transients in Power Systems
Session 35; Page 5/10
Spring 2014
Autotransformer case:
V
V
AUTOTRANS
HV
360V
+
20
30
P
LV
S
v
-
400
[V]
300
200
100
0
-100
-200
-300
-400
0
10
(f ile lect36A.pl4; x-v ar t) v :HV
v :HV
-LV
v :LV
Ground Transformer Example
40
[ms]
50
ECE 524:
Transients in Power Systems
Session 35; Page 6/10
Spring 2014
VSEND
V1
VS
VR
U
U
FAUL
I
LIN3S
GNDP
S
P
S
P
S
I
P
Ground Transformer Resistor Current for SLG fault
15
[A]
10
5
0
-5
-10
-15
35
40
45
50
55
60
(f ile lect36B.pl4; x-v ar t) c:LVA -RNEG
Phase currents to the transformer for SLG fault (note all in phase):
[ms]
65
ECE 524:
Transients in Power Systems
Session 35; Page 7/10
Spring 2014
2.0
[A]
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
48
50
52
54
(f ile lect36B.pl4; x-v ar t) c:VSENDA-GNDPA
56
c:VSENDB-GNDPB
58
60
62
[ms]
64
c:VSENDC-GNDPC
Ground transformer resistor current for a three phase fault:
3.0
[pA]
0.8
-1.4
-3.6
-5.8
-8.0
0.00
0.02
(f ile lect36B.pl4; x-v ar t) c:LVA
0.04
-RNEG
0.06
0.08
[s]
0.10
ECE 524:
Transients in Power Systems
Session 35; Page 8/10
Spring 2014
PSCAD Implementation:
#1
#2
Main dialog box
 Note per unit leakage reactance
 No load losses are from open
circuit test
 Copper losses are from rated
current through the winding
resistances as above
 Note that ideal transformer not
selected.

Note that three phase transformer
uses RMS L-L voltages for ratio
and to convert per unit values to
ohms and mH
ECE 524:
Transients in Power Systems
Session 35; Page 9/10
Spring 2014


Saturation was not enabled. So
the only line that means anything
here is the magnetizing current.
Note that unless the transformer
is specified as ideal the
magnetizing current cannot be set
to zero.
Using default
transformer parameters
other than turns ratio
Vprim  240kV
Vsec  120kV
VS
Vprim#1
#2
Vload
1E6 [ohm]

R=0
Autotransformer case:
ECE 524:
Transients in Power Systems
Session 35; Page 10/10
Spring 2014
Main : Graphs
600
VS
Vprim
Vload
400
y (kV)
200
0
-200
-400
-600
0.075
0.100
0.125
0.150
0.175
0.200
0.225
0.250
0.275