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take note
TRANSFORMERS + SUBSTATIONS
For all the efficiency calculations a per-phase load voltage
V
2
of 220<0°
is used. All calculations performed for the per-phase circuit. The load
current
I
2
is given by the following calculation:
I
2
=
rated% ·
θ
(19)
where
θ
is given by the inverse cosines of the power factor, in this
case 30°. The formulas will be shown completely for the 60 % rated
load. The turns ratio
a
for the Y-Y configuration is 220/220 = 1.
At 60 % the per-phase load current in the primary winding is:
I
2
=
rated% ·
θ
(20)
The induced EMF in the secondary winding is:
E
2
=
V
2
+
[
I
2
(
R
]
L
+
jX
L
)
(21)
The induced voltage in the primary winding is given by:
E
1
=
a
E
2
30
(22)
The current in the primary winding of the transformer is given by:
I
p
=
30
(23)
The per-phase source current is thus given by:
I
2
=
I
p
+
E
1
(
+
)
(24)
where
R
c
– is resistance of the core
The per-phase voltage supplied by the source:
V
1
=
E
1
+ [
I
1
(
R
]
H
+
jX
H
)
(25)
The power input is calculated as follows:
P
out
=
R
e
[
V
2
I
2
]
(26)
Lastly, the efficiency calculated by means of equation:
=
(27)
The calculated data for the transformer is enclosed in
Table 3
.
Table 3: Transformer parameters.
Parameters
Impedance (
Ω
)
R
c
2 450
X
m
j
1707,32
R
H
2,04
R
L
2,04
X
H
j
3,27
X
L
j
3,27
Figure 5: The exact equivalent circuit of the transformer.
The core-loss resistance and the magnetising reactance is much
bigger than the winding resistances and the leakage reactance. The
reactance of the low voltage and high voltage is as expected since the
transformer has a one-to-one ratio and a Y-Y configuration was used.
The practical test was done on a 1 kVA, 380/380 V transformer.
The following measurements were taken down during the laboratory
test (see
Table 4
):
Table 4: The laboratory readings.
Parameters
Open circuit
Short circuit
Voltage (V)
120
20
Current (A)
0,05
1,5
Power 1 (W)
4
12,5
Power 2 (W)
2
15
Total Power (W)
16
27,5
As seen in
Table 4
, the short-circuit test was only done at a rated volt-
age and current and care was taken to not pass the rated current of
the transformer. As expected, there is a great current at a low voltage.
The efficiency of the transformer was calculated at a rated load
of 60 % to 90 % in 5 % increases and can be seen in
Table 5
.
Table 5: Transformer efficiency at different rated loads.
Rated load (%)
Efficiency (%)
60
88,160
65
88,720
70
89,188
75
89,580
80
89,909
85
90,186
90
90.419
s
s
3
3
V
2
V
2
a
R
c
jX
m
I
2
1 1
(
P
out
)
(
P
in
)
• Many plants are served by a supply system that includes
on-site transformers and substations.
• Transformer efficiency is an increasingly important pa-
rameter to understand, and the efficiency improves with
loading (within the specified operating range).
• Open and short circuit tests can be effectively used to
determine the machine parameter, and hence its efficiency.
Electricity+Control
August ‘15
40