Advances in Automatic Control, Modelling & Simulation
Single and three-phase shunt reactors loss measurement
BORUZ MIRCEA ALEXANDRU, MIRCEA PAUL MIHAI, MIRCEA ION
Department of Electrical Engineering, Energetics and Aerospace
University of Craiova
107, Blvd. Decebal, Craiova 200440
ROMANIA
mircea_boruz@yahoo.com, mmircea@elth.ucv.ro, imircea@elth.ucv.ro
Abstract: This paper discusses the relations between measurement of loss shunt reactors of five limb design
under three-phase and single phase excitation. Single phase loss measurement, added for all three phases; give a
higher reading than the symmetrical test. The ratio is stable over a wide range of voltage. It is therefore possible
to base measurements of losses at rated voltage on single phase measurement if a correction factor is
established by additional three-phase and single-phase measurements at reduced voltage.
Key-Words: loss measurement, correction factor, shunt reactor, single/three-phase
measured loss by the square of the ratio of rated
current to the current measured at a reduced voltage
level [1].
For three-phase reactor with a magnetic shield for
zero-sequence flux, by special agreement between
manufacturer and purchaser, a measurement of loss
may be made with single-phase excitation. In this
case, a comparison, at lower voltage, between
single-phase and three-phase measurement must be
made and a suitable correction factor agreed [2].
The method for determination of loss is subjected to
agreement between purchaser and manufacturer;
satisfactory documentation regarding accuracy and
reliability of the proposed method shall be provided.
As the power factor of a shunt reactor is normally
very low, loss measurement using conventional
wattmeter methods may be subjected to
considerable errors [1].
A bridge method may be used to advantage. A
calorimetric method can be used in special cases.
The loss in the various parts of the reactor (I2R loss,
iron loss and additional loss) cannot be separated by
measurements; it is thus preferable, in order to avoid
correction to reference temperature, to perform the
measurement when the average temperature of the
windings is practically equal to the reference
temperature. If this is impracticable, the additional
loss as well as the iron loss shall be deemed
independent of temperature [1].
If several units are to be tested it is recommended
that the unit on which loss measurement is carried
out as a type test at approximately reference
temperature, shall be measured at ambient
temperature also, thus establishing a temperature
coefficient for total loss (assuming linear variation).
Remaining units will be than measured at ambient
1 Introduction
The test for shunt reactors loss measurement is done
by using large capacitors (which are very expensive
because of their large number and also for their
large maintenance expenses). There might be cases
when a testing laboratory can not perform loss
measurement for these shunt reactors because they
do not have that high number of capacitors.
In this paper it will be presented a method for loss
measurement by using half of necessary capacitors.
For small power shunt reactor loss measurement can
be performed by applying three-phase excitation and
in this case losses can be measured by using
wattmeter on each phase. However there might be
cases when these losses can be also determined by
single-phase excitation but in this case there should
be calculated a correction factor between singlephase and three-phase excitation. The IEC 60076-6 /
2007 sub clause 7.8.6.1 says that for loss
measurement on single-phase excitation is possible
only with agreement between manufacturer and
purchaser.
2 Loss measurements according to
IEC 60076-6
The loss shall be measured at rated voltage and
rated frequency. The voltage shall be measured with
a voltmeter responsive to the mean value of voltage
but scaled the R.M.S. value of a sinusoidal wave
having the same value.
In exceptional cases, for example large rated power
and high system voltage, it may be difficult to meet
this test condition. In these cases, the loss at rated
voltage shall be obtained by multiplying the
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Advances in Automatic Control, Modelling & Simulation
temperature only and their loss figure shall be
corrected to reference temperature using the
temperature coefficient established on the type test
unit.
If at rated voltage the current measured is different
from the rated current the measured loss shall be
multiplied by the square of the ratio of rated current
to measured current [1].
3 Power frequency behavior of threephase shunt reactors under threephase and single-phase excitation
Figure 3. Voltage applied on phases U, V and W
The reactors are of gapped core design with
unwound and non-gapped outer core limbs. The
excitation cases to be considered are referred to
single-phase excitation (figures 1 and 2) and three
phase excitation (figure 3).
The significance of the outer limbs.
The outer limbs give the reactor certain properties:
When a single phase winding is energized, the flux
through it finds its return path through the lowreluctance paths of the outer limbs and very little –
bellow one percent – returns through an adjacent
gapped core limbs. This can be demonstrated by the
corresponding low induced voltage in the adjacent
phase winding.
In terms of circuit parameters we can express this by
saying that the mutual inductance or the coupling
factor between phases is low. The phase impedance
are practically independent on whether adjacent
phases are energized or not.
In terms of symmetrical impedance components the
zero-sequence or homopolar impedance is very
closely equal to the positive-sequence impedance.
.
Figure 1. Voltage applied on phase U
4 Anomaly of loss readings under
three-phase excitation
The equivalent circuit diagram for the complete yconnection reactor is as shown in figure 4. R1, r2, r3
represents the loss per limb, and L11, L22, L33 are
the single-phase inductance of each limb. L12, L23,
L31 are the mutual inductances between phases.
These parameters come in with negative sign,
because the coils are placed side by side with the
same winding direction, so that any flux component
from a first winding which intersects a second
winding will do this in the opposite (return)
direction.
Figure 2. Voltage applied on phase V
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Advances in Automatic Control, Modelling & Simulation
If a reactor is energized three-phase and its losses
are measured (which is done phase by phase) then
the recorded values in the three phases are likely to
differ, depending on marginally different inductive
coupling factors between phases, but the sum is
correct. The fact that these differences become
visible, although the coupling factors are low in
themselves is of course that the total per unit loss of
the reactor is down at only 2-3 parts per million.
Systematic difference between losses during
single-phase and three-phase excitation
Suppose that there were energized each phase
separately and add the three loss readings. We have
had figure 1 a two times for the two outer limbs –
and figure 2 once. We have energized a gapped limb
with windings and the whole ungapped frame
altogether three times.
SUM LOSSES fig. 1: 3 x (LIMB) + 3 x (FRAME)
When it was energized three-phase the frame makes
only one common contribution:
SUM LOSSES fig. 3: 3 x (LIMB) + (FRAME)
Already from this simple argument we can see that
there is a systematic difference and that the sum of
single-phase readings will be too high.
Figure 4. Shunt reactor- equivalent circuit diagram
In figure 5 it is drawn the phase diagram of figure 3
for the case when the reactor is energized with three
equal phase currents spaced 120 degrees apart. The
main inductance vector is truncated – its real
magnitude is 102 – 103 times larger than the other
vectors. The added coupling vectors are all oriented
so as to increase the effective phase inductance, but
they also represent contribution in square
(quadrature), which means that the effective loss per
phase may be influenced. It is easy to see from the
figure that a square (quadrature) contribution results
if the two coupling vectors are unlike. It is also
possible to verify, however, that the sum of the
aberrations in the three phases must cancel out,
because every coupling vector appears twice – with
opposite relative orientation – in the diagram.
5 Algorithm for single-phase loss
measurement
a. Before mounting the windings on the magnetic
core the factory should perform a test for iron loss
(PFe) measurement by using “test spire”;
b. Three-phase loss measurement at reduced voltage
at ambient temperature (10% - 20%) x UN;
c. Single-phase loss measurement at reduced voltage
(same voltage as for three-phase excitation split by
√3) for each phase;
d. Determination of loss correction factor:
(1)
Where:
P3f – represents losses for three-phase excitation;
P1f – represents losses for single-phase excitation;
e. Single phase loss measurement at ambient
temperature at UN/ √3 and calculation of total losses
(Ptot):
f. Correction of total losses (Ptot
consideration the measured current:
at IN)
(2)
taking in
(3)
g. Calculation of copper losses al reference
temperature (75°C):
Figure 5. Phase diagram of the studied shunt reactor
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Advances in Automatic Control, Modelling & Simulation
(4)
h. Calculation of supplementary losses (PS) at
ambient temperature:
PS = (f) – (g) – (a) [kW]
(5)
i. Recalculation of supplementary losses at
reference temperature:
(6)
j. Calculation of total losses:
(7)
6 Study case
It is considered a shunt reactor having the
following parameters:
Rated frequency: 50 Hz;
Rated power: 100 000 kVar;
Maximum power: 110 250 kVar;
Vector-group symbol: YN;
Rated voltage: 400 000 V;
Maximum voltage: 420 000;
Rated current: 144.3 A;
Maximum current: 151.6 A
Figure 6. Shunt reactor under test – vector group
Where:
Lx – reactor inductance [H];
Rx – resistive losses on reactor [Ω];
U – ratio current transformer;
M3 – mutual inductance [H];
Cn – standard capacitor [pF];
C4, R4 – measured values on bridge [µF], [Ω].
Figure 7. Test circuit diagram
In table 1 there are presented the measured values:
Table 1 – Measurement results
Applied on reactor
Voltage
[kV]
Current
[A]
60.8
60.8
60.8
38.0
38.5
38.0
60.8
60.8
60.8
37.5
38.0
37.8
230.94
230.94
230.94
143.5
146.5
144.5
242.49
242.49
242.49
152.0
154.5
152.0
121.24
81.0
ISBN: 978-1-61804-189-0
Measured Shearing
bridge
U
Lx
Rx
R4
C4
[Ω]
[µF]
[H]
[Ω]
Three-phase application 105.4 kV
98500
14.487
40
5.109
3.581
110200
14.455
40
5.098
3.200
177000
14.470
40
5.103
1.993
Single –phase application 105.4/√3 kV
92900
14.482
40
5.108
3.796
94800
14.447
40
5.095
3.720
105200
14.466
40
5.102
3.352
Single –phase application 400/√3
92800
14.425
40
5.087
3.800
95000
14.400
40
5.079
3.712
106800
14.418
40
5.085
3.302
Single –phase application 420/√3
92200
14.420
40
5.086
3.825
96300
14.390
40
5.075
3.662
106500
14.407
40
5.081
3.312
Single –phase application 420/√3 kV
138300
14.497
40
5.113
2.550
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Impedance
ωLx
Losses
[Ω]
[kW]
[°C]
1605.1
1601.6
1603.3
5.15
4.68
2.87
31.6
31.6
31.6
1604.6
1600.7
1602.8
5.39
5.37
4.81
31.6
31.6
31.6
1598.3
1595.5
1597.5
78.80
78.72
68.89
31.6
31.6
31.6
1597.7
1594.4
1596.3
88.24
86.06
76.46
31.6
31.6
31.6
1606.2
15.59
43.4
Advances in Automatic Control, Modelling & Simulation
Applied on reactor
Voltage
[kV]
242.49
121.24
Current
[A]
152.5
80.0
Measured Shearing
bridge
R4
C4
[Ω]
[µF]
93000
14.410
139300
14.488
U
Lx
Rx
Impedance
ωLx
40
40
[H]
5.082
5.110
[Ω]
3.792
2.532
[Ω]
1596.6
1605.2
Calculation of shunt reactor loss and loss correction
factor
a. Before mounting the windings on the magnetic
core the factory performed a test for iron loss (PFe)
measurement by using “test spire”;
PFe = 46.8 kW
b. Three and single phase application at 26.4% x
Un (105.4 kV)
Losses 3φ at 31.6°C = 5150 + 4680 + 2870 =
12700.0 W at 105.4 kV;
Losses 1φ (phase U) at 31.6°C = 5390.0 W at
105.4/√3 kV;
Losses 1φ (phase V) at 31.6°C = 5370.0 W at
105.4/√3 kV;
Losses 1φ (phase W) at 31.6°C = 4810.0 W at
105.4/√3 kV.
c. Shunt reactor loss correction factor calculation:
[kW]
87.83
15.30
[°C]
43.4
43.4
i. Recalculation of supplementary losses
reference temperature
PS(75°C) = 27643.9.4 W
j. Calculation of total losses:
PTOT = 195227.8 W
at
7 Conclusions
- There are possibilities to measure shunt reactor
losses under single-phase excitation but there is
necessary cu determine a loss correction factor by
doing a comparison of losses under single and
three-phase voltage application;
- By using this test method there is not necessary to
use many capacitors for performing loss
measurement on shunt reactors;
- Three-phase loss measurement are smaller than
single phase-loss measurement;
- It is evident that iron loss ratio is subjected to
moderate variation from design to design,
depending on geometrical proportions of the
magnetic circuit;
- The resulting correction factor for single-phase
losses is also dependent on the ratio between
copper loss and iron loss.
d. Single phase application at Un (400/√3 kV):
Losses phase U at 31.6°C = 78800.0 W;
Losses phase V at 31.6°C = 78720.0 W;
Losses phase W at 31.6°C = 68980.0 W.
e. Total losses at nominal current (31.6°C) Ptot = k x
(PU+PV+PW) = 184749.5 W
f. Correction of total losses (Ptot at IN) taking in
consideration the measured current:
Ptot at IN = 136675.8 W
al reference
g. Calculation of copper losses
temperature (75°C) knowing that IN = 144.3A and
measured resistance R75°C=1.9463Ω.
PCu = 121580.4 W
h. Supplementary losses (PS) at ambient
temperature:
PS = 32144.1 W
ISBN: 978-1-61804-189-0
Losses
References:
[1]. IEC 60076/6 - 2007, Power transformers – part
6: Reactors, sub clause: 7.8.6 Measurement of
loss (routine test, special test);
[2]. CEI 289 / 1988, Reactors, sub clause 8.7,
Measurement of loss;
[3]. Rapport ZK 82 – 51/19.82 issued by ASEA
Brazil;
[4]. Rapport no. 1ZBR 07-0270 / 2007.
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