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Transformer Tertiary Stabilizing Windings. Part I: Apparent power rating
Conference Paper · September 2012
DOI: 10.1109/ICElMach.2012.6350213
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Transformer Tertiary Stabilizing Windings.
Part I: Apparent Power Rating
Patricia Penabad-Duran, Xose M. Lopez-Fernandez, Casimiro Alvarez-Mariño
Abstract -- This paper presents a calculation method for the
apparent power rating of Tertiary Stabilizing Winding (TSW)
of power transformers, which is scarcely discussed in the
literature. The objetive of the work is to offer an appoach for
the dimensioning of TSWs from the knowledge of expected
unbalanced load conditions. For that purpose, the equivalent
circuit model of a three-winding transformer for single-phase
load and single phase-to-ground fault study is discussed, where
zero sequence impedances are determined by means of several
proposed tests. A practical application is presented and the
equivalent circuit model is validated with Finite Element
Method (FEM) computations. A companion paper which
complements this work evaluates the influence of TSWs on the
overheating hazard on tank walls under unbalanced load
conditions.
Index Terms-- Leakage flux, Zero sequence current, Threephase transformer, Core type, Symmetrical components,
Equivalent circuit, Tertiary stabilizing winding. 1
I.
INTRODUCTION
W
ITH the advent of the three-phase system, two
alternative methods of transformer windings
connection were offered (ie. the Delta and Wye
connections). The Wye connection offers some advantages
such as it provides two different values secondary voltages,
and it makes possible to ground all three phases
symmetrically at a common point. However, it did not take
long to the industry to discover one problem after another
arising from the Yy-connected transformers [1]. For many
years it has been a common practice to include a Tertiary
Stabilizing Winding (TSW), particularly in Yy-connected
transformers. The TSW, which is not intended to connect
any load, is meant instead for purposes such as stabilizing the
neutral point of the fundamental frequency voltages, to
protect the transformer and system from a excessive thirdharmonic, and to provide an internally closed circuit for zero
sequence currents [2]. This practice has been followed so
closely for so many years that it is generally taken for
granted that the stabilizing winding is a necessary part of
such transformers [3]. Whether it is necessary or even
desirable to include a stabilizing winding in all cases,
regardless of the system characteristics and conditions is
discussed in [4]. Nevertheless, it has been generally accepted
never making any winding of a multi-winding transformer
smaller than 35% of the rating of the largest winding [5].
An efficient dimensioning and even the decision on the
actual need of TSW require an appropriate knowledge of
expected unbalanced load conditions on the main windings
and their consequences. The authors purpose is to contribute
P. Penabad-Duran is with Dept. of Electrical Engineering, University of
Vigo, ETSEI, 36210 Vigo, Spain.
X. M. Lopez-Fernandez is with Dept. of Electrical Engineering,
University of Vigo, ETSEI, 36210 Vigo, Spain (e-mail:
xmlopez@uvigo.es).
C. Alvarez-Mariño is with Dept. of Electrical Engineering, University
of Vigo, ETSEI, 36210 Vigo, Spain.
978-1-4673-0142-8/12/$26.00 ©2012 IEEE
with this paper (Part I), as the first part of a work presenting
an approach for the dimensioning TSWs on Yy-connected
transformers. In the second part of the work (Part II),
presented on a companion paper [6], the thermal overheating
hazard in tank walls due to the presence of the zero sequence
flux, arising under unbalanced load conditions, is evaluated
with and without the presence of TSW. Delta-connected
TSWs of Yy-connected transformers are referred to illustrate
the above discussion, and deserve further attention, not only
because of their inherent importance, but also because they
are not covered specifically by the standards.
The aim of this paper is to clearly describe calculation
strategies for the dimensioning of TSW apparent power
rating. For that, two alternatives of calculation are presented
in the following sections. One is the use of an Equivalent
Circuit (EC) based on symmetrical components and the
second is based on the FEM. A practical application which
illustrates the dimensioning of TSWs is presented where both
methods are compared for validating the results.
II.
TERTIARY STABILIZING WINDINGS DIMENSIONING
When used in three-phase systems, transformer windings
are usually Y-connected. For Y-connected main windings it
has become axiomatic to add in each three phase unit a deltaconnected TSW of 35% of the equivalent size of one of the
other two windings (usually the larger). If a delta-connected
TSW is to be used, its size is an important consideration. The
35% rule is much overworked in many cases and may set a
trap for the unsuspecting user. Then, two questions arise to
be considered: Is the tertiary winding needed? If it is needed,
what should be the size?
The purpose of the TSW might be firstly to stabilize the
neutral when unbalanced line-to-neutral single-phase loads
are supplied, and secondly to suppress third-harmonic
voltages. If these last were the only reasons for the TSW its
size could be very small. But in the case of accidental fault a
large current would flow in TSW with disastrous results.
Strictly, there is no definite relation between the thermal
and the short-circuit rating of windings, based on their ability
to store heat and withstand mechanical stresses respectively.
In addition to the short circuit duty, TSWs shall be designed
to withstand the thermal duty of the circulating current
resulting from continuous and temporary load or voltage
unbalance on the main windings. In case no continuous
thermal duty can be established from the users specification,
the manufacturer should design TSWs to be large enough to
carry zero sequence currents caused by a full single-phase
load in the secondary winding.
Since the TSW is not intended to supply any load, then
the possibility of three-phase fault disappears and the TSW
would need to be large enough only to carry zero sequence
currents caused by line-to-neutral faults [3]. Therefore, to
safely attain this economy of establishing the minimum
permissible TSW apparent power rating requires the
2362
prediction of zero sequence currents and it should be based
on the short-circuit duration time.
The final size should withstand the thermal duty for the
specified dimensioning criteria and should be capable of
withstanding the short circuit forces. Based on this, an
amount of copper (or A/mm2 or Watts/kg) and the apparent
power rating can be assigned to the TSW.
In this paper single-phase load and single phase-to-ground
fault currents are calculated on core type transformers by
means of an EC as well as FEM. On the next step, the
thermal performance under these conditions is calculated and
based on the maximum permitted windings temperature an
approach to the dimensioning of TSW is presented.
Moreover, in the particular case of a well-grounded
system, that is one having low zero sequence impedance, will
relieve to some extent the zero sequence current on the
tertiary of the transformer. For this reason it is also necessary
to know the maximum zero sequence impedance
characteristics of the systems that are to be connected to the
transformer if an exact prediction of the necessary size of the
tertiary winding is to be calculated [3].
The real impact of the zero sequence flux, arising in
unbalanced conditions, is scarcely discussed and relevant
information is difficult to find [4]. Authors presented in [9] a
method for the calculation of zero sequence flux over the
tank wall and cover, and discuss its overheating hazard
consequences on a companion paper [6].
III. ZERO SEQUENCE PERFORMANCE
The solution of unbalanced conditions in three-phase
systems can be obtained applying the symmetrical
components. Thus, any unbalanced three-phase currents or
voltages can be formulated in terms of positive, negative and
zero sequence components. In the particular case of
transformers supporting asymmetric faults and loads,
significant zero sequence current might occur for some threephase connections. This current induces a zero sequence flux
in the core resulting in two relevant consequences. The first
one is that unless a magnetic return path for this flux is
provided, the zero sequence flux returns outside the core,
closing its path over tank walls and cover, inducing eddy
currents and causing the heating of those structural metal
elements [4]. The second one is the risk of induced phase
overvoltage. The existence of zero sequence flux either
within or outside the core does not only depend on the
winding connections but also on the core configuration and
the system characteristics.
A delta-connected TSW has little impact on the positive
and negative sequence impedance network. However, it has
large impact on the zero sequence network as it can
effectively cancel or diminish the zero sequence flux (ie. a
circulating current around the delta winding provides
compensating zero sequence ampere-turns). Therefore,
transformer TSW is directly related with the zero sequence
performance, and it is classically modelled by its zero
sequence impedance.
Regarding the magnetic core, three-legged three-phase
core type transformers present a special problem with respect
to zero sequence impedance characteristics. For Yyconnected transformers, the magnetic circuit can be
considered as open circuit, since there is no circuit for the
induced zero phase currents to flow. Three-legged
transformer cores are open magnetic circuits to zero
sequence magnetizing flux, as opposed to five-legged cores
(closed circuits) on which the outer legs provide a return
path for zero sequence flux [8]. Hence, the zero sequence
magnetizing impedances on three-legged cores are
comparatively small and zero sequence magnetizing currents
cannot be assumed to be insignificant. But if a deltaconnected TSW is added to any Yy-connected transformer,
the differences in characteristics due to the two types of core
practically disappear. Because a delta-connected winding
forms a comparatively low short-circuit impedance to zero
sequence and third-harmonic voltages, it makes little
difference whether the magnetic circuit is open or closed, as
long as the delta connection is present [4], [8].
IV. TSW UNDER UNBALANCED CONDITIONS FROM EC
To analyse the normal operation, the symmetrically
supplied and loaded three-phase transformer is fully
described by positive-phase sequence system. Under
unbalanced conditions the transformer operation can be
advantageously analysed using a transformation into
symmetrical components [5]. For this, the single-phase EC of
the zero sequence system is additionally needed.
The particular study of interest of this paper is focused on
Yy-connected transformers with delta-connected TSW. The
positive, negative and zero sequence ECs, as well as the
proposed tests for their impedance calculation are described
in this section. Thus, positive, negative and zero sequence
ECs interconnection for single-phase load and single phaseto-ground fault currents calculation is presented. Note that
the magnetising reactance is neglected in the three sequences
due to the presence of the delta-connected TSW [4], [8].
A.
Zero Sequence Impedance Tests for YNyn Transformers
The zero sequence impedance is different depending on
the transformer construction. It is dependent upon the path
available for the flow of flux generated by equal and inphase currents in the three phases. Zero sequence impedance
for transformer banks is equal to the positive and negative
sequence and it is the transformer leakage impedance. It does
not occur the same in the case of three phase core type
transformers, where the core does not provide an iron flux
path for zero sequence.
A three-winding transformer has zero sequence
impedance for the primary, secondary, and tertiary windings.
The equivalent circuit for the zero sequence impedance of a
YNyn-connected transformer with delta-connected TSW is
illustrated in Fig. 1. In this EC, Z0P, Z0S and Z0T are the zero
sequence impedances in p.u. values of the primary,
secondary and tertiary windings respectively.
The zero sequence impedance characteristics of a
transformer can be determined by means of a set of
impedance tests [10]. Thus, to calculate the three unknown
zero sequence impedances (Z0P, Z0S and Z0T) at least three
equations stated from three tests are needed. Figures 2a to 5a
show four possible connection schemes for testing, though
only three are actually needed. Figures 2b to 5b show the
zero sequence ECs for the connection schemes in Figures 2a
to 5a. Table I shows the relationship between zero sequence
impedances from each test. The described tests provide
sufficient information for determining the branch values of
the three-terminal zero sequence EC shown in Fig. 1.
2363
Fig. 1. Equivalent circuit for zero sequence impedance in p.u. values.
(a)
(a)
(b)
Fig. 4. a) Test 3 and b) equivalent zero sequence circuit for test 3.
(b)
Fig. 2. a) Test 1 and b) equivalent zero sequence circuit for test 1.
(a)
(b)
Fig. 5. a) Test 4 and b) equivalent zero sequence circuit for test 4.
(a)
TABLE I
RELATIONSHIP BETWEEN ZERO SEQUENCE IMPEDANCES FOR EACH TEST
(b)
Fig. 3. a) Test 2 and b) equivalent zero sequence circuit for test 2.
The test source can be connected either at the primary or
secondary windings. Tests are supplied by a single phase AC
source, and there is no need for a three phase AC source for
the measurement of the zero sequence impedance.
It should be noted that in the case of three-legged core
type construction transformers, the zero sequence
impedances of the primary and secondary windings are
influenced by the presence of the transformer tank. The tank,
which encloses the complete core and coil structure, acts as a
magnetically coupled short-circuited turn as far as zero
sequence quantities are concerned.
B.
TEST
ZERO SEQUENCE IMPEDANCE
TEST 1
Z0P + Z0T
TEST 2
Z0P + (Z0S || Z0T )
TEST 3
(Z0S + Z0T)
TEST 4
Z0S + (Z0T || Z0P)
Positive/Negative Sequence Impedance Test
The zero sequence impedance tests have to be completed
with the positive and negative sequence tests as shown in
Fig. 6a. In this EC, Z1P, Z1S and Z1T are the positive/negative
impedance of the primary, secondary and tertiary windings
respectively, all of them in p.u. values. The positive/negative
sequence EC and the measured impedance can be seen in
Fig. 6b and Table II. The measurement of the positive
sequence impedance requires a three phase AC source.
2364
(a)
(b)
Fig. 6. a) Test 5 and b) positive/negative sequence equivalent circuit.
Fig. 7. Positive, Negative, and Zero sequence networks interconnected to
represent a single line-to-ground fault on the low voltage side or singlephase load condition.
TABLE II
POSITIVE/NEGATIVE SEQUENCE IMPEDANCE FOR TEST 5
TEST
POSITIVE/NEGATIVE IMPEDANCE
5
Z1CC= Z2CC= Z1P + Z1S
Thus, for the reference phase
Va = Va1 + Va 2 + Va 0
(3)
and
Note that the impedance to negative sequence current is
always equal to the impedance to positive sequence currents,
and the ECs are similar except that the phase shift, if any is
involved, will always be of the same magnitude for both
sequences voltages and currents but in opposite directions.
ECs Interconnection for Single Phase Faults and Loads
This work is prompted by the need to correctly model and
simulate the unbalanced operation of power transformers for
the apparent power rating of TSWs. Three-phase currents
can be already solved into three sets of symmetrical
component vectors [11] as in (1)
Va = I a Z F
(4)
where ZF is either the fault impedance in the case of single
phase-to-ground short circuit or the phase impedance in the
case of single-phase load in p.u. values.
From (2) and (4), yields
C.
Va = I a 0 3 Z F = I a1 3 Z F = I a 2 3 Z F
(5)
Therefore, under the above conditions, it can be easily
seen from (2) and (5) that suitable positive, negative, and
zero sequence equivalent circuits are interconnected in
series, as shown in Fig. 7.
D.
I a = I a1 + I a 2 + I a 0 = I1 + I 2 + I 0
2
I b = I b1 + I b 2 + I b 0 = α I1 + α I 2 + I 0
(1)
Zero Sequence Current in TSW
From the conditions described in the previous section and
the circuit shown in Fig. 7, the current thought the reference
phase equivalent circuit in p.u. values is calculated as
2
I c = I c1 + I c 2 + I c 0 = α I1 + α I 2 + I 0
where Ia, Ib and Ic are the vectors of the phase currents,
the subscripts 0, 1 and 2 refer respectively to the zero,
positive, and negative sequence components, and the
operator α=e2/3πi is the phase shift vector. For their
representation in single-phase faults and load current
calculations, where a is the reference phase (short-circuited
phase or loaded phase), the current through the other phases
Ib and Ic are equal to zero. Therefore from (1)
I a1 = I a 2 = I a 0
1
=
3
I a1 = I a 2 = I a 0
=
Va
Z 1cc+ Z 2cc+ Z 0+3 Z F
where
Z 0 = Z 0 S + (Z 0T || Z 0 P )
(7)
The current in the primary side in the reference phase a is
then calculated as
I P = I a1 + I a 2 + I 0 P
Ia
(6)
(2)
A three phase set of unbalanced voltage vectors Va, Vb
and Vc can be solved into three balanced or symmetrical sets
of vectors in a manner analogous to that just given for the
resolution of currents [11].
2365
(8)
The current in the secondary side is calculated as
I S = 3 I a1
(9)
And the current in the tertiary winding is
I T = I 0T
(10)
In the case of full single-phase load on the secondary side
the equivalent circuit is that shown in Fig. 7, being ZF the
value of the nominal single-phase load impedance, and Va
the rated voltage, being both in p.u. value equal to 1.
For a single phase-to-ground fault if we ignore earth fault
resistors, reactors or system impedances, ZF=0 in Fig. 7 and
the current flowing through the circuit is then calculated as
from (6).
When working with the equivalent circuit, calculated
currents are in p.u. values and have to be multiplied by the
base currents IN of each winding (either for the primary P or
the secondary S) in order to obtain their real values
IN =
SN
(11)
3U N
Fig. 8. Modeled fictitious transformer geometry.
In the case of the tertiary winding, the p.u. current I0T is
calculated referred to the primary winding and then
multiplied by the transformation ratio in order to calculate
the real value of the current IT in Amperes as
I T = I 0T ·I PN
NP
NT
(12)
where IPN is the base current of the primary winding and
NP and NT are the turns number of the primary and tertiary
windings, respectively.
V.
TSW UNDER UNBALANCED CONDITIONS FROM FEM
Fig. 9. Electric Circuit to be coupled in the FEM model.
As an alternative way to the EC described in Section IV,
the FEM is also used to build the model of the considered
transformer to determine phase currents under unbalanced
conditions, and calculate the TSW apparent power rating. In
this paper, the FEM transformer model also serves to
compare and validate the results obtained from the EC.
The representative transformer geometry to be modeled is
shown in Fig. 8, where each phase windings (U, V and W)
are wounded around a core leg. For current calculations
under unbalanced conditions, electromagnetic coupled
analyses are carried out. The coupled circuit is shown in Fig.
9. Each winding region in the FEM model is associated to a
coil conductor in the electric circuit. Taking into account that
the model is a plane model, each winding is represented by
two regions (IN and OUT), and therefore two associated
coils. This proposed model includes the series inductances to
incorporate the presence of the real 3D leakage flux. The
leakage inductances can be previously assessed by
comparing a plane with an axisymmetric model of one of the
transformer phases. R_LV are the load resistances for each
phase, and R_TW are resistances which act as switches,
either to connect or disconnect the tertiary windings.
In the case of TSW apparent power rating, the current
flowing through the tertiary winding IT is computed under
full single-phase load condition. For that, the resistance value
R_LV connected on the loaded phase (the reference phase) is
the rated phase load, being open-circuited on the other two
phases. In the case of current calculation under single phaseto-ground fault, the resistance value on the reference phase
R_LV is set to zero (short-circuited). The resistance values
R_TW are set to zero in order to have the tertiary winding
connected and allow the flow of zero sequence currents.
VI. THERMAL RATING OF TERTIARY STABILIZING WINDINGS
Transformer TSWs shall be designed to withstand the
thermal duty of carrying zero sequence unbalanced currents
caused either by permanent load or temporary fault in the
secondary winding. The worst case of permanent load would
be a full single-phase load, and of temporary fault a single
phase-to-ground fault with its duration taken into account.
Once the TSW current IT is computed under full singlephase load condition either from EC (12) or FEM
simulations, the apparent power ST of the TSW can be
calculated as
ST = 3 I T U NT
=
3 I T U NP
NT
NP
(13)
where UNP and UNT are the rated voltages of the primary
winding and TSW respectively. Moreover, the TSW current
IT from (12) can be written in terms of the current density JT
(A/m2) yielding to
J T s cu N T = I 0T I PN N P
(14)
where scu is the cross section of the winding copper
conductors. In the case of thermal apparent power rating of
TSW, its dimensioning consists on assigning volume of
copper Vcu (acting either on scu or NT), so that the winding is
capable to store the generated heat during temporary single
phase-to-ground fault or continuous full single-phase load
conditions, protecting the tertiary against destructive
overheating that can damage the windings insulation [2].
This procedure permits to asses average temperatures for the
TSW and dimensioning its apparent power to comply with
maximum allowable temperatures.
2366
TABLE III
COMPUTED LEAKAGE INDUCTANCE OF EACH WINDING
SYMBOL
WINDING
TABLE V
TEST MEASUREMENTS
INDUCTANCE (H)
HV
L_HV
0.27307735
LV
L_LV
-0,0000325
TW
L_TW
0,00086858
TEST
V0 - TEST
VOLTAGE
(V)
I0 - CURRENT
FROM
FEM TESTS (A)
CALCULATED
IMPEDANCE
(OHM)
CALCULATED
IMPEDANCE IN
P.U. VALUES
1
100
0.487
204.95
0.183
2
100
0.608
164.44
0.147
3
100
154.7
0.646
0.046
4
100
196.5
0.508
0.037
5
100
0.557
179.46
0.160
TABLE IV
FEM MODEL VALIDATION
OPEN CIRCUIT TEST
V1
V2
V3
Nameplate rated values
224250 V
24900 V
13800 V
FEM computation
224250 V
24921 V
13757 V
RATED LOAD CONDITION
I1
I2
I3
Nameplate rated values
115.9 A
1043.5 A
≈0A
FEM computation
113.1 A
1029.3 A
8.05 A
VII.
TABLE VI
EQUIVALENT CIRCUIT IMPEDANCES
PRACTICAL APPLICATION AND RESULTS
As practical application of the problem described in the
previous sections a 45 MVA YNyn0 (d1) transformer of
224.25 kV / 24.9 kV / 13.8 kV is considered. The turns
number for the primary or High Voltage (HV) winding is
1250, for the secondary or Low Voltage (LV) winding 139
and for the Tertiary Winding (TW) 133 turns. The HV and
LV windings, are both Wye connected with neutral points
accessible. The HV winding is connected to the local grid,
while the LV is connected to the consumer load. It has a
delta-connected TSW, not connected to any load, with the
purpose to allow the flow of the zero sequence current during
unbalanced conditions.
Since there are not available any transformer test values to
calculate the sequence impedances of the EC, impedance
tests are performed by means of a FE model. Therefore, the
FE transformer model described in Section V serves on one
hand to carry out impedance tests, and also to validate the
transformer EC.
Table III shows the calculated leakage inductance of each
winding, according to Section V. R_LV are resistances
which perform the double role of being load resistances for
each phase, or together with R_TW are resistances which act
as switches, either to connect or disconnect the secondary
and tertiary windings respectively during the sequence
impedance tests, according to IV.A and IV.B subsections.
In order to validate the FEM transformer model, the open
circuit test is carried out and measured voltage values are
compared to the transformer nameplate rated values.
Moreover, computed currents when a balanced three-phase
load is connected to the transformer are compared to the
transformer nameplate rated values. Results are shown in
Table IV and validate the accuracy of the FE model.
A.
Impedance Test Results
Tests for the calculation of equivalent circuit impedances
are performed by means of FEM simulations, as already
mentioned. The model geometry is described in Section V
and shown in Fig. 8. The coupled electrical circuit varies
depending on each test as shown from Fig. 2b to 6b.
SYMBOL
IMPEDANCE IN P.U. VALUES
Z0P
0.1421
Z0S
0.0056
Z0T
0.0412
Z1CC=Z2CC
0.1605
Results from Tests 1 to 5 are shown in Table V, where
test impedances are calculated in Ohms and also in p.u. value
dividing by the base impedance value of each winding. The
base impedances are ZPN=13.78 Ohm in the HV side and
ZSN=1117.51 Ohm in the LV side. By solving the impedance
equations from Table I and Table II, the equivalent circuit
impedances are calculated and results are shown in Table VI.
B.
TSW Current Calculation and Apparent Power Rating
Fault currents are calculated in three winding, three-limb,
core type YNyn connected transformers by means of the
equivalent circuit shown in Fig. 7. Single phase-to-ground
fault (ZF=0) and full single-phase load (ZF= ZPN=13.78 Ohm)
unbalanced conditions are computed. Primary, secondary and
tertiary currents are calculated from (8)-(12) under both
conditions and results are shown in Table VII.
Computed currents by means of EC are compared to those
numerically calculated by FEM, as seen in Table VII. The
relative error is indicated, showing there is good agreement
between results obtained from EC and FEM. Proved the
accuracy of the EC method, it serves as an useful approach to
current calculation under unbalanced conditions for the
estimation of the TSW apparent power rating.
Therefore, from the calculated current values under full
single phase load condition shown in Table VII, the apparent
power of the TSW is calculated from (13). In the case of the
TSW current calculated from EC, IT=252.33 A and being the
TSW rated voltage UNT=13.8 kV, the required TSW apparent
power is 6.03 MVA, far lower from the 35% of the MVA
apparent power of the main windings (15.75 MVA).
C.
TSW Dimensioning
TSW dimensioning consists on assigning volume of
copper Vcu (acting either on scu or NT), so that the winding is
capable to store the generated heat during temporary single
phase-to-ground fault or continuous full single-phase load
conditions, so that the windings temperature does not exceed
the maximum permitted of 80ºC that can damage the
windings insulation [12]. For that, coupled magneto-thermal
FEM simulations are carried out, to estimate the windings
2367
TABLE VII
WINDINGS CURRENT UNDER UNBALANCED LOAD CONDITIONS
UNBALANCED
CONDITION
Single phase
load
Single phaseto-neutral
fault
CALCULATED
VALUE FROM
EC
CALCULATED
VALUE FROM
FEM
RELATIVE
ERROR
(%)
HV
77.05 A
84.74 A
-9.98 %
LV
935.51 A
1033.87 A
-10.51 %
TSW
252.33 A
239.28 A
5.17 %
HV
718.62 A
724.5 A
-0.82 %
LV
8724.29 A
8847.85 A
-1.4 %
TSW
2353.14 A
2045.4 A
13.08 %
WINDING
TABLE VIII
WINDINGS TEMPERATURE UNDER UNBALANCED LOAD CONDITIONS
UNBALANCED
CONDITION
Continuous single
phase load
(time t=2s)
REDUCED COPPER
VOLUME MODEL
VCU
71.5% VCU
HV
66.73 ºC
LV
79.72 ºC
TSW
Temporary single
phase-to-neutral fault
MODEL
ORIGINAL
WINDING
51.68 ºC
56.12 ºC
HV
70.14 ºC
LV
85.55 ºC
TSW
68.26 ºC
designed to withstand the thermal duty of the circulating
current resulting from continuous and temporary load or
voltage unbalance on the main windings. In this paper the
apparent power rating of TSW is calculated by means of a
transformer EC. For that, several tests are proposed for the
calculation of the equivalent circuit positive/negative and
zero sequence impedances. Moreover a FEM transformer
model is also described for the same purpose, which serves
also to validate the EC results.
The TSW apparent power rating is then calculated from
the knowledge of expected unbalanced currents. Moreover,
the TSW thermal dimensioning is based on the maximum
allowable windings temperature, so that the overheating
caused under those unbalanced conditions does not damage
the windings insulation.
A practical application for the TSW thermal dimensioning
of a 45 MVA Yy-connected three-phase three-limb core
form power transformer is presented in this paper. From the
thermal performance under unbalanced continuous and
temporary load conditions, the dimensioning of copper
volume has been reduced a 28.5 % from a proposed original
model.
IX. ACKNOWLEDGMENT
The authors would like to thank Luis Sanchez Lago,
student from University of Vigo, for performing equivalent
circuit and finite element simulations useful in this paper.
79.27 ºC
X.
[1]
temperature under the above conditions. Results are shown in
Table VIII, where the original model is referred as the
studied transformer model with given turns number NT=133,
and a given copper volume Vcu. Though authors are aware
that transformer thermal performance requires complicated
fluid dynamic models [13], an estimation of equivalent
convection coefficients hc, and mean oil temperature Toil is
performed, such as the LV winding temperature is around the
maximum permitted of 80ºC [12]. With the estimated
thermal parameters (hc and Toil), TSW temperature reaches
51.68 ºC under continuous full single-phase load for its given
copper volume. Therefore, the copper volume on the TSW
can be reduced while the maximum permitted temperature of
80ºC is not reached. A new steady state temperature
computation is carried out with a reduced TSW copper
volume of Vcu'=71.5%Vcu increasing up to 56.12ºC, still
lower from the maximum permitted.
Moreover, the temperature reached at temporary single
phase-to-ground fault, before protection mechanisms act (at
about 2s) must also comply with maximum allowable
temperatures. As seen in Table VIII, the values of TSW
temperature reached at single phase-to-ground fault for the
reduced copper volume model Vcu' is still within the limit of
maximum permitted temperature.
The next step in the TSW dimensioning would be to
check whether the strength of conductors chosen for the
reduced copper volume model Vcu' from the thermal rating
withstand the short circuit forces.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
VIII.
CONCLUSION
Historically transformer TSWs are designed to be 35% of
the rated transformer power, but stabilizing windings shall be
[13]
2368
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