Download Design Comparison of Round and Rectangular Wire Winding

Design Comparison of Round and
Rectangular Wire Winding Transformer
Soe Naing, Myo ThetTun

Abstract—Transformer is essential and important
equipment in the role of transmission and distribution system.
It is one of the simplest devices comprising two or more electric
circuits coupled by a common magnetic circuit. According to
the type of service, there are two types of transformer. They are
distribution transformer and power transformer. This journal
show the result of the difference between round conductor
winding and rectangular conductor winding of distribution
transformer.
Three-phase
two
winding
distribution
transformer used in small substation is to step down the voltage.
In the case of very small transformers the conductor are very
thin and round. These can be easily wound on a former with
rectangular or square cross section. In design consideration,
selection of magnetic frame, choice of conductor size, choices of
current density are considered. Estimating all possible
environmental impacts from 5 MVA distribution transformers
such as conductor area, winding construction, no load losses
and full load losses are also described in detail.
Index Terms—Distribution transformer, step core, core
type, round and rectangular, tank and temperature rise.
I. INTRODUCTION
A transformer is a static device that transfers
electrical energy from one circuit to another by
electromagnetic induction without the change in frequency.
The transformer, which can link circuits with different
voltages, has been instrumental in enabling universal use of
the alternating current system for transmission and
distribution of electrical energy. Various components of
power system, viz. generators, transmission lines,
distribution networks and finally the loads, can be operated at
their most suited voltage levels. As the transmission voltages
are increased to higher levels in some part of the power
system, transformers again play a key role in interconnection
of systems at different voltage levels [1].
The apparent power can in principle be determine
individually for each specific installation, but it should be
note that, with respect to reserve capability of spare
transformers and replacement and maintenance requirements,
the number of different types and ratings should be limited.
For transformers to be installed in medium and low-voltage
systems, standardized values of apparent power, impedance
voltages and losses should preferably be used. Transformers
Manuscript received Oct 15, 2011.
SoeNaing, Electrical Power Engineering Department,Mandalay
Technological University,(e-mail: [email protected])Mandalay,
Myanmar
MyoThetTun, Electrical Power Engineering Department,Mandalay
Technological University,(e-mail: [email protected])Mandalay,
Myanmar
used within the high-voltage range in general are designed
individually according to the user’s specification [2].
II. GENERAL CONCEPT OF DISTRIBUTIONTRANSFORMER
On the last transformation step from the power station to
the consumer, distribution transformers (DT) provide the
necessary power for systems and buildings. Accordingly,
their operation must be reliable, efficient and, at the same
time, silent.
Distribution transformer shown in Figure 1 is used
toconvert electrical energy of higher voltage, usually up to 36
kV, to a lower voltage, usually 250 up to 435 V, with an
identical frequency before and after the transformation.
Application of the product is mainly within suburban areas,
public supply authorities and industrial customers.
Distribution transformers are usually the last item in the chain
of electrical energy supply to households and industrial
enterprises.
Distribution transformers are fail-safe, economical and
have a long life expectancy. These fluid-immersed
transformers can be 1-phase or 3-phase. During operation,
the windings can be exposed to high electrical stress by
external overloads and high mechanical stress by
short-circuits. They are made of copper or aluminum.
Low-voltage windings are made of strip or flat wire, and the
high-voltage windings are manufactured from round wire or
flat wire.
I1
V1
I2
V2
I3
V3
V1
V1 I4
V4
V1
I5
V5
Three-phase
winding 1
I6
V6
Three-phase
winding 2
Figure 1. Three-phase two winding transformer
III. CONSTRUCTION OF TRANSFORMER
A transformer consists of a magnetic core made out of
insulated silicon steel laminations. Three distinct sets of
windings, first called primary, second called secondary
winding of each phase are physically wound on a common
core leg [3]. The transformer helps in converting low voltage
into high voltage or visa-versa and accordingly the
transformer is termed step-up or step-down. The winding to
which the voltage applied is called primary winding, whereas
the winding produced low voltage to which the load is
1
connected is called secondary winding. In core form designs,
the winding with the lowest operating voltage nearest to the
grounded core, and the high voltage winding wound around
the low voltage winding. The transformer works on the
principle of electromagnetic induction. Such phenomena can
take place in a static device, only, if the magnetic flux is
continually varying. Primary and secondary windings are
wound on the same core.
The transformer mainly consists of the following;
(1) Core
(2) Windings
(3) Tank
(4) On-load Tap Changer
A. Core
A magnetic circuit or core of a transformer is designed to
provide a path for the magnetic field, which is necessary for
induction of voltages between windings. The core is made
out of special cold rolled grain oriented silicon sheet steel
laminations. In addition to providing a low reluctance path
for the magnetic field, the core is designed to prevent
circulating electric currents within the steel itself. Circulating
currents, called eddy currents, cause heating and energy loss.
They are due to voltages induced in the steel of the core,
which is constantly subject to alternating magnetic fields.
Steel itself is a conductor, and changing lines of magnetic
flux also induce a voltage and current in this conductor. By
using very thin sheets of steel with insulating material
between sheets, eddy currents (losses) are greatly reduced. A
section of both primary and secondary windings are wound
on each leg of the core, the low voltage winding is wound
next to the core, and the high voltage winding is wound over
the low voltage. In a shell-type (shell form) transformer, the
steel magnetic circuit (core) forms a shell surrounding the
windings. In a core form, the windings are on the outside; in a
shell form, the windings are on the inside [4].
B. Windings
The transformer consists of two coils called windings
which are wrapped around a core. The transformer operates
when a source of ac voltage is connected to one of the
windings and a load device is connected to the other. The
winding that is connected to the source is called the primary
winding. The winding that is connected to the load is called
the secondary winding. The concentric windings are
normally constructed in any of the following types depending
on the size and application of the transformer.
(1) Continuous Disc Type
(2) Cross-over Types
(3) Helical Type
The continuous disc type windings consist of number of
disc wound from a single wire or number strip in parallel.
Cross-over type winding is normally employed where rated
currents are up-to about 20 Amperes or so. In helical
winding, the coil consists of a number of rectangular strips
wound in parallel racially such that each separate turn
occupies the total radial depth of the winding [3].
C. Tank
The tank provides adequate cooling surface to dissipate
the heat generated on account of losses inside the
transformer. Normally transformers up-to 50kVA could be
manufactured without external cooling tubes. For
transformers of higher rating, tanks are constructed with
external cooling tubes to provide additional surface for heat
dissipation.
D. On-load Tap Changer
On-load tap changer is used to control large high-voltage
distribution networks and to maintain correct system
voltages. Voltage adjustment under varying load conditions
is required the on load tap changing transformer. The changes
are carried out without interrupting the load current. The
schemes employed for on-load tap changer involved the use
of more complicated and expansive tap changing equipment.
This unit has a three-phase 7-positions linear regulator and
normally ± 2.5% tapping are provided on the primary
winding for regulating the voltage. The normal tapping sets
up at the position 3.
IV. DESIGNTHEORYOF TRANSFORMER
The design of the distribution transformer is to obtain
main dimensions of the magnetic circuit (core), yoke and
window, low voltage and high voltage windings,
performance characteristics and the cooling tank [2].
The e.m.f per turn, Et= K√
kVA
(1)
phase
The e.m.f per turn, Et= 4.44fBmAi
(2)
Where,
Bm= maximum value of flux density in the core, Tesla
f = frequency of supply, Hz
Ai = net cross sectional area of the core, m2
Cross sectional area of the core, Ai= Kid2
(3)
Output of transformer for three-phase,
Q = 3.33fBmδKwAwAiVA
(4)
Where, 𝛿= average value of current density, A/ m2
Window space factor,
kw=
Total copper area in the window
window area
(5)
The window space factor depends upon the voltage
rating of the windings, mainly the highest voltage and kVA
rating of the transformer.
Window area, Aw = L (D - d)
Width of the window, bw= D - d
Overall length of the yoke, W = 2D+0.9d
Gross core section, Ac=
Ai
Iron factor
Gross yoke area, Ay = 1.15 x Ac
Width of the yoke, by = 0.9d
Height of the yoke, hy=
Ay
by
(6)
(7)
(8)
(9)
(10)
(11)
(12)
The core cross-section is rectangular in the case of a
small capacity transformer or polygonal, inscribing a circle,
in the case of a large capacity transformer in order to utilize
2
fully the space available, which mean smaller diameter of the
circle over the stepped core. The number of steps depends
upon the kVA rating of the transformer and its gross core
section. Figure 2 describes the inscribing polygonal of 9 steps
core form.
In Fig 3, main dimension of window consists of the
height and the width of the window. Main dimension of the
yoke consists of overall length (W), width of the yoke and the
height of the yoke.
Total ampere turns for cores and yokes,
AT = ATc + ATy
AT
Total ampere turns per phase =
No. of phase
(23)
(24)
Number of turn per phase in low voltage winding,
V2
T2 =
Et
(25)
The r.m.s value of magnetizing current per phase in terms
of l.v, Im =
j
b
g
i
k
m
l
n
p
r
s
y
q
o
No load current, Io =√Im
z
W
core
center
yoke
L
bw
yoke
D
Figure 3. Main dimensions of magnetic frame[5]
Volume of the core = Nc Ac L
Weight of the core = Volume of the core x
density of steel
Iron losses in the cores = Weight of the core x
losses per kg
Volume of the yoke = NyAyW
Weight of the yoke = Volume of the yoke x
density of steel
Flux density of the yoke, By = 1.5 x
Ac
Ay
Iron losses in the yokes = Weight of the yoke x
losses per kg
Total iron losses = Iron losses in the core +
Iron losses in the yoke
Total ampere turns for three cores,
ATc = 3 x Ampere turns per meter x L
Total ampere turns for two yokes,
ATy = 2 x Ampere turns per meter x W
+Iw 2
(28)
(13)
(14)
(15)
(16)
(17)
(29)
For round conductor,
Cross sectional area, a =
window
D
2
For rectangular conductor,
I
Cross sectional area, a =
δ
Figure 3. Main dimensions of magnetic frame
d
(26)
√2×T2
The r.m.s value of active component of no load current in
terms of l.v,
Total iron losses per phase
Iw =
(27)
phase voltage of low voltage winding
d
a
f
h
Total ampere turns per phase
πD2
(30)
4
Outer diameter of insulating cylinder,
dio = d + 2ti
(31)
Inner diameter of l.v winding,
Di2 = dio + 2to
(32)
Outer diameter of l.v winding,
Do2 = Di2 + 2b2
(33)
Mean diameter of l.v winding,
Di2 +D02
Dm2 =
(34)
2
Mean length of l.v turn, lmt2 =πDm2
(35)
Resistance per phase of l.v winding,
ρlmt2 T2
r2 =
(36)
a2
Total copper losses = 3I2R
(37)
Number of turn per phase in high voltage winding,
V1
T1 = T2×
(38)
Total losses = Total iron losses + Total copper losses
(39)
V2
Q
(18)
Efficiency of transformer =
(19)
Leakage reactance of high voltage winding,
2πfμ0 lmt1 T1 2 b1 a
X1 =
( 3 + 2)
Lc
(20)
(21)
(22)
Q+Total losses
Leakage reactance of low voltage winding,
2πfμ0 lmt2 T2 2 b2 a
X2 =
( 3 + 2)
Lc
(40)
(41)
(42)
3
Total equivalent reactance in terms of l.v,
T2
]
2πfμ0 lmt1 T1
2
(a+
Lc
b1 +b2
3
)
(43)
Per unit reactance,
εx =
I 1 X1
V1
=
2πfμ0 lmt (AT)
Lc Et
(a+
b1 +b2
3
)
=
Total losses
Length of core
L
m
0.83
Length of yoke
W
m
1.52
Height of yoke
hy
m
0.32
Width of the window
bw
m
0.28
Distance between core centre
D
m
0.6
Weight of cores
-
Kg
1532.65
Weight of yokes
-
Kg
1872.4
TABLE III
DESIGN COMPARISON OF DISTRIBUTION TRANSFORMER FOR
L.V WINDING DESIGN
Total losses to be dissipated = 12.5 St θ1 +
(6.5Atθ1 ) 1.35
(51)
Total area of the cooling tubes
Area of one cooling tubes
(52)
VI. ROUND AND RECTANGULAR WIRE OF DISTRIBUTION
TRANSFORMER DESIGN
Output
Q
VA
5×106
Number of phase
-
-
3
H.V winding voltage
V1
V
33000
L.V winding voltage
V2
V
11000
Frequency
F
Hz
50
Connection of H.V/ L.V
Limit of temperature rise
-
-
Delta/Star
𝜃
C
50
TABLE II
SPECIFICATIONS OF DISTRIBUTION TRANSFORMER MAGNETIC FRAME
DESIGN
Specifications
Symbol
Unit
Design
Values
round
Rating
A
262.432
a2
mm2
77
Conductor size
d2
mm2
11.5× 4
Copper weight
Inner diameter of Windings
Di2
kg
mm
534.19
358.6
Outer diameter of Windings
Do2
mm
422.6
Radial width of Windings
b2
mm
64
Resistance per phase
r2

0.06756
Turn per phase
T2
-
212
Phase current
I2
A
262.432
Conductor section
a2
mm2
80.42
Conductor size
d2
mm
3.3
552.456
Copper weight
Unit
-
kg
Inner diameter of Windings
Di2
mm
351
Outer diameter of Windings
Do2
mm
424.12
Radial width of Windings
b2
mm
75.12
Resistance per phase
r2

0.064
Specifications
Symbol
Unit
Turn per phase
Phase current
Conductor section
conductor size
Copper weight
Inner diameter of Windings
Outer diameter of Windings
Radial width of Windings
Resistance per phase
Turn per phase
Phase current
Conductor section
Conductor size
Copper weight
T1
I1
a1
Di1
Do1
b1
r1
T1
I1
a1
d1
-
A
mm2
mm2
kg
mm
mm
mm

A
mm2
mm
kg
Di1
Do1
b1
r1
mm
mm
mm
Ω
Design
Values
1158
50.5
15.75
8.14×2.74
785
461.8
566
104.12
2.37
1158
50.5
15.92
2.7
810.765
TableIV continued
round
Unit
rectangular
TABLE I
SPECIFICATIONS OF DISTRIBUTION TRANSFORMER DESIGN
Symbol
-
I2
Symbol
TABLE IV
DESIGN COMPARISON OF DISTRIBUTION TRANSFORMER FOR
H.V WINDING DESIGN
To calculate the transformer design, first step is based on
the main data and the properly assumed values.
Specifications
T2
Phase current
Conductor section
(50)
Area of cooling tubes =πx diameter of the tube x
length of the tube
Turn per phase
Design
Values
212
Specifications
(49)
12.5×tank area
Number of the tubes =
0.333
(44)
The length of the tank for three-phase transformer,
lt = 2D+d01 +∆l
(45)
The width of the tank for three-phase transformer,
bt = d01 +∆b
(46)
The height of the tank for three-phase transformer,
ht = L +2hy +h
(47)
Where ∆l, ∆b and ∆h are total clearance length-wise,
width-wise and height-wise.
Cooling area of the tank wall, St = 2(bt+lt ht )
(48)
Temp: rise,
m
rectangular
=
T1 2
d
round
X1= X1 + X2[
Diameter of circum circle
Inner diameter of Windings
Outer diameter of Windings
Radial width of Windings
Resistance per phase
465.328
583.72
118.4
2.4
4
TABLE V
PERFORMANCE SUMMARY OF DISTRIBUTION TRANSFORMER
Specifications
Symbol
Unit
Design
Values
(rectangular)
Design
Values
(round)
No load current
I0
A
1.26
1.26
Iron losses
Pi
kW
4.555
4.555
Copper losses
Pc
kW
33.74
34.11
Total losses
Pt
kW
38.295
38.665
Full load
efficiency
η
%
99.17
99.15
[1] Kulkarni,S.V. And Khaparde, S.A. “Transformer
Engineering Design and Practice”Indian Institute of
Technology, Bombay Mumbai, India, (2004).
[2] William M. Flanagan, 1993. “Transformer Design and
Application”Second Edition, McGraw-Hill Inc.
[3] Aurten Stigant, S.1961. A Practical Technological of the
Power Transformer (9th edition)
[4] Colonel Wm. T. Mclyman kg Magnetics, Inc.
“Transformer and Inductor Design Handbook” Third
Edition, Revised and ExpandedIdyllwild, California,
U.S.A. 2004 by Marcel dekker, Inc.
[5] Mittle, V.N. and Arvind Mittal. “Design of Electrical
Machine” 4th Edition, Standard Publishers Distributors,
New Delhi, (1996).
TABLE VI
DESING SUMMARY OF TRANSFORMER FOR TANK
Specifications
Symbol
Unit
Design
Values
(rectangular)
Design
Values
(round)
Length of tank
lt
m
1.94
1.984
Width of tank
bt
m
0.80
0.834
High of tank
ht
m
1.73
1.73
Number of
cooling cubes
-
tubes
260
266
TABLE VII
DESING SUMMARY OF TRANSFORMER FOR REGULATION
Specifications
Per unit
reactance
Per unit
resistance
Per unit
impedance
Regulation at
full load 0.85
P.F
Symbol
Unit
Design
Values
(rectangular)
Design
Values
(round)
Ex
p.u
0.0679
0.081
Er
p.u
0.00675
00.0077
Ez
p.u
0.068
0.081
-
p.u
0.0415
0.048
V. CONCLUSION
In this journal, 5 MVA, 50Hz, 33/11kV, three-phase
two-winding, delta-star connected, core type distribution
transformers are already designed by using round and
rectangular conductor. But magnetic frame designed is used
the same type for both transformer. The design is carried out
based on the given specification by using available material
economically and achieving better operating performance.
This transformer is used to step down the transmission
voltage to the low voltage for the power distribution
requirement with minimize losses and cost, and increase the
distribution capacity of the lines. Two-winding distribution
transformer is more useful and more economical than the use
of two separate transformers in the power transmission and
distribution systems. Therefore, it can be said that the design
of three-phase two-winding distribution transformer is
needed to study as one of the important role in electrical
engineering field.
REFERENCES
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