Design Comparison of Round and Rectangular Wire Winding Transformer
SoeNaing,MyoThetTun
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 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.
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 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 (1)
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, = average value of current density, A/ m2
Window space factor,
kw= (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) (6)
Width of the window, bw= D - d (7)
Overall length of the yoke, W = 2D+0.9d (8)
Gross core section, Ac= (9)
Gross yoke area, Ay = 1.15 x Ac(10)
Width of the yoke, by = 0.9d(11)
Height of the yoke, hy= (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 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.
Figure 3. Main dimensions of magnetic frame
Figure 3. Main dimensions of magnetic frame[5]
Volume of the core = Nc Ac L (13)
Weight of the core = Volume of the core x
density of steel (14)
Iron losses in the cores = Weight of the core x
losses per kg (15)
Volume of the yoke = NyAyW (16)
Weight of the yoke = Volume of the yoke x
density of steel (17)
Flux density of the yoke, By = 1.5 x (18)
Iron losses in the yokes = Weight of the yoke x
losses per kg (19)
Total iron losses = Iron losses in the core +
Iron losses in the yoke (20)
Total ampere turns for three cores,
ATc = 3 x Ampere turns per meter x L (21)
Total ampere turns for two yokes,
ATy = 2 x Ampere turns per meter x W (22)
Total ampere turns for cores and yokes,
AT = ATc + ATy (23)
Total ampere turns per phase = (24)
Number of turn per phase in low voltage winding,
T2 = (25)
The r.m.s value of magnetizing current per phase in terms
of l.v, Im = (26)
The r.m.s value of active component of no load current in
terms of l.v,
Iw =(27)
No load current, Io = (28)
For rectangular conductor,
Cross sectional area, a =(29)
For round conductor,
Cross sectional area, a =(30)
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,
Dm2 = (34)
Mean length of l.v turn, lmt2 =Dm2 (35)
Resistance per phase of l.v winding,
r2 = (36)
Total copper losses = 3I2R (37)
Number of turn per phase in high voltage winding,
T1 = T2×(38)
Total losses = Total iron losses + Total copper losses (39)
Efficiency of transformer =(40)
Leakage reactance of high voltage winding,
X1 = (41)
Leakage reactance of low voltage winding,
X2 = (42)
Total equivalent reactance in terms of l.v,
X1= X1 + X2
= (43)
Per unit reactance,
= = (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, = (49)
Total losses to be dissipated = 12.5 St +
(6.5At) 1.35 (50)
Area of cooling tubes =x diameter of the tube x
length of the tube (51)
Number of the tubes = (52)
VI. ROUND AND RECTANGULAR WIRE OF DISTRIBUTION TRANSFORMER DESIGN
To calculate the transformer design, first step is based on the main data and the properly assumed values.
TABLE I
SPECIFICATIONS OF DISTRIBUTION TRANSFORMER DESIGN
Specifications / Symbol / Unit / RatingOutput / Q / VA / 5106
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 / - / - / Delta/Star
Limit of temperature rise / / C / 50
TABLE II
SPECIFICATIONS OF DISTRIBUTION TRANSFORMER MAGNETIC FRAME DESIGN
Specifications / Symbol / Unit / Design ValuesDiameter of circum circle / d / m / 0.333
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
Specifications / Symbol / Unit / Design Values/ Turn per phase / T2 / - / 212
Phase current / I2 / A / 262.432
Conductor section / a2 / mm2 / 77
Conductor size / d2 / mm2 / 11.5× 4
Copper weight / - / kg / 534.19
Inner diameter of Windings / Di2 / mm / 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
Copper weight / - / kg / 552.456
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
TABLE IV
DESIGN COMPARISON OF DISTRIBUTION TRANSFORMER FOR
H.V WINDING DESIGN
Specifications / Symbol / Unit / Design Values/ Turn per phase / T1 / - / 1158
Phase current / I1 / A / 50.5
Conductor section / a1 / mm2 / 15.75
conductor size / - / mm2 / 8.142.74
Copper weight / - / kg / 785
Inner diameter of Windings / Di1 / mm / 461.8
Outer diameter of Windings / Do1 / mm / 566
Radial width of Windings / b1 / mm / 104.12
Resistance per phase / r1 / / 2.37
Turn per phase / T1 / - / 1158
Phase current / I1 / A / 50.5
Conductor section / a1 / mm2 / 15.92
Conductor size / d1 / mm / 2.7
Copper weight / - / kg / 810.765
TableIV continued
Inner diameter of Windings / Di1 / mm / 465.328Outer diameter of Windings / Do1 / mm / 583.72
Radial width of Windings / b1 / mm / 118.4
Resistance per phase / r1 / / 2.4
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
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 / Symbol / Unit / Design Values(rectangular) / Design Values
(round)
Per unit reactance / Ex / p.u / 0.0679 / 0.081
Per unit resistance / Er / p.u / 0.00675 / 00.0077
Per unit impedance / Ez / p.u / 0.068 / 0.081
Regulation at full load 0.85 P.F / - / 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
[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).
1
Manuscript received Oct 15, 2011.
SoeNaing, Electrical Power Engineering Department,Mandalay Technological University,(e-mail: )Mandalay, Myanmar
MyoThetTun, Electrical Power Engineering Department,Mandalay Technological University,(e-mail: myothettun@gamil.com)Mandalay, Myanmar