- Email: [email protected]
Bundled conductor configuration optimization for compact transmission lines incorporating electromagnetic fields management
Energy Convers.Mgmt Vol. 39, No. 10, pp. 1053-1071, 1998 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain
PII:
s01%-8904(97)10023-1
0196-8904/98
%19.00 + 0.00
BUNDLED CONDUCTOR CONFIGURATION OPTIMIZATION FOR COMPACT TRANSMISSION LINES INCORPORATING ELECTROMAGNETIC FIELDS MANAGEMENT A. S. FARAG,‘* J. M. BAKHASHWAIN,’ A. AL-SHEHRI,’ T. C. CHENG’ and YUMING GAO’ ‘King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia ‘University of Southern California, Los Angeles, U.S.A. ‘Tsinghua University, Beijing, China (Received
20 November
1996)
Abstract-This paper outlines an optimization calculation procedure used for a bundled conductor configuration of compact transmission lines to improve certain operating performance and electromagnetic fields (EMF) management techniques. The objective function of this optimization problem is to allow the charges and surface maximum gradients on all subconductors to be the same and as balanced as possible. As a result, three optimum schemes are induced in this paper for 200 KV transmission lines. The parameters of compact lines and their unbalance, surge impedance, electric field distribution under the line, corona loss and radio noise level are also evaluated. Electromagnetic field management and field minimization over the right-of-way of the optimum schemes are also presented. EMF fields are analyzed, evaluated and compared to attainable fields of standard compact and conventional lines. 0 1998 Elsevier Science Ltd. All rights reserved Bundled conductors
Compact transmission lines
Electromagnetic fields management
INTRODUCTION
Increasing transmission line power transfer capability without increasing the consumption of materials, investment costs, overextending the use of right-of-way (ROW) and electric and magnetic field exposure has always been of paramount importance for utilities design engineers. Development of compact transmission lines can be an advantage for resolving these problems. Compact lines can be designed and developed with reduced phase-to-phase clearances by using large bundled conductors and silicon rubber fiber-glass phase-to-phase insulators as spacers in each span. At the same time, the width of ROW can be safely reduced for the same electric and magnetic fields. In other words, for the same ROW, the electric and magnetic fields can be reduced significantly. The power transmission capability per width of ROW will increase to a great extent. This leads to an enhancement of the economic efficiency of transmission lines. The current degree of knowledge is inadequate for a satisfactory assessment of transmission lines electric and magnetic fields for their impact on human health. A better characterization is needed. For compact transmission lines, smaller phase-to-phase clearances induce stronger phase-tophase coupling. It causes the nonequalization of charge distribution on the subconductors which, in turn, affects the maximum surface gradients of the subconductors. To develop optimized compact transmission lines, the key problems are to configure optimized bundled conductors and arrange the three-phase conductors properly in single-circuit lines. Subconductor size, bundle number and arrangements must be chosen so that it can be realized that charges and maximum surface gradients on all subconductors are as nearly equal as possible, respectively, under acceptable engineering design constraints. The electric and magnetic field management within the ROW is a must, as a constraint, for these optimized configurations. For double-circuit and multi-circuit transmission lines, compact and optimized bundled configurations can be *Author to whom all correspondence should be addressed. 1053
FARAG et al.:
1054
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
applied for new tower designs and new lines configurations to enhance and manage the EMF effects. Certain operating performances of compact transmission lines can be, thus, improved by these optimization procedures. The optimum design for bundled conductor configurations was performed for three different transmission lines of 220 KV. These arrangements include different tower configurations such as horizontal, vertical, inverse triangular (Tee or Delta), circular, cruciform, etc. The numerical method of optimization of bundled conductors configurations for compact lines and its results are introduced. Transmission line parameters, corona loss, radio noise level, electric and magnetic fields underneath the lines and at the right-of-way, calculated at the 3 feet level, are also evaluated and analyzed. Attainable results of the optimized bundled conductor configuration for compact lines are compared to the corresponding results of the standard conventional and compact transmission lines. NUMERICAL
METHOD
OF OPTIMIZATION OF CONFIGURATIONS CONDUCTORS
OF BUNDLED
The optimization process of bundled contractors configuration is performed under the conditions that the tower type, phase-to-phase clearance, minimum height of subconductor to ground, subconductor size and bundle number are all predetermined. Two values of nonequalization about charges and maximum surface gradients of the subconductors which the optimum configuration of the three phase bundled conductors satisfies are predetermined too. As a result of this optimization process, the optimum configurations of three-phase bundled conductors have satisfied the above-stated requirements. The objective function The objective function of the optimization process is given as: minflx) = C, e(g i=l
- l)*+C. a”
e($+i=l
- l)* m,av
(1)
where: 3n n Qi
Q Ezi E m,av C,
is the number of total subconductors, is the bundle number, is the magnitude of charge on subconductor No. (i) in PC/m, is the average of the magnitudes of charges on all (3n) subconductors in PC/m, is the magnitude of maximum surface gradient on subconductor No. (i) in KV/m, is the average of the magnitudes of maximum surface gradients on all (3n) subconductors in KV/m, and and C, are the weighting factors which are taken as unity.
Optimized variables In this optimization process, the optimized variables are the locations of the subconductors (Xi) and (Yi), where the distance (Xi) is the horizontal distance of subconductor No. (i) from the center of the tower while (Yi) is the average height of subconductor No. (i) to ground. The total number of optimized variables is 2(3n + nd), where nd is the number of ground wires. All variables are expressed by an array X. Constraint conditions The constraint conditions for this optimization process are the limitations of variables which express the locations of all subconductors. These conditions should satisfy the requirements determined by a particular transmission line, such as insulation coordination, electrical load, mechanical load, sag limitations, environmental effects, etc. These items are expressed as: (a) (b) (c) (d)
Upper Upper Upper Upper
and and and and
lower lower lower lower
limits limits limits limits
of of of of
phase-to-phase clearances, bundle spaces of bundled conductors, ground wire locations, and average heights to ground of the lowest subconductors.
FARAG et al.:
BUNDLED CONDUCTOR
CONFIGURATION
OPTIMIZATION
1055
These constraint conditions are expressed by the general equation: i= 1,2,...,m
gi(x)IO3
The optimization problem has multi-continuous engineering requirements. The objective function including the variables array directly. This kind Method which is suitable for obtaining a solution
OPTIMIZATION
DESIGN
RESULTS
FOR
(2)
variables, which are constrained by minimum cannot be expressed by an analytical equation of problem is handled by using the Multiplier [l, 21.
220 KV TRANSMISSION
LINES
SYSTEMS
The optimization process for the configuration of 220 KV three phase bundled conductors includes two steps. First, the optimum configuration as a preliminary scheme can be found by using the optimization program (OCCP) (Optimization of Conductor of Compact Line Program). Second, the preliminary scheme is modified to be an engineering scheme which can be easily realized, taking into consideration all the design aspects and minimum standards requirements. For 220 KV transmission line systems, three types of three-phase arrangements and configurations are considered. These are flat, vertical, and inverse triangular (Tee or Delta) arrangements. Con$guration of bundled conductors In traditional transmission lines, regular polygon configuration bundled conductors are considered and adopted. Additionally, the same configurations are used on three phases. This configuration exhibits two major disadvantages: (1) due to the asymmetry of three-phase bundled conductors geometrically, the capacitance of the middle phase is larger than for the two outside phases. This leads to a higher charge on the middle-phase conductors than the two outside phases; (2) due to the interaction of all subconductors, the charges on all subconductors are not equal, and also, the charge along the circular surface of every subconductor is not uniform. This situation becomes more serious with reduction of the phase-to-phase clearance, especially with the conductors in the vertical arrangement. The relative values of the charges on the subconductors of the traditional three-phase conductors and the compact line designs are shown in Figs 1 and 2, respectively. For compact lines, the optimum three-phase bundled conductor configurations can be found by using the optimization program. The general configurations of the three-phase four-bundled conductors for three types of towers are shown in Fig. 3. For these configurations, the relative values of the charges on each subconductor can be equal to one as a maximum value. A charac-
+
22.5’
-
22.5’~
.L ?? o.97 1.2 r .0.97
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
i 1.06
?? o.97
il.06
.0.97
: ’:
2 x 300 mm2 0.4 m (1.2’) 7.5 m (22.5’)
Fig. 1. Charges on subconductors of traditional lines of 220 KV (TrH2).
1056
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
9'
I 1.23% 1.087' '
+
'
9’
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
: : :
(a) Vertical Lines (SV4) 0.934 0946
l-O&O 1
.
Logo
. . .
I i'.llO 0
’
0
1.0107'0.909 1.010
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
: :
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
(b) Tee (Delta) Lines (ST4)
0.8$8 l.040
I 1.1&4
0.8?6 1.089
1: 1.174*
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
::
: :
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
(c) Horizontal Lines (SH4) Fig. 2. Charges on subconductors of compact lines of 220 KV.
teristic of these optimum configurations is that the shapes of the outside phases are nearly like that of a semi-ellipse with larger bundle space than the middle phases; the shape of the middle phase is a polygon or regular polygon with smaller bundle space than the outside phases. For
FARAG et al.:
BUNDLED CONDUCTOR
CONFIGURATION
OPTIMIZATION
1057
(a) Vertical Optimum Configuration (PV4)
(b) Optimum Tee (Delta) Configuration (PT4)
(c) Optimum Horizontal Configuration (PH4) Fig. 3. Optimum configurations of bundled conductors of compact lines.
the three-phase inverse-triangular arrangement (Tee or Delta), the shapes are three trapezoids facing each other as shown in Fig. 3. For the sake of easy construction, these optimum schemes are modified. The three modified schemes are shown in Fig. 4. The differences of charges on each subconductor of the threephase bundled conductors, even for the vertical arrangement, are much lower than those of the compact lines shown in Fig. 2. The results shown in Fig. 4 show that the optimization of bundled conductor configurations is not only necessary but also calculable.
1058
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
1.020.
!
0.960
f
1 .
0
OPTIMIZATION
1 Oh
bo.T
(a> (PV4)
I
’ 40.41r 0.970&p?!1.
0 1
1.050.
. y4
,_&p
!
1.000. 1.007*
(b)
0
( 0
(PT4)
I
0.25
(c> PH4) Fig. 4. Charges on subconductors
of optimum configuration of bundled conductors of compact lines (phase-to-phase clearance is 3 m).
CALCULATIONS OF CONDUCTOR SURFACE ELECTRIC FIELD GRADIENTS The phase-to-phase clearances of compact lines are smaller than those of traditional lines. The effect of the charges on the neighbouring subconductors on the electric field gradient should be considered [3]. The surface electric field gradient of each subconductor and its distribution along the circular surface can be calculated using Equation (3) and the geometrical diagram of
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
1059
Fig. 5. Geometrical diagram of subconductors No. i and No. j.
subconductors
shown in Fig. 5.
Ei(4) =
&
Qi - 2 2
Q-3 J Aij
j=l,$ij
‘OS
(4 - ‘I’,)
1
(3)
where: $7
Aij Aij
4)
is the radius of subconductor i, indicates a point on the circular surface of subconductor i, is the center to center distance between conductors i and j, makes an angle Yli when r$ = 0.
In Equation (3) it is assumed that the charge is set on the center of each subconductor. The geometric diagram shown in Fig. 5 shows any two subconductors ij in a parallel multi-conductor system. The relative values of the maximum surface gradients of all subconductors in traditional lines and optimum compact lines are shown in Figs 6-8, where the average of the maximum surface fields gradients of all subconductors is used as a base value. The maximum values of the maximum surface field gradients of all subconductors for the three types of towers are shown in Table 1. It illustrates that the effectiveness of optimization is very significant. In a three-phase vertical arrangement, the nonequalization of maximum surface gradients can be reduced from +24%, -17% to +6%, -5% which is approximately equivalent to those values of traditional lines. The maximum value of maximum surface field gradients can be reduced from 29.7 KV/m to 22.2 KV/m. It is apparent and clear that the optimum bundled conductor configurations of compact lines will be an advantage to the operating performance of transmission lines. PERFORMANCE
OF OPTIMIZED
COMPACT
TRANSMISSION
LINES
The parameters of transmission lines vary with changes of the phase-to-phase clearances and bundle spaces of the conductors, which may further affect the operating performance of the transmission line.
0.98$ 0.98:
1.060!
0.98: t
1.060 ’ t
0.98:
Fig. 6. Relative values of maximum surface gradient on subconductors of traditional lines of 220 KV
1060
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
l.055 0.83.4 ! I0
.
1.244. 0.98.51 i'
.
1.05; 0.83.3! .
.
!
(a> W4)
0.950 0.910. l.g70 !
0
1
. .
1.020
.
1
1.120 l.O!O. .l.OlO I 00.900 I @I W4)
I 0.872
1.0,20
1.114
00
0.87:
1.020
1.1!4 010I ??
0
0
Fig. 7. Relative values of maximum surface gradient on subconductors of non-optimizing bundled conductors configurations (phase-to-phase clearance is 3.0 m).
Surge impedances For compact lines, it is of paramount importance that the surge impedance be smaller, and that leads to a larger natural power transfer capacity than that of a traditional line. Because of the change of geometry, the inductances of the compact lines are reduced while their capacitances are increased, as shown in Table 2. Comparing the compact lines with traditional lines, the positive sequence inductances of the compact lines is reduced by about 40%, while the positive sequence capacitances are increased by about 70%. This leads to the fact that the surge impedances of compact lines are reduced by about 40% and the natural power transfer capacity increases by 60%. Right-of-way The zones of high electric and magnetic fields underneath compact lines at/or close to ground level become narrower.
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
0.990.
!
OPTIMIZATION
1061
.
0.950 0 I 0 1.060* I e 1.060e 1 ?? 0.950
0 ! 0
09808
1 ??
(a) W4)
O*9600a9Jo.
I
1.040e’*ezO!
.
0
0
.
0.9900
I ??
l.OlOe
) 0
(b)
0’7’4)
Cc) PH4) Fig. 8. Relative values of maximum surface gradient on subconductors of optimizing bundled conductors configurations (phase-to-phase clearance is 3.0 m).
The charges on conductors of compact lines increase with the increased capacitance. The effect of three phase charges on space electric field can counteract each other. This counteraction will be significant when the phase-to-phase clearances are reduced. The maximum electric fields at 3 ft (xl m) above ground level are lower than those of the traditional lines for flat and inverse triangular (Delta or Tee) three-phase arrangements of compact lines. The width of trans-
1062
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
Table 1. Maximum surface gradient of subconductor (KV,,,/m) Tower Type No.
Maximum value
Average value
29.7 24.8 23.8 22.2 21.8 21.6 17.0
23.9 22.1 21.3 20.9 21.0 20.4 16.1
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
Note: Letters used in “Tower Type No.“: are: S, regular polygon bundled conductor for compact line; P, optimized bundled conductor for compact line; Tr, traditional line; H, three phase flat arrangement; V, three phase vertical arrangement; T, three phase triangular arrangement.
mission line corridors with high field are narrower than those of traditional lines in different degrees. For flat and inverse triangular arrangements, it is more apparent. Figure 9 shows the magnetic and electric fields of the traditional lines of 220 KV at 3 ft (1 m) above ground level. The maximum magnetic field is 326 mG at the center of the line, and a value of 50 mG is noticed at 100 ft away from the line center. The maximum electric field is 2.56 KV/m, and a value of 0.4 KV/m is shown at 100 ft from the line. Figure 10 shows the same fields of the compact lines SV4, ST4 and SH4. For the SV4 design (Fig. 10(a)) the maximum magnetic field is 127 mG at the line center and 18 mG at 100 ft away, while the corresponding values for the ST4 design (Fig. 10(b)) are 88 mG and 11 mG, respectively. For the SH4 design (Fig. 10(c)) they are 174 mG and 20 mG, respectively. The electric field values are: for the SV4 design, the maximum value is 2.86 KV/m at the line center and 0.2 KV/m at 100 ft, while for the ST4 design, the maximum value is 1.95 KV/m at the line center and 0.15 KV/m at 100 ft, and for the SH4 design, the maximum value is 2.05 KV/m at 25 ft away from the line center and 0.25 KV/m at 100 ft. For the optimized compact design, Fig. 11 shows the corresponding magnetic and electric fields for the three designs PV4, PT4 and PH4. For the PV4 design (Fig. 1la), the maximum magnetic field is 118 mG at the line center, and a field of 16 mG occurs at 100 f from the line center. For the PT4 design (Fig. 1lb), the corresponding values are 87.8 mG at the line center and 10.0 mG at 100 ft. For the PH4 design (Fig. 11(c)), the corresponding values are 164 mG and 19.6 mG, respectively. The electric field values are: for the PV4 design, the maximum values are 2.75 KV/m at the line center and 0.18 KV/m at 100 ft, while for the PT4 design, the maximum value is 2.01 KV/m at the line center and 0.16 KV/m at 100 ft, while the corresponding values for the PH4 design are: 2.07 KV/m at 25 ft away from the line center and 0.27 KV/m at 100 ft. Unbalances of transmission line parameters
The parameters of three phase transmission lines, no matter what configuration, are unbalanced to different degrees. This unbalance for vertical arrangements is more serious than for others. For optimized configurations, this unbalance can be improved to be nearly the same as for traditional lines. In general, the amount of transmission line unbalance can be represented by the electrostatic unbalance factors and the electromagnetic unbalance factors. It is assumed that the positive Table 2. Performance parameters of 220 KV transmission lines (f = 60 Hz) Tower Type No.
RI (Q)
LI (mH/Km)
Ci &F/Km)
Z, (Q)
P, (MVA)
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
0.0541 0.0532 0.0538 0.0531 0.0530 0.0544 0.0472
0.507 0.532 0.577 0.580 0.567 0.611 0.907
0.0232 0.0215 0.0203 0.0201 0.0201 0.0187 0.0118
177.4 188.8 202.3 203.7 201.6 217.0 345.1
327.5 307.5 287.1 285.0 288.0 267.7 168.3
FARAG et al.:
BUNDLED CONDUCTOR
(i) Magnetic
.._.
3.m
._
CONFIGURATION
OPTIMIZATION
1063
Field Profile
..___.
$
(ii) Electric Field
Profile
Fig. 9. Magnetic and electric fields of traditional line of 220 KV (TrH2).
sequence voltage applies at the sending end of a line with the receiving end open. The ratios between the zero and positive sequence currents, the negative and positive sequence currents are defined as the zero and negative sequence electrostatic unbalance factors, respectively: d,=!Q, 4,
d2 = i2,o 40
1064
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
If the receiving end of the line is shorted out, the ratios between the zero and positive sequence currents, the negative and positive sequence curets are defined as the zero and negative sequence electromagnetic unbalance factors, respectively: m0=7.
m2 = Z1.S
i2 s +-
11,s
Table 3 shows the results of the calculations for the different configurations.
(i) Magnetic Field Profile
Fig. 10(a)-Caption
on p. 1066.
(5)
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
.
.;. 1
.’ .:I / .
.;
.;...
\
L
-ass
-,
..-..
-s
?
e.cJ
i
.....~...---...-.-.....
(i) Magnetic Field Profile
(
(ii) Electric Field Profile Fig. IO(b)--Caption overleaf.
1065
1066
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
(i) Magnetic Field Profile
2
2
5
~..
............
,e
................ i
__... .:_
..i
\ ~~~.
I
-I
--r--v ,
i\ \.--
L B
lee
(ii) Electric Field Profile Fig. 10. (a) Magnetic and electric fields of compact line of 220 KV (SV4). (b) Magnetic and electric fields of compact line of 220 KV (ST4). (c) Magnetic and electric fields of compact line of 220 KV (SH4).
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
1067
Radio noise level
The radio noise level of optimized compact lines under fair weather conditions are slightly higher than for traditional lines but less than for the compact lines.
(i) Magnetic Field Profile
(ii) Electric Field Profile Fig. 1l(a)-Caption
on p.
1069.
1068
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
(i) Magnetic Field Profile
1
.a
.
@*s:..
j
.
. i
.. . . . . . . . . . . . . . .
ii& i...
..;
...’
.. .
.__..... j ,_.__.
;..
. . ;..
:..
.;
u
-1ee *‘strno.
Ice
0
-lee
OS-.”
I.*.r.no.
(ii) Electric Field Profile Fig. 1l(b)-Caption
opposite.
.;
.
1
0.e -3ee
.
2ae
i
308
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
1069
(i) Magnetic Field Profile
-:‘.
._;...
......... ................ ...
..........
_.i._.
........
.;..
.j..
-~
i
........
\
-F
(ii) Electric Field Profile Fig. 11. (a) Magnetic and electric fields of optimal compact line of 220 KV (PV4). (b) Magnetic and electric fields of optimal compact line of 220 KV (PT4). (c) Magnetic and electric fields of optimal compact line of 220 KV (PH4).
In general, radio noise levels are calculated for transmission lines of 345 KV and above. Since the conductor surface gradient of the 220 KV compact lines is higher than that of a traditional line, the radio noise level may be one of the problems of concern to public utilities.
FARAG et al.:
1070
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
Table 3. Unbalance of line parameters (%) Tower Type No.
do
d2
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
3.45 0.21 3.46 5.92 0.19 6.19 2.58
16.8 0.59 15.6 9.30 0.22 8.41 8.49
m2
m0
1.56 0.14 1.37 2.66 0.15 2.46 1.34
16.4 0.47 15.4 9.54 0.11 8.28 9.41
Referring to the concepts of “Generation Function” and 500 KV base-case line RI Generation data [4], radio noise levels under fair and heavy rain weather are evaluated for the different arrangements of traditional, compact and optimized compact lines, as shown in Table 4. These results indicate that, prior to optimization, the radio noise levels of compact lines under fair weather, are much higher than that of the traditional line, while under heavy rain conditions, the levels are almost the same. For the optimized compact lines, the radio noise levels under fair weather are only slightly higher than that of the traditional line, while under heavy rain conditions, the levels are slightly lower than that of the traditional line. These results show that, for effective conductor configurations, optimization is of significance. Corona losses
Corona losses of compact lines are higher than that of the traditional line. The corona loss of a transmission line depends on the surface gradient of a subconductor. The onset gradient of corona (&) on a subconductor surface is given by Peek’s equation: KV/cm
where: m
6 r
is the surface factor, assumed 0.82 is the relative air density, assumed 1.O, and is the subconductor radius.
As an example, four bundled conductors of compact lines have been evaluated, the subconductor size being 150 mm2 (0.54 in dia.). Two bundled conductors of traditional line have also been evaluated, the subconductor size being 300 mm2 (0.77 in dia.). According to Equation (6), the E, of compact lines and traditional lines are 32.93 and 31.7 KV,,&m, respectively. From Table 1, the surface gradients of subconductors of compact lines are about 25% higher than that of the traditional line, leading to the conclusion that the corona loss of compact lines is increased. According to the general experimental curve [5], the corona losses of lines have been evaluated. For three-phase vertical and inverse triangular arrangements of compact lines, the annual average corona losses are 1.6 and 1.42 KW/Km-three phase. They are 6.4 and 5.68 times that of a traditional line, respectively.
Table 4. Radio noise level (dp) Tower Type No. sv4 ST4 SH4 PV4 PT4 PH4 TrH2
Fair Weather
Heavy Rain
55.6 41.8 38.9 34.4 33.2 32.8 25.3
65.7 59.5 57.7 54.5 53.5 53.3 63.5
FARAG
rt al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
1071
CONCLUSIONS
The natural power transfer capacity of transmission lines can be increased, while the right-ofway ROW) is reduced for compact transmission lines. It leads to the conclusion that “ROW” per width of transmission capability can be increased significantly. By adopting the optimum configurations of bundled conductors, the nonequalization of charges and maximum surface gradients on the subconductors of compact lines can be reduced. They can be at the same levels as that of traditional lines for the three phase vertical arrangement. The unbalances of line parameters are reduced as well. Corona losses and radio noise levels of compact lines are higher than that of traditional lines but within the allowable and permitted ranges. Electric and magnetic fields are managed, and lower levels of these fields were noticed in the optimum configuration of bundled conductors. REFERENCES 1. 2. 3. 4. 5.
Kaiming C., Chinese Journal of Operations Research, 1987, Vol. 6, No. 1. Jitternatrum, K., Math Programming 1980, Vol. 18. Alexandrov, G. H., Design of UHV Transmission Lines, Prentice-Hall, 1983. Anderson, J. G., EHV-UHV Transmission Systems, 1975. Burgsdorf, V. 1960. Corona Investigations on EHV Overhead Lines. CIGRE. Report
No. 413
PII:
s01%-8904(97)10023-1
0196-8904/98
%19.00 + 0.00
BUNDLED CONDUCTOR CONFIGURATION OPTIMIZATION FOR COMPACT TRANSMISSION LINES INCORPORATING ELECTROMAGNETIC FIELDS MANAGEMENT A. S. FARAG,‘* J. M. BAKHASHWAIN,’ A. AL-SHEHRI,’ T. C. CHENG’ and YUMING GAO’ ‘King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia ‘University of Southern California, Los Angeles, U.S.A. ‘Tsinghua University, Beijing, China (Received
20 November
1996)
Abstract-This paper outlines an optimization calculation procedure used for a bundled conductor configuration of compact transmission lines to improve certain operating performance and electromagnetic fields (EMF) management techniques. The objective function of this optimization problem is to allow the charges and surface maximum gradients on all subconductors to be the same and as balanced as possible. As a result, three optimum schemes are induced in this paper for 200 KV transmission lines. The parameters of compact lines and their unbalance, surge impedance, electric field distribution under the line, corona loss and radio noise level are also evaluated. Electromagnetic field management and field minimization over the right-of-way of the optimum schemes are also presented. EMF fields are analyzed, evaluated and compared to attainable fields of standard compact and conventional lines. 0 1998 Elsevier Science Ltd. All rights reserved Bundled conductors
Compact transmission lines
Electromagnetic fields management
INTRODUCTION
Increasing transmission line power transfer capability without increasing the consumption of materials, investment costs, overextending the use of right-of-way (ROW) and electric and magnetic field exposure has always been of paramount importance for utilities design engineers. Development of compact transmission lines can be an advantage for resolving these problems. Compact lines can be designed and developed with reduced phase-to-phase clearances by using large bundled conductors and silicon rubber fiber-glass phase-to-phase insulators as spacers in each span. At the same time, the width of ROW can be safely reduced for the same electric and magnetic fields. In other words, for the same ROW, the electric and magnetic fields can be reduced significantly. The power transmission capability per width of ROW will increase to a great extent. This leads to an enhancement of the economic efficiency of transmission lines. The current degree of knowledge is inadequate for a satisfactory assessment of transmission lines electric and magnetic fields for their impact on human health. A better characterization is needed. For compact transmission lines, smaller phase-to-phase clearances induce stronger phase-tophase coupling. It causes the nonequalization of charge distribution on the subconductors which, in turn, affects the maximum surface gradients of the subconductors. To develop optimized compact transmission lines, the key problems are to configure optimized bundled conductors and arrange the three-phase conductors properly in single-circuit lines. Subconductor size, bundle number and arrangements must be chosen so that it can be realized that charges and maximum surface gradients on all subconductors are as nearly equal as possible, respectively, under acceptable engineering design constraints. The electric and magnetic field management within the ROW is a must, as a constraint, for these optimized configurations. For double-circuit and multi-circuit transmission lines, compact and optimized bundled configurations can be *Author to whom all correspondence should be addressed. 1053
FARAG et al.:
1054
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
applied for new tower designs and new lines configurations to enhance and manage the EMF effects. Certain operating performances of compact transmission lines can be, thus, improved by these optimization procedures. The optimum design for bundled conductor configurations was performed for three different transmission lines of 220 KV. These arrangements include different tower configurations such as horizontal, vertical, inverse triangular (Tee or Delta), circular, cruciform, etc. The numerical method of optimization of bundled conductors configurations for compact lines and its results are introduced. Transmission line parameters, corona loss, radio noise level, electric and magnetic fields underneath the lines and at the right-of-way, calculated at the 3 feet level, are also evaluated and analyzed. Attainable results of the optimized bundled conductor configuration for compact lines are compared to the corresponding results of the standard conventional and compact transmission lines. NUMERICAL
METHOD
OF OPTIMIZATION OF CONFIGURATIONS CONDUCTORS
OF BUNDLED
The optimization process of bundled contractors configuration is performed under the conditions that the tower type, phase-to-phase clearance, minimum height of subconductor to ground, subconductor size and bundle number are all predetermined. Two values of nonequalization about charges and maximum surface gradients of the subconductors which the optimum configuration of the three phase bundled conductors satisfies are predetermined too. As a result of this optimization process, the optimum configurations of three-phase bundled conductors have satisfied the above-stated requirements. The objective function The objective function of the optimization process is given as: minflx) = C, e(g i=l
- l)*+C. a”
e($+i=l
- l)* m,av
(1)
where: 3n n Qi
Q Ezi E m,av C,
is the number of total subconductors, is the bundle number, is the magnitude of charge on subconductor No. (i) in PC/m, is the average of the magnitudes of charges on all (3n) subconductors in PC/m, is the magnitude of maximum surface gradient on subconductor No. (i) in KV/m, is the average of the magnitudes of maximum surface gradients on all (3n) subconductors in KV/m, and and C, are the weighting factors which are taken as unity.
Optimized variables In this optimization process, the optimized variables are the locations of the subconductors (Xi) and (Yi), where the distance (Xi) is the horizontal distance of subconductor No. (i) from the center of the tower while (Yi) is the average height of subconductor No. (i) to ground. The total number of optimized variables is 2(3n + nd), where nd is the number of ground wires. All variables are expressed by an array X. Constraint conditions The constraint conditions for this optimization process are the limitations of variables which express the locations of all subconductors. These conditions should satisfy the requirements determined by a particular transmission line, such as insulation coordination, electrical load, mechanical load, sag limitations, environmental effects, etc. These items are expressed as: (a) (b) (c) (d)
Upper Upper Upper Upper
and and and and
lower lower lower lower
limits limits limits limits
of of of of
phase-to-phase clearances, bundle spaces of bundled conductors, ground wire locations, and average heights to ground of the lowest subconductors.
FARAG et al.:
BUNDLED CONDUCTOR
CONFIGURATION
OPTIMIZATION
1055
These constraint conditions are expressed by the general equation: i= 1,2,...,m
gi(x)IO3
The optimization problem has multi-continuous engineering requirements. The objective function including the variables array directly. This kind Method which is suitable for obtaining a solution
OPTIMIZATION
DESIGN
RESULTS
FOR
(2)
variables, which are constrained by minimum cannot be expressed by an analytical equation of problem is handled by using the Multiplier [l, 21.
220 KV TRANSMISSION
LINES
SYSTEMS
The optimization process for the configuration of 220 KV three phase bundled conductors includes two steps. First, the optimum configuration as a preliminary scheme can be found by using the optimization program (OCCP) (Optimization of Conductor of Compact Line Program). Second, the preliminary scheme is modified to be an engineering scheme which can be easily realized, taking into consideration all the design aspects and minimum standards requirements. For 220 KV transmission line systems, three types of three-phase arrangements and configurations are considered. These are flat, vertical, and inverse triangular (Tee or Delta) arrangements. Con$guration of bundled conductors In traditional transmission lines, regular polygon configuration bundled conductors are considered and adopted. Additionally, the same configurations are used on three phases. This configuration exhibits two major disadvantages: (1) due to the asymmetry of three-phase bundled conductors geometrically, the capacitance of the middle phase is larger than for the two outside phases. This leads to a higher charge on the middle-phase conductors than the two outside phases; (2) due to the interaction of all subconductors, the charges on all subconductors are not equal, and also, the charge along the circular surface of every subconductor is not uniform. This situation becomes more serious with reduction of the phase-to-phase clearance, especially with the conductors in the vertical arrangement. The relative values of the charges on the subconductors of the traditional three-phase conductors and the compact line designs are shown in Figs 1 and 2, respectively. For compact lines, the optimum three-phase bundled conductor configurations can be found by using the optimization program. The general configurations of the three-phase four-bundled conductors for three types of towers are shown in Fig. 3. For these configurations, the relative values of the charges on each subconductor can be equal to one as a maximum value. A charac-
+
22.5’
-
22.5’~
.L ?? o.97 1.2 r .0.97
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
i 1.06
?? o.97
il.06
.0.97
: ’:
2 x 300 mm2 0.4 m (1.2’) 7.5 m (22.5’)
Fig. 1. Charges on subconductors of traditional lines of 220 KV (TrH2).
1056
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
9'
I 1.23% 1.087' '
+
'
9’
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
: : :
(a) Vertical Lines (SV4) 0.934 0946
l-O&O 1
.
Logo
. . .
I i'.llO 0
’
0
1.0107'0.909 1.010
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
: :
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
(b) Tee (Delta) Lines (ST4)
0.8$8 l.040
I 1.1&4
0.8?6 1.089
1: 1.174*
Bundled Cnductors Bundle Spacing Phase-to-Phase clearance
::
: :
4x 150mm2 0.6 m (1.8’) 3.0 m (9’)
(c) Horizontal Lines (SH4) Fig. 2. Charges on subconductors of compact lines of 220 KV.
teristic of these optimum configurations is that the shapes of the outside phases are nearly like that of a semi-ellipse with larger bundle space than the middle phases; the shape of the middle phase is a polygon or regular polygon with smaller bundle space than the outside phases. For
FARAG et al.:
BUNDLED CONDUCTOR
CONFIGURATION
OPTIMIZATION
1057
(a) Vertical Optimum Configuration (PV4)
(b) Optimum Tee (Delta) Configuration (PT4)
(c) Optimum Horizontal Configuration (PH4) Fig. 3. Optimum configurations of bundled conductors of compact lines.
the three-phase inverse-triangular arrangement (Tee or Delta), the shapes are three trapezoids facing each other as shown in Fig. 3. For the sake of easy construction, these optimum schemes are modified. The three modified schemes are shown in Fig. 4. The differences of charges on each subconductor of the threephase bundled conductors, even for the vertical arrangement, are much lower than those of the compact lines shown in Fig. 2. The results shown in Fig. 4 show that the optimization of bundled conductor configurations is not only necessary but also calculable.
1058
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
1.020.
!
0.960
f
1 .
0
OPTIMIZATION
1 Oh
bo.T
(a> (PV4)
I
’ 40.41r 0.970&p?!1.
0 1
1.050.
. y4
,_&p
!
1.000. 1.007*
(b)
0
( 0
(PT4)
I
0.25
(c> PH4) Fig. 4. Charges on subconductors
of optimum configuration of bundled conductors of compact lines (phase-to-phase clearance is 3 m).
CALCULATIONS OF CONDUCTOR SURFACE ELECTRIC FIELD GRADIENTS The phase-to-phase clearances of compact lines are smaller than those of traditional lines. The effect of the charges on the neighbouring subconductors on the electric field gradient should be considered [3]. The surface electric field gradient of each subconductor and its distribution along the circular surface can be calculated using Equation (3) and the geometrical diagram of
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
1059
Fig. 5. Geometrical diagram of subconductors No. i and No. j.
subconductors
shown in Fig. 5.
Ei(4) =
&
Qi - 2 2
Q-3 J Aij
j=l,$ij
‘OS
(4 - ‘I’,)
1
(3)
where: $7
Aij Aij
4)
is the radius of subconductor i, indicates a point on the circular surface of subconductor i, is the center to center distance between conductors i and j, makes an angle Yli when r$ = 0.
In Equation (3) it is assumed that the charge is set on the center of each subconductor. The geometric diagram shown in Fig. 5 shows any two subconductors ij in a parallel multi-conductor system. The relative values of the maximum surface gradients of all subconductors in traditional lines and optimum compact lines are shown in Figs 6-8, where the average of the maximum surface fields gradients of all subconductors is used as a base value. The maximum values of the maximum surface field gradients of all subconductors for the three types of towers are shown in Table 1. It illustrates that the effectiveness of optimization is very significant. In a three-phase vertical arrangement, the nonequalization of maximum surface gradients can be reduced from +24%, -17% to +6%, -5% which is approximately equivalent to those values of traditional lines. The maximum value of maximum surface field gradients can be reduced from 29.7 KV/m to 22.2 KV/m. It is apparent and clear that the optimum bundled conductor configurations of compact lines will be an advantage to the operating performance of transmission lines. PERFORMANCE
OF OPTIMIZED
COMPACT
TRANSMISSION
LINES
The parameters of transmission lines vary with changes of the phase-to-phase clearances and bundle spaces of the conductors, which may further affect the operating performance of the transmission line.
0.98$ 0.98:
1.060!
0.98: t
1.060 ’ t
0.98:
Fig. 6. Relative values of maximum surface gradient on subconductors of traditional lines of 220 KV
1060
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
l.055 0.83.4 ! I0
.
1.244. 0.98.51 i'
.
1.05; 0.83.3! .
.
!
(a> W4)
0.950 0.910. l.g70 !
0
1
. .
1.020
.
1
1.120 l.O!O. .l.OlO I 00.900 I @I W4)
I 0.872
1.0,20
1.114
00
0.87:
1.020
1.1!4 010I ??
0
0
Fig. 7. Relative values of maximum surface gradient on subconductors of non-optimizing bundled conductors configurations (phase-to-phase clearance is 3.0 m).
Surge impedances For compact lines, it is of paramount importance that the surge impedance be smaller, and that leads to a larger natural power transfer capacity than that of a traditional line. Because of the change of geometry, the inductances of the compact lines are reduced while their capacitances are increased, as shown in Table 2. Comparing the compact lines with traditional lines, the positive sequence inductances of the compact lines is reduced by about 40%, while the positive sequence capacitances are increased by about 70%. This leads to the fact that the surge impedances of compact lines are reduced by about 40% and the natural power transfer capacity increases by 60%. Right-of-way The zones of high electric and magnetic fields underneath compact lines at/or close to ground level become narrower.
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
0.990.
!
OPTIMIZATION
1061
.
0.950 0 I 0 1.060* I e 1.060e 1 ?? 0.950
0 ! 0
09808
1 ??
(a) W4)
O*9600a9Jo.
I
1.040e’*ezO!
.
0
0
.
0.9900
I ??
l.OlOe
) 0
(b)
0’7’4)
Cc) PH4) Fig. 8. Relative values of maximum surface gradient on subconductors of optimizing bundled conductors configurations (phase-to-phase clearance is 3.0 m).
The charges on conductors of compact lines increase with the increased capacitance. The effect of three phase charges on space electric field can counteract each other. This counteraction will be significant when the phase-to-phase clearances are reduced. The maximum electric fields at 3 ft (xl m) above ground level are lower than those of the traditional lines for flat and inverse triangular (Delta or Tee) three-phase arrangements of compact lines. The width of trans-
1062
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
Table 1. Maximum surface gradient of subconductor (KV,,,/m) Tower Type No.
Maximum value
Average value
29.7 24.8 23.8 22.2 21.8 21.6 17.0
23.9 22.1 21.3 20.9 21.0 20.4 16.1
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
Note: Letters used in “Tower Type No.“: are: S, regular polygon bundled conductor for compact line; P, optimized bundled conductor for compact line; Tr, traditional line; H, three phase flat arrangement; V, three phase vertical arrangement; T, three phase triangular arrangement.
mission line corridors with high field are narrower than those of traditional lines in different degrees. For flat and inverse triangular arrangements, it is more apparent. Figure 9 shows the magnetic and electric fields of the traditional lines of 220 KV at 3 ft (1 m) above ground level. The maximum magnetic field is 326 mG at the center of the line, and a value of 50 mG is noticed at 100 ft away from the line center. The maximum electric field is 2.56 KV/m, and a value of 0.4 KV/m is shown at 100 ft from the line. Figure 10 shows the same fields of the compact lines SV4, ST4 and SH4. For the SV4 design (Fig. 10(a)) the maximum magnetic field is 127 mG at the line center and 18 mG at 100 ft away, while the corresponding values for the ST4 design (Fig. 10(b)) are 88 mG and 11 mG, respectively. For the SH4 design (Fig. 10(c)) they are 174 mG and 20 mG, respectively. The electric field values are: for the SV4 design, the maximum value is 2.86 KV/m at the line center and 0.2 KV/m at 100 ft, while for the ST4 design, the maximum value is 1.95 KV/m at the line center and 0.15 KV/m at 100 ft, and for the SH4 design, the maximum value is 2.05 KV/m at 25 ft away from the line center and 0.25 KV/m at 100 ft. For the optimized compact design, Fig. 11 shows the corresponding magnetic and electric fields for the three designs PV4, PT4 and PH4. For the PV4 design (Fig. 1la), the maximum magnetic field is 118 mG at the line center, and a field of 16 mG occurs at 100 f from the line center. For the PT4 design (Fig. 1lb), the corresponding values are 87.8 mG at the line center and 10.0 mG at 100 ft. For the PH4 design (Fig. 11(c)), the corresponding values are 164 mG and 19.6 mG, respectively. The electric field values are: for the PV4 design, the maximum values are 2.75 KV/m at the line center and 0.18 KV/m at 100 ft, while for the PT4 design, the maximum value is 2.01 KV/m at the line center and 0.16 KV/m at 100 ft, while the corresponding values for the PH4 design are: 2.07 KV/m at 25 ft away from the line center and 0.27 KV/m at 100 ft. Unbalances of transmission line parameters
The parameters of three phase transmission lines, no matter what configuration, are unbalanced to different degrees. This unbalance for vertical arrangements is more serious than for others. For optimized configurations, this unbalance can be improved to be nearly the same as for traditional lines. In general, the amount of transmission line unbalance can be represented by the electrostatic unbalance factors and the electromagnetic unbalance factors. It is assumed that the positive Table 2. Performance parameters of 220 KV transmission lines (f = 60 Hz) Tower Type No.
RI (Q)
LI (mH/Km)
Ci &F/Km)
Z, (Q)
P, (MVA)
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
0.0541 0.0532 0.0538 0.0531 0.0530 0.0544 0.0472
0.507 0.532 0.577 0.580 0.567 0.611 0.907
0.0232 0.0215 0.0203 0.0201 0.0201 0.0187 0.0118
177.4 188.8 202.3 203.7 201.6 217.0 345.1
327.5 307.5 287.1 285.0 288.0 267.7 168.3
FARAG et al.:
BUNDLED CONDUCTOR
(i) Magnetic
.._.
3.m
._
CONFIGURATION
OPTIMIZATION
1063
Field Profile
..___.
$
(ii) Electric Field
Profile
Fig. 9. Magnetic and electric fields of traditional line of 220 KV (TrH2).
sequence voltage applies at the sending end of a line with the receiving end open. The ratios between the zero and positive sequence currents, the negative and positive sequence currents are defined as the zero and negative sequence electrostatic unbalance factors, respectively: d,=!Q, 4,
d2 = i2,o 40
1064
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
If the receiving end of the line is shorted out, the ratios between the zero and positive sequence currents, the negative and positive sequence curets are defined as the zero and negative sequence electromagnetic unbalance factors, respectively: m0=7.
m2 = Z1.S
i2 s +-
11,s
Table 3 shows the results of the calculations for the different configurations.
(i) Magnetic Field Profile
Fig. 10(a)-Caption
on p. 1066.
(5)
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
.
.;. 1
.’ .:I / .
.;
.;...
\
L
-ass
-,
..-..
-s
?
e.cJ
i
.....~...---...-.-.....
(i) Magnetic Field Profile
(
(ii) Electric Field Profile Fig. IO(b)--Caption overleaf.
1065
1066
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
(i) Magnetic Field Profile
2
2
5
~..
............
,e
................ i
__... .:_
..i
\ ~~~.
I
-I
--r--v ,
i\ \.--
L B
lee
(ii) Electric Field Profile Fig. 10. (a) Magnetic and electric fields of compact line of 220 KV (SV4). (b) Magnetic and electric fields of compact line of 220 KV (ST4). (c) Magnetic and electric fields of compact line of 220 KV (SH4).
FARAG et
al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
1067
Radio noise level
The radio noise level of optimized compact lines under fair weather conditions are slightly higher than for traditional lines but less than for the compact lines.
(i) Magnetic Field Profile
(ii) Electric Field Profile Fig. 1l(a)-Caption
on p.
1069.
1068
FARAG et al.:
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
(i) Magnetic Field Profile
1
.a
.
@*s:..
j
.
. i
.. . . . . . . . . . . . . . .
ii& i...
..;
...’
.. .
.__..... j ,_.__.
;..
. . ;..
:..
.;
u
-1ee *‘strno.
Ice
0
-lee
OS-.”
I.*.r.no.
(ii) Electric Field Profile Fig. 1l(b)-Caption
opposite.
.;
.
1
0.e -3ee
.
2ae
i
308
FARAG
et al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
1069
(i) Magnetic Field Profile
-:‘.
._;...
......... ................ ...
..........
_.i._.
........
.;..
.j..
-~
i
........
\
-F
(ii) Electric Field Profile Fig. 11. (a) Magnetic and electric fields of optimal compact line of 220 KV (PV4). (b) Magnetic and electric fields of optimal compact line of 220 KV (PT4). (c) Magnetic and electric fields of optimal compact line of 220 KV (PH4).
In general, radio noise levels are calculated for transmission lines of 345 KV and above. Since the conductor surface gradient of the 220 KV compact lines is higher than that of a traditional line, the radio noise level may be one of the problems of concern to public utilities.
FARAG et al.:
1070
BUNDLED CONDUCTOR CONFIGURATION
OPTIMIZATION
Table 3. Unbalance of line parameters (%) Tower Type No.
do
d2
sv4 ST4 SH4 PV4 PT4 PH4 TrH2
3.45 0.21 3.46 5.92 0.19 6.19 2.58
16.8 0.59 15.6 9.30 0.22 8.41 8.49
m2
m0
1.56 0.14 1.37 2.66 0.15 2.46 1.34
16.4 0.47 15.4 9.54 0.11 8.28 9.41
Referring to the concepts of “Generation Function” and 500 KV base-case line RI Generation data [4], radio noise levels under fair and heavy rain weather are evaluated for the different arrangements of traditional, compact and optimized compact lines, as shown in Table 4. These results indicate that, prior to optimization, the radio noise levels of compact lines under fair weather, are much higher than that of the traditional line, while under heavy rain conditions, the levels are almost the same. For the optimized compact lines, the radio noise levels under fair weather are only slightly higher than that of the traditional line, while under heavy rain conditions, the levels are slightly lower than that of the traditional line. These results show that, for effective conductor configurations, optimization is of significance. Corona losses
Corona losses of compact lines are higher than that of the traditional line. The corona loss of a transmission line depends on the surface gradient of a subconductor. The onset gradient of corona (&) on a subconductor surface is given by Peek’s equation: KV/cm
where: m
6 r
is the surface factor, assumed 0.82 is the relative air density, assumed 1.O, and is the subconductor radius.
As an example, four bundled conductors of compact lines have been evaluated, the subconductor size being 150 mm2 (0.54 in dia.). Two bundled conductors of traditional line have also been evaluated, the subconductor size being 300 mm2 (0.77 in dia.). According to Equation (6), the E, of compact lines and traditional lines are 32.93 and 31.7 KV,,&m, respectively. From Table 1, the surface gradients of subconductors of compact lines are about 25% higher than that of the traditional line, leading to the conclusion that the corona loss of compact lines is increased. According to the general experimental curve [5], the corona losses of lines have been evaluated. For three-phase vertical and inverse triangular arrangements of compact lines, the annual average corona losses are 1.6 and 1.42 KW/Km-three phase. They are 6.4 and 5.68 times that of a traditional line, respectively.
Table 4. Radio noise level (dp) Tower Type No. sv4 ST4 SH4 PV4 PT4 PH4 TrH2
Fair Weather
Heavy Rain
55.6 41.8 38.9 34.4 33.2 32.8 25.3
65.7 59.5 57.7 54.5 53.5 53.3 63.5
FARAG
rt al.:
BUNDLED
CONDUCTOR
CONFIGURATION
OPTIMIZATION
1071
CONCLUSIONS
The natural power transfer capacity of transmission lines can be increased, while the right-ofway ROW) is reduced for compact transmission lines. It leads to the conclusion that “ROW” per width of transmission capability can be increased significantly. By adopting the optimum configurations of bundled conductors, the nonequalization of charges and maximum surface gradients on the subconductors of compact lines can be reduced. They can be at the same levels as that of traditional lines for the three phase vertical arrangement. The unbalances of line parameters are reduced as well. Corona losses and radio noise levels of compact lines are higher than that of traditional lines but within the allowable and permitted ranges. Electric and magnetic fields are managed, and lower levels of these fields were noticed in the optimum configuration of bundled conductors. REFERENCES 1. 2. 3. 4. 5.
Kaiming C., Chinese Journal of Operations Research, 1987, Vol. 6, No. 1. Jitternatrum, K., Math Programming 1980, Vol. 18. Alexandrov, G. H., Design of UHV Transmission Lines, Prentice-Hall, 1983. Anderson, J. G., EHV-UHV Transmission Systems, 1975. Burgsdorf, V. 1960. Corona Investigations on EHV Overhead Lines. CIGRE. Report
No. 413