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Transmission line parameters
CHAPTER 3
Transmission line parameters Contents 3.1 Distributed parameters of transmission line 3.2 Conductors arrangement 3.2.1 Bundled conductors 3.2.2 Three-phase conductors arrangement 3.2.3 Bundled conductors arrangement 3.3 Tower structure References
41 45 45 48 50 52 59
The parameters of ultra-high-voltage (UHV) power transmission lines include the positive sequence distributed capacitance C0 , distributed inductance L0 and distributed resistance R0 of the unit length of the line, conductor radius r0 , the number of bundled conductors n, circular radius of the bundled conductor rp , three-phase arrangement form, the suspension height of the conductor, etc. As the UHV transmission line is well insulated, its leakage conductance G0 is small enough to ignore.
3.1 Distributed parameters of transmission line Construction of UHV power transmission lines requires a huge investment. In order to make the most of the investment and maximize a line’s economic benefits, we should improve its transmission capacity as much as possible. The transmission line’s rated transmission power shall be about the upper and lower limits of its natural power. When the transmission power is greater than the natural power, the voltage loss of the transmission line increases [1] and larger reactive power compensation is required, which leads to increased investment and reduces the line’s economical efficiency. Therefore, increasing the natural power of transmission lines is the main way to increase transmission capacity. Natural power means that when this power is transmitted, the reactive power loss L0 I 2 caused by the current on the line is compensated by the
Protection Technologies of Ultra-High-Voltage AC Transmission Systems ISBN 978-0-12-816205-7 © 2020 China Electric Power Press. Published by Elsevier Inc. https://doi.org/10.1016/B978-0-12-816205-7.00003-0 All rights reserved.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
2 capacitive reactive power C0 Uph generated by the line phase voltage Uph 2 through the line capacitance. That is, L0 I 2 ¼ C0 Uph Now the line impedance becomes wave impedance Zc di.e., rffiffiffiffiffiffi Uph L0 Zc ¼ ¼ (3.1) I C0
Now the transmitted power is called natural power PN di.e., PN ¼ 3Uph I ¼ 3
Uph Uph I U 2 ¼ Zc Uph
(3.2)
U is the rated line voltage in the above equation. It follows that the natural power is inversely proportional to the wave impedance. To reduce the wave impedance, the per-unit-length inductance of the line should be reduced, and the per-unit-length capacitance should be increased. In the meantime, in order to reduce the power loss of the line, resistance should also be reduced. Multiple split wires can reduce resistance, increase wire surface area, and thereby increase capacitance. In cases with the same conductor radius and the same number of bundled conductors, line capacitance is related to maximum electric field intensity allowed on the conductor surface Ep and conductor surface area utilization factor kly , expressed as follows [1]: C0 ¼
Q0 qS0 ε0 Eav S0 ε0 Ep kly S0 ¼ ¼ ¼ Uph Uph Uph Uph
(3.3)
S0 ¼ 2npr0 Q0 q¼ S0 Eav kly ¼ <1 EP C0 dpositive sequence capacitance of per-meter transmission line, F/m. Q0 dcharge of per-meter transmission line. Uph dphase voltage, kV. S0 dtotal surface area of the phase conductor per meter, m2 . qdper-unit-area charge on the transmission line’s conductor surfaced that is, the density of charge
Transmission line parameters
43
ndnumber of bundled conductors. r0 dradius of each conductor, m. ε0 dvacuum (air) permittivity, equals 8.8541012 . Eav dactual average electric field intensity on conductor surface. kLy dconductor surface area utilization factor, typically less than 1. Ep dallowed maximum electric field intensity on the conductor surface, with the condition of corona occurring. Ep should be less than the minimum electric field intensity that can cause the coronadi.e., EP < Ed.y.min dand its value is related to weather conditions and conductor surface conditions, as discussed in Chapter 2. In general, Ed.y.min ¼ 20w21kV =cm. Let kbj be the coefficient considering the uneven distribution of electric field intensity on the conductor surface. It is the ratio of actual maximum electric field intensity on the conductor surface Emax and average intensity of electric field Eav [1]di.e., Emax >1 Eav
(3.4)
Eav Emax Eav Emax 1 ¼ ¼ kbj EP Ep Emax Ep
(3.5)
kbj ¼ Then, kLy ¼
For general high-voltage lines, Emax Ep , Eav Emax Ep , and the utilization coefficient of the conductor surface area is very low. For UHV transmission lines, Eav should be as close as possible to Ep so as to increase the area utilization coefficient of conductor surface areas as much as possible and maximize the economic benefits. Therefore, various measures must be taken to reduce the nonuniformity coefficient kbj to improve the surface utilization coefficient kLy . As for UHV lines, kbj should be minimized as far as possible, which can make kLy reach a range of 0.9e0.93. The inhomogeneity of electric field intensity on conductor surface is caused by the shield and interactions among the phases and bundled conductors, and the difference of the distance to the ground. Only reasonably arranging each phase line and bundled conductor, the inhomogeneity of electric field intensity can be reduced. Electromagnetic waves travel at approximately the same speed as light on overhead transmission line. That is: pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi vB ¼ 1= L0 C0 z vc ¼ 1= ε0 m0 (3.6)
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
In above equation, m0 ¼ 4p 107 , which is the magnetic conductivity in a vacuum. Therefore, the inductance and inductive reactance in per unit length of the line are as follows: L0 ¼
1 vc2 C0
¼
Uph 2 vc ε0 S0 Ep kLy
X0 ¼ uL0 ¼
¼
ε0 m0 Uph m0 Uph 2 107 Uph ¼ ¼ ε0 S0 Ep kLy 2pnr0 Ep kLy nr0 Ep kLy (3.7)
2 107 uUph 6:28 105 Uph z nr0 Ep kLy nr0 Ep kLy
The wave impedance is: rffiffiffiffiffiffi Uph Uph 60 Uph L0 1 Zc ¼ ¼ z ¼ ¼ v B L0 ¼ vB c0 ε0 vB S0 Ep kLy I C0 nr0 Ep kLy
(3.8)
(3.9)
It can be seen that the wave impedance is inversely proportional to the total surface area of phase conductors. In order to reduce the wave impedance, and increase the natural power, the total surface area of phase conductors needs to be enlargeddi.e., we should increase the number of bundled conductors and the radius of circumference made up of the bundled conductors. The effective resistance in per unit length of phase conductor is: r R0 ¼ (3.10) npr02 ce Here r is the resistance coefficient of aluminum cable steel reinforced, which is set 28.3 U$mm2 =km. ce is the filling coefficient (proportion) of conducting material(aluminum) in the conductor, and it’s less than 1. As for aluminum cable steel reinforced, we set 0:61 < ce < 0:67. From Eqs. (3.8) and (3.10), we can get: R0 2ε0 vB2 rEp kLy 107 rEp kLy ¼ ¼ X0 r0 ce uUph 2pur0 ce Uph
(3.11)
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3.2 Conductors arrangement 3.2.1 Bundled conductors The arrangement form of bundled conductors can be any shape [1]. Now we take circular arrangement for example to analyze, as shown in Fig. 3.1. Set n is the number of bundled conductors, r0 is the radius of each bundled conductor, ce is the filling coefficient of conducting material (aluminum) in the cross-section of conductor, rp is radius of circle by bundled conductors, so that the separation distance of conductors d is: p (3.12) d ¼ 2rp sin n Considering the demand of mechanical stability [1,2], d cannot be less than 0.3m. However, it isn’t the optimum value, about which is discussed in the optimization of the arrangement of bundled conductor in this section later. The configuration of the phase conductor shall meet the following basic requirements: (1) To limit the occurrence of corona and radio interference, we should set the actual maximum electric field intensity on the surface of the conductor Emax Ep . (2) When operating with economic current density under rated load, we set J ¼ Jjj , so as to minimize the energy loss. (3) Take full advantage of the surface area of conductors, making kLY z kly:max . According to Soviet experience [3] for UHV transmission lines the maximum permissible electric field intensity on conductor surface Ep can be set as follows: Ep 0:9Ed:y:min
(3.13)
d rp
π n
Figure 3.1 The calculation of separation distance of conductorsd.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
Ed.y.min is the minimum electric field intensity on the surface when corona occurring, and its determining method has been discussed before. Due to the differences of electric field intensity at different points on conductor surface, the ratio of maximum electric field intensity Emax to its average value Eav reflects the inhomogeneity of electric field intensity distribution. It’s been defined that the nonuniform coefficient Kbj ¼ EEmax > av 1, and we know Eav ¼
q Q0 Q0 ¼ ¼ ε0 ε0 S0 ε0 2npr0
(3.14)
Here q is the average charge density (charge on per unit surface area) on the conductor surface. Therefore, we can arrive at the maximum electric field intensity on the conductordi.e.: Emax ¼ kbj Eav ¼
Q0 kbj C0 Uph kbj Uph kbj ¼ ¼ ε0 2npr0 ε0 2npr0 ε0 2npr0 vB Zc Eav ¼
Uph ε0 2npr0 vB Zc
In which pffiffiffiffiffiffiffiffiffiffi C0 ¼ L0 C0
(3.15) (3.16)
rffiffiffiffiffiffi C0 1 ¼ L0 vB Zc
The ratio of average electric field intensity Eav to the maximum permissible electric field intensity Ep on conductor surface, is called utilization factor of conductor surface Kly . We can know from Eq. (3.16) as follows: kLy ¼
Uph Eav ¼ Ep ε0 2npr0 vB Zc EP
(3.17)
And we know from Eq. (3.5) as below: kLy ¼
Eav Emax Eav Emax 1 ¼ ¼ kbj EP Ep Emax Ep
(3.18)
This shows that the more nonuniform the distribution of electric field intensity on the conductor surface is, the bigger kbj may be, and the lower the utilization ratio of conductor surface area may be as well, making the
Transmission line parameters
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utilization factor smaller. Consequently, the main purpose for studying the arrangement of the three phase conductors is to maximize the uniformity of electric field intensity on conductor surface, making Eav as close to Emax and Ep as possible. When Eav ¼ Emax ¼ Ep , Kly ¼ 1. As to current density, we should make the actual current density J as close to economic current density Jjj as possible under rated load P. J¼
P ¼ Jjj 3Uph npr02 ce
(3.19)
Eq. (3.18) can also be written as follows: Uph ¼ kLy Ep ε0 2npr0 vB Zc Dividing above equation on both side by (3.19), we get 3Uph2 Ep kLy r0 ce ¼ Jjj 2ε0 vB PZc Thus we get the equation for r0 as r0 ¼ 2ε0 vB
PEP kLy P EP kLy z PN Jjj ce 60pPN Jjj ce
In this equation, the natural power is PN ¼ above equation of r0 into Eq. (3.15), we get n¼
2 3Uph Zc
(3.20) 2
¼ UZc . By putting the
Uph Jjj Xe P PN Jjj Xe 2 2 z 3600pUph P ðEp kLy Þ2 pð2ε0 vB Þ Zc PN ðEp kLy Þ
(3.21)
From Eqs. (3.20) and (3.21), it is known that the radius r0 of each conductor is irrelevant to rated voltage and only relevant to the ratio of transmission power to natural power and the economic current density. This is applicable to various voltage grades. However, the number of bundled conductors is relevant to rated voltage and transmission power. The selection of economic current density Jjj should minimize the sum of construction and operational costs (the cost of energy loss during transmission) of the power line, and it is complex to consider these factorsdfor example: the price of electricity, utilization hours under rated load, investment scale of the power line, cycle of construction, loan interest, and
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
scheduled years of investment recovery. All these factors should be taken into account.
3.2.2 Three-phase conductors arrangement For a single-circuit line, a three-phase horizontal arrangement is the simplest. We shall use this arrangement for an example to explain the optimization method. To improve the utilization ratio of the conductor surface area, the capacitances of the three phases in a symmetric state should be equal. In a three-phase horizontally arranged line, the geometric mean distance of the middle phase is less than those of the two side phases, and the capacitance of the middle phase is bigger than the capacitance of the side phases. This inhomogeneity reduces the utilization coefficient. For this kind of arrangement, two methods can make the capacitances of the three phases equal: ①making the height above ground of the middle phase a DH higher than that of the side phases; therefore, the height above ground of the middle phase is increased and its capacitance is reduced, as shown in Fig. 3.2; ②making the circumference of the two side phases a little more than that of the middle phase, so the surface areas of the side phase conductors are increased and their capacitances are increased. The two methods just mentioned can be used simultaneously.
2d 0 d 0'
d 0'
d0
d0 ΔH
H1
H eq-b
H2
H1
H eq-b
H eq-b
Figure 3.2 Optimization method of three-phase arrangement.
Transmission line parameters
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When the two methods are used simultaneously with the aim of making the three phase capacitances equal, we can get the relationship between the height DH by which the middle phase needs to be raised and the ratio of the side-phase circular equivalent radius to that of the middle phase by electromagnetic calculation. We can then select an appropriate solution [1]. Set rp1 and rp2 as the side-phase and middle-phase circular radii of the bundled conductors, rep:1 and rep:2 , as the equivalent circular radius arranged on the side phase and middle phase bundled conductors with due regard to the interaction of the conductors. The following relation is valid: rffiffiffiffiffiffi nr0 req:1 ¼ rp1 n rp1 rffiffiffiffiffiffi nr0 req:2 ¼ rp2 n rp2 1 Heq:1 ¼ H1:min þ f1 3 where H1:min is the minimum height above ground of the side-phase conductor when arc sag is considered; Heq:1 ¼ Heq.b is the equivalent height of the side-phase conductor after considering the effect of arc sag; H1 is the actual suspension height of the side-phase conductor in the tower; H2 is the actual suspension height of the middle-phase conductor in the tower; f1 is the arc sag of the side-phase conductor. Thus the ratio of rep:1 to rep:2 can be obtained as Eq. (3.22). Sequentially, we can get the side-phase and middle-phase circular radii of bundled conductors rp1 and rp2 that make the three phase capacitances equal. It should be noted that for the line segment close to the tower, the effect of the tower is equivalent to shortening the distance of the conductor to the ground, so capacitance is increased. Therefore, the circular radius of the bundled conductor should be reduced properly near the tower, where a shielding layer must be installed [1]:
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
req:2 2Heq:1 DH ¼ 1þ Heq:1 req:1 req:1 2Heq:1 2Heq:1 pffiffiffiffi 2 3 ln B A þ ðln AÞ2 ln r B r eq:1 5 eq:1 exp4 2Heq:1 pffiffiffi ln B req:1 B In
this equation, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 2 2 . B ¼ u1 þ D0 DH t Heq:1 Heq:1
(3.22)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Heq:1 1 þ HDH , A ¼ 1 þ D0 eq:1
3.2.3 Bundled conductors arrangement Fig. 3.3 demonstrates the arrangement of the three phases following an equilateral triangle [1], which is the ideal arrangement form. This arrangement form can balance the three-phase capacitance and equalize the circular radii of three-phase bundled conductors. However, the difference of the conductor positions in the circumference of the bundled conductors leads to imbalance of the surface electric field intensity. In three phases, the facing conductors are nearer each other, so the surface electric field intensity between them is larger while that of the opposing ones is smaller. It is Ψ
dΨ
Ψ
dΨ
Figure 3.3 Optimization of bundled conductor arrangement.
Transmission line parameters
51
known from Eq. (3.3) that with the same capacitance, electric field intensity is inversely proportional to surface area S0 . Therefore, if the surface area of the three-phase facing portions is reduced, the larger surface electric field strength can be compensated for, and the surface area of the back-to-back portion can be increased to compensate for the smaller surface electric field strength. On the symmetry axis of three angular bisectors of the equilateral triangle’s three angles in Fig. 3.3, the conductors are arranged symmetrically. Meanwhile, inside the triangle the conductor distance near the symmetry axis is reduceddi.e., the surface area is reduced. Also, the conductor distance near the bisector of the exterior angles of the triangle is increaseddi.e., the surface area is increased. As shown in the figure, hollow dots represent the conductor positions evenly distributed along the circumference, and the solid dots represent optimized conductor positions. How much the conductors should be moved must be specifically calculated. The inhomogeneity of electric field intensity on the bundled conductor surface is caused by three factors: (1) The relative distances of the three phases are asymmetrical, so the capacitances of the three phases are different. This inhomogeneity is denoted by kbj:1 . kbj:1 ¼
3Cmax CA þ CB þ CC
Cmax is the capacitance of the largest phase of the capacitor. CA , CB , and CC are the capacitances of phases A, B and C. It is thus clear that if the three phase capacitances are equal to the one that is maximum, Kbj:1 ¼ 1. (2) The per-unit-area charge q differs in each bundled conductor. As shown in Fig. 3.2, the charges can basically be the same in each conductor, making kbj:2 z 1. (3) When the bundled conductors are arranged in a circle, electric field intensity on the conductor surfaces is asymmetrical because of the interaction of the conductors. This inhomogeneity is denoted by kbj:3 : r0 kbj:3 ¼ 1 þ ðn 1Þ rp In this equation, n stands for the number of bundled conductors. If n ¼ 1di.e., there is only one conductor for each phasedthen kbj:3 ¼ 1.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
The total unevenness coefficient is kbj ¼ kbj:1 kbj:2 kbj:3 . The above discussion is about the optimization method of the threephase arrangement of bundled conductors. Each method requires careful analysis and calculations to be realized. Due to the fully utilized conductor surface, the maximum electric field intensity on the conductor surface is close to the allowed maximum value, so its margin for withstanding overvoltage is much lower than that on a smaller-voltage line. In addition, the capacity of the shunt reactor is large. So inputting and cutting of shunt reactors must be coordinated closely with line protection. These characteristics should all be noted in the design of the relay protection configuration scheme.
3.3 Tower structure The type and size of the transmission line tower have a great influence on line parameters and investment. The type and size of the three kinds of 1000 kV tower are introduced in Fig. 3.6, and some types of 1000 kV line towers are shown in Figs. 3.4e3.9 [4]. The structure and size of Soviet 750 and 1150 kV guyed and self-supporting compact towers are demonstrated in Figs. 3.8 and 3.9 [1e3,5]. In the 1150 kV line, a 12-bundled conductor is used. The conductor is 48-stranded aluminum-conductor steel-reinforced (ACSR), and the sectional area of each conductor is 300mm2 . (B) (A)
Figure 3.4 1000 kV pole towers of cat head type and wine glass type: (A) wine glass type; (B) cat head type.
Transmission line parameters
(A)
(B)
(C)
(D)
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Figure 3.5 Straight pole tower for 1000 kV ultra-high-voltage transmission line: (A) 3Vtype horizontal arrangement; (B) 3V-type triangle arrangement; (C) M-type horizontal arrangement; (D) M-type triangle arrangement.
For UHV transmission lines, compact tower structures should be adopted. The central idea of compact tower design is to try to reduce the phase distance without reducing the phase line to ground (steel frame) insulation gap. Thus, if the floor space of the line corridor, inductance, and wave impedance are reduced, the transmission capacity of the line is increased. The main way to do this is to design the special tower shape and insulator suspension method so that there is no ground component among the phases. The conductors should be suspended with a V-type insulator that can fix the conductors and may not be swayed by the wind. Thus the gaps, both between conductor and the ground component and among the phases, may be reduced. In consequence, the distance of the phases may be reduced. Practice has proven that based on the study on the structure of the
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(A)
(B)
(C)
(D)
(E)
Figure 3.6 UHV tower types designed and adopted overseas: (A) and (E) Soviet; (B) Japanese; (C) American; (D) Italian.
Transmission line parameters
(A)
55
(B)
Figure 3.7 Compact tower: (A) 1150 kV suspension line tower; (B) Delta configuration pulling V-type tower.
tower and line conductor system, it is more economical to improve the transmission capacity of the line than to provide compensating devices. By reference to a Brazil 500 kV line compact tower, the Northwest Power Grid Design Institute of the Soviet Union designed a new 1150 kV line self-supporting compact tower, as shown in Fig. 3.9. In this design, a 12-bundled conductor for each phase is adopted, and each conductor is 48stranded ACSR with a sectional area of 300mm2 (12AC 300/48). The circular radius of the bundled conductor is rp ¼ 0.9 m in the central span, the distance between the two conductors is d ¼ 0.47 m, and rp0 ¼ 0.67 m near the tower. Because of the increasing number of bundled conductors, according to the anticorona requirements, the minimum distance between phases can reach 11 m, and the span distance of the tower can reach 500 m. After the middle phase is elevated 8.05 m, the phase distance of the two sides is reduced to 15 m. However, the phase distance of the two sides in the established noncompact 1150 kV line tower is 46 m. Due to the reduction of the phase distance, the number of bundled conductors is
Figure 3.8 Soviet 750 kV line-pulling compact tower.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
Figure 3.9 Soviet 1150 kV line self-supporting compact tower.
increased so that the wave impedance ZC is reduced and natural power is increased by 0.5 times. The newly designed tower weighs 34 t with the same steel consumption as before, while its occupied area has been greatly reduced. In addition, on this basis, it is an inevitable development trend of the UHV power grid to develop and construct UHV double-circuit/multicircuit/compact transmission lines. The research and construction of UHV double-circuit/multi-circuit/ compact transmission lines are quite extensive abroad. In America, the proportion of transmission lines for which double-circuit lines have been adopted on the same tower in 220and 345 kV voltage grades is 47% and 52%, respectively. In Britain, double-circuit lines on the same tower are adopted on all 400 kV lines. In Japan, double-circuit lines on the same
Transmission line parameters
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tower are adopted on 90% of 500 kV lines, and the structure of doublecircuit lines on the same tower is adopted in all four established 1000 kV UHV lines. As for multiple circuits on the same tower, during the 1970s and 1980s, America studied and built transmission lines with multiple circuits on the same tower to improve transmission capacity in unit corridors. Furthermore, as pioneers of compact transmission technology, the Soviet Union and Japan successively built EHV (extra-high-voltage) multicircuit compact transmission lines on same tower. Double-circuit lines are also widely used in China’s EHV and UHV transmission systems. Fig. 3.10 shows the structure of a double-circuit compact transmission line on the same tower at the 750 kV voltage level, which is closest to UHV. However, there are still many problems to be solved for the tower structure for 1000 kV UHV double-circuit compact transmission on the same tower. The operational experience of the Soviet Union’s and Japan’s UHV transmission lines shows that shielding failure and back flashover of lightning are the main causes of double-circuit fault and interline fault. The conventional double-circuit same-tower structure is beneficial to prevent sleeting jump, while the belt-umbrella tower has the advantage in lightning protection performance. The T-type compact double-circuit same-tower tower shown in Fig. 3.10B is widely used in Chinese 500 kV transmission systems. The distance between conductors of compact double-circuit
Figure 3.10 The 750 kV tower structure of a double-circuit same-tower line (A) 750 kV double-circuit same-tower routine type; (B) 750 kV compact double-circuit same-tower T-type; (C) 750 kV compact double-circuit same-tower with-same-window.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
transmission lines is closer. Especially in the UHV electric field environment, the skin effect that occurs when alternating current circulates between conductor and earth makes the frequency characteristics of the line parameters much more obvious. The structure of a 750 kV compact double-circuit same-tower with same window proposed by China is shown in Fig. 3.10C. Furthermore, China has proposed a vertical, bitriangular arrangement, which is more compact with a better electromagnetic environment than the symmetrical inverted triangle arrangement. The structure of a Chinese 500 kV four-circuit on-same-tower transmission line is shown as Fig. 3.11. It can be seen from Figs. 3.10 and 3.11, influenced by tower structure and conductor arrangement, the electromagnetic and static electricity couplings between the phases and conductors of double or multiple circuits in a line corridor are asymmetrical. Therefore, the imbalance of UHV double-circuit/ multicircuit transmission lines should be researched and demonstrated. (A)
(B)
Figure 3.11 Tower structure of multicircuit lines: (A) 500 kV four-circuit on-same-tower d-type; (B) 500 kV four-circuit on-same-tower e-type.
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References [1] [2] [3] [4] [5]
AC transmission. GH Mark; 1998. About the new voltage level of AC transmission. electricity. 1985. No.1. (in Russian). Electrical equipment installation procedures. Beijing: Electric and Nuclear Press; 1986. Ultra-high voltage grid. Zhenya Liu. Beijing: China Economic Publishing House; 2005. Design of ultra-high voltage transmission lines. GH Mark. Electric and Nuclear Press; 1986.
Transmission line parameters Contents 3.1 Distributed parameters of transmission line 3.2 Conductors arrangement 3.2.1 Bundled conductors 3.2.2 Three-phase conductors arrangement 3.2.3 Bundled conductors arrangement 3.3 Tower structure References
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The parameters of ultra-high-voltage (UHV) power transmission lines include the positive sequence distributed capacitance C0 , distributed inductance L0 and distributed resistance R0 of the unit length of the line, conductor radius r0 , the number of bundled conductors n, circular radius of the bundled conductor rp , three-phase arrangement form, the suspension height of the conductor, etc. As the UHV transmission line is well insulated, its leakage conductance G0 is small enough to ignore.
3.1 Distributed parameters of transmission line Construction of UHV power transmission lines requires a huge investment. In order to make the most of the investment and maximize a line’s economic benefits, we should improve its transmission capacity as much as possible. The transmission line’s rated transmission power shall be about the upper and lower limits of its natural power. When the transmission power is greater than the natural power, the voltage loss of the transmission line increases [1] and larger reactive power compensation is required, which leads to increased investment and reduces the line’s economical efficiency. Therefore, increasing the natural power of transmission lines is the main way to increase transmission capacity. Natural power means that when this power is transmitted, the reactive power loss L0 I 2 caused by the current on the line is compensated by the
Protection Technologies of Ultra-High-Voltage AC Transmission Systems ISBN 978-0-12-816205-7 © 2020 China Electric Power Press. Published by Elsevier Inc. https://doi.org/10.1016/B978-0-12-816205-7.00003-0 All rights reserved.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
2 capacitive reactive power C0 Uph generated by the line phase voltage Uph 2 through the line capacitance. That is, L0 I 2 ¼ C0 Uph Now the line impedance becomes wave impedance Zc di.e., rffiffiffiffiffiffi Uph L0 Zc ¼ ¼ (3.1) I C0
Now the transmitted power is called natural power PN di.e., PN ¼ 3Uph I ¼ 3
Uph Uph I U 2 ¼ Zc Uph
(3.2)
U is the rated line voltage in the above equation. It follows that the natural power is inversely proportional to the wave impedance. To reduce the wave impedance, the per-unit-length inductance of the line should be reduced, and the per-unit-length capacitance should be increased. In the meantime, in order to reduce the power loss of the line, resistance should also be reduced. Multiple split wires can reduce resistance, increase wire surface area, and thereby increase capacitance. In cases with the same conductor radius and the same number of bundled conductors, line capacitance is related to maximum electric field intensity allowed on the conductor surface Ep and conductor surface area utilization factor kly , expressed as follows [1]: C0 ¼
Q0 qS0 ε0 Eav S0 ε0 Ep kly S0 ¼ ¼ ¼ Uph Uph Uph Uph
(3.3)
S0 ¼ 2npr0 Q0 q¼ S0 Eav kly ¼ <1 EP C0 dpositive sequence capacitance of per-meter transmission line, F/m. Q0 dcharge of per-meter transmission line. Uph dphase voltage, kV. S0 dtotal surface area of the phase conductor per meter, m2 . qdper-unit-area charge on the transmission line’s conductor surfaced that is, the density of charge
Transmission line parameters
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ndnumber of bundled conductors. r0 dradius of each conductor, m. ε0 dvacuum (air) permittivity, equals 8.8541012 . Eav dactual average electric field intensity on conductor surface. kLy dconductor surface area utilization factor, typically less than 1. Ep dallowed maximum electric field intensity on the conductor surface, with the condition of corona occurring. Ep should be less than the minimum electric field intensity that can cause the coronadi.e., EP < Ed.y.min dand its value is related to weather conditions and conductor surface conditions, as discussed in Chapter 2. In general, Ed.y.min ¼ 20w21kV =cm. Let kbj be the coefficient considering the uneven distribution of electric field intensity on the conductor surface. It is the ratio of actual maximum electric field intensity on the conductor surface Emax and average intensity of electric field Eav [1]di.e., Emax >1 Eav
(3.4)
Eav Emax Eav Emax 1 ¼ ¼ kbj EP Ep Emax Ep
(3.5)
kbj ¼ Then, kLy ¼
For general high-voltage lines, Emax Ep , Eav Emax Ep , and the utilization coefficient of the conductor surface area is very low. For UHV transmission lines, Eav should be as close as possible to Ep so as to increase the area utilization coefficient of conductor surface areas as much as possible and maximize the economic benefits. Therefore, various measures must be taken to reduce the nonuniformity coefficient kbj to improve the surface utilization coefficient kLy . As for UHV lines, kbj should be minimized as far as possible, which can make kLy reach a range of 0.9e0.93. The inhomogeneity of electric field intensity on conductor surface is caused by the shield and interactions among the phases and bundled conductors, and the difference of the distance to the ground. Only reasonably arranging each phase line and bundled conductor, the inhomogeneity of electric field intensity can be reduced. Electromagnetic waves travel at approximately the same speed as light on overhead transmission line. That is: pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi vB ¼ 1= L0 C0 z vc ¼ 1= ε0 m0 (3.6)
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
In above equation, m0 ¼ 4p 107 , which is the magnetic conductivity in a vacuum. Therefore, the inductance and inductive reactance in per unit length of the line are as follows: L0 ¼
1 vc2 C0
¼
Uph 2 vc ε0 S0 Ep kLy
X0 ¼ uL0 ¼
¼
ε0 m0 Uph m0 Uph 2 107 Uph ¼ ¼ ε0 S0 Ep kLy 2pnr0 Ep kLy nr0 Ep kLy (3.7)
2 107 uUph 6:28 105 Uph z nr0 Ep kLy nr0 Ep kLy
The wave impedance is: rffiffiffiffiffiffi Uph Uph 60 Uph L0 1 Zc ¼ ¼ z ¼ ¼ v B L0 ¼ vB c0 ε0 vB S0 Ep kLy I C0 nr0 Ep kLy
(3.8)
(3.9)
It can be seen that the wave impedance is inversely proportional to the total surface area of phase conductors. In order to reduce the wave impedance, and increase the natural power, the total surface area of phase conductors needs to be enlargeddi.e., we should increase the number of bundled conductors and the radius of circumference made up of the bundled conductors. The effective resistance in per unit length of phase conductor is: r R0 ¼ (3.10) npr02 ce Here r is the resistance coefficient of aluminum cable steel reinforced, which is set 28.3 U$mm2 =km. ce is the filling coefficient (proportion) of conducting material(aluminum) in the conductor, and it’s less than 1. As for aluminum cable steel reinforced, we set 0:61 < ce < 0:67. From Eqs. (3.8) and (3.10), we can get: R0 2ε0 vB2 rEp kLy 107 rEp kLy ¼ ¼ X0 r0 ce uUph 2pur0 ce Uph
(3.11)
Transmission line parameters
45
3.2 Conductors arrangement 3.2.1 Bundled conductors The arrangement form of bundled conductors can be any shape [1]. Now we take circular arrangement for example to analyze, as shown in Fig. 3.1. Set n is the number of bundled conductors, r0 is the radius of each bundled conductor, ce is the filling coefficient of conducting material (aluminum) in the cross-section of conductor, rp is radius of circle by bundled conductors, so that the separation distance of conductors d is: p (3.12) d ¼ 2rp sin n Considering the demand of mechanical stability [1,2], d cannot be less than 0.3m. However, it isn’t the optimum value, about which is discussed in the optimization of the arrangement of bundled conductor in this section later. The configuration of the phase conductor shall meet the following basic requirements: (1) To limit the occurrence of corona and radio interference, we should set the actual maximum electric field intensity on the surface of the conductor Emax Ep . (2) When operating with economic current density under rated load, we set J ¼ Jjj , so as to minimize the energy loss. (3) Take full advantage of the surface area of conductors, making kLY z kly:max . According to Soviet experience [3] for UHV transmission lines the maximum permissible electric field intensity on conductor surface Ep can be set as follows: Ep 0:9Ed:y:min
(3.13)
d rp
π n
Figure 3.1 The calculation of separation distance of conductorsd.
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
Ed.y.min is the minimum electric field intensity on the surface when corona occurring, and its determining method has been discussed before. Due to the differences of electric field intensity at different points on conductor surface, the ratio of maximum electric field intensity Emax to its average value Eav reflects the inhomogeneity of electric field intensity distribution. It’s been defined that the nonuniform coefficient Kbj ¼ EEmax > av 1, and we know Eav ¼
q Q0 Q0 ¼ ¼ ε0 ε0 S0 ε0 2npr0
(3.14)
Here q is the average charge density (charge on per unit surface area) on the conductor surface. Therefore, we can arrive at the maximum electric field intensity on the conductordi.e.: Emax ¼ kbj Eav ¼
Q0 kbj C0 Uph kbj Uph kbj ¼ ¼ ε0 2npr0 ε0 2npr0 ε0 2npr0 vB Zc Eav ¼
Uph ε0 2npr0 vB Zc
In which pffiffiffiffiffiffiffiffiffiffi C0 ¼ L0 C0
(3.15) (3.16)
rffiffiffiffiffiffi C0 1 ¼ L0 vB Zc
The ratio of average electric field intensity Eav to the maximum permissible electric field intensity Ep on conductor surface, is called utilization factor of conductor surface Kly . We can know from Eq. (3.16) as follows: kLy ¼
Uph Eav ¼ Ep ε0 2npr0 vB Zc EP
(3.17)
And we know from Eq. (3.5) as below: kLy ¼
Eav Emax Eav Emax 1 ¼ ¼ kbj EP Ep Emax Ep
(3.18)
This shows that the more nonuniform the distribution of electric field intensity on the conductor surface is, the bigger kbj may be, and the lower the utilization ratio of conductor surface area may be as well, making the
Transmission line parameters
47
utilization factor smaller. Consequently, the main purpose for studying the arrangement of the three phase conductors is to maximize the uniformity of electric field intensity on conductor surface, making Eav as close to Emax and Ep as possible. When Eav ¼ Emax ¼ Ep , Kly ¼ 1. As to current density, we should make the actual current density J as close to economic current density Jjj as possible under rated load P. J¼
P ¼ Jjj 3Uph npr02 ce
(3.19)
Eq. (3.18) can also be written as follows: Uph ¼ kLy Ep ε0 2npr0 vB Zc Dividing above equation on both side by (3.19), we get 3Uph2 Ep kLy r0 ce ¼ Jjj 2ε0 vB PZc Thus we get the equation for r0 as r0 ¼ 2ε0 vB
PEP kLy P EP kLy z PN Jjj ce 60pPN Jjj ce
In this equation, the natural power is PN ¼ above equation of r0 into Eq. (3.15), we get n¼
2 3Uph Zc
(3.20) 2
¼ UZc . By putting the
Uph Jjj Xe P PN Jjj Xe 2 2 z 3600pUph P ðEp kLy Þ2 pð2ε0 vB Þ Zc PN ðEp kLy Þ
(3.21)
From Eqs. (3.20) and (3.21), it is known that the radius r0 of each conductor is irrelevant to rated voltage and only relevant to the ratio of transmission power to natural power and the economic current density. This is applicable to various voltage grades. However, the number of bundled conductors is relevant to rated voltage and transmission power. The selection of economic current density Jjj should minimize the sum of construction and operational costs (the cost of energy loss during transmission) of the power line, and it is complex to consider these factorsdfor example: the price of electricity, utilization hours under rated load, investment scale of the power line, cycle of construction, loan interest, and
48
Protection Technologies of Ultra-High-Voltage AC Transmission Systems
scheduled years of investment recovery. All these factors should be taken into account.
3.2.2 Three-phase conductors arrangement For a single-circuit line, a three-phase horizontal arrangement is the simplest. We shall use this arrangement for an example to explain the optimization method. To improve the utilization ratio of the conductor surface area, the capacitances of the three phases in a symmetric state should be equal. In a three-phase horizontally arranged line, the geometric mean distance of the middle phase is less than those of the two side phases, and the capacitance of the middle phase is bigger than the capacitance of the side phases. This inhomogeneity reduces the utilization coefficient. For this kind of arrangement, two methods can make the capacitances of the three phases equal: ①making the height above ground of the middle phase a DH higher than that of the side phases; therefore, the height above ground of the middle phase is increased and its capacitance is reduced, as shown in Fig. 3.2; ②making the circumference of the two side phases a little more than that of the middle phase, so the surface areas of the side phase conductors are increased and their capacitances are increased. The two methods just mentioned can be used simultaneously.
2d 0 d 0'
d 0'
d0
d0 ΔH
H1
H eq-b
H2
H1
H eq-b
H eq-b
Figure 3.2 Optimization method of three-phase arrangement.
Transmission line parameters
49
When the two methods are used simultaneously with the aim of making the three phase capacitances equal, we can get the relationship between the height DH by which the middle phase needs to be raised and the ratio of the side-phase circular equivalent radius to that of the middle phase by electromagnetic calculation. We can then select an appropriate solution [1]. Set rp1 and rp2 as the side-phase and middle-phase circular radii of the bundled conductors, rep:1 and rep:2 , as the equivalent circular radius arranged on the side phase and middle phase bundled conductors with due regard to the interaction of the conductors. The following relation is valid: rffiffiffiffiffiffi nr0 req:1 ¼ rp1 n rp1 rffiffiffiffiffiffi nr0 req:2 ¼ rp2 n rp2 1 Heq:1 ¼ H1:min þ f1 3 where H1:min is the minimum height above ground of the side-phase conductor when arc sag is considered; Heq:1 ¼ Heq.b is the equivalent height of the side-phase conductor after considering the effect of arc sag; H1 is the actual suspension height of the side-phase conductor in the tower; H2 is the actual suspension height of the middle-phase conductor in the tower; f1 is the arc sag of the side-phase conductor. Thus the ratio of rep:1 to rep:2 can be obtained as Eq. (3.22). Sequentially, we can get the side-phase and middle-phase circular radii of bundled conductors rp1 and rp2 that make the three phase capacitances equal. It should be noted that for the line segment close to the tower, the effect of the tower is equivalent to shortening the distance of the conductor to the ground, so capacitance is increased. Therefore, the circular radius of the bundled conductor should be reduced properly near the tower, where a shielding layer must be installed [1]:
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Protection Technologies of Ultra-High-Voltage AC Transmission Systems
req:2 2Heq:1 DH ¼ 1þ Heq:1 req:1 req:1 2Heq:1 2Heq:1 pffiffiffiffi 2 3 ln B A þ ðln AÞ2 ln r B r eq:1 5 eq:1 exp4 2Heq:1 pffiffiffi ln B req:1 B In
this equation, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 2 2 . B ¼ u1 þ D0 DH t Heq:1 Heq:1
(3.22)
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Heq:1 1 þ HDH , A ¼ 1 þ D0 eq:1
3.2.3 Bundled conductors arrangement Fig. 3.3 demonstrates the arrangement of the three phases following an equilateral triangle [1], which is the ideal arrangement form. This arrangement form can balance the three-phase capacitance and equalize the circular radii of three-phase bundled conductors. However, the difference of the conductor positions in the circumference of the bundled conductors leads to imbalance of the surface electric field intensity. In three phases, the facing conductors are nearer each other, so the surface electric field intensity between them is larger while that of the opposing ones is smaller. It is Ψ
dΨ
Ψ
dΨ
Figure 3.3 Optimization of bundled conductor arrangement.
Transmission line parameters
51
known from Eq. (3.3) that with the same capacitance, electric field intensity is inversely proportional to surface area S0 . Therefore, if the surface area of the three-phase facing portions is reduced, the larger surface electric field strength can be compensated for, and the surface area of the back-to-back portion can be increased to compensate for the smaller surface electric field strength. On the symmetry axis of three angular bisectors of the equilateral triangle’s three angles in Fig. 3.3, the conductors are arranged symmetrically. Meanwhile, inside the triangle the conductor distance near the symmetry axis is reduceddi.e., the surface area is reduced. Also, the conductor distance near the bisector of the exterior angles of the triangle is increaseddi.e., the surface area is increased. As shown in the figure, hollow dots represent the conductor positions evenly distributed along the circumference, and the solid dots represent optimized conductor positions. How much the conductors should be moved must be specifically calculated. The inhomogeneity of electric field intensity on the bundled conductor surface is caused by three factors: (1) The relative distances of the three phases are asymmetrical, so the capacitances of the three phases are different. This inhomogeneity is denoted by kbj:1 . kbj:1 ¼
3Cmax CA þ CB þ CC
Cmax is the capacitance of the largest phase of the capacitor. CA , CB , and CC are the capacitances of phases A, B and C. It is thus clear that if the three phase capacitances are equal to the one that is maximum, Kbj:1 ¼ 1. (2) The per-unit-area charge q differs in each bundled conductor. As shown in Fig. 3.2, the charges can basically be the same in each conductor, making kbj:2 z 1. (3) When the bundled conductors are arranged in a circle, electric field intensity on the conductor surfaces is asymmetrical because of the interaction of the conductors. This inhomogeneity is denoted by kbj:3 : r0 kbj:3 ¼ 1 þ ðn 1Þ rp In this equation, n stands for the number of bundled conductors. If n ¼ 1di.e., there is only one conductor for each phasedthen kbj:3 ¼ 1.
52
Protection Technologies of Ultra-High-Voltage AC Transmission Systems
The total unevenness coefficient is kbj ¼ kbj:1 kbj:2 kbj:3 . The above discussion is about the optimization method of the threephase arrangement of bundled conductors. Each method requires careful analysis and calculations to be realized. Due to the fully utilized conductor surface, the maximum electric field intensity on the conductor surface is close to the allowed maximum value, so its margin for withstanding overvoltage is much lower than that on a smaller-voltage line. In addition, the capacity of the shunt reactor is large. So inputting and cutting of shunt reactors must be coordinated closely with line protection. These characteristics should all be noted in the design of the relay protection configuration scheme.
3.3 Tower structure The type and size of the transmission line tower have a great influence on line parameters and investment. The type and size of the three kinds of 1000 kV tower are introduced in Fig. 3.6, and some types of 1000 kV line towers are shown in Figs. 3.4e3.9 [4]. The structure and size of Soviet 750 and 1150 kV guyed and self-supporting compact towers are demonstrated in Figs. 3.8 and 3.9 [1e3,5]. In the 1150 kV line, a 12-bundled conductor is used. The conductor is 48-stranded aluminum-conductor steel-reinforced (ACSR), and the sectional area of each conductor is 300mm2 . (B) (A)
Figure 3.4 1000 kV pole towers of cat head type and wine glass type: (A) wine glass type; (B) cat head type.
Transmission line parameters
(A)
(B)
(C)
(D)
53
Figure 3.5 Straight pole tower for 1000 kV ultra-high-voltage transmission line: (A) 3Vtype horizontal arrangement; (B) 3V-type triangle arrangement; (C) M-type horizontal arrangement; (D) M-type triangle arrangement.
For UHV transmission lines, compact tower structures should be adopted. The central idea of compact tower design is to try to reduce the phase distance without reducing the phase line to ground (steel frame) insulation gap. Thus, if the floor space of the line corridor, inductance, and wave impedance are reduced, the transmission capacity of the line is increased. The main way to do this is to design the special tower shape and insulator suspension method so that there is no ground component among the phases. The conductors should be suspended with a V-type insulator that can fix the conductors and may not be swayed by the wind. Thus the gaps, both between conductor and the ground component and among the phases, may be reduced. In consequence, the distance of the phases may be reduced. Practice has proven that based on the study on the structure of the
54
Protection Technologies of Ultra-High-Voltage AC Transmission Systems
(A)
(B)
(C)
(D)
(E)
Figure 3.6 UHV tower types designed and adopted overseas: (A) and (E) Soviet; (B) Japanese; (C) American; (D) Italian.
Transmission line parameters
(A)
55
(B)
Figure 3.7 Compact tower: (A) 1150 kV suspension line tower; (B) Delta configuration pulling V-type tower.
tower and line conductor system, it is more economical to improve the transmission capacity of the line than to provide compensating devices. By reference to a Brazil 500 kV line compact tower, the Northwest Power Grid Design Institute of the Soviet Union designed a new 1150 kV line self-supporting compact tower, as shown in Fig. 3.9. In this design, a 12-bundled conductor for each phase is adopted, and each conductor is 48stranded ACSR with a sectional area of 300mm2 (12AC 300/48). The circular radius of the bundled conductor is rp ¼ 0.9 m in the central span, the distance between the two conductors is d ¼ 0.47 m, and rp0 ¼ 0.67 m near the tower. Because of the increasing number of bundled conductors, according to the anticorona requirements, the minimum distance between phases can reach 11 m, and the span distance of the tower can reach 500 m. After the middle phase is elevated 8.05 m, the phase distance of the two sides is reduced to 15 m. However, the phase distance of the two sides in the established noncompact 1150 kV line tower is 46 m. Due to the reduction of the phase distance, the number of bundled conductors is
Figure 3.8 Soviet 750 kV line-pulling compact tower.
56
Protection Technologies of Ultra-High-Voltage AC Transmission Systems
Figure 3.9 Soviet 1150 kV line self-supporting compact tower.
increased so that the wave impedance ZC is reduced and natural power is increased by 0.5 times. The newly designed tower weighs 34 t with the same steel consumption as before, while its occupied area has been greatly reduced. In addition, on this basis, it is an inevitable development trend of the UHV power grid to develop and construct UHV double-circuit/multicircuit/compact transmission lines. The research and construction of UHV double-circuit/multi-circuit/ compact transmission lines are quite extensive abroad. In America, the proportion of transmission lines for which double-circuit lines have been adopted on the same tower in 220and 345 kV voltage grades is 47% and 52%, respectively. In Britain, double-circuit lines on the same tower are adopted on all 400 kV lines. In Japan, double-circuit lines on the same
Transmission line parameters
57
tower are adopted on 90% of 500 kV lines, and the structure of doublecircuit lines on the same tower is adopted in all four established 1000 kV UHV lines. As for multiple circuits on the same tower, during the 1970s and 1980s, America studied and built transmission lines with multiple circuits on the same tower to improve transmission capacity in unit corridors. Furthermore, as pioneers of compact transmission technology, the Soviet Union and Japan successively built EHV (extra-high-voltage) multicircuit compact transmission lines on same tower. Double-circuit lines are also widely used in China’s EHV and UHV transmission systems. Fig. 3.10 shows the structure of a double-circuit compact transmission line on the same tower at the 750 kV voltage level, which is closest to UHV. However, there are still many problems to be solved for the tower structure for 1000 kV UHV double-circuit compact transmission on the same tower. The operational experience of the Soviet Union’s and Japan’s UHV transmission lines shows that shielding failure and back flashover of lightning are the main causes of double-circuit fault and interline fault. The conventional double-circuit same-tower structure is beneficial to prevent sleeting jump, while the belt-umbrella tower has the advantage in lightning protection performance. The T-type compact double-circuit same-tower tower shown in Fig. 3.10B is widely used in Chinese 500 kV transmission systems. The distance between conductors of compact double-circuit
Figure 3.10 The 750 kV tower structure of a double-circuit same-tower line (A) 750 kV double-circuit same-tower routine type; (B) 750 kV compact double-circuit same-tower T-type; (C) 750 kV compact double-circuit same-tower with-same-window.
58
Protection Technologies of Ultra-High-Voltage AC Transmission Systems
transmission lines is closer. Especially in the UHV electric field environment, the skin effect that occurs when alternating current circulates between conductor and earth makes the frequency characteristics of the line parameters much more obvious. The structure of a 750 kV compact double-circuit same-tower with same window proposed by China is shown in Fig. 3.10C. Furthermore, China has proposed a vertical, bitriangular arrangement, which is more compact with a better electromagnetic environment than the symmetrical inverted triangle arrangement. The structure of a Chinese 500 kV four-circuit on-same-tower transmission line is shown as Fig. 3.11. It can be seen from Figs. 3.10 and 3.11, influenced by tower structure and conductor arrangement, the electromagnetic and static electricity couplings between the phases and conductors of double or multiple circuits in a line corridor are asymmetrical. Therefore, the imbalance of UHV double-circuit/ multicircuit transmission lines should be researched and demonstrated. (A)
(B)
Figure 3.11 Tower structure of multicircuit lines: (A) 500 kV four-circuit on-same-tower d-type; (B) 500 kV four-circuit on-same-tower e-type.
Transmission line parameters
59
References [1] [2] [3] [4] [5]
AC transmission. GH Mark; 1998. About the new voltage level of AC transmission. electricity. 1985. No.1. (in Russian). Electrical equipment installation procedures. Beijing: Electric and Nuclear Press; 1986. Ultra-high voltage grid. Zhenya Liu. Beijing: China Economic Publishing House; 2005. Design of ultra-high voltage transmission lines. GH Mark. Electric and Nuclear Press; 1986.