226

IKPROVEMENT OF THE EFFICIENCY OF 3 5 - TO 220-kV LINES

G N Alexandrov and G V Podporkyn

Leningrad Technical University, USSR

INTRODUCTIOI?

It is good practice to limit the ratio of transmitted power to surge impedance loading (SIL, or natural capacity), UPn, to & 1 , with the aim to reduce voltage drop and power losses. This may be achieved by redu- cing phase-to-phase spacings and using sub- conductor bundles instead of single conduc- tors. In so doing, it is possible to ensure S/P 6 1 over a wide range of conductor crofs-sections with the result that voltage drop and power losses become independent of conductor cross-section and the performance and cost characteristics of lines, especial- ly of long ones, are essentially improved. Thus, the use of conductor bundles on 35- to 220-kV compact lines is an important means for improving their efficiency.

It has been shown by Alexandrov et al. (1) that increasing the SIL of a line through an increase in the number of subconductors and a reduction in phase-to-phase spacings sub- stantially improves the conditions of power transmission, thus ensuring reduced voltage drop and power losses a d larger transmis- sion distances. However, experience in de- signing EKV overhead lines suggests that the potentialities of increasing the SIL through an increase in the number of subconductors are limited. This was due to the fact that as the number of subconductors increased, the subspacings remained unchanged and the phase-to-phase spacings were relatively large, the maximum field strength at the conductor surface being below its maximum allowable value as determined from the con- ditions of corona-loss and radio-interfe- rence limiting, E = E . The present paper shows that the S I m f 3 5 5 to 220-kV lines may be increased in proportion to the number of subconductors by adopting simple design measures.

A decrease in or at least a limitation on the ratio S/P with increasing load P ( o r , which is the fame, a decrease in o r a limi- tation on the product Z F with increasiw cross-section F) is posgible through an in- crease in the number of subconductors (not through an increase in the cross-section of a single conductor) in proportion to a r e - quired increase in load, the use of conduc- tor bundles being nowadays a common practice in EHV lines.

PRINCIPLES OF CFSATINIG 2 O S T - E E ’ Z C T I V B i7Tmmma P The power S transmitted through a line is determined by phase voltage Uph? conductor cross-section F and current denslty j,

P = S cos Y = 3 Uph F j cos Y (1 )

The SIL of a line is determined by the sur- face area of conductors, A (rather than their cross-section), the maximum field strength at their surface, E , the voltage and the factor allowing for flalfon-uniform

distribution of field strength over the con- ductor surface, k,, as shov6 in references (2) and ( 3 ) ,

=$ nr, ufi kn Et?h7X

where n and r are the number of subconduc- tors per phas8 and their radius, respec- tively.

The upper limit on E is set by the re- quirement of corona-f%& and radio-interfe- rence limiting (E ,C Ea, the allowable field strength). %%refore, a minimum sur- face area of conductors and thus minimum wind and ice loads of conductors and towers obtain with E k . Substitutm xa = E into (2) and ta- ltfng the ratio of %%nsmi?ted power to S a yields

and a minimum possible

(3 ) S _ = 120r F J k n -60% TO x j k n pn AEcl Ea

whereF = F and F is tRe cross-8ection of phase subcon- ductors.

It follows from these equations that the ra- tio S/P is determined by the ratio between conduct% cross-section and surface area per unit length, F/A, or the ratio between the electron gas flux, F e j = I, and the f lux of the vector of field strength through a unit length of the conductor surface, A-E /kn. The other way around, a specified ra%o SIPn corresponds with a well defined ratio, tween conductor cross-section and surface area per unit length, F/A.

Hence, in order to transmit power economi- cally through overhead lines, it is necessa- ry to emure a certain ratio between conduc- tor cross-section and surface area per unit length,

n = xr2Zn, de = 0.61 to 0.67

be-

As can be seen, the smaller the required ra- tio S/P , the smaller the ratio F/A that must benensured, which, by virtue of ( 4 ) . 18 equivalent to the requirement to reduce ro and/ o r X . If the requirements of corona limiting and of power transmission with an economical current density are satisfied simultaneously, S/P increases as r , i.e., as F , irres- pechve of line voleage class ( 3 ) ? Accor- dingly, the maximum allowable cross-section of subconductors and their radius may be ob- tained from the condition S/P 5 1 for lines, in which the requireme% of corona limitina determines the conductor design,

(5)

227

l.3

Note that E be easily c?ilculatcd by iqcrntionc.

= 1 .3 Afmm ,nwe have F. ~~

depends on r . lionover, ro can

Assumin, S / ? = 1 , 2 = 3.65, Is - j = = 926 k': Ac-

6.25 0.75 10.6 12.5 15.1 80 i-57- 2x3- 31i: 4G1 ~ - - ~ ~

Thus, the m c a x i m m allooable crosxj-section of subconductors is F9 300 mr: for lines with a working vol a, of 220 kV and above. Conductors of larger cross-sections cannot be efficiently used on overhead lir,es. This conclusion has been confirmed by project do- velopments for 750- and 1150-kV lines in the USSR.

Equations (5) and (6) enable us to dotemine the required values of r and F for any specified values of j an8 S/P .oTable 1 lists tlie required values of Po and I' different values of j and SIP nssumi8t: 8 = = 0.65 (the average value fornaluminium- steel conductors) and k = 1. Conversion to ?;y value of kn can be Qasily done using

for

and (6).

I I I I I I I

On 35- to 110-kV lines, E < E practi- cally over the whole rangPa)6f po8sible phase spacings. Accordingly, the listed values of S/P and j correspond with much smaller crcgs-sections and radii of conductors by virtue of (5) and (6).

It is seen from table 1 that virtually any combination of j and S/P may be ensured using the existing condu&ors, which enables us to consider variation of these parmeters over a wide range in an analysis of po'ver transmission regimes.

In the U S S R , conductor-to-conductor spacings are currently adopted mainly on the basin of preventing the whipping of conductors rather than on the basis of a required electric strength of phase-to-phase gaps. Table 2 lists the minimum insulation spacings, S . , required for the operational reliobilitymln of phase-to-phase air gaps.

TABL3 2 - Imiinirlwn 1 h x c - t o-phase spaciws

_-____ 35

1.35

I n table 2 , k is tile rated voitage surge fac- t o i - currently adopted in the USSX (at left) nnd tha-t :.iith deep vo1tac;e surge suppression (at ri",ht) ; G . nnd GI.,,., are the mini- inm ph~sc-to-~~~s~t-pacin&g &"determined by the conditions of reliable operation under lichtnin; *urges ncoordin,n to the USSR Elec- tric Installation Code and under switching surges, respectively.

It is seen that the insulation spacings of tablo 2 n r e much smzller than conductcr-to- conductor spaciws on lines in traditional de ij i;n . .;it11 the use of single conductors, a limit on phase spacin:: is nlso set by corona con- siderations. Figure 1 shows the minimum phase spacinLs ns determined by ccrona sup- p r e s r i o n conditions. A l s o shosm in the fi- s u r e n r e minimwl, insulction spacings as de- tcnnincd bg li;;htning surges according to t a b l o 2. On 35-kV lines, th.e condition of corona suppression shows up only foy conduc- t o r radii below 1.33 cm (I' = 22 m ) (fi- Zur r I , curve I), i . c . , it'does not praoti- cnlly affect the choice of phase spacings. On 113-kV lines, its influence mapfests it- self for r 3.62 cn (P < 78 mm ) (figure 1 , curve 28. On 220-kV lynes, the condition of corona suppression affects the choice of

cings over the vhole renge of o r os s -0 e c, t i on.5 empl oyc d . 2efcrring to table 2, if we adopt on i? 35-kV line, c geonotric mean conductor-to-conductor spacing of 0.5 n, ,which can be ensured by in- st:,.llin& tvio 01- three insulator spacers in a s p a n , the 3 I L of the line with single conduc- t o r s increases to 4.2 - 4.8 XJ depending on conductor diLunoter. This appreciably affects the regime of the lines as compared to lines of t h e s m e concuctor cross-section with t red i t3 .ona l phase spacings.

Similarly, with the uae of the minimum insu- lation spacings according to table 2 and fi- ? w e 1 for n 110-kV line, the SIL of the line increases to 3C - 43 J W . The regimes are al- tered accordingly i3.s shown in reference ( l ) . ?educed conductor spacings do not solve com- 3 1 c t e l y t h e problem of inproving the regimes of overhead lines :.iith relatively thick con- ductors. This brings about the need for con- ductor bundles. F o r three or more subconduc- tors p e r phase , it is advantazeous to use flat phases since t h e y onsure a more compact line desipn as cho1-m by Alexandrov et a1.(4).

3VALUATIGN OF T I E DESIGN PARAKSTERS OF 220-kV LIiTCS L I Z F M T PHASES

The parameters of lines have been evaluated by solving a system of equations with poten- tial coefficients and finding the charges on subconductors. Average working capacitance C is dependent on the ratio of phase cross- sgctional length h to phase spacing G (fi- gure 3 ) . By varying h, for a constant G, the

228

n k

ro (cm)

ratio h/G was varied for the average working capacitance to be equal to the allowable va- lue as determined by the requirement of li- miting the field strength nt the conductor surface,

E o = ca ' ( 7 )

1 2 3 4 5 6 1 1.05 1.15 1.20 1.20 1.29

1.0 0.95 0.87 0.85 0.85 0.85 ___.

where q is the allowable charCe at the s u r - face ofaa phase. The S I L of a line may be expressed through the average working capa- citance C-, according to reference (3),as "

p, = 3 , %i =3vc0 u; S

( 9 )

where Z of the 'line.

= l / ( v Co) is the surge impedance

For an approximate evaluation of the parame- ters of overhead lines, the values of kn, were adopted on the basis of experience in the analysis of line parameters presented by Alexandrov et al. ( 5 ) in accordance with table 3.

TABLE 3 - Values of k and r for different n in flat p f l f a s e s ( P calculated ' for .j = 1 . 3 ~ / m , Osrp n---J- = 3.3 .

A s n increases from 1 to 4 , k increases from 1 to 1.20. F o r larger n,%he value of k = 1.20 may be assumed to be constant. WPth varying k , the optimum subconductor radius r variffs accordin~ly (see table 3 ) . The radi8s is the largestofor single conduc- tors. With n increasing from 1 to 4, it de- creases and thereafter remains constant.

Figures 2 and 3 present the principal calcu- lated parameters of 220-kV lines with flat phases f o r n varying from 2 to 5. Increasing n drastically increases the ower transmitted (figure 2 ) . Indeed, using ( 5 7 and (6), the power transmitted through a line may be writ- ten down in the form

which shows that S varies as n.

However since k varies with increasing n from 2 40 4 (tabye 3), the S vs. n curves somewhat differ from straight lines (figure 2). A s n further increases, k remains con- stant so that S VS. n dependehies become linear and, according to figure 2 , may be extrapolated to any n.

For S/P 250 to 950 W A may be transmitted through n 220-kV line with n increasing from 2 to 5 (figure 2 ) .

It is seen from equation ( 1 0 ) and figure 2 that the power transmitted decreases as the square of S/P . This is due to the fact that decreasing S/f proportionally decreases r (5) with the r8sult that F decreases as t8e square of S/P transmitted (40). It is a l s o seen from (10)

= 1 and j = 1.3 A/mm2, a power of

( 6 ) and so 8oes the power

that, for a specified S/P , the power trans- mitted decreases with inchasing j , which is also a result of decreasing ro and Fo.

As S increases d t h n for a specified S/P the SIL of thc line also increases, which% equivalent to a decrease in Z (figure 2). For S/P = 1 , Z varies from"l80 to 90 R vith n %.rying faom 2 to 5 , respectively.

F i p r e 3 show the required ratios of phase croon-sectional length to phase spacing, h/G, for uhich the 3 vs . n and Z vs. n dependen- cies of figure 2 hold true.s8s seen from fi- gure 3, increasing the number of subconduc- tors per phase, i.e., the total cross-secticn of o phase, increases the ratio h/G, uhich, for a constant G, implies longer phase cross- sections (greater h).

Smaller S/P considerably reduces the phase size by dragtically decreasing the poner transmitted (figure 2 ) and, for a specified S/P , the SIL must be accordin:;ly reduced, i.e?, the average worki capacitance of a phase must be reduced (3, which is obtained just by reducing thc phase size.

Larger rated current density, j, drastically reduces the phase size (figure 3).2E.g., for n = 2 S/P = 0.8 and j = 1 . 3 A / m , we have h/G ='0.4 f o that h = G x 0 4 = 2.5 x 0.4 = = 1 m, and for j = 1.6 B/mm2, we obtain h/G= = 0.16, o r h = 2.5 x 0.16 = 0.4 m, the size of the phase being thus reduced by a factor of Z.?. Bote, howyer, that changip over I r o m J = 1.3 A/mm to j = l.G A / m also de- creases the power transmitted, S , from 180 to 160 IKI ( l o ) , i.e., 11%.

Note that figure 3 gives the phase size for a preliminary evaluation of the parameters of a line from the averaged working capacitance, C , allowance being made for non-uniform caarge and field distribution over subconduc- tors by non-uniformity factor kn. For a spe- cific line design version under study, the data of figures 2 and 3 may be used as a first approximation in elaborating an opti- mum phase design that ensures equal working capacitances of phases and a uniform charge distribution over subconductors, according to reference ( 5 ) . In so doing, the inner phase should be 'compressed' and the outer phases 'stretched' about 20% as compared to the data of figure 3 by arranging the sub- conductors non-uniformly within their phases. A s shown in reference ( 5 ) , the parameters of lines with flat phases are essentially inde- pendent of whether the phases are arranged vertically or horizontally. Therefore, the data of figures 2 and 3 may be a l s o used for evaluating the parameters of lines with ho- rizontally o r otherwise (e.g., parabolical- ly) arranged phases (figure 4). Tho reported data corroborate the feasibili- ty of 220-kV lines using conductor bundles. The phase size (specifically, the cross-sec- tional length) is found to be reasonable even with a large number of subconductors, in which case the SIL is 4 times or more that of lines in traditional design.

3VALUATIOIJ OF THE DESIGN PAhUJETERS OF 35- TO 110-kV LINES VITH FLAT PHASES

As shown above for 35-kV lines (in most ca- ses , this is also valid for 110-kV lines), the electric field strength at the surface of conductors, Emax, lies below an allowable value f o r all actually used conductor types. Therefore, it is not reasonable to choose ro

229

0.6

using (5). The vr?lue of r mcy he chosen Prom the condition €or th8 povier tranomit- ted not to exceed the line SIL with due re- gard to the restrictions imposed by the re- quirements relating to the mechanical strength of conductors.

Table 4 lists the calculated parameters of 35- and 110-kV lines in traditional design, of single-conductor lines with reduced phase spacings and of compact lines with flat pha- ses comprised of different nunbers of suh- conductors with a subspacing of 39 to 60 cm, respectively.

As seen from table 4, the SIL of 35-1cV lines with a geometric mean phase spacing of 4 m is 3 blW. Reducing the phase spacing to 0.5 m (see table 2 ) increases the SIL to 4.3 LX whereas, for flat phases, varying n from 2 to 5 increases the SIL from 7.9 to 16.0 V : I , i.e., for n = 5, the SIL is 5 times t1in.t of lines in traditional design, the condition S/Pn I being satisfied for any n.

Similar dependencies of line parameters on phase spacing and number of subconductors are valid for 110-kV lines (see table.4).

Figures 5 and 6 show the calculated average working capacitances and their proportional SIL's for 35- to 110-kV lines as functions of h/G for different numbers of subconduc- tors in flat phases. It is seen that the SIL of a line can be varied to a large extent by varying h/G. This enables the most suitable phase design to be determined for a specific line version.

CONCLUSIONS

The use of flat phases and reduced phaso s p e cings enable the ratio S/P to be confined to ,C 1 , which considerablynenhances the eco- nomic efficiency and quality of power trans- mission, enables the transmission distance to be increased and the operational lifetime of existing systems to be extended with their increased loads prior to putting into operation new or reconstructed systems.

Conductor bundling and ultimate reduction of phase spacings, down to distances determined by the requirements of reliable operation and lightning surges, allow an increase in the transmission capacity of 35- to 220-kV lines virtually in proportion to the number of subconductors per phase, i.e., by a fac- tor of 3, 4 or more as compared to traditio- nal lines.

An increased transmission capacity of com- pact lines is attained with relatively small phase sizes. A s a guide, the subspacing may be 30 cm on 35-kV lines, 60 cm on 110-kV lines and 1.2 m on 220-kV lines with a phase spacing of 0.5, 1.4 and 2.5 m, respectively.

1 .2 1.8 2.4 mmm7-7i

TIiBLZ 4 - Parametors of 35-BV lines (j = ~ - _ _

1 1 I 1

REFERENCES

1. Alexandrov, G.N., Lisochkina, T.V., Nosov, I.M., Podporkyn, G.V., Seleznev, Yu.G., and Yevdokunin, G.A., 1987, "New Means for Power Transmission in Power Systems", Lenin ad University Press, USSR. (In Russiany

2. Alexandrov, G . N . , Astakhov, Yu.N., Venikov, V.A., Lyslcov, Yu.I., Podporkyn, G . V . , and Postolatiy, V . K . , 1982, "Electric Transmission Lines of Increased Capacity and Reduced Ecologi- cal Effect", CIGRE, 31-03.

G . N . Alexandrov and L.L. Peterson, 1983, Lenin rad, Energoatomizdat. (In Russian?.

Krylov, S . V . , Nosov, I.M., Podporkyn, G.V., Solovyov, E.P., and Trifonov, V . Z . , 1984, "Insulation of Compact Lines, its Electric Strength under Switching Surges and Working Voltage", CIGRE, 11-15.

3. "EIW Transmission Line 'Design", ed. by

4. Alexandrov, G.IT., Alvarez, E.J.,

5. Alexandrov, G J T . , Yevdckunin, G.A., and Podporkyn, G.V., 1982, "The Parameters of Overhead Transmission Lines in Com- pact Design", Elektrichestvo, 4, 10-17. (In Russian. )

6. Alexandrov, G . N . , and Nosov, I.M., 1981, USSR Inventors' Certificate No. 898024.

230

Figure lG,,,i,,as determined by corona l i m i t i n g VS. r : (1) - 35 kV, ( 2 ) - 110 kV, ( 3 ) -'220 kV

10

18

76

1 4

12

y 20 c

0.3

ob

124

02

0 * 2 3 4

n n

Figure 3 h / G VS. n on 220-kV l i n e s for S/Pn= F i g u r e 2 S ( s o l i d ) and Z (dashed) v s . n = 0.6, 0 8, 1.0, and j = 1.3 m c l 1 .6 A / m *

i n a flat ph2sesfor d i f f e r e n t S/Pn: j = 1.3 A/mm

23 1

Figure 4 Tower model for a 220-1cV compact l i n e w i t h p a r a b o l i c phases sugges t ed i n r e f e r e n c e (6)

fa

I7

w

14

13

12 $ a a?

<

10

9

a

7

6

5

h /G

Figure 5 t? ( s o l i d ) and Pn (dashed) VS. h/G f 8 r 35-BV l i n e s : G = 0.5 II

Figure 6 ( s o l i d ) and Pn (dashed) V.S. h / C fXr 110-kV l i n e s : G = 1 ..I II