RELIABILITY ANALYSIS AND COI”ARIS0N OF LONG-DISTANCE HVAC AND HVDC POWER TRANSMISSION LINES

Dr. N. D. Alekseeva, Eng. A.V. Bubnova, Eng. V. S. Chudny, Prof N. N. Tikhodeev, IEEE Senior Member

HVDC Power Transmission Research Institute (NIIPT), St. Petersburg, Russia

Key Words

HVDC AND W A C OVERHEAD LINES, RELI- ABILITY, TOWER, POLE, PHASE

Abstract

Double-circuit HVDC overhead power transmis- sion lines rated at +500 to 750 kV with self-supporting towers and a long current-boosting capacity are capable to assure a maximum performance coefficient K, of 0.996 (per 1000 km) in terms of electric energy trans- mitted. Much promise for densely populated areas is offered by quadrupolar transmission lines, i. e. those with double-circuit towers, calling for a minimum- width right-of-way.

W A C lines of a 500 to 1150 kV rating are infe- rior to their f-500-750 kV counterparts as regards ma- neuverability, right-of-way width and performance coefficient (K, = 0.98-0.99), because the line must be de-energized each time a phase is damaged.

Introduction

The problem discussed in this paper is urgent for vast countries with an emerging integrated power grid which is characterized by long distances between power plants and load centers, a fdure to comply with the “n - 1” rule of interconnection between regional utilities, and a relatively small turning reserve. Under such conditions a new EHV and UHV interconnection overhead line (OL) must meet stringent requirements.

The emergency statistics for 220 to 765 kV over- head lines in Canada and USA [l], CIGRE [2] and ex- USSR [3, 41 shows that, with a 0.4 to 0.6 specific num- ber of stable disturbances (i. e. those occurring per an- num per 100 km of overhead lines), the longest over- head line outages are caused by damage of self- supporting towers (some 10”) or guyed towers (some 3.10-’), the average restoration time being 280 hours for a tower or about 15 hours for a phase or a pole (the case of a broken insulator string etc., some lo-’). For two single-circuit lines sharing a right-of-way, as much as 30% of tower damage occurred on both circuits at the same time because of excessively heavy ice and wind loads.

Reliability assessment of HVDC overhead lines

As the transfer capability Po of an HVDC overhead line rises to 3.0 GW and above, double-circuit lines may become necessary, with alternatives of two paral- lel bipolar lines (the approach taken for the HVDC line from the Itaipu Hydraulic Power Plant in Brazil) or

quadrupolar lines with four poles carried on a tower (Fig. 1). A double-circuit HVDC line offers important advantages, in particular, a radical improvement of reli- ability, both for the line and associated power systems, in case of a long-term emergency load shedding within 0.5 Po. In areas featuring a high population density and a high cost of land, it is much too often difficult to find a right-of-way for two bipolar lines. Here there is no alternative to a quadrupolar overhead line.

Fig. 1. Sketches of HVDC towers

A €3

A: Bipolar line; B: Quadrupolar line

To attain the needed Po, a number of radically dif- ferent overhead line designs can be used, such as two right-of-way-sharing bipolar lines, each with a transfer capability of Pd2 (Alternative I); one single-tower bipolar line with a transfer capability of Po (Alternative IT); or one single-tower quadrupolar line, with a Pd4 transfer capability per pole (Alternative 111).

At the reliability assessment stage of HVDC line planning, it is only possible to take into account parameters of the longest tower- and pole-related out- ages, as well as the mean restoration time for the line components, on the assumption that other outages, such as lightning strokes on the line, would be cleared by reclosing facilities. Three types of damage were consid- ered, viz. a: simultaneous fall of towers on both right- of-way-sharing overhead lines (Alternative I); b: fall of one tower (Alternatives I1 and 111); c: damage of one line pole (all three alternatives of HVDC line configu- ration). Estimated below is the reliability level of the line alternatives under discussion for a reference line length of 1000 km (for AC OL - 2x500 km).

The reliability analysis makes use of the transfer capability distribution function P@); this all-embracing characteristic makes it possible to find two essential reliability parameters of a complex system [5], viz. the performance coefficient ICp, which is the ratio of the average transmitted power s to the rated transmission capacity of the line SN:

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and the average undersupply of energy A W : AW=(l-K,)*SN.8760. (2)

Because, as a rule, energy channels feature a block structure it is possible to consider a finite number 0 I k 5 n of transfer capability levels of a channel, with k = n corresponding to the full transfer capability and k = 0, to total unavailability of energy transmis- sion. Thus the system,transfer capability is a random discrete quantity yk (k = 0, 1, . . ., n being the transfer capability level number). The probability Pk of imple- menting a k level of transfer capability for a s&i- ciently long time T on the assumption of time invari- ance of the functiony(t) [5] is

where i is the implementation number of the k level over the time r; tk, , the sum total of time intervals

with the transfer capability maintained at the k level over the time T. For a power system component which can be in one of two states (fully capable or unavail- able), two level numbers only are used, viz. k = 0 and k = 1. Then po is the probability of the component UM- available state and p l , the probability of the componerrt available state. The latter probability p l is actually the availability factor K, [5-71. According to Eq. (l), p1 == K,, po = 1- K,. The availability factor K, for a compo- nent can be found either from the service statistics us- ing Eq. (3) or, with the average failure rate of the com- ponent per time unit h and the average interruption duration z specified, from the following equation [5-71:

I

K , =PI To determine the resulting transfer capability

distribution function of a system under study, a11 equivalent circuit of parallel- and series-connected components is prepared, for each of which the transfer capability distribution function is known. The equiva- lent circuit must comply with the general rule of the: reliability theory [5-71: components are connected in series (in terms of reliability) if a failure of a compo- nent leads to a failure of the entire group of compo- nents; components are connected in parallel (in terms of reliability) if a failure of a component does not lead to a failure of the entire group of components. Such circuits are given in Fig. 2 showing three types of reli- ability calculation components, viz. BJL1,O: a compo- nent whose failure results in total loss of the line’s transfer capability Po (a fall of a tower or two towers for Alternative I); BJI-45: a component whose failure results in loss of Pd2 (damage of one tower for Alter- native I, broken string for Alternative 11); BJI425: a component whose failure leads to loss of Pd4 (this in- dex applies to a quadrupolar line and two bipolar lines).

To assess the reliability level of.the 1000 km long line alternatives under discussion, it is necessary to determine the availability factors of the equivalent cir- cuit components in terms of reliability and the transfer capability distribution functions for each line alterna-

tive. The reliability analysis of overhead lees with self- supporting towers assumes Ab to be 0.0 1 l/year. 100 km; thus for a 1000 km long line: A,=(0.3Ab~N100)/8760 = 3.4.106 l/hour;

A,=(h,.N100)/8760 = 1.14. lhour. Hence: I\,=(hb*l/100)/ /8760 = 1.14.10-5 !/hour;

K,,=p,,=l/( l+A,*~,)=l/( 1+3.4*10-6-100) = 0.99905; Kub=plb=lA( l+&*Tb)=l/( 1+1.14-10”*100) = 0.99682; K,,=p,,= 1/( ~+A;Z,)= 1/( 1+ 1.14. 15) = 0.99829.

Alternative I

c_I OL-1.0 I A OL-0.25 r I

I I OL-0.25

OL-O,5 Alternative I1

OL-l,o OL-0,s

Alternative 111 - OL-0,25 I

Alternative IV

OL-l,o - OL-0,s H P-0,s H P-0,s P-0.5

Alternative V

OL-l,o P-l,o P-l,o P-l,o

Alternative VI

OL- 1 .o

/

Fig. 2. Equivalent circuits for reliability analysis of HVDC and HVAC lines (Alternatives I through LII and N through VI,

respectively).

Thus obtained, the availability factors of equiva- lent circuit components make it possible to determine the implementation probability pk of the transfer capa- bility at the k level for each component of the reliability diagram and K, for the overhead line alternatives under study:

K p = C Y k P k . (5)

The findings are shown in Table 1. Similar results were obtained for lines with guyed towers, for which a higher starting parameter of the line damage flow was assumed (Ai=0.03 l/year.100 km) while the single pole damage parameter A, was left unchanged.

Table 1 and Fig. 3 show that Alternative I (two bi- polar lines) has a somewhat lower performance coeffi- cient compared to Alternatives I1 and III, owing to a lower probability of towers of two right-of-way-sharing

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lines falling simultaneously. The performance coeffi- cients Kp from Table 1 and Eq. (1) were used to assess the average annual undersupply of energy (energy-not- supplied) AV for each line alternative with S, of 4 GW (1000 km long k500 kV HVDC line).

Table 1 Transfer capability implementation probabilitiesp,

and performance coefficients of line alternatives

Self-supporting towers

Guved towers

0,995

0,99

0,985

0,98

Y 0,975 -

0 0,25 0 s 0,75 1 - Self-supporting towers - guyed towers

2033 171.7 171.7 487.1 388.9 388.9

Fig. 3. Transfer capability functions for HVDC lines tower alternatives

Table 2 quantifies the undersupply of energy for

Table 2

the power transmission lines under discussion.

Annual energy-not-supplied for line alternatives with different tower types

AW, GWyear 1000 km Alternative I IAltemative IIbltemative I Tower type

Tables 1 and 2 make it clear that guyed-tower line alternatives feature substantially lower perfor- mance coefficients than lines with self-supporting

towers. Taking into account a 30% long-term boosting capacity of valves and transformers of the sound pole@), the quantity of electrical energy not served as a result of a poor line reliability increases substantially. Here the performance coefficientsvare found without changing the reliability equivalent circuits (Fig. 2) or the transfer capability implementation probabilities pk for line alternatives (Table 1); changes are introduced only in transfer capability implementation levels yk, which are increased by a factor of 1.3. Table 3 makes it clear that, with a 30% power boosting of the sound poles, the lowest performance coefficient is featured by Alternative I1 (one 4 GW bipolar line). Alternatives I and I11 have identical performance coefficients. With a 30% power boosting of the sound poles, the undersup- ply of energy drops considerably in Alternatives I (by 84.1 GWWyear) and I11 (by 52.6 GWyear); as for Alternative 11, the undersupply of energy drops by as little as 17.6 GWyear only (Fig. 4).

A similar result is also obtained for lines with guy- ed towers (Tables 3 and 4), however, the energy-not- supplied increases by a factor of 2.4 to 2.8.

Table 3 Transfer capability implementation probabilities pk

and performance coefficients of line alternatives with different tower types, taking into account 30%

pole boosting capacity 'owe . Alternative I I Alternative 11 I Alternahve 111 I yk 1 Pk I YkPk I Pk I YkPk I Pt 1 ykpk 1

0 0 1 0.325 0.00006 0.00002 - 2 0.65 0.01858 0.01208 0.00338 0.0022 0.00002 0.00001

- 0.00674 0.00657 3 0.975 8.00666 0.00649 - 4 I 1 .o ~0.97176~0.97176~0.98719~0.98719~0.98381~0.98381

K"* 1 1 0.9904 I 10.9894 I 10.9904

Table 4 Annual energy-not-supplied for line alternatives

with different tower types, talting into account 30% pole boosting capacity

Tower type

A minimum-cost estimate of the loss of profit be- cause of poor reliability assuming, for instance, a M e r - ence of 1-2 cents per kwh between the sending and receiving end cost prices of electric energy, shows that the amount accumulated over the design service life of a transmission line is comparable to the capital invest- ment in the overhead line and much superior to a 5-10% difference in the cost of the self-supporting and guyed tower alternatives or 15-20% difference in the cost of the double-circuit and single-circuit versions. Thus new power transmission projects with a transfer capability of

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Po 2 3 GW should preferably use double-circuit lines with self-supporting towers.

Higher availability factors of both HVAC and HVDC lines can be attained through an appropriate increase of the design ice and wind loads, so as the probability of exceeding them be lowered.

Reliability assessment of HVAC overhead lines

Alternatives to HVDC are single- and double- circuit 4 GW HVAC lines. Their special features are as follows: first, an HVAC line must be de-energized each time a tower or even a phase is damaged; second, no current boosting of sound phases is used, even though an overload of the sound circuit of a double-circuit line is sometimes possible.

Reliability calculation equivalent circuits are shown in Fig. 2 for three 4 GW HVAC line versions, namely: two 750 kV lines sharing a right-of-way, each of a Pd'2 = 2 GW transfer capacity (Alternative IV); one 1150 kV line of a Po = 4 GW capacity (Alternative V); a double-circuit 750 kV line with double-circuit towers, each circuit of a Pd2 = 2 GW capacity (Alternative VI). The designations for these alternatives in Fig. 2 are as follows: OL-1,O: a component whose failure results in total loss of the line's transfer capability Po for 280 hours (damage of one tower in Alternatives V and VI or two towers in Alternative IV); OL-0,5: a component whose failure results in loss of Pd2 (dam- age of one tower for Alternative IV) for 280 hours; P- 1,O: a component whose failure results in loss of Po for 15 hours (a damaged phase in Alternative V); P-0,5: a component whose loss results in loss of Pd2 for 15 hours (a damaged phase in Alternatives IV and VI). Lines with self-supporting towers were assumed to have hb=102 l/year-100 km, those with guyed towers, hboT=3.10-2 l/year-lOO km, and the phase damage pa- rameter, h,=10-' l/year.lOO km, regardless of the tower type. For the three W A C alternatives, Table 5 gives performance coefficients K,, found by the same tech-, niques as described for HVDC lines, and anticipated energy-not-supplied levels owing to insufficient line reliability.

Table 5 Performance coefficients Kb and energy-not-

supplied A W (GWWyear-1000 km) for W A C line

towers

A comparison of the anticipated undersupply of energy for HVDC and HVAC overhead lines of a 1000 km reference length (Tables 4 and 5) prompts a conclu- sion that a HVDC line featuring long-time current- boosting capability and using self-supporting towers (Table 4 Alternative I) makes it possible to lower the expected emergency undersupply of energy by a factor of 2.4 to 2.7 against an HVAC line with self-supporting towers (all Alternatives IV through VI) and, particu- larly? by a factor of 4.3 to 5.2 against a HVAC line

with more economical but less reliable guyed towers that were the preferably type in the ex-USSR. Higher performance coefficients of both HVAC and HVDC lines. can be attained through an appropriate increase of the design ice and wind loads, so as the probability of exceeding them be lowered.

Conclusion

Provided are equivalent circuits, assessment proce- dures, and anticipated reliability indices for several HVDC and HVAC overhead line alternatives ofan identical power transfer capability Po.

Reliability assessment was made for different ar- rangements of a 4 GW, 1000 km long reference power transmission line (two lines in one right-of-way, one full-capacity line with shared towers, one double- circuit line). The performance coefficient and the ex- pected undersupply of energy were determined for all the studied line alternatives.

Lines with self-supporting towers were shown to be much more reliable than those with guyed towers: the former lines feature energy-not-supplied levels 1 .S to 2.8 times as low as the latter.

Double-circuit lines were proved t o be the prefer- able type in terms of reliability among other versions of 4 GWlines.

Again, double-circuit (quadrupolar) HVDC lines of- fer many more important reliability advantages, as compared to similar HVAC counterparts.

References

[ l ] R B Adler et al. An IEEE Survey of U.S. and Ca- nadian Overhead Transmission Outages at 230 kV and above. IEEE Transactions on Power Delivery, Vol. 9, NG 1, January 1994.

[2] A summary of the report on survey of controls and control performance in HVDC schemes. WG 14.02, Electra, 155, 1994.

[3] N. N. Tikhodeev, S . S. Shur. Insulation of Power Grids: Selection Procedures, Statistical Co- Ordination, and Normalization. Leningrad, Energiya Publishers, 1979.

[4] Sporn Ph., Cahen F., Magnien M. Report on the Work of the Study Committee 9 on EHV AC Transmission. CIGRE, 1960, R. 416.

[5] N. D. Alekseeva, D. E. Kadomsky. Reliability analysis of a power transmission systems in terms of transfer capability. Izvestiya NIIPT, 18, 1972.

[6] D. E. Kadomsb. Reliability of discrete channels of dissimilar independent components with a limited transfer capability. Izvestiya NIIPT, 12, 1966.

[7] E. V. Gnedenko, Yu. K. Belyaev, A. D. Solovyev. Mathematical Methods in Reliability Theory. Mos- cow, Nauka Publishers, 1965.

Biographies

Nina D. Alekseeva graduated in 1959 from the Lenin- grad Electrotechnical Institute majoring as Industrial

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Electrical Engineer. In 1980 she received the Candidate of Technical Sciences degree. She is Senior Researcher at NIIPT, specializing in the area of power system reli- ability.

Alexandra V. Bubnova was born in Russia in 1978. She received the Master of Science degree, majoring in Electric Power Systems and Grids, from the St. Petersburg Technical University in 2001. She has been with NIIPT since then as a Researcher, specializing in AC overhead lines.

Vladimir S. Chudny was born in Russia in 1975. He re- ceived the Master of Science degree, majoring in Electric Power Systems and Grids, from the St. Petersburg Polytech- nical University in 1998.He has been with NIPT since then as a Researcher, specializing in HVDC overhead lines. He has 11 publications.

Nikolay N. Tikhodeev (1927) received the Electrical Engi- neer, the Candidate of Techcal Sciences and the Doctor of Technical Sciences degrees in 1952, 1955, and 1966, respec- tively, from the Leningrad Polytechnic Institute; at present he lectures at the LPI (now St. Petersburg Polytecbnical Univer- sity) as Professor. In 1980 he was awarded the National Prize

for his contribution to development of 750 kV AC power transmission lines. In 1979 he was elected a Corresponding Member of the USSR (now Russian) Academy of Sciences where he became anAcademician (Full Member) in 1992. Within CIGRE, where for 12 years he was a member of SC33 "Overvoltages and Insulation Coordination", he is now a Distinguished Member of CIGRE. He became an IEEE Senior Member in 1990. Since 1955 Prof. Tikhodeev has been with High Voltage Technology Department of HVDC Power Transmission Re- search Institute in St. Petersburg. He directed the Department from 1958 to 1996, sihce 1997 he is Scientific Director of the Department. The area of his major interest is EHV and UHV AC and DC power transmission. He authored and co- authored eight books and many articles on high voltage engi- neering.

HVDC Power Transmission Research Institute (NIIPT) 1/39 Kurchatov Street, St. Petersburg 194223 Russia Tel. (7-812) 555-1880. Fax (7-812) 555-4931, E-mail:

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