Reliability evaluation of hybrid multiterminal HVDC subtransmission systems

R. Billinton, M. Fotuhi-Firuzabad and S.O. Faried

Abstract: An approach to determining the r$@hility of a hybrid multiterminal HVDC suh- traiisniission system is presented. The performance analysis of a inultiterminal HVDC subtransmission system is divided into three indin scgrnents: the rcctifiers, the inverters and the underground cable system. The reliability models associated with the three segments are developed and a reliability evaluation procedure is prescnted. Two sets of indices. namely the hasic load point indices and the system performance indices, are calculated to nieitsure the reliability of a system. The proposed technique is applied to a hypothetical multitenninal HVDC subtransmission scheme and the results are presented.

1 Introduction

For economical, environmental and safety reasons, most of the subtransmission and distribution networks in the urban arcas of large cities are underground HVAC cable system. One reason for not using HVDC transmission in such systems is the need for local power generation in the receiving network, which is not available in most networks. This weakness can now be overcome by using voltage source converters (VSC) which have been developed for high voltage application [ I , 21. In such converters: the current can he turned off and therefore, there is no need for a network to commutate against.

Reliability evaluation of a hybrid multiterniinal HVDC subtransmission system is presented. The performance assessment of a multiterminal HVDC subtransmission system can he conducted by evaluating the capabilities of the rectifier, inverler and underground cable segments. Reliability models associated with the three segments are developed for the purpose of reliability analysis. A procedure is then presented to calculate the reliability of an HVDC multiterminal subtransmission system and the contribution of each segment. Two sets of indices, namely the basic load point indices and the system perforniance indices, can he calculated for measuring the reliability of n system. The proposed technique is applied to ;I hypothetical multiterminal HVDC subtransmission scheme and the results are presented.

2 Hybrid multiterminal HVDC subtransmission systems

A hybrid multiterminal HVDC system is a configuration in which some of the AC/DC converter stations consist of line commutated current source converters (CSC) and other converter stations consist of VSC. Fig. I shows a single line

rectifier ~

inverter : ...........................

................... ............ ~ HVDC master contloller ..................................................................

Fig. 1 Hybrid i i~i~l l i ,c~,~~i ,~ul I1 VDC ai,l,rrrr,,.s,,,;.~.sision .sy.mw

diagram of a hybrid niultiterininal HVDC subtransniission system. This system is taken from [I]. This ring network consists of underground cable systems and i s suitable for urban areas in large citics. The network consists of two CSC rectifier stations, eight VSC inverter stations; an HVDC cable system and the system controller. The maximum load carrying capabilities of a rectifier and an inverter are assumed to he I I O and 30MW, respectively. Power is transferred from the rectifiers to the inverters through the underground cables. Since the total sum of the currents from all the converters of a multiterminal HVDC system inust he zero. the main task of the controllers of such a hybrid system is to generate the current orders to the two rectifiers to satisflr the loads of the eight inverters. Figs. 2 and 3 show the main components in the CSC and VSC converter stations.

smoothing reactor

F---- AC bus

synchronous

_ - - -

571

3 Reliability modelling

Reliability studies involve the scparate and distinct steps of understanding the system opcration, deciding the failure modes, identifying the consequences of failure. selecting appropriate reliability models and finally cvaluating the reliability [3, 41. These steps apply equally to multitenninal HVDC subtransmission components and to the system in which they are embedded.

The conventional single line diagram shown in Fig. 1 cannot be used directly for reliability analysis. Construction of the reliability diagram from the single line diagram is a key component in the analysis. The reliability diagram is a directed graph, in which the nodes represent the various components of the single line diagram. and the arc between them represents the relationship hctween the components. This diagram also identifies the elements of thc single line diagram and their system dependency. It can be constructed by accurately inodelling the individual components coni- posing the system. The perfonnance or the overall multi- terminal HVDC subtransmission system caii hc considered in terms of the performance of the main segnents. The reliability analysis can thereforc be achievcd by creating appropriate reliability models Tor the rectifiers. inverters and underground cable systems.

The reliability block diagrams for a rectifier and an inverter in Fig. 1 are shown in Fig. 4(r1) and 4(b). respectively. In these models. equipment such as smoothing reactors, circuit breakers, transformers and ~a lvcs . which when failed. cause a loss of transmission capability of the

auxiliary power

transformer

DC line

auxiliary power

transformer

capmtor

smoothing reactor smoothing reactor

rectitier or inverter capacity, are connected in series. On the AC side of each rectifier. there is a capacitor hank (XC) and a bank of filters (Fr). These elements are placed in parallel and the assumed associated system capacities are shown in Table 1

Table 1: Filters and capacitors capacw (rectified

filters+capacitors in operation capacity. p.u.

2 Fr+2 XC 1 .o 2 Fr+XC 0.8

2 Fr 0.63

Frt2 XC or FrtXC 0.60 Fr 0.37

Others 0.0

On the AC side of the inverter, there are four banks of high-pass A C filters. These elements are placed in parallel in the model ; i d are associated with the system capacities shown in Table 2 . The capacities in both tables are shown in p.u. on the basis of the rated capacities of the rectifier and inverter. The rated capacities associated with each rectifier and inverter are assumed to be IlOMW and 30MW. respectively, in the studies presented in this paper.

Table 2: AC filter capacity (inverter)

AC filters capacity, p.u.

Fl+FZ+F3+F4 1 .o Fl+F2+F3 orFl+F3tF4 0.37

Fl+F2 or F3+F4 0.22

Others 0.0

The reliability data associated with the models shown in Fig. 4 are from [5] and are given in Appendix Section 9.

4 Reliability indices

The reliability of a multitenninal HVDC subtransmission system can be expressed in temis of the load point and system perfonnance indices. The load point indices are important with respect to a particular service point in the system The system performance indices give an overall appreciatioii of the area or system perfonnance [4].

4.1 Load point indices The following indices can be calculated in order to measure the perfonnance of a inultiterniinal HVDC with respect to the supply adequacy at the customer load points. The basic indices are the probability and frequency of failure at the individual load points. Additional indices can be created from these generic values.

Q = probability of load curtailment: the probability that the load at the kth load point exceeds the tnaximum load that can be supplied. i. = expected frequency of load curtailment. occ./y; the number of contingencies requiring load to he curtailed a t the kth load point or the isolation of load point k during the time period considered. r = average outage duration, h/int.

IEE Rnr -Gimcr. Trunwi. Dhirih.. Vol. 149. M,. 5. S q m r d w 2002

EEh'S= expected energy not supplied, MWh/y; the total energy no1 supplied at the kth load point in a year. due to load being curtailed at load point k or due to isolation of the load point.

4.2 System indices There is a wide range of possible system performance indices [4]. The indices used in this application are as follows:

SAIFI = system average interruption frequency index, interruption/custonier year SAID/= system average interruption duration index, h/ customer year CAIDI= custonicr average interruption duration index, h/ customer/interruption

SAID/ CAIDI = ~

SAIFI . ~~~ ~

ASAI = average system availability index .4SUI= average system unavailability index AENS= average energy not supplied, MWh/customer year

The basic definition and mathematical formulation of these indices are given in [4, 61. Several of the above indices arc utilised by the Canadian Electricity Association (CW [71.

5 Evaluation procedure

The following assumptions were inade in the studies presented in this paper.

(i) The supply at each of the two I-ectifiers is assumed to be fully reliable. (ii) Failure rates of all the busbars and isolators are considered to be zero. (iii) All possible contingencies associated with the rectifiers and inverters are included in the analysis. (iv) Up to second-order failures of the underground cable system are considered.

As noted earlier. the rectifiers, inverters and underground cable systems are the three main segments affecting the load point and the system indices of the multitenninal HVDC subtranslnission system shown in Fig. 1. The reliability indices are therefore affccted by the reliability of these main segments. The reliability indices at the load points and the overall system can he determined for two different cases. In the first case, the impact on the load point and systcm reliability indices of outages of elements in each main segment is determined. In this assessment, the influence of outages of elements of one of the segments is considered, while the other two segments of the system are assumed to be fully reliable and capable of performing their intended functions. In the second case, the influence of outages of elements in all the three segments is considered. The first assessment highlights tlie importance of each individual segment in the reliability analysis while in the second study a more comprehensive appraisal of the load point and overall system performance is provided. In each study it is neccssary to detennine a perfonnance table at the load point in order to calculate tlie reliability indices. The complexity will increase as tlie number of segments considcred in the analysis is increased.

IKE Pror - G o w Tror~vri D;,m;h.. Yrrl. M Y , A'a 5 Sqmwhw 21M2

5.1 Rectifier considerations In this case, only component outages in the reliability model of the two rectifiers are considered. while the inverters and cables are assumed to be fully reliable. The load point and system indices are afkcted by rectifier element outages. Using the given data and the reliability model. a rectifier and an inverter can be represented by a multistate model. Each state is associated with a performance level (PL), which represents the percentage power capability of the rectifier and the associated probability. frequency and duration. A perfoimance table for the two rectifiers is determined by coiivolving the performance table associated with each individual rectifier. The cumulative probability Prlr2 (Ck) and cumulative frequency F,l,2(Ck) associated with tlie kth perfonnance level are detennined using ( I ) and (2). Detailed discussion on cumulative probability and frequency concepts can be found in 141.

'2'2

P, .1,2(Ckj=CP,-I(G-C) x [pr2(c~)-e.2(cz+I)1 ( 1 ) i=l

+ (F;.z(C,) - &(G+I)j x E.l(Ck - C;)] where

Nz = number of thc performance level in the performance table of the second rectifier (here both rectificrs arc identical), Ck= capacity associated with the kth performance level PrI. Pr2, rectifiers 1 and 2, respectively. where.

&=cumulative probability and frequency for

(Ck - C,) <o (Ck - C,) 2 CI ( 3 )

CA(Cj+I) C,+l .(Ck - Ci)<C, p,.l(C, - C,) =

CI 5 (Ck - C,)<0 (4) 6.1 (C, - C;) = h:,+l) Cj+l<(Ck-C;)<C,

Equations (3) and (4) can also be applied to Pr2 and &.> using the probabilities and frequencies associated with rectifier 2.

The probabilities associated with some performance levels are very small and therefore the performance tables can be truncated by omitting all pcrfonnance levels for which the probability is less than a specified amount. Table 3 shows the truncated perfonnance table, which consists of five pcrfomance levels of loo%, SO%, 50%. 30% and 0.0% [4].

The performance table at each load point can be determined using the results presented in Table 3. I t should

Table 3 Truncated performance table for the two rectifiers

PL individual individual cumulative duration, probability frequency frequenw h

100% 0.88118289 14.245 0 540.39

80% 0.00061008 0.89452 14.245 5.96

50% 0,11445108 14.2872 13.370 69.98

30% 3.96178E-05 0.06239 0.93302 5.55

0.0% 0.00371632 0.86773 0.87125 37.41

100%=220 MW.

573

be noted that. in this analysis. the underground cable system is assumed to be fully reliable and the rated capacity of each inverter is 30MW. The basic question is, how would the available capacity be distributed among the load points or, in other words. if a contingency results in load curtailment. how would the utility distribute the reduction among its customers? Different power ut es will take different actioiis based on their experience, judgement and other ciiteria. I n this piper the cap;sity of each performance level in the rectifiers performance table is distributed among the load points in proportion to their peak load. Other load curtailment philosophies can be utiliscd where appkdble. For instance. the available capacities associated with the 100'!4 perfonnance level (i.e. 220 MW. at load points 1 to 8 are 30_ 24.1. 27.7. 30. 26.5, 30. 30 and 21.7MW, respectively). This is done for all pcrformance levels and finally a performance table at each load point is created. The indices at each load point arc then determined usiiig the associated perfomunce table and the load profile at the bus. The system indices are determined after calculating the load point indices.

5.2 Inverter considerations I n this case. the two rectifiers and the underground cables are assumed to be fully reliahle. The pcrformance table at the load point is therefore determined by considering the influence of inverter element outages. The truncated performance table for the inverter is shown in Table4 where the 22% perfonnance levcl has been omitted.

Table 4 Truncated performance table for an inverter

PL individual individual cumulative duration, probability frequency frequency h

100% 0.95333789 6.7963 0.0 1225.41

37% 0.00039291 0.57484 6.7963 5.97

0.0% 0.04626919 7.3706 7.3706 54.84

100% = 30 MW.

5.3 Underground cable system considerations In this assessment? the influence of underground cable outages is considered. The rectifiers and inverters are assumed to be fully reliable and capable of performing their intended functions. Up to second-order f. di 'I ures are considered in this analysis. All failures are assumed to be active. Higher-order active failures are not considered as the probability of their occurrence is very small. All the load points are affected and temporarily disconnectcd in the event of first- and second-order active failures. The control system [ I . X I is assumed to he fully reliable. such that the isolation time of the faulted cable is in the order of microseconds. A three-state modcl is used for an under- ground cable [4].

Assuming that the control system is fully reliable, no load curtailment occurs for the first-order active failures. The faulted cable is repaired and restored as described by the repair time. In the case of a second-order active failure, a load point($ might be isolated or the subtransmission system split into two sections. For instance_ a second-order active failure on cables 'b' and 'd' will result in isolation of load points L2 and L3. The restoration time Rhil is determined using ( 5 ) where R,, and R,/ are the repair times of underground cables 'b and 'd.. respectively. A second- order active failure on 'c' and 'h' results in splitting the

574

subtransmission system and, in this case, if load curtailment is necessary, the power reduction is distributed among the load points in proportion to their peak loads.

5.4 Rectifier, inverter and cable considerations In this analysis_ a performance table is determined at cach load point considering rectifier and inverter outages where simultaneous outages in the rectifiers and inverters are considered. The load point and the system indices are determined using the calculated performance tables. The indices are then modified using the conditional probability approach by includiiig the impact on the indices associated with the underground cable system. The study results show that the contribution of the cable system to the load point and system indices is Icss that 0.01%. Outages in the cable system can result in either isolation of some load points or partial load curtailment. The failure probability, frequency and EENS due to an isolation case is directly added to the affected load point indices, as isolation affects all the customers at the load point. The indices due to partial load curtailment at each load point are weighted by the probability of the rectifiers and inverters being in servicc and added to the calculated indices associated with that load point. The system indices are then calculated using the load point indices. The assumption in this case is that no simultaneous outages of underground cable system and HVDC components (I-ectifiers and inverters) occur.

6 Study results

The system shown in Fig. I is uscd in this paper to examine the reliability of a multitenninal HVDC subtransmission system. The system consists of eight load points with different types and nuinbcrs of customers. The load point customer data is given in Appendix Section 9. The load profiles for each load point are assumed to be straight line load duration curves (LDC) [4] with the load factors shown in Appendix Section 9. The failure rate and repair time of the underground cables are also given in Appendix Section 9. Table 5 shows the load point indices when only rectifier component outages are taken into account. The truncated performance table shown in Table 3 was used as the rectifier perfonnance table.

Table 5 Load point indices due to only rectifier component outages

LP probability frequency, EENS, r, hlint. O C C b MWhh

L1

L2

L3

L4

L5

L6

L7

L8

0.07330691

0.10113087

0.08490172

0.06460809

0.07330691

0.1 1832141

0,11835956

0.06460809

8.57

11.63

9.85

7.61

8.57

13.53

13.58

7.61

4034.65

4079.3

3965.8

3294.4

3287.4

6743.7

8439.5

2371.9

74.69

75.93

75.28

74.16

74.69

76.37

76.09

74.16

LP. load point. P, average outage time, hiinterruption.

Table 6 shows the load point indices when only inverter coniponcnt outages are considered. The rectifiers and

I E E P m . . G m m Tliiwri Dirwili.. Vi,/. 149. MI. 5, Sqimvho. Z(02

Table 6 Load point indices considering only inverter component outages

LP probability frequency, EENS. r, hhnt. OCCIY MWhly

L1

L2

L3

L4

L5

L6

L7

L8

0.04660037

0.0466621 1

0.04663591

0.04654424

0.04658353

0.0466621 1

0.0466621 1

0.04654424

6.88

6.79

6.83

6.96

6.91

6.79

6.79

6.96

7171.7

6124.7

6574.8

6130.5

5841.5

8821.9

9720.8

4413.8

59.12

59.98

59.61

58.35

58.88

59.98

59.98

58.35

underground cable system are assumed to be fully reliable and capable of perfonning their intended functions. Compared to the results shown in Table 5 , it can be secn that the rectifier segment outages have more impact on the probabilities and frequencies of failure than the inverter component outages. The EENS. however, is higher in the case of inverter component outages. The i-eason for this is that most inverter component outages will result in isolation of the associated load point. Only simultaiieous outages in the two rectifiers result in load point isolations. Other outage combinations will result in partial load curtailment at different load points.

Table 7 shows tlie load point indices due to Failures in the underground cable system. Compared to tlie results shown

Table 7 Load point indices considering only failures in the underground cable system

LP

- L1

L2

L3

L4

L5

L6

L7

L8

probability, ( x 10-'1

7.12810

8.30214

8.30214

6.79266

6.79266

8.302 14

8.30214

7.12810

frequency, OGdY

0.000249

0.000290

0.000290

0.000237

0.000237

0.000290

'0.000290

0.000249

EENS, MWhly

0.052888

0.055545

0.059796

0.044760

0.042666

0.079977

0.087675

0.0326047

r. hiint.

25 25

25

25 25

25 25

25

in Tablcs 5 and 6, it can be seen that the impact on the load point indices of underground cable system Failures is very small. This is due to the ability of the control system to isolate the faulted cable in a very short timc. It should be noted that. in the results presented in this paper, it is assumed that the control system is fully reliable. I f the control system fails. the faulted line must be isolated manually.

Table 8 shows the system indices associated with the three dilrerent case studies (CS). I t can bc seen from the results that the system indices are more afected by rectifier or inverter component outages than failures i n the under- ground cable system. The average system availability index (ASAI) for the third case study (C3) is almost unity compared to those associated with the other case studies (i.e. CI and C2).

IEE P m ~ ~ G e m ~ r . Twt,sm DimB , l'd i l Y , A'<!. 5. Sqmmho- 2002

Table 8: System indices for different case studies

CS SAlFl SAID1 C A D ENS ASAl ASUl

C1 8.3533 623.08 74.5 1.86 0.92867 0.071324 C2 6.9589 406.66 58.4 2.81 0.95344 0.046551 C3 2.5E-4 6.2E-3 25.0 2.3E-5 0.99999 7.00E-07

C1, considering only rectifier component outages. C2, considering only inverter component outages. C3. considering only failures in the underground cable system.

Table9 shows the load point indices when outages associated with all the three main segments in the system are considered. The results were obtained using the procedure presented in Subsection 5.4. The system indices associated with this case study are shown in Table I O (CS-A).

Table 9 Overall load point indices

LP probability frequency. EENS. c hlint occiv MWhiv

L1

L2

L3

L4

L5

L6

L7

L8 -

0,11648686 14.56

0,14303097 17.26

0.12754996 15.68

0.10813803 13.78

0.11643654 14.63

0,15946243 18.89

0.15949880 18.94

0.10805462 13.90

10990.5

9986.19

10329.5

9245.78

8949.90

15223.2

17737.7

6650.96

69.88

72.37

71.03

68.53 69.50

73.73

73.54

67.88

Table 10 Overall system indices

CS SAlFl SAID1 C A D ENS ASAI ASUl

A 14.437 1000.7 69.3 4.58 0.8854524 0.1145476

B 15.727 320.79 20.4 1.22 0.9632790 0.0367210

A. without backup. B. with backup.

6. I Inclusion of spare components The previous studies did not include any spare or back-up componsnts for the smoothing reactors and transformers. This means that. if a transformer or a smoothing reactor fails, it cannot be replaced until the failed coinponent is repaired. Providing spares will improve the system relia- bility_ as the repair time of these elements is high. Assume that a spare is provided for each transformer and smoothing reactor with a replacement time of 98.2 and 41.9 hours, respectively. It should be noted that the original perfor- mance tables were determined using repair times for the transformers and smoothing reactors of I 110.75 and 262.5 hours, respcctively [5].

Fiz. 5 coinpares the load point indices for the two cases of with and without spares. The system indices associated with the case of with spares are presented i n Table I O (CS- B). It can be seen from the results that the load point indices are considerably improvcd by providing spares for the transformers and smoothing reactors.

571

1 I 1

I with backup I

I 2 13 L4 15 L6 17 IO load point

1. with backup I

I t 12 13 14 15 16 17 I O load point

I with backup I

I 1 I2 i 13 I,i 14 I , J l , i 15 16 1,3111, 17

load point

I 00 r

L I 70

ai 60 E

50 ?& $ 40

," 30 I 20 m

I 10

n

LO

A I O

bock-rip

7 Conclusion

A reliability evaluation of a hybrid niultitetminal HVDC subtransmission system is presented. Reliability models associated with the rectifier: inverter. and underground cable segments are developed for the purpose of reliability analysis. A procedure is presented to evaluate the reliability of an HVDC multiterminal subtransmission system and the contribution of each segnent to the reliability indices. Two sets of indices. the basic load point indices and thc system performance indices: are used to measure the reliability of the system. The results prcsented indicate that the contribution of the cable system to the load point and system indices is very smilll relative to that associated with

516

the rectifier and inverter systems. This is mainly duc to the assumption that the control system is both fast and highly reliable. The possible impacts on the load point and system indices of providing transfoiiner and smoothing reactor sparcs are also illustrated.

8 Appendix

Tables 11-13,

Table 11: Load point customer data

load customer no. of peak load, load point type customer IMWl factor

L1

L2

L3

L4

L5

L6

L7

L8

residential

commercial

govt. & inst.

residential

residential

large users

small ind.

residential

5400

1200

20

5000 4400

10

10

3400

21

20

23

25

22

27

28

18

65% 75% 70%

60%

65%

80%

85%

60%

Table 12: Rectifier and inverter component outage data

element failure rate, repair time to

spare, h f& time, h install

synchronous 2.0 72 -

valves 3.0 4 - auxilialy power 2.0 8 -

breakers 0.01 48 - DC lines 0.01 72 - transformers 0.093 1110.75 98.2

smoothing reactors 0.28 262.5 41.9

Fr 0.25 6 - xc 0.002 12 -

compensators

supplies

F1 to F3 0.35 6 - F4 0.25 6 -

Table 13: Underground cable system data

component aCtive failure. length, repair f/v km km time, h

cable a, e, f. i 0.008 6 50

cable b. c. d. 4. h. i 0.008 4 50

9 References

1 JIANG. H.. and EKSTROM. A,: 'Mullilcm?inal HVDC systems ill urban areas uf large cities'. IELX 'fiwx P w w DcB:. 1998. 13. pp.

cngineeing systems' (Pirnum Press. Ncw Yoik. l994f

4 BILLINTON. R.. and ALLAN. R.N.: 'Reliahility cvilliiation of elcctric powci systems' (2nd edn.. Plcnum Press. Ncw~ York. 199h)

CHARD. M.: 'Reliahilitv as~~ssment of HVDC tliinsmission'. 5 DESROCHER. c.. LEFEBVRE. s.. RIOUX. n.. ~ I K I BLAN-

Gmidian Electrical Assoc:ation. Rupon CEA 222 T 506. Prepared hy IREQ, 1987 FONG, C.C., BILLINTON. R., and GUNDERSON. R.O. el al.: 'Bulk s ~ t e m ~~liahiiity-measuicment and indiccn'. IEEE Tru,ii. Pmwr Syx, 1989. 4. (3). pp. X29-835

h

7 'Bulk electricity system delivcry point interruptions 1988-190 Report'. Canadkin Eltitricity Association Eqoipmcnt Reliability Information System Report. Ocrokr, 1992 NOSAKA. N.. TSUBOTA. Y.. MATSUKAWA, IC.. and SAKA~ MOTO. K.: 'Simulation studies on a control and nrotection scheme for

8

hybrid ~miilti-leiminill HVDC systems'. Proceedings of the IEEE 1999 PES Winter Merlins. New York. I999

577