Reliability calculation of MV-distribution networks with regard to ageing in XLPE-insulated cables

M.Stotzel, M.Zdrallek and W.H.Wellssow

Abstract: Failure statistics of German utilities show that more than 8OYo of the supply interruptions of medium voltage (MV) customers are caused by component outages located in the MV network itself. For these networks a model as near to reality as possible is required to correctly determine customers’ quality of supply. One aspect so far neglected in reliability calculations of MV networks is that the failure rate of most components is not constant for the whole lifetime, but rises over the years according to the increasing right wing of the well-known bathtub curve. Due to the water-treeing phenomenon, XLPE-insulated MV cables manufactured during the 1970s show heavy ageing problems after some years of operation, resulting in a strongly increasing failure rate. An approach is presented to take these increasing failure rates into account in reliability calculations of MV networks. The cable-failure models used in the investigation are described in detail as well as the data received from a special evaluation of the VDEW-statistics of XLPE-insulated MV cables reflecting the ageing phenomenon. Several calculations of an actual lOkV cable network supplying parts of a German city are presented to show the impact of increasing cable failure rates on the reliability of MV customers’ power supply.

1 Introduction

Generally network components in reliability calculations of electrical power systems are modelled according to the states ‘in operation’ and ‘repair’. Failure and repair rates for the transition between both states are assumed to be constant during the whole lifetime of the component. This models the component outage behaviour according only to phase I1 of the well-known bathtub curve [ 11, describing the component failure rate during its lifetime (Fig. 1). During phase I1 the component failure rate is constant. Manufac- turing defectives (phase I) are neglected as is the increasing failure rate near to the end of component lifetime due to ageing (phase 111). For most components this simplification has to be accepted, because proper data to model their whole lifetime is not available. Moreover, it can be accepted in most cases without distorting reality, because the duration of phase I is quite short and network compo- nents are generally replaced before they reach phase 111.

But for XLPE-insulated MV cables manufactured during the middle of the 1970s, neither neglect of the ageing proc- ess nor the absence of a database can be accepted. The VDEW-statistic of MV-XLPE-cables [2] provides data about the rapid increase of failure rate of these cables after about 10-12 years of operation. long before the cable is normally replaced. This increasing failure rate has to be taken into account during the reliability calculation of MV cable networks. Therefore the Monte Carlo simulation part

0 IEE, 2001 IEE Proceedings online no. 20010505 DO1 IO. lO49/ipgtd20010505 Paper fuxt received 15th August 2000 and in revised form 1st March 2001 M. Stotzel and M. Zdrallek are with the University of Siegen, HolderlinStr. 3, 57068 Siegeii, Germany W.H. Wellssow is with FGH e. V., Hallenweg 40,68201 Mannheim, Germany

of the reliability calculation program ZuBer [3] has been enhanced to consider time-dependent failure rates accord- ing to the whole bathtub curve, although only phase I1 and phase I11 are used to investigate the influence of cable age- ing on network reliability.

age of component ’ t Fig. 1 Bathtuh curve &scribing components juilure rate during lijetime [ I ]

Based on failure rate and outage duration of network components, the time-sequential Monte Carlo simulation used in ZuBer generates many sequences showing the beginnings and endings of component outages. The analy- sis of the sequences of outages, supply interruptions and remedial measures results in customers quality of supply described by the well-known reliability indices.

To analyse the impact of cable ageing on MV customers quality of supply, the sources of cable failures have to be determined. The ageing process of XLPE-cables has to be analysed especially carefully and transformed into failure models. It turns out that two main kinds of cable failure lead to supply interruptions in MV networks. They are dis- cussed in the following Section.

2 Failure models for XLPE-insulated MV cables

2.1 Cable failure model I: Active failure Short circuits caused by excavator work or other mechani- cal damage are one main reason for MV cable failures.

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Table 1: Reliability indices of MV components

Failure model Component h i n Ila Tin h p

Active failure XLPE-insulated cable 0.004/km 15 - MV busbar 0.0052 5.5 - secondary transformer substation 0.0007 2 -

Earth fault XLPE-insulated cable see Fig. 3 - -

MV busbar 0.0007 - -

Multiple earth fault

secondary transformer substation 0.0002

XLPE-insulated cable - 15 see Fig. 5

MV busbar - 3.1 0.0041 secondary transformer substation - 15 0.0019

Malfunction of protection device protection device - 0.5 0.009

Unnecessary protection operation protection device - 0.5 0.00013

hfailure rate; Toutage duration; p conditional probability

This leads to a supply interruption to all MV customers located in the affected half-ring as shown in Fig. 2a if the protection device properly clears the short circuit: After the location of the short circuit is found the separation point is moved and the affected cable sequence is switched off Therefore all MV customers are resupplied within a rela- tively short time (Fig. 2b). This kind of failure is almost totally independent of cable age, so the probability of its appearance is assumed to be constant during the whole life- time of a cable. Constant failure and repair rates for this failure model for XLPE-insulated MV cables can be derived from [4] (Table 1).

from the special VDEW-statistics of XLPE-insulated MV cables [2] as well as the interpolated exponential distribu- tions for the analysed manufacturing years 1975, 1977, 1979 and 1981 depending on the age of the cable. It can be seen in Fig. 3 that [2] provides worthy earth failure rates for only a few years, while values for the other years have to be added according to engineering estimates. In this investigation it is assumed that a faulty cable section is not replaced completely but only repaired. So a cable section’s earth failure rate grows exponentially with cable age. It can be deduced empirically from [2] according to the increasing wing of the bathtub curve with

X e a r t h f a z l u r e ( t ) = C + N e ( $ ) with C , N , T > 0 (1) During the first years of a cable’s lifetime the earth failure rate is constantly low for all manufacturing years (Fig. 3). But after about 1&12 years of operation the ageing phe- nomenon causes an exponential increase of earth failure rate of cables manufactured between 1975 and 1977, while cables of the manufacturing years 1979 and 1980 do not show any ageing phenomena at all. The values of C, N and T derived from the VDEW-statistics of XLPE-insulated MV cables are quoted in Table 2.

.closed separation li overcurrent-time relay ir MV customer

Oopen separation L overcurrent.time relay / short circuit

0.5

4

point and circuit breaker

point and circuit breaker (switched off) -J MV customer not supplied P

a b Fig. 2 CdIe failure model 1: active failure

2.2 Cable failure model 2: Multiple earth fault This model is based on an earth fault (single phase to ground fault) on a network component. In the case of XLPE cables, the reason for such an earth fault usually is a water tree [5] which starts growing from inhomogenities in the cable insulation (shrink holes, contaminations etc.) until it finally bridges the whole insulation. When the insulation is bridged by the water tree it still withstands the opera- tional voltage so that no earth fault occurs immediately. However, a current starts to flow which dries out the water tree. If the drying procedure is finished (this may take one year depending on temperature, the amount of water etc.) the water tree finally changes into. an electrical tree. The dielectric strength of the tree decreases rapidly and the insu- lation breaks down during about one day.

For some manufacturing years of XLPE-insulated MV cables the whole procedure, including the earth failure rate, is strongly correlated to the age of the cable. Fig. 3 shows the earth failure rate of XLPE-insulated MV cables derived

0.3 e

E

0 - ii 0.2

I

.-

.c 0.1

0.0 0 2 4 6 8 1 0 1 2 1 4

age of cables, a Fig.3 munufacture Data derived from [2] and interpolated exponential distributions __ manuracturing year 1975 (interpolation)

manufacturing year 1977 (interpolation) ---- inanufacturing year 1979 (interpolation) . . . . . . . . . . . . manufacturing year 198 1 (interpolation) -+- data derived from [3] (1975) - -+- - data derivcd from [3] (1977) - - + - - data derived from [3] (1979) ..-.+..... data derived from [3] (1981)

Earth fnilure rate of XLPE-insulated MV cables of d$?erent years of

In networks operated with resonant earthing a single earth fault does not initiate an operation of the protection system due to the small short-circuit current. Therefore no supply interruptions occur at first (Fig. 44 . However, the increase of the phase-to-ground voltage of the remaining phases may cause a second earth failure of another compo-

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nent. This double earth fault causes the operation of the protection system and in most cases (about 90%) both trip- ping areas concerned are switched off automatically as shown in Fig. 4b. In the remaining 10%, of all cases only one tripping area is switched off by the protection system and the other one can be switched off by operator action, sometimes avoiding a supply interruption. It has to be con- sidered that, due to the increase of the phase-to-ground voltage in the case of a first earth fault, the probability of the occurrence of a second earth failure is much higher than the probability for the first earth failure. The conver- sion of a water tree into an electrical tree and the final insu- lation breakdown are accelerated strongly under earth fault conditions, when the phase-to-ground voltage is d3-times the one during normal operating conditions.

Table 2: Time dependent earth failure rates according to eqn. 1

Year of manufacture Cin l/a N i n I/a Tin a

1975 t< 7a 0.022 0 - 7a5 t s 15a 0.013 0.00034 2.09

1977 t< 8a 0.018 0 - 8as t s 15a 0.004 0.00046 2.33

1979 t< 9a 0.013 0 - 9as t s 15a 0.011 0.00012 3.1

1981 0.003 0 -

110 kV 110 kV

a b

110 kV

Fig. 4 Cable fuilure model 2: miiltiple earth fault

The fact that a large number of cables are operated for a long time with water trees that have already bridged the insulation underlines the assumption that other water trees exist which have already bridged the insulation, if a first earth fault has occurred. Then a conditional probability P,second jhilure can be defined such that one of these water trees converts into an electrical tree causing an insulation breakdown when it is exposed to earth-fault conditions for an infinite time span. This conditional probability depends strongly on the cable age too, and can be described by a Weibull distribution with P.seconcl eflrfhf~ilt[,.e(t+=OO) = 1. Since the hypothetical case t-00 with P,,econ, le~, . Ih~, i~u, .e( t~~) = 1 is not reached because a cable section of such a poor quality cannot be operated any longer, only the exponentially increasing part of the Weibull distribution is taken into

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account which can be described sufficiently with

Psecond ear th f a t l u r e ( t ) c + N e ( & ) (2) The term 0.9T considers the extremely accelerated conver- sion of a water tree in an electrical tree if the water tree is exposed to earth fault conditions.

In contrast to the assumption of never-ending earth-Fault conditions, in real MV networks they last until the earth fault is located, the separation point moved and the affected cable sequence switched off. In the MV network investigated the whole procedure lasts about TT,vltch c.fl,th = 2 h. From [6] it can be derived that the probability of an existing water tree conversion in an elec- trical tree which finally leads to a breakdown of the insula- tion during two hours is Ph,eakclo,vn, 2h = 0.75. With this assumption, the conditional probability for a second earth failure occurring within two hours after a first earth fault has occurred is

psecond e a r l h f a z l u r e , 2 h ( t ) - - p5econd ear th f azlure ( t ) p b r e a k d o w n , 2 h (3)

This conditional probability for a second earth failure within two hours is shown in Fig. 5 for the different manu- facturing years of XLPE-insulated MV cables. U

8 P

0 3 6 9 12 15 age of cables, a

Fi 5 Conditional proliability ,for second earth fnilure of XLPE-inmluted M L b l ' , 's f or &@rent years of manufacture -0- 1975 -A- 1977 -x- 1979 -M- 1981

2.3 Complications following cable failures If cable failures occur according to failure models 1 and 2, the short-circuit current is switched off by the proper pro- tection devices. In these cases the incident may expand due to a malfunction or an unnecessary operation of protection devices. The reliability data used to model these complica- tions is given in Table 1.

3 Example calculation

3. I Description of network The MV network investigated represents a typical German urban l0kV network operated with resonant earthing. It is fed by the higher-level 1 l0kV network via one transformer substation. Several lower-level 0.4 kV networks and some MV industrial customers are modelled as connected loads at 71 secondary substations. For these substations, subse- quently called customers, the reliability of supply is calcu- lated. Most customers are supplied via typical open half- ring configurations, while three customers (D 1 , D2, D3) are located in a radial feeder. The network structure is dis- played in Fig. 6. Table I shows the component reliability indices used in this investigation received from [4, 71. A small network's statistics are given in Table 3.

Originally 99% of the total cable length of about 27km consisted of paper-insulated mass-impregnated cables. But

599

MV-customer separation point (secondary substation)

Fig. 6 Structure ojexample network

due the fact that these cable types do not show any signifi- cant ageing, it is assumed for this investigation that the whole network consists of XLPE-insulated MV cables manufactured in the same year in which they all started to operate at the same time (year 0).

Table 3: Data of urban 10 kV network

Transformer substations (110/10kV) 1

Secondary transformer substations (10/0.4kV) 71

Total length of cables

Peak load demand 28.19 MVA

27.28 km

3.2 Calculation results without ageing phenomena At first a reliability calculation of the described MV network is carried through for the first year of operation. All cable sections are assumed to be manufactured in 1979 and to be new so that no ageing phenomena have to be taken into account. As a result Fig. 7 shows the frequency of supply interruptions of selected MV customers. If Fig. 7 is compared toFig. 6 it can be seen that all customers located in the same cable half-ring suffer the same number of supply interruptions. This is caused by the structure of the protection system of the MV network. An overcurrent- time relay switches off the whole half-ring if a short circuit on any cable section occurs. So all MV customers of the half-ring face a supply interruption (compare Fig. 2b with

MV customers Fig. 7 Frequency of supply interruptionsfor selected M V custonws

Fig. 4b). Therefore MV customers located in the longer cable half-rings show a higher frequency of supply interrup- tion than those located in shorter half-rings.

After the short circuit is switched off by the protection device, the failure location is determined and the faulty cable sequence is switched off and has to be repaired. The separation point is moved and the healthy cable sequences are switched on again to resupply the customers in short time. This procedure lasts for about half an hour. As dis- played in Fig. 8, the mean duration of supply interruptions of most customers is about half an hour, while the mean duration of supply interruptions of four customers (Dl, D2, D3, E5) is obviously lugher. These customers are sup- plied via a radial cable feeder so if one cable sequence of this feeder fkils, there is no possibility to resupply the cus- tomers located behind the fmlty cable section until the cable is repaired (T,.epnjr = 15h, compare Table 1). There- fore, customer D3 located at the end of the radial feeder experiences a longer mean interruption duration than cus- tomer DI located near to the 110/10kV transformer substa- tion.

.- 6}

MV customers Fig. 8 Mean duration of supply interruptionsfol. selected M V custoniers

3.3 Calculation results considering ageing of XLPE-insulated MV cables

3.3.1 System reliability results for MV network: Fig. 9 shows the frequency of interruptions (system value) for the first 15 years of operation and different manufactur-

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ing years of XLPE-insulated MV cables. The system is interrupted if at least one customer suffers an interruption of supply. It can be seen for manufacturing years 1975 and 1977 that the interruption frequency does not increase before ageing problems set in after eight-to-ten years of operation according to Figs. 3 and 5. Assuming that the faulty cable sequences are not removed but only repaired after 15 years of operation the interruption frequency rises to 15 times (manufacturing year 1977) and 25 times (manu- facturing year 1975) the value without ageing problems, respectively. Since XLPE-insulated MV cables manufac- tured after 1979 show no significant ageing, the interrup- tion frequency (system value) is nearly constant during the years for these calculations. Fig. 10 displays the energy not delivered in time (system value). Similar to the interruption frequency the energy not delivered in time for the manufac- turing years 1975 and 1977 increases after eight-to-ten years of operation, but the increase is much more rapid. This is caused by the fact that after eight years of operation the mean duration of interruptions increases too, due to an increase of the number of multiple earth faults, with both earth faults located in the same cable ring. In this case those customers that are located in the affected cable ring between both earth-fault locations cannot be resupplied by switching actions but only by long-lasting repair (T,.,,. = 15h) of the cable (compare Fig. 4c). Similar to the inter- ruption frequency, the energy not delivered in time for the calculation with XLPE-insulated cables manufactured after 1977 is nearly constant.

age of cables, a Fig. 9 -+- 1975 -0- 1977 -A- 1979 -.- 1981

Frequency ofmpp!+ interruptions (system volue)

age of cables, a Fig. 10 -+- 1975 -0- 1977 -A- 1979 -.- 1981

Energy not delivered in tine (.ytetn vdue)

3.3.2 Results for selected customers: The impact of the ageing phenomenon on the quality of MV customers' supply differs with the way the customer is connected to the MV network. This is underlined by Fig. 11, which

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presents the frequency of interruptions of three MV cus- tomers for the first 15 years of operation assuming all XLPE-insulated MV cable to be manufactured in 1975 again. The three selected customers are located in cable half-rings of quite different length. As discussed, these cus- tomers (e.g. customer E3) located in a half-ring of long length (4/cj,lg length = 3,600m) face a higher frequency of sup- ply interruptions for each age of cables than those located in a half-ring with medium (customer J6, k',nec,ju,n -

1,SOOm) or low (customer 12, e,,,., lengtlz = 800m) length of cables. But at the beginning of the cable's lifetime those customers located in a half-ring of long length are supplied quite reliably, and face less than one supply interruption in the first ten years of operation. The number of supply interruptions increases rapidly after an operational time of ten years or more. While the quality of supply of those cus- tomers included in a short half-ring with less than two interruptions per year after 15 years of operation might still be acceptable, an interruption frequency of Anrer,.ul,tion = 5lu, as calculated for customers included in a long half-ring, is surely not acceptable anymore.

-

I!

age of cables, a Fig. 1 1 work in dijlerent wuy.s -+- large length of cable (E3) -A- medium length (56) -.- short length (12)

Frequency OfsuppIj interruptions of MV customer connected io net-

"0 2 4 6 8 10 12 14 age of cables, a

Fig. 12 centuge,s of bad cables -.- 10% XLPE cable (1975) -+- 20% XLPE cable (1977) -A- 50% XLPE cable (1979) -x- 100% XLPE cable (1981)

Frequency of swpp!+ interruptions (system volue) for diferent per-

3.3.3 Influence of few ageing XLPE-cables: The assumption that the whole network consist of XLPE-insu- lated MV cables manufactured in the same year which started to operate at the same time is surely hypothetical for most existing German MV cable networks. Generally these networks have grown through several decades, thus they consist of many different cable types of all ages and manufacturing years. Most of them, especially paper-insu- lated mass-impregnated MV cables and XLPE-insulated cables manufactured after 1977, do not show any signifi-

601

cant ageing problems. Only those few XLPE-insulated cable sections manufactured in the middle of the 1970s that show heavy ageing problems lead to a decreasing quality of customers’ supply. This paragraph investigates how strong a small number of bad cable sections influences the reliabil- ity of the whole MV network. It is assumed that a particu- lar percentage of cables widely spread over the whole network is XLPE-insulated and manufactured in 1975 and therefore shows heavy ageing problems, whle the majority of cables has a constant low failure rate. So in each half- ring the same minority of the cable length is modelled as bad XLPE-insulated cable manufactured in 1975 (data see Table 2), while the majority is modelled with a constant low failure rate (see Table 2, XLPE-cables manufactured in 1981).

Fig. 12 compares the frequency of interruptions calcu- lated for the whole network assuming 10, 20 and 50% of the cables to be bad with the results calculated on the assumption that all cables are XLPE-insulated and manu- factured in 1975. As expected, the influence of ageing of XLPE-insulated cables on the reliability of the whole net- work decreases rapidly with the percentage of these cables. If only 10 (20>% of the cables are XLPE-insulated and manufactured in 1975 after 15 years of operation the number of supply interruptions increases to about one (two) per year. This quality is still acceptable for customers, but at this time the utility operating the network has to start countermeasures to avoid a rapid increase of the inter- ruption frequency during subsequent years. Especially if the bad cables are not spread widely over the whole network but located in the same half-ring countermeasures must be carried out immediately to guarantee the quality of supply of customers placed in this half-ring during the following years of network operation.

4 Conclusions

This paper presented an investigation that takes the ageing of XLPE-insulated cables into account in reliability calcula- tions of MV networks. Therefore the physical ageing

phenomena of XLPE-insulated cables have been trans- ferred into failure models. A special evaluation of the VDEW-statistics of XLPE-insulated MV cables showed that only the XLPE cables manufactured during the middle of the 1970s showed heavy ageing problems. Several calcu- lations of an MV network showed no influence of the ageing procedure on the quality of customers supply for the first ten years of cable operation even when the network consisted completely of XLPE cables manufactured in 1975. After ten years of operation the quality of supply decreased rapidly if the network consists of XLPE-insu- lated cables manufactured during the middle of the 1970s, while there was no loss of quality in networks which consisted of XLPE cables manufactured after 1980 because they showed no significant ageing problems. In spite of the fact that German MV networks today generally include only a few bad XLPE-insulated cables manufactured during the 197Os, the operating utility should carry through countermeasures when the number of failures on these cables begins to increase.

References

ALLAN, R.N., and BILLINTON R.: ‘Relkdbility evaluation of engi- neering systems’ (Plenum Press, New York, London, 1992) FISCHER, M.: ‘VDEW-Umfrage zu Schaden an VPE-Kabeln’, Ele- ktrizitiitsM,ivf,sC/7Llft 96, 1997, 20, pp. 11541 158, in German BACKES, J., KOGLIN, H.-J., and KLEIN, L.: ‘A flexible tool for planning transmission and distribution networks with special regard to uncertain reliability criteria’. Proceedings of 12th PSSC, Dresden, 1996, pp. 567-573 VDEW: ‘Storungs- und Schadensstatistik 1994 - 1997, Bundesrepublik Deutschland gesamt’ (Verlags- und Wirtschaftsgesellschaft der Ele- ktrizitiitswerke mbH, Frankfurt, 1998), in German SHAW, M.T., and SHAW, S.H.: ‘Water-treeing in solid dielectrics’, IEEE T m s . Electr.. Insul., 1984, EI-19, (5), pp. 419452 WECK, K.-H.: ‘Stufentest ZUI‘ Ermittlung des Isolationszustandes belrieblich vorbeaiispruchter PE- und VPE-Mittelspannungskabel’, E l e k f r i z i t i i t s w i ~ t ~ ~ ~ ~ ~ ~ , 1989, 88, pp. 470-473, in German HEIIJ, A.: ‘Zur Frage der abschnittweisen Verkabelung von Mittels- pannungs-Verteilungsnetzen’. Postgraduate thesis, RWTH, Aachen, 1990. in German

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