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Electric Power Systems Research 81 (2011) 1709–1714

Contents lists available at ScienceDirect

Electric Power Systems Research

journa l homepage: www.e lsev ier .com/ locate /epsr

ge-dependent maintenance strategies of medium-voltage circuit-breakers andransformers�

iang Zhang ∗, Ernst Gockenbachnstitute of Electric Power Systems, Division of High Voltage Engineering, Leibniz University of Hannover, Callinstrasse 25A, Hanover 30167, Germany

r t i c l e i n f o

rticle history:eceived 14 October 2008eceived in revised form 13 February 2011ccepted 10 March 2011vailable online 7 May 2011

a b s t r a c t

The general life and reliability models of electrical equipment are essential to evaluate their actual con-ditions because of the degradation of equipment. To optimize the maintenance strategies for maximalreliability and minimal cost in a quantitative way, available maintenance models of ageing equipmentshall be found to describe actual maintenance actions in time-series processes. In particular, a functionalrelationship between failure rate and maintenance measures is to be developed for electrical equipment.This paper demonstrates some actual examples by applying these models and the results show the value

eywords:geircuit-breakerostailure rateaintenance strategy

ransformer

of using a systematic quantitative approach to investigate the effect of different maintenance strategies.© 2011 Elsevier B.V. All rights reserved.

. Introduction

Deregulation of the power system market has forced electrictilities to scrutinize investment and maintenance expendi-ures much more rigorously than in the past. Many focus theirnvestments on maintaining the competitive position of power gen-rating assets, while trying to squeeze more performance fromgeing power delivery assets with less expenditure. However, in theower transmission and distribution systems, the annual expen-itures for maintenance and replacement average only 1% or lessequal to 20 billion Euro for distribution systems in Germany and00 billion Dollar for transmission systems in USA), which corre-ponds to an expected lifetime for more than 100 years of electricalquipment [1]. Owing to the limited reinvestments, the age of elec-rical equipment will increase so that the utilities have to facearious market requirements. On the one hand, customers areaying for a service and the authorities are imposed regulation,upervision, and compensation depending on the degree to which

ontracts and other obligations are fulfilled. On the other hand,tilities must ensure that their expenditure is cost-effective.

� This work was supported by the National Research Council of Germany underhe Contract SPP 1101.∗ Corresponding author.

E-mail address: zhang@si.uni-hannover.de (X. Zhang).

378-7796/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2011.03.018

The easiest way and the most widely used strategy today isthe time-based maintenance (TBM) [2]. There are fixed time inter-vals for inspections and for certain maintenance works. However,it seems that the time intervals chosen are far from the safe sideand the total replacement expenditure is extremely expensive, asthere are many inspections revealing no problems at all. So, thetime intervals obviously can be extended – the question is fromwhich point of time the occurrence of failures will increase signif-icantly.

In order to obtain useful information about the actual conditionsof equipment, condition monitoring technique and condition-based maintenance (CBM) has been well developed [3–5].Condition monitoring technique means mainly sensor develop-ment, data acquisition, data analysis, and development of methodsfor determination of equipment condition and early fault recogni-tion. The importance of monitoring methods can recognize whichmeasured parameter affects the ageing of equipment to a greateror lesser degree. It should support the introduction of condition-based maintenance and help to avoid unexpected outages. The costof sufficient instrumentation can often be quite large and off-linemeasurement even causes more significant outage. In the majorityof cases, there are neither communication links nor suitable sen-sors available for monitoring from remote. In terms of numerical

protection devices and control systems, those engineers are suf-fering from data overload. Also, from the technical side, it is notalways as simple as possible. Even if some types of equipment caneasily be observed by measuring simple values as temperature or

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710 X. Zhang, E. Gockenbach / Electric Pow

ressure, it is not trivial to turn this measured data into actionablenowledge about health of the equipment.

In recent years, the reliability centered maintenance (RCM)as been established [6–8]. RCM is an industrial improvementpproach focused on identifying and establishing the operational,aintenance, and capital improvement policies that will manage

he risks (combination of severity and frequency) of equipmentailure most effectively. As an economic and reliable life cycle

anagement, the condition and the importance of the equipmentust be combined and evaluated in order to create a cost-effectiveaintenance strategy, addressing dominant modes and causes of

quipment failure. The artificial neutral network which exhibits theon-linear input–output relationships between equipment reli-bility and system maintenance is integrated into maintenanceanagement system (expert system) via a commercial software

ool. The reliability centered maintenance based on the analy-is of “condition-importance” and the use of “weighting factors”,epends heavily on practical experiences in diagnostic analysis andaintenance measures.That has followed so-called reliability centered asset manage-

ent (RCAM) since the last years [9–12]. The research approacheals with the life assessment (e.g. failure rate) and the main-enance tasks (e.g. inspection rate) based on several discretexponential distributions. The assumption of exponential distri-ution spent in each stage implies constant failure/maintenanceate which is assigning to each operation state. In that way, theeterioration processes of equipment consist of a chain of discretearkov models. Therefore, this parameter evaluated by using time

etween failures as input data for special network facility, is of theost concern in the analysis. These chosen parameters represent

ast experience by single facts or numbers, without assigning anyegree of likelihood to future expectation. Therefore the approachoes not provide enduring analytical models of the deteriorationrocesses, by which the consequences of each failure can be effec-ively used on a predictive basis for the future. On the basis of thexponential distribution, the fitted curves are only a mathemati-al simulation that is not concerned with any information abouthe technical parameters and the operating conditions of electricalquipment, thus they can not give a complete understanding of thehysical implications in failures.

Up to now, the impacts of maintenance on reliability and costan be analyzed only for those selected strategies. The reason is aack of an available reliability model for the deteriorating electricalquipment and a theoretical maintenance model put into practiceor power systems. In fact, only a continuous quantitative descrip-ion (mathematical models) can lead to an optimal solution of theystematic maintenance strategies. Therefore, this broad perspec-ive of asset management is recognized as “relating maintenanceffort to system availability and total cost, with the aim to reachn optimal maintenance management”. This new research topic isorld-wide challenge for all researchers on asset management of

he power transmission and distribution systems.

. Age-dependent reliability model

The failure causes may identify the origin of detrimental effects,ontributing to the failure of electrical equipment. The influenceactors producing an ageing change of equipment are divided in dif-erent stresses such as electrical, thermal, mechanical and ambienttresses.

The stresses of electric ageing are partial discharges, tracking,

reeing, electrolysis and space charges. The intensity and progressf electrical ageing depends on the electric field strength in thensulation. The consequences of thermal ageing comprise chemical,hysical and thermal–dynamic changes by chemical degradation,

tems Research 81 (2011) 1709–1714

polymerization, depolymerization of organic materials, diffusionand thermal–mechanical effects as a result of thermal extension orcontraction. A mechanical ageing of equipment can only occur bysolid material as a result of mechanical tractive and shear forcesduring transportation, installation and operation. The substantialreasons of mechanical ageing are electrodynamic, electromagneticand thermal forces. Ageing caused by ambient conditions comesfrom the reaction of material to humidity, air, chemical, biologi-cal substances, weathering, pollution and radiation. But more orless the electrical equipment is simultaneously stressed by variousinfluence factors.

A thorough electro-thermo-mechanical life model of the electri-cal component can be established according to the Inverse PowerLaw and the Arrhenius Model. This can simply be done by assum-ing that ageing rate under these combined stresses is the productof ageing rates under each single stress [13,14]:

L = L0

(E

E0

)−(n−bT)·(

M

M0

)−m

· e−BT , T = 1ϑ0

− 1ϑ

(1)

where E, M, T and L are the electrical, mechanical, thermal stressesand lifetime, respectively. E0 and M0 are the scale-parameters forthe lower limit of electrical and mechanical stresses respectively(below which the ageing can be neglected) and L0 is the correspond-ing lifetime. n, m and B are the voltage-endurance coefficient, themechanical stress-endurance coefficient and the activation energyof thermal degradation reaction, respectively. b is the correct coef-ficient which takes into account the reaction of materials due tocombined stress application. ϑ and ϑ0 are the absolute temperatureand the reference temperature.

The failure of an electrical component may occur if over-voltageor mechanical stress is applied, or if the electrical component isaged by temperature or time. A criterion for the ageing of electricalcomponents is consistent with the electrical, thermal or mechanicalstress. Thus the relationship between lifetime and failure probabil-ity of electrical equipment may be determined by:

Pr(L) = 1 − exp

[−(

E

E0

)˛(n−bT)·(

M

M0

)m˛

·(

L

L0

)˛

· e˛BT

](2)

Therefore, the lifetime L of an ageing component as arandom variable t has a cumulative probability distributionF(t) ≡ Pr{L ≤ t} with right continuous, and a probability densityfunction f(t) = dF(t)/dt

F(t) ≡ Pr{L ≤ t} = 1 − exp

[−(

E

E0

)˛[n−b((1/ϑ0)−(1/ϑ))]·(

M

M0

)m˛

×(

t

L0

)˛

· e˛B((1/ϑ0)−(1/ϑ))

](3)

Ageing is usually measured based on the term of a failure ratefunction. Failure rate is the most important quantity in mainte-nance theory. The instant failure rate function h(t) is defined as

h(t) = f (t)

F̄(t)= 1

F̄(t)· dF(t)

dt(4)

The failure rate is the most important reliability items for elec-trical equipment. The failure rate allows electrical equipment in

different asset classes to be compared with each other, and to makereference to several criteria like age, number of maintenance, timebetween events, etc. Whatever criteria for assessment are chosen,proper maintenance activities can be performed.

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It is expected to decide at which intervals to maintain the com-ponent and whether to keep the component in an old state orreplace the component with an identical component. These deci-

X. Zhang, E. Gockenbach / Electric Pow

. Modeling risk and costs

.1. Defining strategies and their contributions

During its life, the equipment might undergo several mainte-ance activities in order to improve its reliability, which is achievedy knowing its operability or by reducing its age. For circuit-reakers or transformers, all the typical activities are grouped inwo strategies:

trategy 1. Maintenance with sequential preventive maintenance

Consider a process where the component is subject to age-basedequential replacement. Imperfect repair between successiveeplacements is made after each failure so that the failure rateemains below a certain threshold level.

trategy 2. Maintenance with periodic preventive maintenance

The component is operated under a block-based periodiceplacement. Imperfect repair between successive replacements isade after each failure so that the failure rate remains below a

ertain threshold level.

ssumption. All maintenance time is negligible.

otation. Imperfect repair

When using a replacement, the system is “as good as new”fter the repair action is completed. When the minimal repair issed, the component is “as bad as old” after the repair action. Theeplacement and minimal repair may thus be considered as twoxtreme cases, and components subject to imperfect repair will beomewhere between these two extremes [15]. Hence, an imperfectepair model is suggested for a component: the repair is a perfectepair with a certain failure probability Pr(t); the repair is a minimalne with 1 − Pr(t). In the case, the successive perfect repair timesorm a renewal process with interarrival time distribution

(t) = 1 − exp

{−

∫ t

0

Pr(x)h(x) dx

}(5)

nd the corresponding failure rate Pr(t)·h(t).

.2. Modeling strategies

Within each strategy there are several component states andach one contributes to component risk. To calculate the variousontributions to the total cost for each strategy, the renewal theorys used in time-series processes. In our maintenance model, two

aintenance strategies are performed by the different combina-ions of preventive maintenance, repair or corrective replacement.

or Strategy 1. Let C denotes the total expected maintenanceost per unit of time over an indefinitely long period. By defini-ion the total expected cost C(�) of one cycle � is given by the sumf cost rates of preventive maintenance and repair or correctiveeplacement and repair:

(�)={[cr · (expected number of repairs during a corrective replac+ [cr · (expected number of repairs during a preventive rep

one cycl

here cc, cp and cr are the costs of the corrective- and consequentialeplacement, preventive replacement and imperfect repair respec-ively. cc includes unplanned replacement cost and unplannednavailability cost.

Thus, the total expected maintenance cost rate C(�) is equal to

(�) = {[crE{Z� |L < �} + cc] · S(�) + [crE{Z� |L ≥ �} + cp] · S̄(�)}∫ � ¯

0

S(x) dx

tems Research 81 (2011) 1709–1714 1711

nt) + cc] · cumulative probability of a corrective replacementent) + cp] · cumulative probability of a preventive replacement}replacement

(6)

=cr

[∫ �

0S̄(x)h(x) dx − S(�)

]+ ccS(�) + cpS̄(�)∫ �

0S̄(x) dx

(7)

Proof 1. Assume that Z� represents the number of minimal repairsduring the time interval (0, min {�, L}), we have the expected num-ber of repairs when L < � [16]

E{Z� |L < �} = 1S(�)

∫ �

0

∫ y

0

P̄r(x)h(x) dx dS(y) (8)

or the expected number of repairs when L ≥ � [16]

E{Z� |L ≥ �} =∫ �

0

P̄r(x)h(x) dx (9)

For Strategy 2. By definition the total expected cost C(�) of onecycle is given by the sum of preventive replacement cost, correctivereplacement cost and repair cost within a preventive replacement:

C(�) =

[cr · (expected number of repairs during a preventive replacement)+ cc · (expected number of corrective replacements duringa preventive replacement) + cp]

one cycle of a preventive replacment(10)

The total expected maintenance cost rate C(�) when using theinterval time � is equal to

C(�) = crNr(�) + ccNc(�) + cp

�(11)

Proof 2. If N(�) represents the number of failures during (0, �],N(�) is obviously the renewal function for the renewal process withthe interarrival time distribution S(t) and can be determined by thesolution method to the renewal function in renewal theory [16].Therefore, the expected number of corrective replacements can begotten.

Nc(�) = S(�) +∫ �

0

Nc(� − x) dS(x) (12)

and the expected number of repairs

Nr (�) = expected number of repairs during a corrective replacement ·

cumulative probability of a corrective replacement

+ expected number of repairs during a preventive replacement ·

cumulative probability of a preventive replacement

+∫ �

0

Nr (� − x) dS(x) = E{Z� |L < �}S(�) + E{Z� |L ≥ �}S̄(�)

+∫ �

0

Nr (� − x) dS(x) =∫ �

0

S̄(x) h(x) dx − S(�) +∫ �

0

Nr (� − x) dS(x)

(13)

3.3. Optimizing strategies

sions are made by comparing the annual cost of the component and

1712 X. Zhang, E. Gockenbach / Electric Power Systems Research 81 (2011) 1709–1714

maintenance frequency

cost

rate

Optimum frequency

corrective-&consequential maintenance

repair

preventive maintenance

total cost rate

Fig. 1. Optimization of maintenance frequency.

Table 1The parameters of Eq. (3).

n m b (K) B (K)

7.0 2.3 6000 17,000

cems

eh(ttmcab

4

ccctcmnuas

ce

TT

Table 3Costs of different components (D ).

Component

cp cc cr

Transformer 3535 4771 172Circuit-breaker 260 6270 55

35282114700

0.1

0.2

0.3

failu

re ra

te (1

/yea

r)

and transformers should be planned at 20 and 34 operationyears, respectively. It is obvious that transformers have morenumbers of repair and replacement than circuit-breakers. The

0.05

0.1

cor

rect

ive

repl

acem

ent

L0 (year) ϑ0 (K) E0 (kV/mm) M0 (N/mm2)

4.5 × 104 298 5.0 2.4 × 10−4

hecking whether the component has reached its economic life. Theconomic life is also referred to as the minimum cost life or opti-al maintenance interval. The optimal maintenance interval is the

olution that minimizes the sum of these maintenance cost rates:

dC(�)d�

= 0 (14)

Fig. 1 shows that the cost rate of preventive maintenance gen-rally increases with higher maintenance frequency. On the otherand, the cost rates of corrective and consequential maintenanceincluding repair) associated with failures decrease as the main-enance frequency increases. The total cost rate, the sum of thesehree individual cost rates, exhibits a minimum, and so an “opti-

um” or target level of reliability is achieved. Thus the integratedost benefit analyses involving customers and their decisions, in ansset management’s view, could be a more rewarding and applica-le approach.

. Simulation results from application studies

The significant requirement in applying reliability models is ahoice of the model parameters. This research work is initiated toollect nearly 120,000 failure data of historical events of electri-al equipment in the special failure statistic from the year 1920o 2005 [1]. These failure record data is dependent more on theomponent age than the calendar year. Furthermore, certain infor-ation on specific damage data, especially without disturbance of

etwork operation, has been acquired. Therefore, the detailed fail-re statistic can provide information about the actual conditionsnd economic assessment of these increasingly old components as

hown in Tables 1–3.

In light of this goal, this work attempts to integrate so suffi-ient failure data into the reliability models that failure rate oflectrical equipment can be modeled as a function of operating

able 2he parameters of Eq. (3).

Component

˛ E M ϑ

Transformer 11.6 2.2E0 6.8M0 40 ◦CCircuit-breaker 8.3 2.0E0 7.2M0 40 ◦C

year

Fig. 2. Calculated failure rates for circuit-breakers and transformers (dotted).

history, operational stresses and component type (Fig. 2). The fail-ure rates increase with operation year and their increases becomelarger after a certain operation year. When a circuit-breaker is over-hauled, the value of failure rate decreases to the value of the morenew equipment. However, as wear parts without exchange mayremain, the value of failure rate will increase like the shift curve.

Under the maintenance policy of strategy 2, repair and cor-rective replacement are likely to be performed several timesduring the lifetime of equipment. Figs. 3 and 4 show the repairand replacement characteristics of circuit-breakers and transform-ers with a series of increments. Since the ageing leads to thedegradation of equipment, the number of repair and replace-ment for circuit-breakers and transformers begins to grow rapidly.This means that the preventive replacement of circuit-breakers

201000

year

num

ber o

f rep

air a

nd

Fig. 3. Calculated expected number of repair and corrective replacement (dotted)for circuit-breakers according to strategy 2.

X. Zhang, E. Gockenbach / Electric Power Systems Research 81 (2011) 1709–1714 1713

35282114700

0.2

0.4

year

num

ber o

f rep

air a

nd c

orre

ctiv

e re

plac

emen

t

Ff

nm

ccogotppdmhit

swmrtrbueus

asm

TAi

30201000

0.5

1

year

num

ber o

f rep

air a

nd re

plac

emen

t

Fig. 5. Calculated expected number of repair (below-dotted), corrective and pre-ventive (above-dotted) replacements for circuit-breakers according to strategy 1.

30201000

0.5

1

year

num

ber o

f rep

air a

nd re

plac

emen

t

ig. 4. Calculated expected number of repair (dotted) and corrective replacementor transformers according to strategy 2.

umber of occasions depends on the failure rate of the equip-ent.When the failure rate increases, the number and cost rate of

orrective and consequential maintenance (including repair) asso-iated with failures increase as the operation time increases. On thether hand, the number and cost rate of preventive maintenanceenerally decreases under the age-dependent strategy 1. In the casef either strategy 1 or strategy 2, those failed circuit breakers andransformers have more repairs than corrective replacements. Therobability of the equipment degradation increases, so we woulderform more corrective maintenance. Taking into account thisependence it is clear that the contributions due to preventiveaintenance should decrease, because corrective maintenances

ave opposite effect. The total cost rate, the sum of these threendividual cost rates, exhibits a minimum, and so an “optimum” orarget level of reliability is achieved.

It will be useful to compare strategy 1 (Figs. 5 and 6) withtrategy 2 for circuit breakers and transformers. In accordanceith strategy 1 or strategy 2, circuit breakers have different opti-al preventive intervals of 28 or 20 years with minimum cost

ate, respectively. Strategy 2 is more wasteful since more preven-ive replacements occur and more unfailed circuit-breakers areemoved than those under a similar policy based on age. As mighte suspected however, the cost rate of transformers will be morender strategy 1. This is because stochastic failures cause morexpensive costs of corrective and consequential maintenance. Astilizing strategy 1, the preventive replacement cannot be fullycheduled, and the policy may therefore be complex to administer.

The final result in the economic evaluation is to estimate thennual cost of maintenance according to different maintenancetrategies of strategy 1 and strategy 2. Table 4 shows the annualaintenance cost and optimal maintenance interval according to

able 4nnual maintenance cost (D /year) and optimal maintenance interval (year) accord-

ng to different maintenance strategies.

Strategy Circuit-breaker Transformer

Cost rate Interval Cost rate Interval

Statistic 260 10 3535 21 100 28 266 262 158 20 250 34

Fig. 6. Calculated expected number of repair (below-dotted), corrective and pre-ventive (above-dotted) replacements for transformers according to strategy 1.)

different maintenance strategies. From the failure statistic [1],circuit breakers and transformers have the actual cost rate of260 D /year and 3535 D /year for maintenance when a preventivemaintenance is executed every 10 and 2 years.

However, different optimal intervals and annual costs of main-tenance for circuit breakers and transformers can be obtainedaccording to strategy 1 or strategy 2. By minimizing the cost rateof 100 and 158 D /year, the interval of preventive maintenance isoptimized by 28 or 20 years if strategy 1 or strategy 2 is caughtinto effect for circuit-breakers, respectively. Under these circum-stances of strategies 1 and 2, transformers have cost rate of 266 or250 D /year with the interval of 26 and 34 years, respectively. Com-paring the actual cost rate of 260 and 3535 D /year, circuit breakersand transformers have a significant decrease in cost rate by theimplement of effective maintenance strategies.

5. Conclusion

Assuming that all the activities have the same period of oper-

ation, the block based maintenance yields a fewer failure and ahigher cost than the age based maintenance. In this case the min-imum cost rate with an optimized interval can be obtained sincethe contribution from preventive maintenance is compensated by

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714 X. Zhang, E. Gockenbach / Electric Pow

he contributions from repair and corrective maintenance. Thenly way to find the minimum risk is to optimize the mainte-ance process to obtain the appropriate value of the operationeriod and the maintenance duration for a set of fixed reliabil-

ty parameters. The optimization process also impacts the cost,ecause risks not only strongly depend on the failure rate of thequipment in the operation activity but also on the cost of themplementing maintenance actions. The results show that it isot difficult to conclude which strategy is better in a generalense. For circuit-breakers, the better strategy is strategy 1 andhe worse strategy is to perform strategy 2 in view of cost rate.o the contrary, transformers have the minimum cost rate withtrategy 2.

eferences

[1] U. Zickler, A. Machkine, M. Schwan, A. Schnettler, X. Zhang, E. Gockenbach,Asset management in distribution systems considering new knowledge oncomponent reliability and damage costs, in: 15th Power Systems ComputationConference, Session 6, Belgium, 2005.

[2] J. Endrenyi, S. Aboresheid, R.N. Allan, G.J. Anders, S. Asgarpoor, R. Billinton,N. Chowdhury, E.N. Dialynas, M. Fipper, R.H. Fletcher, C. Grigg, J. McCalley, S.Meliopoulos, T.C. Mielnik, P. Nitu, N. Rau, N.D. Reppen, L. Salvaderi, A. Schnei-der, Ch. Singh, The present status of maintenance strategies and the impact ofmaintenance on reliability, IEEE Transactions on Power Systems 16 (November(4)) (2001) 638–646.

[3] X. Zhang, E. Gockenbach, Asset management of transformers based on condi-tion monitoring and standard diagnosis, IEEE Electrical Insulation Magazine 4(2008) 26–40.

[4] C. Neumann, R. Huber, D. Meurer, R. Plath, U. Schichler, S. Tenbohlen, K.H.Weck, The impact of insulation monitoring and diagnostics on reliability andexploitation of service life, in: GIGRE, C4-201, Paris, 2006.

[5] M. Bengtsson, E. Olsson, P. Funk, M. Jackson, Technical design of conditionbased maintenance system – a case study using sound analysis and case-basedreasoning, in: Proceedings of the 8th Maintenance and Reliability Conference,

Knoxville, USA, 2004.

[6] Z.Y. Wang, Y.L. Liu, P.J. Griffin, Neutral net and expert system diagnose trans-former faults, IEEE Computer Applications in Power 13 (1) (2000) 50–55.

[7] J. Schlabbach, Reliability centered maintenance of MV circuit-breakers, in: IEEEPorto Power Tech. Conference, Portugal, September, 2001.

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[8] G. Balzer, Condition assessment and reliability centered maintenance of highvoltage equipment, in: Proceeding of International Symposium on ElectricalInsulating Materials, Kitakyushu, Japan, June, 2005, pp. 259–264.

[9] L. Bertling, A reliability-centered asset maintenance method for assessing theimpact of maintenance in power distribution systems, IEEE Transactions onPower Systems 20 (February (1)) (2005) 75–82.

10] Y. Jiang, Z. Zhang, T. Van Voorhis, J. McCalley, Risk-based maintenance opti-mization for transmission equipment, in: Proceeding of 35th North AmericanPower Symposium, Rolla, USA, October, 2003, pp. 416–423.

11] S. Martorell, A. Munoz, V. Serradell, Age-dependent models for evaluating riskand costs of surveillance and maintenance of components, IEEE Transactionson Reliability 45 (1996) 433–442.

12] P. Jirutitijaroen, C. Singh, The effect of transformer maintenance parameters onreliability and cost: a probabilistic model, Electric Power Systems Research 72(3) (2004) 213–224.

13] X. Zhang, E. Gockenbach, Assessment of the actual condition of the electricalcomponents in the medium-voltage networks, IEEE Transaction on Reliability55 (2) (2006) 361–368.

14] X. Zhang, E. Gockenbach, Modeling the component reliability of distribu-tion systems based on the evaluation of failure statistic, IEEE Transaction onDielectrics and Electrical Insulation 14 (5) (2007) 1183–1191.

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Xiang Zhang received the B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering fromXi’an Jiaotong University, Xi’an, China, in 1989, 1992, and from the Aachen Universityof Technology, Aachen, Germany, in 2002, respectively. From 1992 to 1997 she wasa research engineer at Xi’an High Voltage Apparatus Research Institute, Xi’an, China.Currently she is a research fellow on asset management of electrical equipment andnetworks of the Schering-Institute of High Voltage Technology at the University ofHanover, Germany. Her main areas of interest include high voltage apparatus, gasdischarge, arc modeling, and asset management.

Ernst Gockenbach (M’83-SM’88-F’01) received the M.Sc. and Ph.D. degrees in Electri-cal Engineering from the Technical University of Darmstadt, Darmstadt, Germany, in1974 and 1979, respectively. From 1979 to 1982, he worked at Siemens AG, Berlin,Germany. From 1982 to 1990, he worked with E. Haefely AG, Basel, Switzerland.Since 1990, he has been professor and director of the Schering-Institute of High Volt-

age Technology at the University of Hanover, Germany. He is member of VDE andCIGRE, chairman of GIGRE Study Committee D1 Materials and Emerging Technolo-gies for Electro-technology, and a member of national and international WorkingGroups (IEC, IEEE) for Standardization of High Voltage Test and Measuring Proce-dures.