Method for effects evaluation of some forms of power transformers preventive maintenance

Available online at www.sciencedirect.com

Electric Power Systems Research 78 (2008) 765–776

Method for effects evaluation of some forms of power transformers preventive maintenance Vladica Mijailovic ∗ ˇ cak, Serbia Technical Faculty, University of Kragujevac, Svetog Save 65, 32000 Caˇ Received 13 April 2006; received in revised form 7 May 2007; accepted 31 May 2007 Available online 23 July 2007

Abstract The paper suggests a method for effects evaluation of a few activities and measures, undertaken as a part of preventive maintenance of power transformers. The method enables calculation of expected failures repair cost and load curtailment cost. The method identifies minor and major failures. Power transformer is a complex system, consisting of five components (functional parts). It is assumed that each component has two independent, competing failure modes: wear-out failure mode, modeled by two-parameter Weibull distribution, and a chance failure mode, characterized by an exponential distribution. The application of the method is demonstrated for one transformer station (TS) 110/x kV/kV with 2 × 31.5 MVA transformers. Also, by applying the method, influence of system for condition monitoring of transformer windings and oil on failures repair cost and load curtailment cost is evaluated. © 2007 Elsevier B.V. All rights reserved. Keywords: Power transformer; Preventive maintenance; Failures repair cost; Load curtailment cost

1. Introduction With regard that equipment in substations is growing older, maintenance organization in each electric power company has one of the most important functions. The goal of effective preventive maintenance is minimizing the unplanned outages, i.e. reduction of long and expensive failures repair and load curtailment cost. Having in mind their functions, purchase costs, number of installed units and techno-economical consequences of unplanned outages, preventive maintenance of power transformers has an essential importance. The aim of this paper is to propose a model enabling the evaluation of effects of a few activities and measures, undertaken as a part of power transformers preventive maintenance. In the following sections, a model for calculation of expected failure repair cost and a model for calculation of load curtailment cost are formulated. 2. Basic assumptions At any point of time, status of power transformer can be classified as either operating or failed. Failed status is a result of minor failures and/or major failures. Minor failures can be repaired for t ≤ 24 h. Hence, probability that the component “k” of power transformer is in operating status equals Rk (t) = e−(λk,mf +λk,MF )t e−(t/αk )

βk

(1)

i.e. we assume that the component has two independent failure modes: a chance failure mode, characterized by the exponential distribution, and a wear-out mode, modelled by two-parameter Weibull distribution. ∗

Correspondence address: 36000 Kraljevo, 17 Mirka Belobrka St., Serbia. Tel.: +381 32 226 503/36 399 950; fax: +381 32 342 101/63 7783 557. E-mail addresses: [email protected], [email protected].

0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2007.05.024

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Power transformer consists of five components-functional parts [5,7,10,14]: (1) Windings and Core + Oil, (2) Bushings, (3) Tank, (4) On-load tap-changer, and (5) Other accessories. The main failures occurring on each functional part of power transformer are as follows [6,15]: • Windings, core, oil. Partial discharges, abnormal oil and cellulose ageing, loose connections, oil contamination, excessive water content, overheating of laminations, overheating due to circulating currents, turn-to-turn failures, phase-to-phase failures, mechanical failures, open winding, and external faults. • Bushings. Moisture contamination due to deterioration of gasket material or cracks in terminal connections, and partial discharges. • Tank. Poor tank weld, corrosion, and external damages. • On-load tap-changer. Local hotspots due to contact overheating, significant increase in required torque, sparking, oil leaks, and partial discharges. • Other accessories. Arcing, local overheating, electrical failures of pumps and fans, and internal or external blocking of radiators resulting in poor heat exchange. With regard to the failure repair time, there are three failure classes: • (i = 1) failures which can be repaired for t ≤ 1 day (minor failures), • (i = 2) failures which can be repaired for 1 day < t < 30 days, • (i = 3) failures which can be repaired for t ≥ 30 days. 3. Model development Six forms of power transformer preventive maintenance will be analyzed: (3.1) Operation with non-preventive maintenance (run to failure); (3.2) One-day preventive maintenance (practically, 8 h)—visual examination, checking the state of the transformer and replacing worn-out parts (without tank opening-windings, core and oil are not involved); (3.3) Oil regeneration + (3.2). These activities will be performed in 5 days; (3.4) Insulation system regeneration + (3.2). These activities will be performed in 10 days; (3.5) Power transformer refurbishment. After this, transformer will be “as good as new”. After each year of operation, transformer value goes down for 0.015 × Cnew /year. Process of refurbishment will be performed in 28 days; (3.6) Installing of system for condition monitoring of windings and oil. Expected life-time of commercially available systems is 10 years. Detection rate is about 80% [10,11]. Detecting of failures in the early stage of development prevents an outage of power transformer and reduce cost and time of repair. Neglecting of detected failures repair cost seems to be too optimistic. Because of reasons of certainty, an assumption is adopted: all detected major failures on windings and oil will be treated as faults, which can be repaired in 5 days and for D 5000. (3.1) If the transformer operates without performing preventive maintenance expected cost per year during period of length T equals [1,4] CET (0, T ) =  T 0

b

Rtot (t) dt

fk



i=1 pk,i Ck,i , b fk + (1 − Rtot (T )) k=1 i=1 pk,i rk,i

[1 − Rtot (T )]

k=1

Rtot (t) =

b 

Rk (t)

(2)

k=1

The numerator in Eq. (2) is the expected cost of failures repair during time period T. First term in denominator is the mean time to failure and second term is the expected time of failures repair during period T. An average unavailability of transformer during period of length T equals UET (0, T ) =  T 0

[1 − Rtot (T )]

b

k=1

fk

i=1 pk,i rk,i fk k=1 i=1 pk,i rk,i

Rtot (t) dt + (1 − Rtot (T ))

b

(3)

For planning of preventive maintenance activities, it is more convenient to calculate an average failure repair cost during time interval (T, N):   k pk,i Ck,i [1 − (Rtot (N)/Rtot (T ))] bk=1 fi=1 CET (T, N) =  N (4) b fk T Rtot (t) dt + [1 − (Rtot (N)/Rtot (T ))] k=1 i=1 pk,i rk,i

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The numerator in Eq. (4) is the expected cost of failures repair during time interval (T, N) if transformer has not failed before T. (3.2) If the transformer operates without failure for a period of length m, 1-day preventive maintenance will be performed. An average cost during time interval (m, N) equals [1,4] fk   R(m)Cpm + E(m)[1 − (Rtot (N)/Rtot (m))] bk=1 i=1 pk,i Ck,i ,  CET (m, N) = N   k R(m)(8 h/8760) + E(m) m Rtot (t) dt + [1 − (Rtot (N)/Rtot (m))] bk=1 fi=1 pk,i rk,i

E(m) = exp

b



(λk,mf + λk,MF )m

(5)

k=2

With term E(m) we assume as follows: after performing 1-day preventive maintenance on component “k”, k = 2, . . ., b factors which may cause chance failures will be eliminated. An average unavailability of transformer during time interval (m, N) can be determined as   k E(m)[1 − (Rtot (N)/Rtot (m))] bk=1 fi=1 pk,i rk,i   UET (m, N) = (6)   k N R(m)(8 h/8760) + E(m) m Rtot (t) dt + [1 − (Rtot (N)/Rtot (m))] bk=1 fi=1 pk,i rk,i (3.3) If the transformer operates without failure for a period of length Toil , oil regeneration will be performed. An average cost and an unavailability of transformer during time interval (Toil , N) are [1,4] fk   Rtot (Toil )Creg,oil + E(Toil )[1−(Rtot (N)/Rtot (Toil ))] bk=1 i=1 pk,i Ck,i   CET (Toil , N)= (7)   k N Rtot (Toil )(5 days/365) + E(Toil ) Toil Rtot (t) dt+[1 − (Rtot (N)/Rtot (Toil ))] bk=1 fi=1 pk,i rk,i UET (Toil , N) =

  k pk,i rk,i E(Toil )[1 − (Rtot (N)/Rtot (Toil ))] bk=1 fi=1 ,    k N R(Toil )(5 days/365) + E(Toil ) Toil Rtot (t) dt + [1 − (Rtot (N)/Rtot (Toil ))] bk=1 fi=1 pk,i rk,i

E(Toil ) = exp [(λ1,mf + λ1,MF )Toil ] exp

b



(λk,mf + λk,MF )Toil

(8)

k=2

Here, with term E(Toil ), we made assumption after oil regeneration factors which may cause chance failures on all power transformer components will be eliminated. (3.4) After insulation system regeneration, “technical age” of paper insulation will be reduced for x = (20–30)% [9]. After insulation system regeneration, reliability of transformer component k = 1 will be   t(1 − x) β1 (9) R1,reg (t) = exp(−λ1,MF t) exp − α1 and a reliability of transformer Rt,reg (t) = R1,reg (t)

b

Rk (t)

(10)

k=2

An average cost and an unavailability of transformer during time interval (Treg , N) are [1,4] CET (Treg , N)

fk   Rtot (Treg )Creg,ins + E(Treg )[1 − (Rt,reg (N)/Rt,reg (Treg ))] bk=1 i=1 pk,i Ck,i   =   k N Rtot (Treg )(10 days/365) + E(Treg ) Treg Rt,reg (t) dt+[1 − (Rt,reg (N)/Rt,reg (Toil ))] bk=1 fi=1 pk,i rk,i

(11)

  k pk,i rk,i E(Treg )[1−(Rt,reg (N)/Rt,reg (Treg ))] bk=1 fi=1 ,  UET (Treg , N)=   k N Rtot (Treg )(10 days/365)+E(Treg ) Treg Rt,reg (t) dt+[1−(Rt,reg (N)/Rt,reg (Toil ))] bk=1 fi=1 pk,i rk,i

E(Treg ) = exp[(λ1,mf + λ1,MF )Treg ] exp

b

k=2



(λk,mf + λk,MF )Treg

(12)

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(3.5) According to the assumptions we made, after Tref years of transformer operation without failures cost of refurbishment will be Cref (Tref ) = 0.015 × Tref × Cnew .An average cost and an unavailability of transformer during time interval (Tref , N) will be calculated as [1,4] fk   Rtot (Tref )Cref (Tref ) + (1 − Rtot (N − Tref )) bk=1 i=1 pk,i Ck,i CET (Tref , N) = (13)  N−T   k Rtot (Tref )(28 days/365) + Tref ref Rtot (t) dt + (1 − Rtot (N − Tref )) bk=1 fi=1 pk,i rk,i   k pk,i rk,i (1 − Rtot (N − Tref )) bk=1 fi=1 UET (Tref , N) =  N−Tref   k Rtot (Tref )(28 days/365) + Tref Rtot (t) dt + (1 − Rtot (N − Tref )) bk=1 fi=1 pk,i rk,i

(14)

(3.6) System for condition monitoring of windings and oil enabling detection of failures in the early stage of development. It brings to the reduction of major failure rate and increasing of minor failure rate [8,10,11,13]. As a result of major failure rate reduction, the Weibull scale parameter will be raised. Therefore, the Weibull scale parameter of transformer component k = 1 after installing of condition monitoring system will be marked as α1 . Condition monitoring system will be installed after operation period of length Ts without failures. During next 10 years of operation [10,11], reliability of transformer will be Rtot (t) ≈ R1 (Ts )R1 (t − Ts )

b 

Rk (t)

(15)

k=2

β1  z R1 (z) = exp[−(λ1,MF + λ1,mf )z] exp −  α1

(16)

4. Application An application of the model will be demonstrated for one TS 110/x kV/kV, with two power transformers installed, Pinst = 2 × 31.5 MVA = 63 MVA. Calculations are made for planning period of N = 40 years. The annual hourly load–duration diagram for the substation is displayed in Fig. 1. Peak load is 80% and minimum load is 40%, with regard to the installed capacity. Average yearly duration of one transformer down-time during time interval (t1 , t2 ) equals [1]: τ1 (t1 , t2 ) (h) = UET (t1 , t2 ) × 8760

(17)

Average yearly duration of both transformers down-time during time interval (t1 , t2 ) equals [1] τ2 (t1 , t2 ) (h) = UET (t1 , t2 )2 × 8760 With regard to Figs. 1, Eq. (17) and (18), for energy not delivered we have:  a1 − b1 τ1(2) (t1 , t2 ) Pinst y1(2) = a1 − 8760 W1 = 2 W2 =

(18)

(19)

 (a1 Pinst − 0.5Pinst ) + (y1 − 0.5Pinst ) τ1 (t1 , t2 ) = (y1 + (a1 Pinst − Pinst ))τ1 (t1 , t2 ), 2

a1 Pinst + y2 τ2 (t1 , t2 ) 2

(20)

Fig. 1. Annual hourly load–duration diagram (a1 = 0.8, b1 = 0.4).

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Table 1 Power transformer components costs [2,5,9–11] k

Transformer component

Cnew, k (D )

1 2 3 4 5

Windings and core Bushing Tank On-load tap-changer Other accessories

2,20,000 570 20,000 15,000 15,000

Table 2 Power transformer components reliability data [2,5,9–11] k 1 2

3

4

5

Component

pk (%)

Failure class, i

rk,i

pk,i (%)

Ck,i

Windings and core

35

2 3

15 days 120 days

18.35 81.65

0.2 × Cnew,1 + Cu 0.5 × Cnew,1 + Cu

Bushing

14

1 2 3

1 day 3 days 30 days

15.83 54.16 30.01

0.4 × Cnew,2 Cnew,2 Cnew,2 + Cu

Tank

6

1 2 3

1 day 3 days 60 days

63.29 25.32 11.39

0.1 × Cnew,3 0.2 × Cnew,3 + Cu Cnew,3 + Cu

On-load tap-changer

40

1 2 3

1 day 3 days 30 days

28.74 51.60 19.66

0.1 × Cnew,4 0.2 × Cnew,4 0.4 × Cnew,4

Other accessories

5

1 2

1 day 15 days

66 34

0.1 × Cnew,5 Cnew,5

Average yearly energy not delivered equals WTS,year (D ) = CEN [W1 + W2 ]

(21)

Loss of revenue and load curtailment cost per kWh not delivered is CEN = D 0.05/kWh (Serbian data). Relevant data for power transformer components are presented in Tables 1 and 2 [2,5,9–11]. Purchase cost of new oil is Cnew,oil = D 25,000. Cost of oil filtration and drying is Cu = 0.2 × Cnew,oil . Parameters in Eq. (1) are determined, based on Fig. 2 [3], by applying the least-squares method. For λ00 = λ00,MF + λ00,mf = 0.01 = 1% (Serbian data), based on the data given in Table 2, we obtain λ00,MF = 0.0079187, λ00,mf = 0.0020813. For combination of exponential and Weibull distribution, major failure rate equals λMF (t) = λ00,MF +

β β−1 t αβ

Fig. 2. Statistical data about major failure rate λ0t,MF during time interval (1973–2003).

(22)

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Table 3 Weibull distribution parameters k

Component

βk

αk

1 2 3 4 5

Windings and core Bushing Tank On-load tap-changer Other accessories

3.58 3.58 3.58 3.58 3.58

31.6610 42.5135 67.9384 33.2174 73.0118

Applying the least-squares method, parameters of Weibull distribution are determined as solutions of Eqs. (24) and (25): ε(α, β) =

30

t=1

2

(λMF (t) − λ0t,MF )

(23)

∂ε(α, β) =0 ∂α

(24)

∂ε(α, β) =0 ∂β

(25)

The partial derivative with respect to β (Eq. (25)) is not practically usable because of complexity. For precise modeling of curve from Fig. 2 with (22), following procedure is performed: for βk > 1, with step of 0.01, values of αk , with regards to Table 2, are calculated. For αk and βk we adopted those values for which Eq. (23) has minimum, Table 3. The other data used for calculations are as follows: • Cpm = D 100, Cref,oil = D 7000, x = 0.3, and Creg,ins = D 10,000; • purchase and installing cost of condition monitoring system is D 30,000 and maintenance cost is D 500/year [10–13]. Figs. 3 and 4 show an expected failure repair cost and expected load curtailment cost, respectively, in the case of operation with non-preventive maintenance. Figs. 5 and 6 show an expected cost and expected load curtailment cost, respectively, in the case of performing 1-day preventive maintenance. Figs. 7 and 8 show an expected cost and expected load curtailment cost, respectively, in the case of performing oil regeneration. Fig. 9 shows data about transformer reliability in the case of operation with non-preventive maintenance (curve a) and the case of performing oil regeneration (curve b). A comparative overview of expected cost for the case of operation with non-preventive maintenance (curve a) and the case of performing insulation system regeneration (curve b) is given in Fig. 10.

Fig. 3. Expected yearly failure repair cost during time interval (T, N) in the case of operation with non-preventive maintenance.

Fig. 4. Expected yearly load curtailment cost during time interval (T, N) in the case of operation with non-preventive maintenance.

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Fig. 5. Expected yearly cost during time interval (m, N) in the case of performing 1-day preventive maintenance.

Fig. 6. Expected yearly load curtailment cost during time interval (m, N) in the case of performing 1-day preventive maintenance.

Fig. 7. Expected yearly cost during time interval (Toil , N) in the case of performing oil regeneration.

A comparative overview of expected load curtailment cost for the case of operation with non-preventive maintenance (curve a) and the case of performing insulation system regeneration (curve b) is given in Fig. 11. Fig. 12 shows a comparative overview of transformer reliability for the case of operation with non-preventive maintenance and the case of performing insulation system regeneration. Figs. 13 and 14 show a comparative overview of expected cost and a comparative overview of expected load curtailment cost, respectively, for the case of operation with non-preventive maintenance (curve a) and the case of performing transformer refurbishment (curve b).

Fig. 8. Expected yearly load curtailment cost during time interval (Toil , N) in the case of performing oil regeneration.

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Fig. 9. Transformer reliability in the case of operation with non-preventive maintenance (curve a) and the case of performing oil regeneration (curve b).

Fig. 10. A comparative overview of yearly expected cost for the case of operation with non-preventive maintenance (curve a) and the case of performing insulation system regeneration (curve b).

Fig. 11. A comparative overview of yearly expected load curtailment cost for the case of operation with non-preventive maintenance (curve a) and the case of performing insulation system regeneration (curve b).

After installing of system for condition monitoring of windings and oil, for detection rate of 80%, we have: λ1,MF = 0.2λ1,MF ,

λ1,mf = λ1,mf + 0.8λ1,MF ,

α1 = 49.08

A comparative overview of expected cost and load curtailment cost for the case of operation with non-preventive maintenance and for the case of operation with condition monitoring system installed is given in Table 4.

Fig. 12. A comparative overview of transformer reliability for the case of operation with non-preventive maintenance and the case of performing insulation system regeneration.

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Fig. 13. A comparative overview of yearly expected cost for the case of operation with non-preventive maintenance (curve a) and the case of performing transformer refurbishment (curve b).

Fig. 14. A comparative overview of yearly expected load curtailment cost for the case of operation with non-preventive maintenance (curve a) and the case of performing transformer refurbishment (curve b). Table 4 A comparative overview of expected cost and load curtailment cost for the case of operation with non-preventive maintenance and for the case of operation with condition monitoring system installed Time interval (years)

1–10 11–20 21–30 31–40

Operation with non-preventive maintenance

Operation with condition monitoring system installed

Yearly expected cost (D /year)

Yearly expected load curtailment cost (D /year)

Yearly expected cost (D /year)

Yearly expected load curtailment cost (D /year)

337.587 2172.4 10108.3 78381.4

29579.8 119,965 567,951 5 millions

3848.25 4221.9 5406.9 10882.7

11914.4 34060.3 122,852 643,791

5. Conclusions The paper suggests a method for evaluation effects of different forms of power transformer preventive maintenance. First, let us compare an expected failure repair cost with an expected cost for each of analyzed forms of preventive maintenance. Comparison will be made between: • • • •

CET (T, N) (4) and CET (m, N) (5), CET (T, N) (4) and CET (Toil , N) (7), CET (T, N) (4) and CET (Treg , N) (11), CET (T, N) (4) and CET (Tref , N) (13).

After calculation of the following ratios: (CET (T, N)/CET (m, N))|T = m , (CET (T, N)/CET (Toil , N))|T =Toil , (CET (T, N)/CET (Treg , N))|T =Treg , and (CET (T, N)/CET (Tref , N))|T =Tref , Figs. 15–17, we can conclude as follows: From Fig. 15 it is obvious that, from economic point of view, performing of 1-day preventive maintenance and/or oil regeneration is not justified. An expected yearly cost will be reduced if insulation system regeneration, Fig. 16, or transformer refurbishment, Fig. 17, be performed after 11 years of exploitation. Also by comparing (Figs. 3 and 5) and (Figs. 4 and 6), we can conclude as follows:

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Fig. 15. Curve (a): (CET (T, N)/CET (m, N))|T = m vs. time; curve (b): (CET (T, N)/CET (Toil , N))|T =Toil vs. time.

Fig. 16. (CET (T, N)/CET (Treg , N))|T =Treg vs. time.

• during time interval (0, 5) reduction of expected load curtailment cost is equal to increasing of expected failure repair cost. If we perform 1-day preventive maintenance after 6 years of operation without failures, total reduction of expected cost and load curtailment cost during time interval (6, 40) will be D 3/year; If we compare expected cost and load curtailment cost for the case of operation with non-preventive maintenance with expected cost and load curtailment cost for the case of operation with performing of oil regeneration we can conclude as follows: • Performing of oil regeneration during time interval (0, 19) is not economically justified. • If we perform oil regeneration:  after 19 years of operation, total reduction of expected cost and load curtailment cost during time interval (20, 40) will be D 95/year;  after 20 years of operation, total reduction of expected cost and load curtailment cost during time interval (21, 40) will be D 257/year;  after 21 years of operation, total reduction of expected cost and load curtailment cost during time interval (22, 40) will be D 477/year; According to the criterion of expected load curtailment cost, installing of system for condition monitoring of windings and oil is economical solution from the first year of transformer operation. According to the criterion of expected failure repair cost, installing of system for condition monitoring of windings and oil is economical solution after 20 years of transformer operation.

Fig. 17. (CET (T, N)/CET (Tref , N))|T =Tref vs. time.

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Acknowledgements I would like to express my utmost gratitude for Prof. Dr. Jovan Nahman for his help and support. I am grateful to the Ministry of Science of Serbia and Electric Company “Elektrosrbija” Kraljevo that supported this work. Appendix A. List of symbols

b Ck,i Cnew Cnew,k Cpm Creg,ins Creg,oil Cu CEN fk N pk pk,i

number of functional parts-components of power transformer repair cost of class “i” failure on component “k” purchase cost of new power transformer purchase cost of power transformer component “k” cost of material for performing 1-day preventive maintenance cost of insulation system regeneration cost of oil regeneration cost of oil filtration and drying loss of revenue and load curtailment cost per kWh not delivered number of failure classes of power transformer component “k” with regard to the failure repair time duration of the planning period, expressed in years   b probability that the failure occurs on power transformer component “k” p = 1 k k=1 pk × pk,i

  fk  =1 pk,i probability that the failure of class “i” occurs on component “k” p i=1 k,i Pinst substation installed capacity repair time of class “i” failure on component “k” rk,i R(t) reliability t time TS transformer station U(t) unavailability WTS,year average yearly energy not delivered W1 average yearly energy not delivered due to outage of one transformer W2 average yearly energy not delivered due to outage of both transformers Greek letters α the Weibull scale parameter β the Weibull shape parameter λk,mf minor failure rate of component “k” λk,MF major failure rate of component “k” λmf (t) minor failure rate at time t λMF (t) major failure rate at time t λ0t,MF initial (statistical) data for major failure rate at time t  λ0t,MF t=0 λ0t,MF λ00,mf initial (statistical) data for minor failure rate at time t = 0 0 λ0 λ00,MF + λ00,mf τ 1 (t1 , t2 ) average yearly down-time of one transformer during time interval (t1 , t2 ) τ 2 (t1 , t2 ) average yearly down-time of both transformers during time interval (t1 , t2 ) References [1] [2] [3] [4] [5] [6] [7] [8]

J.M. Nahman, Dependability of Engineering Systems, Springer, 2002. R. Fischer, Maintenance and diagnosis strategies for high voltage substations, in: Proceedings of the Tettex Instruments, April 28, 2004. B. Augenstein, Outsourced monitoring and reliability of critical assets, in: Proceedings of the DistribuTech, Las Vegas, February 4–6, 2003. D.M. Reineke, et al., Improving availability and cost performance for complex systems with preventive maintenance, in: Annual Reliability and Maintainability Symposium, 1999. An international survey on failures in large power transformers in service, ELECTRA No. 88, 1983. P. Gill, Electrical Power Equipment Maintenance and Testing, Dekker, 1998. R.C. Dorf (Editor-in-Chief), The Electrical Engineering Handbook, IEEE, 1998. V. Mijailovic, Probabilistic method for planning of maintenance activities of substation components, Int. J. Electr. Power Syst. Res. 64 (2003) 53–58.

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[9] V.V. Smekalov et al., Condition assessment and life time extension of power transformer, CIGRE Session 2002, pp. 12–102. [10] S. Tenbohlen et al., Experienced based evaluation of economic benefits of on-line monitoring systems for power transformers, CIGRE Session 2002, pp. 12–110. [11] T. Breckenridge et al., The impact of economic and reliability considerations on decisions regarding the life management of power transformers, CIGRE Session 2002, pp. 12–115. [12] P. Boss et al., Life assessment of power transformers to prepare rehabilitation based on a technical-economical analysis, CIGRE Session 2002, p. 12–106. [13] P. Boss et al., Economical aspects and practical experiences of power transformer on-line monitoring, CIGRE Session 2000, pp. 12–202. [14] J.W. Harley, V. Sokolov, Contribution for panel on modern maintenance techniques for enhancing the reliability of insulation of power transmission systems, CIGRE Session 2000, pp. 1–06. [15] J.H. Harlow (Ed.), Electric Power Transformer Engineering, CRC Press, 2004. Vladica Mijailovic was born in Kraljevo, Serbia, on 14 March 1966. He received the B.Sc., M.Sc. and Ph.D. degrees from University of Belgrade, Faculty of Electrical Engineering, in 1991, 1995, and 1999, respectively. Since 1991, he is with Technical Faculty in Cacak, University of Kragujevac. Currently he is an assistant-professor in Department for Power Systems. His area of interest includes substations reliability and modern maintenance techniques.