A Comprehensive Scheme for Reliability-Centered Maintenance in Power Distribution Systems—Part II Numerical Analysis

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IEEE TRANSACTIONS ON POWER DELIVERY 1

A Comprehensive Scheme for Reliability-CenteredMaintenance in Power Distribution SystemsPart II:

Numerical AnalysisPayman Dehghanian, Student Member, IEEE, Mahmud Fotuhi-Firuzabad, Senior Member, IEEE,

Farrokh Aminifar, Member, IEEE, and Roy Billinton, Life Fellow, IEEE

AbstractThe aim of this two-part paper is to present a com-prehensive reliability-centerd maintenance framework tailored topower distribution systems. The first paper discusses the funda-mental concepts, presents the developed algorithm, and introducesthe required mathematical formulations. This second paper is fo-cused on the application of the proposed methodology on a realdistribution system. Considerable effort is devoted to examine theproposedmethod in a step-by-stepmanner to clarify the implemen-tation procedure. The required data for the procedure are takenfrom available references and follow reasonable technical assump-tions. Practical aspects are incorporated, and the results obtainedare thoroughly discussed. The concluding remarks are outlined tosummarize the paper set which also brings to light superiorities ofthe proposed scheme.

Index TermsBenefit to cost ratio, corrective maintenance, crit-ical component, maintenance strategy, preventivemaintenance, re-liability-centered maintenance (RCM).

For the Nomenclature, the readers are referred to the nomen-clature presented in Part I of this two-part paper. New mathe-matical symbols used in Part II of this paper set are introducedwithin the text where necessary.

I. INTRODUCTION

R ELIABILITY-CENTERED maintenance (RCM) hasbeen proposed as an efficient key to cost-effectivesolutions for the challenging problems of maintenance inrestructured power systems [1], [2]. To obviate the need for anall-inclusive RCM framework for power distribution systems,the first paper in this joint two-paper set introduces the conceptsand generally discusses the prepared framework and stages[3]. The steps associated with the presented algorithm areintroduced and the associated formulations are provided in thecompanion paper [3].

Manuscript received March 06, 2012; revised July 12, 2012; accepted Oc-tober 28, 2012. Paper no. TPWRD-00237-2012.P. Dehghanian, M. Fotuhi-Firuzabad, and F. Aminifar are with the

Department of Electrical Engineering, Center of Excellence in PowerSystem Management and Control, Sharif University of Technology,Tehran, Iran (e-mail: [email protected]; [email protected];[email protected]).R. Billinton is with the Department of Electrical Engineering, University of

Saskatchewan, Saskatoon, SK S7N 5A9, Canada (e-mail: [email protected]).Digital Object Identifier 10.1109/TPWRD.2012.2227833

Fig. 1. Birka system in Stockholm.

This paper accomplishes the goal of step-by-step presentationby applying the proposed RCM scheme to a real power distri-bution system in Stockholm, Sweden.

II. ILLUSTRATIVE EXAMPLE

A. System DescriptionAs a case study, the proposed algorithm is applied to a distri-

bution system affiliated with the Birka Nat distribution systemin Sweden. The Birka utility supplies the largest number of cus-tomers compared to the others in Sweden [4] and brings thetransmission voltage level of 220 kV down, respectively, to 33kV, 11 kV, and the household customer level of 400 V [5]. Inthis paper, a special segment of the network shown in Fig. 1,has been adopted for the case study.The system at hand is comprised of the Birka Nat 220/110

kV Bredang station joined to the 33/11 kV Liljeholmen station(LH11) via two parallel 110 kV cables. There are 32 outgoing 11kV feeders connected to this load point that are responsible forsupplying the southern part of central Stockholm [6]. The LH11load point is shown as an equivalent component since it consistsof customers attached to these 11 kV parallel feeders and servesa total of 14 200 customers. The other network customers are

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Fig. 2. Reliability block diagram of the system with respect to LH11.

represented by two 33 kV load points [i.e., Hogalid station (HD)and Statens Jarnvagar railway line (SJ)].

B. Pre-AnalysisAs illustrated in the Part I paper, the Pre-Analysis stage

covers all of the requirements for the following analysis by theproposed algorithm. This need is hereby obviated as follows.Step 1) System single-line preparation

The system single-line diagram is shown in Fig. 1.Step 2) Fulfilling data requirements

All of the data and information required for theprocess continuation, including both load pointsand component reliability data, are prepared. Eco-nomic information associated with the componentsand different preventive and corrective maintenancestrategies are also provided. These are either takenfrom the relevant references [4][9], or reasonablyassumed by experts and specialists in consultationwith the authors [10]. All of the data and infor-mation needed are summarized in the concludingremarks in Section III.

Step 3) System boundary identificationThe system consists of the three main load pointsSJ, HD, and LH11, which form the system boundaryto be studied. As shown in Table I, the customersare classified into three major groups designated asindustrial, commercial, and residential [5]. LH11 isconsidered to be a very important load point since ithas a good distribution of the different customer cat-egories [4]. Also, this load point is adopted for thisstudy due to the fact that the Stockholm City distri-bution system is dominated by underground cables,70% of which are 11 kV feeders [6]. The remainingstudies are conducted on this load point, and RCMis applied with the aim of improving the LH11 reli-ability indices.

In this study, the 220 kV and 110 kV levels of theBirka system are assumed to be fully reliable sincesuch an assumption is common in the reliability as-sessment of power distribution systems. The distri-bution part of the Birka system is then under con-sideration which is a combination of various com-ponents in series and parallel. The reliability blockdiagram of the system is shown in Fig. 2. The blockshave the same numbers as the components shownin Fig. 1. As shown in Fig. 2, parallel componentsare equivalence with and . The equivalentfailure rate and repair time are found using(1) and(2) [11]

(1a)(1b)(1c)(1d)(1e)

(2a)

(2b)

(2c)

(2d)

(2e)

Step 4) Component-type selection to be analyzedThe network under RCM investigation includes 58major pieces of equipment which essentially con-sists of the following five component types:i) 33, and 11 kV busbars;ii) 33 and 11 kV breakers;iii) 33 and 11 kV underground cables;iv) 33/11 kV transformers;v) 0.4 kV fuse.

All of the components within the distribution sectorare considered as candidates to have the RCMapplied on. Among these distribution componenttypes, the 0.4 kV fuse is excluded from maintenancescheduling due to its designation as a run-to-failurecomponent; whereas, all of the other maintainableones can be put under evaluation in the studies.The fuse vital role in the evaluation of reliabilityindices, however, should not be disregarded. All ofthe other component types within the generationand transmission sectors also play a major role inserving the load points and have to be incorpo-rated in reliability assessment. However, they areassumed fully reliable in this study.

Step 5) System reliability goals/target determinationAs an assumption, it is considered that the Birka Natutility has projected some preset reliability-basedtargets to be met through its reinforcement schemes,


DEHGHANIAN et al.: COMPREHENSIVE SCHEME FOR RCM IN POWER DISTRIBUTION SYSTEMSPART II 3

TABLE ICUSTOMER DATA FOR THE BIRKA DISTRIBUTION SYSTEM

TABLE IIRELIABILITY INDICES AS THE UTILITY TARGETS

TABLE IIILOAD-POINT RELIABILITY INDICES FOR C28 IN THE 1ST AND 2ND SCENARIOS

TABLE IVC28 CONTRIBUTION TO THE LH11 LOAD-POINT RELIABILITY INDICES

operation policies, and maintenance process. Theutility reliability targets are specified in Table II.

C. Main-Analysis

The Main-Analysis introduces the kernel of the main RCMprocedure as follows.Step 1) Critical component identification

The first step in the Main-Analysis is to identify the mostcritical system components from a reliability point of view.As demonstrated in [3], the proposed analytical approachspecifies the criticality of system components by runningtwo scenarios associated with each component. The proce-dure is presented in Table III for component C28. The re-liability data required for the first scenario are the averagevalue associated with each component and are all providedin [10].The EENS index of load point LH11 with respect to thefailure-rate variation of component C28 is 10.339 and10.033 kWh/yr.cust. for the first and second scenarios,

respectively. Component C28 contribution to reliabilityperformance of the load point under study is shown inTable IV.Upon execution of the aforementioned procedure for allcomponents, the associated criticality factors are accord-ingly calculated. The coefficients , , and needed forcalculating the criticality factors are assumed to be, re-spectively, 2, 3, and 5. They are determined in such a waythat reflects the indices importance from the utilitys pointof view. In such circumstances, and employing the previ-ously introduced [3, (1)], the criticality factor is 0.3507. Asimilar procedure is conducted for the other components,and the obtained criticality factors are then prioritized aspresented in Table V. It can be seen from the results thattransformer C33, cables C30 and C31, and breaker C28 arethe most critical components of the system. The questionarises which of the identified critical components have aconsiderable impact on the load-point reliability indices.In other words, the next step involves finding out the mostsuitable number of critical components to be retained inthe proposed algorithm. The cumulative criticality factorspresented in Table V are employed and the appropriatenumber of components obtained for LH11 is such that thesatisfaction constraint can be met. Table VI shows the de-sired reliability indices and accordingly the desired criti-cality factor as the qualifying criterion for the sake of crit-ical component identification.According to the proposed inequality constraint, intro-duced in [3, (2)], and assuming the coefficient to be 1.2,the constraint yields the following:

(3)

Comparing the obtained satisfaction value of 1.312 withthe cumulative criticality factors of Table V leads to thefirst three components to be selected as the system-criticalcomponents.

Step 2)4) Failure-mode detection, and critical failure-mode/cause recognition of critical componentsFollowing the identification of critical components, thenext step is to determine the associated failure modeswhich make a contribution to the component failure rate.For the critical transformer and two underground cables,possible failure modes and failure causes are outlined inTable VII [8], [9]. It is important to note that other failuremodes and the associated failure causes, if any, should beadded to those of Table VII.

Step 5) Failure-rate modeling of critical componentsAs stated in the first part paper, failure-rate modeling ofcritical components can be accomplished in an exponen-tial manner through the weighting tables, introduced in [7].In the case of transformer C33 and the two undergroundcables C30 and C31, the associated failure-rate functionsin terms of their conditions are, respectively, presented in(4) and (5). The coefficients of these equations are takenfrom practical/experimental studies [10]. Their estimation



TABLE VCOMPONENT CRITICALITY FACTORS WITH RESPECT TO LH11

TABLE VIDESIRED CRITICALITY FACTOR

is possible using historical dataset and parameter estima-tion methods. A brief explanation on how these equationsare derived is presented in Appendix A

(4)(5)

The values reflect the component conditions and areobtained using the corresponding weighting tables. As anexample, a weighting table is framed for transformer C33as shown in Table VIII. Both weights and scores are setthrough the engineering judgments applied by the utilityasset manager, system and component experts, and con-dition inspectors. The weights correspond to the failuremodes and causes reflect their importance, and primarilydepend on past data and historical records of componentfailures. These weights can be constant for a specific com-ponent and are not a function of time. The scores are as-signed by the maintenance crew and component expertswhile inspecting the component condition from the failure-mode perspective. These scores reflect the component con-dition at the time of inspection and change after mainte-nance tasks fulfilled on the component.As shown in this table, the weighted-sum value for thiscomponent is calculated as 55.125. A similar procedurehas to be established for other critical components (i.e.,cables C30 and C31). The weighted-sum values associated

TABLE VIIFAILURE MODES AND CAUSES OF CRITICAL COMPONENTS

with the underground cables are evaluated as 33.350 and38.425, respectively, for the components C30 and C31.Having obtained these weighted-sum score values, the cor-responding weighted-average values, referring to as thecomponent condition score, are equal to 0.69042, 0.4764,and 0.5490, respectively, for components C33, C30, andC31. The next task involves calculating values to getto the component failure rates at the time of inspection. Thebest and worst possible scores for the critical componentshave to be assumed. The value of the critical componentat time , , is computed using the following equation

[7], [8]:

(6)

where is the condition score value of the th crit-ical component at time , , and are, respectively, theworst and the best possible condition scores of the th crit-ical component. These scores correspond to the worst andbest historical failure rates of the component under con-sideration, respectively, and they can be readily obtainedby referring to the component failure records. All requiredinformation on how they are assigned and how they aretreated in the modeling are available in [7] and [8]. The

and values for critical components are given in



TABLE VIIIINSPECTION FAILURE-RATE ESTIMATION OF TRANSFORMER C33

TABLE IXCRITICAL COMPONENTS BEST AND WORST CONDITION SCORES

TABLE XCRITICAL COMPONENTS CONDITION SCORES AND FAILURE RATES AT THE

TIME OF INSPECTION.

TABLE XILOAD POINT LH11 RELIABILITY INDICES AT THE TIME OF INSPECTION

Table IX. Having employed the obtained values in thefailure- rate functions, previously introduced in (4) and (5),the components failure rates at the time of study can be thenobtained. These are all presented in Table X.

Step 6) Load-point/system reliability evaluationThe failure rates of critical components have been deter-mined and it is time to evaluate the current system con-dition from a reliability viewpoint to determine whetherthe load point under consideration is in need of any main-tenance at this time or not. This is performed by com-paring the current reliability indices and the utilitys de-

TABLE XIIPOSSIBLE MAINTENANCE STRATEGIES FOR TRANSFORMER C33

sired values. The reliability indices associated with loadpoint LH11 are calculated based on the failure rates ob-tained for critical components in Table X and the averagefailure-rate values of the noncritical components. The ob-tained results are given in Table XI.It is evident that the present-time reliability indices asso-ciated with LH11 are worse than the desired ones shownin Table VI. Hence, the necessity is to put further mainte-nance strategies in practice to provide reliability improve-ment of the system.

Step 7) Outlining possible maintenance strategiesAll possible maintenance strategies for the critical compo-nents have to be aggregated in a similar manner to thosepresented for the transformer C33 in Table XII. A point tobe emphasized is that the maintenance polices have to beput under some feasibility/applicability analysis. In otherwords, a practical fact is that in practice, when a compo-nent is going to undergo maintenance actions, it is econom-ically justifiable to conduct some other maintenance taskstogether and at the same time. This type of scheduling isreferred to as component-based coordinated maintenanceand not only saves human and financial resources, but evenimposes lower energy not supplied. A clustering processcan be so carried out on the maintenance strategies to cat-egorize the possible maintenance policies to be done at thesame time. These clustered plans can be regarded as theinputs to the rest of the studies (i.e., cost-benefit analysis).Experts knowledge and experience would be helpful inthis respect too.

Step 8) Cost-benefit analysis and ranking of strategiesIn accordance with the principles explored in [3], the nextstep is to assess the cost-effectiveness of maintenanceplans associated with critical components. Hence, foreach maintenance plan, the associated cost and benefitfunctions are estimated, and the BCR index is computed



TABLE XIIICOST-BENEFIT ANALYSIS OF MAINTENANCE PLANS OF TRANSFORMER C33

TABLE XIVMODIFIED INSPECTION FAILURE-RATE EVALUATION OF TRANSFORMER C33

TABLE XVLH11 RELIABILITY INDICES HAVING CONDUCTED THE COST-EFFECTIVE

MAINTENANCE STRATEGIES ON TRANSFORMER C33

[3]. The cost and benefit terms are evaluated as shownin Table XIII. The considered data and information areassumed based on consultation with utility experts andmanagers and are as provided in [10]. Details on the costand benefit evaluation processes are illustrated in [3].It can be seen from Table XIII that maintenance plans 6, 8,5, and 9 have the largest BCRs and as the most cost-effec-tive strategies, should be applied on the critical componentC33.

Step 9) Selection of optimal maintenance strategiesFollowing the determination of cost-effective maintenancestrategies for the systems most critical component, thenext step is to investigate the outcome reliability indicesof the load point in question. In other words, once a main-tenance plan is applied on the C33, the possibility of thefailure mode/cause of C33, which is considered to be im-proved by that plan, would be modified. Thus, the respec-tive failure mode/cause would obtain a higher score inthe weighting table and this will lead to a lower amountof C33 failure rate as a direct result. The new weightingtable for transformer C33 subsequent to the first cost-ef-fective maintenance plan (#6) is shown in Table XIV. Theweighted-average score associated with the new compo-nent condition is 0.6988. The new value is calculatedto be 0.3902, which leads to the failure rate of 0.37543.Consequent to the change in the critical component failurerate, the new load-point reliability indices are calculatedas shown in Table XV. It can be observed that the desiredindices are far from those obtained subsequent to the main-tenance plan. The need for a future cost-effective mainte-nance strategy on C33 still exists. The second cost-effec-tive maintenance strategy, namely, plan 8, is thus applied;the component condition score and consequently its failurerate are then updated, and reliability indices are calculated.The desired EENS has been almost met while the specifiedof and of are still not satisfied. As

presented in Table XV, the third and fourth cost-effectiveplans are thereafter required to be applied on C33, whichresults in the desired reliability targets of the Birka utilitybeing satisfactorily met.The important point is that once applying the first cost-ef-fectivemaintenance plan, the reliability performance of theload point under consideration would be improved and, asa result, it might lead to a different order of maintenanceplans to be applied. The reason lies in the fact that theEENSindex of the load point is involved in the BCR calculationand due to its variation after each maintenance plan, theBCR indices would be changed as a consequence. Thiscalls for a recalculation of BCRs after each maintenanceplan is applied. This order of maintenance plans in thisstudy, however, was not changed after applying the mainte-nance plans. Tant issue is that even if the desired reliability



TABLE XVIREQUIRED DATA FOR IMPLEMENTATION OF THE PROPOSED RCM SCHEME

targets of the utility are not met through all of the main-tenance plans for the first system critical component, thesame process is continued through the next critical compo-nents. If the goals are not met by applying all of the main-tenance plans on all critical components, it is implied thatthe specified reliability index values are not realistic andconsequently need to be revised or redecided.

D. Post-Analysis

This step is done to feed future analysis on the distributionsystem which involves documentation of the obtained econom-ical and technical information and might necessitate moderndata-management tools. The aforementioned steps describe thefirst cycle of RCM implementation; however, it is an iterativeprocess and deemed to be performed at regular inspection inter-vals. The time intervals could be determined either in a dynamicor static manner depending on the RCM effectiveness and allo-cated financial resources. This subject could be further consid-ered as an open research topic.

III. CONCLUSIONThis two-paper set addresses an important need, namely

RCM, as a power distribution system maintenance process. Itprovides a framework toward practical implementation of RCMon power distribution systems. It clearly and simply introducesthe expected visions and principles. Considerable effort hasbeen made to incorporate in the proposed algorithm almost allof the pragmatic concerns in the three main stages designatedas Pre-Analysis, Main-Analysis, and Post-Analysis. Each stageconsists of various steps which are illustrated in the Part Ipaper and numerically examined in the Part II paper. Dealingwith such a wide and all-inclusive approach is always harderin practice than in principle. There are always some problemsor constraints in reality that prevent a comprehensive andtheoretically proved approach to be thoroughly implementedin practice.This paper, as the outcome of an industrial project, incorpo-

rates the practical viewpoints in the algorithm verified by theexperts and electric power industry. The presented approach



is hence beneficial and of interest to both academics and in-dustry. The identification of system-critical components in asystematic reliability-based manner is done in such a way thatthe components criticality can be evaluated not from the com-ponent, but from the system viewpoint. Component failure-ratemodeling based on the inspection condition scores is carriedout and a practical approach is pursued in the maintenanceprocess based on coordinative maintenance in power systems.Economic analyses through the BCR index are accomplishedand mathematically investigated. As discussed, the BCR index,on one hand, deals with the costs associated with maintenancestrategies, labor, materials, and interruptions that occur due tothe PM process. On the other hand, it includes benefits throughCM postponement via the execution of RCM procedures. Themethodology is applied on a distribution test network and itsapplicability is illustrated through the analysis. This paper setpinpoints the vital technical and economic data requirementsincluding reliability parameters. This necessitates data-gath-ering organized structures in distribution systems. All of therequired data, such as component reliability data and economicdata (e.g., maintenance costs, associated labor costs, and so on)are summarized in Table XVI.Generally speaking, the notable features of the proposed

RCM scheme are as follows. It does not contain theoretical complexities or necessitatea significant learning process for practitioners.

Focusing on todays limited maintenance resources, com-ponents with severe outage consequences are recognizedas critical ones and are put under RCMcost-effective plans.

Condition-based failure-rate estimation is effectively ful-filled by mapping the inspection scores to the componentcondition score and accordingly to the failure-rate value.

The proposed approach provides a framework to quantifymaintenance procedures from a reliability point of view,which helps to minimize subjective judgments in theprocess. It can be considered as a benchmarking scheme tobe employed in different industries, specifically in powerdistribution systems.

It is also capable of being implemented with minimumprogramming effort. The proposed scheme is a straight-forward algorithm that can be easily implemented evenin large-scale networks with minimum computational andprogramming burden.

APPENDIXThis section is devoted to an explanation on the derivation

of (4) and (5) [7], [8]. Practically speaking, there has been stilla shortage of enough historical data to map the inspection re-sults of components to their failure rates through regression-based equations. However, the interpolation-based approachesare well capable of providing the approximate results. The inter-polation approach at least requires the component failure ratescorresponding to the worst and best condition scores, obtainedfrom the weighting tables. It also requires one or more interiorpoints for the nonlinear relationships to be determined. The au-thors in [7] empirically found that an exponential model offers

the best relationship between the component condition scoreand its failure rates. The exponential model is as follows:

(A1)

where is the failure rate and is the condition score of a com-ponent under supervision. To find the required parameters A,B, and C, three data pairs are necessary. The weighting tablesapproach followed in this paper, and presented in detail in [7],[8], results in the best (1), average (0.5), and worst (0) condi-tion scores of a component. By either employing the averagefailure rate across many components or using the average failurerates accepted in relevant literature, the failure rates associatedwith the average condition score can be approximated. On thecontrary, determination of and are rather difficult andshould be done through benchmarking, statistical analysis, orheuristics [7]. Given these three values ,the associated functions to reach the required parameters are de-veloped as follows:

(A2)

(A3)

(A4)

Benchmarking of equipment failure rates is presented in de-tail in [12].

REFERENCES

[1] J. Moubray, Reliability-Centered Maintenance. Oxford, U.K.: But-terworth-Heine-mann, 1991.

[2] A. M. Smith and G. R. Hinchcliffe, RCM-Gateway to World ClassMaintenance. Oxford, U.K.: Butterworth-Heinemann, 2004.

[3] P. Dehghanian, M. Fotuhi-Firuzabad, F. Aminifar, and R. Billinton, Acomprehensive scheme for reliability centered maintenance in powerdistribution systems-Part I: Methodology, IEEE Trans. Power Del.,vol. 28, no. 2, Apr. 2013.

[4] L. Bertling, Reliability centered maintenance for electric power dis-tribution systems, Ph.D. dissertation, Dept. Elect. Eng., KTH, Stock-holm, Sweden, 2002.

[5] Birka Energy AB, Sweden, Annu. Rep. 2000, 2001.[6] L. Bertling, R. Eriksson, R. N. Allan, L. A. Gustafsson, and M. Ahlen,

Survey of causes of failures based on statistics and practice for im-provements of preventive maintenance plans, presented at the 14thPower Syst. Comput. Conf., Sevilla, Spain, Jun. 2002.

[7] R. E. Brown, G. Frimpong, and H. L. Willis, Failure rate modelingusing equipment inspection data, IEEE Trans. Power Syst., vol. 19,no. 2, pp. 782787, May 2004.

[8] W. Jewell, J. Warner, J. McCalley, Y. Li, and S. R. Kumar-Yeddana-pudi, Risk based resource allocation for distribution system mainte-nance, Final Project Rep., PSERC Publ. 0626, Aug. 2006. [Online].Available: www.pserc.org, Final Project Rep

[9] Transformer condition assessments. [Online]. Available: www.siemens.com/energy

[10] [Online]. Available: http://ee.sharif.ir/~fotuhi/distribution_sys-tems.pdf

[11] R. Billinton and R. N. Allan, Reliability Evaluation of Engineering Sys-tems: Concepts and Techniques, 2nd ed. New York: Plenum, 1992.

[12] R. E. Brown, Electric Power Distribution Reliability. New York:Marcel Dekker, 2002.

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A Comprehensive Scheme for Reliability-Centered Maintenance in Power Distribution Systems—Part II Numerical Analysis