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Abstract— Many utilities have aging underground cable sys-

tems that are failing at an increasing rate. Unfortunately, aggres-sive underground cable replacement programs are often difficult to justify since it is difficult to know whether any specific cable section will fail in the near future. This paper presents a simula-tion based methodology to justify a proactive cable replacement program. Its application at a large US utility is demonstrated. This methodology involves the sampling of representative cir-cuits, the development of cable failure rate models and system reliability models that can track expected reliability over a twen-ty year period, and the sequential simulation of system reliability. Three proactive cable replacement scenarios are examined and their economics are compared, considering the integration of other reliability improvement projects.

Index Terms—aging infrastructure, cost-benefit analysis, proactive cable replacement, reliability, time value of money.

I. INTRODUCTION ANY utilities face the aging infrastructure issue. A large amount of equipment is approaching the end of its use-

ful life; in addition, the amount of old equipment is increasing every year. This will result in increased equipment failures, more customer interruptions, and higher restoration costs. If nothing is done, age-related failures will continue to increase and eventually cause customer reliability to dramatically wor-sen. Much of the issue is related to underground distribution cable, much of which has approached or exceeded its expected lifetime.

Utilities typically use reactive cable replacement strategies. However, reactive replacement results in unplanned customer interruptions, worsening reliability indices, and more expen-sive replacement costs (due to overtime wages and fault loca-tion costs). If relying exclusively on reactive cable replace-ment, utilities can expect a very large number of in-service failures in the near future, given the large population of aging cable. Eventually, there will be more in-service cable failures than a utility can effectively manage with pure reactive re-placement.

For these reasons and others (such as safety), the prudent approach for utilities is to have a proactive replacement pro-gram. Replacing old but still in service cable will prevent fu-ture outages due to in-service cable failures. However, proac-tive replacement requires that money to be spent earlier, effec-tively accruing the interest amount over the period of ad-vancement. As a result, proactive underground replacement programs are often considered difficult to justify since it is

L. Xu and R.E. Brown are with Quanta Technology, 4020 Westchase Blvd. Raleigh NC 27607 USA (e-mail: lxu@quanta-technology.com; rbrown@quanta-technology.com).

difficult to know whether the replaced cable section will ac-tually fail in the near future. Various studies such as [1] and [2] have been carried out to estimate the remaining life of un-derground cable.

Typical existing distribution reliability studies do not cope with the temporal factor, such as [3] and [4]; instead, they assume component failure rates to be constant and investigate the effectiveness of various reliability improvement options. When aging infrastructure is a prominent factor of a study, this approach becomes insufficient. This paper examines the im-pact of aging underground cable to system reliability and pro-poses a simulation based methodology to investigate the costs associated with proactive underground cable replacement so as to justify its effectiveness economically. The application of the proposed method at a large US utility study is presented in this article as an example. Some proprietary information has been processed to be suitable for public demonstration.

Section II of this paper briefly presents a representative cir-cuit approach that selects a set of distribution circuits on which the study implemented can be extrapolated to the entire system in a statistically sound way. Section III examines the impact of aging underground cable to system reliability, with only reactive cable program. Section IV demonstrates the si-mulation approach that studies the affect of proactive cable replacement program to system reliability. Section V assesses the cost-effectiveness of proactive cable programs, followed by the conclusions of the paper in Section VI.

II. REPRESENTATIVE CIRCUIT APPROACH A typical distribution system consists of hundreds to thou-

sands of circuits. Their characteristics such as age, customer base, and configurations may vary substantially. It is prohibi-tively expensive and inefficient, also unnecessary, to study every circuit in order to understand the impact of a certain aspect to the system. The proposed representative circuit ap-proach uses a statistical assessment of circuit data to select a small set of representative circuits for a study. The study of a representative circuit can be used to approximate the results of its associated circuit group, further allowing the result of the entire system to be estimated.

The representative circuit set is selected using statistical clustering methods. The most commonly used algorithm is k-mean clustering. This article is not intended to restate mathe-matical derivations of the algorithm, which can be found in many textbooks such as [5] or online resources such as [6]. Instead, three practical aspects that can affect the representa-tiveness of the circuit set are discussed.

Justifying the Proactive Replacement of Cable Le Xu, Member, IEEE and Richard E. Brown, Fellow, IEEE

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A. Feature Selection In cluster analysis, similar circuits are grouped into the

same subset while dissimilar circuits are separated into differ-ent ones. The degree of similarity is determined based on cir-cuit features. The selection of circuit features is study-dependent. For example, underground cable age is important for a reliability study, but may not be as critical for a load fo-recasting study. On the other hand, not all the relevant features are equally important to a study. For example, the peak load should be weighed more than the feeder length for a Plug-in Electric Vehicle impact study. The feature selection can rely on engineering judgment or statistical methods such as corre-lation analysis or regression analysis.

As a reliability study, a stepwise regression with Customer Minutes of Interruption (CMI) as the dependent variable and other circuit features as independent variables is utilized for feature selection and weight determination. The stepwise re-gression calculates the capability of different features explain-ing the variation in CMI values, presented by the sample coef-ficient of determination (R2), and chooses the relevant va-riables for the study. The incremental R2 values are used as the weighting factors for the selected features. Features with high-er weight have more influence in determining the similarity of two circuits than those with lower weight.

B. Cluster Number Determination Typically, more circuit groups lead to better representative-

ness. If each circuit, as an individual cluster, only represents itself, then the system level result can be aggregated from cir-cuit studies and there exists no approximation. However, more circuit groups result in more study effort and cost. Therefore, finding the best number of clusters requires a balance between the representativeness and the effort. The marginal benefit gained in the system representativeness generally decreases with the number of groups. The relationship between the mar-ginal benefit and the group number can be studied by a series run of analysis with different cluster numbers. This study se-lects 25 representative circuits to represents a system with a few thousands of circuits.

C. System Extrapolation With the representative circuit approach, system characte-

ristics are represented by different circuit groups and each group of similar circuits is represented by a typical circuit. The study of aging underground cable is conducted on the repre-sentative circuits. Since a representative circuit represents the most common reliability relevant characteristics of the group, the impact of cable replacement, reactive or proactive, to this circuit is similar to other circuits in the same cluster. There-fore, the study can be extrapolated to the cluster level, and then the system level results can be aggregated from different clusters.

There are various system extrapolation approaches such as optimization. The most straightforward method is to weigh the study conducted on any representative circuit by the number of circuits within its cluster. This approach generates the weighting factors that are easy to understand and interpolate; and has the widest acceptance among utility engineers.

III. IMPACT OF AGING UNDERGROUND CABLE In order to analyze the impact of aging cable to system re-

liability, it is critical to understand the trend of underground cable failures against its age. Some studies like [7] proposed practical method to develop cable failure rate models. Fig.1 presents the probability of failure for four main types of un-derground cables at different ages. These failure rate models are developed by the utility according to its cable installation data and outage history.

Fig.1. Underground cable failure rate model

As shown in the figure, the probability of underground ca-

ble failure increases exponentially with the cable age, regard-less of type. With the underground cable failure rate increas-ing, customers will experience more interruptions and system reliability will become worse. A 20-year simulation (from 2010 to 2030) is implemented to examine the change of sys-tem reliability indices with underground cable aging. In the simulation, no reliability improvement projects other than reg-ular replacement upon failures, or reactive cable replacement, are considered.

During the simulation, all the underground cable sections in the circuit models are scanned and the in-service failure events are generated based on the age dependent failure rates of dif-ferent cable types. The average cable length replaced per in-service failure for this particular utility is 0.3 conductor miles. Therefore, approximately this length of cable section will be replaced in the simulation once a failure event is generated. In addition, the simulated cable replacement follows the actual replacement practice. For example, HMW and XLPE cables are generally replaced by new TR-XLPE cable.

It is understood that the randomness in generating cable failure events may cause the calculated circuit reliability in-dices to vary from simulation to simulation. For a pure numer-ical study, multiple simulations are typically implemented to derive an expected outcome. However, this study needs a base model, instead of just a base case result, to compare various reliability improvement options. Therefore, a model resulted from one single simulation is kept as the base case model. Since there are thousands of cable sections included in the circuit models, the failure event simulation among cable sec-tions has already mitigated some of the variation, to some ex-tent. Experiment has shown that the variance of the calculated

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reliability indices is less than 5%. So it can be assumed that the simulation results from the selected base case model are statistically representative.

Fig.2 shows how the system reliability, measured by SAIFI and SAIDI, will deteriorate over the next twenty years due to aging cable, given only reactive cable replacement. These normalized system level indices are extrapolated from the si-mulation results for the representative circuits.

Fig.2. System reliability with aging cable and reactive replacement

SAIFI is a measure of how many sustained interruptions an

average customer will experience over the course of a year, while SAIDI is a measure of how many interruption hours an average customer will experience over the course of a year. As can be seen, aging cable will result in an increase in SAIDI and SAIDI of about 50% over the next twenty years. This is not likely to be acceptable to customers and other stakehold-ers.

The total amount of cable that will fail over the next twenty year can be estimated according to the cable failure rate mod-els and the age distribution of the underground cable of the utility. This amount of cable will have to be replaced, either reactively when it fails in service or proactively in a planned manner. The prudent approach for the utility is to include proactive replacement in its planning. The only question is to the amount, the approach, and the timing.

IV. PROACTIVE CABLE REPLACEMENT PROGRAM Proactively cable program replaces the most failure-prone

underground cable so that future outages due to in-service failures can be avoided. This program typically comes hand in hand with the traditional reactive cable replacement program. The relationship between the amount of reactive cable re-placement and the amount of proactive cable replacement has to be carefully determined. A large portion of proactive re-placement may not be cost-effective since cable sections with relatively long expected remaining life will be replaced before needed; on the other hand, a small portion of proactive re-placement results in more in-service cable failures and worse system reliability.

Based on its cable population and the corresponding age distribution, the utility in this study is particularly interested in investigating three scenarios, i.e., proactively replacing 150, 415, and 700 conductor miles of underground cable each year.

The impact of different proactive cable replacement pro-grams is studied through a simulation approach, in which the same 20-year period (2010-2030) is sequentially simulated. In each simulation year, both reactive and proactive cable pro-grams are implemented. The simulation of reactive cable re-placement follows the similar approach as described in section II: cable failure events are probabilistically generated to de-termine the to-be-replaced cable sections. The proactive cable program aims to replace the most failure-prone sections, which are the ones with the highest failure rate. In the simula-tion, this population is typically consistent with the oldest ca-ble sections in the circuit models, even though different cable types may have certain variance in its failure rate as shown in Fig.1. According to the total conductor miles of cable to be proactively replaced throughout the system, a proportionally scaled amount for 25 representative circuits is computed. The simulation then follows the utility’s cable practice to replace the designated amount of failure-prone cable sections. More proactive cable replacement will lead to less reactive cable replacement over the years.

The simulated system reliability indices, SAIFI and SAIDI, under three proposed proactive cable replacement scenarios are shown in Fig. 3 and Fig. 4, respectively.

Fig. 3. SAIFI trend under various cable replacement programs

Fig. 4. SAIDI trend under various cable replacement programs

It is observed from the simulation records that approximate-

ly the same amount of cable has been replaced, reactively and proactively, under different scenarios. In other words, more cable is proactively replaced and less cable is replaced upon

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in-service failures in the 700-mile/year scenario, comparing with the other two. The difference of total amount of cable replacement between the 415-mile/year scenario and the 150-mile/year scenario is less than 1%, while the 700-mile/year scenario replaces 6.5% more. This observation ensures that the system reliabilities in different scenarios are compared on the same ground.

As shown in Fig. 3 and Fig. 4, the system reliability in terms of SAIFI and SAIDI gets worse due to aging under-ground cable over the next 20 years, however, integrating proactive cable replacement can significantly lessen the degree of performance deterioration. The SAIFI values at 2030 are reduced by 8%, 20%, and 33% in three scenarios, respective-ly; The SAIDI values at 2030 are reduced by 10%, 23%, and 36%, respectively. It is of no surprise that the 150 mile/year scenario has the least improvement and the 700 mile/year sce-nario has the most.

It is worthy to point out that the trend of SAIDI values in the 700 mile/year scenario becomes steady towards the end of the 20-year simulation period, which implies that the impact of cable aging starts to be compensated by the proactive cable replacement. The steady stage of the system reliability can be expected to occur earlier if more cable is proactively replaced every year.

V. COST-BENEFIT ANALYSIS OF PROACTIVE CABLE REPLACEMENT PROGRAM

As the simulation results show, replacing cable before in-service failures occur can prevent some of the outages and improve system reliability. However, since the cable replace-ment expenditure takes place earlier, which accrues additional cost that is effectively the interest amount over the period of advancement. As a result, it is important to carefully select the amount of proactive cable replacement based on the assess-ment of its costs and benefits.

SAIDI reduction is typically a utility’s main goal of system reliability improvement, thus it is used as the main driver for evaluating the cost-effectiveness of each alternative, even though SAIFI reduction is also monitored during the analysis. Typically, the cost-effectiveness of a reliability improvement project is defined as the ratio of the cost of implementing it to its corresponding reliability benefits in terms of Customer Minutes of Interruption (CMI) reduction, which is proportion-al to SAIDI reduction.

Different from a traditional reliability improvement project in which the total expense is the cost considered in the eco-nomic analysis; the cost associated with proactive cable re-placement for an economic analysis is the incremental cost comparing to reactive cable replacement. When a cable sec-tion is approaching the end of its useful life, it will be re-placed, sooner or later. If it is replaced after the in-service failure, then no reliability benefit is gained from the cost of replacement. However, the outage due to the in-service failure can be avoided with proactive replacement, so some reliability benefit is gained. This benefit is because of the spending of the incremental cost. As a result, the cost-effectiveness of a proactive cable replacement program is effectively the ratio of its associated borrowing cost to its contribution to CMI reduc-tion.

The concept of the time value of money is critical for un-derstanding the borrowing cost. The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time [8]. For example, 105 dollars next year has a present value of 100 dollars to the reci-pient who assumes 5% interest. Assuming a non-inflatable expense of 105 dollars for one task, if the task is to be imple-mented next year, then the task cost has a present value of 100 dollars; however, if the task is pursued this year, then the present value of the task cost is 105 dollars. The borrowing cost, or the incremental cost, of implementing the task one year earlier is 5 dollars.

According to the utility’s finance department, a 10% pre-tax weighted average cost of capital (WACC), that represents the average annual borrowing cost from all sources of debt and equity financing, and a constant cable replacement cost are assumed in this study.

Due to the impact of compound interest, the critical factor of achieving a cost-effective proactive cable program is the timing of replacement. Replacing a cable section too early accrues more interest and leads to low cost-effectiveness. But it is not always possible to identify a failing cable and replace it right before its failure so as to achieve a very cost-effective project. The remaining useful life of a cable section can be estimated based on its failure rate. For instance, an in-service cable that has a failure rate of 0.5 failures per year is expected to fail in two years on average. If this section is replaced today as part of a proactive cable program, the money that otherwise would have been spent in two years is spent today. The cost to the utility is equal to the amount of interest for borrowing the money for two years.

During the simulation, when a cable section is identified for proactive replacement, its expected remaining life is first esti-mated as the recipient of its failure rate and then the borrowing cost is calculated based on its expected life. The total cost for the representative circuits and then throughout the system can be estimated for the cost-effectiveness analysis. Fig. 5 and Fig. 6 show the average age and the average ex-pected remaining life of proactively replaced cable every year in three scenarios .

Fig. 5. Average ages of replaced cable

As shown in Fig. 5, the age of replaced cable is generally

increases over the simulation years, implying that the pace of cable replacement is behind the aging of cable. The average age of replaced cable in the 150-mile/year scenario is higher

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than the 415-mile/year scenario, and then the 715-mile/year scenario. Since proactive cable program aims at clearing the oldest cable that is most prone to in-service failures, replacing more cable will inevitably include some younger cable that otherwise would not be replaced and consequently lower the average age of the population.

Fig. 6. Average expected remaining life of replaced cable

Older cable has higher failure rates and its expected remain-ing life is consequently shorter. As shown in Fig. 6, the aver-age expected remaining life of replaced cable is generally get-ting shorter over the simulation years. With 150 conductor miles of cable being replaced each year, the expected remain-ing life of the replaced cable is less than 2 years towards the end of the simulation period. In other words, this cable is be-ing replaced about 2 years earlier than it would have been in the reactive mode. With 415 miles of cable replaced each year, the average expected remaining life of the replaced cable is around 2.5 years at year 2030. With 715 miles of cable re-placed each year, the average expected remaining life of the replaced cable is around 3.5 years at year 2030. It has been demonstrated that more proactively replaced cable every year will improve the system reliability but also cost more because the average remaining life of the replaced cable is longer and accrues more borrowing cost. Fig. 7 presents the cost-effectiveness of the proactive cable program over the 20 simulated years for three studied scenarios.

Fig. 7. Cost-effectiveness of proactive cable replacement

$/CMI-reduction is used as the measure; its value indicates

the cost needed for reducing one customer minute of interrup-tion. Apparently a lower value is preferred. For a clearer pres-entation, Fig. 7 shows smoothed curves of the actual simulated

$/CMI-reduction values. The comparison shows that the 150-mile/year scenario is the most cost-effective throughout the simulation period and the 700-mile/year scenario is the least. The difference between the 415-mile/year scenario and the 700-mile/year scenario is not significant, except the first three years.

For all scenarios, the $/CMI-reduction value decreases over years. Examining the total costs of proactive cable program and the total reliability benefits over the 20 years gives an estimate of the average cost-effectiveness of the program. The 150-mile/year scenario has a value of 2.1 dollars per CMI re-duction, i.e., it costs on average $2.10 to reduce one customer minute of interruption if 150 conductor miles of old cable is proactively replaced every year. The 415-mile/year scenario and the 700-mile/year scenario have an average value of $2.83/CMI-reduction and $3.40/CMI-reduction, respectively. For proactive cable program itself, a larger scale of re-placement typically is not as cost effective as a smaller one. But proactively replacing too little cable will result in more cable that has to be replaced upon in-service failures, which will eventually put the utility in a position where there is more aging cable than it can effectively manage, especially given the implication from Fig. 5 that the pace of cable replacement is behind the aging of cable even with a big portion of the 700-mile/year scenario. As a result, the proactive replacement efforts should be in-tegrated with reactive cable replacement program which as-sumes no reliability benefit and other programs such as worst performing circuit projects which focus on relatively poor reliability and equity of service among customers.

A broad range of reliability improvement projects have been considered according to the utility practice and simulated in the study. These tactics include distribution automation, lateral fuse addition, 3-phase recloser addition, fault indicator installation, and manual sectionalizaiton. Different from the proactive cable program, all the expenditure of these projects are spent for the gained reliability benefit. The overall cost-effectiveness of these worst performing circuit projects is cal-culated as the ratio of the total reliability improvement in terms of CMI reduction to the total project cost. Generally, the most cost-effective projects will be implemented first and then the less cost-effective ones. The sequence of these reliability projects is a complex matter; this study utilizes the average value, which is $9.15/CMI-reduction over the 20 simulation years, for comparisons with the proactive cable program. With the integration of the worst performing circuit pro-gram as well as the reactive cable replacement program, the 150-mile/year proactive cable replacement scenario has a cost-effectiveness of $5.06/CMI-reduction, the 415-mile/year sce-nario has a value of $4.57/CMI-reduction, and the 700-mile/year scenario has a value of $4.77/CMI-reduction. The 415-mile/year scenario now becomes the most cost-effective case.

Considering proactive cable replacement alone, smaller scale is more cost effective. However, less proactive cable replacement will lead to more reactive cable replacement which has no reliability benefit. In addition, the worse per-forming circuit is much less cost effective than any of the proactive cable replacement scenarios. When three parts con-sidered together, the contribution of the proactive cable pro-

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gram increases with the program scale. Since the 150-mile/year program has less cost and less benefits, even though the program itself is very cost-effective, the overall reliability programs is not as effective as the 415-mile/year scenario, in which enough cable is being replaced but not too much to lower the overall cost effectiveness as the 700-mile/year sce-nario. Fig. 8 shows the estimated cost-effectiveness of the integrated reliability programs over years. The smoothed curves of the actual simulated $/CMI-reduction values are presented.

Fig. 8. Cost-effectiveness of integrated reliability programs

Even though the program cost-effectiveness increases over

years, it does not mean that the proactive cable program should be postponed to a later time. First of all, about the same amount of cable will have to be replaced each year as afore-mentioned, either reactively or reactively. Second, due to the expensive cable replacement cost and the significant amount of old in-service cable, it is not possible to solve the issue in a short period. Instead, a long term plan should be made in order to effectively manage this problem.

In three studied scenarios, a constant amount of cable is proactively replaced annually for the next 20 years. 415 con-ductor miles every year is considered as an appropriate and cost-justified amount for the utility. But eventually, the amount of proactive cable replacement will likely have to be changed. This depends on various factors such as the age dis-tribution of utility’s cable population and reliability perfor-mance target.

VI. CONCLUSIONS Many utilities have aging underground cable systems. If

nothing is done, age-related failures will continue to increase and eventually cause customer reliability to dramatically wor-sen. Proactively replacement old but still in service cable will prevent future outages. However, proactive cable replacement requires additional borrowing cost comparing with reactive replacement and is often considered difficult to justify since it is difficult to know whether the replaced cable will actually fail in the near future. This paper presents a methodology to justify proactive cable programs. First of all, a statistical cluster analysis is adopted to sample representative circuits so that a credible system analy-sis can be done on a small set of circuits. Then the impact of aging underground cable to the system reliability, under reac-

tive cable program only and with the integration of proactive cable program, is examined. Three specific proactive cable replacement scenarios that interest the utility to which the me-thod is applied are studied. There is always a trade-off in a well-managed system be-tween customer reliability and cost; the proactive portion of cable replacement should be carefully chosen based on the program cost-effectiveness as well as other reliability im-provement programs. The cost-effectiveness of three proposed scenarios are assessed and compared in this article.

VII. REFRENCES [1] W. Li, J. Zhou, J. Lu, and W. Yan, “A Probabilistic Analysis Approach

to Making Decision on Retirement of Aged Equipment in Transmission Systems”, IEEE Trans on Power Delivery, Vol. 22, No. 3, pp. 1891-1896, 2007

[2] N. van Schaik, M.G. Kruithor, and E.F. Steennis, “Estimation of risk of operation (remaining life) of underground MV power cable systems”, 18th International Conference and Exhibition on Electricity Distribution (CIRED), Turin, Italy, 2005.

[3] J.R. Aguero, J. Spare, E. Phillips, C. O'Meally, J. Wang, and R.E. Brown, “Distribution system reliability improvement using predictive models”, IEEE Power & Energy Society General Meeting, Calgary, AB, Canada, 2009.

[4] A.A. Chowdhury and D.E. Custer, “Reliability cost-benefit assessments in urban distribution systems planning”, IEEE PES Power Systems Con-ference and Exposition, 2004.

[5] Jiawei Han and Micheline Kamber, Data Mining: Concepts and Tech-niques. San Francisco: Academic Press, Morgan Kaufmann Publishers, 2001.

[6] http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/ [7] Y. Zhou and R.E. Brown, “A Practical Method for Cable Failure Rate

Modeling”, IEEE Transmission and Distribution Conference and Exhibi-tion, Dallas, TX, 2006

[8] http://en.wikipedia.org/wiki/Time_value_of_money

VIII. BIOGRAPHIES Le Xu (S’01-M’07) received the B.Eng. degree in 2001 from Tsinghua Uni-versity, Beijing, China, and the M.S and Ph.D. degree in 2003 and 2006, respectively, from North Carolina State University, Raleigh, NC. He is a principal engineer at Quanta Technology, Raleigh, NC. His areas of expertise include data mining and its utility applications including PEV and PV impact, distribution reliability, storm hardening, load forecasting, and associated risk analysis. Richard E. Brown (F’07) is the Senior Vice President of Operations for Quanta Technology. He has published more than 80 technical papers related to distribution system reliability and asset management; is a regular instructor on these topics; is author of the book Electric Power Distribution Reliability; and is a registered professional engineer. He is an IEEE Fellow. Dr. Brown earned his BSEE, MSEE, and PhD from the University of Washington in Seattle, and his MBA from the University of North Carolina at Chapel Hill.

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