IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 6, NOVEMBER/DECEMBER 2005 1493

Development of Probabilistic Models for ComputingOptimal Distribution Substation Spare Transformers

Ali A. Chowdhury, Senior Member, IEEE, and Don O. Koval, Fellow, IEEE

Abstract—This paper presents probabilistic models developedbased on the Poisson probability distribution for determiningthe optimal number of transformer spares for distribution trans-former systems. The outage of a transformer is a random eventand the probability mathematics can best describe this type offailure process. The developed models have been illustrated usingillustrative 72-kV distribution transformer systems. Industry-average catastrophic transformer failure rate and a 1-year trans-former repair or procurement time have been utilized in theexamples considered in the paper. Among the models developedfor determining the optimum number of transformer spares, thestatistical economics model provides the best result as it attemptsto minimize the total system cost including the cost of sparescarried in the system.

Index Terms—Catastrophic transformer failure, probabilitymathematics, reliability cost/reliability benefit, spare transformer,statistical economics.

I. INTRODUCTION

I T IS recognized that some equipment failures in an electricalsystem are unavoidable. An electric utility delivery system

must be designed to withstand occasional equipment failuresby including redundant or standby equipment into the overallsystem operation plan. The question of what would be theoptimal number of spare equipment for a given system is thesubject matter of the analyses performed in this paper.

This paper attempts to answer the question above and dealswith the usage of distribution substation transformer spares,particularly in determining the required number of transformerspares to maintain an acceptable level of system reliability.The question of how many spares should be carried in asystem depends on the system reliability requirements andcost of having that reliability level. As the number of sparescarried is increased, the capital and operations and management(O&M) costs of the system also increase. In order to ascertainthe optimal number of spares, it is necessary to perform aneconomic comparison between the increased economic returndue to increased system reliability and the required capital andO&M investment to achieve the increased reliability.

Paper ICPSD-05-16, presented at the 2005 IEEE/IAS Industrial and Com-mercial Power Systems Technical Conference, Saratoga Springs, NY, May8–11, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY

APPLICATIONS by the Power Systems Engineering Committee of the IEEEIndustry Application Society. Manuscript submitted for review May 12, 2005and released for publication August 25, 2005.

A. A. Chowdhury is with MidAmerican Energy Company, Davenport, IA52801 USA.

D. O. Koval is with the Department of Electrical and Computer Engineering,University of Alberta, Edmonton, AB T6G 1G4, Canada.

Digital Object Identifier 10.1109/TIA.2005.858310

Considerable efforts have been devoted to power systemprobabilistic planning and design for the last four decades[1]–[4]. Very little attention has been paid from a viewpointof probabilistic methods to power equipment spare planning[5]. The paper presents probabilistic models for computing theoptimal number of transformer spares for electric distributiontransformer systems. Although the models are developed usingprobability mathematics, the reader will require no backgroundin probability mathematics to be able to utilize the models toa number of electric equipment types and situations encoun-tered in electric power delivery systems. The number of sparetransformers maintained by a utility has a direct bearing on thereliability levels of industrial and commercial facilities.

II. DEVELOPMENT OF PROBABILISTIC MODELS

FOR DETERMINING OPTIMAL NUMBER

OF TRANSFORMER SPARES

A particular unit of equipment, such as transformer, line, andbreaker, has a failure rate that varies over the life of that unit.It is recognized that populations of equipment normally tendto attain equipment static age distributions; thereby allowingfailures to be modeled as stationary random processes. Thispermits the construction of statistical models to predict systemperformance and to build in an appropriate level of systemredundancy. General concepts associated with failure probabil-ities associated with three developed probabilistic models aredetailed in the following.

A. Reliability Criterion Model for Determining the OptimalNumber of Transformer Spares

The Poisson probability distribution represents the probabil-ity of an isolated event occurring a specified number of timesin a given interval of time or space when the rate of occur-rence, hazard rate, in a continuum of time or space is constant[2]–[4]. In such situations, the hazard rate is normally termedas the failure rate.

The failure of a single unit of equipment is a random eventand must be affected by chance alone. The parameter λ isthe failure rate of a given type of equipment, defined as themean number of failures per unit year in service. Let dt be asufficiently small interval of time such that the probability ofmore than one failure occurring during this interval is negligibleand can be neglected.

λdt = probability of failure in the interval dt, i.e., in the pe-riod (t, t + dt). Let Px(t) be the probability of failure oc-curring x times in the interval (0, t), then the probability ofzero failures in the interval (0, t + dt) equals the probability

0093-9994/$20.00 © 2005 IEEE

1494 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 6, NOVEMBER/DECEMBER 2005

of zero failures in the interval (0, t) times the probability ofzero failures in the interval (t, t + dt). Then, P0(t + dt) =P0(t) × (1 − λdt), assuming event independence, {P0(t +dt) − P0(t)}/dt = −λP0(t). As dt approaches zero or be-comes incrementally small, dP0(t)/dt = −λP0(t), which, byintegrating, becomes ln P0(t) = −λP0(t) + C.

At t = 0, the equipment is known to be operating. Therefore,at t = 0, P0(0) = 1, ln P0(t) = 0, and C = 0, giving P0(t) =e−λt. This expression provides the probability of zero failuresin a specified time period t. If λ(t) = λ, a constant, then forzero failures, R(t) = e−λt. This is the first term of the Poissonprobability distribution and is widely used to calculate thereliability of a system.

From the equations deduced earlier, it can be concluded thatthe probability that a given equipment will survive for a periodof t years in service Px(t) is determined by the exponentialdecay function Px(t) = e−λt. For a population of N suchequipment, the mean number of failures per year is equal toNλ. If failures are statistically independent, the probability ofexactly x failures occurring over the period t years Px(t) isgiven by the Poisson probability distribution

Px(t) =e−Nλt(Nλt)x

x!. (1)

This Poisson reliability model can be utilized for calculatingreliability of a system with n spares as given in

R(t) = e−Nλt

[1 + Nλt +

(Nλt)2

2!+

(Nλt)3

3!

+(Nλt)4

4!+ . . . . . . +

(Nλt)n

n!

]. (2)

B. Mean Time Between Failures (MTBFu) Criterion Modelfor Determining the Optimal Number of Transformer Spares

In (2), the system reliability is given by the sum of thefirst n terms of the Poisson probability distribution. Poissonstatistics can, therefore, be effectively utilized to determine theequipment unavailability in a mature population of N units inservice including a number of n spare units. The mean numberof units entering the repair status per year equals the meannumber of failures per year, which is Nλ. Let MTTR be definedas the mean time to repair for a unit or to procure a new unitif the failed unit is scrapped. The mean number of units inthe underrepair status at any given instant in time µr is themean number of units entering the underrepair status in the timeinterval MTTR. Therefore

µr = Nλ MTTR. (3)

Since the probability of exactly n units entering the under-repair status in any time interval MTTR is determined by thePoisson probability distribution, the probability of exactly nunits existing in the underrepair status Px(t) is given by thesame Poisson probability distribution

Px(t) =(e−µrµx

r )x!

. (4)

If there are n units assigned as spare units, the probabilitythat all n units are depleted at any instant in time Pu equals thesum of probabilities in (4) for x ≥ n

Pu = Px(x ≥ n) = 1 − Px(x < n) = 1 −n−1∑x=0

e−µrµxr

x!. (5)

Let MTBFu equal the MTBF on the system when all spareshave been depleted. This time interval is the mean time betweenequipment unavailabilities

MTBFu =1

(NλPu). (6)

Let µu equal the mean number of units in the population atany instant in time, which are unavailable due to the fact that nspare units were depleted from prior failures

µu =

N+n∑x=n

(x − n)e−µrµxr

x!

≈µr − n +

n−1∑x=0

(n − x)e−µrµxr

x!. (7)

Let MTTRu equal the mean time that an unavailable inservice unit will remain out of service until the first underrepairunit is repaired

MTTRu = µu MTBFu. (8)

C. Determination of Optimal Transformer Spares Based onthe Model of Statistical Economics

It is important to note that as the number of spares carriedin a system is increased, the capital and the O&M costs of thesystem also increase. In order to determine the optimum num-ber of spares in a system, it is necessary to make an economiccomparison between the cost and the benefit of carrying acertain number of spares. Economic aspects, therefore, becomean important factor in deciding the required level of systemreliability.

Economic analyses including customer outage costs can alsobe used to determine the optimum number of spares. LetCu equal the cost increase due to a unit of equipment beingunavailable for service, expressed in terms of dollars per unityear out of service. Since µu is the average number of unitsunavailable at any instant in time, the expected annual cost ofhaving units unavailable is µu × Cu. Let Cs equal the cost ofowning and maintaining one spare unit of equipment, expressedas carrying charge in dollars per unit year. If there are n suchunits in the inventory, the total cost of maintaining the inventoryis n × Cs. The optimal number of units in the inventory isthe figure of n such that the total cost µu × Cu + n × Cs isminimized.

The probability models presented here and in Sections II-Aand II-B are utilized in Section III in determining opti-mum spare transformer requirements for illustrative distributiontransformer systems.

CHOWDHURY AND KOVAL: PROBABILISTIC MODELS FOR COMPUTING OPTIMAL DISTRIBUTION SUBSTATION SPARE TRANSFORMERS 1495

TABLE INUMBER OF DISTRIBUTION SUBSTATION TRANSFORMERS REQUIRING

SPARE BACKUP FOR THE N − 1 OR FIRST CONTINGENCY

(72- AND 25-kV SECONDARY)

III. OPTIMAL TRANSFORMER SPARES FOR ILLUSTRATIVE

72-kV DISTRIBUTION TRANSFORMER SYSTEMS

The N − 1 reliability criterion is widely used in the sub-station transformer planning and design [6]–[9]. Each substa-tion is normally designed to have two or more transformersin parallel so that the peak load can be supplied when onetransformer fails. This is a reliable but expensive substationdesign criterion [8]. Utilization of common spare transformershas been a common practice in many utilities in planning anddesign of substations. The policy of using common sparescan be extended to multiple-transformer substations and newsingle transformer substation design. For example, for a two-transformer substation, where either one will not be able tomeet the peak load due to load growth, the substation canbecome a member of the substation group with the sameclass of transformers to share common spares rather than athird transformer be added in the individual substation. Fornoncritical loads, single-transformer substations instead of twotransformers in parallel can be considered with shared commonspares. Compared to the N − 1 contingency design principle ineach substation, common spare transformers shared by multiplesubstations can avoid significant capital and O&M expenditure,and still provide adequate service reliability.

There are two failure modes for a transformer, namely:1) field-repairable failure and 2) non-field-repairable or catas-trophic failure [6]. The installation time for a spare transformer,which is 1–5 days, is comparable with the field repairable timefrom 1 to 10 days from a random repairable failure and muchshorter than the replacement or procurement time of 1.0–1.5years of buying or rebuilding a transformer in the case of acatastrophic failure and no spare available.

The number of transformers requiring spare backup for theillustrative 72-kV distribution systems considered in this paperfor different transformer megavolt ampere (MVA) ratings aresummarized in Table I.

The catastrophic failure rate for distribution transformersof 0.011 failures per transformer per year has been used inthe analyses performed in this paper [10]. Canadian Electric-ity Association publishes transformer failure statistics for allCanadian utilities annually. Using the catastrophic failure rateof 0.011 failures per transformer per year for the transformersof all MVA ratings in Table I, the 72-kV transformer systems’failure rates per year have been calculated and presented inTable II.

Transformer outages in general are somewhat different be-cause while they are infrequent compared to transmission lineoutages, restoration/repair times are normally long. This isespecially true for catastrophic failures. For a catastrophicfailure, the damaged transformer or its replacement may be

TABLE IICALCULATED CATASTROPHIC TRANSFORMER FAILURE RATE PER YEAR

BY TRANSFORMER MVA RATINGS FOR 72-kV SYSTEMS

unavailable for up to a year. Extended repair times normallyresult from problems with winding, core, leads, bushings, andload tap changer that require untanking and/or a trip to therepair facility. If the damage to the failed transformer is suchthat the transformer is beyond repair and is scrapped, then a newtransformer is required to be purchased, which might normallytake a year or more. In the analysis for determining the optimalnumber of spares, it is considered that the repair/restorationtime of the failed transformer or the procurement time of a newtransformer would be one year.

Three different probabilistic models are utilized in this paperin determining optimal transformer spares, such as satisfyingthe minimum MTBF requirements for the system, satisfying theminimum reliability requirements for the system, and satisfyingthe minimum statistical economics criterion for the system.In the following subsections, three example calculations fordetermining optimal transformer spares using the developedprobabilistic models are illustrated. The transformers used inthe example calculations are for the 72-kV transformers ofMVA rating equal to and greater than 16 MVA shown inTable I. Similar mathematical models can be utilized for otherMVA ratings.

A. Determination of Optimal Transformer Spares Based onthe Minimum Reliability Criterion

The example of 72-kV transformers with MVA rating of≥ 16 MVA is utilized in this subsection to illustrate the op-timum transformer spare calculation methodology using thereliability criterion. Equation (2) is utilized for calculating thesystem reliability for different spare levels. In this example,there are 132 transformers (see Table I). The system failurerate is 1.452 failures per year (see Table II). Consider thatthe system failure occurs when any one transformer fails andthe repair time of the failed unit or the procurement timefor a replacement transformer is 1 year. If the system is tohave a minimum reliability of 0.9950, a number typically usedin the electric utility industry, what is the minimum numberof spares that must be carried as immediate replacements?The calculated reliability figures and corresponding number ofspare requirements are presented in Table III.

It can be seen from Table III that the number of spares shouldbe 5 in order to achieve a minimum reliability of 0.9950. Theresults for remaining MVA ratings using the reliability criterionof 0.9950 are summarized in Table IV.

B. Determination of Optimal Transformer Spares Based onthe Minimum MTBFu Criterion

The example transformer system considered has 132(72–25 kV) transformers with MVA rating of equal to and

1496 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 6, NOVEMBER/DECEMBER 2005

TABLE IIIRELIABILITY THAT n SPARES WILL BE DEPLETED IN THE SYSTEM

The system has 132 transformers with ≥ 16 MVArating using the system failure rate of 1.452 failuresper year and a transformer repair/procurement timeof 1 year.

TABLE IVOPTIMUM NUMBER OF TRANSFORMER SPARES FOR DIFFERENT MVA

RATING USING THE RELIABILITY CRITERION OF 0.9950

greater than 16 MVA (see Table I). The failure rate for thetransformer system is 1.452 failures per year, and the MTTR,which is the replacement or the procurement time for the failedtransformer unit is one year. How many spares, n, will beneeded to assure that the mean time between prolonged outageson the system is greater than 35 years, which is the averageuseful life of transformer?

From (3)

µr =Nλ MTTR

= 132 × 0.011 × 1= 1.452 units under repair

where µr is the mean number of transformers entering the un-derrepair status in the time interval MTTR, N is the populationof the transformers, and λ is the catastrophic failure rate of atransformer.

From (6)

MTBFu =1

(NλPu)> 35 years

Pu <1

1.452× 35 = 0.0197

where MTBFu is the MTBF on the system when all spareshave been depleted and Pu is the probability that all n unitsare depleted at any instant in time.

Using (5) to determine Pu as a function of n, the followingresults are computed and presented in Table V.

Therefore, n=5 spares will satisfy the condition thatMTBFu >35 years. With n=5, using (6), MTBFu is 42 years.

Using the similar approach, the optimum number of trans-former spares for remaining MVA ratings has been computedand summarized in Table VI.

C. Determination of Optimal Transformer Spares Based onthe Criterion of Statistical Economics

The example system used here and in Section III-B con-taining 132 (72 kV) transformers of ≥ 16 MVA rating is

TABLE VRESULTS FOR SPARES ANALYSIS USING THE MTBFu CRITERION

TABLE VIOPTIMUM NUMBER OF TRANSFORMER SPARES FOR DIFFERENT

MVA RATING USING THE MTBFu CRITERION OF 35 YEARS

The results are identical to those obtained using the reliability criterionmethod.

utilized to illustrate the statistical economics methodology indetermining the optimal number of spare transformers for the il-lustrative distribution systems. In this case, a typical 72–25-kVtransformer of 12/16/20/22.4 MVA rating is considered forthe calculations of the kilowatthour loss cost increase, therevenue lost cost, the customer outage cost, and the capi-tal cost for the spare transformer. As indicated earlier, the132-transformer-system failure rate is 1.452 failures per year.The repair time/replacement time/procurement time for a newunit (if the failed unit is beyond repair) is considered to be1 year. The loss of a transformer would normally increasesystem power losses. The estimated system O&M cost in-crease due to the catastrophic failure of a 12/16/20/22.4-MVA72-kV transformer is $7160 per unit year. This cost is derivedassuming 1.73 cents/kWh as loss cost, 0.5241 system loadfactor, and loss factor being 45%.

For the catastrophic failure of a 12/16/20/22.4-MVA 72-kVtransformer, the average megawatts (MW) not supplied at0.87 power factor and 0.5241 load factor if the transformer wassupplying a peak load of 16 MVA is 7.3 MW. The expectedenergy lost for the down time of 1 year with the catastrophicfailure frequency of 0.011 per unit per year is 703 MWh/year.The computed annual revenue lost at assumed 6.25 cents/kWhwould be $43 938 per unit per year. The calculated customeroutages cost at assumed $10.76/kWh not supplied would be$7 564 280 per unit per year. Therefore, Cu for a transformerout of service is ($7160 + $43 938 + $7 564 280) $7 615 378per year. If the estimated capital cost of a 12/16/20/22.4-MVA72-kV transformer spare is $350 000, then the carrying chargefor the spare (at 15%)would be Cs = $52 500 per year. Again,the MTTR to fixthe failed transformer, to get a replacementtransformer or to procure a new transformer is considered tobe 1 year in the reliability cost/reliability benefit computationprocess. The question now is: How many transformers shouldbe stocked as spares?

From (3), µr = 132 × 0.0110 × 1 = 1.452 units on order.From (7), µu as a function of n can be computed. The results

are presented in Table VII.

CHOWDHURY AND KOVAL: PROBABILISTIC MODELS FOR COMPUTING OPTIMAL DISTRIBUTION SUBSTATION SPARE TRANSFORMERS 1497

TABLE VIIOPTIMUM NUMBER OF TRANSFORMER SPARES COMPUTED

USING THE STATISTICAL ECONOMICS CRITERION FOR

72-kV TRANSFORMERS ≥ 16 MVA RATING

TABLE VIIIOPTIMUM NUMBER OF TRANSFORMER SPARES FOR DIFFERENT MVA

RATINGS USING THE STATISTICAL ECONOMICS CRITERION

TABLE IXCUMULATIVE PRESENT VALUE OF RELIABILITY COST/BENEFITS FOR

CALCULATED OPTIMUM SPARE TRANSFORMERS

These results indicate that the optimal number of transformerspares is n = 5, since this number minimizes the total cost.

The results for remaining MVA ratings using the statisticaleconomics criterion are summarized in Table VIII. The esti-mated costs for a 72–25-kV 10/13.3-MVA spare transformerand for a 72–25-kV 5/6.25-MVA spare transformer were esti-mated to be $200 000 and $150 000, respectively.

It is worth noting that the three probabilistic models yield thesame number of spares for all transformer categories. This ismere a coincidence due to the fact that if the MTBFu and thereliability criterion used were different than used in the calcu-lations, the calculated optimum spares provided by the threemodels could have been different. Reliability cost/reliabilitybenefit analyses were performed for calculated optimum num-ber of spares for different transformer MVA ratings as shownin Table VIII. The cumulative present values (CPVs) in 2005dollars for the spare costs and the reliability benefits have beencomputed considering a 30-year project life, a 7.7% discountrate, and a 2.5% inflation rate. The results of the cost/benefitanalyses are summarized in Table IX.

As shown in Table IX, the CPV of the reliability benefitsexceeds the CPV of the revenue requirements of the capital

expenditures required for having the optimum number of sparesstocked in the system.

IV. CONCLUSION

This paper presents three probabilistic models developedbased on the Poisson probability distribution for determiningthe optimal number of spare distribution transformers. Theoutage of a transformer is a random event, and the probabilitymathematics can best describe this type of failure process.Three developed models have been illustrated using 72-kVtransformer systems. Industry-average catastrophic transformerfailure rate and a 1-year transformer repair or procurement timehave been utilized in the examples considered in distributiontransformer analyses. Among the three models considered fordetermining the optimum number of transformer spares, the sta-tistical economics model provides the best result as it attemptsto minimize the total system cost including the cost of sparescarried in the system.

It is important to note that the developed probabilistic modelsutilize the failure rates, repair times, and transformer inventoryinformation as input to the models. The optimum number oftransformer spares for a system is a function of the aforemen-tioned input parameters. The number of spare requirementsfor a system also depends on the reliability level demandedfrom the system. Substation design and operation policiescan greatly impact the number of spare requirements. Forexample, for multiple-transformer substations, for the N − 1or first contingency, if the remaining transformer(s) can carrythe substation peak demand, then there is no need for a sparetransformer to backup the next N − 2 or second transformercontingency. In the case of a single-transformer substation, ifthe adjacent substations and the local distribution network canabsorb the substation load for the period of time when thefailed transformer is being fixed, then there is no need for aspare transformer to be brought into the substation. The overallsystem capacity to ride through the N − 1 or first contingencywould greatly reduce the number of transformer inventory,which, in turn, would reduce the number of spares to be stockedin the system.

A uniform substation design and consistent operating volt-ages across the system also greatly reduce the number ofspare transformers requirements. In addition, spares with dualprimary and secondary voltages could also reduce the numberof spare requirements in the system. It is important to note thateach of the aforementioned system design and operating poli-cies would greatly reduce the number of spare requirements,which, in turn, would reduce the system capital and O&M costswithout compromising the service reliability.

It is a well known fact that a population of transformers hav-ing a high failure rate and a long repair or replacement time willhave a high system unavailability until a large number of sparesare maintained in the system. Spare inventories incur hugecosts that warrant serious considerations in system planning,design, operation, and maintenance activities so that a utilitysystem would not become a prohibitively high-cost system. It isimportant to note that the higher the equipment failure rate andthe repair time, the higher the number of spare requirements for

1498 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 6, NOVEMBER/DECEMBER 2005

maintaining an adequate level of system reliability would be.The paper clearly demonstrates the impact of utility spare trans-former policies on the reliability of industrial and commercialfacilities particularly when the utility substations are near theiruseful life. The models can be directly applied to any industrialand commercial substation configuration to optimize the sparetransformer policies in maintaining acceptable reliability levels.

REFERENCES

[1] R. N. Allan, R. Billinton, A. M. Breipohl, and C. H. Grigg, “Bibliographyon the application of probability methods in power system reliabilityevaluation: 1967–1991,” IEEE Trans. Power Syst., vol. 9, no. 1, pp. 41–49,Feb. 1994.

[2] J. Endrenyi, Reliability Modelling in Electric Power Systems.Chichester, U.K.: Wiley, 1978.

[3] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems.New York: Plenum, 1984.

[4] ——, Reliability Evaluation of Engineering Systems. New York:Plenum, 1983.

[5] R. Sahu, “Using transformer failure data to set spare equipment invento-ries,” Electr. Light Power, pp. 41–42, Oct. 1980.

[6] V. I. Kogan, J. A. Fleeman, J. H. Provanzana, and C. H. Shih, “Failureanalysis of EHV transformers,” IEEE Trans. Power Del., vol. 3, no. 2,pp. 672–683, Apr. 1988.

[7] G. E. Henry, III, “A method for economic evaluation of field failures suchas low voltage side lightning surge failure of distribution transformers,”IEEE Trans. Power Del., vol. 3, no. 2, pp. 813–818, Apr. 1988.

[8] IEEE Working Group D1 on Operating and Reliability Aspects for Sub-station Design of the Distribution Substation Subcommittee, SubstationSubcommittee of the Power Engineering Society, “Bibliography for reli-ability and availability engineering for substations,” IEEE Trans. PowerDel., vol. 4, no. 3, pp. 1689–1694, Jul. 1989.

[9] W. J. McNutt and G. H. Kaufman, “Evaluation of a functional life modelfor power transformers,” IEEE Trans. Power App. Syst., vol. 102, no. 5,pp. 1151–1162, May 1983.

[10] Forced Outage Performance of Transmission Equipment for the PeriodJanuary 1, 1995 to December 31, 1999, Canadian Electricity Assoc.,Montreal, QC, Canada, 2000.

Ali A. Chowdhury (A’83–S’86–M’88–SM’94) re-ceived the M.Sc. degree (with honors) in electricalengineering from the Belarus Polytechnic Institute,Minsk, Belarus, in 1980, the M.Sc. and Ph.D. de-grees in electrical engineering with specializationin power systems reliability and security from theUniversity of Saskatchewan, Saskatoon, SK, Canada,in 1983 and 1988, respectively, and the M.B.A.degree from St. Ambrose University, Davenport, IA,in 2002.

He has over 25 years of electric utility, electricequipment manufacturing industry, consulting, teaching, and R&D experiencein power system reliability and security assessments, planning, and analysis.He is actively involved in the development of probabilistic models, criteria, andsoftware for use in power system planning, operating, and maintenance. He haslectured on power system reliability and security nationally and internationally.He has published over 90 technical papers including four prize paper awards onpower system reliability and value-based facility planning and design topics.He is currently with MidAmerican Energy Company, Davenport, IA.

Dr. Chowdhury is a Fellow of the Institution of Electrical Engineers, U.K.,a Chartered Engineer in the U.K., and a Registered Professional Engineer in theState of Texas and in the Province of Alberta, Canada. He is a recipient of nu-merous national and international talent scheme scholarships. He has receivedthe IEEE Region 4 “2003 Outstanding Engineer of the Year” Award for hiscontributions to power system reliability and value-based facility planning. Hehas been listed in the International Biographical Center’s 2004 Living Legendsand in Marquis’ Who’s Who in America, Who’s Who in the World, Who’s Whoin Finance and Business, and Who’s Who in Science and Engineering.

Don O. Koval (S’64–M’65–SM’79–F’90) is aFull Professor in the Department of Electrical andComputer Engineering at the University of Alberta,Edmonton, AB, Canada. He teaches classes in re-liability engineering, power quality, power systemanalysis, and “IEEE Gold Book.” He worked for12 years as a Distribution Special Studies Engineerfor B.C. Hydro and Power Authority in Vancouver,BC, Canada, and for two years as a SubtransmissionDesign Engineer for Saskatchewan Power in Regina,SK, Canada. He has authored or coauthored over

350 technical publications in the fields of emergency and standby powersystems, power system reliability, human reliability, power system disturbancesand outages, power quality, and computer system performance.

Dr. Koval is a Registered Professional Engineer in the Provinces of Albertaand British Columbia, Canada, a Fellow of the American Biographical Institute,and a Life Fellow of the International Biographical Center (Cambridge, U.K.).He is listed in Marquis’ Who’s Who in the West, Who’s Who in America,Who’s Who in World, Personalities of the Americans, Who’s Who in Scienceand Engineering, and 5000 Personalities of the World, and in the InternationalBiographical Center’s International Leaders of Achievement, InternationalWho’s Who of Intellectuals, and Men of Achievement. He serves on the Boardof Directors of several international societies (e.g., IASTED, ICSRIC). He wasthe Editor of the IASTED International Proceedings on High Technology in thePower Industry in 1996. He was Co-Chairman of the 1998 I&CPS Conferenceheld in Edmonton, AB, Canada. He is the Chairman of IEEE Std. 493 (IEEEGold Book). He was elected as one of the six Distinguished Lecturers of theIEEE Industry Applications Society (IAS) for the period 2000–2001. He wasappointed to the rank of Distinguished Visiting Professor and elected Fellowby the International Institute for Advanced Studies in Systems Research andCybernetics in Germany.