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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007 597

Selective Maintenance Schedule of DistributionNetworks Based on Risk Management Approach

Aleksandar D. Janjic , Member, IEEE , and Dragan S. Popovic , Member, IEEE

Abstract—This paper presents a methodology for optimal long-term maintenance schedule of distribution networks. The method-ology is based on risk management approach and the new model of decoupled risk factors and state transition based on decision treediagram. Risk approach provides more realistic modeling of com-ponent failure and estimation of expected consequences, while de-coupled risk factors enable definition of selective plan for preven-tive actions. Theproposed methodology is testedon a real overheaddistribution network, but it can be used for other parts of distribu-tion system as well. Obtained results have shown that the expectedcosts of distribution network maintenance can be reduced and therisk of emerging of significant operation costs minimized, by de-

tailed and realistic modeling of risk factors. Index Terms—Distribution network, dynamic programming,

maintenance schedule, risk management.

I. INTRODUCTION

MAINTENANCE schedule of distribution system is

timely action plan with purpose to extend life cycle of

the system, in order to reduce overall operation costs. Mainte-

nance is closely related to reliability. If maintenance actions

are performed rarely, it can cause a large number of faults and

outages, while done too often, costs will be greatly increased.

Therefore, it is necessary to make an appropriate balance

between maintenance costs and outage duration costs. Two

main approaches in the maintenance strategy determination are

a) corrective, or “run to failure,” approach and b) preventive

maintenance. Preventive maintenance strategies may be further

divided into several different types: scheduled maintenance,

condition based and Reliability centered maintenance (RCM).

Risk based maintenance can also be considered as a special

case of RCM. Overview of status in application of various

maintenance strategies is provided in report of IEEE Task

Force [1].

According to mathematical model, or definition of objective

function, maintenance schedule problem is developed in four di-

rections: 1) maintenance costs minimization; 2) reliability max-

imization; 3) overall costs minimization; and 4) overall risk

minimization.

In the first approach, the criteria function is defined as the

minimum of maintenance costs [2]. Reliability is defined as a

Manuscript received July 12, 2006; revised October 27, 2006. This work wassupported in part by theDMS Group,Ltd.,NoviSad, Serbia. Paperno. TPWRS-00419-2006.

A. Janjic is with the Electric Power Industry, Belgrade, Serbia. (e-mail:[email protected]).

D. Popovic is with DMS Group Ltd., Novi Sad, Serbia (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPWRS.2007.894863

limit, or minimal requested level. In the second approach, an

optimal maintenance strategy is determined that achieves the

highest reliability of the system, or EENS indexes [3], [4].

In the third approach, in the criteria function, beside mainte-

nance costs, reliability costs are added as well (costs of outage

frequency and duration from the consumer’s side) [5]–[8]. More

flexible models, that enable the combination of minimizing cost

for a given reliability and maximizing reliability for a given cost

[9], or cost benefit analysis, are also developed [10]–[13].

Risk management based maintenance is the latest approach

based on evaluating risk of equipment failure and consequencessuch failure can produce of functioning of the system [14]. In-

troducing the risk approach provides more realistic modeling

of equipment failure and estimation of expected consequences.

More precisely, quantification of risk enables determining an

optimal levelof risk that provides the most efficient maintenance

strategy for distribution networks.

In all of the above mentioned approaches, usually only one

kind of maintenance action has been analyzed -replacement or

repair of a particular component [2]–[4], [7], or just one specific

activity (inspection, tree trimming [8], [9]. Long term planning

is performed either by determining fixed time intervals [4]–[7]

or from year to year by quasi-dynamic approach [8], [9]. On the

other hand, prioritizing of maintenance activities does not pro-

vide a global optimum of costs [10]–[13]. Finally, in [15] is pro-

posed the model of decoupling risk factors and related preven-

tive actions, but in this model simultaneous treatment of more

components and risk approach has not been used. In a method-

ology for determining optimal maintenance strategy, it is there-

fore necessary to define a model that would unite following de-

mands: 1) decoupling risk factors and related preventive actions,

2) determining strategy for long term period, and 3) simulta-

neous treatment of more components. This paper is dedicated

to these problems.

The proposed methodology in this paper determines an op-

timal plan of actions for multiyear maintenance schedule. It isbased on the risk approach and the model of decoupled failure

risk factors in distribution network. Risk approach enabled more

realistic modeling of component failure and estimation of ex-

pected consequences, while decoupling risk factors provided an

overview of quantitative influence of individual risk factors to

reliability and determining the optimal plan of selected actions

that have impact to individual risk factors. Within that method-

ology, the new model of state transition based on decision tree

diagram is also proposed. New state variables – number of years

since the last repair for each preventive maintenance action have

been introduced into this model. Introducing these new vari-

ables provides a simple modeling of state transition, as well as

0885-8950/$25.00 © 2007 IEEE



598 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 2, MAY 2007

ef ficient application of dynamic programming for solving the

model for multiyear period.

The paper consists of four parts. The first part is introduction.

The second part presents procedure for selective maintenance

schedule. Third part displays test results, while in fourth part a

conclusion is presented. Detailed display of objective function

calculation is given in the Appendix.

II. RISK MANAGEMENT PROCEDURE FOR

MAINTENANCE SCHEDULE

To determine an optimal multiyear maintenance scenario it

is necessary to analyze all possible scenarios and associate to

each of them appropriate expected risk. Finally, it is necessary to

choose the scenario that minimizes risk of emerging significant

operation costs by using appropriate criteria for risk evaluation.

For such analysis, the most suitable is the risk management ap-

proach that is a process whereby organization methodically ad-

dresses the risks attached to maintenance activities with the goal

of achieving sustained benefit within each activity and across all

activities.

The crucial step is to analyze, e.g., to assess consequences,

likelihood, and the level of risk. The first task in the process of

risk analysis is to determine the model of component failure. In

the model proposed in this paper, decoupling of risk factors and

analysis of risk increase in time was performed. Next, all pos-

sible preventive actions that set these decoupled risk factors to

initial value were overviewed. Lastly, each of these preventive

actions leads the system into a particular state in which evalu-

ating of consequences, or expected costs, is performed. Tran-

sition from one state to another is modeled through the state

transition model in form of decision tree. This model provides

multiyear evaluation of all possible scenarios and estimation of total expected costs associated with each scenario. The dynamic

programming technique is used for solving the proposed model,

or determining the optimal maintenance scenario. In the end,

the model extension for treatment of multiple components was

presented.

A. Risk and Decoupling of Risk Factors

In spite of considerable overlap in the word “risk ” and “re-

liability,” it is assumed that the two words have the identical

implication. Higher risk means lower reliability, and vice versa.

Risk and risk management has a wide-ranging content [16]. The

following definitions have been used in this paper: risk, failurerate, and risk factors.

Risk is defined as multiplication of probability that a failure

(fault) can happen, on one side, and expected value of costs that

cause this failure in the system, on the other side. The risk is

defined on the level of the considered system.

Failure rate ( ) describes probability of failure of the consid-

ered component, or the number of times per year that a compo-

nent can expect to experience a failure. Failure rate is defined on

the level of the component. Total failure rate of one component

can be decoupled to several different failure rates

(1)

Fig. 1. Failure rate for different influencing factors.

where th failure rates resulted from corresponding th risk

factor and is the number of influencing risk factors.

Each of the different failure rates is associated with one cor-

responding risk factor that influences reliability of this element.For example, different failure rates of one overhead line can be

caused by different risk factor influences (vegetation influence,

insulation and supporting equipment failures and faults due to

mechanical damage of the poles). The decoupling of failure rate

and corresponding risk factors provides more realistic overview

of quantitative influence of separate risk factors to reliability.

Decoupling is not based on technological separation (line sep-

aration to poles, insulators, disconnectors, etc.) but functional,

according to influential risk factor – vegetation related failures,

earth faults due to the pollution of insulators, etc. These indi-

vidual influences can be estimated based on statistics and mon-

itoring of line faults, and consequently, the appropriate function

for the increase of those individual factors in time can be de-

termined. In Fig. 1, an average diagram of failure rates for sev-

eral important parameters is presented, based on statistical data

of influencing parameters for the sum of 2000 km long 10 kV

overhead lines in Southern Serbia Distribution Company. This

figure shows that failure rates increase in time, unless preven-

tive maintenance actions are performed. Modeling of compo-

nent failure is mostly based on using constant failure rates as-

sociated with exponential probability distribution of staying in

particular states. However, failure rates are not constant but in-

crease in time. As the closest probability distribution of time du-

ration between faults has proven to be Weibull distribution that

realistically presents aging of equipment and increased failurerate in time [7]. With the use of selective maintenance model,

it is possible to use different probability functions, including a

Weibull distribution.

B. Preventive Maintenance Actions

Above-mentioned risk factors can be reduced by applying

preventive actions. For example, a) minor damages are solved

by inspection and minor repairs; b) major damages are solved by

larger overhauls; and c) vegetation influence is removed by trim-

ming the trees surrounding the power lines. In case in year one

of the mentioned actions is performed, the value of appropriate

failure rate for this particular factor drops to initial value. In thisway, the object after repair is not considered as being “new”, but



JANJIC AND POPOVIC: SELECTIVE MAINTENANCE SCHEDULE OF DISTRIBUTION NETWORKS BASED ON RISK MANAGEMENT APPROACH 599

TABLE IACTIVITIES IN OVERHEAD LINE MAINTENANCE

the risk is reduced only by the one risk factor for which a selec-

tive preventive or corrective action has been performed. This de-

composition to individual factors provides the influence impact

of separate maintenance actions to entire reliability of the dis-

tribution network. In general, possible actions that can be taken

during maintenance of one object are 1) not doing any mainte-

nance activity; 2) performing minor repairs and overhaul based

on inspection results; 3) performing overhauls in fixed intervals;

and 4) performing selective actions on a predefined timetable.

Some of these actions must be performed on no-load conditions,

and some under load. Detailed display of most frequent main-

tenance actions on an overhead line are given in Table I.

By decoupling individual risk factors it is possible to simul-

taneously overview several preventive maintenance actions. In

fact, each of the influencing factors is associated with one of the

actions, which contributes to selective approach that in bottomline reduces total costs.

C. Maintenance Model of Distribution System

Distribution system, for purposes of maintenance schedule

is modeled as technical system susceptible to aging. Several

models for reliability assessment and evaluation of risk take in

account aging of the system and influence of separate activities

[4]–[9], [16]–[19]. Choice of model depends on complexity of

the networks, available data, and requested accuracy of results.

Serial/parallel networks [18] models a distribution network

as connection of serial/parallel elements. Optimal interval

between activities is determined by Newton-Raphson method.This model optimizes only total failure frequency. In addition,

the results of using this model are always fixed intervals be-

tween preventive maintenance activities.

Marcov model is based on state space and it can model all

possible states that one object can be found in. Two basic as-

sumptions for applying this model are 1) the possibility of tran-

sition to the next state depends only on present state (and not

the way it was reached) and 2) rates of transition between states

are constant, which considers existence of exponential proba-

bility distribution of duration of staying in states. This model,

as well as modified stochastic Petri net model, is frequently

used in maintenance [4]–[6], [17], [19]. However, this model

has certain deficiencies. First, the Marcov model does not pro-vide dynamic overview of actions in long-term period, because

Fig. 2. Model of system aging (a) without decoupling and (b) with decoupling

( : system state in th moment of aging for th influencing factor, –fault).

the states in individual years are considered separately. More-

over, in this model, transition rates from individual states areunknown without large historical statistic data. Finally, in this

model, only exponential distribution of staying in certain states

can be applied, and this probability distribution does not match

the process of aging.

This paper proposes a decoupled model of state transition

where these deficiencies have been overcome. The proposed

model, unlike the ones previously mentioned, uses decision tree

as a model for transition from actual to the next state. Distri-

bution network is modeled as serial/parallel connection of el-

ements and its reliability is calculated through failure rates. A

maintenance model introduces new state variables – number of

years since the last selective action for each of the preventive

actions. One combination of state variables presents one systemstate at a particular moment. This state is characterized by ap-

propriate failure rates that depend on number of years since the

last performed action, for each action separately. Transition rate

from one state to another is defined by total costs of actions per-

formed in this state, or cost increase in case that these actions

were not performed. In this way, the state space is not consid-

ered in a stationary, but in a dynamic way.

Introducing of new variables provides simple modeling of

state transition as well as ef ficient application of dynamic pro-

gramming for solving combinatory problem such as mainte-

nance schedule for multiyear period. Additional improvement

has been achieved by decoupling the risk factors that influenceaging of the system. While in usual model of aging only aging of

the entire system is considered, Fig. 2(a), in decomposed model

the reliability of the system is calculated as sum of individual

failure rates that impact the reliability of the system Fig. 2(b).

It is assumed there is no mutual dependence between separate

influencing factors. In this way, by decoupling risk factors, the

analysis of different combinations of selective maintenance ac-

tions is available. For example, individual states within state

of line aging can be states of individual line components, or

different aging factors. Each of these actions can be influenced

by appropriate selective action directed only to a particular risk

factor (for example, cleaning of insulators improves only the

condition of insulation, trimming branches influences vegeta-tion related failures, etc.).




Fig. 3. Decision-tree for three-year maintenance scenario.

In each year, failure rates are changed for each of the in flu-

encing factors. Therefore, it is possible to apply random func-

tions of possibility distribution, especially Weibull’s, which best

considers systems prone to aging. The model assumes that ac-

tions are preformed in the beginning of the considered year and

that all risk values are calculated by values of failure rates at

this moment (Fig. 1). Executing each of the individual actions in

maintenance brings back a particular risk factor to initial value,

or failure rate. In this way, the influence of individual actions

has been considered in a more realistic way, so the number and

order of actions can be combined depending on state of aging

for the network.

D. Decision Tree for One Element

Decision tree for choosing selective actions in maintenance

of one overhead line for three-year considered period is pre-

sented in Fig. 3. Basic tree components are the decision node

(depicted as rectangle in Fig. 3) and chance node (depicted as a

circle in Fig. 3). In each node, decisions are defined as different

preventive maintenance scenarios ( ). These scenarios are

obtained by combining separate actions. Each of the scenarios

is presented with a branch that starts at the decision node and

terminates at the chance node. For each of the scenarios ( )

there is an appropriate number of possible outcome or conse-quences ( ) that depends on characteristics of the system itself.

Finally, is possible outcome with precisely de-

fined values of variables , ,, in state space. Each of these

consequences is presented with a branch that starts at the chance

node in Fig. 3. Subsequently, costs are calculated for each of the

consequences ( ). Costs of consequences in each of

the scenarios ( ) are formed by taken preventive ac-

tions for this scenario (e.g., costs of inspection and cleaning cor-ridor, cost due to undelivered energy and costs of repair works).

The method of calculating these maintenance costs and costs re-

sulting from faults is given in the Appendix.

Each path in presented tree (graph) represents one multiyear

scenario of preventive maintenance ( ). The transition

scheme for a line is given with three possible actions:

1) inspection and eliminating minor faults;

2) major line overhaul and eliminating major defects;

3) trimming trees surrounding the line.

The marks time in years since the previous action of type

( , 2, 3). If a certain action is not performed, the value of ap-

propriate variable is increased by 1 (element is 1 year older),

and if action has been performed, the value is set back to 0 (con-dition of the element is returned to initial for determined set of

influences eliminated by corrective action). Also, a scheme of

all possible transitions from initial state to all possible states in

the next time periods is given. By observing possible transitions

from the figure, it is clear that, for example state (0, 0, 0) in

second year matches feeder where all three actions were pre-

formed and all possible damaging influences eliminated. State

matches the feeder where inspection and elim-

ination of minor faults has been performed, but the time since

the previous major overhaul and trimming trees increases for 1.

With the scheme of possible transitions it is possible to consider

specifics also of the entire system in terms of various combina-

tions of maintenance actions.

This paper considers a practice that during line inspection

elimination of minor faults is performed also, but a system

where it is impossible to approach one of the actions unless

an inspection has been performed can also be considered.

Observing the tree in Fig. 4 can lead to a conclusion that the

number of possible states increases in geometrical progression

with years, but because of contraction of individual states, the

number of possible states is compressed, which reduces di-

mension of the problem. In this case, inspection itself does not

increase the reliability of the system, but the transitions from

one state to another without previous inspection are forbidden.

For the purpose of illustrating possible transitions, Fig. 4presents a scheme of transitions for initial state , ,

. The last actions on the line are performed before 2,

larger overhaul before 3 and tree trimming before 4 years.

However, Fig. 4 does not present a decision tree diagram and

it is not completely identical with Fig. 3. Actually, it displays

only possible transitions from one state to another. The aim of

this illustration is to show that not all transitions are possible,

or how much the number of states is reduced from year to year.

E. Application of Dynamic Programming

The graph in Fig. 3 clearly points to dynamic character of

decision making in maintenance process, which points to ap-plication of dynamic programming for determining the optimal




Fig. 4. Possible transitions for initial states and three periods.

multiyear scenario of preventive maintenance. Optimal mainte-

nance scenario ( ) is chosen based on maximum Ex-

pected Monetary Value (max EMV) criteria for ranking risks

[20]. This criterion for risk evaluation corresponds to mainte-

nance scenario in which the total expected costs of maintenance

are minimal

(2)

With the following constraints:

total expected costs in year ;

maximum allowed costs in year ;

, discount rate, planning period.

Dynamic programming uses algorithm of minimal path that

is based on well known recursive relation [21]

(3)

where

number of stages (years);

current period, ;

state label in period ;

control variable vector in period ;

value of control variable that minimizes

;costs of transition to state ;

Fig. 5. Part of decision tree for

lines.

budget constraint in year ;

cost contributions of stages to

objective function if system starts in state at

stage (year) , immediate decision is , and

optimal decisions are made thereafter:

(4)

Constraints in the proposed model are within budget pre-

dicted for conducting actions in maintenance and in available

number of teams for preventive actions. In case of violating con-

straints in one year, penalty factor is introduced that multiplies

achieved value of costs. This method provides finding a global

minimum.

F. Simultaneous Optimization of Multiple Components

For a distribution company that owns hundreds of lines, it is

necessary to coordinate all activities in maintenance, in order to

achieve the maximum effect, with simultaneous fulfillment of

constraints. The proposed model provides simultaneous obser-

vation of multiple elements of the system (several feeders in one

particular area). This is achieved by introducing -sets of state

for each element (Fig. 5). Each -set determines actions in th

element

Larger number of analyzed elements brings to progressive in-

crease of states in following periods (“curse of dimensionality”).

In this sense, searching for the global optimum can be cancelled

and the advantage should be given to certain methods for prior-

itization of maintenance. Prioritization in this case can be per-

formed also by objects that would carry the execution of activi-

ties and selection of maintenance activities themselves. The first

step in this process is an independent analysis for individual el-

ements of the system, according to proposed model. In second

step, the ranking of variants according to one of the accepted

parameters is performed [10], [22]. However, in this way it isnot possible to determine the global optimum of the system.




Fig. 6. Test network of 10 kV lines.

TABLE IIINPUT DATA FOR TEST CASE OF OVER HEADLINE

TABLE IIIBUDGET CONSTRAINTS PER YEAR

III. TEST RESULTS

The proposed methodology for maintenance schedule is veri-

fied on test network given in Fig. 6, with presented electrical pa-

rameters, while the other dates are given in Table II. Line failure

rate increases in time are given in Fig. 1. Budget constraints for

the considered period of five years are given in Table III.

In analyzed maintenance strategies three possible kinds of ac-

tions are considered: ) line inspection, ) clearing the cor-

ridor, ) major overhaul. The initial state in the network is rep-

resented in Fig. 6. denotes the length of power line (in km);

is failure rate of power line per one year and 100 km of lenght ( ), in the first year; is minimal,

TABLE IV

STATE VARIABLES WITHOUT PREVENTIVE ACTIONS

TABLE VCOMPLETE MAINTENANCE IN FIXED INTERVALS

and a maximal registered value of power on the beginning

of the power line (in MVA).

) The last inspection of the first line is executed 2 yearsago ( ), of second line one year ago ( ) and

third line two years ago ( ).

) corridor clearing, on the first line was performed three

years ( ), second line five years ( ) and third

line two years ago ( ).

) major overhaul of the first line was performed four

years ( ), second line three years ( ) and third

line two years ago ( ).

In the considered five year period, the following three main-

tenance strategies are analyzed.

I) Maintenance is not performed. State variables for this

case are given in Table IV.II) Application of complete preventive actions in fixed time

intervals, in the beginning of the first and the fifth year,

Table V.

III) Application of selective preventive actions in variable

time intervals, Table VI.

In Table VII, value of expected costs for three considered

strategies for maintenance schedule is given. If maintenance is

not performed, expected exploitation costs are 114 702 Euro.

Total expected exploitation costs are reduced for about 4% in

case when two network overhauls are performed (in the begin-

ning and in the end of the considered period). Radical reduc-

tion of total expected exploitation costs of 35% is obtained only

after the selective maintenance schedule is performed, that isproposed in this paper.




TABLE VI

SELECTIVE MAINTENANCE WITH VARIABLE INTERVALS

TABLE VIICOMPARISON OF COSTS FOR THREE MAINTENANCE STRATEGIES

IV. CONCLUSION

This paper presents a methodology for determining the op-

timal multiyear scenario of preventive maintenance that is based

on application of risk evaluation and risk management tools and

of dynamic programming technique. The essence of the pro-

posed methodology consists of decoupling the risk factors and

determining selective action plan, which provides that total risk

of expected operation costs in a particular time period is min-

imal. Analysis performed in this paper have shown that by appli-cation of one such sophisticated method the expected operation

costs are significantly reduced in comparison with usual tradi-

tional approach of applying overhauls in regular time intervals.

In this way, the proposed methodology can become an important

analytic tool in conditions of open competition where reducing

of operating costs in distribution networks has a great value.

APPENDIX

Total annual costs related to maintenance of an overhead line

consist of the following.

• Costs of line inspection and costs of eliminating minor

faults –• Costs of clearing corridors: .

• Costs of capital overhauls: .

• Costs of unplanned outages: .

• Costs of energy losses: .

As costs of energy losses, for the same feeder whose charac-

teristics do not change over years (diameter of the conductor),

are equal for the entire considered period, they will not be taken

in consideration.

Annual costs of preventive actions, marked with

, are presented with the following sum:

(A.1)

Inspection costs include the component of man power and

they are given with relation (A.2) Costs of eliminating minor

faults, include costs of material used during repairs noted in vi-

sual inspection. Visual inspection does not require switching off

the line, but during minor repairs the line is brought into off load

state. This is a planned power cut, so the costs of shut down

are calculated as costs of planned shut down. Besides the costsof single outage, the company suffers damage due to undeliv-

ered energy that is included by the last member in the following

expression:

(A.2)

price of one working hour necessary for inspection,

overhaul, or elimination of fault;

number of working hours necessary for inspection

per one kilometer;

price of used material necessary for minor repairsper one kilometer;

length of feeder;

cost per disconnected MVA for planned shut downs;

power at which is performed planned shut down;

duration of inspection;

total number of necessary shut downs for

performing inspection;

average selling price of one kWh;

annual load increase rate.

Other costs are presented in relations (A.3)–(A.4)

(A.3)

price of one working hour for corridor clearing;

number of working hours necessary for corridor

clearing per one kilometer;

total number of shut downs necessary for corridor

cleaning;

duration of corridor cleaning.

(A.4)

price of used material per one kilometer, necessary

for overhaul;

number of working hours necessary for overhaul

per one kilometer;

total number of necessary shut downs during

overhaul;

duration of overhaul.

(A.5)




price of used material necessary for fault

elimination;

number of working hours necessary for fault

elimination;

average duration of unplanned outage (fault);

cost per MVA of undelivered power for unplanned

outages;rate of average towards maximum power on the

line.

(A.6)

failure rate on feeder in year ;

failure rate depending on defects that could be

observed during inspection;

failure rate depending on branches grown in

feeder conductors;

failure rate depending on defects that could be

eliminated by overhaul.

(A.7)

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IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 928–933, Jul. 1999.[19] M. M. Hosseini, R. Kerr, and B. Randall, “An inspection model with

minimal and major maintenance for a system with deterioration andPoisson failures,” IEEE Trans. Rel., vol. 49, no. 1, pp. 88–98, Mar.2000.

[20] D. S. Popovic and Z. N. Popovic, “A risk management procedure forsupply restoration in distribution networks,” IEEE Trans. Power Syst.,vol. 19, no. 1, pp. 221–228, Feb. 2004.

[21] F. Hillier and G. Lieberman , Introduction to Operations Researchs.New York: McGraw-Hill, 2001.

[22] H. Willis, G. Welch, and R. Schrieber , Aging Power Delivery Infra-

structures. New York: Marcel Dekker, 2001.

Aleksandar D. Janjic (M’00) was born in 1966. He received the B.Sc. degree

in 1989 and the M.Sc. degree in 1999, both from the University of Belgrade,Yugoslavia.

He is currently working in the electric power industry in Serbia. His researchinterests are distribution systems planning, automation, and distribution man-agement systems.

Mr. Janjic is chairman of the distribution planning session of the CIREDNational Committee.

Dragan S. Popovic (M’95) received the B.Sc. degree from the University of Novi Sad, Yugoslavia, in 1985, and the M.Sc. and Ph.D. degrees from the Uni-versity of Belgrade, Yugoslavia, in 1990 and 1995, respectively.

He is currently a Professor with the Faculty of Engineering, University of Novi Sad. He has worked for many years in researching fields of bulk powersystem analysis, control, and stability. Presently he is engaged in researching

and developing application software for distribution management systems. Hehas also been the Project Manager on several projects in the field of distributionautomation and distribution management system.

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