Capacitor Placement for Conservative Voltage Reduction on Distribution Feeders

1360 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 3, JULY 2004

Capacitor Placement for Conservative VoltageReduction on Distribution Feeders

Borka Milosevic, Student Member, IEEE, and Miroslav Begovic, Senior Member, IEEE

Abstract—This paper proposes a strategy for placing capacitorsat multiple locations on a distribution feeder to allow: 1) deeperlevels of substation voltage reduction for peak load reduction; 2)power factor correction; and 3) power loss reduction. By reducingpeak demand, a utility can avoid paying high prices when pur-chasing power or it may sell excess generation at high prices. Byminimizing system losses, savings are obtained through reduceddemand and energy charges. Besides a positive economic response,load reduction associated with improved power factor at the sub-station has a beneficial effect on voltage stability by increasing thesystem stability limit margin.

Index Terms—Capacitor placement, load reduction, nondomi-nated sorting genetic algorithm (NSGA), voltage reduction.

I. INTRODUCTION

COMMON UTILITY practice regarding operation of distri-bution system is to keep voltage profile on a feeder within

limits under all load constraints. The American National Stan-dards Institute (ANSI) requires that voltage be supplied to resi-dential customers at . To maintain the voltages ac-ceptable at the service point, the voltage at substation needs tobe kept at high enough values as the power demand increases.This typically increases load consumption.

Since appliances, such as lights bulbs and other electrical de-vices operate efficiently at reduced voltages, utilities can pro-vide service at the lower end of the acceptable voltage with nodetriment to the customers. Both the utility and customers ben-efit from voltage reduction at the substation level. The utilitynot only saves energy and capacity when the spot-market en-ergy prices are high, but also increases the system voltage sta-bility margin [1]. Customers save money on electricity bill, be-cause voltage-sensitive loads tend to consume less power whensupplied at a lower voltage, while the life of appliances are ex-tended.

The improvement of the power factor has a beneficial effecton the system voltage stability [2]. As the power factor im-proves, the system voltage margin increases. It is advantageousto keep the power factor close to the unity.

Normally, capacitors are installed on distribution feeders forpower loss reduction. However, if adequately sized and installedalong the feeder, capacitors can be used to regulate the volt-ages on the feeder and the power factor at the substation [3].When the voltage level is reduced at the substation during thepeak times, capacitors provide acceptable voltage levels to thecustomers throughout the feeder. The reduction of voltage level

Manuscript received October 22, 2002.The authors are with the Department of Electrical and Computer Engi-

neering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPWRD.2004.824400

would force all voltage dependent loads to decrease power con-sumption; therefore, the need for costly generation would beavoided at the peak load times. The percentage of power re-duction per volt reduction, and, therefore, the benefit/cost ratio,depends on the feeder load characteristic. It increases when thevoltage dependence of the load changes from a constant powertype to a constant impedance type. During the off-peak times,some of the installed capacitors can be controlled for powerfactor correction, loss reduction in both transmission and dis-tribution systems, and load reduction when necessary.

II. CAPACITOR PLACEMENT METHODOLOGIES

In the past, many capacitor-placement methodologies havebeen proposed [4]–[8]. The general capacitor problem is definedas a problem of finding the optimal locations and sizes of capac-itor batteries, such that the cost of energy loss and the cost ofcapacitors are minimized, and operational constraints satisfiedunder different load conditions. The authors [4]–[8] assumedloads on the feeder being of constant power types. The solu-tion techniques range from nonlinear programming techniques,mixed-integer programming techniques, to methods based ona heuristic search techniques, such as simulated annealing, ge-netic algorithms and tabu search [9]. However, none of the pro-posed methods optimizes the placement and capacitor sizes forvoltage profile improvement and power factor correction. Thesemethods were used only to minimize the total energy and capac-itor costs.

In this paper, a new formulation for the capacitor placementis proposed, and a specially tailored nondominated sorting ge-netic algorithm (NSGA) is used as a solution. The problem isto find optimal locations of capacitor banks along the feeder,enabling it to enter into deeper voltage reduction modes duringemergencies, as well as to function as a loss-efficient mecha-nism during normal operation. This is a multiobjective problem,which can be efficiently solved using the concept of Pareto op-timality, based on a suitable designed NSGA.

III. PROBLEM FORMULATION

A capacitor placement problem is a mixed-integer, multiob-jective, nondifferentiable optimization problem with a numberof equality and inequality constraints, as follows:

(1)

0885-8977/04$20.00 © 2004 IEEE

MILOSEVIC AND BEGOVIC: CAPACITOR PLACEMENT FOR CONSERVATIVE VOLTAGE REDUCTION ON DISTRIBUTION FEEDERS 1361

where are the objectives, , is a vector of de-cision variables, i.e., sizes of capacitor banks at specified loca-tions, is a state vector, are the power-flow constraints,

and are the power factor, measured at the substation,and its lower permissible limit, respectively, is the voltage atbus , is the total number of the feeder buses, andare the lower and the upper limits of the permissible voltagevariation on the feeder, and superscript “ ” stands for “permis-sible”.

A. Objective Functions

1) Minimize the Deviation of the Bus Voltages, , WithRegard to the Substation Voltage: This objective attempts toflatten the voltage profile along the feeder

(2)

where is the voltage deviation of bus withrespect to the substation voltage and is the total number ofthe feeder buses.

2) Minimize the Active Power Loss in the Feeder, loss: Theactive power lost in a line depends on the line parameters andthe voltage drop across the line

loss (3)

where is a set of doubles whose elements are indices ofbuses connected by the line segments, and are the re-sistance and the impedance of the segment connecting busesand , and is a voltage drop across the line segment con-necting buses and .

3) Minimize the Total Active Power Demand at the Substa-tion : When the feeder has a voltage-dependent load charac-teristic, voltage reduction at the substation can be used for loadmanagement

(4)

where is the active load at bus given as a function of thebus voltage , load and loss are the total load demand andtotal active power loss in the feeder, respectively, and , ,and are as defined in (3).

4) Minimize Capacitor Cost, : The capacitor cost con-sists of two terms. The first term denotes the purchase cost,while the second term represents the installation and mainte-nance costs

(5)

where is the number of capacitor locations, is the annualinstallation and maintenance cost ($/year), is the annual pur-chase capacitor cost ($/kVAr-year), and is the size of the ca-pacitor(s) installed at the corresponding location, .

Note that the processes that govern the voltage flatteningalong a feeder, substation power factor improvement, loadreduction, and loss reduction may be conflicting. Flattening ofthe feeder voltage profile reduces the active power loss loss,but it may increases the loads load. The voltage-dependentloads decrease, while the active power losses may increase witha decrease of voltage applied at the substation. The subsequentimprovement of the substation power factor positively affectsboth load reduction and loss reduction. However, both leadingand lagging power factors cause line losses to increase.

B. Constraint Violation Functions

The problem of satisfying a number of (in)equality con-straints is the multi-objective problem of minimizing thecorresponding constraint violation functions, until the solu-tion feasibility is reached. In the capacitor placement problem(1), the constraint violation functions are defined as follows:

(6)

where

otherwise(7)

IV. OPTIMAL CAPACITOR PLACEMENT METHODOLOGY

The methodology is based on the following observations.

• To perform voltage reduction at the substation, the feedermust have a voltage profile sufficiently above the min-imum allowed voltage delivery levels.

• The voltage profile is to be supported by adding capacitorsalong the feeder.

• The capacitor costs have to be justified by revenues (ordecreased expenditures).

• The wholesale energy price is neither fixed nor guaran-teed. Consequently, the benefits of voltage reduction mayvary considerably with time.

• The number of capacitors that are required to enable ef-fective load management through the substation voltagereduction is generally higher than the number of capaci-tors that are necessary for loss reduction. It is, therefore,advantageous to add the same group of the capacitors onthe feeder for both voltage support during the peak times,when the substation voltage is reduced, and during theoff-peak times, when loss reduction is of concern.

In this context, the following methodology for the capacitorplacement along the feeder is proposed.

Step 1) Assuming the peak load conditions,

add a minimum number of capacitor banks on

the distribution feeder, necessary to flatten

the voltage profile, while keeping the power

factor in a small band around the unity (0.99

lagging/leading). That is, simultaneously


Fig. 1. Voltage profile along a distribution feeder during the peak hourswithout (–) and with (-) voltage reduction at the substation.

optimize objectives (2) and (5) until the fol-

lowing conditions are met:

pf � 0:99 (lagging or leading)

0:95 �Vj � 1:05 j = 1; . . . ; N: (8)

Step 2) Estimate the range in which the sub-

station voltage, V , can be varied during the

peak times so that the end-of line voltage is

acceptable (see Fig. 1). That is V 2 [V pmin+fV ;

V pmax], where V

p

min and V pmax are the minimum and

maximum allowable voltages on the feeder, and

fV is the maximum acceptable voltage drop on

the feeder found in the previous step.

Step 3) Having installed the capacitors on the

feeder, as suggested in Step 1, analyze the

effects of the substation voltage reductions

on the load/loss reduction.

Step 4) Chose a new (lower) value for the sub-

station voltage, Vsp 2 [V p

min + fV ; V pmax].

Step 5) Lower the substation voltage V to a

desired voltage level Vsp. Determine the op-

timal locations, types and number of capacitor

banks to minimize both the active power demand

at the substation (4) and the active power

loss (3) under constraints (8) during the peak

hours. Analyze the results. If the results

do satisfy the decision maker (DM) (in terms

of the total active load reduction and loss

reduction), proceed with the next step. Other-

wise, return to Step 5.

Step 6)Optimally control the capacitors during

the off-peak hours so that the active power

losses (3) are minimized under the power-flow

constraints, and the following voltage and

power factor constrains are satisfied:

pf � 0:95 (lagging)

0:95 �Vj � 1:05 j = 1; . . . ; N: (9)

During the off-peak hours, the power factor

requirements may be relaxed.

Step 7)Perform the cost/benefit analysis.

A. Cost/Benefit Analysis

The benefits are obtained from load and loss reductions, whilethe cost depends on the prices of capacitor banks and their in-stallation costs. A reduction in peak demand decreases the needto build new generation and/or transmission facilities (avoidedcapacity)

loss

(10)

where is the annual cost of new generation ($/kW-year),is the cost of per unit energy during the peak times ($/kWh),is the cost of per unit energy loss ($/kWh) at any load level

with a time duration ( ), is the system peakload reduction, is the feeder peak active power demandat load level , and , , and are as defined in (5).

V. MULTIOBJECTIVE OPTIMIZATION

A multicriteria optimization problem requires simultaneousoptimization of a number of objectives with different individualoptima [11], [14]. Objectives are such that none of them canbe improved without degradation of another. Hence, insteadof a unique optimal solution, there exists a set of optimaltrade-offs between the objectives, the so-called Pareto-optimalsolutions. Depending on how the DM values the objectives,different Pareto-optimal solutions may be more appropriate. Inmultiobjective optimization, the solutions are compared witheach other based on nondominance property.

A. Concept of Nondominance

For a multiobjective problem having objective functions tobe simultaneously minimized, a solution is said to dominatethe other solution if is better than for at least one objective

and is not worse for any other , where and.

(11)

The symbol “ ” denotes domination operator, and index “ ”refers to the objective functions. A solution , which dom-inates any other solution ( , and denotes the en-tire search space), is called a nondominated solution in . Thesolutions that are nondominated over the entire search spaceare called Pareto-optimal solutions.

Note that the single objective optimization is a special caseof the multi-objective optimization. For a single objective op-timization problem, the principle of nondomination (13) trans-lates to: The solution dominates the solution , if

, where is the objective function to be minimized.

B. Genetic Algorithms (GAs)

GAs, known for their good features [11], are widely used tosolve a broad range of single objective optimization problems.GAs can deal with qualitatively different types of variables, such


Fig. 2. Population ranking into fronts and the crowding distance calculationin a biobjective minimization problem [14].

as continuous variables, discrete variables, or mixed-type vari-ables. They do not require any knowledge of gradient informa-tion about objectives to be optimized. Moreover, GAs can easilyincorporate the nondominance principle into their search algo-rithm to successfully solve the conflicting optimization prob-lems [11]–[15]. Since they are population-based, GAs are ca-pable of finding a number of Pareto-optimal solutions in a singlerun. In addition, GAs are less susceptible to the shape, or con-tinuity of the Pareto front than traditional programming tech-niques. Nondominated sorting genetic algorithms (NSGAs) arethe multiobjective GAs that have been proven to perform thebest in finding Pareto-optimal solutions, and dispersing them onthe Pareto-optimal front [13]–[15].

VI. NSGA FOR CAPACITOR PLACEMENT PROBLEM

In NSGA, the concept of nondominance is used to rank thepopulation (see Fig. 2). Front 1 and rank identifier areassigned to the nondominated individuals in the population. Allindividuals in the first front are then temporally discounted, andthe rest of the population is classified to find nondominated in-dividuals forming front 2. This process continues until all frontsare identified. The lower the rank value, the more dominated anindividual will be.

A. Constrained Domination Operator

To handle the constraints, the objective function domination

operator in (11) is redefined as follows:

(12)

That is, every feasible solution dominates every infeasible so-lution . If and are two infeasible solutions then dominates

if has smaller constraint violation for at least one constraintthan , and it not worse for any other constraint. The symbol“ ” denotes domination operator with respect to the constraintviolation functions denoted as “ ”. The symbols and de-note the feasible and the unfeasible parts of the search space

. When the population is sorted for nondominance,the infeasible individuals will be at the end of the list. Their rankis directly related to the extent to which they violate the imposedconstraints.

The nondomination constraint operator forces feasible solu-tions to evolve toward optimal ones by imposed objective func-

tions, and the infeasible solutions to evolve toward feasible onesby the imposed constraint violation functions.

B. Crowded Comparison Operator

This operator ranks the individuals that belong to the samefront, i.e., it ranks the individuals that share the same nondom-ination properties. When the crowded comparison operator isapplied on two solutions with different nondominated levels(ranks), the preference is given to the solution with the lowerrank. When both solutions belong to the same front, the prefer-ence is given to the solution that is located in the lesser-crowdedregion (according to some metric):

(13)

where , denotes the individual’s rank identifier. Theis so-called crowding distance of a solution (see Fig. 2)

and represents the size of the largest polytope containing point“without including any other point in the population” [14]. By

giving a greater chance of reproducing to the isolated individ-uals, the crowded comparison enforces competition among theindividuals belonging to the same front and having the similarobjective function values. Therefore, the crowded comparisonhelps to keep diversity in a population.

C. Algorithm

In -location -capacitor banks problem, the decision vari-ables, , are the sizes of capacitor banks at specified locations.Those are not coded, but real-valued variables. The size of thesearch space is . Each individual within the populationrepresents a candidate solution of the capacitor bank problem.Lengths of all individuals are the same and equal to the numberof candidate locations .

The algorithm begins with a population of randomly selectedinitial solutions. Each of these initially picked members of the

population is evaluated for fitness with respect to each objectivefunction in (1) and for each constraint violation function in (6).Thereafter, the members of the population are reproduced tocreate the next population.

Population Ranking: All members of the population areranked according to the level of nondomination (see Fig. 2) byusing the constrained nondomination operator (11).

Density Estimation: Besides the front identifier, , thecrowded distance attribute is assigned to every individual inthe population [14]. It is suitable defined as

(14)

where

(15)

The value represents the distance of the th individualfrom the closest individuals in the front with respect to the-th objective function. The and define the range of

objective function values.


TABLE ILOAD DURATION DATA

TABLE IIBASE CASE POWER-FLOW RESULTS FOR THE 69-SEGMENT

Reproduction, Crossover, and Mutation: The mating pool isformed by the binary tournament selection process. Thereafter,a single-point crossover is first applied, and later mutation [11].The binary tournament selection works as follows: 1) choosetwo individuals from the population randomly; 2) compare theselected individuals by using the crowded comparison operator(13); 3) copy the better of the two individuals into the interme-diate pool; and 4) repeat this procedure times, where rep-resents the population size.

Additional Nondominated Sorting: The algorithm retains thesolutions with good nondominated characteristics (the “elite”)found so far. After producing new individuals through crossoverand mutation, the algorithm creates a pool by combining theparent and progeny populations. Thereafter, it sorts the individ-uals from this combined pool according to nondomination andselects the best solutions.

The termination condition for the algorithm is either apredefined maximum number of generations to be executed,or any other suitably defined exit strategy.A summary of thepower-flow solutions before capacitor placement and substa-tion voltage reduction is given in Table II. The results indicatethat the system has a high voltage drop and a low power factor.

VII. RESULTS

The proposed methodology has been tested on the modified69-segment, 9-lateral feeder studied in [5]. For voltage reduc-tion to be effective, a feeder must have a significant componentof the impedance load types. Therefore, it is assumed that the69-sement feeder has a voltage-dependent load characteristic(10% are the constant power loads, and the remaining 90% arethe impedance type loads). Load levels and load duration dataare given in Table I.

For the sake of example, somewhat random, but reasonablechoice of parameters has been made. The nominal price of theenergy on the open market is in the range from 0.02 to $0.05per kilowatt hour. During the peak times, the energy pricesmay assume values from 0.05 $/kWh to 0.5 $/kWh. It is assumedthat the annual new generation cost .The constants adopted for capacitor marginal costs and for thecapacitor fixed costs are and ,respectively. The other assumptions are: 1) the size of one ca-pacitor bank is 300 KVAr; 2) the maximum number of capacitorbanks at each location is 6; and 3) the substation has a regu-

TABLE IIISUMMARY OF TEST RESULTS FOR LOAD LEVEL L = 1:0 P:U

Fig. 3. Feeder voltage profiles corresponding to the capacitor placementsolutions in Table III.

TABLE IVPOWER-FLOW RESULTS FOR THE CAPACITOR PLACEMENT SOLUTIONS

PRESENTED IN TABLE III (L = 1 P:U)

lating transformer with tap range and 10 tap positions. Inall the experiments, the crossover probability and the probabilityof mutation are set to 0.9 and 0.01, respectively. Experiments areconducted for a fixed number of generations.

A. Peak Load Conditions

Initially, a minimization optimization problem is solved withthe objectives (2) and (5), under the power-flow conditions andthe constraints given in (8), assuming the peak load conditions,

and the base case substation voltage . All thebuses are considered as candidate locations for capacitor place-ment. The size of the search space is 2.05 . The chosenpopulation size and the maximum number of iterations are setto 1000 and 500, respectively.

The optimal tradeoffs between the minimum voltage devia-tion objective and the minimum cost objective are pre-sented in Table III, while the corresponding voltage profiles areillustrated in Fig. 3. Jumps in voltage come from buses being indifferent laterals.

Table IV shows the power savings that could be achieved witheach of the capacitor placement solutions from Table III by re-ducing the substation voltage to the lowest allowable value. The


Fig. 4. The optimal tradeoffs, i.e., the Pareto-optimal solutions, obtainedamong the three objectives: 1) maximum power reduction at the substation;�P ; 2) maximum loss reduction�Ploss; and 3) minimum capacitor cost f .

TABLE VSUMMARY OF THE DATA PRESENTED IN FIG. 4 (�V = 5%)

results are sorted in descending order of the peak power reduc-tions . The case when the substation voltage is reduced to 1p.u. results in the largest peak power and power loss savingsand loss, respectively. The power savings would be higher ifcapacitors were optimally placed/sized for the maximum powerload/loss reduction while the substation voltage is reduced to 1p.u. Results in Tables III and IV are only provided to give anidea about theacceptable voltage reductions at the substation,total costs, and the kilowatt benefits associated with differentsolutions.

In the next step, the substation voltage is reduced to( ) assuming the peak load conditions .

The capacitor locations on the feeder, and their sizes, are deter-mined by simultaneously optimizing the following objectives:1) minimize the total active power demand at the substation, ;2) minimize the active power loss loss; and 3) minimize thecapacitor cost . The first and the second objective translate to:1) maximize active power reduction at the substation, and2) maximize active power loss reduction, loss, with respectto the base case (see Table II), respectively. All the feeder busesare still assumed as candidate locations. Fig. 4 shows the optimaltradeoffs among the three objectives, i.e., the Pareto-optimal so-lutions. The total number of solutions is 65. Refer to Table V fora summary of the results obtained in this step.

B. Off-Peak Load Conditions

The results shown in Table V are satisfactory. For each can-didate capacitor placement solution, the substation voltage re-duction of 5% results in the andthe .

During off-peak hours, the installed capacitors are optimallycontrolled for maximum loss reduction. The kilowatt savingsobtained at different load levels are shown in Fig. 5.

Fig. 5. Power loss reduction at different load levels that would be achieved byoptimally controlling the capacitors installed at candidate locations found in theprevious step (see Fig. 4).

Fig. 6. Frequency comparison between the fitted distribution (line graph) andthe distribution of measurements (bar graph) for (a) peak energy prices and(b) off-peak energy prices in the zone NP15, North California, 1999 [16].

C. Cost/Benefit Analysis

Because of the volatility in electricity prices, the net revenuefrom the capacitors added for load power and loss reductionscannot be calculated deterministically, but it can be determinedprobabilistically. Fig. 6 shows the frequency distributions of thepeak and the off-peak energy prices in the zone NP15 (NorthernCalifornia) in 1999 [16], along with the fitted theoretical distri-bution functions.

The Kolmogorov-Smirnov (K-S) goodness-of-fit test [17] isused to decide what distribution models the best zone NP15 en-ergy price data. The result of the K-S test is the so-called “fit-ting test statistic”, which represents the largest vertical distance

between a sample cumulative distribution function (cdf) anda fitted cdf. Any distribution probability fit that has a value ofthe test statistic below the critical value could be accepted.

The peak energy price tends to follow a gamma distribu-tion

(16)

where is the gamma function and , , and are location,shape, and scale parameters, respectively. The maximum like-lihood estimates for the parameters of the gamma distribution,fitting the NP15 peak prices in 1999, are ,

, and . The distribution test statistic is


Fig. 7. Cumulative probability distribution (cdf) of annular dollar savings frompeak load relief and loss reduction obtained with capacitors optimally placedand controlled on the 69-segment feeder with 4.9-MVA peak load.

TABLE VISUMMARY OF THE TEST RESULTS SHOWN IN FIG. 7

, while the critical value is 1.1981, assuming 0.05 signifi-cance level. The range of observed peak energy prices is dividedinto 50 classes.

The off-peak energy price is modeled as a triangular dis-tributed random variable with the density (17). A triangular dis-tribution describes well the sample in which values near the min-imum and maximum are less likely to occur than thosenear the most likely value . We have

(17)

where . The distribution parameters are ex-tracted from the data in Fig. 6(b): , , and

. The distribution test statistic is equal to ,which is much smaller than the critical value 0.1981, determinedfor 0.05 significance level. The number of the off-peak priceclasses is 50. Based on the K-S test, the triangular distributionis suitable for modeling the off-peak energy prices in Fig. 6(b).

A number of simulations is run to evaluate the annual dollarsavings, , associated with each of 65capacitor placement alternatives, using the accepted peak andoff-peak price distributions (16), (17), respectively. Fig. 7shows the cdf chart of the annual dollar savings found after25 000 runs. The cdf gives the probability that the variabletakes a value less than or equal to some specified value .

Table VI shows the percentiles, which represent the certaintylevel of achieving a profit below a particular threshold. Theand represent minimum and maximum dollar savings atdifferent percentile levels. There is 0% chance that any of thecapacitor placement alternatives will result in an annual dollarsavings less than $22 093 per year. When there are no intersec-tions among the cdf curves (as it is in this example), the cdf on

TABLE VIIOPTIMAL CAPACITOR LOCATIONS AND SIZES FOR SOLUTIONS #3 AND #4 AT

DIFFERENT LOAD LEVELS

TABLE VIIISUMMARY OF THE RESULTS FOR SOLUTIONS #3 AND #4

the far right of the cdf chart defines the best alternative for ca-pacitor placement. That solution offers the best opportunity forachieving the highest annual dollar savings at every confidencelevel of all solutions, and it is denoted as optimal. If the cdfcurves, which correspond to the different capacitor placementalternatives, intersect, the best solution is the one that gives thehighest savings with the predefined certainty level.

In this example, the optimal solution is #3. The next best alter-native is #4. Table VII shows the capacitor locations and sizes atdifferent load levels. As can be seen, solutions #3 and #4 differin capacitor locations, but not in sizes. The capacitor types (fixedor switched) can be determined by looking at the table. The sizeof a fixed capacitor installed at the certain location is determinedas the minimum capacitor size required at any load level. Allother capacitors are assumed switched capacitors in 300-kVArincrements. Power-flow data for capacitor placement solutions#3 and #4 are shown in Table VIII. Note improvements in powerfactor and voltage profile at all load levels.

VIII. CONCLUSION

In this paper, a new strategy for capacitor placement problemhas been presented, and a specially tailored nondominatedsorting GA has been proposed as a solution algorithm. Thecapacitor placement problem is defined as optimal allocation ofthe reactive resources along the feeder, which would enable it toenter deeper voltage reduction modes during the emergencies,as well as to function as a loss-reduction mechanism duringnormal operation. The algorithm allocates the capacitors onthe feeder so that the same group of the capacitors is used for


both the end-of-line voltage support during the peak times, andduring the off-peak times, when loss reduction is a concern. Theinstalled capacitors support the voltage profile along the lineduring the peak hours so that voltage reduction does not com-promise the quality of the customer supply. When calculatingthe net revenue from the capacitors, the proposed algorithm forcapacitor allocation takes into account the volatility in energyprices.

REFERENCES

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[14] K. Deb, S. Agrawal, and A. Pratap, “A fast elitist non-dominated sortinggenetic algorithm for multi-objective optimization: NSGA-II,” IndianInst. Technol., Kanpur, India, Tech. Rep. 200 001, 2000.

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Borka Milosevic (S’98) received the B.S. degreefrom the University of Belgrade, Belgrade, Yu-goslavia, in 1992 and the M.S. degree from GeorgiaInstitute of Technology, Atlanta, in 1998, both inelectrical engineering. She is currently persuing thePh.D. degree at Georgia Institute of Technology.

From 1994 to 1997, she was a Research Engineerat the Electrical Engineering Institute “NikolaTesla” in Belgrade. Her research interests includepower system security assessment and stabilityand application of multi-agent systems and genetic

algorithms to power systems monitoring and control.

Miroslav Begovic (S’87–M’89–SM ’92) receivedthe B.S. and M.S. degrees, both in electricalengineering, from Belgrade University, Belgrade,Yugoslavia, and the Ph.D. degree in electricalengineering from Virginia Polytechnic Institute andState University, Blacksburg.

He is currently an Associate Professor in theSchool of Electrical and Computer Engineering,Georgia Institute of Technolog, Atlanta. His interestsare in the general area of computer applications inpower system monitoring, protection and control,

and design and analysis of renewable energy sources.

Documents

Capacitor Placement for Conservative Voltage Reduction on Distribution Feeders