Optimal Distributed Generation Allocation and Sizing in Distribution Systems via Artificial Bee Colony Algorithm

2090 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 4, OCTOBER 2011

Optimal Distributed Generation Allocationand Sizing in Distribution Systems via

Artificial Bee Colony AlgorithmFahad S. Abu-Mouti, Student Member, IEEE, and M. E. El-Hawary, Fellow, IEEE

AbstractDistributed generation (DG) has been utilized insome electric power networks. Power loss reduction, environ-mental friendliness, voltage improvement, postponement ofsystem upgrading, and increasing reliability are some advantagesof DG-unit application. This paper presents a new optimizationapproach that employs an artificial bee colony (ABC) algorithm todetermine the optimal DG-units size, power factor, and locationin order to minimize the total system real power loss. The ABCalgorithm is a new metaheuristic, population-based optimizationtechnique inspired by the intelligent foraging behavior of the hon-eybee swarm. To reveal the validity of the ABC algorithm, sampleradial distribution feeder systems are examined with different testcases. Furthermore, the results obtained by the proposed ABCalgorithm are compared with those attained via other methods.The outcomes verify that the ABC algorithm is efficient, robust,and capable of handling mixed integer nonlinear optimizationproblems. The ABC algorithm has only two parameters to betuned. Therefore, the updating of the two parameters towards themost effective values has a higher likelihood of success than inother competing metaheuristic methods.

Index TermsArtificial bee colony (ABC), distributed genera-tion (DG), metaheuristic optimization algorithm, power losses re-duction.

NOMENCLATURE

Number of buses.Real power flows from bus to bus .Reactive power flows from bus to bus .Real power load at bus .Reactive power load at bus .Bus voltage at bus .Resistance of line connecting buses and .Reactance of line connecting buses and .Real power loss between buses and .Active power magnitude injected at bus .

Manuscript received August 12, 2009; revised March 13, 2010; accepted May13, 2011. Date of current version October 07, 2011. Paper no. TPWRD-00609-2009.

The authors are with the Department of Electrical and Computer Engineering,Dalhousie University, Halifax, NS B3J 1Z1 Canada (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2011.2158246

Reactive power magnitude injected at bus .Real power multiplier set to zero when there isno active power source or set to 1 when there isan active power source.Reactive power multiplier set to zero when thereis no reactive power source or set to whenthere is a reactive power source.System voltage at bus .

Specified allowable voltage value.

System apparent power flows from bus to bus.

System apparent power flows from bus tobus .System rated apparent power flows from bus tobus or vice versa.Minimum distributed generation (DG)-unit sizein kilovolt amperes.Maximum DG-unit size in kilovolt amperes.Minimum DG-units operating power factor.

Maximum DG-units operating power factor.Apparent power load at bus .

I. INTRODUCTION

B ECAUSE of the considerable advantages of DG-unitapplication (e.g., power loss reduction, environmentalfriendliness, voltage improvement, postponement of systemupgrading, and increasing reliability), there has been a signif-icant rise in interest by researchers. Practical application ofthe DG-unit, however, proves difficult. Social, economic, andpolitical factors affect the final optimal attained solution.

Solution techniques for DG-unit deployment are attained viaoptimization methods. The DG-unit application can be inter-preted as a mixed integer nonlinear optimization problem. Usu-ally, it includes maximizing the system voltages or minimizingpower loss and cost. The solution criteria vary from one appli-cation to another. Therefore, as more objectives and constraintsare considered in the algorithm, more data is required, whichtends to add difficulty to implementation.

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ABU-MOUTI AND EL-HAWARY: OPTIMAL DG ALLOCATION AND SIZING IN DISTRIBUTION SYSTEMS 2091

Optimization tools have been employed to solve differentDG-unit problems. Tools such as genetic algorithm (GA), evo-lutionary programming (EP), and particle swarm optimization(PSO) are promising and still evolving in this field. Some ofthose techniques have been modified to enhance their solutionperformance or to overcome other limitations. In addition, mostof these tools have many parameters to be tuned.

A methodology for evaluating the impact of DG-units onpower loss, reliability, and voltage profile of distribution net-works was presented in reference [1]. The authors represented aDG-unit as a PV bus that is different from what radial distribu-tion feeders are designed for. The authors implied that on-linesystems including DG-units can achieve better reliability duringinterruption situations to keep customers supplied. The authorsstated that the simplest representation of DG-units operatingin parallel with the system, especially in radial feeders, is asnegative active and reactive power injections, independent ofthe system voltage at the terminal bus. When using multipleDG-units as PV configurations, it is unrealistic to manage theseDG-units as available for dispatching because they may not becontrolled by the utility. According to the IEEE standard, dis-tributed resources (DR or DG) are not preferred to regulate thevoltage (i.e., PV-bus) at the point of installation [2]. Distributionsystems were designed for one-way power flow (i.e., from theutility power source to the end user). The insertion of DG in thedistribution system violates this basic assumption and can dis-rupt distribution operation if not carefully employed, potentiallycausing islanding, protection disturbances, upset voltage regu-lation, and other power quality problems. DGs normally followthe utility voltage and inject a constant amount of real and reac-tive power [3].

In reference [4] the optimal size and location of DG-unit(for planning purposes) based on a predetermined power lossreduction level (up to 25%) were proposed. The objective ofthe method was to reach that level with minimum net DG-unitcost (i.e., DG-unit cost subtracted from saving). The maximumnumber and size of the DG-units was found to be two and 40%of peak loads, respectively. The solution was achieved using se-quential quadratic programming.

Maximizing the voltage support in radial distribution feedersusing a DG-unit was discussed in [5]. The method used a voltagesensitivity index to determine the DG-units optimal location.Then, the DG-unit active and reactive powers were adjusted toobtain maximum voltage support. The weakest bus was identi-fied using Thevenins theorem.

Minimizing power loss by finding the optimal size, locationand operation point of DG-unit was suggested in [6]. A sensi-tivity analysis relating the power loss with respect to DG-unitcurrent injection was used to identify the DG-unit size andoperation point. The proposed method was tested for constantimpedance and a constant current model. One of the test sys-tems assumed that loads were uniformly distributed, which israre in practical feeder systems. The location of the DG-unitwas based on the assumption of downstream load buses, whichmay not be appropriate for different feeder configurations.

The authors of [7] employed the GA for optimal power flow(OPF) to minimize the DG-units active and reactive power cost.Two examples of DG-unit optimization cases were considered,

Fig. 1. Single-line diagram of a two-bus system.

with and without reactive power injection. Significant reductionin the search space was attained by eliminating the DG-unit size.However, DG-unit dispatching can cause operational problemsin the distribution feeders.

An algorithm was offered in [8] to maximize the reduction ofload supply costs as well as operational schedules for all feederload levels exploiting EP. The optimal solution was selectedbased on maximum cost reduction, which was attained throughevaluating the cost of DG-unit supply scenarios based on thebase case.

The authors of [9] proposed an analytical method to calculatethe optimal DG-unit size. In addition, an approximate loss for-mula to identify the optimal DG-unit placement was suggested.The method offered was based on the exact loss formula. Thepower flow was employed twice, with and without the DG-unit.The adopted DG-unit injected only active power.

In this paper, a new optimization approach that utilizes an ar-tificial bee colony (ABC) algorithm to determine the optimalDG-units size, power factor, and location in order to minimizethe total system real power loss is proposed. Sample feeder sys-tems are examined, as well as various test cases. The resultsreveal that the ABC algorithm is efficient, fast-converging, andcapable of handling complex optimization problems.

The remainder of the paper is organized as follows. Section IIIpresents the mathematical formulations of the problem, Sec-tion IV explains the ABC algorithm, Section V describes theABC algorithm in solving the DG-unit application, Section VIincludes results and discussion, and Section VII outlines theconclusions.

II. PROBLEM FORMULATIONOne advantage of deploying a DG-unit in distribution net-

works is to minimize the total system real power loss while satis-fying certain operating constraints. In other words, the problemof DG-unit application can be interpreted as finding the optimalsize and location of that DG-unit to satisfy the desired objec-tive function subject to equality and inequality constraints. Re-liability, accuracy, and flexibility of the DG-unit solution algo-rithm are influenced by the power-flow analysis used. Therefore,the overall algorithm accuracy is highly reliant on that analysis.It can be said that the power-flow analysis is the heart of theDG-unit solution algorithm. Accordingly, the power-flow algo-rithm offered in [10] is applied in this paper. Consider, as shownin Fig. 1, a sample two bus system including DG-unit.

The mathematical formulations of the mixed integer non-linear optimization problem for the DG-unit application are asfollows:


The objective function is to minimize the total system realpower loss

(1)

The equality constraints are the three nonlinear recursivepower-flow equations describing the system [10]

(2)

(3)

(4)

where . The inequality constraints are the systems voltage limits,

that is, 5% of the nominal voltage value

(5) In addition, the thermal capacity limits of the networks

feeder lines are treated as inequality constraints

(6) The boundary (discrete) inequality constraints are the

DG-units size (kVA) and power factor

(7)(8)

Practical concerns in terms of DG-unit sizes and powerfactors are considered in the proposed method. Since therounded-off issues of the DG-units size or are treatedinitially in the proposed method, the accuracy of the re-sults is guaranteed. The preselected (discretized) DG-unitsizes are from 10%80% of the total system demands (i.e.,

), approximated to integer values with a 100-stepinterval between sizes.

The DG-units is set to operate at practical values [11],thta is, unity, 0.95, 0.90, and 0.85 towards the optimal result.Moreover, the operating DG-units (i.e., lagging or leading)must be dissimilar to the buss load at which the DG-unitis placed [12]. Consequently, the net total of both active andreactive powers of that bus (where the DG-unit is placed) willdecrease.

III. ARTIFICIAL BEE COLONY (ABC) ALGORITHMThe artificial bee colony (ABC) algorithm is a new meta-

heuristic optimization approach, introduced in 2005 byKaraboga [13]. Initially, it was proposed for unconstrainedoptimization problems. Then, an extended version of the ABC

algorithm was offered to handle constrained optimizationproblems [15]. Furthermore, the performance of the ABCalgorithm was compared with those of some other well-knownpopulation-based optimization algorithms, and the results andthe quality of the solutions outperformed or matched thoseobtained using other methods [15][19].

The colony of artificial bees consists of three groups of bees:employed, onlookers, and scout bees. The employed bees arethose which randomly search for food-source positions (solu-tions.) Then, by dancing, they share the information of that foodsource, that is., nectar amounts (solutions qualities), with thebees waiting in the dance area of the hive. Onlookers are thosebees waiting in the hives dance area. The duration of a danceis proportional to the nectar content (fitness value) of the foodsource currently being exploited by the employed bee. Hence,onlooker bees watch various dances before choosing a food-source position according to the probability proportional to thequality of that food source. Consequently, a good food-sourceposition (solution) attracts more bees than a bad one. Onlookersand scout bees, once they discover a new food-source position(solution), may change their status to become employed bees.Furthermore, when the food-source position (solution) has beenvisited (tested) fully, the employed bee associated with it aban-dons it, and may once more become a scout or onlooker bee. Ina robust search process, exploration and exploitation processesmust be carried out simultaneously [13], [20]. In the ABC al-gorithm, onlookers and employed bees perform the explorationprocess in the search space, while on the other hand, scouts con-trol the exploration process. Inspired by the aforementioned in-telligent foraging behavior of the honey bee [13], the ABC al-gorithm was introduced.

One half of the colony size of the ABC algorithm representsthe number of employed bees, and the second half stands forthe number of onlooker bees. For every food-sources position,only one employed bee is assigned. In other words, the numberof food-source positions (possible solutions) surrounding thehive is equal to the number of employed bees. The scoutinitiates its search cycle once the employed bee has exhaustedits food-source position (solution.) The number of trials forthe food source to be called exhausted is controlled by thelimit value of the ABC algorithms parameter. Each cycle ofthe ABC algorithm comprises three steps: first, sending theemployed bee to the possible food-source positions (solutions)and measuring their nectar amounts (fitness values); second,onlookers selecting a food source after sharing the informationfrom the employed bees in the previous step; third, deter-mining the scout bees and then sending them into entirely newfood-source positions.

The ABC algorithm creates a randomly distributed initialpopulation of solutions , where signifiesthe size of population and is the number of employedbees. Each solution is a -dimensional vector, whereis the number of parameters to be optimized. The position ofa food-source, in the ABC algorithm, represents a possiblesolution to the optimization problem, and the nectar amountof a food source corresponds to the quality (fitness value) ofthe associated solution. After initialization, the population ofthe positions (solutions) is subjected to repeated cycles of the


search processes for the employed, onlooker, and scout beescycle , where is the maximum

cycle number of the search process. Then, an employed beemodifies the position (solution) in her memory depending onthe local information (visual information) and tests the nectaramount (fitness value) of the new position (modified solution.)If the nectar amount of the new one is higher than that ofthe previous one, the bee memorizes the new position andforgets the old one. Otherwise, she keeps the position of theprevious one in her memory. After all employed bees havecompleted the search process, they share the nectar informationof the food sources and their position information with theonlooker bees waiting in the dance area. An onlooker beeevaluates the nectar information taken from all employed beesand chooses a food source with a probability related to itsnectar amount. The same procedure of position modificationand selection criterion used by the employed bees is appliedto onlooker bees. The greedy-selection process is suitable forunconstrained optimization problems. However, to overcomethe greedy-selection limitation specifically in a constrainedoptimization problem [13], Debs constrained handling method[21] is adopted. It employs a tournament selection operator,where two solutions are compared at a time when the followingconditions are imposed: 1) any feasible solution is preferredover an infeasible one; 2) among two feasible solutions, the onewith better objective function value is preferred;and 3) amongtwo infeasible solutions, the one having the smaller constraintviolation is preferred.

The probability of selecting a food-source by onlookerbees is calculated as follows:

fitness (9)

where is the fitness value of a solution , and is thetotal number of food-source positions (solutions) or, in otherwords, half of the colony size. Clearly, resulting from using (9),a good food source (solution) will attract more onlooker beesthan a bad one. Subsequent to onlookers selecting their preferredfood-source, they produce a neighbor food-source positionto the selected one , and compare the nectar amount (fitnessvalue) of that neighbor position with the old position.The same selection criterion used by the employed bees is ap-plied to onlooker bees as well. This sequence is repeated until allonlookers are distributed. Furthermore, if a solution does notimprove for a specified number of times (limit), the employedbee associated with this solution abandons it, and she becomesa scout and searches for a new random food-source position.Once the new position is determined, another ABC algorithmcycle starts. The same procedures are repeated untilthe stopping criteria are met.

In order to determine a neighbouring food-source position(solution) to the old one in memory, the ABC algorithm altersone randomly chosen parameter and keeps the remaining pa-rameters unchanged. In other words, by adding to the currentchosen parameter value the product of the uniform variant

and the difference between the chosen parameter value

and other random solution parameter value, the neighborfood-source position is created. The following expressionverifies that:

(10)where and both are . The multiplieris a random number between and .In other words, is the th parameter of a solution thatwas selected to be modified. When the food-source position hasbeen abandoned, the employed bee associated with it becomesa scout. The scout produces a completely new food-source po-sition as follows:

(11)where (11) applies to all parameters and is a randomnumber between . If a parameter value produced using(10) and/or (11) exceeds its predetermined limit, the parametercan be set to an acceptable value [13]. In this paper, the valueof the parameter exceeding its limit is forced to the nearest(discrete) boundary limit value associated with it. Furthermore,the random multiplier number is set to be betweeninstead of .

Thus, the ABC algorithm has the following control parame-ters: 1) the colony size , that consists of employed beesplus onlooker bees ; 2) the limit value, which is the numberof trials for a food-source position (solution) to be abandoned;and 3) the maximum cycle number .

IV. ABC ALGORITHM FOR DG-UNIT APPLICATION PROBLEMThe flowchart of the ABC algorithm is illustrated in Fig. 2.

The solution steps of the proposed ABC algorithm for DG-unitapplication are described as follows.Step 1) Initialize the food-source positions (solutions pop-

ulation), where . The solutionform is as follows.

Step 2) Calculate the nectar amount of the population bymeans of their fitness values using

fitness (12)

where represents the response of (1) atsolution .

Step 3) Produce neighbor solutions for the employed bees byusing (10) and evaluate them as indicated by Step 2).

Step 4) Apply the selection process.Step 5) If all onlooker bees are distributed, go to Step 9).

Otherwise, go to the next step.Step 6) Calculate the probability values for the solutions

using (9).Step 7) Produce neighbor solutions for the selected onlooker

bee, depending on the value, using (10) and evaluatethem as Step 2) indicates.

Step 8) Follow Step 4).Step 9) Determine the abandoned solution for the scout bees,

if it exists, and replace it with a completely newsolution sing (11) and evaluate them as indicated inStep 2).


Fig. 2. Flowchart of the ABC algorithm.

Step 10) Memorize the best solution attained so far.Step 11) If MCN, stop and print result. Otherwise

follow Step 3).Employed and onlooker bees select new food sources in the

neighbourhood of the previous one in their memory dependingon visual information. Visual information is based on the com-parison of food-source positions [16]. On the other hand, scoutbees, without any guidance while looking for a food-source po-sition, explore a completely new food-source position. There-

Fig. 3. Single-line diagram of the 69-bus feeder system.

fore, scouts are characterized, based on their behavior, by lowsearch costs and a low average in food-source quality. Occasion-ally, the scouts can fortunately discover rich, entirely unknown,food sources. In the case of artificial bees, the artificial scoutscould have the fast discovery of the group of feasible solutionsas a task [22].

Parameter-tuning, in metaheuristic optimization algorithms,influences the performance of the algorithm significantly. Diver-gence, becoming trapped in local extrema, and time-consump-tion are such consequences of setting the parameters improp-erly. The ABC algorithm, as an advantage, has few controlledparameters. Since initializing a population randomly with afeasible region is sometimes cumbersome, the ABC algorithmdoes not depend on the initial population to be in a feasible re-gion. Instead, its performance directs the population to the fea-sible region sufficiently [14].

The controlled parameter (limit) is an important parameter inthe ABC algorithm. Indeed, it governs the algorithm from beingtrapped in a local extrema. Therefore, it is suggested in [13] thatit has the value of or at least .

V. RESULTS AND DISCUSSIONTo check the validity of the proposed ABC algorithm, the

69-bus radial distribution feeder system was considered in dif-ferent test cases. In addition, the results of sample feeder sys-tems were compared with those obtained via other methods. Theproposed ABC algorithm is implemented in C, and was exe-cuted on an Intel core 2 duo PC with 2.66-GHz speed and4 GB RAM.

Furthermore, we studied two load scenarios, scenario I andscenario II. For the first scenario, the loads are identical to thevalues given in [24]. In other words, the total demands of the69-bus system are 3802.19 kW and 2694.60 kVar. Scenario II,on the other hand, represents the situation where the loads ofthe feeder system increased by 50%. The single-line diagram ofthe 69-bus feeder system is shown in Fig. 3. The voltage pro-files of the feeder system due to different load scenarios are il-lustrated in Fig. 4. Table I lists the default case results of thechosen feeder system. The substation voltage and load powerfactors in both scenarios were considered as 1.0 p.u. and lag-ging , respectively.

The test cases conducted were applied at both load scenariosto solve the mixed integer nonlinear optimization problem de-scribed in Section III. Single and multiple DG-unit applicationsrepresent test case 1 and test case 2, respectively. The third test


Fig. 4. Voltage profiles of the 69-bus system at different load scenarios.

TABLE ISUMMARY OF THE 69-BUS SYSTEM DEFAULT CASE

case utilizes a single DG-unit and a capacitor. The fourth testcase is similar to the third test case; however, the DG-unit is con-trolled to supply active power only. Fixing the DG-units sizeto a predetermined value is involved in the fifth test case, whichis commonly the case from a practical perspective. The objec-tive functions in all tested cases are to minimize the systemsreal power loss. However, overall system voltage improvementis considered as an additional goal in test case 2. To avoid over-compensation situations, the DG-unit size constraint is set w.r.t.scenario I in all tested cases. In addition, the capacitor size (dis-crete constraint) is set from 1504050 kVar with a 150-step in-terval between sizes [25].

The proposed ABC algorithm results were obtained after car-rying out 30 independent runs. In other words, the initial pop-ulation was randomly generated in each run by using differentseeds. In this paper, the controlled parameter (limit) is tuned assuggested in [13], and half of the colony size is the number ofemployed bees. Thus, since the ABC algorithm has only twoparameters (unlike other well-known metaheuristic algorithms)to be tuned, the number of trial-and-error experiments will besignificantly fewer, which is one merit of the ABC algorithm.

A. Test Case 1

In this test case, an exact solution method was created toverify the results of the proposed ABC algorithm. The exactmethod provided the optimal result by examining all possiblesolution combinations and then retaining the optimal one. Al-though the exact method is time and memory consuming, itwill answer the pertinent question raised: how far is the pro-posed algorithms optimal result from the exact optimal one?Table II lists the optimal solutions obtained by the exact methodfor both scenarios. Finally, the proposed ABC algorithm resultsare recorded in Table III.

Clearly, as shown in Table III, the best results of the proposedABC algorithm, in both scenarios, were identical to those opti-

TABLE IIEXACT METHOD OPTIMAL RESULT OF TEST CASE 1

Fig. 5. Compensation results of test case 1 for 69-bus system due to load sce-nario I.

mally obtained using the exact method. The real power loss re-ductions at both scenarios were 89% and 90%, respectively. Fur-thermore, under scenarios I and II, the system improvedby 0.0631 p.u. and 0.103 p.u., respectively. The enhancementresults in terms of voltage profiles and loss reductions are illus-trated in Figs. 5 and 6. Approximately 120 W was the differencebetween the best and the worst (local minima) results under sce-nario II. This was due to the DG-unit size in the worst resultbeing 100 kVA less.

B. Test Case 2The number of possible solution combinations for this test

case and the remaining ones were tremendously large. Conse-quently, the exact method in these test cases would have re-quired massive amounts of time and memory. As an alternative,the proposed ABC algorithm was exhaustively utilized to solvethose test cases with a 2000 . The convergence charac-teristic of the exhaustive ABC algorithm under different sce-narios is shown in Fig. 7. It is important to state that the proposedABC and exhaustive-ABC algorithms successfully achieved thesame best solutions for test cases 2 4. As Table IV shows, fur-ther compensation to the system under different load scenarios


TABLE IIISIMULATION RESULTS OF THE ABC ALGORITHM OVER 30 INDEPENDENT RUNS AT TEST CASE 1

Fig. 6. Compensation results of test case 1 for 69-bus system due to load sce-nario II.

was attained when another DG-unit was added. In other words,15.92 kW and 36.73 kW were the additional power loss reduc-tions at scenarios I and II, respectively, w.r.t. single DG-unit ap-plication. In addition, the systems at both scenarios wereenhanced to be virtually 1.0 p.u.. Figs. 8 and 9 illustrate theseresults. The insignificant difference (i.e., 1.2 W) at scenario IIbetween the best and worst (local minimal) results was causedby placing the second DG-unit at bus 18 instead of the optimallocation (bus 17).C. Test Case 3

In this test case, we demonstrated the effect of installing (op-timally) a reactive power source as well as a DG-unit simultane-ously in order to satisfy the objective function. Once more, theconvergence characteristic of the exhaustive ABC algorithmof this test case is illustrated in Fig. 10. The proposed ABC algo-rithm, as shown in Table V, successfully identifies the optimalsolutions in each run. The real power loss reductions at bothscenarios were 92%. The system improved by 0.0675p.u. and 0.11 p.u. at scenarios I and II, respectively. Figs. 11and 12 illustrate the enhancement results at scenarios I and II,respectively.

Fig. 7. Convergence characteristics of the exhaustive-ABC algorithm at testcase 2.

D. Test Case 4The DG-unit in this test case was restricted to supply real

power only. The convergence characteristic of the exhaustiveABC algorithm is exemplified in Fig. 13. Noticeably, as shownin Table VI, the proposed ABC algorithm in both scenariosachieved the optimal solution in every independent run. Fur-thermore, the real power loss reductions as well as the systems

, at both scenarios, were slightly improved in w.r.t. testcase 1. In addition, the optimal location for the DG-unit and ca-pacitor was at bus 61. In other words, the solution of this testcase represented a DG-unit running at 0.8 leading power factor.The enhancement results in terms of voltage profile and loss re-duction are illustrated in Figs. 14 and 15. A summary of all testcases best results obtained by the proposed ABC algorithm interms of voltage profile improvements and power loss reduc-tions are demonstrated in Figs. 16 and 17, respectively. Amongall test cases, test case 2 showed the maximum power loss re-ductions, as well as voltage profile improvements.

E. Test Case 5Practical application of the DG-unit, however, proves diffi-

cult. Social, economic, and political factors affect the final op-timal attained solution. Therefore, the DG-units size, in thistest case, is constrained to 1000 kVA. In other words, the des-ignated value is approximately 20% of the total systems loads.In this experiment, load scenario I of the 69-bus feeder systemwas adopted.

As Table VII shows, the optimal solution obtained by the pro-posed ABC algorithm is identical to the one attained by the exactmethod. The real power loss reduction after deploying the op-timal DG-unit of this test case was 63.4%, which is less than


TABLE IVSIMULATION RESULTS OF THE ABC ALGORITHM OVER 30 INDEPENDENT RUNS AT TEST CASE 2

Fig. 8. Compensation results of test case 2 for 69-bus system due to load sce-nario I.

that obtained without limiting the DG-unit size. The enhance-ment results in terms of voltage profile and loss reduction areillustrated in Fig. 18.

F. Comparative Study

Although the proposed ABC algorithm proved its robustnessin solving the previous test cases, an additional radial distribu-tion feeder system was considered. The IEEE 33-bus and 69-busradial distribution feeder systems were adopted for comparisonpurposes. Therefore, the results of the proposed ABC algorithmwere compared with the solutions obtained based on the analyt-ical method [9] and GA method [26]. Tables VIII and IX sum-marize the optimal solutions achieved by these methods. TheDG-unit applications in [9] and [26] were limited to supply realpower only. In addition, scenario I was utilized in this com-parison. The single-line diagram of the 33-bus feeder systemis shown in Fig. 19.

Observing Tables VIII and IX, the results in terms of op-timal placement of the DG-unit were identical. However, if theoptimal DG-unit sizes in the analytical or GA methods were

Fig. 9. Compensation results of test case 2 for the 69-bus system due to loadscenario II.


rounded off to the closest practical rate, the accuracy of the re-sults would be affected. The proposed algorithm avoids this lim-itation and the accuracy of the results is guaranteed. Besidesthat, a slight improvement in loss reduction is achieved by theproposed ABC algorithm in both systems.


TABLE VSIMULATION RESULTS OF THE ABC ALGORITHM OVER 30 INDEPENDENT RUNS AT TEST CASE 3

Fig. 11. Compensation results of test case 3 for the 69-bus system due to loadscenario I.

G. Discussion

Deregulating electric power networks is one of the fac-tors that hasten DG-unit applications. In addition, renewableresources push the DG-unit applications problem to a dif-ferent-dimension (i.e., supply-uncertainty). Both consumersand utilities benefit from the DG-unit application, for example,in terms of reliability and energy savings. However, employingthe DG-unit practically is not an easy task. Many factors:environmental, social, economical, and even political, affect thefinal optimal attainment solution. Therefore, the decision-makerhas some different questions to consider in the optimizationproblem: whether the optimal DG-unit placement is practicallyavailable; whether the appropriate DG-units type is allowableat that location; which one, utility or consumer, has control onthat DG-unit, and so on. All of these variables will significantlyinfluence the optimal solution. Consequently, different DG-unitapplication problems have their own practical constraints and,thus, the results obtained for one problem are not necessarilyvalid for another.



Since the DG-unit is relatively small in size compared to acentral generation plant, an independent producer or distribu-tion network operator (DNO) could own one. However, individ-uals could own their own DG-units, attempting to reduce theirload demands at peak-times or even to go off-grid. Furthermore,


TABLE VISIMULATION RESULTS OF THE ABC ALGORITHM OVER 30 INDEPENDENT RUNS AT TEST CASE 4

Fig. 14. Compensation results of test case 4 for the 69-bus system due to loadscenario I.

some individuals could supply back to the grid to reduce theirelectric bill after an agreement with the utility. All of these as-pects are significant in future research.

Mostly, the DG-unit application problem is solved during theplanning stage. One advantage of that is time consumption is nota major factor in the solution algorithms performance. How-ever, in the case of a dynamical problem (online situation), thetime factor is highly significant due to system state security (i.e.,dynamic and transient conditions).

VI. CONCLUSIONIn this paper, a new population-based ABC has been proposed

to solve the mixed integer nonlinear optimization problem. Theobjective function was to minimize the total system real powerloss subject to equality and inequality constraints. Simulationswere conducted on the IEEE 33- and 69-bus radial distribu-tion feeder systems. The proposed ABC algorithm successfullyachieved the optimal solutions at various test cases, as the exactand exhaustive ABC algorithms prove. The results of the pro-posed ABC algorithm were compared with those attained by


Fig. 16. Voltage profile enhancement of all test cases due to different load sce-narios.

other methods. Among all test cases, test case 2 had the max-imum power loss reductions as well as voltage improvements.


Fig. 17. Power loss reductions of all test cases due to different load scenarios.

TABLE VIISIMULATION RESULTS OF THE ABC ALGORITHM OVER 30 INDEPENDENT RUNS

AT TEST CASE 5

Fig. 18. Compensation results of test case 5 for the 69-bus system due to alimited DG-unit size.

The ABC algorithm is simple, easy to implement, and capableof handling complex optimization problems. The convergencetendency of the proposed ABC algorithm in all test cases shows

TABLE VIIICOMPARISON OF OPTIMAL DG-UNIT RESULTS FOR THE 33-BUS FEEDER

SYSTEM

TABLE IXCOMPARISON OF OPTIMAL DG-UNIT RESULTS FOR THE 69-BUS FEEDER

SYSTEM

Fig. 19. Single-line diagram of the 33-bus feeder system.

that the algorithm relatively converges in fewer numbers.Further insight of the solution quality achieved by carrying out30 independent runs for all test cases as the statistical resultswas reported in Tables IIIVI. Evidently, the ABC algorithmhas excellent solution quality and convergence characteristics.The efficiency of the proposed ABC algorithm is confirmed bythe fact that the standard deviation of the results attained for30 independent runs is virtually zero. Furthermore, parameter-tuning in metaheuristic optimization algorithms influences theperformance of the algorithm significantly. Other well-knownmetaheuristic algorithms (e.g., PSO, GA, and EP) have manyparameters to tune. In contrast, the ABC algorithm has only twoparameters (colony size and max. iteration number) to be tuned.Therefore, the updating of the two parameters towards the mosteffective values has a higher likelihood of success than in othercompeting metaheuristic algorithms.

The performance of the proposed ABC algorithm shows itssuperiority and the potential for solving complex power systemproblems in future publications.

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Fahad S. Abu-Mouti (S07) received the B.Sc. de-gree in electrical engineering from Qatar University,Doha, Qatar, in 2003 and the M.A.Sc. degree inelectrical engineering from Dalhousie University,Halifax, NS, Canada, in 2008, where he is currentlypursuing the Ph.D. degree.

From 2003 to 2006, he joined the Saudi ElectricityCompany, Riyadh, Saudi Arabia, where he was incharge of the O&M section. In 2009, he receiveda government scholarship. His research interestsinclude distributed generation and renewable energy

resources applications, power system operation and control, planning, andmetaheuristic optimization algorithms.

Mr. Abu-Mouti is a member of the Saudi Council of Engineers.

M. E. El-Hawary (S68M72F90) received the B.Eng. degree in electricalengineering (Hons.) from the University of Alexandria, Alexandria, Egypt, in1965, and the Ph.D. degree from the University of Alberta, Edmonton, AB,Canada, in 1972.

Currently, he is Associate Dean of Engineering and has been Professorof Electrical and Computer Engineering at Dalhousie University, Halifax,NS, Canada, where he has been since 1981. He served on the faculty andwas a Chair of the Electrical Engineering Department, Memorial Universityof Newfoundland, for eight years. He was Associate Professor of ElectricalEngineering at the Federal University of Rio de Janeiro, Rio de Janeiro, Brazil,for two years and was Instructor at the University of Alexandria. He pioneeredmany computational and artificial-intelligence solutions to problems in eco-nomic/environmental operation of power systems. He has written ten textbooksand monographs, and many refereed journal articles. He has consulted andtaught for more than 30 years.

Dr. El-Hawary is a Fellow of the Engineering Institute of Canada (EIC) andthe Canadian Academy of Engineering (CAE). He was a Killam MemorialFellow with the University of Alberta.

Optimal Distributed Generation Allocation and Sizing in Distribution Systems via Artificial Bee Colony Algorithm

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