cuckoo search algorithm for emission reliable economic multi-objective dispatch problem

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Cuckoo Search Algorithm for Emission ReliableEconomic Multi-objective Dispatch ProblemK. Chandrasekarana, Sishaj P. Simonb & Narayana Prasad Padhyc

a Department of Electrical and Electronics Engineering, National Institute of TechnologyPuducherry, Karaikal, Indiab Department of Electrical and Electronics Engineering, National Institute of Technology,Tiruchirappalli, Indiac Department of Electrical and Electronics Engineering, Indian Institute of Technology,Roorkee, IndiaPublished online: 19 Jun 2014.

To cite this article: K. Chandrasekaran, Sishaj P. Simon & Narayana Prasad Padhy (2014) Cuckoo Search Algorithm for EmissionReliable Economic Multi-objective Dispatch Problem, IETE Journal of Research, 60:2, 128-138

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Cuckoo Search Algorithm for Emission Reliable EconomicMulti-objective Dispatch ProblemK. Chandrasekaran1, Sishaj P. Simon2 and Narayana Prasad Padhy3

1Department of Electrical and Electronics Engineering, National Institute of Technology Puducherry, Karaikal, India, 2Department of Electricaland Electronics Engineering, National Institute of Technology, Tiruchirappalli, India, 3Department of Electrical and Electronics Engineering,

Indian Institute of Technology, Roorkee, India

ABSTRACT

This paper presents a novel emission/reliable/economic dispatch (ERED) problem using a newly developed multi-objec-tive cuckoo search algorithm (CSA). Traditionally, electric power systems are operated in such a way that the total fuelcost is minimized regardless of the emission and reliability level of the system. Recently, the restructured power systemstresses the need for non-polluting, reliable, and economic operation. Hence, three conflicting objective functions suchas emission, reliability, and fuel cost functions are considered in the practical economic dispatch (ED) problem. TheERED problem is formulated as a non-smooth and non-convex multi-objective ED problem incorporating valve-pointeffects of thermal units. The CSA utilizes the breeding behaviour of cuckoos, where each individual searches the mostsuitable nest to lay an egg (compromise solution) in order to maximize the egg’s survival rate and achieve the best hab-itat society. The fuzzy set theory is used to find a best compromise solution from the Pareto-optimal set. The effective-ness of the proposed methodology is tested on a benchmark of 6-unit test system, IEEE RTS 24 bus system, and IEEE118 bus system. The results are validated and compared with the solution available in the existing literature.

Keywords:Cuckoo search algorithm, Fuzzy set theory, Environmental/reliable/economic dispatch problem, Multi-objective eco-nomic dispatch problem.

Nomenclature

Fc Fuel cost function ($)ai,bi,ci Cost coefficient of ith generator unit.

ei,fi Valve-point coefficient of ith generator unitai,bi,g i Emission coefficient of ith generator unit

di,di Exponential coefficient of ith generator unitBij ijth element of loss coefficient of symmet-

ric matrix BBi0 ith element of the loss coefficient vectorB00 Loss coefficient constant

C(x) Objective functionE Emission function (ton)

EENS Reliability function (expected energy notsupplied)

En Number of equality constraintsIn Number of inequality constraintsmpj Membership value for the objective func-

tion j 2 fFc,EgFjmin

and Fjmax

Minimum and maximum values of jthobjective function among all non-domi-nated solutions, respectively

Fj Degree of the objective function in thefuzzy domain

mpr Membership value for the objective func-

tion EENS

Fr Degree of the objective (EENS) in thefuzzy domain

Fr,min, Fr,avg,and Fr,max

Minimum, average, and maximum valueof EENS among all non-dominated solu-tions, respectively.

Lj Load curtailment due to generator contin-gency j

LC Total number of contingencies leading toload curtailment

PD Total system demand, MWPL Total system losses, MWPi Generation power output of unit i

Pi,max Maximum power output of unit iPi,min Minimum power output of unit iPRj Probability of availability that corre-

sponds to jth state of capacity outageprobability table

Proj Survival probability rate of the cuckoo’segg

T Total number of objective functionsVpq, Vfq Host nest position

g, h Equality and inequality constraintsm Total number of nest position.D Number of parameters to be optimizedN Number of generating unit

128 IETE JOURNAL OF RESEARCH | VOL 60 | NO 2 | APR 2014

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Index

i Generating unit index (subscript)k Time index (subscript)

p, f Host nest position

1. INTRODUCTION

The objective of the economic dispatch (ED) problem isto determine the optimal dispatch of the committed gen-erating units such that the total fuel cost is minimizedwhile satisfying the system and unit constraints [1].However, the optimum schedule obtained by solvingED problem may not be the best, since emission and reli-ability are vital in the restructured power system. Thepassage of clean Kyoto Protocol Act Amendments in1990 forced the utilities to reduce the emission from fos-sil fuel fired thermal station [2]. A recent achievement inthis direction is the international treaty and an agree-ment signed under which industrialized countries willreduce their collective emissions of greenhouse gases by5% over the five-year period of 2008�2012 compared tothe year 1990. Hence, the power industries are forced toconsider the emission as other objective function;thereby, traditional ED problem has been formulated asemission economic dispatch (EED) problem.

Recently, the reliability issues of power industries areaddressed in the passage of the Energy Policy Act of2005 (EP Act) in a number of ways. In 2006, NorthAmerican Electric Reliability Corporation (NERC) wasassigned as the Electric Reliability Organization (ERO)of the USA by the Federal Energy Regulatory Commis-sion [3, 4]. Thereby, the NERC is responsible for estab-lishing and enforcing electric reliability standards [5] inpower industries. Not only the USA, but other coun-tries also understood the significance and started imple-menting various norms on reliability standards whichis seen as a major step in this direction. This forces thepower utilities to consider reliability level as anotherobjective function in the EED problem. Therefore, theED problem becomes multi-objective ED problem(MOED) and can be called as ERED problem.

A number of optimization techniques have beenattempted to solve multi-objective optimization prob-lem, such as multi-objective evolutionary algorithms(MOEAs) [6, 7], evolutionary programming techniquesincluding differential evolution [8�11], particle swarmoptimization (PSO) based approaches [12�14], harmonysearch algorithm (HAS) [15], biography-based algorithm(BBO) [16], and fuzzy adapted heuristic approach [17,18]. MOEA which use Pareto-based approach has beenreported to solve the EED problem. Most MOEAsreported in the literature use non-dominated sorting/

ranking (NSGA) and fast non-dominated sorting/rank-ing (NSGA-II) approach to obtain a Pareto-optimal set.However, some non-dominated solutions may be lostduring the search process, while some dominated solu-tions may be misclassified as non-dominated ones dueto the selection process used. In recent years, PSO hasbeen successfully implemented to solve multi-objectiveED problem with an impressive success. Although PSOcan be used to handle non-smooth and non-convex opti-mization problems, it suffers from premature conver-gence especially while handling problems with morelocal optima. Population techniques such as PSO, HAS,BBO, etc. are found to be good for searching the nearglobal optimal solution and can be considered successfulto a certain extent. However, in recent years, a newnature-inspired metaheuristic algorithm known as thecuckoo search algorithm (CSA) developed by Xin-SheYang is successfully applied to solve non-linear andnon-convex optimization problems [19, 20]. In this con-text, an attempt is made to solve multi-objective EREDproblem using CSA.

2. PROPOSED WORK

The aim of this paper is to show the robustness and effi-ciency of CSA for solving the novel ERED problem.Similar to other evolutionary methods, CSA starts withan initial fixed number of population of host nests(nests built by birds other than cuckoo), where eachnest is assumed to contain a cuckoo’s egg. At the end ofevery generation of cuckoos, the size of host nestsincreases when compared to the initial number of nests.Then, the fuzzy fitness is used to pick up the best com-promise solution (which is equal to the initial numberof host nests) that would be alive for the coming gener-ations. At the end of every generation, the host birdwill destroy the nest or abandon the solution (nest)which is far away from the best solution.

The rest of the sections are organized as follows: In Sec-tion 3, the problem formulation of ERED problem is pre-sented. Sections 4 and 5 describe the process of multi-objective optimization and the formulation of fuzzymembership function for different objectives, respec-tively. Sections 6 and 7 explain the basic behaviour ofCSA and the implementation of CSA for ERED. In Sec-tion 8, the effectiveness of the proposed approach is dem-onstrated on different test systems and the results arediscussed. Finally, the conclusion is given in Section 9.

3. ERED PROBLEM FORMULATION

The present formulation treats emission reliable eco-nomic environmental dispatch problem as a multi-objective mathematical programming problem. Itattempts to optimize cost, emission, and reliability levelof the system simultaneously, while satisfying both

Chandrasekaran K, et al.: Cuckoo Search Algorithm for Emission Reliable Economic Multi-objective Dispatch Problem

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equality and inequality constraints. The followingobjectives and constraints are taken into account in theformulation of ERED problem.

3.1 Objective Functions

3.1.1 Fuel Cost Function

The fuel cost function of each fossil fuel fired generator,considering the valve-point effect [13], is expressed asthe sum of a quadratic and a sinusoidal function. Thetotal fuel cost in terms of real power output can beexpressed as follows:

Min Fc ¼XNi ¼ 1

�ai þ bi:Pi þ ci:P2

i

�þjei:sinðfi:ðPi,min � PiÞÞj

� �ð1Þ

where ai, bi, and ci are the cost coefficients of ith genera-tor unit and ei and fi are the valve-point coefficients ofith generator unit. Pi represents the output of the gener-ating units which is determined in ERED problemusing real coded CSA.

3.1.2 Emission Function

The atmospheric pollutants such as sulphur oxides(SOx), nitrogen oxides (NOx), and carbon dioxide (CO2)caused by fossil fuel fired generator can be modelled,separately. However, for comparison purposes, thetotal emission (E) of these pollutants which is the sumof a quadratic and an exponential function [13] can beexpressed as follows:

Min E ¼XNi ¼ 1

�ai þ bi:Pi þ g i:P

2i

�þ di:expðdi:PiÞ

� �ð2Þ

where ai, bi, and g i are the emission coefficients of ithgenerator unit and di and di are the exponential coeffi-cients of ith generator unit.

3.1.3 Reliability Function

The reliability issues of the generation are the majorfocus for the system operators in daily power systemplanning and operation. Hence, in ED problem, it isnecessary to consider the reliability level while dis-patching the generating units. Reliability level of thepower system is calculated using Eq. (3)

Min EENS ¼ PrfUðPiÞg � Lj ¼Xj ¼ LC

PRjLj ðKWhÞ ð3Þ

where PRj is the probability of unavailability of state jobtained from capacity outage probability table [21]and Lj is the load curtailment due to generator contin-gency j. Here, a high value of EENS indicates low reli-ability level and vice versa. A reduction in time can beachieved by omitting the outage level for which the

cumulative probabilities of the generation availabilityis less than a predefined limit (e.g. 10�7) [21].

3.2 Constraints

3.2.1 Equality Constraint: Real Power Balance Constraint

The total power generated must be equal to the sum ofthe total system load (PD) and the real power losses (PL)in the transmission line. It can be defined as

XNi ¼ 1

ðPiÞ ¼ PD þ PL ð4Þ

The network losses are taken into account as functionsof respective generating units’ output, using B-losscoefficient matrix.

PL ¼XNi ¼ 1

XNj ¼ 1

PiBijPj þXNi ¼ 1

Bi0Pi þ B00 ð5Þ

3.2.2 Inequality Constraint: Generation Capacity Limit

The real power output of each generator is constrainedby minimum and maximum limits. i.e.

Pi,min � Pi � Pi,max ð6Þ

3.3 Formulation of ERED Problem

In this article, three conflicting objective functions suchas fuel cost, emission output of the generating units,and reliability level of the system are considered, simul-taneously. Then, the multi-objective ERED problem isformulated as follows:

Minimize ½Fc, E, EENS� ð7Þ

subject to the constraints (4)�(6).

In Sections 3.1.1, 3.1.2, and 3.1.3, P(i ¼ 1 to N) are the realvariables. It is used to indicate the output of the gener-ating units which is determined in ERED problemusing real coded CSA. Hence, in CSA, Pi is the controlvariable that is determined with the minimization ofmulti-objective function (7) subject to the constraints(4)�(6).

4. FORMULATION OF MULTI-OBJECTIVEFUNCTION

The real-time optimization problems in power systeminvolve simultaneous optimization of several objectivefunctions. Generally, these functions are non-commen-surable, competing, and conflicting objectives. Thepractical multi-objective optimization problem is



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presented as follows:

Minimize CðxÞ ¼ ½C1ðxÞ; C2ðxÞ; :::::,CTðxÞ� ð8Þ

subject to

geðxÞ � 0, e ¼ 1,2,::::,In ð9ÞhieðxÞ ¼ 0, ie ¼ 1,2,:::,En ð10Þ

Multi-objective optimization having such conflictingobjective functions gives rise to a set of optimal solu-tions instead of single optimal solution, because nosolution can be considered to be better than any otherwith respect to all objective functions. The solutionsthat are non-dominated within the entire search spaceare denoted as Pareto-optimal and constitute the Par-eto-optimal set. This set is also known as Pareto-opti-mal front.

5. FUZZY MEMBERSHIP FUNCTIONFORMULATION

In the proposed ERED problem, three objective func-tions such as fuel cost, emission output of the generat-ing unit, and reliability level of the system areconsidered, simultaneously. Here, choosing a best com-promise solution is important in decision-making pro-cess while solving multi-objective optimizationproblem. In this paper, fuzzy membership approach isused to find the best compromise solution. The bestcompromise solution is the solution that has maximumfitness value which is calculated using Eq. (11).

FITp ¼ ðmpc þ m

pe þ m

pr ÞP

p ¼ 1tomðmpc þ m

pe þ m

pr Þ

ð11Þ

where m is the total number of non-dominated solu-tions or population of the host nest. Here, mc,me, andmrare the fuzzy membership values that will indicate thedegree of satisfaction of the objective functions Fc, E,and EENS, respectively. Hence, to determine the mem-bership value of each objective function, it is requiredto formulate a fuzzy membership function for eachobjective function.

5.1 Formulation of Fuzzy Membership Function for Fcand E

In the proposed ERED problem, the membership func-tion chosen for the objective function Fc and E is shownin Figure 1.

The fuzzy membership function value is computedusing Eq. (12). Based on the value of membership func-tion, it will do participate in the optimization

process.

mpj ¼

1, for Fi � FiminðFjmax � FjÞðFjmax � FjminÞ , for Fjmin < Fj < Fjmax

0, for Fj � Fjmax

8>><>>:

ð12Þ

5.2 Formulation of Fuzzy Membership Function for EENS

The membership function chosen for the EENS functionis shown in Figure 2.

The fuzzy membership function value is computedusing Eq. (13). Based on the value of membership func-tion, it will do participate in the optimization process.

mpr ¼

0, for Fr � Fr,min;ðFr,avg � FrÞ

ðFr,avg � FrminÞ , for Frmin < Fr < Fr,avg;

1 for Fr ¼ Fr,avgðFr,max � FrÞ

ðFr,max � Fr,avgÞ , for Fr,avg < Fr < Fr,max;

0, for Fr > Fr,max;

8>>>>>>>><>>>>>>>>:

ð13Þ

Figure 1: Fuzzy membership function for Fc and E.

Figure 2: Fuzzy membership function for EENS.



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6. OVERVIEW OF CUCKOO SEARCH ALGORITHM

Cuckoo search algorithm (CSA) is one of the mostrecently developed metaheuristic algorithms [19, 20] byXin-She Yang and Suash Deb in 2009. It has been devel-oped by replicating the intellectual breeding behaviourof cuckoos. CSA is a population-based search proce-dure which is validated in solving complex, non-linear,and non-convex optimization problems [19, 20].

Female parasitic cuckoos specialize and lay eggs thatclosely resemble the eggs of their chosen host nest (i.e.nest is built by other species bird). Cuckoo choosesthis host nest by natural selection. The shell of thecuckoo egg is usually thick. They have two distinctlayers with an outer chalky layer that is believed toprovide resistance to cracking when the eggs aredropped in the host nest. The cuckoo egg hatches ear-lier than the host bird’s egg, and the cuckoo chickgrows faster. Alien eggs (i.e. remaining eggs in thenest) are detected by the host birds with a randomlygenerated probability value, Pa 2 [0, 1]. Then, theseeggs are thrown away or the nest is abandoned, and acompletely new nest is built, in a new location by thehost bird. The host bird identifies the alien egg by com-paring the randomly generated probability value, Pawith the probability value, Prop associated with thequality of an egg in the nest position which is calculatedusing Eq. (14).

Prop ¼ ð0:9� Fitp=maxðFitÞÞ þ 0:1 ð14Þ

where Fitp is the fitness value of the solution, p which isproportional to the quality of an egg in the nest posi-tion, p and Prop gives the survival probability rate ofthe cuckoo’s egg. If the randomly generated probabil-ity, Pa 2 [0, 1] is greater than the Prop, then the alienegg is identified by the host bird. Then, the host birddestroys the alien egg or abandon the nest and finds anew host nest (in new position) using Eq. (15) for layingan egg. Otherwise, the egg grows up and is alive for thenext generation, based on the fuzzy fitness function(see Section 7.1, step 6):

xp ¼ xpmin þ r and ð0,1Þ � ðxpmax � xpminÞ ð15Þ

where xpmin and xpmax are the minimum and maximumlimits of the parameter to be optimized. The maturecuckoo forms societies and each society has its habitatregion to live in. The best habitat among all the societieswill be the destination for the cuckoos to live in. Then,they immigrate towards this best habitat.

6.1 Selection of Host Nest Position

The cuckoo randomly chooses new host nest position(Vpq) to lay an egg using the following equations:

Vgen þ 1Pq ¼ Vgen

Pq þ spq � LevyðλÞ � a ð16Þ

LevyðλÞ ¼ Gð1 þ λÞ � sin p � λ2

� �G ð1 þ λÞ

2

� �� λ � s

ðλ � 1Þ2

Pq

��

��

1λ

ð17Þ

where λ is a constant (1 � λ � 3) and a is a randomnumber generated between [�1, 1]. Also, s > 0 is thestep size which should be related to the search space ofthe problem of interest. If s is too large, then the newsolution generated will be too far away from the oldsolution (or even jump out of the bounds). Then, such amove is unlikely to be accepted. If it is too small, thechange is too small to be significant, and consequentlysuch search is not efficient. Therefore, a proper step sizehas to be chosen to maintain the search, as efficiently aspossible. Hence, the step size is calculated as follows:

spq ¼ VgenPq � Vgen

fq ð18Þ

where p, f 2{1, 2,. . .,m} and q 2{1, 2,. . .,D} are randomlychosen indexes. Although f is determined randomly, ithas to be different from p. Here, Vpq and Vfq are the hostnest positions.

7. IMPLEMENTATION OF CSA FOR ERED PROBLEM

In this section, CSA is implemented to determine thedispatch of each generating unit for a system load inorder to get the best compromise solution. The step-by-step procedure for the proposed algorithm is as follows:

7.1 Step-by-Step CSA for ERED Problem

Step 1: Specify system data and initialize the controlparameter of CSA. The maximum generation is set tostop the process.

Step 2: Initialization of population

With respect to the initial control parameter, the popu-lation is randomly generated.

Step 3: Modification of host nest position

The host nest produces a modification on the currentposition using Eq. (16).

Step 4: Repair and evaluate EDP

Whenever the position of host nest is modified by realcoded CSA, the violation of constraints (4)�(6) has to



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be checked for each of the pth string in the population.The flowchart for constraint management is shown inFigure 3.

Step 5: Evaluation of fuzzy fitness of the population

The fuzzy set theory is employed to obtain a best com-promise solution from the Pareto-optimal set. For eachnon-dominated solution (nest position), the normalizedmembership fuzzy fitness function (FIT) is calculatedusing Eq. (11).

Step 6: Identification of alien egg

For each nest position, a host bird discovers an alien eggwith a probability Proi using Eq. (14) which is related toits fitness value. Now, a new nest position is generated,using Eq. (15) and is added into the existing nest popula-tion. That is, the total number of host nest added will begreater than or equal to m and lesser than or equal to 2m.

Step 7: Fitness evaluation for newly added nestpositions

For the newly added nest positions, constraints (4)�(6)are checked for violations. If there is any violation inthe constraints, then they undergo the repair mecha-nism as given in Figure 3.

Step 8: Abandon sources exploited by the cuckoos

Arrange fitness function in descending order and pickup the first m number of nest position and abandon theremaining nest positions. That is, whenever an alienegg is identified with a probability (Step 6) and fitnessvalue (Step 7), those nests with low quality solutionsare abandoned.

Step 9: Memorize the best solution achieved so far.Increment the generation count.

Step 10: Terminate the iteration, if the maximum gener-ation is reached. Otherwise, go to Step 3. The best fit-ness and the corresponding position of the host nest areretained in the memory once the algorithm is termi-nated. The flowchart for the proposed method is givenin Figure 4.

8. RESULTS AND DISCUSSIONS

All the programs are developed and simulated usingMATLAB 7.01. The system configuration is Pentium IVprocessor with 3.2 GHz speed and 2 GB RAM. Twodifferent test case studies (Cases and 2) are consideredto validate the robustness and efficiency of the CSA insolving the multi-objective ED problem. The

Figure 4: Flow chart for the proposed method.

Figure 3: Repair strategy for constraint management.



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importance of incorporating the reliability function in apractical EED problem is also demonstrated.

Case 1 To validate the efficiency of CSA in a multi-objective optimization problem, emissioneconomic dispatch (EED) problem is solvedconsidering two objective functions such asfuel cost (Fc) and emission (E). The obtainedresults are compared with the solutionavailable in the existing literature.

Case 2 Here, the proposed methodology is appliedfor three objective functions (i.e. fuel cost,emission, and reliability) for solving EREDproblem.

8.1 Test System 1 � 6-Unit System

This system consists of six generators. The system datais adopted from [22]. Here, the forecasted load is con-sidered as 1200 MW.

8.1.1 Effect of Variation of CSA Parameters

Optimal converge behaviour can be obtained if the twocontrol parameters, namely host nest population (Hn)and constant (λ), are optimally set. Setting of thesecuckoo parameters optimally would also yield bettersolution and lesser computational time. As per the stepsgiven in [23], the CSA parameters are calculated andgiven in Table 1.

8.1.2 Case 1 � EED Problem

The two competing objectives (fuel cost and emission)are solved simultaneously, by the proposed CSA andthe membership functions given in Section 5 are usedto identify the best compromise solution from the Par-eto-optimal set.

Out of 10 trials, the best compromise solution using thefuzzy membership approach is given in Table 2. To val-idate the proposed approach with the existing techni-ques, using the steps given in [24�26], the price penaltyfactor for 6-unit system is calculated as 62.0357 $/lbwhich is used to obtain the total cost. It is observedfrom Table 2 that the proposed approach provides bet-ter results than the solutions reported in the availableliterature [22] for EED problem.

8.1.3 Solution Quality

To validate the computational efficiency of the pro-posed CSA, the EED problem is solved for the 6-unitsystem using existing swarm intelligent techniquessuch as standard PSO algorithm [13] and artificial beecolony (ABC) algorithm [27]. In all the three methods(PSO, ABC, and CSA), the maximum number of itera-tion is fixed as 300. Also, it is to be noted that the initialrandom generated population is taken same for all thethree techniques (PSO, ABC, and CSA). From Table 3, itis observed that the minimum cost produced by CSA islesser than the solution obtained using ABC and PSOalgorithms.

After obtaining the solutions from each of the threealgorithms individually, Pareto-optimal front is shownin Figure 5. Figure 6 shows the distribution of total pro-duction cost obtained from 10 trial runs for Case 1using PSO, ABC, and CSA. Out of 10 trials, the fre-quency of achieving a cost better than the mean cost inCSA algorithm is 7, which is higher compared to PSO

Table 1: CSA parameter settings � 6-unit system � Case 1

Host nestpopulation (Hn)

Averagetotal cost ($)

Constant(λ)

Average totalcost ($)

25 144,561.23 0.5 144,315.4150 144,510.26 1 144,421.00100 144,452.07 1.5 144,587.07150 144,478.48 2 144,358.48200 144,485.69 2.5 144,372.90300 144,467.24 3 144,321.22

Table 2: EED Problem solution � 6-unit system � Case 1

Solution techniques MODE [[22]] PDE [22] NSGA II [22] SPEA [22] CSA

P1,MW 108.62 107.39 113.12 104.15 111.20P2,MW 115.94 122.14 116.44 122.98 126.17P3,MW 206.79 206.75 217.41 214.95 205.50P4,MW 210.0 203.70 207.94 203.13 202.06P5,MW 301.88 308.10 304.66 316.03 308.94P6,MW 308.41 303.37 291.59 289.93 297.36PL, MW 51.67 51.48 51.20 51.20 51.26Fuel cost, $ 64,843 64,920 64,962 64,884 65,080.60Emission, lb 1286 1281 1281 1285 1273.07Penalty factor $/lb 62.03 62.03 62.03 62.03 62.03Total cost, $ 144,620.9 144,387.7 144,429.7 144,599.87 144,056.48EENS, KWh 7985.90 7987.42 7938.51 7953.50 7976.89Time, sec 3.09 3.52 5.42 7.05 7.2



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(five times) and ABC (six times). This shows that theproposed CSA method gives better quality solution.

8.1.4 Case 2�ERED Problem

The proposed methodology is applied for three objec-tive functions (i.e. fuel cost, emission, and reliability)for solving ERED problem.

The reliability data for 6-unit system is given in Table 4.To demonstrate the importance of incorporation of reli-

ability function in an economic dispatch problem, 6-unit system is individually solved for all the threeobjective functions (Fc, E, and EENS) and the corre-sponding variation in other objectives are evaluatedwhich are given in Table 5. From the Table 5, it is obvi-ous that the variation in the system reliability level issignificant with respect to different objective functionsand cannot be neglected. Therefore, it justifies the incor-poration of the reliability function in an EED problem,thereby the novel ERED problem is formulated toobtain a best compromise solution.

The proposed methodology is applied for three objec-tive functions (i.e. fuel cost, emission, and reliability)for solving ERED problem. The membership functionsgiven in Section 5 are used to identify the best compro-mise solution from the Pareto-optimal set. Out of 10 tri-als, the best compromise solution using the fuzzymembership approach is given in the last column ofTable 5. The CSA takes 18.15 sec of the CPU time on anaverage to converge to an optimal solution. Once thealgorithm terminates, feasible designs are filtered in thedesign space to obtain a Pareto-optimal set. The Pareto-optimal set consists of 30 solutions which are repre-sented as 30 points in Figure 7. However, it should benoted that all the 30 points are not visible in this figure,since some points overlap each other.

8.2 Test System 2�IEEE RTS 24 Bus System

This system consists of 26 generators. The system datais adopted from [28]. Here, the forecasted load is con-sidered as 2670 MW and system loss is calculated byload flow calculation using Newton�Raphson method.

Table 4: Reliability data � 6-unit system

Unit maximum capacity, MW FOR Unit maximum capacity, MW FOR

125 0.1 210 0.13150 0.1 325 0.15225 0.13 315 0.15

Note: FOR ¼ forced outage rate.

Table 3: Solution quality � Case 1

Solution techniques PSO ABC CSA

P1,MW 106.8610 109.2591 111.20P2,MW 120.4594 121.3821 126.17P3,MW 209.9495 202.6737 205.50P4,MW 207.2737 209.7349 202.06P5,MW 303.1949 306.2035 308.94P6,MW 303.6778 302.2426 297.36PL, MW 51.4163 51.4958 51.26Fuel cost, $ 64,888.73 64,956.42 65,080.60Emission, lb 1282.77 1279.74 1273.0716Penalty factor $/lb 62.0357 62.0357 62.03Total cost, $ 144,466.72 144,345.98 144,056.48EENS, KWh 7955.41 7972.21 7976.89Time, sec 8.1 7.9 7.2

Figure 5: Pareto-optimal front � 6-unit system � Case 1.

Figure 6: Distribution of total production cost for 10 differ-ent trial runs � Case 1.

Table 5: Solution for different objectives � 6-unit system �Case 2

Objective function Min Fc Min E Min EENS ERED solution

P1 84.4353 125 124.9951 125.0000P2 93.3639 150 149.9968 125.4400P3 225 201.1816 224.9962 225.0000P4 210 199.5454 209.9957 205.5900P5 325 287.6191 311.5389 313.6700P6 315 286.8137 227.7261 255.6600Power loss, MW 52.7991 50.15 49.2488 50.36Fuel cost, $ 64,083.1 65,991 66,152.27 65,487Emission, lb 1345.5 1240.7 1264.39 1270.9EENS, KWh 8087.4 7869.87 7782.9 7907.8



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8.2.1 Case 1� EED Problem

The final combination of parameters that provided thebest results for IEEE RTS 24 bus (26 unit) system iswhen λ ¼ 1:2 and Hn ¼ 200. Out of 10 trials, the bestcompromise solution using PSO, ABC, and CSA isgiven in Table 6. It is clear from Table 6 that CSA pro-vides better results than the solutions obtained usingPSO and ABC.

8.2.2 Case 2 � ERED Problem

The proposed methodology is applied for three objectivefunctions (i.e. fuel cost, emission, and reliability) for solv-ing ERED problem. An IEEE RTS 24 bus system issolved by considering all the three objective functions(Fc, E, and EENS) simultaneously. The best compromisesolution satisfying all the constraints is given in Table 7.This shows the efficiency of the proposed algorithm.

8.3 Test System 3 � IEEE 118 Bus System

The proposed methodology is applied for a larger sys-tem of IEEE 118 bus system. The system consists of 54generating units. The generating unit data for 54-unitsystem is adapted from [29] and reliability data isadapted from http://motor.ece.iit.edu/data/IEEE118-busdata.xls. For IEEE 118 bus system, ERED problem issolved using CSA and best compromise solution satis-fying all the constraints is given in Table 8. At the endof the solutions obtained using CSA, feasible designsare filtered in design space to obtain a Pareto-optimalfront and are shown in Figure 8.

9. CONCLUSION

This paper has employed the breeding behaviour ofcuckoos and the characteristics of Levy flights on theconstrained optimization problem. The searchingbehaviour of cuckoos for laying an egg in the host nestis modelled and used for solving complex, non-linear,non-convex, and conflicting objective functions.

Table 7: ERED problem solution � IEEE RTS 24 bus system �Case 2

PSO ABC CSA

Fuel cost, $ 44,495 44,216 43,901Emission, ton 25,941 25,777 25,747EENS, KWh 9161.2 9233.3 9138.2

Table 6: EED problem solution � IEEE RTS 24 bus system �Case 1

PSO ABC CSA

Fuel cost, $41,706 41,304 42,014

Emission, ton25,834 25,868 25,390

Total cost, $213,910 213,740 211,260

Figure 7: Pareto-optimal front � 6-unit system � Case 2.

Table 8: ERED solution � IEEE 118 bus system � Case 2

Generated dispatch, MW

Obj. fun.MinFC

MinE

MinEENS

Min Fc, E, andEENS

Fuel cost Fc, $ 113,984.1 115,879.08 118,036.75 115,600Emission E, ton 1,674,369 210,036 1,288,072 213,680EENS, KWh 15.3912 15.3688 14.9452 15.2860

Figure 8: Pareto-optimal front � IEEE 118 bus system �Case 2.



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� The CSA when applied to practical EED problem isfound to provide a better compromise solution withrespect to other techniques reported in the literature.

� The membership function for reliability level of thesystem is modelled and the importance of incorporat-ing the reliability function in a practical EED problemis demonstrated.

� Finally, the CSA is applied to the proposed EREDproblem and the best compromise solution ispresented.

The feasibility and robustness of the proposed method-ology is demonstrated and validated on 6-unit (smallsystem), IEEE RTS 24 bus system and IEEE 118 bus sys-tem (large-scale system) for a MOED problem. Fromthe results, it is obvious that the proposed method isable to give a healthy distributed Pareto-optimal setand is capable of finding a desirable best compromisesolution.

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AuthorsK. Chandrasekaran was born in India and receivedhis Bachelor’s of Engineering (Electrical and Elec-tronics Engineering) and Master’s of Engineering(Power system) at Anna University, Chennai, Indiain the year 2005 and 2007. He obtained his PhD,(Power System Engineering) at National Instituteof Technology (NIT), Tiruchirappalli, India in theyear 2012. Currently he is an assistant professor inthe Department of Electrical and Electronics Engi-

neering at National Institute of Technology Puducherry (NITPy), Karaikal,India.

His research interest includes Deregulation of Power system and Power Sys-tems Planning and Reliability, Application of Swarm Intelligence to powersystem, Renewable generation system.

E-mail: [email protected]

Sishaj Pulikottil Simon was born in India andreceived his Bachelor’s of Engineering (Electricaland Electronics Engineering) and Master’s of Engi-neering (Applied Electronics) at Bharathiar Univer-sity, Coimbatore, India in the year 1999 and 2001.He obtained his PhD, (Power System Engineering)at Indian Institute of Technology (IIT), Roorkee,India in the year 2006. Currently he is an assistantprofessor in the Department of Electrical and

Electronics Engineering at National Institute of Technology (NIT) (formerlyRegional Engineering College), Tiruchirappalli, Tamil nadu, India.

He has taught courses in Basic Electrical Engineering, Power Systems Plan-ning and Reliability, Artificial Intelligence and Artificial Neural Networks. Hisfield of interest is in the area of Deregulation of Power System, Power Sys-tem Operations and Control, Application of Artificial Intelligence, and NewOptimization Techniques to Power System.


Narayana Prasad Padhy, born in India, SeniorMember (2009) IEEE, received his PhD, (PowerSystems Engineering) from Anna University, Chen-nai, India in the year 1997. He is working as a pro-fessor in the Department of Electrical Engineering,Indian Institute of Technology (IIT) Roorkee, India.During 2005-06 he worked as a Research Fellow inthe Department of Electronics and Electrical Engi-neering, University of Bath, UK, under the BOY-

SCAST Fellowship from the Govt. of India. He has been awarded theHumboldt Research Fellowship for Experienced Researchers in 2009 tocarry out research at University Duisburg-Essen, Germany. His researchinterests are in power systems analysis, pricing, economics, optimizationand AI.


DOI: 10.1080/03772063.2014.901592; Copyright © 2014 by the IETE



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mailto:chansekaran23&commat;gmail.com

mailto:chansekaran23&commat;gmail.com

mailto:sishajpsimon&commat;nitt.edu

mailto:sishajpsimon&commat;nitt.edu

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cuckoo search algorithm for emission reliable economic multi-objective dispatch problem

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