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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of ...

International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.



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  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291224 | P a g eCombined Economic Load And Emission Dispatch EvalutionUsing Bat Algorithm1Rakesh.V, 2Mrs.S.B.Aruna, 3Dr.T. Deva Raju1(PG Student (M.TechElectrical Power Systems), SreeVidyanikethan Engineering College, Tirupati.)2(Assistant Professor, Dept. of EEE, SreeVidyanikethan Engineering College, Tirupati.)3(Professor & HOD, Dept. of EEE, SreeVidyanikethan Engineering College, Tirupati.)AbstractThis paper presents an application ofBAT algorithm for multi-objective optimizationproblem in power system. Considering theenvironmental impacts that grow from theemissions produced by fossil-fuelled power plant,the economic dispatch that minimizes only thetotal fuel cost can no longer be considered assingle objective. Application of BAT algorithm inthis paper is based on mathematical modelling tosolve economic, emission and combined economicand emissions dispatch problems by a singleequivalent objective function. BAT algorithm hasbeen applied to two realistic systems at differentload condition. Results obtained with proposedmethod are compared with other techniquespresented in literature. BAT algorithm is easy toimplement and much superior to otheralgorithms in terms of accuracy and efficiency.Keywords: Economic dispatch; BAT algorithm;Artificial Bee Colony algorithm; Combinedeconomic and emission dispatch; Mathematicalmodelling.I. INTRODUCTIONThis paper introduce the economic dispatchproblem in a power system to determine the optimalcombination of power output for all generating unitswhich will minimize the total fuel cost whilesatisfying load and operational constraints. Theeconomic dispatch problem is very complex to solvebecause of a non-linear objective function, and alarge number of constraints.Well known long-established techniquessuch as integer programming2, dynamicprogramming3, and lagarangian relaxation4have beenused to solve the economic dispatch problem.Recently other optimization methods such asSimulated Annealing5, Genetic Algorithm6, ParticleSwarm optimization7, and Tabu SearchAlgorithm8are presented to solve the economicdispatch problem. This single objective economicdispatch can no longer considered due to theenvironmental concerns that arise from the emissionproduced by fossil-fuelled electric power plants.Economic and environmental dispatch is a multi-objective problem.Recently, various modern heuristics multi-objectiveevolutionary algorithms such as Non-dominatedSorting Genetic Algorithm- II9(NSGA-II),Evolutionary Programming algorithm10(EP),Strength Pareto Evolutionary Algorithm11(SPEA)and Multi-Objective Particle Swam Optimizationalgorithm12(MOPSO)may prove to be efficient insolving EED problem by tackling both twoobjectives of EED problem simultaneously ascompeting objectives. But all these methods seem tobe lack of ability to find the Pareto-optimal front dueto their drawbacks: NSGA-II and SPEA may obtainonly near Pareto-optimal front with long simulationtime when applied to solve EED problem because ofthe premature convergence of Genetic Algorithm(GA) which they are based on; EP suffers from theoscillation of the solution, and computational timemay be too long when applying EP to solve EEDproblem; the premature convergence of PSO maylead optimization progresses of MOPSO methods tothe local Pareto-optimum front, which woulddegrade their performance in solving EED problem.In [17-18] including emission constrains to theeconomic dispatch and unit commitment problemshave been presented,under cost-minimizationenvironment.In this paper a multi-objective optimizationproblem i.e., BAT algorithm is proposed to solvecombined economic and emissions dispatchproblems is presented and the effectiveness ofproposed algorithm is demonstrated using three andsix generating unit test systems.II. COMBINEDENVIRONMENTALECONOMICDISPATCHThe traditional economic dispatch problemhas been defined as minimizing of an objectivefunction i.e., the generation cost function subject toequality constraints (total power generated should beequal to total system load plus losses for allsolutions) and inequality constraints (generationsshould lie between their respective maximum andminimum specified values). The objective function(1) is minimised subjected to equality constraint (2)and inequality constraints (3).(1)
  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291225 | P a g e(2)(3)Where x is a state variable, Pi is the control variable,i.e., real power setting of generator and n is thenumber of units or generators.There are several ways to include emissioninto the problem of economic dispatch. Reference[19] summarizes the various algorithms for solvingenvironmental dispatch problem with differentconstraints. One approach is to include the reductionof emission as an objective. In this work, onlyreduction is considered because it is asignificant issue at the global level. A price penaltyfactor (h) is used in the objective function tocombine the fuel cost, Rs/hr and emission functions,kg/hr of quadric form.The combined economic and emission dispatchproblem can be formulated as to minimize(4)+ ) / (5)Subject to equality and inequality constraint definedby equations (2), (3). Once price penalty factor (h) isknown, equation (5) can be rewritten as)} / (6)This has the resemblance of the familiarfuel cost equation, once h is determined. A practicalway of determining h is discussed by Palanichamyand Srikrishan [8]. Consider that the system isoperating with a load of PD MW, it is necessary toevaluate the maximum cost of each generator at itsmaximum output, i.e.,(i) Evaluate the maximum cost of each generatorat its maximum output, i.e.,(7)(ii) Evaluate the maximum emission ofeach generator at its maximum output, ie,(8)(iii) Divide the maximum cost of each generatorby its maximum emission, i.e.,(9)Recalling thatRs/kg (10)(iv) Arrange hi (I = 1,2,......,n) in ascendingorder.(v) Add the maximum capacity of each unit,one at a time, starting from the smallest unit untiltotal demand is met as shown below.(11)At this stage, hi associated with the last unit in theprocess is the price penalty factor h Rs/Kg for thegiven load.Arrange hi in ascending order. Let ‘h’ be avector having ‘h’ values in ascending order.(12)For a load of PD starting from the lowest hivalue unit, maximum capacity of unit is added oneby one and when this total equals or exceeds theload, hi associated with the last unit in the process isthe price penalty factor for the given PD. Thenequation (6) can be solved to obtain environmentaleconomic dispatch using lambda iteration method.III. Bat AlgorithmBats are fascinating animals. They are theonly mammals with wings and they also haveadvanced capability of echolocation. Most of batsuses echolocation to a certain degree; among all thespecies,microbats are famous example as microbatsuse echolocation extensively, while megabats do not.Microbats use a type of sonar, called echolocation,to detect prey, avoid obstacles, and locate theirroosting crevices in the dark.If we idealize some of the echolocationcharacteristics of microbats, we can develop variousbat-inspired algorithms or bat algorithms. Forsimplicity, we now use the following approximate oridealized rules:1.All bats use echolocation to sense distance, andthey also know the difference between food/prey andbackground barriers.2.Bats fly randomly with velocity at positionwith a fixed frequency (or wavelength λ),varying wavelength λ (or frequency f) and loudnessto search for prey. They can automatically adjustthe wavelength (or frequency) of their emitted pulsesand adjust the rate of pulse emission rϵ [0,1],depending on the proximity of their targets;3.Although the loudness can vary in many ways, weassume that the loudness varies from a large(positive) to a minimum value .
  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291226 | P a g eAnother obvious simplification is that noray tracing is used in estimating the time delay andthree dimensional topography. In addition to thesesimplified assumptions, we also use the followingapproximations, for simplicity. In general thefrequency f in a range [ ] corresponds to arange of wavelengths [ ]. For example, afrequency range of [20 kHz, 500 kHz] correspondsto a range of wavelengths from 0.7mm to 17mm.In simulations, we use virtual bats naturally. Wehave to define the rules how their positions andvelocities in a d-dimensional search space areupdated. The new solutions and velocities attime step t are given by(13)(14)whereβϵ [0, 1] is a random vector drawn from auniform distribution. Here is the current globalbest location (solution) which is located aftercomparing all the solutions among all the n bats. Asthe product is the velocity increment, we canuse either (or ) to adjust the velocity changewhile fixing the other factor (or ), depending onthe type of the problem of interest. For the localsearch part, once a solution is selected among thecurrent best solutions, a new solution for each bat isgenerated locally using random walk(15)Where ϵ ϵ [−1, 1] is a random number,while =< >is the average loudness of all thebats at this time step.Based on the above approximations andidealization, the pseudo-codeof the Bat Algorithm(BA) can be summarized below.3.1 PSEUDO-CODE OF THE BAT LGORITHMObjective function f(x), x =Initialize the bat population (i = 1, 2, .., n) andDefine pulse frequency atInitialize pulse rates and the loudnesswhile(t <Max number of iterations)Generate new solutions by adjusting frequency,and updating velocities and locations/solutions[equations (13) to (15)]if(rand > )Select a solution among the best solutionsGenerate a local solution around the selected bestsolutionend ifGenerate a new solution by flying randomlyif(rand < &f( ) < f( ))Accept the new solutionsIncrease and reduceend ifRank the bats and find the current bestend whilePost process results and visualizationIV. SIMULATION RESULT ANDDISCUSSIONSThe applicability and efficiency of BATalgorithm for practical applications has been testedon two test cases. The programs are developed usingMATLAB 7.9.The Parameters for BAT algorithmconsidered here are: n=20; A=0.9; r=0.1; ;.Test case 1: The system consists of three thermalunits. The parameters of all thermal units areadapted from [1].Table: 1 Comparison of test results for Three Generating unitsLoaddemandh*,Rs/kgPerformanceConventionalMethod [7]SGA [7] RGA [7] ABC BAT400MW44.788Fuel cost,Rs/hr20898.83 20831.54 20801.81 20838.729 208378.277Emission,kg/hr201.5 201.35 201.21 200.198 200.211Power loss,MW7.41 7.69 7.39 7.403120 7.401407Total cost,Rs/hr29922 29820 29812 29805.615 29804.905500MW 44.788Fuel cost,Rs/hr25486.64 25474.56 25491.64 25494.904 254939.128Emission,kg/hr312.0 311.89 311.33 311.125 311.133Power loss,MW11.88 11.80 11.70 11.679210 11.67600Total cost, 39458 39441 39433 39429.646 39429.040
  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291227 | P a g eRs/hr700MW 47.82Fuel cost,Rs/hr35485.05 35478.44 35471.4 35462.826 35462.501Emission,kg/hr652.55 652.04 651.60 354.628 651.505Power loss,MW23.37 23.29 23.28 23.334221 23.3300Total cost,Rs/hr66690 66659 66631 66617.903 66617.505Table: 1 shows the summarized result ofCEED problem for load demand of 400MW,500MW and 700MW are obtained by the proposedBAT algorithm with stopping criteria based onmaximum-generation=100.Form Table: 1, it is clear that BATalgorithm gives optimum result in terms ofminimum fuel cost, emission level and the totaloperating cost compared to other algorithms.Table: 2 gives the best optimum poweroutput of generators for CEED problem using BAT&ABC algorithm for load demand 400MW,500MW and 700MW.Table: 2 Optimum Power dispatch Results by ABC, Proposed BAT method for three units systemLoad demand,MWAlgorithm P1 P2 P3 Iterations400MWABC 102.5546 152.7996 152.0485 29BAT 102.5589 153.7197 151.1228 8500MWABC 128.8494 191.4610 191.3687 56BAT 128.8501 192.5603 190.2657 18700MWABC 182.6259 270.3542 270.3541 44BAT 182.6477 271.2397 269.4426 7The convergence tendency of proposedBAT algorithm based strategy for power demand of400MW, 500MW and 700 MW is plotted in figure:1. It shows that the technique converges inrelatively fewer cycles thereby possessing goodconvergence property.Figure: 1 convergence of three generating units system for load demand values 400MW, 500MW & 700MW.Test case II: The system consists of six thermalunits. The parameters of all thermal units areadapted from [1]. The summarized result of CEEDproblem for load demand of 500MW and 900MWare obtained by the proposed BAT algorithm withstopping criteria based on maximum-generation=100 is presented in Table: 3.Table: 3 comparison of test Results for six generating unit systemLoaddemandh*,Rs/kgPerformance ConventionalMethod [9]RGA[9]HybridGA [9]HybridGTA [9]ABC BAT500MW 43.898 Fuel cost,Rs/hr27638.300 27692.1 27695 27613.4 27613.247 27612.749Emission,kg/hr262.454 263.472 263.37 263.00 263.013 263.006Power loss, 8.830 10.172 10.135 8.93 8.934145 8.933858
  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291228 | P a g eMWTotal cost,Rs/hr39159.500 39258.1 39257.5 39158.9 39158.9 39158.199900MW 47.822 Fuel cost,Rs/hr48892.900 48567.7 48567.5 48360.9 48350.683 48350.163Emission,kg/hr701.428 694.169 694.172 693.570 693.788 693.772Power loss,MW35.230 29.725 29.718 28.004 28.009673 28.008975Total cost,Rs/hr82436.580 81764.5 81764.4 81529.1 81529.00 81527.739Form Table: 3, it is clear that BATalgorithm gives the optimum result in terms ofminimum fuel cost, emission level and the totaloperating cost compared to other algorithms.Table: 4 gives the best optimum poweroutput of generators for CEED problem using BAT& ABC algorithms for load demand 500MW and900MW.Table: 4 Optimum Power dispatch results by ABC Approach for six unit systemLoaddemand,MWAlgorithm P1 P2 P3 P4 P5 P6 Iterations500ABC 33.2733 26.8554 89.9135 90.4852 135.6435 132.7631 120BAT 33.2703 26.85061 89.91347 90.48638 135.6411 132.762 18900ABC 92.3297 98.3912 150.1948 148.5588 220.4043 218.1307 132BAT 92.3288 98.3910 150.1132 148.5586 220.4007 218.1267 25The convergence tendency of proposedBAT algorithm based strategy for power demand of500MW and 900 MW is plotted in figure:2. Itshows that the technique converges in relativelyfewer cycles thereby possessing good convergenceproperty.Figure: 2 convergence of six generating unit system for load demand values of 500MW and 900MW.V. CONCLUSIONIn this paper, a new optimization of BATalgorithm has been proposed. In order to prove theeffectiveness of algorithm it is applied to CEEDproblem with three and six generating unit. Theresults obtained by proposed method werecompared to those obtained conventional method,RGA and SGA and Hybrid GA and ABC. Thecomparison shows that BAT algorithm performsbetter than above mentioned methods. The BATalgorithm has superior features, including qualityof solution, stable convergence characteristics andgood computational efficiency. Therefore, thisresults shows that BAT optimization is a promisingtechnique for solving complicated problems inpower system.REFERENCES[1] Gaurav Prasad Dixit, Hari Mohan Dubey,ManjareePandit, B. K. Panigrahi,“Artificial Bee Colony Optimization forCombined Economic Load and EmissionDispatch”,International Conference onSustainable Energy and Intelligent System(SEISCON 2011) ,Dr. M.G.R. University,Maduravoyal, Chennai, Tamil Nadu,India. July.20-22, 2011.[2] Xin-She Yang, A new metaheuristic bat-inspired algorithm.[3] Wood, A. J. and Wollenberg, B. F., PowerGeneration, Operation, and Control, 1996,Wiley, New York, 2nd ed.[4] K.P. wang, C.C. Fung, “Simulatedannealing based economic dispatch
  • Rakesh.V, Mrs.S.B.Aruna, Dr.T. Deva Raju / International Journal of Engineering Researchand Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1224-12291229 | P a g ealgorithm,” IEE Proc. C 140, volume.6,Nov. 1993 pp. 507-513.[5] L.G. Damousis, A.G. Bakirtzis, S.Dokopoulos, , “Networkconstrainteconomic dispatch using real codedgenetic algorithm,”IEEE Trans. PowerSyst., volume 1, Feb 2003 pp.198-205.[6] C. Palanichamy, K. Srikrishna, “Economicthermal power dispatch with emissionconstraint” J. Institute OfEngg.(India)volume-72, April-1991, 11.[7] M. Sudhakaran, S.M.R Slochanal, R.Sreeram and N Chandrasekhar,“Application of Refined genetic AlgorithmtoCombined Economic and EmissionDispatch” J. Institute Of Engg. (India)volume-85, Sep. 2004pp. 115-119.[8] A. Immanuel Selvakumar, K.Dhanushkodi, J. Jaya Kumar, C. KumarCharlie Pual, “Particle swarmoptimization solutionto emission andeconomic dispatch problem ,”IEEEConference Tencon, paper ID-075Oct.2003[9] M. Sudhakaran and S.M.R Slochanal,“Integrating Genetic Algorithm and TabuSearch for Emission and EconomicDispatch Problem” J. Institute OfEngg.(India) volume-86, June.2005, pp-22-27.[10] Rughooputh HCS, King RTFA.,“Environmental economic dispatch ofthermal units using an elitist multi-objectiveevolutionary algorithm” InProceeding of the IEEE internationalconference on Indus trial technology,ICIT’03, Maribor, Slovenia;. December10–14, 2003 pp. 48–53..[11] Tsay MT, Lin WM., “Application ofevolutionary programming for economicdispatch of cogeneration systems underemission constraints. Electr Power Systvolume: 23(8):pp.805–12. 2001.[12] Abido MA., “Environmental/economicpower dispatch using multi-objectiveevolutionary algorithms.” IEEETransPower Syst. volume: 18(4): 2003,pp.1529–37.[13] Abido MA., “Multiobjective particleswarm optimization for environmental/economic dispatch problem.” ElectrPowerSyst Res; volume: 79(7): 2009 pp.1105–13.[14] D. Karaboga, B. Basturk, On ThePerformance Of Artificial Bee Colony(ABC) Algorithm, Applied SoftComputing,volume 8, Issue 1, January2008, pp- 687-697 .[15] D. Karaboga, B. Basturk, “A Powerful andefficient algorithm for numerical functionoptimization :Artificial BeeColony (ABC)Algorithm, journal of Global optimization,volume 39, Issue 3, 2007, pp- 459-471 .[16] DervisKaraboga, BahriyeAkay, “Acomparative study of artificial bee colonyalgorithm” App. Mathematicsandcomputation, Elsevier, 2009 pp.108-132.[17] C.M. Huang,Y.C. Huang,Anovel“Approach to real-time economic emissionpower dispatch”, IEEE Trans.PowerSystems , volume-18,no. 1 (2003)pp.288–294.[18] M. Muslu, “Economic dispatch withenvironmental considerations: tradeoffcurves and emission reductionrates”,Electric Power Syst. Res. 71 no.2,2004,pp 153–158[19] K. Senthil and K. Manikandan, “EconomicThermal Power Dispatch with emissionconstraint and valve point effect Loadingusing inmprovedTabu search algorithm”Int. Journalof Computer App.,volume.3,no.9,July-2010, pp.6-11.*h values are considered based on literature.