Sudip Kumar Ghorui 1, Roshan Ghosh2, Subhashis Maity
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-55181Economic Load Dispatch of Power System UsingGrey Wolf Optimization with Constriction FactorSudip Kumar Ghorui1, Roshan Ghosh2, Subhashis Maity3,1Assistant Professor, Department of Electrical EngineeringBudge Budge Institute of ant Professor, Electrical engineering DepartmentBudge Budge Institute of TechnologyKolkataghosh.roshan@gmail.com3Student, Department of Electrical EngineeringBudge Budge Institute of TechnologyKolkataashiscool7@gmail.comAbstract: In this paper, we propose a new meta-heuristic, nature inspired technique known as Grey Wolf Optimization to solveEconomic Load Dispatch (ELD) problems of thermal power units considering transmission losses, and constraints such as ramp ratelimits and prohibited operating zones. Grey Wolf Optimization Algorithm (GWOA) is a relatively new optimization technique.Mathematical models of this algorithm demonstrate the efficiency, quality of solution and convergence speed of the method andsuccessful application of the algorithm on economic load dispatch problems. Simulation results found that the proposed approachoutperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency.Results also be confirmed the robustness of the proposed methodology.IJSERKeywords: Economic load dispatch, Grey Wolf optimization technique, prohibited operating zone, quadratic cost function, ramprate limits,1. IntroductionEconomic load dispatch (ELD) is applied in electric powerutilities is to provide high-quality, reliable power supply tothe consumers at the lowest possible tariff. It can be definedin normal condition the operation of generation facilities isto produce electrical power at the lowest cost to reliablyserve consumers, recognizing any operational limits ofgeneration and transmission facilities. It is an important rolein electrical power system operation for allocatinggeneration among the committed units such that theimposed constraints and the energy requirement aresatisfied. The characteristics of fuel cost for moderngenerating units are highly nonlinear with demand forsolution techniques having no restrictions on to the shape ofthe fuel cost curves. For science and engineering, manyoptimization techniques are developed for used in ELDproblem to accomplish to the main goal. But the calculusbased methods [1] are not fulfillment to solving ELDproblems, as these techniques are required smooth,differentiable objective function. Another method which isLinear programming method [2] is speedy and reliable but ithas some drawback related with the piecewise linear costapproximation. In power system small improvements in theunit output scheduling can give significant cost savings. Sothe dynamic programming approach was proposed by Woodand Wollenberg [3] to solve ELD problems but thistechnique does not impose any restriction on the nature ofthe cost curves, but suffers from the “curse ofdimensionality” or local optimality and larger simulationtime. In order to overcome this problem in current years,several attempts have been made to solve ELD withintelligent and modern technique which is meta-heuristicalgorithm is helpful for solution of complex ELD problemsthey are Genetic algorithm [4], particle swarm optimization[5], Simulated Annealing (SA)[6], Artificial NeuralNetworks [7] ,Differential evolution [8], Tabu search [9],Evolutionary Programming (EP) [10], Ant colonyoptimization [11] , Artificial immune system (AIS) [12],Bacterial Foraging Algorithm (BFA) [13], Biogeographybased Optimization (BBO) [14] etc. This mentioned methodmay confirm to be very effective for solving nonlinear ELDproblems without any restriction on the shape of the costcurves. They often provide a fast, reasonable nearly globaloptimal solution but these methods do not always assuranceglobal best solutions, they often achieve a fast and nearglobal optimal solution. In recent years, differenthybridization and modification of GA, EP, PSO, DE, BBOlike improved GA with multiplier updating (IGA-MU) [15]directional search genetic algorithm (DSGA) [16], hybridgenetic algorithm (GA)-pattern search (PS)-sequentialquadratic programming (SQP) (GA-PS-SQP) [17],improved fast evolutionary programming (IFEP) [18], newPSO with local random search (NPSO LRS) [19], adaptivePSO (APSO) [20], self-organizing hierarchical PSO (SOHPSO) [21], improved coordinated aggregation based PSO(ICA-PSO) [22], improved PSO [23], combined particleswarm optimization with real-valued mutation (CBPSORVM)[24], DE with generator of chaos sequences andIJSER 2016http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-5518sequential quadratic programming (DEC-SQP) [25],variable scaling hybrid differential evolution (VSHDE) [26],hybrid differential evolution (DE) [27], bacterial foragingwith Nelder–Mead algorithm (BF-NM) [28], hybriddifferential evolution with biogeography-based optimization(DE/BBO) [29] etc are being anticipated to solve ELD forsearch better excellence and fast solution. Population basedbio-inspired algorithm are Evolutionary algorithms, swarmintelligence and bacterial foraging etc. But they havecommon disadvantages which is these algorithms arecomplicated computation for using many parameters. Forthat reason it is also difficult to understand these algorithmsfor beginners.2(4)Where Pi min and Pi max are the minimum and maximum powergenerated by generator ith unit, respectively.2.1.3 Ramp Rate Limit Constraint:This paper presents, a new global optimization techniquewhich is GWOA, influenced by grey wolves’ leadership andhunting behaviors to solve Economic Load Dispatch (ELD)problem. For superior performance of GWOA, it is used tosolve ELD problem. Section 2 discusses the mathematicalproblem formulation of ELD while brief description ofGWOA technique is presented in Section 3.Simulationstudies are presented and discussed in Section 4. Theconclusion is drawn in Section 5.The power P i generated by the ith generator in certaininterval could not exceed that of previous interval P i0 bymore than a certain amount U Ri is the up-ramp rate limitand neither may it be less than that of the previous intervalby more than some amount D Ri the down-ramp rate limit ofthe generator. These give rise to the following constraints.As generation increases,Pi Pi 0 U Ri(5)As generation decreases,Pi 0 Pi DRi(6)Modified generation limits after considering ramp ratelimits are given bellowmax(7)max( Pi min , Pi 0 DRi ) Pi min( Pi , Pi 0 U Ri )2. MATHEMATICAL MODELING OF THE ELD2.1.4 Prohibited Operating Zone:PROBLEMThe prohibited operating zones are the range of outputpower of any generator where the operation causes unduevibration of the turbine shaft. Generally such vibrationoccurs at the point of opening or closing of the steam valvewhich might cause damage to the shaft and bearings. It isdifficult to determine the exact prohibited zone by actualtesting or from operating records. Normally operation isavoided in such regions.Hence mathematically the feasible operating zones of unitcan be described as follows:Pi min Pi Pi ,l1IJSERThe traditional formulation of the ELD problem is tominimize the fuel cost of generations for both convex andnon-convex nonlinear constrained optimization problem. Inthis section, ELD problems have been formulated and solvedby GWOA approach. These are presented below:2.1 ELD with quadratic cost function, ramp rate limit,prohibited operating zone and transmission lossThe overall objective function F T of ELD problem maybe written as(( )NN2FTmin Fi Pi min ai b i Pi ci Pi i 1 i 1)(1)2.1.1. Real Power balance constraint:Ni 1i(2) (PD PL ) 0Where, P D is the total load demand by consumer; P L is thetotal transmission loss in power system; Calculation of P Lusing the B- coefficients matrix is expressed as:PL NN P Bi 1j 1iijui , niPWhere, F i (P i ), is fuel cost function of the ith generator,and is usually expressed as a quadratic polynomial function;N is the total number of committed generators; a i , b i and c iare the cost coefficients of the ith generator; P i is thegenerated power of the ith generator. The ELD problemconsists in minimizing FT subject to following constraints: PPi ,uj 1 Pi Pi ,l j ;NPj B0 i Pi B00i 1 Pi Pi(8)Where j represents the number of prohibited operatingzones of unit i. Pi ,uj 1 is the upper and Pi ,l j is the lower limitof jth prohibited operating zone of ith unit. ni is the totalnumber of prohibited operating zone of the ith unit.2.2 Calculation for slack generator:Let N committed generating units are delivering theirpower output maintaining the power balance constraint (2)and the respective capacity constraints of (4) and/or (7), (8).Itis assumed that the power loadings of first (N-1) generatorsare known, the power level of Nth generator (called SlackGenerator) is given by( N 1)(9)P P P PN(3)2.1.2 Generation capacity constraint:There is a limit on the amount of active powergeneration. For normal condition, real power output of eachgenerator is restricted by lower and upper bounds as follows:j 2,3, nimaxDL i 1iThe transmission loss PL , which is a function of all thegenerator outputs including the slack generator, is given byN 1 N 1 N 1 PL Pi Bij Pj 2 PN B Ni Pi B NN PN2i 1 i 1 i 1 Pi min Pi Pi maxN 1 Boi Pi BON PN B00i 1IJSER 2016http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-5518(10)By expanding and rearranging, (10) becomes N 1 B NN PN2 2 B Ni Pi BON 1 PN i 1 N 1 N 1N 1N 1 PD Pi Bij Pj BOi Pi Pi BOO 0i 1 j 1i 1i 1 (11)Using standard algebraic method, loading of the dependentgenerator (i.e., Nth) can be found out by solving (11). Theabove equation can be simplified as(12)XPN2 YPN Z 03 Where A and C are the coefficient vectors, X P is the prey’s position vector, X denotes the grey wolf’s positionvector and‘t’ is the current iteration. The mathematical calculation of vectors A and C is doneas follows [30]: A 2.a.r1 .a(16) C 2.r2WhereX B NN N 1 Y 2 B Ni Pi BoN 1 i 1N 1 N 1N 1N 1 z PD Pi Bij Pj Boi Pi Pi Boo i 1 j 1i 1i 1 (17) Where values of ‘ a ’ are linearly reduced from 2 to 0during the course of iterations and r 1 , r 2 are arbitraryvectors in the gap [0, 1].The positive roots of the equation are obtained as Y Y 2 4 XZ ,WhereY 2 4 XZ 0P B. Hunting: Alpha, beta and delta guided the entire groupwith their better knowledge about the potential location ofprey. The other agents update their positions according tothe best search agent’s position. The update of their agentscan be expressed as follows [30] Dα C1 . X α X Dβ C 2 . X β X Dδ Cδ . . X δ X (18) X 1 X α A1 . Dα X 2 X β A2 . Dβ X 3 X δ A3 Dδ (19) X1 X 2 X 3X (t 1) 3(20)N2X(13)In order to satisfy the equality constraint (9), the positiveroot of (13) is taken as output of the Nth generator. If thepositive root of quadratic equation violates operation limitconstraint of (4) at the initialization process of thealgorithm, then Generation value of first (N-1) generators isreinitialized until the positive root satisfies the operationlimit and other constraints (if any).IJSER3. GREY WOLF OPTIMIZATION ALGORITHM(GWOA)This section presents an interesting new optimizationalgorithm called grey wolf optimization algorithm (GWOA)which was proposed by Mirjalili and Mirjalili [30]. Thistechnique based on behaviour of grey wolf in searching andhunting of their quarry. The leaders of the group, a maleand a female are called alpha (α). The next levels of greywolves, which are subordinate wolves mainly provide helpto the leaders for decision making or in other activities, arecalled beta (β). The third level of grey wolves dominate theomega which are known as delta (δ). The last rank of thegrey wolves is called omega (ω), which surrenders to all theother governing wolves. The proposed technique (GWOA)is provided in the mathematical models as follows:A. Social hierarchy: If we draw a mathematical model ofthis algorithm, we consider social hierarchy of the greywolves; here alpha (α) has best fittest solution. The secondbest solution beta (β) and third best solution delta (δ) belongto the grey wolf family. The omega (ω) is the last candidatesolution. Therefore alpha (α), beta (β) and delta (δ) helpedin the GWO technique (hunting). The last member, of thewolves ω follows these three wolves.Encircling Prey: The wolf during hunting period tends toencircle their prey. The following equations express thebehavior[30]: [] D C . X p (t ) X (t )(14) X (t 1) X p (t ) A.D(15)( )( )( )C. Search for prey and attacking prey This is the finalposition of this algorithm. Under this circumstance they willbe in a random position within a circle which is defined bythe positions of the alpha, beta, and delta in the searchspace. In fact alpha, beta, and delta estimate the victim’sposition and other wolves update their positions randomlyaround the victim.3.2. METHODOLOGYSince the appraisal variables for ELD problem are realpower output for each generator but here they are used torepresent the wolf’s population structure where P is totalpopulation for each group and n is number of groups. Thewhole population is n*P. Each individual populationstructure represents the real power output for each generatorand also fulfillment (4). For initialization purpose we canchoose the number of generating units N and total numberof population structure PopSize.By the following the complete population structure isrepresented asWhere, i 1, 2, .PopSize.P Pi [P1 , P2 , P3 ,.Ppopsize ]Here the population set is P which is each individualelement of the population structure of matrix. Thispopulation set P is initialized randomly within theIJSER 2016http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-551811fulfillment real power balance constant and generatorcapacity constant. This initialization is based on (4), (7) and12(8) when consider ramp rate limit, prohibited operating13zone. For this initialization process, choose no. of generator14units N and also Specify maximum and minimum capacity15of each generator, power demand, B-coefficients matrix forcalculation of transmission loss.In ELD problem here fitness value is fuel cost of generationfor all the generators which calculated using (1) for thesystem having quadratic fuel cost characteristic. This Eq. (1)applies to determine performance evolution of ELD problemuntil the optimum cost is achieved. The technique willcontinue until the maximum no. of iteration is met and theoptimum result is 019295555205532312.40.004447555520TABLE NO. 02PROHIBITED ZONES OF GENERATING UNITSUnitProhibited zones (MW)25[185 225] [305 335] [420 450][180 200] [305 335] [390 420]6[230 225] [365 395] [430 455]12[30 40] [55 65]TABLE 3BEST POWER OUTPUT FOR 15-GENERATORS SYSTEM(P D 2630MW)UnitProposedGA [5]PSO [5]4. RESULTS AND DISCUSSIONSProposed GWOA has been applied for solving ELDproblem in a test system and its performance has beencompared to several other optimization technique like GA[5], CTPSO [23] and PSO [5, 23] for verifying its feasibility.The essential codes has been written in MATLAB-7language and executed on a 2.0 GHz Intel Pentium (R) DualCore personal computer with 1-GB .9853129.9925130.0000130.0000IJSER4.1. Description of the Test SystemTest System 1: In this paper, 15 generating units with ramprate limit and prohibited operating zones constraints hasbeen considered and transmission loss has been alsoincluded in this problem. Consumer power demands are2630 MW and the characteristics of the fifteen thermal unitsare given in Tables 1 and 2. The loss coefficients are givenin [5]. This paper results obtained from proposed GWOA,PSO [5] and different versions of PSO [23] and othermethod are presented in this paper. Their best results areshown in Table 3. Minimum, average and maximum fuelcosts obtained by GWOA and different versions of PSO[23], over 50 trials are presented in Table 4.TABLE NO. 01GENERATING UNIT DATACONSUMER POWER DEMANDS ARE 2630 MWUnitPimin(MW)Pimaxai ( )(MW)βi( /MW)γiURi2( /MW ) (MW/h)Pi 0(MW/h) 20.000183801203003201303744201305150470613578CTPSO [23] CSPSO 1445113.493658.918658.9207P 10160.00000089.2567101.1142160.0000160.0000P 1180.00000060.057233.911680.000080.0000P 1280.00000049.999879.958380.000080.0000P 1326.52365238.771325.004225.000025.0000P 1414.96232141.942541.414015.000015.0000P 270432704Fuel Cost32701.870839( /hr.)TABLE 4COMPARISON BETWEEN DIFFERENT METHODS TAKEN AFTER50 TRIALS (15-GENERATORS SYSTEM)MethodsGeneration Cost ( /hr.)Time/Iterat No. of hitsion (Sec)tominimumsolutionMax.Min.AverageGWOA 32705.452356 32701.870839 32702.15735CTPSO[23] 32704.4514 32704.4514 32704.451414.2522.546NA*CSPSO[23] 32704.451432704.451432704.451416.1NACOPSO[23] 32704.451432704.451432704.451485.1NACCPSO[23] 32704.451432704.451432704.451416.2NA* NA:- Data4.2. Comparative study:1) Solution Quality: Table 3 represents comparable studiesof GWOA algorithm with other optimization methods and itis found that GWOA algorithm reaches the best result offuel costs in power system. Table 4 gives comparativeIJSER 2016http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-5518studies for minimum, maximum and average values fordifferent technique with other method. From these results itis observed that the performance of GWOA is better, interms of quality of solutions obtained.2) Computational Efficiency: Table 3, shows 15 units whilecomparing it with other technique and the cost is found tobe 32701.870839 /hr., The cost is compared to the resultsobtained by many previously developed techniques and it isfound to be lesser. The time taken by GWOA to achieveminimum fuel costs is quite less compared to that obtainedby many other techniques. These are shown in Table 4.These outputs prove significantly better computationalefficiency of GWOA.3) Robustness: Performance of any heuristic algorithmscannot be judged by the results of a single run. Normallytheir performance is judged after running the programs ofthose algorithms for certain number of trials. A largenumbers of trials with different initializations of populationsize should be made to obtain a useful conclusion about theperformance of the technique. An algorithm is said to berobust, if it gives consistent result during all trials. Thisperformance is much superior compared to many otheralgorithms, presented in the different literatures in table 4.Therefore, the above results establish the enhancedcapability of GWOA to achieve superior quality solutions, ina computational efficient and robust way.CONCLUSION[6] C. K. Panigrahi, P. K. Chattopadhyay, R. N. Chakrabarti, andM. Basu, “Simulated annealing technique for dynamic economicdispatch”, Elect. Power components and syst., vol. 34, no.5,pp.577-586, May 2006.[7] C.-T. Su and C.-T. Lin, “New approach with a Hopfieldmodeling framework to economic dispatch”, IEEE Trans. PowerSyst., vol. 15, no. 2, pp. 541, May 2000.[8] N. Nomana and H. Iba, “Differential evolution for economicload dispatch problems”, Elect. Power Syst. Res., Vol. 78, No. 3,pp. 1322–1331, 2008.[9] S. Khamsawang, C. Boonseng and S. Pothiya, “Solving theeconomic dispatch problem with Tabu search algorithm”. IEEEInt. Conf. Ind. Technol., vol. 1, pp. 274–278, 2002.[10] T. Jayabharathi, K. Jayaprakash, N. Jeyakumar, and T.Raghunathan, “Evolutionary programming techniques for differentkinds of economic dispatch problems,” Elect. Power Syst. Res.,vol. 73, no. 2, pp.169-176, February 2005.[11] Y. H. Hou, Y. W. Wu, L. J. Lu, X. Y. Xiong, “GeneralizedAnt Colony Optimization for Economic Dispatch of powersystems”, Proceedings of International Conference on Power Syst.Technology, Power-Con 2002, Vol. 1, pp. 225-29, 13 – 17 October2002.[12] B. K. Panigrahi, S. R. Yadav, S. Agrawal, and M. K. Tiwari,“A clonal algorithm to solve economic load dispatch”, Elect.Power Syst. Res., Vol. 77, No. 10, pp. 1381–1389, 2007.[13] B. K. Panigrahi and V. R. Pandi, “Bacterial foragingoptimization: Nelder-Mead hybrid algorithm for economic loaddispatch,” IET Gener., Transm., Distrib., Vol. 2, No. 4, pp. 556–565, 2008.[14] A. Bhattacharya, P. K. Chattopadhyay, “Biogeography-BasedOptimization for Different Economic Load Dispatch Problems”,IEEE Trans. Power Syst., vol. 25, no. 2, pp. 1064-1077, May 2010.[15] C.-L Chiang, “Improved genetic algorithm for powereconomic dispatch of units with valve-point effects and multiplefuels”, IEEE Trans. Power Syst., vol. 20, no. 4, pp. 1690–1699,2005.[16] T. Adhinarayanan, and M. Sydulu, “A directional searchgenetic algorithm to the economic dispatch problem withprohibited operating zones”, in Proc. IEEE/PES Transm. andDistrib. Conference Expo. 2008, vol. 1, pp. 1–5, Chicago, IL, 21–24 April 2008.[17] J. S. Alsumait, J. K. Sykulski, A. K. Al-Othman, “A hybridGA–PS–SQP method to solve power system valve-point economicdispatch problems”, Appl. Energy, vol. 87, no.5, pp. 1773–1781.2010.[18] N. Sinha, R. Chakrabarti, P. K. Chattopadhyay, “Evolutionaryprogramming techniques for economic load dispatch”, IEEE Trans.Evol. Comput., vol. 7, no. 1, pp. 83–94. 2003.[19] I. Selvakumar and K. Thanushkodi, “A New Particle SwarmOptimization Solution to Nonconvex Economic DispatchProblems”, IEEE Trans. Power Syst., vol. 22, no. 1, February2007.[20] B. K. Panigrahi, V. R. Pandi, S. Das, “Adaptive particleswarm optimization approach for static and dynamic economic loaddispatch”, Energy Conversion & Managt., vol.49, no.6, pp.1407–15, 2008.[21] K. T. Chaturvedi, M. Pandit, L. Srivastava, “Self-OrganizingHierarchical Particle Swarm Optimization for NonconvexEconomic Dispatch”, IEEE Trans. Power Syst, vol. 23, no. 3, pp.1079, August 2008.[22] J. K Vlachogiannis, and Y. Lee Kwang, “Economic LoadDispatch—A Comparative Study on Heuristic OptimizationTechniques With an Improved Coordinated Aggregation-BasedPSO”, IEEE Trans. Power Syst., vol. 24, no. 2, pp. 991-1001, May2009.[23] J.-B. Park, Y.-W. Jeong, J.-R. Shin, Y. Lee Kwang, “Animproved particle swarm optimization for nonconvex economicIJSERIn this paper, we present a newly developed GWOAmethod, which is very flexible, quite efficient, rarely getstrapped in global minima. It does not requirecomputationally expensive derivatives, and is quite easy. Ithas been successfully implemented to solve differentconstraints, ELD problems. This simulation results provedthat the performance of GWOA is better as compared to thatof several previously developed optimization techniques.Therefore GWOA process can be considered as one of thepowerful tool to solve ELD problem. In future, GWOA canalso be tried for solution of complex hydrothermalscheduling, optimal power flow problems and dynamicELD, in the search for good characteristics results.REFERENCES[1] A. A. El-Keib, H. Ma, J. L. Hart, “Environmentallyconstrained economic dispatch using the Lagrangian relaxationmethod”, IEEE Trans. Power Syst., Vol. 9, no.4, pp. 1723–1729,November 1994.[2] S. Fanshel, E. S. Lynes, “Economic Power Generation UsingLinear Programming”, IEEE Trans. on Power Apparatus and Syst.,vol. PAS-83, no. 4, pp. 347-356, 1964.[3] J. Wood, B. F. Wollenberg, “Power Generation, Operation,and Control”, John Wiley and Sons, 2nd Edition, 1984.[4] D. C. Walters and G. B. Sheble, “Genetic algorithm solutionof economic dispatch with valve point loadings”, IEEE Trans.Power Syst., vol. 8, no.3, pp.1325-1331, August 1993.[5] Z.-L. Gaing, “Particle swarm optimization to solving theeconomic dispatch considering the generator constraints,” IEEETrans. Power Syst., vol. 18, no.3, pp. 1187-1195, August 2003.5IJSER 2016http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016ISSN 2229-5518dispatch problems”, IEEE Trans. Power Syst., vol 25, no. 1, pp.156–166. 2010.[24] H. Lu, P. Sriyanyong, Y. H. Song, T. Dillon, “Experimentalstudy of a new hybrid PSO with mutation for economic dispatchwith non-smooth cost function”, Int. J. Elect. Power Energy Syst.,vol. 32, no. 9, pp. 921–935, 2010.[25] Leandro dos Santos Coelho and V. C. Mariani, “Combining ofChaotic Differential Evolution and Quadratic Programming forEconomic Dispatch Optimization With Valve-Point Effect”, IEEETrans. Power Syst., vol. 21, no. 2, pp. 989-996, May 2006.[26] J.-P. Chiou, “Variable scaling hybrid differential evolution forlarge-scale economic dispatch problems”, Elect. Power Syst. Res.,vol. 77, no. 3-4, pp. 212–218, March 2007.[27] N. Duvvuru, and K. S. Swarup, “A Hybrid Interior PointAssisted Differential Evolution Algorithm for Economic Dispatch”,IEEE Trans. Power Syst., vol. 26, no. 2, pp. 541–549, 2011.[28] B. K. Panigrahi, V. R. Pandi, “Bacterial foragingoptimization: Nelder–Mead hybrid algorithm for economic loaddispatch”, Proc. Inst. Elect. Eng. Gener. Transm. Distrib., vol. 2,no. 4, pp. 556–565, 2008.[29] A. Bhattacharya, P. K. Chattopadhyay, “Hybrid differentialevolution with biogeography-based optimization for solution ofeconomic load dispatch”, IEEE Trans. Power Syst., vol. 25,no. 4,pp. 1955-1964, 2010.[30] S. Mirjalili, S. M. Mirjalili, & A. Lewis “Grey WolfOptimizer”. Advances in Engineering Software, vol. 69, pp. 46-61,March 2014.Author Profile:IJSERSudip Kumar Ghorui is Assistant professor,Department of Electrical Engineering, Budge BudgeInstitute of technology. He obtained B-Tech (ElectricalEngineering) in 2011 and M-Tech (Power System) in 2013. He has3 years teaching experience. His research interests include powersystem operation, optimization, neural networks and fuzzy logic.Roshan Ghosh is Assistant professor, Department ofElectrical Engineering, Budge Budge Institute oftechnology. He obtained B-Tech (Electrical Engineering)in 2008 and M-Tech (Electrical Engineering) in 2012. He has 3years teaching experience. His research interests include powerelectronics and electric drives, Non-conventional energy sources.Subhashis Maity is a student, Department of ElectricalEngineering, Budge Budge Institute of technology. Hisresearch interests include Power System, Power systemOperation.IJSER 2016http://www.ijser.org6
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STD-11-M DAY 1 2 3 8:00 to 9:00 9:10 to 10:10 10:30 to 11:30 Monday Subject ECONOMICS ENGLISH POLITICAL SCIENCE Teacher DR ROSHAN SHARMA SUNIL KUMAR DR. SUVRA M Tuesday Subject ECONOMICS ENGLISH POLITICAL SCIENCE Teacher DR ROSHAN SHARMA SUNIL KUMAR
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Level 2B Korean is a further study of the Korean language and some aspects of Korean culture and daily life as the fourth phase of an elementary Korean language course. Through synchronous online sessions, the integrated development of language skills (listening, speaking, reading, and writing) will be promoted. To further develop basic communicative competence, .
