Water Evaporation algorithm to solve combined Economic and Emission dispatch problems

Transcription

1 Global Journal of Pure and Appled Mathematcs. ISSN Volume 3, Number 3 (207), pp Research Inda Publcatons Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems Venkadesh Rajarathnam and Anandhakumar Radhakrshnan 2 Assstant Professor, Department of Electrcal Engneerng, Annamala Unversty, Annamala nagar , Taml Nadu, Inda. 2 Assstant Professor, Department of Electrcal Engneerng, Annamala Unversty, Annamala nagar , Taml Nadu, Inda. Abstract Ths paper presents a new Water Evaporaton Optmzaton (WEO) algorthm s proposed to solve an emsson constraned Economc Load Dspatch (ELD) problem. The objectve of the problem s to obtan the mnmum producton cost wth lowest amount of emsson. The proposed water evaporaton optmzaton algorthm s based on the evaporaton of a tny amount of water molecules on the sold surfaces wth dfferent wettablty whch can be studed by molecular dynamcs smulatons. In order to show the profcency of the proposed WEO algorthm t has been mplemented to solve the economc load dspatch, economc emsson dspatch and combned economc emsson dspatch. The performance of the WEO algorthm s tested on three unt system, sx unt systems and fourteen unt systems wth varous load demand, loss and emsson coeffcents. The comparson of the smulaton results prove that the proposed WEO algorthm have a better performance than the exstng methods. Keywords: Economc dspatch, Emsson dspatch, Envronmental dspatch, Water evaporaton optmzaton, Transmsson losses.. INTRODUCTION In a tradtonal economc load dspatch problem the objectve s to mnmze the producton costs by an optmal allocaton of load demands to the onlne partcpatng

2 50 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan generatng unts subject to satsfyng system constrants []. The pollutant from the fossl fuel plant threatenng the entre world and ensure that the amount of emsson such as sulfur doxde (SO2) and ntrogen oxdes (NOx) must be reduced. Hence t s necessary that the emsson constrant must combne wth economc dspatch problem and ts objectve s to mnmze producton cost wth lowest emsson [2-4]. The mathematcal approaches lke Interactve Search (IS) approach, Newton Raphson (NR) method, Non Lnear Programmng (NLP), and Quadratc Programmng (QP) have been appled to solve economc emsson dspatch [5-9]. The classcal methods may have dffcultes n fndng an optmal soluton due to the longest executon tme and presence of non lnear & dscontnuty n the problem. As a result varety of artfcal ntellgence technques such as Fuzzy Logc (FL), Evolutonary Programmng (EP), Hopfeld Neural Networks (HNN), Adaptve HNN, Modfed Partcle Swarm Optmzaton (MPSO), Dfferental Evoluton (DE), Bacteral Foragng (BF), Gravtatonal Search (GS), opposton based Harmony Search (HS), Artfcal Bee Colony (ABC), Modfed ABC, Cultural Algorthm, and quas oppostonal based Teachng Learnng Based Optmzaton (TLBO) were developed and appled for aforementoned problems[-22]. Recently swarm ntellgence technques play a vtal role n solvng optmzaton problem n power system. One of the swarm ntellgence technque called Flower Pollnaton (FP) algorthm, that s nspred by the pollnaton process of flowerng plants have been proposed to solve combned economc and emsson dspatch problems [23]. The hybrd methods also proven ther ablty to solve an engneerng optmzaton problem. The combnaton of DE and Bogeography based Optmzaton (BBO) algorthm has been developed and mplemented to solve the Economc Envronmental Load Dspatch problem [24]. The hybrd ant optmzaton system for economc emsson load dspatch under fuzzness was presented [25]. The combnaton of PSO and gravtatonal search algorthm to solve EELD problem has also been dscussed [26]. The hybrdzaton of two recent meta-heurstcs technques nspred by nature, fre fly algorthm and bat algorthm has been developed to solve combned economc / envronmental dspatch (CEED) problem [27]. Recently, motvated by the shallow water theory, researchers have proposed Water Evaporaton Optmzaton (WEO) algorthm for solvng global optmzaton problem []. The WEO algorthm s conceptually smple and easy to mplement. The WEO algorthmc search conssts of both global and local search. Ths guarantees that the proposed algorthm s compettve wth other effcent well-known meta-heurstcs. The objectve of ths papers t to use WEO algorthm to obtan the optmal dspatches wth lowest amount of emsson and compare the performances n terms of qualty of soluton wth the recent reports.

3 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 5 The rest of ths paper s organzed as follows. EELD problem s formulated n Secton "Problem Formulaton". The next secton "Water Evaporaton Optmzaton" brefly descrbes the algorthm. The numercal smulaton results and dscusson s presented n the Secton "Examples and Smulaton Results". The fnal Secton outlnes the "Concluson" followed by reference. 2. PROBLEM FORMULATION The man objectve of CEED s to mnmze two nconsstent objectves such as fuel cost and emsson, whle satsfyng operatng and loadng constrants. Generally the problem s formulated as follows 2.. Economc dspatch A smple smooth quadratc functon of fuel cost curve of each generator s gven by F a p 2 b p c Where F s the fuel cost of each generator n ($/h). a, b, c are the cost coeffcent each generator n ($/h). p s the real power of generator n MW. () Under the followng constrants: p p p, mn,max (2) ng p p D p L (3) Where PD s the total demand and PL represents the actve transmsson losses. P,mn and P,max are the mnmum and maxmum lmts, respectvely for the producton of the th unt. The expresson of transmsson loss as a functon of the generated power s gven by: p L ng ng j p B j p j (4) Where Bj s the constant called the losses coeffcent 2.2. Emsson dspatch Total emsson of generaton E can be E p 2 p (5)

4 52 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan E s the functon of emssons n (Kg/h) and α, β and γ are the co-effcent of emsson characterstcs specfc to each producton unt The combned economc/envronmental dspatch (CEED) The CEED studes are desgned to seek the smultaneous mnmzaton of two functons descrbed by the same varable objects yeldng a dual objectve optmzaton problem or b-crtera. The prmary dffculty wth such an optmzaton problem s assocated wth the presence of conflcts between two features. For whch, we have converted ths problem nto a sngle-objectve optmzaton problem by ntroducng a prce penalty factor "he", therefore, the objectve functon to be optmzed s defned as follows: ng MnC F ng p he E p (6) 2.4. Calculatng the coeffcent he The coeffcent he, called prce penalty factor s expressed by the followng functon: h e F E p p,max,max To determne the prce penalty factor he assocated wth a gven load, the followng steps must be followed. Calculate the rato F(P;max)/E(P;max) for each generator 2. Sort the factor values obtaned n ascendng order; 3. Add the maxmum generated power of each generator (P,max) one by one, startng wth the plant capacty wth the lowest prce factor correspondng to the gven load. Once P, max PD, stop calculaton; 4. At ths stage, he connected to the last unt n the summng process s the prce penalty factor correspondng to the gven load. For verfyng the equalty constrants n equaton 3, we calculated delta of each method as follows delta ng P P D P L (7) (8) 3. WATER EVAPORATION OPTIMIZATION The evaporaton of water s very mportant n bologcal and envronmental scence. The water evaporaton from bulk surface such as a lake or a rver s dfferent from

5 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 53 evaporaton of water restrcted on the surface of sold materals. In ths WEO algorthm water molecules are consdered as algorthm ndvduals. Sold surface or substrate wth varable wettablty s reflected as the search space. Decreasng the surface wettablty (substrate changed from hydrophlty to hydrophobcty) reforms the water aggregaton from a monolayer to a sessle droplet. Such a behavor s consstent wth how the layout of ndvduals changes to each other as the algorthm progresses. And the decreasng wettablty of surface can represent the decrease of objectve functon for a mnmzng optmzaton problem. Evaporaton flux rate of the water molecules s consdered as the most approprate measure for updatng ndvduals whch ts pattern of change s n good agreement wth the local and global search ablty of the algorthm and make ths algorthm have well converged behavor and smple algorthmc structure. The detals of the water evaporaton optmzaton algorthm are well presented n []. In the WEO algorthm, each cycle of the search conssts of followng three steps () Monolayer Evaporaton Phase, ths phase s consdered as the global search ablty of the algorthm () Droplet Evaporaton Phase, ths phase can be consdered as the local search ablty of the algorthm and () Updatng Water Molecules, the updatng mechansm of ndvduals. 3. Monolayer Evaporaton Phase In the monolayer evaporaton phase the objectve functon of the each ndvduals Ft t s scaled to the nterval [-3.5, -0.5] and represented by the correspondng Esub() t nserted to each ndvdual (substrate energy vector), va the followng scalng functon. E sub t t Emax Emn Ft MnFt Emn MaX Ft MnFt where Emax and Emn are the maxmum and mnmum values of Esub respectvely. After generatng the substrate energy vector, the Monolayer Evaporaton Matrx (MEP) s constructed by the followng equaton. MEP t j f rand 0f rand j j exp E exp E sub sub t t Where MEPt j s the updatng probablty for the j th varable of the th ndvdual or water molecule n the t th teraton of the algorthm. In ths way an ndvdual wth better objectve functon s more lkely to reman unchanged n the search space. (9) ()

6 54 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan 3.2 Droplet Evaporaton Phase In the droplet evaporaton phase, the evaporaton flux s calculated by the followng equaton. J cos 3 J P cos o cos o where Jo and Po are constant values. The evaporaton flux value s depends upon the contact angle ϴ, whenever ths angle s greater and as a result wll have less evaporaton. The contact angle vector s represented the followng scalng functon. t t max mn Ft MnFt mn MaxFt MnFt Where the mn and max are the mnmum and maxmum functons. The ϴ mn & ϴ max values are chosen between -50 o < ϴ < -20 o s qute sutable for WEO. After generatng contact angle vector ϴ () t the Droplet Probablty Matrx (DEP) s constructed by the followng equaton. DEP t j f rand 0f rand j j J J t t Where DEP t j s the updatng probablty for the j th varable of the th ndvdual or water molecule n the t th teraton of the algorthm. 3.3 Updatng Water Molecules In the WEO algorthm the number of algorthm ndvduals or number of water molecules (nwm) s consdered constant n all tth teratons, where t s the number of current teratons. Consderng a maxmum value for algorthm teratons (tmax) s essental for ths algorthm to determne the evaporaton phase and for stoppng crteron. When a water molecule s evaporated t should be renewed. Updatng or evaporaton of the current water molecules s made wth the am of mprovng objectve functon. The best strategy for regeneratng the evaporated water molecules s usng the current set of water molecules (WM(t)). In ths way a random permutaton based step sze can be consdered for possble modfcaton of ndvdual as: t t permute j WM permute 2 j S rand. WM Where rand s a random number n [0,] range, permuteand permute 2 are dfferent rows of permutaton functons. s the number of water molecule, j s the number of dmensons of the problem. The next set of molecules (WM (t+) ) s generated by () (2) (3) (4)

7 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems addng ths random permutaton based step sze multpled by the correspondng updatng probablty (monolayer evaporaton and droplet evaporaton probablty) and can be stated mathematcally as: WM t t WM MEP S DEP t t t t t t max max / 2 / 2 (5) Each water molecule s compared and replaced by the correspondng renewed molecule based on objectve functon. It should be noted that random permutaton based step sze can help n two aspects. In the frst phase, water molecules are more far from each other than the second phase. In ths way the generated permutaton based step sze wll guarantee global and local capablty n each phase. The WEO algorthm can be summarzed as follows: Step : Intalze all the algorthm and problem parameters, randomly ntalze all water molecules. Step 2: Generatng water evaporaton matrx Every water molecule follow the evaporaton probablty rules specfed for each phase of the algorthm based on the Eqs. () and (5). For t tmax /2, water molecules are globally evaporated based on monolayer evaporaton probablty MEP by usng Eq (). for t > tmax /2, evaporaton occurs based on the droplet evaporaton probablty DEP by usng Eq (3). It should be noted that for generatng monolayer and droplet evaporaton probablty matrces, t s necessary to generate the correspondent substrate energy vector and contact angle vector by usng Eqs (9) and (2) respectvely. Step 3: Generatng random permutaton based step sze matrx A random permutaton based step sze matrx s generated accordng to Eq. (4) Step 4: Generatng evaporated water molecules and updatng the matrx of water molecules The evaporated set of water molecules WM (t+) s generated by addng the product of step sze matrx and evaporaton matrx to the current set of molecules WM (t) by usng Eq. (5). These molecules are evaluated based on the objectve functon. For the molecule ( =,2,...nWM) f the newly generated molecule s better than the current one, the latter should be replaced. Return the best water molecule as the output of the algorthm

8 56 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan Start Read Input data Intalze system parameter Intalze water molecules (WM (0) ), Evaluate the ftness values by Eq. (), (5) & (6 )wth subject to constrants gven by Eq. (2) - (4) Yes t < = tmax / 2? No MEP DEP Generate Esub (t) vector usng Eq. (9) Generate ϴ (t) vector usng Eq.(2) Generate MEP (t) matrx usng Eq. () Generate DEP (t) matrx usng Eq. (3) Generate S matrx usng Eq. (4) Generate S matrx usng Eq. (4) Generate Evaporate molecules WM (t+) = WM (t) + S MEP Generate Evaporated molecules WM (t+) = WM (t) + S DEP t = t+ NO t < = tmax / 2? Yes Prnt "optmal results" Stop Fgure : Flowchart for the proposed WEO algorthm to solve EELD

9 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 57 Step 5: Termnatng condton check If the number of teraton of the algorthm (t) becomes larger than the maxmum number of teratons (tmax), the algorthm termnates. Otherwse go to step 2. The detaled flowchart for the mplementaton of WEO algorthm for solvng EELD problem s shown n Fg.. 4. EXAMPLES AND SIMULATION RESULTS The proposed methodology has been tested wth dfferent sample systems and the proposed algorthm s developed n Matlab envronment and s mplemented usng Intel(R) Core(TM) U CPU@.60 GHz 2.30 GHz processor. The effectveness of the proposed WEO algorthm for ELD problem has been valdated by comparng the smulaton results obtaned from the other methods whch are avalable n lterature. The WEO algorthm parameters for all test systems are chosen as the number of water molecules (nwm) =, maxmum number of algorthm teraton (tmax) =, MEPmn = 0.03, MEPmax = 0.6, DEPmn = 0.6, DEPmax =. 4. Test System The proposed WEO algorthm s appled to CEED problem consstng of 3 generatng unts. The each generatng unt cost coeffcents, power generaton lmts, emsson coeffcents have been presented n the lterature [27]. In ths test system four dfferent load demands 400MW, 500MW, 600MW and 700MW are consdered wth losses. The results obtaned by the proposed WEO algorthm n comparson wth exstng technques FA, BA, HYB and GA s presented n table. The results shows that proposed and exstng algorthms meet the demand and satsfyng system constrants. From the comparson t s clear that the proposed algorthm acheve the mnmzed cost wth lowest amount of emsson wth least loss for all load demands. The convergence characterstc of proposed algorthm for test system s shown n fgure 2. The converged results ensure that objectve value s mnmzed from maxmum value to mnmum for the load demands of 400 MW, 500 MW, 600 MW and 700 MW mply that the proposed WEO algorthm outperforms the exstng methods. 4.2 Test System 2 In order to test the performance of the WEO algorthm, the sample system consdered wth 6 generatng unts wth transmsson loss, emsson wth a load demands of 700MW, 800MW, 900MW & 0MW. The generatng unt s data are taken from [27]. In order to show the superorty of the proposed WEO algorthm, t has been mplemented to obtan economc dspatch to mnmze the cost, envronment dspatch to mnmze emsson and combned economc emsson dspatch to mnmze both cost as well as emsson.

10 58 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan Table : Optmal dspatches obtaned by the proposed WEO algorthm for test system Power demand Methods P P 2 P 3 Pl Emsson (kg/h) Total cost ($/h) he ($/kg) 400 FA [27] BA[27] HYB[27] GA[27] WEO FA [27] BA[27] HYB[27] GA[27] WEO FA [27] BA[27] HYB[27] GA[27] WEO FA [27] BA[27] HYB[27] GA[27] WEO

11 Total Cost ($/hr) Total Cost ($/hr) Total Cost ($/hr) Total Cost ($/hr) Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems (Pd = 400 MW) (Pd=500 MW) Iteratons Iteratons (Pd=600 MW) (Pd=700 MW) Iteratons Iteratons Fgure.2. Convergence characterstcs of test system 4.2. Economc Load Dspatch In an Economc Load Dspatch (ELD) problem the objectve s to mnmze the total fuel cost subject to satsfyng system constrants wthout consderng the emsson and loss. An optmal economc dspatch obtaned by the proposed as well as exstng algorthms for the load demands of 700 MW, 800MW, 900MW, and 0MW s presented n Table 2. From the results t s clear that the proposed algorthm acheve the least cost then the FA, BA, and HYB algorthms for all load demands and all the algorthms are satsfyng system constrants completely. The objectve values versus teratons are depcted n fgure 3. The converged results ndcate that the proposed algorthm s hghly compettve wth recent technques.

12 Fuel Cost ($/h) Fuel Cost ($/h) Fuel Cost ($/h) Fuel Cost ($/h) 60 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan Economc Dspatch (Pd=700MW) Economc Dspatch (Pd=800MW) Iteratons Iteratons Economc Dspatch (Pd=900 MW) Economc Dspatch (Pd=0 MW) Iteratons Iteratons Fgure.3. Objectve values versus teratons of test system 2 for ELD Table 2: Economc dspatch results obtaned by the WEO, FA, BA, and HYB algorthms for test system 2 Power demand Method P P2 P3 P4 P5 P6 Pl Cost ($/h) Emsson (kg/h) Delta T (s) 700 FA BA HYB WEO FA BA HYB WEO FA BA HYB

13 Emsson (Kg/hr) Emsson (Kg/hr) Emsson (Kg/hr) Emsson (Kg/hr) Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 6 WEO FA BA HYB WEO Economc Envronmental Dspatch (EED) In an EED problem the objectve s to mnmze the emsson wth satsfyng system constrants despte of fuel cost and loss. An optmal EED obtaned by the proposed as well as exstng algorthms for all load demands wth fulfllng constrants are presented n Table 3. The EED results ensure that the proposed WEO algorthm obtans the mnmzed emsson of NOx for all the four load demands then the exstng algorthms reported n the lterature. The emsson convergence characterstcs are plotted n the fgure 4. The converged result ndcates that the proposed WEO algorthm s capable of producng better outcome then other algorthms. Emsson Dspatch (Pd=700MW) Emsson Dspatch (Pd=800MW) Iteratons Iteratons Emsson Dspatch (Pd=900MW) Emsson Dspatch (Pd=0MW) Iteratons Iteratons Fgure.4. Objectve values versus teratons of test system 2 for EED

14 62 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan Table 3: Comparson of economc envronmental dspatch results for test system 2 Power demand Method P P2 P3 P4 P5 P6 Pl Cost ($/h) Emsson (kg/h) Delta T(s) 700 FA BA HYB WEO FA BA HYB WEO FA BA HYB WEO FA BA HYB WEO Combned Economc Envronmental Dspatch (CEED) In the CEED problem the objectve s to mnmze the total fuel cost wth small amount of emsson subject to meet all system constrants. The table 4 shows the smulaton results of CEED problem got by the WEO, FA, BA and HYB algorthms. The results demonstrate that all algorthms are clearly satsfes the load demands and power generaton lmts. The result also mples that the proposed WEO algorthm alone got the mnmum fuel cost wth least emsson then the earler technques for all load demands. The objectve value versus teratons graph shows n fgure 5 mply that the cost s mnmzed from larger value and t wll guarantee that the proposed algorthm s capable of obtanng compettve results then exstng algorthms.

15 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 63 Fgure.5. Objectve values versus teratons of test system 2 for CEED Table 4: Comparson of CEED result for test system 2 Power demand Method P P2 P3 P4 P5 P6 Pl Cost ($/h) Emsson (kg/h) Total cost ($/h) he ($/kg) Delta T(s) Total Cost ($/h) Total Cost ($/h) Total Cost ($/h) Total Cost ($/h) CEED (Pd=700MW) CEED (Pd=800MW) Iteratons Iteratons CEED (Pd=900MW) CEED (Pd=0MW) Iteratons Iteratons 700 FA BA HYB WEO FA BA HYB WEO FA BA HYB WEO FA BA HYB WEO

16 Total Cost ($/hr) Total Cost ($/hr) Total Cost ($/hr) Venkadesh Rajarathnam and Anandhakumar Radhakrshnan 4.3 Test System 3 To examne the superor qualty of soluton and robustness of the proposed WEO algorthm, a fourteen unt system s consdered. The data for ths system s provded n [27]. In ths test system the losses are ncluded. The load demands are 750 MW, 250 MW and 2650 MW. The results obtaned by the proposed WEO as well as exstng algorthms are gven n the Table 5. The results ensure that the WEO algorthm reach the mnmzed fuel cost wth least emsson then FA, BA and HYB algorthms for all three load demands subject to satsfyng all system constrants. The cost convergence characterstcs curves are depcted n fgure 6. The converged results ndcate that the proposed algorthm s hghly compettve wth recent technques Pd = 750MW Pd = 250 MW Iteratons Iteratons Pd = 2650 MW Iteratons Fgure.6. Objectve values versus teratons of test system 3 for CEED Table 5: Results obtaned by dfferent method for CEED of test system 3 Power Demand Method FA BA HYB WEO FA BA HYB WEO FA BA HYB WEO P P

17 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 65 P P P P P P P P P P P P Pl Cost($/h) Emsson(Kg/h) Total Cost($/h) h e($/kg) Delta T(s) CONCLUSION The mnmzaton of emssons lke carbon doxde (CO2), sulfur doxde (SO2) and ntrogen oxdes (NOx) from fossl fueled electrc power plants has receved sgnfcant attenton n recent years because these emssons can creates an atmospherc polluton. Hence t s necessary to nclude envronmental emssons n a tradtonal economc load dspatch problem. Here the objectve s to mnmze the fuel cost wth least emsson. In ths paper a new Water Evaporaton Optmzaton (WEO) algorthm has been appled successfully to solve an ELD, EED and CEED problems. The feasblty of the proposed WEO algorthm s demonstrated on three dfferent test systems and the smulaton results are compared wth GA, FA, BA, and HYB algorthms. The comparson of the results shows that the proposed algorthm

18 66 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan outperforms the exstng algorthms n terms of achevng mnmzed fuel cost wth small amount of emsson. REFERENCES [] Wood A. J and Wollenberg B. F, 96. Power generaton, operaton and control, Second Edton, John Wley and Sons. New York. [2] Dhllon J.S, Part S. C and Kothar D. P, 93. Stochastc economc emsson load dspatch, Electrc Power Systems Research. 26: pp [3] Arya L. D, Choube S.C and Kothar D. P, 97. Emsson constraned secure economc dspatch, Electrc Power and Energy Systems. (5): pp [4] Ramanathan R, 94. Emsson constraned economc dspatch, IEEE Transactons on Power Systems. 9(4): pp [5] Spens W. Y and Lee F. N, 97. Iteratve search approach to emsson constraned dspatch, IEEE Transactons on Power Systems. 2(2): pp [6] Shn-Der Chen and Jann-Fuh Chen, 97. A new algorthm based on the Newton Raphson approach for real-tme emsson dspatch, Electrc Power Systems Research. 40: pp. -4. [7] Shn-Der Chen and Jann-Fuh Chen, A drect Newton Raphson economc emsson dspatch, Electrc Power and Energy Systems. 25: pp [8] Mbamalu G. A. N, Effect of demand prortzaton and load curtalment polcy on mnmum emsson dspatch, Electrc Power Systems Research. 53: pp. -5. [9] Nanda J, Har L, and Kothar M. L, 94. Economc emsson load dspatch wth lne flow constrans usng a classcal technque, IEE Proceedngs Generaton, Transmsson and Dstrbuton. 4(): pp. -. [] Hota P. K, Chakrabart R and Chattopadhyay P. K, Economc emsson load dspatch through an nteractve fuzzy satsfyng method, Electrc Power Systems Research. 54: pp [] Tsay M. T, Ln W. M and Lee J. L, 200. Applcaton of evolutonary programmng for economc dspatch of cogeneraton systems under emsson constrants, Electrc Power and Energy Systems. 23:pp [2] Basu M, Fuel constraned economc emsson load dspatch usng Hopfeld neural networks, Electrc Power Systems Research. 63: pp [3] Balakrshnan S, Kannan P. S, Aravndan C and Subathra P, On-lne emsson and economc load dspatch usng adaptve Hopfeld neural network, Appled Soft Computng. 2: pp [4] Wang L and Sngh C, Stochastc economc emsson load dspatch through a modfed partcle swarm optmzaton algorthm, Electrc Power Systems Research. 78: pp [5] Abou El Ela A. A, Abdo M. A and Spea S. R., 20. Dfferental evoluton algorthm for emsson constraned economc power dspatch problem, Electrc Power Systems Research. 80: pp

19 Water Evaporaton algorthm to solve combned Economc and Emsson dspatch problems 67 [6] Hota P. K, Barsal A. K and Chakrabart R, 20. Economc emsson load dspatch through fuzzy based bacteral foragng algorthm, Electrc Power and Energy Systems. 32: pp [7] Guvenc U, Sonmez Y, Duman S and Yorukeren N, 202. Combned economc and emsson dspatch soluton usng gravtatonal search algorthm, Scenta Iranca.(6): pp [8] Chatterjee A, Ghoshal S. P and Mukherjee V, 202. Soluton of combned economc and emsson dspatch problems of power systems by an opposton-based harmony search algorthm, Electrc Power and Energy Systems. 39: pp [] Rajesh Kumar, Abhnav Sadu, Rudesh Kumar and Panda S. K, 202. A novel mult-objectve drected bee colony optmzaton algorthm for multobjectve emsson constraned economc power dspatch, Electrc Power and Energy Systems. 43: pp [20] Zhang R, Zhou J, Mo L, Ouyang S and Lao X, 203. Economc envronmental dspatch usng an enhanced mult-objectve cultural algorthm, Electrc Power Systems Research. 99: pp [2] [Roy P. K and Bhu S, 203. Mult-objectve quas-oppostonal teachng learnng based optmzaton for economc emsson load dspatch problem, Electrc Power and Energy Systems. 53: pp [22] Secu D. C, 205. A new modfed artfcal bee colony algorthm for the economc dspatch problem, Energy Converson and Management. 89: pp [23] Abdelazz A. Y, Al E. S and Abd Elazm S. M, 206. Flower pollnaton algorthm to solve combned economc and emsson dspatch problems, Engneerng Scence and Technology, an Internatonal Journal. : pp [24] A. Bhattacharya., and P. K. Chattopadhyay., 20. Solvng economc emsson load dspatch problems usng hybrd dfferental evoluton, Appled Soft Computng. : pp [25] Abd Allah A and Mousa, 204. Hybrd ant optmzaton system for mult objectve economc emsson load dspatch problem under fuzzness, Swarm and Evolutonary Computaton. 8: pp. -2. [26] Jang S, J Z and Shen Y, 204. A novel hybrd partcle swarm optmzaton and gravtatonal search algorthm for solvng economc emsson load dspatch problems wth varous practcal constrants, Electrc Power and Energy Systems. : pp [27] Gherb Y. A, Bouzeboudja H and Gherb F. H, 206. The combned economc envronmental dspatch usng new hybrd metaheurstc, Energy. 5: pp [] Kaveh A and Bakhshpoor T, 206. Water Evaporaton Optmzaton: A novel physcally nspred optmzaton algorthm, Computer and Structures. 67: pp

20 68 Venkadesh Rajarathnam and Anandhakumar Radhakrshnan