A Novel Gravitational Search Algorithm for Combined Economic and Emission Dispatch

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1 A Novel Gravtatonal Search Algorthm for Combned Economc and Emsson Dspatch 1 Muhammad Yaseen Malk, 2 Hmanshu Gupta 1 Student, 2 Assstant Professor 1 Electrcal Engneerng 1 E-Max Group of Insttutons, Haryana, Inda Abstract - Economc Load Dspatch s a well known problem and has been a major concern for researchers and ndustralsts all around the world. The paper proposes to solve the problem of Economc Load Dspatch usng a novel Gravtatonal Search Algorthm. The target s to mplement a meta-heurstc algorthm whch wll be able to fnd the optmal capacty of the generatng unts n mult-generatng unt system. The paper mplements a novel technque of Modfed Gravtatonal Search Algorthm for combned economc and emsson dspatch. Three data sets were used for the testng purpose and the ftness values are compared. The results consdered valve pont effect and the results were found to be qute encouragng. Keywords - EPD, ELD, GSA. I. INTRODUCTION The economc dspatch problem relates to optmum generaton schedulng of present generators n power system to mnmze total fuel cost whle to satsfy the load demand and operatonal constrants. The economc dspatch problem plays a vtal role n plannng operaton and control of the modern power systems. Over last few years, a number of approaches were developed for solvng operaton usng classcal mathematcal programmng methods. Moreover, classcal optmzaton methods are largely senstve to ntal pont and converge frequently to local optmzaton soluton or dverge altogether. Lnear programmng methods are fast and relable but man dsadvantages assocated wth the pecewse lnear cost approxmaton. The economc operaton n the power system plays a man role to decde the electrcty prce n regulated and deregulated market. The economc load dspatch assgns the generators powers to complete certan demand whle the generatng cost mnmsng under several systems and unts -related the constraned envronment. The mnmsng s a nonlnear optmsaton problem whose complexty prolongs when constrants lke valve-pont effect and generators have prohbted zones undertaken. Economc load dspatch has been studed by numerous engneers and researchers. These efforts are mathematcal programmng based on varous optmsaton technques. In the power system, the operaton cost needs to be mnmzed at each tme va economc load dspatch. Tradtonally, cost functon of generator was approxmately represented by sngle quadratc cost functon. Practcally, operatng condtons of multple generatng unts need the generaton cost functon be dvded as pecewse quadratc functons. The networks have been used n several dfferent applcatons. The vtal property of the Hopfeld neural network s decrease n energy by amount whenever there s change n nputs. Thus, the Hopfeld neural network has been used for optmzaton. Tank and Hopfeld defned how varous optmzaton problems rapdly solve hghly nterconnected networks of smple analogy processor that s an mplementaton of the Hopfeld neural network. Park and others dsplayed the economc load dspatch for pecewse quadratc cost these functons usng Hopfeld neural network. The results were compared very well wth numercal method n an herarchcal approach appled to Hopfeld neural network n economc and envronmental dspatch of the electrc power systems. These several applcatons nvolved a huge number of teratons and shown oscllatons durng transents. It suggests a need for mprovement n convergence through an adaptve method, such as adaptve learnng rate technque developed by Ku and Lee for a dagonal recurrent neural network. The bblographcal study on economc load dspatch suggests, lately as opposed to the mathematcal technques, varous heurstc optmsaton strateges smlar as genetc algorthm and varant real-coded Gravtatonal Algorthm, tabu search, smulated annealng, ant colony optmsaton, fuzzy systems, neural network, partcle swarm optmsaton, hybrd evolutonary programmng and bogeography-based optmsaton have capable of generatng hgh-qualty economc load dspatch solutons. Although heurstc technques dd not guarantee to dscover globally the optmal solutons n the fnte tme, they manly offer fast and reasonable solutons. After analyses exstng methods lke Hopfeld neural network do consder pecewse quadratc prohbted zones and fuel cost, the convergence rate are slow causng usage of sgmod functon. Gravtatonal Algorthm method s usually manly faster than SA tech due to parallel search capabltes. Although, when objectve parameters were hghly related to each other, the chromosomes tend to express the smlar structure and average ftness become hgher. Although Partcle Swarm Optmzaton s capable of generatng good soluton, however, the performance s largely dependent on parameter senstvty or IJEDR Internatonal Journal of Engneerng Development and Research ( 1729

2 balancng between the local and global search capabltes. Most of the methods are mentoned above used quadratc fuel cost that s an approxmaton of hgher order fuel cost. II. RELATED WORK In ths paper, Balamurugan R et al. [1] proposed an effcent scheme wth hybrd nteger dfferental evoluton dynamc programmng approach s used to solve economc dspatch problem wth several fuel optons. A dynamc programmng has based on the smplfed recursve algorthm whch has developed for a fxed schedulng of generatng unts n economc dspatch problem. The test result dsplays the hybrd ICDEDP algorthm wth superor convergence, shorter computaton tme and hgh qualty soluton characterstcs. In ths paper, Rayapud, S. Rao et al. [2] proposed ELD s a technque to determne low-cost, relable operaton and most effcent power system to dspatch present electrcty generaton resources to transfer the load on system. The man objectve of economc dspatch s to decrease total cost of generated operatonal constrants of presently generaton resources. Numercal results dsplayed good convergence property and better n qualty of the soluton. In ths paper, Snha, Ndul et al. [3] proposed a hybrd method whch ntegrates the all major features of evolutonary programmng and partcle swarm optmzaton for soluton of non-convex ELD problems havng non-lneartes such as valve pont loadngs. Park, J et al. [4] proposed a method to solve a problem of EPD wth the pecewse quadratc cost functon whle usng Hopfeld neural network. Addtonally a cost functon for each generator s supposed. Though more realstc to dsplay cost functon as pecewse quadratc functon rather to the convex functon. In ths paper, Baskar, G. et al. [5]. proposed an objectve to nvolve effectve and smple methods to economc load dspatch problem wth securty constrants n thermal unts that are obtanng economc schedulng for the utlty system. In ths, mproved partcle swarm optmzaton method, a newest velocty equaton has been formulated for large scale system or characterstcs of constrcton factor approach are also ncorporated nto ths approach. Basu, M. et al. [6] proposed mult-objectve optmzaton technque for ELD of fxed thermal plants and head hydro plants wth emsson level functons and non-smooth fuel cost s presented. The problem deals wth economc and emsson as the competng objectves. Bhattacharya Anruddha et al. [7] proposed bogeography-based optmzaton algorthm to solve non-convex and convex economc load dspatch problems of thermal generators of power system. T Nanda, J et al. [8] Proposed emsson load dspatch problem that measures for mnmzaton both emsson and cost whch s multple, conflct objectve of functon problem. A goal programmng technque has sutable for these type of problems. In ths, emsson load dspatch problem can be solved wth non-lnear and lnear goal programmng algorthms. The applcaton and valdty of the proposed algorthms are demonstrated for a system havng sx generators. In ths paper, Chang, C-L et al. [9] proposed genetc algorthm to solve practcal power economc load dspatch problems of ndvdual complextes and szes wth cost curves, where mathematcal conventonal methods are developed napplcable. An mproved genetc algorthm gves a well evolutonary mgratng operator and drecton operator to enable effcent actvely explore and search solutons. Baskar G., et al. [10] proposed a contngency constraned ELD usng conventonal partcle swarm optmzaton, mproved swarm optmzaton, programmng methods lke, fast-ep classcal EP and classcal and fast EP to allevate lne overloadng. III. PROBLEM FORMULATION Economc Load Dspatch s a well known problem and has been a major concern for researchers and ndustralsts all around the world. Ths paper ams to solve the problem of Economc Load Dspatch wth a novel proposed Gravtatonal Search Algorthm. The problem conssts of dvson of formulaton of the model for fuel consumpton and then development of the mnmzng algorthm and applyng the same on the economc load dspatch problem. It s not as smple as s sounds as the solutons not only have to fnd the global mnma but also are constraned. Thus t forms a constraned optmzaton problem. To determne the economc dstrbuton of a load amongst the dfferent unts of a plant, the varable operatng costs of each unt must be expressed n terms of ts power output. The fuel cost s the man cost n a thermal or nuclear unt. Then the fuel cost must be expressed n terms of the power output. Other costs, such as the operaton and mantenance costs, can also be expressed n terms of the power output. Fxed costs, such as the captal cost, deprecaton etc., are not ncluded n the fuel cost. The fuel requrement of each generator s gven n terms of the Rupees/hour. Let us defne the nput cost of an unt-, f n Rs./h and the power output of the unt as P. Then the nput cost can be expressed n terms of the power output as f a 2 P 2 b P c Rs./h The operatng cost gven by the above quadratc equaton s obtaned by approxmatng the power n MW versus the cost n Rupees curve. The ncremental operatng cost of each unt s then computed as IJEDR Internatonal Journal of Engneerng Development and Research ( 1730

3 IV. PROPOSED METHODOLOGY df ap b Rs./MWh dp The paper proposes to solve the problem of Economc Load Dspatch usng a novel Gravtatonal Search Algorthm. The target s to mplement a meta-heurstc algorthm whch wll be able to fnd the optmal capacty of the generatng unts n mult-generatng unt system. The system of dfferent number of generator sets would be taken so that the algorthm s tested for dfferent datasets. The framework for the development of Gravtatonal Search algorthm s frst developed. The rules for the GSA to work are lad down whch forms the bass of the optmzng process. The partcles are ntalzed randomly and moved n the search space as they search for the global optma and care also needs to be taken for keepng the partcles n the feasble space so that both equalty and nequalty constrants are not volated. GRAVITATIONAL SEARCH ALGORITHM GSA s a heurstc optmzaton algorthm whch has been ganng nterest among the scentfc communty recently. GSA s a nature nspred algorthm whch s based on the Newton s law of gravty and the law of moton. GSA s grouped under the populaton based approach and s reported to be more ntutve. The algorthm s ntended to mprove the performance n the exploraton and explotaton capabltes of a populaton based algorthm, based on gravty rules. However, recently GSA has been crtczed for not genunely based on the law of gravty [3]. GSA s reported to exclude the dstance between masses n ts formula, whereas mass and dstance are both ntegral parts of the law of gravty. Despte the crtcsm, the algorthm s stll beng explored and accepted by the scentfc communty. GSA was ntroduced by Rashed et al. n 2009 and s ntended to solve optmzaton problems. The populaton-based heurstc algorthm s based on the law of gravty and mass nteractons. The algorthm s comprsed of collecton of searcher agents that nteract wth each other through the gravty force. The agents are consdered as objects and ther performance s measured by ther masses. The gravty force causes a global movement where all objects move towards other objects wth heaver masses. The slow movement of heaver masses guarantees the explotaton step of the algorthm and corresponds to good solutons. V. RESULTS The varous smulaton results obtaned by mplementng the proposed algorthm. All the smulatons have been done MATLAB R 2013b wth a 6GB RAM computer wth core 5 processor. Three types of datasets have been utlzed Fg.5.1: Optmal generatng capacty for three generator Fg.5.2: Convergence plot of three generator data Fgure 5.1 shows the optmal capacty of the generatng unts of each generator sets. As can be observed each unts are wthn the mnmum and maxmum lmts and follows the equalty constrants also. As t can be observed from Fgure. 5.2 the convergence of ftness functon s shown. The devaton among the solutons ntally s very hgh whle t starts to converge after certan teratons. Ths s desrable and shows the effcacy of our algorthm. IJEDR Internatonal Journal of Engneerng Development and Research ( 1731

4 Fg.5.4: Convergence plot of three generator data Fg.5.3:Optmal generatng capacty for three generator Fgure5.3 shows the optmal capacty of the generatng unts of each generator sets. As can be observed each unts are wthn the mnmum and maxmum lmts and follows the equalty constrants also. As can be observed from Fgure 5.4 the convergence of ftness functon s shown. The devaton among the solutons ntally s very hgh whle t starts to converge after certan teratons. Ths s desrable and shows the effcacy of our algorthm. Fg. 5.5 : Optmal generatng capacty for three generator Fgure 5.5 shows the optmal capacty of the generatng unts of each generator sets. As can be observed each unts are wthn the mnmum and maxmum lmts and follows the equalty constrants also. IJEDR Internatonal Journal of Engneerng Development and Research ( 1732

5 Fgure 5.6: Convergence plot of three generator data As can be observed from Fg. 5.6 the convergence of ftness functon s shown. The devaton among the solutons ntally s very hgh whle t starts to converge after certan teratons. Ths s desrable and shows the effcacy of our algorthm. VI. CONCLUSION AND FUTURE SCOPE The paper mplements a novel technque of Modfed Gravtatonal Search Algorthm for combned economc and emsson dspatch. The problem taken s a mult-objectve problem and the algorthm was mplemented to fnd the optmal generaton capacty of all the generators. Three data sets were used for the testng purpose and the ftness values are compared. The results consdered valve pont effect and the results were found to be qute encouragng. In future other algorthms can be mplemented for the same and the problem can be tested for other datasets. Furthermore the results can be analysed n terms of convergence and hybrd algorthms can be utlsed for the same. REFERENCES [1] Balamurugan, R., and S. Subramanan. "Hybrd nteger coded dfferental evoluton dynamc programmng approach for economc load dspatch wth multple fuel optons." Energy Converson and Management 49.4 (2008): [2] Rayapud, S. Rao. "An ntellgent water drop algorthm for solvng economc load dspatch problem." Internatonal Journal of Electrcal and Electroncs Engneerng 5.2 (2011): [3] Snha, Ndul, and B. Purkayastha. "PSO embedded evolutonary programmng technque for nonconvex economc load dspatch." Power Systems Conference and Exposton, IEEE PES. IEEE, [4] Park, J. H., et al. "Economc load dspatch for pecewse quadratc cost functon usng Hopfeld neural network." Power Systems, IEEE Transactons on 8.3 (1993): [5] Baskar, G., and M. R. Mohan. "Securty constraned economc load dspatch usng mproved partcle swarm optmzaton sutable for utlty system."internatonal Journal of Electrcal Power & Energy Systems (2008): [6] Basu, M. "A smulated annealng-based goal-attanment method for economc emsson load dspatch of fxed head hydrothermal power systems." Internatonal Journal of Electrcal Power & Energy Systems 27.2 (2005): [7] Bhattacharya, Anruddha, and Pranab Kumar Chattopadhyay. "Solvng complex economc load dspatch problems usng bogeography-based optmzaton." Expert Systems wth Applcatons 37.5 (2010): [8] Nanda, J., D. P. Kothar, and K. S. Lngamurthy. "Economc-emsson load dspatch through goal programmng technques." (1988). [9] Chang, C-L. "Genetc-based algorthm for power economc load dspatch."generaton, Transmsson & Dstrbuton, IET 1.2 (2007): [10] Baskar, G., and M. R. Mohan. "Contngency constraned economc load dspatch usng mproved partcle swarm optmzaton for securty enhancement." Electrc Power Systems Research 79.4 (2009): IJEDR Internatonal Journal of Engneerng Development and Research ( 1733