Optimization of Corridor Observation Method to Solve Environmental and Economic Dispatch Problem

Transcription

1 ISSN (e): Vol, 04 Issue, 11 November 2014 Internatonal Journal of Computatonal Engneerng Research (IJCER) Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc Dspatch Problem Stève Perab Ngoffe 1, Salomé Ndjaomo Essane 2, Adolphe Mouengue Imano 3, Grégore Abessolo Ondoa 4 1 Doctorate Student, Electronc, Electrotechnc, Automatc and Telecommuncatons Laboratory, ERSEE, Unversty of Douala - Cameroon 2 Lecturer, Electronc, Electrotechnc, Automatc and Telecommuncatons Laboratory, ERSEE, Unversty of Douala - Cameroon 3 Assocate Professor, Electronc, Electrotechnc, Automatc and Telecommuncatons Laboratory, ERSEE, Unversty of Douala, BP Douala Cameroon 4 Master of Scences wth thess student, Electronc, Electrotechnc, Automatc and Telecommuncatons Laboratory, ERSEE, Unversty of Douala - Cameroon ABSTRACT: Ths paper presents an optmzaton of corrdor observaton method (COM) whch s an applcable optmzaton algorthm based on the evolutonary algorthm to solve an envronmental and economc Dspatch (EED) problem. Ths problem s seen le a b-objectve optmzaton problem where fuel cost and gas emsson are objectves. In ths method, the optmal Pareto front s found usng the concept of corrdor observaton and the best compromsed soluton s obtaned by fuzzy logc. The optmzaton of ths method conssts to fnd best parameters (number of corrdor, number of ntal populaton and number of generaton) whch mprove soluton and reduce a computatonal tme. The smulated results usng power system wth dfferent numbers of generaton unts showed that the new parameters amelorate the soluton eep her stablty and reduce consderably the CPU tme (tme s mnmum dvde by 4) comparatvely at parameterzaton wth orgnals parameters. Keywords: b-objectve, corrdors observaton, fuel cost, gas emsson, new parameters, optmal Pareto front, optmzaton, orgnal settngs I. INTRODUCTION The economc dspatchng (ED) s one of the ey problems n power system operaton and plannng. The basc objectve of economc dspatch s to schedule the commtted generatng unt outputs so as to meet the load demand at mnmum operatng cost, whle satsfyng all equalty and nequalty constrants. Ths maes the ED problem a large scale hghly constraned non-lnear optmzaton problem. In addton, the ncreasng publc awareness of the envronmental protecton and the passage of the Clean Ar Act Amendments of 1990 have forced the utltes to modfy ther desgn or operatonal strateges to reduce polluton and atmospherc emssons of the thermal power plant. Several strateges to reduce the atmospherc emssons have been proposed and dscussed. These nclude: nstallaton of pollutant cleanng equpment, swtchng to low emsson fuels, replacement of the aged fuel-burners wth cleaner ones, and emsson dspatchng. The frst three optons requre nstallaton of new equpment and/or modfcaton of the exstng ones that nvolve consderable captal outlay and, hence, they can be consdered as long-term optons. The emsson dspatchng opton s an attractve short-term alternatve n whch the emsson n addton to the fuel cost objectve s to be mnmzed. Thus, the ED problem can be handled as a mult-objectve optmzaton problem wth non-commensurable and contradctory objectves. In recent years, ths opton has receved much attenton [1 5] snce t requres only small modfcaton of the basc ED to nclude emssons. In the lterature concernng envronmental/economc dspatch (EED) problem, dfferent techncs have been appled to solve EED problem. In [1, 2] the problem was reduced to a sngle objectve problem by treatng the emsson as a constrant. Ths formulaton, however, has a severe dffculty n gettng the trade-off relatons between cost and emsson. Alternatvely, mnmzng the emsson has been handled as another objectve n addton to the cost [5]. However, many mathematcal assumptons have to be gven to smplfy the problem. Open Access Journal Page 1

2 Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc urthermore, ths approach does not gve any nformaton regardng the trade-offs nvolved. In other research drecton, the mult-objectve EED problem was converted to a sngle objectve problem by lnear combnaton of dfferent objectves as a weghted sum [3], [6]. The mportant aspect of ths weghted sum method s that a set of non-nferor (or Pareto-optmal) solutons can be obtaned by varyng the weghts. Unfortunately, ths requres multple runs as many tmes as the number of desred Pareto-optmal solutons. urthermore, ths method cannot be used n problems havng a non-convex Pareto optmal front. To overcome t, certan method optmzes the most preferred objectve and consders the other objectves as constrants bounded by some allowable levels [5]. The most obvous weanesses of ths approach are that, they are tme-consumng and tend to observe wealy non-domnated solutons [5]. The other drecton s to consder both objectves smultaneously as competng objectves. The recent revew to the Unt Commtment and Methods for Solvng [7] showed that evolutonary algorthms are the most used n ths case; certanly because they can effcently elmnate most of the dffcultes of classcal methods [5]. The major problems of these algorthms, s to fnd the Pareto optmal front, to conserve the non- domnated solutons durng the search and relatvely long tme to fnd the soluton. In [8] we have proposed one method, based on the evolutonary method where the optmal Pareto front s obtaned by the concept of corrdor observaton and the loses of non-domnated soluton s reduce by the dynamsm of archves durng the dfferent generatons. The qualty of soluton and CPU tme depend to the number of corrdors, the ntal populaton and the number of generatons. In ths paper, we propose some parameters whch eep stable the soluton and reduce consderably CPU tme of COM. In the second part of ths paper, we present materals and methods to solve the EED problem and n the thrd part, smulaton and results are presented to enable us to fnd the new parameters and demonstrate ther effectveness by comparng t wth the orgnal settngs. II. MATERIALS AND METHODS [8] In ths part, we formulate the EED problem and present our approach to solve t Problem formulaton The EED problem s to mnmze two competng objectve functons, fuel cost and emsson, whle satsfyng several equalty and nequalty constrants. Generally the problem s formulated as follows: Problem objectves Mnmzaton of fuel cost The generator cost curves are represented generally by quadratc functons. The total fuel cost ($/h) n terms of perod T, can be expressed as: (2) where c ( 2 p ) a b p c p f, t, t, t and c ) s the generator fuel cost functon; a, b and c are the cost coeffcents of th generator; P,t, s the ( p f,t electrcal output of th generator; Ng s the number of generators commtted to the operatng system ; I,t the statut of dfferent generators; ST the start-up cost. Mnmzaton of gas emsson The atmospherc pollutants such as sulphur doxdes (SO 2 ) and ntrogen oxdes (NO X ) caused by fossl-fuelled thermal unts can be modelled separately. However, for comparson purposes, the total emsson (ton/h) n one perod T of these pollutants can be expressed as: T Ng p e p I, t ( ) f, t t E, where e p c p I ST I I, t ( ) (1 ) f, t, t, t, t 1 t f ( P T t 1 1 (3) t ) ( p p ) (4), t, t, t and α, β, δ are the emsson coeffcents of the th generator Objectve constrants Power balance constrant Ng, (1) Open Access Journal Page 2

3 Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc p load Ng p I 0, t, t, t 1 Spnnng reserve constrant : p load Ng R p I 0, t t max,, t 1 Generaton lmt constrants :, 1... Ng p I p p I mn,, t, t max,, t Mnmum up and tme constrant : on up 1 f T T off I 0 f T T, t 0 or 1 otherwse (5) (6) (7) (8) Where T up represent the mnmum up tme of unt- ; T the mnmum tme of unt T off s the contnuously off tme of unt and T on the contnuously on tme of unt-. Start-up cost ST HST f T CST f T T off off T T cold T T cold 2.2. The corrdors observaton method [8] The dfferent steps of the COM are presented n the followng fgure Generate ntal populaton Evaluate functon cost Evaluate emsson cost Segment objectves space functon n corrdor orm a new populaton Search the best persons n corrdors Archve the best persons Apply cross and mutaton operator Stoppng crtera determne the pareto front determne the best compromze soluton End gure 1: Dfferent steps of the algorthms [8] Step 1 In the frst step, we start wth to the status of dfferent unts generaton, where we create randomly the ntal populaton. Each ndvdual s a combnaton of each power generaton unt Step 2 In the second, usng equatons (1) and (3) we evaluate the objectve functons of ths populaton Open Access Journal Page 3

4 Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc Step 3 Usng the mnmum of the dfferent objectve functons of ndvduals who respect the constrants (5) to (8), we defne the space soluton and segment t to the corrdors observatons followng the dfferent axes whch are specfy by each functon. Step 4 In each corrdor, we search the best ndvduals who have the mnmum objectves functons, and the non feasble solutons are classfed usng the number and the rate of volaton constrants. Those solutons wll be used to ncrease the number of feasble solutons. Step 5 We eep n the archves those best ndvduals Step 6 We verfy the stoppng crtera defne as [10]: where ln( d ) N cl t t 1 1 j, j, d j 1 Cl 1 max mn (10) Explan the metrc progresson of the best ndvduals n each corrdor. N s the number of objectves functons ; Cl the number of corrdor ; t j,, t-1 j, the j th objectve functon of the best ndvdual n th corrdor ; mn and max the mnmum and maxmum of the j functon ; t s the present generaton, t-1 the anteror generaton. At tmes the maxmum number of generaton can be the alternatve stoppng crtera step 7 If the stoppng crtera s not verfed, we construct the new populaton usng the selecton, cross and mutaton operators apply to the archve populaton and we return to step 2. Step 8 If the stoppng crtera s verfed we fnd the best compromse soluton among the ndvduals of the Pareto front. Due to mprecse nature of the decson maer s judgment, each objectve functon of the -th soluton s represented by a membershp functon defned as max max 1 mn 0 f f f mn mn or each non-domnated soluton, the normalzed membershp functon s M N 1 N max max calculated as : 1 1 (12) where M s the number of non-domnated solutons. The best compromse soluton s the one havng the maxmum of. III. SIMULATION AND RESULTS In order to fnd the new parameters of COM and solve the EED, a 3-unts generaton system s tested [11]. And extent at 6, 10 and 15 unts generaton. These parameters are appled n COM wth the same software and computer used n [8]. The results are compared wth the orgnals settngs of COM. The data concernng the unts generaton are gven n tables 1 and 2 [11]. (9) (11) Open Access Journal Page 4

5 emsson globale(ton/h) cost($) Unts Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc Table 1. The 3-unts system data Unt max P mn P a ($ /h) b ($ /MWh) c ($ /MW 2 h) up R ($ /MW) R ($ /MWh) (ton/h) so 2 Table 2. SO 2 and NOx coeffcents emsson gas data of 3-unts Nox (ton/mwh) so 2 (ton/h) Nox (ton/mwh) (ton/mw 2 h) so 2 Nox (ton/mw 2 h) 1 0, , , , e -6 1,6103e -6 1, e , , , , e -5 5,4658 e -6 3, e , , , , e -4 5,4658 e -6 1, e -6 In the mplementaton, we add the dfferent coeffcents of each gas per groups to have the coeffcent of the whole gas 3.1. Study of objectves accordng to the number of generaton The study of convergence wth the same parameters of [8].e., 50 corrdors, 300 number of ntal populaton s presented n fgure cost convergence wth generaton generaton emsson convergence wth generaton generaton gure 2: Convergence of fuel cost ($) and gas emssons (ton/h) objectve functons (1000MW). These curves convergence show that snce the 500 generatons fuel cost and gas emsson s unform so, f we choose the number of generatons at the value greater or equal than 500 generatons the soluton wll be the same. So we can tae 500 le the new number of generatons Study of objectves accordng to the number of corrdors The representaton of objectves, accordng to the number of corrdor, wth ntal populaton number and number of generatons set respectvely at 300 and 1000 s shown n fgure 3. Open Access Journal Page 5

6 gaz emsson(ton/h) Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc gure 3: Evoluton of fuel cost ($) and gas emssons (ton/h) accordng to the number of corrdors (850 MW). These curves shows that from 20 corrdors fuel cost and gas emsson are almost unform. The Pareto front at ths value of number of corrdors s represented n fgure generaton ndvdual of populaton feasble ndvdual Best compromse soluton fuel cost($) gure 4: Pareto front wth the new parameters. Comparng wth the Pareto front obtaned wth the orgnal parameters [8] n fgure 5 Open Access Journal Page 6

7 gaz emsson (ton/h) fuel cost($) gaz emsson (ton/h) Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc generaton ndvdual of populaton feasble ndvdual Best compromse soluton fuel cost($) gure 5: Pareto front wth the orgnal parameters. We can conclude that the ncrease of corrdors number mproves the Pareto front but from 20 corrdors, the optmal soluton s almost unform. So we can consder 20 le new number of corrdor Study of objectves accordng to the number of ntal populaton The representaton of objectves, accordng to ntal populaton, wth number of corrdor and number of generatons set respectvely at 50 and 1000 s shown n fgure number of ntal ndvduals number of ntal ndvduals gure 6: Evoluton of fuel cost ($) and gas emssons (ton/h) accordng to the number of ntal ndvduals (850MW) These representatons show that from an ntal populaton of 200, fuel cost and gas emsson are almost unform. So we can set ths parameter at Comparatve study between the orgnal parameters and new To present the effectveness of the new parameters n COM to unt commtment and EED, we appled t to a producton plan of 3-unts durng 5 hours and made the comparson study wth the orgnal settng. Open Access Journal Page 7

8 Hours (H) Optmzaton of Corrdor Observaton Method to Solve Envronmental and Economc Table 3. Unt commtment and EED durng 5 hours wth the two groups of parameters Demands P1 P2 P3 uel cost X10 3 ($) Emsson gaz (ton/h) Wth orgnal parameters Wth new parameters Average CPU tme (s) The fndngs of ths table are as follows: n terms of unt commtment, the results are dentcal; sensbly the same n terms of EED but the CPU average tmes s consderably reduced. Ths study have extended wth 6, 10, and 15 unt n table 4 fndngs was the same but the convergence speed accordng to the number of unts s reduce wth news parameters Table 4. Comparatve study wth 3, 6, 10 and 15 unts generaton Number of unts Wth orgnal parameters uel cost x 10 3 ($) Gas emsson(ton/h) Average tmes (s) Wth new parameters uel cost x10 3 ($) Gas emsson (ton/h) Average tme (s) IV. CONCLUSION In ths paper, news parameters are proposed to optmze COM. COM have been proposed n [8] to solve envronmental/economc power dspatch optmzaton problem and unt commtment. The study of objectves accordng to the number of generaton, of corrdors and ntal populaton have allowed us to propose new parameters that are 20 corrdors, 200 ndvduals for ntal populaton and 500 generatons. The parameterzaton of COM wth these settngs conserves the qualty of soluton n terms of unt commtment and EED. The prncpal advantages of ths parameterzaton are the reducton of CPU tme (the tme s mnmum dvded by 4) and the convergence speed accordng to the number of generaton unts comparatvely at the parameterzaton wth orgnals settngs (50 corrdors, 200 ndvduals and 1000 generaton). REERENCES [1]. Brodesy S, Hahn RW. Assessng the nfluence of power pools on emsson constraned economc dspatch. IEEE Trans Power Syst 1986; 1 (1). PP: [2]. Granell GP, Montagna M, Pasn GL, Marannno P. Emsson constraned dynamc dspatch. Electr Power Syst Res 1992; 24. pp: [3]. Chang CS, Wong KP, an B. Securty-constraned multobjectve generaton dspatch usng bcrteron global optmzaton. IEE Proc Gener Transm Dstrb 1995;142 (4) : [4]. R Manoj Kumar. Bavsett, T.Kranth Kran. Optmzaton Of Combned Economc and Emsson Dspatch Problem A Comparatve Study for 30 Bus Systems. IOSR Journal of Electrcal and Electroncs Engneerng (IOSR-JEEE) 2012 ; Vol 2. PP [5]. M. A. Abdo. Envronmental/Economc Power Dspatch Usng Multobjectve Evolutonary Algorthms. IEEE transactons on power systems; 2003 Vol. 18, N O. 4. PP : [6]. Alhall ras. «Supervson, économe et mpact sur l envronnement d un système d'énerge électrque assocé à une centrale photovoltaïque»thèse de Doctorat Pars tech [7]. Saman.h, Razmezan.M and Naseh.M.R.. Unt Commtment and Methods for Solvng; a Revew. J. Basc. Appl. Sc. Res; 2013, 3(2s) [8]. S. Ndjaomo Essane, S. Perab Ngoffe, A. Mouengue Imano, G. Abessolo Ondoa. B-objectve Optmzaton Apply to Envronmental and Economc Dspatch Problem Usng the Method of Corrdor Observatons. Internatonal Journal of Computatonal Engneerng Research (IJCER); 2014; Vol 4. PP: [9]. Lubng Xe, Songlng Wang & Zhquan Wu. Study on Economc, Rapd and Envronmental Power Dspatch. Modern appled scence vol.3 N Pp : [10]. Jean Dpama. «Optmsaton mult-objectf des systèmes énergétques».thèse soutenue à l unversté de MONTREAL [11]. ard Benhamda, Rachd Belhachem. Dynamc Constraned Economc/Emsson Dspatch Schedulng Usng Neural Networ. Power Engneerng and Electrcal Engneerng. Vol: 11 N pp : Open Access Journal Page 8