Adaptive Teaching Learning Based Strategy for Unit Commitment with Emissions

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1 Inernaonal Journal of Engneerng Research and Technology ISSN Volume 8, Number 2 (205), pp Inernaonal Research Publcaon House hp://wwwrphousecom Adapve Teachng Learnng Based Sraegy for Un Commmen wh Emssons KP Balasubramanan and Dr RK Sanh 2 Research scholar, Deparmen of Elecrcal Engneerng, Annamala Unversy, Tamlnadu, Inda bala 2 Professor, Deparmen of Elecrcal Engneerng, Annamala Unversy, Tamlnadu, Inda Absrac The generaon of elecrcy from fossl fuel releases several conamnans such as sulphur doxdes, nrogen oxdes and carbon doxde no he amosphere The envronmenal awareness led o mpose rgd envronmenal polces such as US Clean ar amendmens of 990 on power ules o mnmze he emssons Ths paper presens an adapve eachng learnng based soluon echnque for un commmen wh an objecve of mnmzng he emssons The algorhm adopvely adjuss he eachng facor n une wh he performance funcon Numercal resuls on sysems up o 00 generang uns demonsrae he effecveness of he proposed sraegy Key Words: Un commmen, eachng learnng based opmzaon, lambda eraon mehod Nomenclaure CST Cold sarup cos of un ($) UC Un Commmen TLBO Teachng learnng based opmzaon ATLBO Adapve TLBO d,e,f Emsson coeffcens E ( P G ) Emsson funcon (lb/h) Φ F ( P G, U ) Objecve funcon o be mnmzed over he schedulng perod HST Ho sarup cos of un ($) max er Maxmum number of eraons

2 44 KP Balasubramanan and Dr RK Sanh N Toal number of generang uns max P G Maxmum real power generaon of un (MW) mn P G Mnmum real power generaon of un (MW) P P D Generaon oupu power of un a -h nerval (MW) Load demand a -h nerval (MW) PI, Performance ndex of -h suden a -h eraon eacher, PI Performance ndex of he eacher a -h eraon R Spnnng reserve a -h nerval (MW) rand A random number generaed n he range [0,] ST Sarup cos of un a -h nerval ($) T Toal number of hours cold T Cold sar hour of un (hours) down T Mnmum down me of un (hours) off T Connuously off me of un (hours) on T Connuously on me of un- (hours) up, f T Mnmum up me of un- (hours) Teachng facor of -h suden a -h eraon U, Saus of un- a -h nerval ( on =, off = 0) INTRODUCTION Un Commmen (UC) s anoher mporan compuaonal process n he daly operaon and plannng of power sysem I deermnes he opmal schedulng of he generang uns along wh her generaon levels a mnmum operang coss whle sasfyng he sysem and un consrans The decson varables nclude he bnary UC varables and varables assocaed wh real power generang The UC varables descrbe he ON/OFF saus whle he real varables ndcae he generaon levels of he generaors a each hour of he plannng perod Thus, he UC problem can be formulaed as a non-lnear, large-scale, mxed-neger combnaoral opmzaon problem, whch s que dffcul due o s nheren hgh dmensonal, non-convex, dscree and nonlnear naure Besdes, he dmenson of he problem ncreases rapdly wh he sysem sze and he schedulng horzon [] The generaon of elecrcy from fossl fuel releases several conamnans such as sulphur doxdes, nrogen oxdes and carbon doxde no he amosphere In he pas few decades, envronmenal awareness led o mpose rgd envronmenal polces such as US Clean ar amendmens of 990 on power ules o mnmze her emssons A hos of sraeges are n vogue o reduce power plan emssons le nsallng pos-combuson cleanng equpmen, swchng o low emsson fuels and replacemen of he aged fuel burners or dspachng wh emsson consderaons The

3 Adapve Teachng Learnng Based Sraegy for Un Commmen 45 laer opon s preferred n many cases due o economc reasons and s mmedae avalably for shor-erm operaon However, he oher alernaves are consdered as a long erm opon as hey ncur addonal capal cos [2] Many mehods wh varous degrees of near-opmaly, effcency, ably o handle dffcul consrans and heurscs, have been suggesed n he leraure A one end of he specrum, here are smple and fas bu hghly heursc prory ls [3] mehods A he oher end, here are dynamc programmng [4,5] and branch-and bound [6,7], whch are n general, flexble, bu ofen prone o he curse of dmensonaly Beween he wo exremes, here are Lagrangan relaxaon (LR) mehods [8,9], whch are effcen and appear o be a desrable compromse, and well sued for large-scale UC However under ceran consrans such as crew consrans, hese mehods demand addonal heurscs dermenal o effcency of he mehod Mea-heursc mehods such as genec algorhms [0] smulaed annealng [] and evoluonary programmng [2] have been consdered for he soluon of UC n he recen years wh a vew of overcomng he drawbacs of classcal approaches Recenly, a populaon based Teachng-Learnng-Based Opmzaon (TLBO) algorhm ha wors on he effec of nfluence of a eacher on he oupu of learners n a class room has been oulned by Rao e al [3-5] for solvng mulmodal opmzaon problems I s an algorhm-specfc parameer-less algorhm, as requres only common conrollng parameers le populaon sze and number of generaons for s worng Snce s nroducon, has been appled o a varey of problems ncludng parameer opmzaon of modern machnng processes [6], opmal reacve power flow [7] and opmal power flow [8] and found o yeld sasfacory resuls Ths paper ams o develop an adapve TLBO (ATLBO) mehod for solvng UC problem wh an objecve of mnmzng only he emssons he developed mehod adapvely adjuss s parameer The proposed mehod (PM) has been appled on sx es sysems wh a vew o demonsrae s performance 2 PROBLEM DESCRIPTION The man objecve of UC problem s o mnmze he overall emssons of all he generang uns over he scheduled me horzon under he spnnng reserve and operaonal consrans of generaor uns Ths consraned opmzaon problem s formulaed as { } U T N Mnmze E( G, U) = E ( PG) + ST ( U, ) Φ () Subjec o, Power balance consran: D N P, = = P P U 0 (2) = G, = Spnnng reserve consran:

4 46 KP Balasubramanan and Dr RK Sanh P D + R N = max G P U, Generaon lm consrans: mn max P G U, PG PG U, 0 (3) =,2, L, N (4) Mnmum up and down me consrans: on up f T < T off down U, = 0 f T < T (5) 0 or oherwse Sar-up Cos: down off cold down = HST f T T T + T ST (6) off cold CST > + down f T T T Where, G 2 G G E ( P ) = d P + e P + f (7) 3 TLBO TLBO, nspred from eachng-learnng process n class rooms, s suggesed for solvng mulmodal opmzaon problems In hs approach, each suden comprsng grade pons of dfferen subjecs represens a soluon pon and hs/her performance s analogous o fness value of he problem The bes suden n he populaon s consdered as he eacher A group of sudens comprsng a eacher forms he populaon and he soluon process s governed by wo basc operaons, namely eachng and learnng phases, whch are brefed below: Teachng Phase: The eachng phase represens he global search propery of he TLBO algorhm Durng hs phase, he eacher, who s he mos experenced and nowledgeable person n he class, mpars nowledge o all he sudens wh a vew of mprovng he performance of he whole class from nal level o hs own level The eachng ncreases he mean grade pon of he subjec The change n he grade pon of he suden can be expressed as j ave Δ S = rand ( 0,) ( S j j eacher f S ) (8) Where j ave S s he mean grade of he j-h subjec a -h eraon and compued by S j ave j eacher = ns ns = S j S s he grade pon of he j-h subjec of he eacher a -h eraon f s he eachng facor, whch decdes he value of mean o be changed and can be eher or 2, evaluaed by (9)

5 Adapve Teachng Learnng Based Sraegy for Un Commmen 47 f = round ([ + rand (0,){,2}] (0) The new grade pon of he j-h subjec of he -h suden, as a resul of eachng, s mahemacally modeled by j + j j S = S + ΔS () The grade pons of all he sudens a he eachng phase are furher mproved by he learnng phase Learnng Phase: In hs phase, he sudens enrch her nowledge by neracon among hemselves, whch helps n mprovng her performances The nfluence on he grade pons due o he neracon of p -h suden wh q -h suden may be mahemacally expressed as follows: j S j + p S p = j S p PI p and PI q respecvely + rand + rand ( S j j p Sq ) ( S j S j ) q p f f PI PI p p > PI < PI q q (2) s he performance, ndcang he fness, of he p -h and q -h suden 4 ADAPTIVE TLBO The eachng facor of TLBO, narraed n secon 3, decdes he value of mean o be changed I s adapvely modfed a -h eraon as [9], PI eacher,, = f PI 0 eacher, f PI (3) oherwse I does no requre he facor o be specfed a he begnnng of he opmzaon process The TLBO wh adapve mechansm s hereafer represened as adapve TLBO (ATLBO) hroughou he hess 5 PROPOSED METHOD The proposed mehod (PM) uses ATLBO wh a goal of enhancng he search process, mprovng he compuaonal effcency and obanng he global bes soluon for UC problem wh emssons I also nvolves he represenaon of problem varables and formaon of a performance ndex funcon 5 Represenaon of Grade Pons The grade pons S of each suden n he PM s represened o denoe he bnary UC varable, U,, whch represens on/off saus of -h un a -h nerval n marx form as shown n Fg

6 48 KP Balasubramanan and Dr RK Sanh 2 N U, U,2 U,T 2 U 2, U 2,2 U 2,T S = T U N, U N,2 U N,T Fg Represenaon of a suden 52 Performance Index Funcon The algorhm searches for opmal soluon by maxmzng a PI funcon, whch s formulaed from he objecve funcon of Eq () The performance ndex funcon s wren as Maxmze PI = (4) + Φ E ( PG, U) 56 Soluon Process An nal populaon of sudens s obaned by generang random values whn her respecve lms o every ndvdual n he populaon The PI s calculaed by consderng grade pons of each suden; and he eachng and learnng phases are performed for all he sudens n he populaon wh a vew of maxmzng her performances The erave process s connued ll convergence 6 Smulaon Resuls The PM has been esed on sysems wh 0, 20, 40, 60, 80 and 00 generang uns The un daa and load demand daa for 24 hours for he sysem wh 0 uns are avalable n [20] The emsson coeffcens are aen from [2] The daa for oher larger sysems are obaned by duplcang he daa of 0 un sysem and adjusng he load demand n proporon o he sysem sze The populaon sze s chosen as 30 for all he es problems The maxmum number of generaons for convergence chec s aen as 200, 300, 500, 700, 900 and 000 for 0, 20, 40, 60, 80 and 00 un sysems respecvely The spnnng reserve requremens are assumed o be 0% of he load demand For each case, oally 50 rals are performed o verfy he robusness of he PM

7 Adapve Teachng Learnng Based Sraegy for Un Commmen 49 Table UC Schedule over schedulng horzon for 0 un sysem by PM I N T E R V al Un Emssons lb/h Ne Emssons The dealed resuls comprsng UC schedule and ne emssons for 0-un sysem, obaned by PM, are presened n Table The generaon of UC schedule over he schedulng horzon are shown n Fg 2 The ne emssons for 0, 20, 40, 60, 80 and 00 un sysems of he PM are gven n Table 2 The bes, wors and he average emssons are presened n Table 3 for 0 and 00 un sysems Ths able also comprses resuls of he mehod avalable n [2] wh a vew of demonsrang he effecveness of he PM Analyzng he resuls for 0-un sysem, s very clear ha he PM offers he lowes emssons of lb/ h compared o ha of he mehod presened n [2] The mechansm perms he sysem o offer he desred amoun of power wh smaller emssons, even smaller han ha of he exsng echnque I s very clear from hs able ha PM produces comparavely lower emssons han hose

8 50 KP Balasubramanan and Dr RK Sanh of he exsng approach, hereby ensurng ha he PM s able o produce he global bes soluon D D2 D3 D4 D5 D6 D7 D8 D9 D0 Fg2 Generaon of Commed Uns for 0 un sysem by PM Table 2 Emssons of all es sysems by PM Uns Ne Emsson lb/h Table 3 Comparson of Resuls for 0 and 00 un sysems Tes Sysem Mehod Bes Wors Average 0-uns MEO [2] PM uns MEO [2] PM CONCLUSIONS A new algorhm nvolvng ATLBO for UC wh an objecve of mnmzng he emssons has been presened I has been alored o adapvely conrol he eachng facor so as o enhance he search process The resuls on varous es sysems have

9 Adapve Teachng Learnng Based Sraegy for Un Commmen 5 clearly exhbed he superor performance of he PM and ndcaed ha he mehod s deally suable for praccal applcaons ACKNOWLEDGEMENT The auhors graefully acnowledge he auhores of Annamala Unversy for he facles offered o carry ou hs wor REFERENCES AJ Wood and BF Wollenberg, Power generaon, operaon and conrol, John Wley and sons, New Yor, Lamon JW and Obesss EV (995) Emsson dspach models and algorhms for he 990 s, IEEE Trans on Power Sysems, 0(2), Baldwn, CJ KM Dale, RF Drch, A sudy of econmc shudown of generang uns n daly dspach, AIEE Tr on PAS, Vol 78, 960, pp WL Snyder, HD Powell, Jr, JC Rayburn Dynamc programmng Approach o un commmen, IEEE Transacons on power sysems, Vol PWRS S-2, No 2, May 987, pp WJ Hobbs, G Hermon, S Warner, GB Sheble, An Enhanced Dynamc programmng Approach for un commmen, IEEE Trans on PAS, Vol PAS 0, pp 79-86, January TS Dllon, Ineger Programmng Approach o he problem of opmal un commmen wh probablsc reserve Deermnaon, IEEE Trans on PAS, Vol PAS-97 7 AI Cohen, MYoshmura, A Branch and Bound Algorhm for un commmen, IEEE Trans on PAS, Vol PAS-02, pp , Feb FN Lee, A Fuel-consraned un commmen mehod, IEEE Transacons on Power sysem, Vol 4, No3, Augus 989, pp CP Cheng, CW Lu and CC Lu, Un commmen by Lagrangan Relaxaon and genec algorhem, IEEE Trans Power Sys, Vol 5, pp , May HTyang, PC Yang, and CL Huang, Evoluonary Programmng based economc dspach for uns wh nosmooh fuel cos funcons, IEEE Trans Power sys, Vol, pp 2-7, feb, 996 AH Manawy, YL Abdel-Magd and SZ Selm, A Smulaed annealng algorhm for un commmen, IEEE Trans Power Sys Vol 3, pp , Feb KA Juse, H Ka, E Tanaa and J Hasegawa, An evoluonary programmng soluon o he un commmen problem, IEEE Trans Power Sys, Vol 4, pp , Nov Rao RV, Savsan VJ and Vahara DP (20) Teachng-learnng-based opmzaon: A novel mehod for consraned mechancal desgn opmzaon problems, Compuer Aded Desgn, 43(3):

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