Optimal operation scheme for diesel power plant units of PT. PLN-Manokwari Branch using Lagrange Multiplier Method

Transcription

1 Avalable onlne at roceda Envronmental Scences 17 ( 2013 ) The 3 rd Internatonal Conference on Sustanable Future for Human Securty SUSTAIN 2012 Optmal operaton scheme for desel power plant unts of T. LN-Manokwar Branch usng Lagrange Multpler Method Adelhard Ben Rehara a, *, Sabar Setawdayat b, Elas Kondorura Bawan a a Engneerng Department, Unversty of apua, Jl.Gunung Salju, Manokwar 98314,Indonesa b Elecrcal Engneerng Department, Unversty of Wdyagama, Jl. Taman Borobudur Indah, Malang 65142, Indonesa Abstract Economc dspatch has been used n many power plants to optmze the plants operaton. As one of method n economc dspatch, Lagrange multpler method was utlzed for calculatng the economc operaton n power system of T. LN-Manokwar branch whch s the electrcal company workng n area of Manokwar. Ths power system ncludes nne unts and the other rental unts of desel power plant. Based on some schemes whch had been desgned and calculated wth Lagrange multpler method, the most economc unt refers to desel power plant unt 1 wth prme mover DEUTZ BV8M 628 whle desel power plant unt 6 wth prme mover MITSUBISHI S12 R-TA s ndcated as the least economc unt at the system. The system shows exstence of good effcency when workng for schemes 3500 to 6000 kw and for schemes above 6000 kw, the operatng expenses are ncreasng sgnfcantly n the consequence of operatng of the low effcent unts. Result of calculaton usng average daly generatng power shows that ths power system wll be very optmal usng economc dspatch The Authors. ublshed by Elsever B.V. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under under responsblty of SUSTAIN of SUSTAIN conference s conferences commttee commttee and and supported supported by Kyoto by Kyoto Unversty; (OIR), Unversty; (GCOE-ES), (OIR), (GCOE-ES), (GCOE-HSE), (GCOE-HSE), (CSEAS), (RISH), (CSEAS), (GCOE-ARS) (RISH), (GCOE-ARS) and (GSS) as and co-hosts. (GSS) as co-hosts. Keywords: Economc dspatch; Lagrange; desel power plant; * Correspondng author. Tel.: ; fax: E-mal address: adelhard.rehara@fmpa.unpa.ac.d The Authors. ublshed by Elsever B.V. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty of SUSTAIN conference s commttee and supported by Kyoto Unversty; (OIR), (GCOE-ES), (GCOE-HSE), (CSEAS), (RISH), (GCOE-ARS) and (GSS) as co-hosts. do: /j.proenv

2 558 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) Introducton Development of energy sources to obtan the other actvty s the mportant key to ncrease the contnual lfe level for people, anywhere they resde n. The bggest challenges, whch are faced by the world today, are how to provde energy wherever t s needed, how to alter the energy to the other form and how to use t wthout producng any polluton. Desel power plant (D) s a type of power plant that converts fossl fuel to be electrcal energy. The best effcency of a converson machne s about 80% but mostly t wll be lad n between 40-60% [12]; therefore the converson process n D may not over 80% of the effcency and t wll delver some pollutants as the effect of the process. Accordng to hgh moblty and smple to be nstalled, the D s somewhat the best chosen to be used n remote area. The dsadvantage of the D s hgh operaton cost for both fuel and mantenance. By operatng the D n economc operaton, the D wll become optmal n producng energy and then the pollutants can be reduced. The factors nfluencng power-generaton at mnmum cost are operatng effcences of generators, fuel cost, and transmsson losses. The most effcent generator n the system does not guarantee mnmum cost as t may be located n an area where cost to get the fuel s hgh. In the same way, transmsson losses may be consderable hgher and then the plant may be overly un-economcal, f the plant s located far from the load center. Hence, the problem s to determne the generaton of dfferent plants such that the total operatng cost s mnmum [10]. T. LN-Manokwar branch s an Indonesan government company that handles electrcal energy productons n the area of Manokwar, whch s the captal cty of West apua rovnce, Indonesa. In the effort to ncrease effcency and to reduce the generaton cost, the company wll operate hgh effcent machne and contnue to mddle and to low effcent machnes together wth ncreasng of the load. Even wthout takng the power transmsson loss nto account, ths effort s faled to reduce producton cost [9]. Many researches had been done to optmze power generaton unts n dfferent way [1-8], but most of the researches refer to the basc economc dspatch formulaton. Ths paper wll explan and smulate economc dspatch for all machnes of T. LN- Manokwar branch n some schemes by gnorng transmsson losses. Nomenclature number of unt a,b the coeffcent of the cost nput of the -th generator c equvalent to fuel consumpton of the generatng unt operaton wthout power output n total number of unts n the system F R mn, fuel cost functon of the unts generaton of unt total system load lower lmt of the unt max, upper lmt of the unt L Lagrange functon the Lagrange multpler.

3 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) Economc Dspatch The defnton of economc dspatch (ED) s gven by Kumar et. al (2008) as the operaton of generaton facltes to produce energy at the lowest cost to relably serve consumers, recognzng any operatonal lmts of generaton and transmsson facltes. In tradtonal economc dspatch, the operatng cost s reduced by proper allocaton of the amount of power to be generated by dfferent generatng unts. However, the optmum economc dspatch may not be the best nterms of the envronmental crtera. Recently many countres throughout the world have concentrated on the reducton of the amount of pollutants from fossl fuel power generatng unts [8]. The ED problem s how to mnmze a total generaton cost of power system for a gven demand load wth satsfy varous constrants ncludng power balance constrant and generaton power lmts of each unt. Whle the load has been varated, the output of generators has to balance the load varaton. The fundamental of the ED problem s the set of nput-output characterstc of the power generatng unt and the ED problem can be expressed as [1-10]: Mnmze F T n 1 F (1) 2 F ( ) ( a b c) (2) Subject to : n 1 R (3) mn max (4) 3. Lagrange Multpler Method The fundamental components n ED are plannng for future dspatch and dspatchng the power system today. Generally target functon of ED can be nvestgated by Lagrange multpler method, frst or second order gradent method, and lambda teraton but these methods may encounter some dffcultes for complex generaton cost functons [3]. Lagrange formulaton can be rewrtten as [9-11]: n L F F ( ) (5) T 1 R n 1 The functon of output generatng power s assumed that optmal condton s reached f gradent operaton equal to zero. In other word, the frst dervatve of the Lagrange functon L wth respect to each of the ndependent varables has to be set equal to zero as follows.

4 560 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) L 0 (6) F T L FT R 0 (7) By solvng 7 th equaton, we get : F F ( 0 1) 0 (8) Eq. 8 shows that optmum condton can be reached f the ncremental of each power generaton connected to the system s equal. Ths condton should respect to the constrant defned n eq Dscusson 4.1. Defnng fuel cost functon T. LN-Manokwar branch has operated nne desel power plant unts to produce maxmum electrcal energy about 7610 kw. The power plant unts of are operated n same locaton and drectly connected to the grd system. The specfcaton of each machne s provded n table 1. Table 1. Machne specfcatons Machne number Type of machne Sere maxmum Output power, kw mnmum 1 DEUTZ BV8M DEUTZ BV8M MAN 6L 26/32 H MAN 6L 26/32 H DAIHATSU 6DL MITSUBISHI S12 R -TA MITSUBISHI S12 H -TA MITSUBISHI S16 R -TA KOMATSU SAA 6D Data of power output n kwh and fuel cost for every machne unt had been used for defnng the fuel cost characterstc of the machnes usng second polnomal functon as shown n fgure 1.

5 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) Fg. 1.(a) to () Curve of machne unt 1 to 9 The lnes n fg. 1 (a) to () are gven by quadratc polnomal functon to connect each data pont of machne unt 1 to 9. All of the fuel cost curves on the fgure are non lnear curves but the curve for machne 5 (fg. 1.e) seems to be lnear curve. The fuel cost functons for each machne unt appear on the fgure as Y and X varables. The functons can be rewrtten by substtutng both varables wth F and as shown n eq. 9. F 1 = -1.42e ; for F 2 = 1.17e ; for F 3 = ; for F 4 = 2.38e e ; for F 5 = 1.23e ; for (9) F 6 = ; for F 7 = ; for F 8 = 4.64e ; for F 9 = ; for

6 562 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) Applyng economc dspatch Lambda for each generaton unt can be defned by solvng dervatve functon of the machne fuel cost equatons n eq. 9 as follows. = = = = = = = = = = (10) = = = = = = = = The frst dervatve equaton of each unt n eq. 10 can now be used to determne total lambda by referng to eq. 3 as follows (11) R 1 By solvng lambda for R about 3500 kw, lambda n eq. 11 s found about For the other generatng schemes, lambda can be solve n same way as rewrten n table 2 and 3. Table 2. Generatng power for fulfllng demand power Demand power, kw Output power of desel power plant unts, kw , , , , , , Machne unt 1 s very effcent whle t s used n operaton schemes that are less than 4000 kw and for schemes more than 4000 kw, ths unt tends to work n ts lower lmt. On the other hand, unt 6 s started for schemes more than 6000 kw. The other unts whch are unt 2, 3, 4, 5, 7, 8 and 9 are

7 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) occoped from earler schemes and by ncreasng the schemes power, then these unts wll produce more power untl each upper lmt. Table 3 shows that unt 6 s hardly not effcent whch s marked wth the cost of lambda value. Ths unt works wth cost about 0.5 US$/h at mnmum power. Ths unt s maybe better to be operated at hgh demand power although the cost of system wll ncrease as ts consequence. The other possblty s to deactvate ths machne for lower demand power; therefore ts load wll be generated by the other unt whch s more effcent. Table 3. Fuel cost for ncreasng demand power Demand power, kw Fuel cost of desel power plant unts, US$/h Total Cost, US$/h Compared to the other unts n the system of T. LN-Manokwar branch, unt 1 shows hgh economc functon. By workng to generate 950 kw, ths unt only uses cost US$/h. On the contrary, producton cost wll ncrease f the unt s operated to generate low power. In the schemes, t uses US$/h to produce 180 kw. Ths unt dffers wth the other system unts whch tend to apply hgh fuel cost along wth the ncreasng of power generated. Fg. 2.Fuel cost vs demand power Based on fg. 2, t can be seen from the desgned schemes that there s a proportonal relatonshp between demand power and fuel cost. Together wth the growng of demand power, fuel cost wll ncrease. Steep slopes n the begnng and endng of the curve show spacng transtons that nfluence the

8 564 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) lnearty of the curve. The relatonshp seems to be lnear n between 4000 and 6000 kw of schemes. On the other hand, n lower and upper demand power of the schemes, the curve tends to be non lnear. Fg. 2 also shows that as a whole system would more effcent f t s workng for demand power n between 3500 and 6000 kw. Whle demand power s more than 6000 kw, unt 6 whch s the least effcent unt would perforce to be worked; therefore t wll make producton cost larger. For demand power under 3500 kw, t s better to deactvate the least economc unt(s) to force unt 1 as the most economc unt to work n ts maxmum lmt Case study As the case study, the real of total generatng power of the nne D machnes for May 2012 s gven about kwh wth cost US$ The average daly generaton wll be kwh wth cost US$ and so total system generaton for every hour wll be kw. By applyng the amount of total system generaton about kw and solve the lambda of the system equaton n eq. 11, t wll gve lambda about and total cost US$/h. It means that after workng for 24 hours, the machnes wll produce kwh wth cost US$ Ths cost s only 0.122% of the average daly cost and t was sgnfcantly reduced from manual operaton wthout ED. The data for calculaton n ths case s average data and so the result s not always true. Output power s not always constant and so lambda wll ncrease for peak load and t wll ncrease daly cost. In general, the calculaton shows that by usng ED, total cost can be reduced and the system wll be optmal n operaton. 5. Summary Desel power plant unt 1, whch s one of the nne desel power plant unts operated by T. LN- Manokwar branch, s the most effcent unt. Usng prme mover DEUTZ BV8M 628, ths unt can produce up to 950 kw wth producton cost about US$/h. In ths unt, producton cost tends to ncrease along wth lowerng of power producton. On the other hand, unt 6 wth prme mover MITSUBISHI S12 R-TA s unt wth hgh producton cost; therefore wth economc dspatch, ths unt wll be forced to work n lower lmt. Ths unt wll start to work n effectve way for hgh demand power. Result of calculaton n a case study usng average daly generatng power of power system of T. LN-Manokwar branch n May 2012 shows that by applyng economc dspatch for the system, t wll produce kwh wth cost US$ The cost s only 0.122% of US$ whch s the cost of daly average operaton. Economc dspatch s not applcable to turn on or off machnes n a power system, so that a combnaton wth unt commtment needs to be done n other schemes. By applyng the unt commtment, the low effcent generator wll be turn on and off n such a way to reduce the producton cost. Acknowledgements Specal apprecaton goes to the head and the staff of T. LN-Manokwar branch, many thanks for ther cooperaton along the research. Authors also want to thank to those who ndrectly contrbuted n ths research.

9 Adelhard Ben Rehara et al. / roceda Envronmental Scences 17 ( 2013 ) References [1] T. Yalcnoz, H. Altun, M. Uzam. Economc Dspatch Soluton Usng A Genetc Algorthm Based on Arthmetc Crossover IEEE orto ower Tech Conference, September [2] C. L. Chen,S. L. Chen. Short-term Unt Commtment wth Smplfed Economc Dspatch. Electrc ower Systems Research, 1991;21: [3] M. Zare, A. Roozegar, R. Kazemzadeh, J.M. Kauffmann. Two Area ower Systems Economc Dspatch roblem Solvng Consderng Transmsson Capacty Constrants. World Academy of Scence, Engneerng and Technology 2007; 33: [4] Jong-Bae ark, Member, IEEE, K-Song Lee, Joong-Rn Shn, and Kwang Y. Lee, Fellow, IEEE. A artcle Swarm Optmzaton for Economc Dspatch Wth Nonsmooth Cost Functons. IEEE Transactons on ower Systems, February 2005; 20: [5] Sh Yao Lm, Mohammad Montakhab, Hassan Nour. Economc Dspatch of ower System Usng artcle Swarm Optmzaton wth Constrcton Factor. Internatonal Journal of Innovatons n Energy Systems and ower, October 2009;4: [6] X. S. Han, H. B. Goo, Danel S. Krschen. Dynamc Economc Dspatch: Feasble and Optmal Solutons. IEEE Transactons On ower Systems, February 2001;16: [7] A. K. Al-Othman, F. S. Al-Fares, and K. M. EL-Nagger. ower System Securty Constraned Economc Dspatch Usng Real Coded Quantum Inspred Evoluton Algorthm. World Academy of Scence, Engneerng and Technology, 2007;29:7-14. [8] K. Sathsh Kumar, V. Tamlselvan, N. Mural, R. Rajaram, N. ShanmugaSundaram, T. Jayabarath. Economc Load Dspatch wth Emsson Constrants usng Varous SO Algorthms. Wseas Transactons on ower Systems, September 2008:9. [9] Wllam D. Stevenson Jr. Element of ower System Analyss. 4rd ed. New York: McGraw-Hll; [10] H. Saadat. ower System Analyss, 2rd ed. New York: McGraw-Hll; [11] Allen J. Wood, Bruce F Wollenberg. ower Generaton, Operaton, and Control, 2rd ed. New York:Wley-Interscence; [12] Gancolly. hyscs. 4rd ed. New York:rentceHall;