Optimal Scheduling of Hydro Power Generation Using Deconvolution Technique: A Case Study of Thai Power System

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1 Optmal Schedulng of Hydro Power Generaton Usng Deconvoluton Technque: A Case Study of Tha Power System Keerat Chayakulkheeree Abstract In ths paper, the deconvoluton technque s appled to determne an optmal daly schedulng of hydro power plants n Thaland. The hydro generatng unts are model as lmted energy unts (LEUs) or assgned energy (AE) unts. The energy specfed of each hydro unt s compared wth the calculated expected energy served (EES) to determne an optmal schedulng condton. The method s compared to the daly schedulng wthout deconvoluton process. The smulaton results ncludng Loss of Load Probablty (LOLP), Loss of Load Hour (LOLH), Expected Energy Not Served (EENS), and the Equvalent Total Cost (ETC), ntroduced n the paper are shown and dscussed. Wth the same EES of hydro generatng unts, the ETC of the optmal schedulng of usng deconvoluton s lower than that of schedulng wthout deconvoluton. The results shows that the deconvoluton technque based optmal LEUs schedulng can dspatch all of daly energy specfed at the optmal condton leadng to the lower daly operatng cost than that of schedulng wthout deconvoluton calculaton. The method can effcently determne the optmal schedulng of hydro generatng unts. The developed program s potentally applcable for prelmnary schedulng of LEUs before solvng the unt commtment problem. Keywords Energy lmted unt, capacty model buldng, equvalent load duraton curve, convoluton, deconvoluton.. INTRODUCTION In a power generaton schedulng, the operatng costs of the unts can be found by loadng the unts under ther correspondng equvalent load duraton curves (s) accordng to the fuel cost and computng the energy generated by each unt. The algorthm can easly be mplemented f the energy generated by each unt s not lmted and ts operatng condton s only based on ts generatng capacty and avalablty, for example, coalfred, ol fred, gas turbnes and nuclear unts. However, there are unts whose energy s constraned by some other factors. Such unts are categorzed as lmted energy unts (LEUs) or assgned energy (AE) unts. In case of hydroelectrc plants, ths constrant may be due to lmted reservor sze, run-of-the-rver constrant or seasonal ranfall lmtaton. The cost assocated wth producton of ths energy s typcally very low and t s most advantageous to use all of the avalable energy. In case of a fossl fueled unts, the constrant may be due to lmted fuel supply or the lmts on emssons. In case of nuclear, the constrant may be due to nsuffcent core energy whch prevents the unt beng run on base load. Besde ths energy constrant, the LEUs are also lmted by ts generatng capacty and avalablty. In Thaland, the electrcty supply ndustry s presently a vertcally ntegrated structure. The Electrcty Generatng Authorty of Thaland (EGAT) owns and operates transmsson network and most of the generatons. The Metropoltan Electrcty Authorty (MEA) and the Provncal Electrcty Authorty (PEA) own and operate geographcal dstrbuton systems. Snce 99, the prvate nvestment n the generaton sector through small power producers (SPPs) and ndependent power producers (IPPs) programs has been successfully ntroduced. Both SPPs and IPPs sell the electrcty to EGAT based on the long term power purchase agreements (PPAs). EGAT s a sngle buyer who subsequently sells the electrcty to the MEA, PEA and lmted number of drect consumers. Fg. shows the structure of present Tha power system []. As of fscal year 28, hydro power shares about % of total power generaton n Thaland. In Thaland, hydro power plants schedulng are strctly based on rrgaton requrement. The reservors dscharge volumes are specfed by the Royal Irrgaton Department (RID) on daly bass. Therefore, hydro power plants can be modeled as the ELUs and t s productve to develop the tool for optmal schedulng of the hydro generatng unts. Generaton SPPs ( %) EGAT (87 EGCO (2 %) %) Transmsson Dstrbuton EGA ( EGAT T (%) IPPs PEA (58 MEA Drect %) Customers Customers Custom Customers Plannng & Investment Prcng Plannng & Investment Prcng N at o n al Energy E Polcy n er and Plannng g y Offce P ol c y O ff e c Keerat Chayakulkheeree s wth Department of Electrcal Engneerng, Faculty of Engneerng, Srpatum Unversty, 6, Pahonyothn Rd., Senankom, Jatujak, Bangkok, Thaland, 9, emal: keerat.ch@spu.ac.th. Fg.. The structure of present Tha power system. Many technques have been proposed to determne 83

2 optmal schedulng of LEUs n power systems. Bloom [2] proposed an teratve decomposton type framework where reservor utlzaton decsons were made by lnear programmng master problem and assocated margnal costs and benefts were evaluated by a subproblem. The algorthms requred multple soluton of subproblem to fnd the optmal usage of reservors. Some heurstc and artfcal based optmzaton technques have also been appled to solve the optmal hydro-thermal schedulng [3-6]. However, the probabltes of the unt outages are not ncluded n the problem formulatons. To ncorporate the probabltes of the unt outages nto optmal hydro generatng unts schedulng, the algorthm to optmze the reservor utlzaton by probablty producton costng has been proposed by Malk and Cory [7]. Nevertheless, the framework for applyng the technque to practcal problem has not been fully developed due to ts ntensve mathematcal computaton. In ths paper, the program for computng the capacty model buldng and deconvoluton for large generaton systems s developed. The deconvoluton technque s appled to determne an optmal daly schedulng of hydro power plant. The hydro generatng unts are model as LEUs. The energy specfed of each hydro unt s compared wth the calculated expected energy served (EES) to determne an optmal schedulng condton. The method s compared to the daly schedulng wthout deconvoluton process. The results shown that deconvoluton technque can dspatch effcently utlze the specfed energy of hydro generatng unts, leadng to lower total fuel cost. The method s potentally applcable for prelmnary schedulng of LEUs before solvng the unt commtment problem. 2. PROBLEM MULATION OPTIMAL SCHEDULI OF ENERGY LIMITED UNITS 2. A Recursve Algorthm for Capacty Model Buldng Wth mert order operaton, f generatng unts were completely relable and thus always avalable when called upon to generate, the areas occuped by each unt under the orgnal load duraton curve (LDC) would be suffcent to determne unt specfc generated energy. However, generatng unts are unantcpatedly forced out of servce resultng n ncreased calls for generaton on unts hgher n the mert order. The ncreased demand for generaton by a specfc unt resultng from the forced outage rates () of all prevously loaded unts s accounted by modfyng the LDC to reflect these forced outages. Ths s accomplshed by computng the equvalent load on a partcular unt whch s the sum of customer demand and forced outage of prevously loaded generators. The cumulatve probablty dstrbuton, or, gves the total probablty that customer load plus the capacty on forced outage equals or exceeds a gven value X when the generatng system through the th unt out of total unts s beng consdered. Each tme a unt s loaded, ts forced outages have to be added to the current to derve the new whch reflect the demand seen by the next unt n the mert order. Ths addton depends on the probablty dstrbuton characterzng the forced outages the unt. After the outages of all avalable unts have been added to the customer load, the EENS may be obtaned as an area under the resultng, thus provdng a measure of system relablty. The heght of the same curve at the capacty pont of the system s the loss of load probablty (LOLP), that s, the expected proporton of tme that customer demand may exceed avalable generatng capacty. By a recursve algorthm for capacty model buldng [8], the cumulatve probablty of a partcular capacty outage state of X MW or the equvalent load duraton curve, after a unt generatng at PG MW and force outage rate s consdered, s gven by, where, P G ( X ) = ( ) ( X ) + () ( X P ), = the real power generaton of unt (MW), (X) = the equvalent load duraton curve when the unt s consdered, (X) = the equvalent load duraton curve when all unts are consdered, ( X ) = LDC( X ) = the orgnal system load duraton curve, = the of generator, and ST = the step sze used n the calculaton (MW). The Appendx llustrates the probablty table of the recursve algorthm for capacty model buldng. To generalze the algorthm, the step sze (ST) used n ths paper s one MW. Fg. 2 shows the after taken nto account the unts. LOLP (X) (X) (LDC) IC IC ( - (X) X ) dx G (X) θ IC ( X ) dx IC - IC IC θ X (MW) Fg. 2. obtaned by a recursve algorthm for capacty model buldng. 2.2 Deconvoluton Process Deconvoluton s the reverse process of convoluton. From (), to fnd the prevous, wth the outage of unt removed from the, the outage of unt can be deconvolved by rearrangng () as follows: 84

3 ( X ) = ( X ) + ( X P Smlarly on the, the outage effect of unt j, whch was loaded prevously and not necessarly adjacent to unt can be removed by the followng (3). / The new ( ) after the effect of unt j, can be computed as, ' ( X ) = ' G ( X ) + ( X P 2.3 Expected Energy Served and Not Served ) Gj ) (2) (3) The expected energy served by generator s calculated by, ES = IC ( ) T IC and the total daly operatng cost s, ETC = = FC = = PFC ES ( X ) dx The expected energy not served s calculated by, where θ (4) (5) EENS = T ( X ) dx (6) IC ES = the expected energy served by generator (MWh), T = total perod under consderaton (24 h), IC - = the sum of capacty when the generatng system through the -th unt s beng consdered wth mert order operaton (MW), IC = the sum of capacty when the generatng system through the th unt s beng consdered wth mert order operaton (MW), FC = Daly fuel cost of generator (THB), PFC = Per unt fuel cost of generator (THB/MWh). EENS = the expected energy not served (MWh) IC = total nstalled capacty (MW) θ = X ( X ) = (MW). = the equvalent system peak load Read Input Data; daly load curve, thermal power generatng unts, and ELUs Compute by convolvng all thermal unts Compute by convolvng the jth ELU Does the EES j match the specfed energy of the jth ELU? NO Compute / by deconvolvng the jth ELU Have all ELUs been convolved? NO j = j+ STOP Fg. 3. Computatonal procedure. YES YES The computaton of ES and EENS s llustrated n Fg. 2. The deconvoluton of each LEU s preceded untl ts EENS matches ts daly energy assgned. The computatonal procedure s shown n Fg SIMULATION RESULTS The test data are arbtrarly chosen from hstorcal data of Thaland power system. The data are smplfed and unavalable data are chosen from standard values. There are 99 power generatng unts, ncludng hydro plants taken nto account n the smulaton. SPP power plants, wth ther nstalled capacty of MW, are dspatched based on the power purchase agreements whch are not based on ts prces. They are modeled n the load curve based on the power purchase agreement to operate at full capacty from 8. a.m. to 8. p.m. on weekdays and at 65% of the full capacty from 8. p.m. to 8. a.m. on weekdays, and whole Saturday and Sunday. IPP and EGAT power plants are operated accordng to the mert order. The daly load curve of Thaland peak day n 28, shown n Fg. 4, wth the peak of MW, s used n the smulaton. The smulaton results are based on comparson of two methods as shown n Case and 2, wthout and wth deconvoluton technque, respectvely, as follows. Case : Hydro power plants are modeled n the load curve by usng the equvalent MW from the hstorcal water dscharge data wthout usng deconvoluton technque and Case 2: Hydro power plants are convolved and deconvolved usng the deconvoluton technque. 85

4 2 x 4 system, the total annual savngs n THB could be substantal. Ths mples that deconvoluton can effcently utlze the specfed energy of hydro generatng unts S ystem Loa d D urato n C urve (LD C ) wth modeled SPPs and H ydro Pow er P lant Installed C apacty E xcludng S P P s H ydro P ow er P lants.5 Duraton.6.5 E quvalent L oad D uraton C urve (E L D C ) H our Fg. 4. Daly load curve of Thaland peak day n 28. The wth and wthout deconvolutons are shown n Fg. 5 and 6, respectvely. Table shows the smulaton results ncludng LOLP, LOLH, EENS, ETC, and the total ES of hydro generatng unts of Case and Case 2. In Fg. 5., the hydro power plants are modeled n the load curve and nstalled capacty excludng the hydro power plants and SPP s shown. The daly load curve wth hydro power plants loadng s shown n Fg. 6. In Fg. 7, the hydro power plants are loadng n to the usng deconvoluton technque and the nstalled capacty ncludng hydro power plant but excludng SPP s shown. Table. The summary results x 4 Fg. 5. The results from capacty model buldng wthout deconvoluton (Case ) x 4 H ydro Power Item System Peak (MW) EENS (MWh) LOLP Total ES by hydro unts (MWh) ETC (MTHB) Average Loadng for Hydro Unt Case x x Case wthout deconvoluton technque x x Case 2 wth deconvoluton technque x x H our Fg. 6. The daly load curve wth hstorcal hydro power plants loadng (Case ). D uraton Syste m L oa d Duraton Curve (LDC) w th m ode le d SP P s Operatng C ond ton of H yd ro Pow er Plan ts Installe d C apa cty E xcludng S PP s E qu valent L oa d D ura ton C urve (E LD C ) In ths smulaton, the LOLP of schedulng wth deconvoluton s shown to be hgher than that of schedulng wthout deconvoluton leadng to the hgher LOLH and EENS. However, wth the same EES of hydro generatng unts, the ETC of the optmal schedulng of usng deconvoluton s lower than that wthout deconvoluton. The optmal condton for hydro generatng unts schedulng s to operate them n between 82.5 MW to MW of the load curve as shown n Fg.7. Despte the small daly savng of the Tha x 4 Fg. 7. The result from deconvoluton for optmal schedulng of hydro generatng unts (Case 2). 86

5 4. CONCLUSION The deconvoluton technque base optmal schedulng of LEUs n power system has been nvestgated. The method can effcently determne the optmal schedulng of hydro generatng unts. The developed program s potentally applcable for prelmnary schedulng of LEUs before solvng the unt commtment problem. ACKNOWLEDGMENT Ths work s supported by The Thaland Research Fund under contract number RDG5556. REFERENCES [] Electrcty Generatng Authorty of Thaland, 28. Statstcal Report Fscal Year 28, Thaland. [2] J. A. Bloom. 98. Long-Range Generaton Plannng wth lmted energy and storage unts: Part and 2, Techncal report 486 and 487, School of operatng research and ndustral engneerng, Cornell Unversty. [3] Rudolf and R. Bayrlethner A genetc algorthm for solvng the unt commtment problem of hydro-thermal power system. IEEE Trans. Power System, Vol. 4, No. 4, pp [4] Chaa-An L, R. B. Johnson, A. J. Svoboda, Chung- L Tseng, and E. Hsu A robust unt commtment algorthm for hydro-thermal optmzaton. IEEE Trans. Power Systems, Vol. 3, No. 3, pp [5] N. J. Redondo and A. J. Conejo Short-term hydro-thermal coordnaton by Lagrangan relaxaton: soluton of the dual problem. IEEE Trans. Power Systems, Vol. 4, No., pp [6] Xaomn Ba and S. M. Shahdehpour Hydro-thermal, schedulng by tabu search and decomposton method. IEEE Trans Power Systems, Vol., No. 2, pp [7] S. Malk and B. J. Cory Effcent algorthm to optmse the energy generaton by pumped storage unts n probablstc producton costng. IEE Proc.-Gener. Transm. Dstrb., pp [8] R. Bllnton and R. N. Allan Relablty Evaluaton of Power Systems. New York, NY: Plenum Press. APPENDIX The reclusve algorthm for capacty model buldng. 87

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