Power Generation Scheduling of Thermal Units Considering Gas Pipelines Constraints

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1 ower Generaton Schedulng of Thermal Unts Consderng Gas pelnes Constrants Sara Mohtasham and Habb Raab Mashhad Abstract W e grow of electrcty generaton from gas energy gas ppelne relablty can substantally mpact e electrc generaton. A physcal dsrupton to ppelne or to a compressor staton can nterrupt e flow of gas or reduce e pressure and lead to loss of multple gas-fred electrc generators, whch could dramatcally reduce e suppled power and reaten e power system securty. Gas pressure drops durng peak loadng tme on ppelne system, s a common problem n network w no enough transportaton capacty whch lmts gas transportaton and causes many problem for ermal doman power systems n supplyng er demand. For a feasble generaton schedulng plannng n networks w no suffcent gas transportaton capacty, t s requred to consder gas ppelne constrants n solvng e optmzaton problem and evaluate e mpacts of gas consumpton n power plants on gas ppelnes operatng condton. Ths paper studes about operatng of gas fred power plants n crtcal condtons when e demand of gas and electrcty peak togeer. An ntegrated model of gas and electrc model s used to consder e gas ppelne constrants n e economc dspatch problem of gas-fueled ermal generator unts. I. INTRODUCTION The grow of power generaton n Iran and several oer countres s manly based on constructons of combned-cycle power plants. The ncrease electrcty generaton by s technology has tghtly lnked e electrcal system and natural gas system togeer. As e energy systems move nto era of ncreased nterdependency between e gas and electrcty sectors, e decentralzed approach does not address e nteractons between ese two sectors w regard to operatonal, securty and relablty ssues. It s us useful to undertake e operatonal and plannng analyss n an ntegrated manner. Gas ppelne relablty can substantally mpact e electrc generaton. A physcal dsrupton to ppelne or to a compressor staton can nterrupt e flow of gas or reduce e pressure and lead to loss of multple gas-fred electrc generators, whch could dramatcally reduce e suppled power and reaten e power system securty. Alough n case of certan knd of ppelne contngences, under ground storage facltes can provde e back up for natural gas supply to some of e unts, e power dspatch decsons could be affected by gas ppelne constrants. Gas pressure drop durng peak loadng tme on ppelne system, s anoer S. Mohtasham s w Iran ower Generaton, Transmsson and Dstrbuton Management Co. (e-mal: srmohtasham@yahoo.com) H. R. Mashhad s w e Department of Electcal Engneerng, Ferdows Unvesty of Mashhad, Iran. (e-mal: raab_mashhad@yahoo.com) problem whch lmts gas transportaton capacty and usually happens n systems w nadequate transportaton capacty. Alough ere s enough gas supples n countres lke Iran, lack of enough ppelne capacty causes many problem n supplyng e gas demand durng peak tmes. To perform generaton schedulng of ermal unts, e maxmum amount of power at can be suppled by each unt s requred. Wout consderng e gas ppelne mpacts on generaton unts operatng, e maxmum power s constant parameter. Nevereless, maxmum amount of power s a nonlnear functon of e amount of avalable fuel for generators. For a feasble generaton schedulng plannng n networks w no suffcent gas transportaton capacty, t s requred to consder gas ppelne constrants n solvng e optmzaton problem and evaluate e mpacts of gas consumpton n power plants on gas ppelnes operatng condtons. Optmal operatng of power plants attracts a great deal of attenton, as a modest reducton n fuel cost leads to a large savng n system operaton cost. One of e mportant schedulng problems s e economc dspatch problem. The am of ED problem s allocatng of e requred load demand between e avalable generaton unts, such at e operaton cost n mnmzed whle satsfyng system constrants. But n some operatng condtons for nstance durng e peak demand of gas ppelne system, e man problem of system operator s to fnd a feasble soluton to supply e electrc grd demand by gas-fueled generators. At e tme of peak loadng n ppelne, e gas transportaton system s operatng near ts stablty borders and pressure drop s very lkely n e system. So e ppelne system may not be capable to supply e gas-fueled unts demand completely. Therefore, to fnd a feasble soluton for generaton schedulng, t s necessary to use an ntegrated model of gas and electrc model to consder e gas ppelnes constrants. As e gas-fueled power generators are maor natural gas consumers, ere s a close nteracton between er operaton and e ppelnes operatng condton. The dspatch of gasfueled power plants affects e gas flow rate and ts pressure n ppelne systems. A wse generaton dspatch w regards to gas pressure constrants can prevent e pressure drop n ppelne system and meanwhle supply e electrcty demand by gas-fueled power plants. Ths paper studes about operatng of gas fueled power plants n crtcal condtons when e demand of gas and electrcty peak togeer. An ntegrated model of ppelne system and gas-fred power plants s used to evaluate e effect of each generator gas usage on e gas flow rate and ts 935

2 pressure n ppelne system. By usng s model we can dspatch e electrcty demand between e exstng generator unts such at no pressure drop happens rough e ppelnes. II. NATURAL GAS MODELING Natural gas s transported from gas wellheads to dfferent customers by gas transmsson network. The NG transportaton network model conssts of four basc components namely, gas wellheads, ppelnes, compressor statons and nterconnecton nodes. Fgure 1 shows a smplfed NG transportaton network whch s utlzed n s study for analyzng e mpacts of natural gas system operaton on e economc dspatch. The transportaton ppelnes connect e gas wellhead, usually far from load centers, to dstrbuton system or large ndustral users. The compressors act lke step-up transformers n electrc networks [4]. As gas flows rough e ppelnes, ts pressure wll drop. Thus e compressors are an essental component n e natural gas system to mantan e desred pressure level n e transportaton ppelnes. f = ppelne flow rate, mmscf/hr S = +1 f - > = -1 f - < F = ppelne frcton factor D = nternal dameter of ppelne (nches) G = gas specfc gravty L = ppelne leng between nodes (mles) = pressure at node, psa = pressure at node, psa = standard pressure, psa T = standard temperature, R T a = average gas temperature, R Z a = average gas compressblty factor Equaton 1 s a nonlnear equaton at defnes e relaton between e flow rate rough a ppelne and ts termnal nodes pressures. B. Compressor Model Gas flow loses a part of ts energy durng transportaton along e ppelnes due to ts frctonal resstance whch results n a loss of pressure. To mantan e gas pressure at a desrable level, compressor statons are nstalled n e network. The amount of energy consumed by compressor statons, can be computed based on e horsepower equaton as follows: [1] Z( 1)/ H B. f [( / ) 1] (2) Where: H: compressor rate of work (horsepower) Fgure 1: Gas ppelne system [4] The maematcal formulaton of NG system components are presented as follows: A. Flow Equaton n pelne The flow equatons n gas transportaton network descrbe e relaton between gas flow rate, e pressures at e two ends of ppelnes. For soermal gas flow n long horzontal ppelne, whch begns at node and ends at node, e general steady state flow rate ( n mmscf 2 /hr) s often expressed by e followng formula[1]: T ( ) D f S.8531 S (1) FGLT a Z a where: 2 -mllon standard cubc feet B.8531T / * ( / 1) f : flow rate rough compressor, mmscf/hr : compressor sucton pressure, psa : compressor dscharge pressure, psa Z : gas compressblty factor at compressor nlet, R T : compressor sucton temperature, : specfc heat rato (cp=cv ) : compressor effcency The above equaton shows e rate of work of each compressor as a functon of e gas flow rate rough e compressor and e pressure rato between e nlet and outlet gas. The compressor statons can use steam, electrcty and natural gas as e energy source. Usually, n large ppelne systems, e most economc source s e natural gas, whch s avalable and flowng rough e compressors. The amount of gas wdrawn to power a gas turbne to operate e compressor can be approxmated as: 936

3 2. H. H (3) Where s e amount of gas used by compressor, H s horsepower requred for gas compressor n equaton (2) and,, are e compressor coeffcents. C. Gas-fred ower lants Modelng Gas and electrc networks nterconnect at gas-fred power generaton staton. The nput-output characterstc of e power plants expresses e relaton between e two networks. It determnes e gas consumpton flow rate n e power plant ( q, mmscf/hr) as a functon of e generated electrc power. Ths s obtaned by dvdng e plant s heat energy functon ( H, MBtu/hr)) by e gas gross heatng value (GHV, MBtu/ mmscf). 1 q H. (4) GHV Also, we have: F C. H (5) where: F : e cost functon of e plant H : e heat energy functon of e plant C: e gas energy cost($/mbtu) Replacng F H n equaton 4 w C we have: 1 1 q F.. (6) GHV C Equaton 6 expresses e gas consumpton flow rate of e power plant as a lnear functon of e plant cost functon. D. Gas load flow problem The problem of smulaton of gas network w N nodes n steady state, known as loadflow, s usually at of computng e values of node pressure and flow rates n ndvdual ppes for known values of source pressures and gas necton n all oer nodes. For more studes you can see loadflow statement and soluton n [2]. Fgure 2: Natural gas network and power plants schematc III. ECONOMIC DISATCH OF DUAL-FUEL THERMAL UNITS CONSIDERING IELINES CONSTRAINTS Fgure 2 shows a typcal ppelne system at transports gas from wellhead to fve electrc power plants and oer gas consumers. The gas ppelne system s composed of one gas source node and ree branches. Branch 1 supples two power plants (#1, #2) and none electrcal ndustral users whch are presented as D1. The second branch transports gas to power plant #4 and #5 and a gas dstrbuton network, D2. On e rd branch, ere are power plant #3 and oer non-electrcal consumers at are represented as D3. Each power plant has multple gas-fueled generator unts. The techncal parameters of power plants and er generators are lsted n table 1. The gas ppelne system has fve compressor statons, two at branch 1, two at branch 2 and one at branch 3. The techncal parameters of compressors refers to equaton 2 and3 are n table 2. Let s consder e gas and electrcty demand of a cold wnter day. Frst we use e typcal economc dspatch meod to determne e power plants generaton power. In s case e ED problem s formulated as: Mn Subect to: p 1 F ( p ) 1 (7) D p mn p pmax 1,2,..., (9) Table 3 shows e results of e above optmzaton problem. (8) 937

4 Table1: Generators characterstcs parameters mn max No Number a b c of unts ( MW ) ( MW ) ($ / hr) ($ / MW. hr) ($ / MW 2. hr Sum unts, 39 MW Table 2- compressors and gas turbne data No Effcency / Turbne Fuel Rate Coeffcents e-3.2 e e-3.25e e-3.3e e-3.3e e-3.3e-3 Table 3- The economc dspatch result lant No. Unts no. MW 1 1,2,3, , ,8,9, ,12,13, ,16, Total demand 3 Total cost Now let s see e ppelnes operatng condtons n e acheved result. Frst we should calculate e gas consumpton of each power plant usng e equatons 4-6.When e gas demands of power plants are obtaned, e gas flow algorm s appled to e ppelne system. The smulaton result of gas ppelnes s shown n table 4. The gas ppelnes model used n gas smulaton s presented n appendx. Table 4: gas smulaton results for ED result n table 3 Node No. ressure Node No. ressure The smulaton result shows at e gas pressure at nodes 9, 1, 11 n branch 3 are not real quantty. Ths magnary numbers state at e ED result s not a feasble answer due to e gas ppelne system. The ppelne system does not have e adequate capacty to supply e gas demands n branch 3. As e prorty at natural gas network s to serve non-electrcal gas consumpton, e generaton of plant 3 should be reduced due to lack of gas supply and nstead e generaton of plant 5 should be ncreased (plants 1, 2 and 4 are generatng er maxmum capacty). If e ncrease of generaton at plant 5 also leads to gas pressure drop n branch 2, en t would be not possble to supply e electrcty demand all by gas energy. Most of ermal plants have ol storage facltes to use n case of dsrupton of gas supply. Now e economc dspatch of ermal unts w dual-fuel capacty s formulated regards to ppelnes constrants. For e system n fgure 2 f all e generator unts are equpped w ol storage facltes e economc dspatch problem s formulated as: Mn [ C ( ) (1 ) C ( ) ] c (1) Subect to: ( D ) 1 loss mn max mn (11),1 C : gas prce $/mmscf C ( ) power generaton cost n plant when t uses gas = G * H ( ) C ( ) power generaton cost n plant when t uses ol H ( ) = L * H ( ) Heat energy characterstc o unt, Mbtu/h G : gas energy cost $/Mbtu L : ol energy cost $/Mbtu The optmzaton varables are out put power of generator unts and decson varables: w. When w =1, e unt consumes gas as prmary energy and when w = t consumes ol. Due to varous non-lnear equatons and constrants n smulatng e gas ppelnes network and also because of e nteger varables ( w ), genetc algorm s appled to e optmzaton problem. Genetc algorm (GAs) s an evolutonary optmzaton approach whch s alternatve to tradtonal optmzaton 938

5 meods. GAs are most apprecate for complex non-lnear models where locaton of e global s dffcult task. Unlke tradtonal optmzaton meods, GAs s better at handlng nteger varable an contnuous varables. To solve e optmzaton problem w GA, a chromosome s a bt strng composes of varables and varables. The ftness functon s defned as: Ftness functon = 5 ( ( ) (1 ) ( ) ) cos ( ) 1 C C t k 1 2 D ( ) loss 1 1 mn Where 2 and are penalty factors and defned as: w (12) 5 1 f mn (13) 1 oerwse In e prevous formulaton e ED soluton was not acceptable regards to ppelnes constrants. Now w s new formulaton e best economcal power dspatch s obtaned w respect to bo gas and electrcty networks. The gas and ol prces are defned as er prces n Iran. (Gas prce = 7 Rals/m3, ol prce= 6 Rals/lt). Table 5 shows e optmum generaton schedule. Table 5- The economc dspatch result ower lant No. Gen. No. MW Natural Gas / Resdual Fuel Ol G 1 5 NG 1 G 2 5 NG G 3 5 NG G 4 5 NG 2 G 5 25 NG G 6 25 NG 3 G 7 4 NG G 8 4 NG G resdual fuel ol G 1 4 NG 4 G 11 2 NG G 12 2 NG G 13 2 NG G 14 2 NG 5 G NG G resdual fuel ol G 26 NG Table 6: gas pressure n two ED results Node pressure Consderng ppelnes constrant wout Consderng ppelnes constrant At e optmum condton of e prevous part e gas pressure n nodes 9, 1 and 11 were magnary and e pressure n node 15 n branch 2 was very close to ts lower lmt. In new generaton schedulng one of e generator unts of power plant 3 s swtched on ol fuel and us e pressure drop rough branch 3 s removed. The total generaton of plant 5 s ncreased an e prevous soluton. Therefore, to avod e gas pressure drop rough branch 2, one of ts generator unts s swtched on ol fuel. As table 6 shows e pressure constrant s actve n branch 2 and 3. It ndcates at e man goal n solvng e optmzaton problem was to fnd a feasble soluton to supply e electrc demand by gas energy as much as possble. Ths s because e gas energy n Iran s much cheaper an ol energy. IV. CONCLUSIONS The contnual and rapd grow of NG-fueled electrcty generatng plants has ncreased e nterdependency of natural gas and electrcty ndustres. As e electrc power plants are maor NG consumers, ere s a close nteracton between e gas-fred power plants operaton and e gas supply system operaton. The dspatch of e NG fueled power plants affects e gas flow n e ppelne system and, on e oer hand; e ppelne operatng constrants can mpose lmts on power plants generaton. For a secure operaton of gas and electrcty system, t s necessary to mpose some extra constrants on electrcty system operaton n case of some partcular operatng condtons. For nstance n severe weaer stuatons (e.g., hot summer and cold wnter days) when demands for gas and electrcty peak togeer, e pressure drop n ppelnes s very lkely. In ese cases, t s unavodable to lmt e amount of gas used by some power plants to prevent e loss of multple gas consumers. Ths paper studed about operatng of gas fred power plants n crtcal condtons when e demand of gas and electrcty peak togeer. An ntegrated model of ppelne system and gasfueled power plants was used to evaluate e effect of each generator gas usage on e gas flow rate and ts pressure n ppelne system. By usng s model e economc dspatch of ermal unts was formulated consderng e ppelnes constrants. By solvng s new economc dspatch problem, e power demand s dspatched between e ermal unts n such a way at prevents pressure drops n ppelne system and loss of multple gas consumers. Table 6 compares e gas pressure n ese two operatng ponts. 939

6 V. AENDIX Fgure appendx 1. gas ppelne model for solvng gas loadflow B matrces of e loss formula [7] A. Wood, B. Wollenberg, " ower Generaton, Operaton & Control," Wley-Inersence, 1996, ISBN [8] Danel D. wolf, Maematcal ropertes of formulatons of e Gas Transmsson roblem, GREMARS, Unversty of Lllle 3, France. Aprl 23. [9] Samer Takrt, Chonawee Supatgat, Llan Wu. Coordnatng Fuel Inventory and Electrc ower Generaton Under Uncertanty, IEEE Transactons on ower Systems, Vol. 16, No. 4, November 21 [1] Roger Z. Ros Mercado, Sumng Wu, L.R. Scott, E.A. Boyd, A Reducton Technque for Natural Gas Transmsson Network Optmzaton roblems, Annals of operaton Research 1,2-234, 22. [11] C.C. von Wezacker, J. erner, An ntegrated smuaton madel for European electrcty and natural gas supply, Electrcal Engneerng 83 (21) , Sprnger-Verlag 21. [12] Ch-Keung Woo, A. Olson, Ira Horowtz, S.Luk, B-drectonal causalty n Calforna s electrcty and natural-gas markets, Energy olcy 34 (26), pp [13] Won-Woo Lee, US lessons for energy ndustry restructurng: based on natural gas and Calforna electrcty ncdences, Energy olcy 23 (24), pp [14] Challenges, Rsks, and Opportuntes foe Natural Gas from Electrc ower Industry Restructurng, Energy Informaton Admnstraton/ The challenges of Electrc ower Industry Restructurng for Fuel Supples B B B.4357 loss T T B B B VI. REFERENCES [1] Qung L, Seugwon An and Thomas W. Gedra, Natural Gas and Electrcty Optmal ower Flow, roceedngs of e IEEE/ES Transmsson and Dstrbuton Conference, and presented at e conference n Dallas TX, September 8, 23. aper number 3TD27. [2] Qung L, Seugwon An and Thomas W. Gedra, Solvng Natural Gas Load problem Usng Electrc Loadflow Teqnques, roceedngs of e Nor Amercan ower Symposum, at Unversty of Mssour-Rolla, October 2-21, 23. [3] Oderson Das de Mello, Takaak Ohsh, An Integrated Dspatch Model of Gas Supply and Thermoelectrc Systems, presented at 15 ower Systems Computaton Conference,August 22-26, 25,Lege, Belgum. [4] M. Shahdehpour, Y.Fu and T. Wedman, Impact of Natural Gas Infrastructure on Electrc ower Systems, roceedngs of e IEEE, vol. 93, No.5.May 25. [5] Hane Chen, Ross Baldck, Optmzaton Short-Term Natural Gas Supply ortfolo For Utlty Companes, IEEE Transacton on ower Systems, vol.22, No.1, Februry 27 [6] M.S.Moras, J.W. Marangon Lma, Natural Gas Network rcng and Its Influence on Electrcty and Gas Markets, In: IEEE Bologona owertech Conference, Jun 23, Bologona, Italy 94

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