Optimal Operation of a Wind and Fuel Cell Power Plant Based CHP System for Grid-Parallel Residential Micro-Grid

Transcription

1 Optmal Operaton of a Wnd and Fuel Cell Power Plant Based CHP System for Grd-Parallel Resdental Mcro-Grd M. Y. EL-SHARKH, M. TARIOVE, A. RAHMA, M. S. ALAM Department of Electrcal and Computer Engneerng, Unversty of South Alabama, Moble, AL 6688, U.S.A. Abstract: -Ths paper presents an evolutonary programmng based approach to evaluate the mpact of ntegratng wnd and fuel cell power plants (FCPP) n a combned heat and power (CHP) system on the performance and operatonal cost. The fluctuatng nature of wnd energy (WE) has a dfferent effect on the system operatonal cost and constrants. Besdes, FCPPs are capable of producng both electrcal and thermal energy. By combnng WE and FCPP n a hybrd structure for CHP system yelds lower operatonal cost than that of ndvdual unts. An ntegrated cost model for FCPP and WE s constructed, whch ncludes producton cost of energy, thermal recovery from the FCPP, electrcal power from WE, power trade wth the local grd and mantenance cost. An hourly electrcal and thermal load profle for a resdental mcro-grd communty s employed along wth the wnd speed varaton to determne the best cost effectve strategy. The operaton of the FCPP system s scheduled accordng to avalable wnd power, and electrcal and thermal load demand to optmze operatonal cost. An evolutonary programmng (EP)-based technque s used to fnd a near-optmal soluton of the problem. The method ncorporates the Hll-Clmbng technque (HCT) to mantan feasblty durng the soluton process. Results are encouragng and ndcate vablty of the proposed technque. Key-Words: - Fuel Cell economcs, PEM Fuel Cell, CHP, Wnd Energy, Evolutonary Programmng, Mcro- Grd. Introducton umerous renewable energy system applcatons, such as wnd energy (WE) and fuel cell power plant (FCPP) systems have spread rapdly. Because of the nature WE sources (fluctuatng behavor and relatvely small sze), they should be accompaned wth conventonal or other energy sources such as FCPP. The ntegraton of WE and FCPP systems n the form of combned heat and power (CHP) system can be consdered as a potental opton to satsfy thermal and electrcal demand of resdental mcrogrd. In such type of system, the electrcal and thermal energy generaton can be managed n a way to mnmze the overall cost. In the lterature, fuel cell economcs and economcal aspects have been presented n references []- [5]. In [], [] an economc model has been ntroduced to estmate the optmal output power from the FCPP whle satsfyng system operatonal constrants. The model only consders the possblty of sellng and buyng energy from the local grd, and the usage of thermal power output from the fuel cell. In ths paper the model n [], [] has been extended to ntegrate WE power, whch s derved from the avalable wnd speed. Dfferent strateges to manage the power from WE and FCPP unts can be consdered. In ths paper, the WE system s operated at ts full capacty all the tme. Accordng to avalable thermal load demand and remanng electrcal load, FCPP s then managed n order to get mnmum operatonal cost. The model s represented as a cost optmzaton problem subect to system and operatonal constrants. To estmate the daly optmal operatonal strategy for FCPP and WE a hybrd technque based on evolutonary programmng (EP) and Hll-Clmbng (HC) method [], [6] [6] s used. The evolutonary programmng s employed to search for the near optmal soluton whle the HC method s used to ensure feasblty durng the soluton process. The paper s organzed as follows: Secton ntroduces an economc model for a fuel cell system. Secton presents the soluton methodology. Test results are presented n Secton 4. Secton 5 presents the conclusons. Fuel cell system economc model At full load condtons, the FCPP produces thermal energy as a by product, approxmately equal to the electrcal energy [7]. Mathematcal expressons to

2 approxmate the effcency and the thermal output of the FCPP have been developed n Ref. [7] as follows: For PLR <.5 η =. 76, rte, =. 68 () For PLR η =. 9PLR. 9996PLR +. 65PLR r TE,. 74PLR +. 46PLR () 4 =. 785PLR. 979PLR +. 55PLR (). 87PLR where, η s the FCPP effcency, PLR the part load rato, r TE the thermal energy to electrcal energy rato. The effcency and the thermal energy to electrcal energy rato are functons of the part load rato (equal to electrcal generated power/maxmum power). In ths case, the thermal power recovered from the fuel cell accordng to the electrcal power output can be calculated as follows: P = r ( P + P ) (4) th, TE a In Refs. [], [], the authors ntroduced an economc model for the FCPP operatng strategy. In ths paper, the model has been extended to nclude wnd energy (WE). The model consders the electrcal power output, the thermal power recovery, and the power trade wth the local network. The economc model conssts of two man parts.e. frstly, the costs due to energy producton, whch are purchased energy to compensate unsuppled electrcal and thermal power demand and the cost of operaton and mantenance, and secondly the savngs from excess electrcal energy sale. Ths economc model can be represented as a cost optmzaton problem subect to system techncal and operatonal constrants, and can be summarzed as follows: Obectve Functon = mn C Ρ (5) where, C = c T n n c T P + Pa + cel, ptmax( Lel, PW, P,) + (6) η max( L th, P th,,) + c T om ( P + P W, ) + ( α + β ( e toff τ )) Ρ = c el, st max( P + PW, Lel,,) (7) Subect to: P mn max P P (8) P P ΔP (9) P u P ΔPD () ( on T MUT)( U U ). () off T MDT )( U U ). () ( n max start stop () where, c n : prce of natural gas for FCPP ($/kwh) T : length of tme nterval (h) P : electrcal power produced at nterval (kw) P a : power for auxlary devces (kw) P W, : power from wnd energy at nterval (kw) η : cell effcency at nterval c el,p : tarff for purchasng electrcty ($/kwh) c el,s : tarff for sellng electrcty ($/kwh) L el, : electrcal load demand at nterval (kw) c n : fuel prce for resdental loads ($/kwh) c om : operaton and mantenance cost ($/kwh) L th, : thermal load demand at nterval (kw) P th, : thermal load produced at nterval (kw) α,β : hot and cold start up cost respectvely t off : tme the FCPP has been off (h) τ : fuel cell coolng tme constant (h) P mn : mnmum lmt of generatng power (kw) P max : maxmum lmt of generatng power (kw) ΔP u : upper lmt of the ramp rate ΔP D : lower lmt of the ramp rate T on : FCPP on-tme (number of ntervals) T off : FCPP off-tme (number of ntervals) MUT : mnmum up-tme (number of ntervals) MDT : mnmum down-tme (number of ntervals) U : FCPP on-off status, U = for runnng, U = for stoppng max : maxmum number of start-stop events start-stop : number of start-stop events Frst term of the Eq. (6) s the daly fuel cost for the fuel cell ($). Second term s the daly cost of electrcal energy purchased f the demand exceeds the electrcal energy produced ($). The thrd term s the daly cost of purchased gas for resdental thermal loads f the thermal energy produced s not enough to meet the thermal energy demand ($). The

3 forth term s the operaton and mantenance cost of the FCPP and WE ($). The last term s the start up cost ($) of the FCPP. Eq. (7) represents the daly ncome from the electrcal energy sale f the electrcal energy produced exceeds the demand ($). The electrc power output of the wnd turbne, P W, at nterval wth respect to wnd speed v can be expressed as below [8]: ( ) v < vc P + + < a b v c v vc v v P W, = (4) P v v < v c o v vc o where, v c-, v and v c-o are the cut-n, nomnal and cut-out wnd speeds respectvely for wnd turbne generator. The constants, a, b and c are determned by the followng equaton. a = b = c = ( v v ) ( v v ) v 4 ( v + v ) ( v + v ) ( v + v ) v + v 4 4v v + v v ( ) v v v v + v v v (5) The evolutonary programmng (EP)- based soluton methodology Evolutonary programmng can be traced back to the early 95 s when Turng dscovered a relatonshp between machne learnng and evoluton [9]- []. Later, Bremermann, Box, Fredberg, and others developed evolutonary computaton as a tool for machne learnng and optmzaton. Great attenton was gven to EP as a powerful tool when Fogal, Burgn, Atmar, and others used t to predct the events of fnte state machnes on the bases of old observatons. Durng the 98 s evolutonary programmng, wth advances n computer technology was used to solve dffcult real-world optmzaton problems. In the power systems area, EP has been used to solve a number of power systems problems []. Evolutonary programmng s a search optmzaton method. It moves from one soluton to another usng a probablstc search technque. Evolutonary programmng starts wth random ndvduals. Each ndvdual represents a complete soluton for the problem under study. The ndvduals are moved from one generaton (or teraton) to the other after passng through two man steps, mutaton and competton. Durng a mutaton step a new ndvdual s produced when a Gaussan random varable wth unform probablty s added to the current ndvdual. The competton step s a probablstc selecton scheme used to assgn a weght to each ndvdual accordng to a comparson between current ndvdual and a randomly chosen one. It may happen that the new soluton s nfeasble. Therefore, usng EP alone may requre a long tme to reach the optmal soluton or t may get trapped n a local optmum. Ths lmtaton was overcome by the use of the Hll-Clmbng technque (HCT) [] to move new nfeasble solutons nto the feasble regon. The followng algorthm detals the proposed approach to solve the problem:. Generate ntal random solutons for the output power from the FCPP at each nterval. S = {x} =,,m (6) where, x s a set of output power from the FCPP at each nterval, m s the number of ndvdual n the current generaton. The random soluton s expected to satsfy the system constrants.. For each ndvdual n the current generaton, calculate the obectve functon value usng (5).. Mutate each ndvdual and assgn t to S +m accordng to (7). S +m = S + (,β v(s )+z ) (7) where, S s the th ndvdual, (μ,σ ) s Gaussan random varable wth mean μ and varance σ, β s a constant to scale v(s ), z s an offset to guarantee a mnmum amount of varance. 4. Check the feasblty of each new ndvdual aganst the constrants. If there s no volaton go to step 5. Otherwse go to step Calculate the obectve functon value for the feasble soluton usng (5) and go to step Use the Hll-Clmbng algorthm to drve the nfeasble ndvduals nto feasblty. If no feasble soluton can be found go to step. 7. Assgn a ftness score v(s ) to each ndvdual S +m (=,,m). The score s assgned equal to the cost functon. 8. Usng (8), calculate a weght W for each

4 ndvdual S, =,,m. These weghts are to be calculated durng a random competton between ndvduals based on the obectve functon value. W = W, = (8) where, s a randomly generated competton number, W, s ether or dependng on the competton of the ndvdual wth another ndvdual selected randomly from the populaton. The value of W, can be calculated as follows: W, = f v(s ) v(s p ) (9) otherwse where p = [mu + ], p and u ~ U(,). 9. Rank the soluton S (=,,m) n descendng order accordng to ther values of W (f more than one soluton has the same W, use the actual score of v(s ) to rank them). Use the frst m solutons along wth ther score values v(s ) as a new generaton for the potental optmal soluton.. Check for convergence. Crtera used for convergence nclude the maxmum generaton number and the average/maxmum ftness rato beng less than a predetermned small value. If convergence s acheved, stop; otherwse go to step. 4 Tests and Results The proposed model has been appled to a 5 kw FCPP and 5 kw WE unt, whch are grd-parallel and supply a resdental mcro-grd. The IEEE-RTS load profle wth a peak of 5 kw [] s used to smulate the hourly electrcal load profle of the mcro-grd. The wnter hot water usage and space heatng load for Atlanta, Georga [7] s consdered to represent the thermal load profle. Due to the lack of thermal load nformaton for the summer and sprng/fall, thermal load data are estmated from the avalable wnter data. The thermal load s used along wth the electrcal load profle to smulate total hourly operaton of the FCPP and WE. Table gves gas prces and FCPP/EP parameters for the case studes for dfferent seasons. Base Case: In ths test case, the model s tested wthout consderng the WE for wnter, sprng/fall and summer seasons. Cost components for dfferent seasons are gven n Table. Table. FCPP and evolutonary program parameters. Maxmum lmt of generatng power, P max (kw) 5 Mnmum lmt of generatng power, P mn (kw). Length of tme nterval, T (h).5 Upper lmt of the ramp rate, ΔP u (kw) 5 Lower lmt of the ramp rate, ΔP D (kw) Prce of natural gas for FCPP, c n ($/kwh).4 Tarff for purchasng electrcty, c el,p ($/kwh). Tarff for sellng electrcty, c el,s ($/kwh).8 Fuel prce for resdental loads, c n ($/kwh).5 Operaton and mantenance cost, c om ($/kwh) Hot start up cost, α ($).5 Cold start up cost, β ($).5 The fuel cell coolng tme constant, τ (h).75 Mnmum up-tme, MUT (ntervals) Mnmum down-tme, MDT (ntervals) Maxmum number of start-stop tme, max 5 Maxmum number of evolutonary generaton umber of ndvduals Case : In ths case, n addton to the FCPP unt the model s tested usng a total capacty of 5 kw WE system, whch s operated at ts full capacty all the tme. Same synthetc wnd speed data, Fg., s used to calculate the power output of WE for all seasons. The dfferent cost components and savngs for usng WE and FCPP are presented n Table. Table. Cost comparson between Base case and Wnd case. Daly cost components ($) Base Case Wnter Summer Sprng/Fall Fuel cost Proft from electrcty sold... Purchased electrcty Resdental natural gas FCPP O&M cost Total cost Case Fuel cost Proft from electrcty sold...6 Purchased electrcty Resdental natural gas FCPP O&M cost Wnd O&M cost Total cost Savngs of Case versus Base Case ($) Total cost Wnd Speed (m/s) Fg., Wnd speed data for 4-hours.

5 Power trade wth the local network, electrcal load/electrcal outputs from FCPP and WE, and thermal load/thermal power outputs from the FCPP for dfferent seasons are shown n Fgs., and 4, respectvely. Electrcal Power (kw) Electrcal Power (kw) Thermal Power (kw) P Sold P Purch (a) Pgen Pload Pwnd (b) P_Th_gen P_Th-Load (c) Fg., (a) Wnter electrcal power trade wth the grd (b) Wnter electrcal load and power generaton (c) Wnter thermal load and generaton. It s evdent from Fgs., and 4 that ntegrated generaton system buys almost zero electrcal energy for all seasons, nstead the system sells excess electrcal energy all the tme. Ths excess electrcal energy s hgh durng the low thermal load for summer and wnter cases. For the sprng/fall case, surplus electrcal energy s low durng the low thermal load ntervals and hgh durng the low thermal load perods. Electrcal Power (kw) Electrcal Power (kw) Thermal Power (kw) P Sold P Purch (a) Pgen Pload Pwnd (b) P_Th_gen P_Th-Load (c) Fg., (a) Summer electrcal power trade wth the grd (b) Summer electrcal load and power generaton (c) Summer thermal load and generaton. 5 Conclusons Ths paper ntroduces the ntegraton of FCPP and WE system n an economc model whch ncludes power trade wth the local grd and thermal recovery from FCPP. The paper offers practcal concepts concernng operatonal cost modelng of the system. Two test cases were evaluated usng IEEE test system load profles for dfferent seasons. Based on the avalable power from WE, the fuel cell power plant supples both electrcal and thermal power to a small mcro-grd communty. Based on the system economcs, results shows that, WE runs at full capacty most of the tme based on wnd speed. Thermal load s the man factor that affects the operaton of the FCPP. For example, based on the system economcs, FCPP tends to produce electrcal energy more than the electrc load durng hgh

6 thermal load perods and generates low electrcal energy durng low thermal perods. Test results on a 5 kw WE and 5 kw fuel cell power plants ndcate the vablty of the proposed approach and ts potental to fnd the optmal power output from the fuel cell power plant subect to the assocated constrants and WE power. Electrcal Power (kw) Electrcal Power (kw) Thermal Power (kw) P Sold P Purch (a) Pgen Pload Pwnd (b) P_Th_gen P_Th-Load (c) Fg. 4, (a) Sprng/fall electrcal power trade wth the grd (b) Sprng/fall electrcal load and power generaton (c) Sprng/fall thermal load and generaton. Acknowledgment Ths research was supported by a grant from the Department of Energy (DE-FG-ER676). References: [] M. Y. El-Sharkh, A. Rahman, M. S. Alam, Evolutonary Programmng-Based Methodology for Economcal Output Power from PEM Fuel Cell for Mcro-Grd Applcaton, Journal of Power Sources, vol. 9, ssues -, pp , January 5. [] S Ahmed M. Azmy, and István Erlch, Onlne Optmal Management of PEM Fuel Cells Usng eural etworks, IEEE Transactons on Power Delvery, vol., no., pp. 5-58, Aprl 5. [] F. Barbr and T. Gomez, Effcency and Economcs of Proton Exchange Membrane (PEM) Fuel Cell, Internatonal Journal of Hydrogen Energy, vol., no, pp. 89-9,996. [4] Y. Zoka, H. Sasak, J. Kubokawa, R. Yokoyama, and H. Tanaka, An optmal deployment of fuel cells n dstrbuton systems by usng genetc algorthms, IEEE Internatonal Conference on, vol., pp , Dec 996. [5] Georg Erdmann, Future economcs of the fuel cell housng market, Internatonal Journal of Hydrogen Energy, vol. 8, pp ,. [6] M. Y. El-Sharkh, A. A. El-Keb, Mantenance Schedulng of Power System Generaton and Transmsson Usng Fuzzy Evolutonary Programmng, IEEE Transactons on Power Systems, vol. 8, no., May. [7] Mehmet Burak Gunes, Investgaton of a Fuel Cell Based Total Energy System for Resdental Applcatons, Master of Scence Thess, Dept. Mechancal Engneerng, Vrgna Polytechnc Insttute and State Unversty,. [8] Bllnton R., Guang B., Adequacy evaluaton of generaton systems ncludng wnd energy, IEEE Canadan Conference on Electrcal and Computer Engneerng, vol., pp. 4-9, May. [9] D. B. Fogel Evolutonary Computaton toward a ew Phlosophy of Machne Intellgence nd ed, Wley-IEEE Press, 999. [] T. Back, U. Hammel, H. P. Schwefel, Evolutonary Computaton: Comments on the Hstory and Current State IEEE Transactons on Evolutonary computaton, vol., no., pp. -7, Aprl 997. [] V. Mranda, D. Srnvasan, L. M. Proenca, Evolutonary Computaton n Power System Electrcal Power and Energy Systems, vol., no., pp , 998. [] P. H. Wnston, Artfcal Intellgence rd ed, Addson-Wesley Publshng Company. 99. [] Relablty Test System Task Force of the Applcaton of Probablty Methods Subcommttee, IEEE Relablty Test System, IEEE Trans. Power Apparatus and Systems, vol. PAS-98, no. 6, pp , 979.