Development of Investment Strategies for Wind Power Generation

Transcription

1 Development of Investment Strateges for Wnd Power Generaton Chanapan Kongnam, Student Member, IEEE, and Somboon uchprayoon, Member, IEEE Abstract--Ths paper develops nvestment strateges for wnd power generaton under the assumpton that generaton capacty and nvestment resources are flexble. The nvestment problem s formulated as a mxed-nteger programmng problem wth the constrants specfed as ntervals and the net present value of generaton profts as the objectve. The optmum solutons are expressed n terms of number and sze of each wnd turbne model. The screenng & rankng method s proposed to dentfy the most attractve nvestment plan among multple optmum solutons. Senstvty analyss s then performed to assess the mpact of nvestment parameters. umercal smulatons have been tested wth actual wnd speed data and a smplfed model of wnd power project n the southern coast of Thaland. Index Terms--Investment plannng, optmzaton methods, wnd power generaton. OMECLATURE A nstallaton area for the wnd turbne model (m 2 ) A max maxmum area avalable for wnd park (m 2 ) C captal cost of wnd turbne model (US$) C max maxmum spendng on captal costs (US$) CF capacty factor D dameter of the wnd turbne model (m) E energy generaton of the wnd turbne model (kwh/yr) E max maxmum energy generaton of a wnd park (kwh/yr) ED energy densty of a wnd park (kwh/yr/m 2 ) GP net present value of generaton proft of a wnd park (US$) H hub heght of the wnd turbne model (m) h j number of hours per year for the wnd speed level j J m value of ndcator m max J m maxmum value of ndcator m K number of years n study perod M number of wnd speed levels number of wnd turbne models n number of generators for the wnd turbne model O operatng and mantenance costs of the wnd turbne model (US$) P maxmum generaton capacty of wnd park (kw) Ths work was supported n part by the Jont Graduate School of Energy and Envronment, Kng Mongkut Unversty of Technology-Thonbur. C. Kongnam s wth the Electrcty Generatng Authorty of Thaland, onthabur, Thaland (e-mal: chanapan.k@egat.co.th). S. uchprayoon s wth the Electrcal Engneerng Department, Chang Ma Unversty, Thaland (e-mal: sn@eng.cmu.ac.th). P j power output from the wnd turbne model at the wnd speed level j (kw) P R,j rated power of the wnd turbne model (kw) PA proft-to-area rato (US$/m 2 ) PC proft-to-cost rato PI penalty ndex p k electrcty rate averaged over the year k r dscount rate per annum (%) TC net present value of total costs of a wnd park (US$) V wnd speed (m/s) V m mean wnd speed (m/s) V C, cut-n wnd speed of the wnd turbne model (m/s) V R, rated wnd speed of the wnd turbne model (m/s) V F, cut-out wnd speed of the wnd turbne model (m/s) weghtng factor of ndcator m w m A I. ITRODUCTIO lthough t s wdely recognzed that wnd power generaton s clean and envronmental frendly as well as ncreasngly compettve, but wnd turbne power plant s hghly captal-nvested and reles on the ntermttent and unpredctable nature of the wnd. The major concerns s that wnd power can be nether storable nor schedulng so that the wnd generaton may not concde wth electrcty demand. Consequently, electrc utlty would have to add more capacty reserve n the presence of wnd power generaton. The compettveness of wnd power generaton becomes questonable when the wnd speed s low because, by far, the ndustry has focused on developng generaton technologes for moderate-to-hgh wnd speed areas. In Thaland, for nstance, most areas have a mean wnd speed of 4-6 m/s, whle hgher wnd speed areas can be found along the coastlnes and on the top of mountans. As a result, the wnd power generaton n Thaland may not be cost effectve when compared wth conventonal power plants. Thus, an nvestment decson must be made very carefully gven the uncertanty and varablty characterstcs of wnd power generaton. In general, the objectve of wnd power nvestment would be to maxmze the net present value of generaton proft (generaton revenue less total costs) gven that the nvestment resources are lmted. The constrants beng consdered n the optmzaton problem are both techncal (such as generaton capacty and energy generaton) and fnancal (such as avalable budget and ste area) constrants. The decson varables are number and sze of each wnd turbne model.

2 2 Pror works have contrbuted on economc and rsk assessments of wnd power projects. Scenaro analyss and economc worth analyses (by means of net present value, payback perod, nternal rate of return) were performed. It was found that the generaton cost of wnd energy s a functon of nstalled capacty [] and locaton [2]. The larger the nstalled capacty of wnd turbne, the smaller the generatng cost. Gven proper szng of nstallaton wth wnd speed, t was shown that the generatng cost could be even lower. The relaton between nvestment and operaton of dfferent wnd turbne szes ( kw) and mean wnd speed was also nvestgated [3]. Senstvty analyss s usually performed as post-optmalty result to determne the mpact of varous parameters such as costs, electrcty rates, as well as nterest and nflaton rates [4]. When the generaton capacty of wnd power plant s able to vary over a certan range, the optmal szng problem can be solved under the condton that the nvestment resources are known and fxed. In ths paper, however, t s assumed that the nvestment resources should also be able to vary so that the soluton space may be broader and better optmum soluton could be attaned. But, the optmzaton problem becomes somewhat complcated when both generaton capacty and nvestment resources are flexble snce multple optmum solutons wth dfferent generaton capactes and utlzed resources would exst. Thus, the optmzaton problem s formulated and the nvestment strateges are developed n ths paper to support nvestment decson under such crcumstance. In secton II, the nvestment plannng problem of wnd power generaton wth flexble generaton capacty and nvestment resources are formulated as a mxed-nteger problem. The soluton method, by means of the screenng & rankng method, s then descrbed. In secton III, a bref overvew of wnd power nvestment project n the southern coast of Thaland s provded. Ths project s then taken as a test system. umercal smulaton results are n Secton IV. Senstvty analyss of the results s provded n Secton V. Fnally, ths work s concluded n secton VI. II. THE OPTIMIZATIO PROBLEM A. Problem Formulaton To formulate the nvestment plannng problem for wnd power generaton; the objectve functon, shown n (), s to maxmze the net present value (PV) of generaton proft, defned as generaton revenue less the total generaton costs. To calculate the generaton revenue, the electrcty rates s forecasted and averaged on an annual bass. The total costs of wnd power generaton comprse captal nvestment cost plus operatng and mantenance costs. The cost of land use s gnored by assumng that the nvestment project s beng consdered at a partcular locaton. Each cost component s calculated as unformed annualzed cost. The fnancal constrants of the problem, shown n (2)-(3), are total captal nvestment costs and total areas need for wnd turbne nstallaton, respectvely. The techncal constrants of the problem, shown n (4)-(5), are generaton capacty and annual energy generaton requrement, respectvely. It s mpled that both constrants were calculated n such a way that electrc utlty can mantan ts operaton economcally and relably. It should be emphaszed that the rght-hand sde of each constrant s stated as an nterval to reflect flexblty that each constrant s bounded wthn a certan range, not just a sngle value. K M p Maxmze k nh P j j k k ( r ) = + j= = k ( + r) nc no k = r( + r) = = () subject to nc C,C (2) 2 π nh A,A (3) = np P,P (4) R, = M nh P E,E (5) j j j= = The power output from each wnd turbne at specfc wnd speed can be determned from ts power-speed curve, whch depends on cut-n, rated, and cut-out wnd speeds. In ths paper, t s assumed that the power-speed relaton s lnear and defned [5] as follows: 0 0< V V j V V P V V V P = j P V < V V 0 V < V F, j C, j C, < R, C, j R, V V R, C, R, R, j C,j The number of hours per year at specfc wnd speed can be determned from ether hstorcal data collected from meteorologcal staton or a mathematcal model known as wnd speed dstrbuton functon. It should be noted that the total areas constrant n (3) s smplfed by assumng that each wnd turbne s requred to be nstalled on a crcular area. Ths crcular area can be calculated by consderng the hub heght as a radus. In practce, safety spacng for surroundng constructon would also be requred. An nstallaton area of each wnd turbne would be rectangular and larger [6], [7]. B. Soluton Methodology The optmzaton problem stated n ()-(5) are would have (6)

3 multple optmal solutons because all constrants have been defned as ntervals. To dentfy the best soluton, consdered as the most attractve nvestment plan, t s proposed n ths paper to apply the screenng & rankng method. The screenng process s ntended to select the best nvestment plan among all optmum solutons at each generaton capacty. Then, the rankng method s ntended to select the best nvestment plan among all optmal solutons obtaned from the screenng process. Durng the screenng process, the optmzaton problem s solved by fxng generaton capacty, whle other constrants are vared step by step over ther lmts. Therefore, multple optmum solutons are obtaned at each generaton capacty. The optmum soluton wth the lowest captal cost s taken as a base case and ntally consdered as the best soluton of the gven generaton capacty. It s proposed to compute the rato of ncremental proft to ncremental cost of captal to justfy the goodness of nvestment plan. When compared wth the base case, the optmum soluton wth the rato greater than unty s consdered as a better nvestment choce. Thus, the nvestment plan wth the hghest rato s consdered as the best nvestment plan at gven generaton capacty. After fnshng the screenng process, there s a sngle optmum soluton at each generaton capacty. The rakng process s then employed to justfy whch nvestment plan (or generaton capacty) s the most attractve plan. Generally speakng, t s necessary to have at least one ndcator for the sake of rakng. In ths paper, four ndcators are proposed to rank or measure both techncal and economc effcences of nvestment plans. Capacty factor and energy densty defned n (7) and (8), respectvely, are proposed to measure techncal effcency. Proft-to-cost rato and proft-toarea rato defned n (9) and (0), respectvely, are proposed to measure economc effcency. CF = E P j h ED E A PC j (7) = (8) = GP / TC (9) PA = GP A (0) Because multple ndcators have been used, a weghtng factor for each ndcator must be assgned. In ths paper, the penalty ndex of an nvestment plan, computed from four proposed ndcators, can be expressed as follows: PI = 4 m= w m J max J m m max J m 4 w = 0. (2) m m= The large value of penalty ndex ndcates hgh devaton from the best effcency acheved from the nvestment plans beng consdered durng the rankng process. The nvestment plan wth the lowest penalty ndex s thus consdered as the hghest rankng (or the most attractve) plan. III. DESCRIPTIO OF TEST SYSTEM A prelmnary study of wnd power generaton n the southern coast area of Thaland s taken as a test system. The wnd speed dstrbuton, measured on an hourly bass at the heght of 45 m durng at Khaosoon meteorologcal staton, s shown n Fg.. Accordng to the nvestment data and crtera of the Electrcty Generatng Authorty of Thaland (EGAT), the generaton capacty at ths locaton s between 500-,000 kw. The wnd power capacty nstallaton was ntally set for 750 kw. It s estmated that the electrcty rate would be 0.2 US$/kWh for wnd power generaton. The dscount rate s assumed at 0 percent per annum and the study horzon s assumed for 20 years. The captal spendng for ths nvestment project s between mllon US$ and the total nstallaton area s between 35,000-60,000 m 2. Wnd turbne data were smplfed from publc doman [7], [8]. Table I shows essental data of 9 wnd turbne models consdered for ths nvestment project. ote that all wnd turbne models have relatvely low cut-n speed. For the sake of smplcty, the operatng & mantenance (O&M) cost are assumed to be percent of the captal cost [9]. When the hub heght s changed, the mean wnd speed must also be adjusted [0], [] as follows: V V H = H 2 2 α 3 (2) where α s the exponent dependng on a surface roughness factor. For nstance, the most adopted value of 0.4 s wdely applcable to low surface and well exposed ste. Probablty densty Wnd speed (m/s) () Fg.. Wnd speed dstrbuton measured at Khaosoon meteorologcal staton, akornsrthammarat, Thaland, durng

4 4 TABLE I WID TURBIE DATA COSIDERED FOR IVESTMET PROJECT I THAILAD P (k W) H (m) D (m) V C ( m/s) V R ( m/s) V F ( m/s) C (US$) , , , , , , , , , , , , , , , , , ,000, ,000 IV. SIMULATIO RESULTS The optmum solutons were obtaned by usng the General Algebrac Modelng System (GAMS ) solves the optmzaton problems, provded the smulaton data n secton IV. It was found that there are 3 nvestment plans avalable. Table II shows optmum solutons of those plans. In case of 500 kw, the nvestment plan number 3 s taken as a base case because ts captal cost s the lowest (0.550 mllon US$). Then, t was found that the nvestment plan number 2 s more attractve because the rato of ncremental proft to ncremental cost of captal s greater than unty (2.6046). So, t may be concluded that the nvestment plan number 3 s a sngle canddate for generaton capacty of 500 kw. Smlarly, the screenng process s also appled for generaton capactes of 750, 800, 900, and,000 kw. In case of 600 and 700 kw, there s no need to apply the screenng process because there s only sngle optmum soluton for each generaton capacty. At the end of the screenng process, there were 7 nvestment plans left and they become the canddates at the begnnng of the rankng process. Table III shows numercal values of four ndcators used for measurng techncal and economc effcences of those 7 nvestment plans. Those values were then used for calculatng the penalty ndex defned n (). The rankng of 7 nvestment plans were set accordng to ther penalty ndexes. It s shown n Table IV that the penalty ndex was defned n 3 cases. The frst case (w = w 2 = 0.5, w 3 = w 4 = 0.0) consders only techncal effcency. In contrary, the second case (w = w 2 = 0.0, w 3 = w 4 = 0.5) consders only economc effcency. The thrd case consders both techncal and economc effcency by gvng weghtng factor to all four ndcators equally (w = w 2 = w 3 = w 4 = 0.25). It can be seen that the rankngs are slghtly dfferent. In all three cases, the 800-kW and 500-kW capactes are the most and least attractve nvestment plans, respectvely. The ntally nvestment plan (750 kw) s obvously not attractve. TABLE II OPTIMUM SOLUTIOS FOR DIFFERET GEERATIO CAPACITIES OF IVESTMET I WID POWER GEERATIO Plan P GP C A E (k W) (M US$) (M US$) (M m 2 ) (M k Wh/yr) , x x TABLE III BEST SOLUTIOS FOR EACH GEERATIO CAPACITY OF IVESTMET I WID POWER GEERATIO Plan P CF ED PC PA (k W) (kwh/yr/ m 2 ) (US$/ m 3, x TABLE IV PEALTY IDEXES AD RAKIG OF IVESTMET PLAS I WID POWER GEERATIO Weghtng Factors P ( kw) Penalty Index Rank, w = w2 = w 3 = w4 = x , w = w2 = w 3 = w4 = x , w = w2 = w 3 = w4 = x When ether capacty factor or proft-to-cost margn was only consdered, the 800-kW and the 500-kW capactes were stll the most and least attractve nvestment plans, respectvely. On the other hand, t was found that the 600-kW capacty was the most attractve nvestment plan when ether the energy densty or the proft-to-area rato s only consdered (w 2 =.0 or w 4 =.0). So, the 600-kW would be the most area-effcent nvestment plan. 2 )

5 ) 5 V. SESITIVITY AALYSIS Gven t hat the 800-kW s dentfed as the most attractve plan for ths nvestment project and taken as an optmum soluton, senstvty analyss s then performed to assess the mpact of four nvestment parameters,.e. electrcty rate, dscount rate, O&M cost, and servce lfetme of a wnd turbne generator. Fg. 2 and 3 llustrate the PV of generaton proft of 800- kw wnd power project by means of spder plot and tornado dagram, respectvely. In the spder plot; the electrcty rate s vared from US$/kWh, the dscount rate s vared from 5-5 percent per annum, the O&M cost s vared from -3 percent of the captal cost, and the servce lfetme of a wnd turbne generator s vared from 4-26 years. In the tornado dagram, each parameter has 0 percent devaton from ts orgnal value. It can be seen that the PV ncreases when ether the electrcty rate s hgher or the servce lfetme s longer, and vce versa. On the other hand, the PV decreases when ether the dscount rate s lower or the O&M cost s hgher, and vce versa. The PV s most senstve to the electrcty rate and least senstve to the O&M cost. 4,000,000 To llustrate the mpact of mean wnd speed, the hub heght was rased from 45 to 55 and 65 m. Consequently, the captal cost and wnd speed dstrbuton were adjusted accordngly [2], [3]. Fg. 4 llustrates the average cost of generaton from the 800-kW wnd power project, gven that the dscount rate was vared from 4-20 percent per annum. From the optmum soluton obtaned earler, the average cost s US$/kWh, whch s lower than the electrcty rate. The average cost reduces to and US$/kWh when the hub heght was rased to 55 and 65 m, respectvely. In these three cases, the PV s postve and ths nvestment project s fnancally attractve. As the dscount rate ncreases, the average cost also ncreases. Smlarly, Fg. 5 llustrates the average cost of generaton at three hub heghts, gven that the servce lfetme was vared from 4-26 years. It s shown that the average cost slghtly decreases when the servce lfetme ncreases. The average cost was vared from to US$/kWh over the entre range of servce lfetme. Hence, the servce lfetme has only a lttle mpact on the average cost of generaton PV of Generaton proft (US$) 3,000,000 2,000,000,000,000 Electrcty rate Dscount rate O&M cost Lfetme 0-60% -40% -20% 0% 20% 40% 60% 80% 00% % Devaton Fg. 2. Spder plot for net present value of generaton proft n wnd power nvestment project wth 800-kW nstalled capacty Average cost (US$/kWh) Fg % 6% 8% 0% 2% 4% 6% 8% 20% Dscount rate 45 m 55 m 65 m Impact of dscount rate on average cost of wnd power generaton gven 800-kW wnd turbne generator gven three hub heghts Electrcty rate ± 0% Dscount rate ± 0% Lfetme ± 0% O&M cost ± 0% negatve postve Average cost (US$/kWh) m 55 m 65 m Change of PV of generaton proft (%) Lfetme (year) Fg. 3. Tornado dagram for net present value of generaton proft n wnd power nvestment project wth 800-kW nstalled capacty Fg. 5. Impact of servce lfetme on average cost of wnd power generaton from 800-kW wnd turbne generator gven three hub heghts

6 6 Fnally, Fg. 6 llustrates the average cost of generaton at three hub heghts, gven that the O&M cost were vared from -3 percent of the captal cost. It can be seen that the average cost slowly ncreases as the O&M cost are hgher. The average cost was vared from to US$/kWh over the entre range of O&M cost. The O&M cost have only a lttle mpact on the average cost of generaton as well. It can be concluded that (a) the hgher dscount rate or O&M cost, the hgher average cost of generaton; (b) the hgher servce lfetme of a wnd turbne generator, the lower average cost of generaton; and (c) the hgher mean wnd speed, the lower average cost of generaton. Average cost (US$/kWh) Fg %.50% 2.00% 2.50% O&M cost (% of nvestment cost) 45 m 55 m 65 m 3.00% Impact of operatng and mantenance cost on average cost of wnd power generaton from 800-kW wnd turbne generator gven three hub heghts VI. COCLUSIO The nvestment strateges for wnd power generaton were developed n ths paper, provded that generaton capacty and nvestment resources are flexble over certan ranges. The proposed strateges may be broadly dvded nto two processes and called the screenng & rankng method. The screenng process s to obtan the optmum solutons for each generaton capacty, whle the rankng process s to dentfy the most attractve nvestment plan based on the penalty ndex. Capacty factor, energy densty, proft-to-cost rato, and proftto-area rato have been used to calculate the penalty ndex. The proposed strateges have been used to evaluate the nvestment project n the southern coastal area of Thaland, whch has relatvely low mean wnd speed. It was found that the optmum generaton capacty s slghtly greater than that of the ntal assessment. By performng senstvty analyss, t s mentoned that the wnd power project s most senstve to electrcty rate and least senstve to O&M cost. The mean wnd speed may affect the economc worth of an nvestment project but may not alter the nvestment decson. ACKOWLEDGMET The authors would lke to thank S. Skhabundt and the research & development department, EGAT, for helpng on wnd speed data. REFERECES [] B. Ozerdem, S. Ozer, and M. Tosun, "Feasblty study of wnd farms: A case study of Izmr, Turkey," Journal of Wnd Engneerng and Industral Aerodynamcs, 2006, Artcle n Press. [2] S. Rehman, T. O. Halawan, and M. Mohandes, "Wnd power cost assessment at twenty locatons n the kngdom of Saud Araba," Renewable Energy, vol. 28, 2003, pp [3] D. P. Papadopoulos and J. C. Dermentzoglou, "Economc vablty analyss of planned WEC system nstallatons for electrcal power producton," Renewable Energy, vol. 25, 2002, pp [4] J. K. Kaldells and T. J. Gavras, "The economc vablty of commercal wnd plants n Greece: A complete senstvty analyss," Energy Polcy, vol. 28, 2000, pp [5] I. Abouzahr and R. Ramakumar, "An approach to assess the performance of utlty-nteractve wnd electrc converson systems," IEEE Transactons on Energy Converson, vol. 6, pp , Dec. 99. [6] K. Q. guyen, "Wnd energy n Vetnam: Resource assessment, development status and future mplcatons," Energy Polcy, vol. 35, 2007, pp [7] G. M. Masters, Renewable and Effcent Electrc Power Systems, ew York: John Wley & Sons, [8] The European Wnd Energy Assocaton (EWEA), Wnd Energy - The Facts, The European Commsson s Drectorate General for Transport and Energy (DG TRE), [9] J. F. Manwell, J. G. McGowan, and A. L. Rogers, Wnd Energy Explaned: Theory, Desgn and Applcaton, ew York: John Wley & Sons, [0] E. Kavak Akpnar and S. Akpnar, "A statstcal analyss of wnd speed data used n nstallaton of wnd energy converson systems," Energy Converson and Management, vol. 46, 2005, pp [] G. L. Johnson. (200, Dec 0). Wnd Energy Systems. [Onlne]. Avalable: [2] L. Lu, H. Yang, and J. Burnett, "Investgaton on wnd power potental on Hong Kong slands - An analyss of wnd power and wnd turbne characterstcs," Renewable Energy, vol. 27, 2002, pp. -2. [3] J. L. Torres, E. Preto, A. Garca, M. De Blas, F. Ramrez, and A. De Francsco, "Effects of the model selected for the power curve on the ste effectveness and the capacty factor of a ptch regulated wnd turbne," Solar Energy, vol. 74, 2003, pp BIOGRAPHIES Chanapan Kongnam receved B.Eng. n electrcal engneerng from Kng Mongkut Insttute of Technology orth-bangkok, Thaland n 995. Snce 995, he was wth the turbne and generator control system secton, electrcal mantenance department, Electrcty Generatng Authorty of Thaland. In 2004, he receved M. Eng. n electrcal engneerng and nformaton technology from Rosenhem Unversty of Appled Scences, Germany. He s currently a Ph.D. student n the Electrcal Engneerng Department, Chang Ma Unversty, Thaland. Somboon uchprayoon receved B.Eng. n electrcal engneerng from Chang Ma Unversty, Thaland n 995, M.S. n electrc power engneerng from Rensselaer Polytechnc Insttute, USA n 997, and Ph.D. n electrcal engneerng from Georga Insttute of Technology, USA n He s currently an assstant professor n the Electrcal Engneerng Department, Chang Ma Unversty, Thaland. Hs research nterests are n the area of power system operaton and economcs.