Advances in Wind Energy Conversion Technology

Transcription

1 Environmental Siene and Engineering Advanes in Wind Energy Conversion Tehnology Bearbeitet von Mathew Sathyajith, Geeta Susan Philip 1. Auflage 211. Buh. viii, 216 S. Hardover ISBN Format (B x L): 15,5 x 23,5 m Gewiht: 535 g Weitere Fahgebiete > Tehni > Energietehni, Eletrotehni Zu Inhaltsverzeihnis shnell und portofrei erhältlih bei Die Online-Fahbuhhandlung be-shop.de ist spezialisiert auf Fahbüher, insbesondere Reht, Steuern und Wirtshaft. Im Sortiment finden Sie alle Medien (Büher, Zeitshriften, CDs, eboos, et.) aller Verlage. Ergänzt wird das Programm durh Servies wie Neuersheinungsdienst oder Zusammenstellungen von Bühern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produte.

2 Analysis of Wind Regimes and Performane of Wind Turbines Sathyajith Mathew, Geetha Susan Philip and Chee Ming Lim With the present day s energy risis and growing environmental onsiousness, the global perspetive in energy onversion and onsumption is shifting towards sustainable resoures and tehnologies. This resulted in an appreiable inrease in the renewable energy installations in different part of the world. For example, Wind power ould register an annual growth rate over 25% for the past 7 years, maing it the fastest growing energy soure in the world. The global wind power apaity has rossed well above 16 GW today [1] and several Multi-Megawatt projets-both on shore and offshore-are in the pipeline. Hene, wind energy is going to be the major player in realizing our dream of meeting at least 2% of the global energy demand by new-renewables by 22. Assessing the wind energy potential at a andidate site and understanding how a wind turbine would respond to the resoure flutuations are the initial steps in the planning and development of a wind farm projet. Energy yield from the Wind Energy Conversion System (WECS) at a given site depends on (1) strength and distribution of wind spetra available at the site (2) performane harateristis of the wind turbine to be installed at the site and more importantly (3) the interation between the wind spetra and the turbine under flutuating onditions of the wind regime. Thus, models whih integrate the wind resoure as well as the turbine performane parameters are to be used in estimating the system performane. Based on the above parameters, methods for assessing the available wind energy resoure at S. Mathew (&) and C. M. Lim Faulty of Siene, University of Brunei Darussalam, Jalan Tungu Lin, Gadong, BE141 Negra, Brunei Darussalam windboo@gmail.om G. S. Philip Faulty of Engineering, KAU, Kerala, India S. Mathew and G. S. Philip (eds.), Advanes in Wind Energy Conversion Tehnology, Environmental Siene and Engineering, DOI: 1.17/ _2, Ó Springer-Verlag Berlin Heidelberg

3 72 S. Mathew et al. a andidate site and the performane expeted from a wind turbine installed at this site are presented in this hapter. 1 Wind Regime Charateristis In this setion we will disuss how the harateristis of the wind regimes an be inorporated in assessing the wind energy potential as well as estimating the output from a wind energy onversion system. 1.1 Boundary Layer Effets The first fator to be onsidered while estimating the wind resoure and wind turbine performane at a given site is the variations in wind veloity due to the boundary layer effet. Due to the fritional resistane offered by the earth surfae (aused by roughness of the ground, vegetations et.) to the wind flow, the wind veloity may vary signifiantly with the height above the ground. For example, wind profile at a site is shown in Fig. 1. Variations in the wind veloity with height are quite evident in the figure. Thus, if the wind data available are not olleted from the hub height of the turbine, the data are to be orreted for the boundary layer effet. Ground resistane against the wind flow is represented by the roughness lass or the roughness height (Z ). The roughness height of a surfae may be lose to zero (surfae of the sea) or even as high as 2 (town enters). Fig. 1 Variation of wind veloity with height [2] 12 1 Wind veloity, m/s Distane from the ground, m

4 Analysis of Wind Regimes and Performane of Wind Turbines 73 Some typial values for the roughness heights are.5 for flat and smooth terrains,.25.1 for open grass lands,.2.3 for row rops,.5 1 for orhards and shrubs and 1 2 for forests, town enters et. On the basis of the roughness height of the terrain, wind data olleted at different heights are to be extrapolated to the hub height of the turbine. If the wind data are available at a height Z and the roughness height is Z, then the veloity at a height Z R is given by [3, 4]. VðZ R Þ ¼ VðZÞ ln Z R=Z ln Z ð1þ = Z where V(Z R ) and V(Z) are the veloities at heights Z R and Z respetively. Thus, if the veloity of wind measured at a height of 1 m is 7 m/s and the roughness height is.1, the veloity at the hub height say 1 m is 1.5 m/s. It should be noted that the power available at 1 m would be 3.4 times higher than at 1 m. In some ases, we may have data from a referene loation (meteorologial station for example) at a ertain height. This data is to be transformed to a different height at another loation with similar wind profile but different roughness height (for example, the wind turbine site). Under suh situations, it is logial to assume that the wind veloity is not signifiantly affeted by the surfae harateristis beyond a ertain height. This height may be taen as 6 m from the ground level [5]. With this assumption and equating the veloities at 6 m height at both the sites as per Eq. 1, we get 1 ln 6=Z OR ln Z=ZO VðZÞ ¼VðZ R ln 6 = ZO ln Z A ð2þ R= ZOR where Z OR is the roughness height at the referene loation. 1.2 Wind Veloity Distribution Being a stohasti phenomena, speed and diretion of wind varies widely with time. Apart from the seasonal variations, the differenes an be onsiderable even within a short span of time. These variations an signifiantly affet the energy yield from the turbine at a given site. For example, a turbine may deliver entirely different amount of energy when it is installed in two sites with the same average wind veloity but different veloity distributions. Similarly, two wind turbines with the same output rating but different in the ut-in, rated and ut-out veloities may behave differently at the same site. Statistial distributions are used to tae are of these variations in wind energy alulations. Several attempts were made to identify the statistial distribution most suitable for defining the harateristis of wind regime. A wide range of distributions are

5 74 S. Mathew et al. being tried by the researhers. The Weibull distribution, whih is a speial ase of Pierson lass III distribution, is well aepted and ommonly used for the wind energy analysis as it an represent the wind variations with an aeptable level of auray [6 9]. In some situations, Rayleigh distribution whih is a simplified form of Weibull distribution is also being used. It is worth mentioning that some innovative attempts are also been made by applying the Minimum Cross Entropy (MinxEnt) [1] and Maximum Entropy (ME) [11] priniples in wind energy analysis. However, a reent study omparing various statistial distributions in wind energy analysis has established the aeptability of Weibull distribution [9]. Hene we will follow the Weibull distribution in our analysis. The Weibull distribution an be defined by its probability density funtion f(v) and umulative distribution funtion F(V) where: f ðvþ ¼ V 1 e ðv= Þ ð3þ and Z FðVÞ ¼ f ðvþ dv ¼ 1 e ðv= Þ ð4þ where is the Weibull shape fator, the sale fator and V is the veloity of interest. Here, f(v) represents the fration of time (or probability) for whih the wind blows with a veloity V and F(V) indiates the fration of time (or probability) that the wind veloity is equal or lower than V. From Eqs. 3 and 4, it is evident that and are the fators determining the nature of the wind spetra within a given regime. Effets and on the probability density and umulative distribution of wind veloity are demonstrated using the wind data from three potential wind farm sites in Figs. 2 and 3. The site wind veloities are represented in Table 1. Fig. 2 Effet of Weibull shape fator on the probability density of wind veloity of some potential sites

6 Analysis of Wind Regimes and Performane of Wind Turbines 75 Fig. 3 Effet Weibull shape fator on the umulative distribution of wind veloity at some potential sites Table 1 Weibull shape and sale fators of some wind farm sites Site no. Mean wind veloity, m/s Standard deviation, m/s, m/s There are several methods for determining and from the site wind data. Some of the ommon methods are the graphial method, moment method, maximum lielihood method, energy pattern fator method and the standard deviation method [2]. For example, in the standard deviation approah, the relationship between the mean (V m ) and standard deviation (r V ) of the wind veloities and are orrelated as r 2 V ¼ C 1 þ 2 V m C 2 1 þ 1 1 ð5þ One Vm and r V are alulated for a given data set, then an be determined by solving the above expression numerially. One is determined, is given by ¼ V m C 1 þ 1 ð6þ In a simpler approah, an aeptable approximation for an be made as [7, 12] ¼ r 1:9 V ð7þ V m and an be approximated as ¼ 2 p Vm ffiffiffi p ð8þ

7 76 S. Mathew et al. 1.3 Energy Density The power available in a wind stream of veloity V, per unit rotor area, is given by P V ¼ 1 2 q a V 3 ð9þ where P V is the power and q a is the density of air. The fration of time for whih this veloity V prevails in the regime is given by the probability density funtion f(v). Thus, the energy ontributed by V, per unit time and unit rotor area, is P V f(v). Hene, the total energy ontributed by all possible veloities in the wind regime, available for unit rotor area in unit time (that is energy density, E D ) may be expressed as E D ¼ Z 1 P V f ðvþ dv ð1þ Substituting for P(V) and f(v) in the above expression and simplifying, we get E D ¼ 1 2 q a Z 1 This an further be simplified as [2] E D ¼ 3 2 q 3 a C 3 V ðþ2þ e ðv= Þ dv ð11þ ð12þ 2 Veloity Power Response of the Turbine Power urve of a 2 MW pith ontrolled wind turbine is shown in Fig. 4. The turbine has ut-in, rated and ut-out veloities 3.5, 13.5 and 25 m/s respetively. The given urve is a theoretial one and in pratie we may observe the veloity power variation in a rather sattered pattern. In this urve, we an observe that the turbine has four distint performane regions. 1. For veloities from to the ut-in (V I ), the turbine does not yield any power. 2. Between the ut-in and rated veloities (V I to V R ), the power inreases with the wind veloity. Though, theoretially, this inrease should be ubi in nature, in pratie it an be linear, quadrati, ubi and even higher powers and its ombinations, depending upon the design of the turbine. 3. From the rated to ut-out wind speed (V R to V O ), the power is onstant at the rated power P R, irrespetive of the hange in wind veloity. 4. Beyond the ut-out veloity, the turbine is shut down due to safety reasons.

8 Analysis of Wind Regimes and Performane of Wind Turbines 77 Fig. 4 Theoretial power urve of a 2 MW wind turbine 25 2 P R Power, W V I V R V O Veloity, m/s So, the wind turbine is produtive only between the veloities V I and V O. For any wind veloity between V I and V R, the power P V an generally be expressed as P V ¼ av n þ b ð13þ where a and b are onstants and n is the veloity power proportionality. Now onsider the performane of the system at V I and V R.AtV I, the power developed by the turbine is zero. Thus At V R power generated is P R.Thatis: av n I þ b ¼ ð14þ av n R þ b ¼ P R ð15þ Solving Eqs. 14 and 15 for a and b and substituting in Eq. 13 yields V n V n I P V ¼ P R VR n ð16þ Vn I Above equation gives us the power response of the turbine between the ut-in and rated wind speeds. Obviously, the power between V R and V O is P R. In the above expression, the major fator deiding the variations in power with veloity in the ut-into rated wind speed region is n. Value of n differs from turbine to turbine, depending on the design features. For example, Fig. 5 ompares the power responses of two ommerial wind turbines in this performane region. The urves are derived from data available from the manufatures. It should be noted that, although both the turbines are of the same 2 MW rated apaity, their power responses in the ut-into rated veloity region differ signifiantly. For a speifi turbine, n an be alulated from its power urve data, available from the manufaturer. For example, the ut-in, rated and ut-out wind veloities

9 78 S. Mathew et al. Fig. 5 Variations in output power from ut-into ut-out veloities for two wind turbines of 2 MW rated apaity Table 2 Cut-in, rated and ut-out wind veloities of the turbines Turbine no. Cut-in veloity, m/s Rated veloity, m/s Cut-out veloity, m/s of the two turbines ompared above are shown in Table 2. Putting these values in Eq. 16 we get P V ½T1Š ¼ 2 Vn 3 n 12 n 3 n and P V ½T2Š ¼ 2 Vn 4 n 16 n 4 n where T1 and T2 represents the turbines 1 and 2 respetively. Solving the above relationship with the veloity power data for the turbines (available from the manufaturer or obtained by digitizing the power urve) we an find out the value of n.any standard urve fitting paage an be used for the solution. Following this method, n for the turbines T1 and T2 are 1.8 (R 2 =.97) and.6 (R 2 =.95) respetively. Instantaneous values of wind veloity and orresponding power were reorded from a 225 W wind turbine installed at a wind farm and are plotted in Fig. 6. Cutin and rated wind veloities of this turbine are 3.5 and 14.5 m/s respetively. Sattered points represent the measured power where as the ontinuous line represents the power omputed using Eq. 16. Reasonable agreement ould be observed between measured and omputed values. 3 The Energy Model To estimate the energy generated by the turbine at a given site over a period, the power harateristis of the turbine is to be integrated with the probabilities of different wind veloities expeted at the site. For example, power urve of a wind

10 Analysis of Wind Regimes and Performane of Wind Turbines 79 Fig. 6 Field performane of a 225 W wind turbine (a) 12 (b).1 Power, W P(V) Probability f(v) 2.2 V V Wind veloity, m/s Wind veloity, m/s Fig. 7 Integrating the power (a) and probability (b) urves to derive the energy yield turbine is shown in Fig. 7a whereas Fig. 7b presents the Weibull probability density funtion of a andidate site. In the wind regime, the fration of energy ontributed by any wind veloity V is the produt of power orresponding to V in the power urve, that is P(V) and the probability of V in the probability density urve, whih is f(v). Thus, at this site, the total energy generated by the turbine E, over a period T, an be estimated by E ¼ T Z V o V i P V f ðvþ dv ð17þ As we have disussed, the power urve has two distint produtive regions from V I to V R and V R to V O. Thus, let us tae E ¼ E IR þ E RO ð18þ

11 8 S. Mathew et al. where E IR and E RO are the energy yield orresponding to V I to V R and V R to V O respetively. From the foregoing disussions, we have and E IR ¼ T Z V R E RO ¼ TP R Z VO V i P V f ðvþ dv ð19þ V R f ðvþdv ð2þ Substituting for f(v) and P(V) from Eqs. 3 and 16 in Eq. 19, we get E IR ¼ P R T ¼ V n R Z V R V I P R T Vn I V n VI n VR n Vn I Z V R V I V n V n I V 1 e ðv= Þ dv V 1 e ðv= Þ dv ð21þ For simplifying the above expression and bringing it to a resolvable form, let us introdue the variable X suh that X ¼ V ð22þ Then, dx ¼ V 1 and V ¼ X 1 ð23þ With Eq. 22, we have X I ¼ V I ; X R ¼ V R and X O ¼ V O ð24þ With this substitution, and simplifiation thereafter, E IR an be expressed as E IR ¼ P R T n ðvr n Vn I Þ Z X R X I X n= X e dx P R T VI n ðvr n Vn I Þ e X I e X R ð25þ

12 Analysis of Wind Regimes and Performane of Wind Turbines 81 Now onsider the seond performane region. From Eq. 2, E RO may be represented as E RO ¼ P R T Z V O V R V 1 e ðv= Þ dv ð26þ As R f ðvþ dv ¼ FðVÞ, from Eqs. 4 and 16, the above equation an be simplified as E RO ¼ TP R e X R e X O ð27þ The above expressions an be evaluated numerially. The apaity fator C F whih is the ratio of the energy atually produed by the turbine to the energy that ould have been produed by it, if the mahine would have operated at its rated power throughout the time period is given by Thus, CF ¼ C F ¼ n VR n Vn I VI n VR n Vn I E P R T ¼ E IR þ E RO P R T Z X R X I X n= X e dx e X I e X R þ e X R e X O ð28þ ð29þ The energy model disussed above is validated with the field performane of a 1 W wind turbine [13] in Fig. 8. The turbine onsidered here has ut-in, rated and ut-out wind speeds of 3., 13.5 and 25 m/s respetively. From the manufaturer s power urve, the veloity power proportionality for the design was Fig. 8 Comparison between estimated and measured daily energy yield from a 1 KW wind turbine Energy, Wh Predited Measured Days

13 82 S. Mathew et al. Fig. 9 Comparative performane of two 2 MW wind turbines in different wind regimes found to be It an be observed that the predited performane losely follows the measured values throughout the period. 4 Conlusion A method for assessing the wind energy resoure available at a potential wind farm site has been presented in the above setions. Model for simulating the performane of wind turbines at a given site has also been disussed. For example, the performanes expeted from the turbines given in Table 2, when installed at the sites desribed in Table 1 are ompared in Fig. 9. Though both the turbines have the same rated power of 2 MW, the first turbine is expeted to generate more energy from all the three sites. This is obvious as (1) the first turbine has lower ut-in and higher ut-out veloities, maing it apable of exploiting a broader range of wind spetra available at the site (2) The first turbine shows better power response between the ut-into rated wind speeds as seen from Fig. 5. The methods desribed above an be useful in the preliminary planning of wind power projet. However, for a final investment deision, apart from a more rigorous tehnial analysis, eonomial and environmental dimensions of the projet should be investigated. Referenes 1. Renewable Energy World (21) Global Wind Installations Boom, Up 31% in 29. Retrieved from 2. Mathew S (26) Wind Energy: Fundamentals, Resoure Analysis and Eonomis. Springer- Verlag, Berlin Heidelberg

14 Analysis of Wind Regimes and Performane of Wind Turbines Mahias AV, Sios, GD (1992) Fuzzy ris index for wind sites. IEEE Transations on Energy Conversion 7(4): Mathew S, Pandey KP, Anil KV (22) Analysis of wind regimes for energy estimation. Renewable Energy 25: Lysen EH (1983) Introdution to wind energy. CWD, Amersfoort, Netherlands 6. Hennessey JP (1977) Some aspets of wind power statistis. J Applied Meteorology 16: Justus CG, Hargraves WR, Mihail A, Graber D (1978) Methods of estimating wind speed frequeny distribution. J Applied Meteorology 17: Stevens MJM, Smulders PT (1979) The estimation of parameters of the Weibull wind speed distribution for wind energy utilization purposes. Wind Engineering 3(2): Carta J A P. Ramírez P Velázquez S (29) A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands. Renewable and Sustainable Energy Reviews 13(5): Yeliz MK, Ilhan U (28) Analysis of wind speed distributions: Wind distribution funtion derived from minimum ross entropy priniples as better alternative to Weibull funtion Energy Conversion and Management 49(5): Meishen L, Xianguo Li (25) MEP-type distribution funtion: a better alternative to Weibull funtion for wind speed distributions Renewable Energy 3(8): Boweden GJ, Barer PR, Shestopal VO, Twidell JW (1983) The Weibull distribution funtion and wind statistis. Wind Engineering 7: The Vermont Small-Sale Wind Energy Demonstration Program (21) Retrieved from Author Biography Dr. Sathyajith Mathew is an Assoiate Professor at the Faulty of Engineering, KAU and holds a onurrent faulty position at the University of Brunei Darussalam. He has more than 15 years of teahing, researh and development experiene on Wind Energy Conversion Systems in different parts of the world. Dr. Mathew has published extensively in this area of researh. His reent boo Wind Energy: Fundamentals, Resoure Analysis and Eonomis whih is published by Springer has been adopted as the text boo for wind energy programmes in Universities around the world. Dr. Mathew is also a freelane wind energy onsultant and serves as a resoure person to several International Training Programmes on Wind Energy.