The wind energy system performance overview: capacity factor vs. technical efficiency

Transcription

1 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS The wind energy system permance oeriew: capacity factor s. technical efficiency Ciprian Nemes, Florin Munteanu Abstract The main objectie of the paper is to deelop a probabilistic model capacity factor and technical efficiency estimation a wind turbine located in a specific area, model based on the output power distribution of wind turbine. This model was applied a wind turbine located to a region in the North-ast of Romania, the model results being alidated by results from Monte- Carlo simulation. Finally, the model was used to ealuate the effects of wind turbine generator parameters, a gien wind profile, on the capacity factor and technical efficiency alues. Keywords wind energy, eibull distribution, output power distribution, capacity factor, technical efficiency. I. INTRODUCTION NVIRONMNTAL factors such as global warming and pollution hae heightened the need to introduce into the generation mix a greater percentage of renewable sources. In the last time, wind power has drawn much attention as a promising renewable energy resource, which has shown some prospects in curtailing fuel consumption and reducing the emission of pollutants into the atmosphere. Unlike other renewable energy sources, wind energy has become competitie with conentional power generation sources and theree application of wind turbine generators has the most growth among other sources. ind is one of fastest growing energy source and is considered as an important alternatie to conentional power generating sources. The energy production from a wind turbine or a wind park, in a specific location, depends by many factors. The main factors include the wind speed conditions from the area, and most importantly, the characteristics of the wind turbine generator itself, particularly the cut-in, and cut-off wind speed parameters. The output power of a wind turbine generator does not ary linearly with the wind speed. The output power increases with the wind speed between the cut-in speed and the wind speed, after that the power output remains constant at the power leel, until the cut-out speed, when the turbine is stopped safety reasons [,2]. Different types of wind turbines are commercially aailable on the market. It is theree desirable to select a wind turbine which is best suited a particular location in order to obtain a maximum power from power transposed by the wind. These important aspects bring suitability concerns regarded by the energy potential of a specific location and the selection of the Corresponding author: Tel , cnemes@ee.tuiasi.ro suitable wind turbine a specific wind profile. A measure of the suitability of wind turbine to a specific location is gien by the capacity factor and efficiency alues. The capacity factor is defined as the ratio of the expected output power oer a period of time to the power of wind turbine generator. All power plants hae capacity factors, and they ary depending on resource, technology and purpose. Typical wind power capacity factors are 2-4%, with alues at the upper end of the range in particularly faourable areas [4]. The capacity factor is not an indicator of efficiency. A measure of turbine efficiency is the power coefficient. This coefficient indicates how efficiently a turbine conerts the wind energy into electricity. This coefficient aries with the wind speed [2]. fficiency is the expected power coefficient, oer a period of time, and is defined as ratio of the useful output energy to the input wind energy. In literature are presented arious approaches capacity factor and efficiency estimations, mostly obtained from simulations techniques based on wind speed data [5,6] and sometimes from computational models [,7], that need numerical integration techniques or some approximations. Haing in iew the stochastic nature of the primary energy, the probabilistic methods can be proper solutions capacity factor and efficiency ealuations. In the paper, a probabilistic model is deeloped to ealuate these alues and to analyze the dependence of the wind turbine generator characteristics. The proposed model is based on probability density function of output power gene by the wind turbine. In order to alidate the model, the results model were compared with the results of the other model, namely with Monte Carlo technique. The model has the adantage that can be easily implemented in computer programs and require a computing time considerably less than in the case of simulation or numerical methods. Selection of the optimal wind turbine was discussed in different manner in arious papers, among which the maximization of capacity factor and/or efficiency [5,6,7]. The choice of turbine inoles choosing parameters that lead to maximizing these factors. The turbines must be chosen with the parameters that match those of wind profile area. Based on these issues, in the paper, a numerical analysis is realized to hae a comparison between effects of different parameters of the wind turbine generator on capacity factor and efficiency alues, analyzing the importance and weight of each parameter of those alues. Issue, Volume 5, 2 59

2 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS II. IND AND OUTUT OR IND TURBIN ROBABILISTIC CHARACTRISTICS The output power from a wind turbine depends by the aailability of the energy source, namely the wind speed and the power-wind characteristics of the wind turbine generator. A. robabilistic model of wind speed ind is a turbulent moement mass of air resulting from the differential pressure at different locations on the earth surface. One of the main characteristics of wind is that it is highly ariable in time and space, the ariation of wind exists from instantaneous, hourly, daily to seasonal, and its properties ary from one location to another. The wind property of interest in the power generation problems is the wind speed probabilistic model. The speed of the wind is continuously changing, making it desirable to be described by the probabilistic models. The probability density function of wind speed is important in numerous wind energy applications. A large number of studies hae been published in scientific literature related to wind energy, which propose the use of a ariety of functions to describe wind speed frequency distributions [9],[]. The conclusion of these studies is that the eibull distribution of two parameters may be successfully utilized to describe the principle wind speed ariation. The eibull probability density and cumulatie distribution function are gien by: f ( = α α exp α ; F ( = exp ( α The scale parameter α (m/s and a shape parameter (dimensionless of the eibull distribution can be found using different estimation methods [2],[4]. ach method has a criterion, which yields estimates that are best in some situations. Different results are produced based on that criterion. The most commonly methods are Maximum Likelihood stimator, Method of Moments, Least Squares Method or Regression Method. The Maximum Likelihood stimator is so commonly applied in engineering and mathematics problems [6], so, this method is used in this paper to establish the parameters of wind speed distribution. In many studies, the shape parameter is often chose to 2 and theree a Rayleigh distribution can be used, with a same accuracy and with a simpler model. The wind blows faster at higher altitudes because of the reduced influence of drag of the surface and lower air iscosity. The effect of the altitudes in the wind speed is most dramatic near the surface and is affected by topography, surface roughness, and wind obstacles such as trees or buildings. The most common expression the ariation of wind speed with hub height is the power law haing the following logarithmic profile model [8],[9]. ( z = ( z r ( ln( z z ln( z r z (2 where (z and (z r are the wind speeds at a desired z and registered z r height, and z is the surface roughness length, a characterization of a ground terrain. To establish the parameters of probability density distribution is necessary an accurate dataset of wind speed. The wind speed database can be obtained from meteorological station, where, usually, the measurement point (anemometer height aboe the surface may be to m or 5 m. Depending by the wind measurement leel, the speed data must be adjusted the change in height desired according to a logarithmic profile preiously mentioned. B. ind speed-power relationship The power transported by an air stream flowing with a gien speed,, can be calculated according to [] using the following simple expression: V = 2 A ρ ( where ρ is the air density and A the area of the air stream, measured in a perpendicular plane to the direction of the wind speed. The calculation of the mechanical power that can be extracted by the rotor of a wind turbine, requires Betz law to be taken into account. This law specifies that only a maximum 6/27 of the wind energy can be conerted into mechanical power. This alue is known as the Betz limit. In practice, the collection efficiency of a rotor is not as high as 59%. A more typical efficiency is 5% to 45%. The mechanical power is conerted in electrical power by generator, so, the output electric power of a wind turbine is a function of the wind speed. The power cure gies a relation between the wind speed and the output electric power, a typical cure of the wind turbine generator is nonlinear related to the wind speed. Howeer, the assumption of the linear characteristic of power with the wind speed, brings a significantly simplifies of calculations, without roughly errors. The power output characteristic can be assumed in such way: it starts generating power when the speed wind exceeds the minimum wind speed, namely cut-in speed ( cut-in ; the power output increases with the wind speed, when wind aries between cut-in and speed wind (, alue that the power achiees the power (. the power of a wind turbine, generally the maximum power output of a generator at highest efficiency, is produced when the speed lies between and cut-off wind speed ( cut-off. cut-off wind speed is the maximum wind speed at which the turbine is allowed to produce power, usually limited by engineering design and safety constraints. Thus, the electric power may be calculated from the wind speed as follows: ( < < ( (4 ( = < < cut off other else This cure comes aailable from the wind turbine manufacturer or plotted using recorded wind speed and corresponding output power data, a typical cure of the wind Issue, Volume 5, 2 6

3 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS turbine generator is shown in the figure. lectric power (M cut-in cut-off ind speed (m/s Fig. The power cure of a wind turbine quations ( and (4 express the instantaneous alues of wind power and electric output power, as a function of the instantaneous wind speed. Howeer, the wind speed may ary during a period of time. To consider this effect, we are going to work with the wind speed probability distribution function. C. robabilistic model of wind power and wind turbine output power The probability distribution functions of wind power and of the wind turbine output power can be obtained using the analytical dependence between wind speed, wind power, and the output power respectiely, operating a change of ariables. Lets assume that is a continuous random ariable with cumulatie distribution function, F V ( and that =J( defines a one-to-one transmation from a region of the wind-space, to a region of the power-space, with inerse transmation =J - (, the cumulatie distribution function of power can be calculated according [6],[7]: F ( = r( < p = r( J ( X < p = = r( X < J ( p = F ( J ( p In order to obtain the probability density function, a differential of cumulatie distribution function must be ope. In figure 2 is presented the intuitie process of the random ariables transmation, the wind speed ariables being transmed in wind power ariable, on the right, respectiely in the output electrical power ariable, on the left., V f ( f V ( =J ( V =J 2 ( V f V ( V Fig. 2 Transmation of the wind speed ariable If (5 is applied the wind power relationship (, haing in iew the eibull distribution, the probability density function of the wind power may be expressed as a function of the ariable V : (5 f V 2 2 V ( V = exp V A Aρα Aρα ( ρα Theree the power transported by the wind can be represented by a eibull distribution, with α and parameters gien by: (6 α' = 2 A ρ α, ' = (7 where ρ is the air density, A the area of the wind turbine rotor, and α, are the wind distribution parameters. The output power probabilistic model a wind turbine and its practical ealuations were deeloped and ealuated by authors in [],[2]. Similar results has also been obtained by others authors in [ ],[4]. The possible alues of F T ( may be roughly classified in, and in the interal that lies between mentioned alues, respectiely. ach possible alue has been ealuated, haing in iew the probability to achiee that alue. The cumulatie distribution function of the output power of the wind turbine is: F F [ F ( F ( ] cut off ( = T ( + F ( F ( < = < = The probability density function results from differential of cumulatie distribution function: f ( where: R ( = R2 f ( < R = [ F ( F ( ] = F ( cut off < = = (8 (9, represents the alue of output power cumulatie distribution function in the point, R = F ( F ( = F (, 2 cut off represents the increase alue of the cumulatie distribution function in the alue, and. = ( + III. CAACITY FACTOR AND FFICINCY VALUATIONS Capacity factor and efficiency depend both on the wind speed distributions in the area and the turbine parameters. To illustrate the effect of wind turbine parameters on capacity factor and efficiency alues, a probabilistic model these indicators is deeloped. The capacity factor (CF of wind turbine is the ratio of expected output power oer a period of time to power. The efficiency (F of wind turbine is the ratio of useful output energy to the input wind energy, or expected power output from wind machine to expected power aailable in wind oer a period of time. The expected output power is used in both on the capacity factor and efficiency ealuations, so, it will be firstly ealuated. Issue, Volume 5, 2 6

4 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS A. The expected output power of a wind turbine The expected output power of a wind turbine depends on the output power alues and the probability to achiee that power, described by the probability distribution functions of output power. The expected output power (( from a wind turbine generator can be estimated from its power-wind and wind characteristics, being represented by the probability distribution of wind speed. This is gien by [] as: ( = f ( d ( where is the output power function ariable and f ( is probability density function of output power from wind turbine. Haing in iew the expression of output power distribution function, from (9, the expected output power can be obtained by: ( = R+ = rat r ated cut in f ( d f + R2 = ( d + R. ( where f ( is a probability density function of wind speed. Taking into account that df ( = f ( d, the equation ( may be written as: ( = F cut off cut in cut α ( exp( ( / d = exp( ( / α = d exp( ( cut off / α (2 cut in The integration can be accomplished by making the change in ariable y = ( / α, and theree dy = ( / α d ( / α. After substitution of integration limits and their reduction to the minimum number of terms, the result is: α Γ (, cut in, = ( cut in α α exp( ( cut off / α where Γ ( and ( are the gamma and the lower incomplete gamma functions, respectiely [5]. B. The expected output power model of a wind turbine As it has been presented in (6, considering the wind power haing a eibull distribution, the expected alue of the wind power can be expressed as a function of the parameters α, and the Gamma function: in [ V ] =α Γ ' + (4 ' C. The probabilistic model capacity factor and technical efficiency The capacity factor of a wind turbine means its energy output diided by the theoretical maximum output, if the wind turbine generator were running at its (maximum power during all the time. So, the capacity factor is the ratio of the expected output power oer a period of time to the power of wind turbine generator. CF = = α Γ cut,, α α exp( ( / α (5 ( in cut off The efficiency is a measurement of how much energy from the wind is conerted in electrical power energy. For that, the expected output power must be diided to the expected wind power input to measure how technically efficient is the wind turbine. α Γ ( F= =,, ( V α α α Γ ' + ' (6 exp( ( cut off / α α Γ ' + ' The equations (5 and (6 show the results of authors research based on laborious calculations and detailed analysis of statistical distributions. This relationship represents an equation which shows the effects of cut-in,, and cut-off speeds parameters on the capacity factor alue. For a gien wind regime, with known α and parameters, we can select that alues of cut-in, and cut-off that maximize the expected output power, and thereby maximize the capacity factor. IV. MODL VALIDATION AND NUMRICAL XAML For alidation of probabilistic model, its results hae been compared with results from other model. The Monte Carlo simulation has been used to proide inmation related to the aerage alues of the capacity factor. A Matlab program has been deeloped to alidate the probabilistic model. The program has been structured by two main functions. First function is based on a probabilistic model preiously deeloped and modelled with (5 and (6, respectiely. Second function has been deeloped based on Monte Carlo simulations technique. This technique generates different alues of wind speed, in accordance with their eibull distribution (with the shape and scale parameters estimated from the real data base and these wind alues are used to generate the output power, haing in iew the characteristics of the wind turbine generator. The expected output power from a wind turbine is the power produced at each wind speed sample, integ oer all possible wind speeds. The required capacity factor alues may be obsered from the aerage of all output power alues, oer a long number of samples. The efficiency is obsered from aerage of all output power alues, and also from all power transported by any alues of wind speed. The simulation can be stopped when a specified degree of confidence has been achieed. The methodology presented in this paper was applied to a real wind turbine and a real wind speed database, to alidate the probabilistic model and to ealuate the influence Issue, Volume 5, 2 62

5 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS of main parameters of wind turbine generator to capacity factor and efficiency alue. The wind speed database was collected from the north-east area of Romania, a measurement interal to one hour the year 28. The figures.a,b present the wind speed collected from wind station height (m and adjusted to the hub wind turbine height (8m. wind speed (m/s wind speed (m/s 5 5 ind speed to measured height (m time (hr ind speed to 8 m height time (hr Fig..a,b ind speed data base from the north-east area of Romania, m, respectiely 8 m height The parameters of the eibull distribution hae been estimated using the hourly wind data base. The probability density and the density function fitted different wind speed alues in m/s steps are presented in figure 4. The probability distribution function used to fit is a eibull distribution with scale parameter α= m/s and a shape parameter = Density ind speed data eibull fit ind speed data (m/s Fig. 4 The wind data base associated distribution The wind turbine chose analyze is an actie blade pitch control wind turbine, namely.5 XL G-nergy, manufactured by G nergy [8], with their technical specifications presented in table : Table Technical specifications of wind turbine G nergy Rated Cut-in Rated Cut-off Rotor power speed speed speed diameter (M (m/s (m/s (m/s (m Turbine Model.5xle - G nergy Hub Heights (m The probability density function (DF and cumulatie distribution function (CDF of the output power a.5 XL wind turbine, considering a eibull distribution with mentioned parameters, are presented in the figure 5.a,b. pdf(el cdf(el robability density function.5 XL ind Turbine (G.5.5 el[m] Cumulatie distribution function fot.5 XL ind Turbine (G el[m] Fig.5.a,b The DF and CDF of output power wind turbine Considering the ρ=.225 kg/m the air density (at 5 C and the rotor are A=546 m 2, in the preious equation (7, the scale parameter and shape parameter of eibull distribution parameters are obtained as α = m/s and =.629, respectiely. The probability density function and cumulatie distribution function of the wind power are in accordance with eibull distribution with mentioned parameters. pdf(w 2 x ind ower w [M] Issue, Volume 5, 2 6

6 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS cdf(w fficiency (% TG.5xle - G nergy Vin=.5 m/s Vrat=.5 m/s Voff=2 m/s bl(a=4.8225;b= ind ower w [M] Fig.6.a,b The DF and CDF of wind power Using the output power and wind power distribution functions in the probabilistic model preiously deeloped, the capacity factor and efficiency alues were ealuated and presented in table 2 and. For alidation, in the following is presented an example of capacity factor and efficiency ealuation, a.5 XL G-nergy wind turbine, using the Monte Carlo Simulation technique (MCS. This technique creates a fluctuating conergence coefficient of ariation range arious numbers of samples capacity factor (in figure 7 and efficiency (in figure 8. The coefficient of ariation of the wind speed gene range can be used to improe the effectieness of MCS, this being often used as the conergence criterion in simulation techniques. Number of simulations results from condition that the deiation of the coefficient of ariation of CF and F ranges to expected alue to be under a settled alue. Using simulations techniques, a settled alue (,% is obtained about. necessary samples, the conergence process of CF being presented in the figure 7, and F in figure 8. Capacity Factor (% TG.5xle - G nergy Vin=.5 m/s Vrat=.5 m/s Voff=2 m/s bl(a=4.8225;b= Number of samples Fig. 7 Capacity factor result from Monte Carlo simulation Number of samples Fig. 8 fficiency result from Monte Carlo simulation The capacity factor alues proided by probabilistic model and sequential Monte Carlo simulation are shown in Table 2. For a better comparison between models, three ranges of speed parameters of wind turbine were considered in capacity factor ealuation. Commercial wind turbines typically hae cut-in speeds between 2.5 and 4.5m/s, a wind speeds between and 5 m/s and a cut-off speeds between 2 and 25 m/s. Table 2. Capacity factor alues from probabilistic model (M and Monte Carlo simulation (MCS Capacity Factor rat=.5m/s cut-off=2m/s Capacity Factor cut-in=.5m/s cut-off=2m/s Capacity Factor cut-in=.5m/s rat=.5m/s cutin M MCS rat M MCS cutoff M MCS As described aboe, table shows the efficiency alues different alues of cut-in, and cut-off turbine speeds. Table. fficiency alues from probabilistic model (M and Monte Carlo simulation (MCS fficiency rat=.5m/s cut-off=2m/s fficiency cut-in=.5m/s cut-off=2m/s fficiency cut-in=.5m/s rat=.5m/s cutin M MCS rat M MCS cutoff M MCS It can be seen that the results obtained from both methods are ery close. The probabilistic method proides comparatie results with Monte Carlo simulation, these proing the accuracy of probabilistic model, deeloped in equations (5 and (6. The analytical expressions deeloped in (5 and (6 were Issue, Volume 5, 2 64

7 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS used to study the effect of mean wind speed on both coefficients. Graphic representation of dependence is shown in figure 9, with solid line efficiency and dashed line capacity factor. 25 Vcut-in (.5 m/s affected by wind speed steps V (.5 m/s affected by wind speed steps Vcut-off (2 m/s affected by wind speed steps Capacity factor and efficiency Capaciy factor fficiency Capacity Factor (% wind speed step (m/s. Fig. ffect of wind turbine parameters on capacity factor Mean wind spead (m/s Fig. 9 ffect of mean wind speed on CF and F.5.45 Vcut-in (.5m/s V (.5 m/s Vcut-off (2.5 m/s As it can be seen, the wind turbine efficiency is largest (in this case 5% at a relatiely low wind speeds, around some 4 m/s. But, at low wind speeds, efficiency is not so important, because there is not much energy to be conerted. At higher wind speeds, the turbine can not conert the excess energy that exceeds the limits of the generator. So, the efficiency is not the best indicator ealuating the suitability of wind turbine to a specific location. For suitability ealuation, the capacity factor is a better indicator. If the wind turbine is located in an area with an aerage speed around some m/s, the maximum output power will be gene, een if the efficiency is low. So, it is not an aim in itself to hae a high technical efficiency of a wind turbine. Since the fuel is free, the technical efficiency is not important, the wind energy can be used or will be lost. hat really matters is the amount of gene energy, een with a lower efficiency Also, the proposed model may be used to analyze the effects of different cut-in, and cut-off wind speeds on the capacity factor alue. Using a.5-xl G nergy wind turbine, placed in Iasi location, with preiously wind profile, the capacity factor will be 6.85% and the efficiency, 28.5%. this wind profile, from table 2, it can see, a wind turbine generator can be expected to operate with a maximum capacity factor of 22.% and a maximum efficiency of 7.57% a wind turbine generator characterised by a wind speed parameters set to cut-in =2.5m/s, =.5m/s and cutoff=2m/s, respectiely. A capacity factor of 22.% from a.5k wind generator means a mean output power of.5 k or an annual power output of kh. The effects of the wind turbine generator parameters on the capacity factor and efficiency are shown in figure, and figure, respectiely. In the same system coordinates is shown the dependence of capacity factor and efficiency arious wind speeds alues around of wind turbine generator parameters (cut-in,, cut-off speeds. fficiency (% wind speed step (m/s Fig. ffect of wind turbine parameters on efficiency alues As it can be seen from the figure 9, a certain alue of capacity factor or efficiency can be achieed by changing the two parameters of wind turbine generator. Most important parameter and proiding the greatest degree of freedom is cutin wind speed. It has been shown that the cut-in wind speed has a significant effect on the capacity factor and efficiency alues. Their alues decrease approximately linearly as the cut-in wind speed increases. The second parameter of wind turbine generator with effect on the capacity factor and efficiency is the wind speed. It has been shown that the wind speed has a relatiely small effect on these alues. The wind speed growth leads to the capacity factor and efficiency alues decrease, but this effect is less significant than that of the cut-in wind speed It has been shown that the cut-off wind speed has no effect on either the capacity factor nor efficiency alues. The cut-off wind speed is a safety parameter and is usually large. For relatiely few times the instantaneous wind speed at a particular area will be greater than the cut-off speed. The selection of the cut-off speed parameter is theree less important than that of the cut-in and the wind speed parameters. Issue, Volume 5, 2 65

8 INTRNATIONAL JOURNAL OF MATHMATICAL MODLS AND MTHODS IN ALID SCINCS V. CONCLUSION Integration of wind energy is an important actiity in the deeloping process of the electric power system. Knowing the capacity factor alues is a key factor when examining wind energy potential a wind turbine located in a specific area. The probabilistic methods are the recommended solution wind integration analysis, since they can take into account the wind power uncertainty. This paper presents a probabilistic model to ealuate the capacity factor and technical efficiency of a wind turbine based on the output power distribution. The results were alidated using the Monte Carlo simulations, and the analysis demonstrates that the probabilistic model results are ery accurate. The model has the adantage that can be easily implemented in computer programs and require a computing time considerably less than in the case of simulation methods. The electric energy output of a wind turbine a specific area depends on many factors. These factors include the wind speed conditions at the area, and the characteristics of the wind turbine generator. The case studies show that turbine cut-in wind speed has a significant effect on the both capacity factor and technical efficiency alues while the cut-off wind speed has almost no effect. Significant benefits can be obtained by selecting suitable wind turbine parameters the specific wind profile. RFRNCS [] Tony Burton, Daid Sharpe, Nick Jenkins, rin Bossanyi, ind nergy Handbook, John iley & Sons 2. [2] Thomas Ackermann, ind ower in ower Systems, d. John iley & Sons 25. [] R. Billinton,. Y. Li, Reliability assessment of electrical power systems using Monte Carlo method, lenum ress, New York, 994. [4] Nicolas Boccard, Capacity Factor of ind ower, Realized Values s. stimates, Raport project SJ Depart. d conomia, Uniersitat de Girona, Spain. October 28. [5] Z. M. Salameh, I. Safari, Optimum windmill site matching, I Trans. nergy Coners., ol. 4, no. 7, pp , 992. [6] Tsang-Jung Changa, Yi-Long Tua, aluation of monthly capacity factor of CS using chronological and probabilistic wind speed data: A case study of Taiwan, Renewable nergy 2, 27, pp [7]. Kaak Akpinar, S. Akpinar, An assessment on seasonal analysis of wind energy characteristics and wind turbine characteristics nergy Conersion and Management 46, 25, pp [8] Isaac Y. F. Lun, Joseph C. Lam, A study of eibull parameters using long-term wind obserations Renewable nergy Journal, Volume 2, Issue 2, June 2, pages [9] J.A. Carta,. Ramırez, A reiew of wind speed probability distributions used in wind energy analysis. Case studies in the Canary Islands Renewable and Sustainable nergy Reiews, olume, Issue 5, June 29, pp [] Mohammad A. Al-Fawzan, Algorithms stimating the arameters of the eibull Distribution Interstat Journal, October 2. [] Nemes C., Munteanu F., Optimal Selection of ind Turbine a Specific Area, OTIM 2, Braso, Romania //26. '2 I, pp [2] Nemes, C., Munteanu, F., Deelopment of Reliability Model ind Farm ower Generation, Adances in lectrical and Computer ngineering, ISSN , e-issn , ol., no. 2, 2pp [] M.H. Albadia,.F. l-saadanyb New method estimating CF of pitch-regulated wind turbines, lectric ower Systems Research 8 ( [4] D. Villanuea, A. Feijoo, ind power distributions: A reiew of their applications, Renewable and Sustainable nergy Reiews 4 ( [5] Mathorks roducts. Statistics Toolbox. Function Reference, Gamma Distribution. [6] L. Bain, M. ngelhardt, Introduction to robability and Mathematical Statistics, Duxbury ress, Calinia, 992. [7] A. apoulis, robability, Random Variables and Stochastic rocesses, McGraw-Hill, New York, 984. [8] /wind_turbines/ Ciprian Nemes was born in Turda, Romania, on May, 975. He graduated from Gh. Asachi Technical Uniersity of Iasi and receied the MSc degree in electrical engineering and hd degree in reliability engineering. He is currently a Senior Lecturer and research interests are in the area of power equipment reliability, power system planning based on risk assessment, renewable energy sources operation and planning. Florin Munteanu was born in Campina, Romania, on April, 954. He graduated from Gh. Asachi Technical Uniersity of Iasi and he receied the MSc degree in ower ngineering in 979 and hd degree in Reliability ngineering in 995. Starting with 984 he is with Gh. Asachi Technical Uniersity of Iasi where, from 999, he is holding a full time professor position and from 28 he is also the head of ower ngineering Department. The main fields of interest included transients of power systems, power quality and reliability. Issue, Volume 5, 2 66