Modelling wind speed parameters for computer generation of wind speed in Flanders

Transcription

1 Modelling wind speed parameters for computer generation of wind speed in Flanders A case study using small wind turines in an uran environment Michaël Gay, Michel Van Dessel Dept. of Applied Engineering Lessius Mechelen, Campus De Nayer Mechelen, Belgium michael.gay@lessius.eu Astract The calculation of wind energy parameters is made for small wind turines on moderate height in a suuran environment. After using the measured data, the same parameters were calculated using first order Markov chain computer generated data. Some characteristics of the wind and the wind power were preserved using Markov, others were not. Keywords; small wind turines; uran environment; wind power generation; Markov model; synthetic wind data; I. INTRODUCTION Due to growing consensus on the importance of renewale energy generation, an increased interest in small scale wind turines has risen. Two important numers that characterize a single wind turine on a specific location are the yearly energy yield and the energy storage needed to flatten the power output of the turine with storage ackup. This might e a simplistic model of a grid in islanding mode where there is a flat power demand, while the energy production is done y a small wind turine which has no flat power output. Information aout the wind at the installation site has to e availale, in order to estimate the yearly energy production of wind turines. The information needed to compute the yearly energy yield, is different [1] to the information needed to size energy storage. The information for the latter involves the time sequence of wind data, while the energy yield can e calculated from the wind speed frequency distriution. One way to estimate oth the energy yield and the necessary energy storage is y the use of long term on-site measurements. While these measurements might e the most accurate, they are in most instances not availale on eforehand and certainly expensive. The use of computer models that generate wind data that afterwards can e used in simulations is faster and less expensive. Another advantage of computer simulation is that no measurement gaps due to measurement failure will e encountered. This paper aims to generate wind data y the use of a Markov model and indicates for what purposes the time series might e used and where the pitfalls lie with using the model. II. MEASUREMENTS Since Septemer wind speed measurements are conducted using an ultrasonic Doppler anemometer. The Johan Driesen Dept. of Electrical Engineering / ESAT University of Leuven Leuven, Belgium johan.driesen@esat.kuleuven.e anemometer is mounted on a uilding in mid Flanders (Belgium) at a height of 1.3 meters referred to local ground level and takes samples at a frequency of Hertz. The environment can e classified as typically suuran with high surface roughness, since trees and uildings with comparale height as the wind meter are in the direct neighorhood. An overview of the measured data is given in Tale 1. For the year 11 the total numer of measurement lines equals 3379 lines. TABLE I. MEASURED DATA Physical Quantity Areviation Unit Components of the wind speed vector U,V,W m/s Length of the D and 3D wind speed vector D, 3D m/s Azimuth and elevation of the wind speed vector α, φ deg. ( ) Speed of sound Sos m/s Sonic temperature Ts K Timestamp T s III. CALCULATIONS First the raw data is used to calculate some of the important parameters. Fig. 1 shows some random measurement days where the raw data is averaged on one minute intervals. Wind speed (one minute vector mean of the 3D components) [m/s] 1 One minute mean of 3D wind speed form /5/11 until 3/5/11 5//11 5/3 5/ 5/5 5/ 5/7 5/ 5/9 5/3 Figure 1. Variation of the one minute interval mean wind speed

2 A. Proaility density function From the proaility density function (PDF) an estimate is made for a small wind turine on moderate height, mounted on a uilding in mid Flanders. Fig. gives a plot of the PDF for the mean 3D wind speed taken on 15 minutes intervals. Proaility density function of the 3D vector average taken on 15 minute intervals minute mean of 3D vector with v 3 as weight.3 with v as weight An approximate calculation of the proaility of a wind speed at this location greater than m/s is 3.%. Since typical cut-in wind speeds of small wind turines are aout 3 m/s [] the amount of time when the turine is not producing power is % for this site. Luckily since the Weiull function is right skewed and the wind power is related to the cue of the wind speed, most of the energy production will e made at wind speeds higher than 3 m/s. Some authors [3], [] prefer to specify the Weiull function as: Proaility density function [ ] mean 3D wind speed =.9 m/s k x f( x) =.. λ λ k k 1 x e λ With x the wind speed and λ the scale parameter and k the shape parameter. The relation etween oth Weiull descriptions is found y (3) and (): (3) Wind speed 3D vector mean [m/s] 1 a = k λ () Figure. Proaility density function The fitted curves on the PDF show that for this location the function corresponds with a Weiull function instead of a Raleigh function. There are 3 curves shown in Fig. 1 that fit the original data. While the least squares fit will visually appear to e a etter fit, the cue weighted fit will give a more realistic power output, since wind power is related to the cue of the wind speed. Therefore higher wind speeds are given a higher weight while fitting. The Weiull function is given y: 1 a. x f( x) = ax... e (1) = k (5) B. Wind rose The distriution for wind direction is called a wind rose and is visualized for this location in Fig.3. The main wind direction for this location is WSW (West Southwest). 33 N 3 3 With x the wind speed (x ) and a and parameters that determine the scale and shape of the Weiull function. For a value of = the Weiull function ecomes a Raleigh function. The values for parameters a and in (1) are listed in Tale. W E TABLE II. WEIBULL PARAMETERS 1 Weiull parameters for the fitted curves in Fig. 1 Function name with v 3 as weight with v as weight a [95% conf. int.] a [95% conf. int.] a [ ] [ ].1 1. [ ] [ ] [ ] [ ] a. 95% conf.int. meaning 95% confidence interval From these proaility density functions the proaility of a wind speed X t is given y: 1 a. x Px ( X) ax... e dx t = () Xt Figure 3. Wind rose 1 S C. Yearly energy yield Once the proaility density function is estalished, the yearly energy yield can e estimated. For this estimation some assumptions have een made. A first assumption is that the wind speed will not vary more quickly than the lades and rotor of a wind turine can follow. This can e made clear with the andwidth of the components. A second assumption is that of a constant air density. A third assumption is that the power coefficient of the turine 15

3 equals the Betz limit. With this assumption the transfer of kinetic energy to mechanical energy of the turine is assumed to e ideal. The last assumption is that of a constant electrical efficiency which is assumed to e %. This % is a realistic value for optimized small wind turine generators. [5] 1) Wind power The power availale in the wind is given y the formula: Pwind = ρ Av () Where ρ is the density of air. The density is assumed to e constant and equals the density of air at C which is 1. kg/m 3. The parameter A is the frontal swept area of the rotor lades expressed in m². Using () the wind power per square meter can e calculated as P wind /A (W/m²). When this result is multiplied y the frequency distriution the result is a power density distriution. If this power density distriution is multiplied y the numer of hours in a full year, an energy distriution is the result which has units of kwh/(year.m²). The result of these multiplications is visualized in Fig.. Annual energy production distriution [kwh/(m.year)] Energy density versus proaility density in function of wind speed 5 15 Figure. Yearly annual energy yield in function of the wind speed ) Wind energy The integral over the possile wind speeds will yield the annual energy production. The result of the integration over all wind speeds equals kwh/m.year. If the assumption of a cut-in wind speed of 3m/s is adopted, the annual energy production equals 351 kwh/m.year. The difference in output is less than might e expected from the % off-time. The % off-time results in only 1% energy loss. 3) Mechanical energy These figures are for the kinetic energy in the wind. This energy is converted in mechanical energy using the turine lades. These lades have different efficiencies while converting wind speed in rotor angular velocity depending on tip speed ratio and angle of attack. For the yearly energy yield calculation this efficiency dynamics are simplified to an ideal conversion from kinetic to mechanical energy captured in the Betz limit. This limit states that only 1/7 percent of the primal wind energy ecomes mechanical Proaility density function [ ] energy. More realistic values lie etween.3 and.5 [] for small wind turines. ) Electrical energy The rotation of the turine powers a generator. Since well constructed generators for small wind turines can achieve high efficiencies for a large range of angular velocities, an average efficiency of % is adopted. 5) Total electrical energy yield These calculations lead to an estimation of the yearly energy production of a wind turine. In this case, with these assumptions and this location, the final result is 17 kwh/m².year. When compared to solar irradiation on the location of the measurements these are the results: From [] appears that that the yearly sum of gloal irradiation is 1 kwh/m².year. The efficiency of the solar power system in [] is assumed to e 75%. This yields a 5 kwh/m².year. ) Constant power output If the resulted yearly energy would e consumed at a constant power, this would e at 19 Watts for 1 m² of swept area. This numer is compared to power input in Fig. 5. 7) Energy storage requirement The largest difference etween the cumulative power input and cumulative power output results in a value of the energy storage required. The storage needed for 1 m² is kwh. 3D mean wind speed [m/s] Electrical power [kw/m ] 5//11 5/3 5/ 5/5 5/ 5/7 5/ 5/9 5/3 Electrical power output per m in kw for 15 minutes mean D wind speed values for 15 minutes mean Electrical power input y the tuine Mean constant power output of the turine and storage system 5//11 5/3 5/ 5/5 5/ 5/7 5/ 5/9 5/3 Figure 5. Comparison of wind speed versus electrical power IV. MARKOV MODEL For the construction of a computer model used to reproduce wind data the choice was made for a Markov model ecause of its straightforwardness of implementation. It is widely used y many authors [3] [7] in order to create synthetic wind data. A. Construction of a Markov chain Construction of a Markov model for wind time series is explained in [1] and [3]. The construction of wind power series is explained in [1]. This paper will elaorate further on the construction methodology. 1) Discrete transition proaility matrix

4 The fundamentals of a Markov chain lie in the transition of a parameter on one discrete time step to the next time step. The final result is a matrix where the transition proailities are descried y the matrix elements. This matrix is called the transition proaility matrix. The total numer of discretizations of the wind speed determines the amount of possile states, which in their turn determine the size of the Markov matrix. N discrete states produce a N y N Markov matrix for a first order Markov chain. The order of a Markov chain is equal to the amount of previous states that are used to calculate the next state. A first order matrix only looks at the current state to determine the proaility of the next state. When using a Markov chain to construct a wind time series the cumulative discrete proaility matrix is needed. B. Simulation of wind speed using the Markov matrix In Fig. a comparison is made etween the real mean 3D wind data in 15 minute intervals and the simulated data for 15 minute intervals. Measured 3D wind speed /9/ / /11 /1 /13 /1 /15 /1 /17 Simulated 3D wind speed /9/ / /11 /1 /13 /1 /15 /1 /17 simulated wind speeds ecause the result here is kwh/m² storage requirements. Proaility density [ ] Proaility density function of the simulated data Simulated data Least sqares fit with v 3 as weight Figure 7. Proaility density function of the simulated data 3) Prolems with the amplitude spectrum As can e seen in Fig. the diurnal variation in the simulated data is nonexistent. Peaks in wind speed normally occur during the day dough a little shifted to the evening. This is ecause of thermal winds produced y solar irradiation. The simulated wind data lack this phenomenon. This is illustrated in Fig.. Wind speed [m/s] Amplitude spectum of the measured 3D wind wind speed Lower frequency changes in the windspeed due to changin weather patterns that vary weekly monthly or yearly Diurnal peak Higher harmonics of the diurnal peak Figure : Time series comparison etween measured versus simulated data 1.5 Amplitude spectum of the simulated 3D wind speed 1) Proaility density function of the simulated data In Fig. 7 the PDF of the simulated data is given together with the fitted Weiull functions on the PDF. When the PDF of the simulated data is compared to the real data the similarities are striking, as would also appear from Tale 3 where the Weiull parameters of the fitted curves are given. The parameters in Tale 3 are similar to those in Tale. TABLE III. WEIBULL PARAMETERS OF THE SIMULATED DATA Weiull parameters for the fitted curves in Fig. 1 Function name with v 3 as weight a [95% conf. int.] a [95% conf. int.] a [ ] [ ] [ ] [ ] a. 95% conf.int. meaning 95% confidence interval ) Simulated yearly energy yield and energy storage The yearly kinetic energy in the wind with the PDF of the simulated data would e 35 kwh/m.year. The total electrical energy yield would e exactly the same as with the measured data and equals 17 kwh/m².year. The required energy storage is incorrectly calculated when using the Wind speed [m/s] 1.5 Some spectral information is lost y using Markov chains No peaks Frequency [1/hour] Figure. Amplitude spectrum comparison etween the measured versus simulated data V. CONCLUSION The first part of this paper gives an outline to determine some important parameters for sizing a small wind turine project in an uran environment. The second part of the paper handles aout computer generated wind data. A Markov chain, which is a widely spread tool for generating stochastic data, will not exactly match real wind data. For some calculations the synthetic data will produce the exact result, for other calculations the simulated data can lead to incorrect results. A good summary where the data can or can t e used is found in [1]. For example, using a Markov chain will produce the correct PDF as well as a correct yearly energy yield. For energy storage calculations the simulated data is unreliale.

5 VI. FURTHER WORK Wind is correlated with solar irradiation as might e seen in the diurnal ehavior of the wind data. Because the diurnal and seasonal information is lost in a single Markov matrix, the use of multiple Markov matrices was thought to give a solution to the prolem of information loss. The sudividing of the Markov matrix in multiple matrixes was ased on daily sunrise and sunset times. The synthetic data has een tested ut the results are not noticealy improved y this method. This is the case for 15 minute time steps. The method might improve the results for other time steps as proven in [1]. The computer model must e refined to e ale to calculate system parameters more exactly. Maye higher order Markov processes may e improved y this method. ACKNOWLEDGMENT The authors wish to thank the IOF ( Industriëel Onderzoeks Fonds ) funding which makes this research possile. REFERENCES [1] K. Brokish and J. Kirtley, Pitfalls of modeling wind power using Markov chains, Power Systems Conference and Exposition, 9, pp 1-. [] T. Ackermann, Wind Power in Power Systems. John Wiley & Sons, Ltd, England, 5. [3] P. Souto Pérez, Improved modelling methodologies for the integration of large-scale wind power in the electricity grid, Doctoral thesis, 11. [] F. Youcef Ettoumi, H. Sauvageot, A. -E. -H. Adane, Statistical ivariate modeling of wind using first order Markov chain and Weiull distriution. Renewale Energy., 3, pp [5] M. Van Dessel and G. Deconinck, "Power electronic grid connection of PM synchronous generator for wind turines," in Proc. 3th Annual Conf. of IEEE Industrial Electronics Society (IECON-) Orlando (FL), USA: IEEE,, pp. -5. [] Šúri M., Huld T.A., Dunlop E.D. Ossenrink H.A., 7. Potential of solar electricity generation in the European Union memer states and candidate countries. Solar Energy, 1, , [7] A. Shamad, M. A. Bawadi, W. M. A. Wan Hussin, T.A. Majid, S. A. M. Samussi, First and second order Markov chain models for synthetic generation of wind speed time series. Energy. 3,5, pp 93-7.