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Climatic conditions for operation of wind turbines in Hungary
Renewable Energy 36 (2011) 510e518
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Climatic conditions for operation of wind turbines in Hungary Károly Tar a, *, István Farkas b, Kornél Rózsavölgyi c a
Department of Meteorology, University of Debrecen, H-4010 Debrecen, P.O. Box 13, Hungary }, Hungary Department of Physics and Process Control, Szent István University, Gödöllo c Wind Science and Engineering Research Center, Texas Tech University, Texas, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2009 Accepted 24 June 2010 Available online 14 August 2010
According to wind-climatic requirement of wind farms wind speed should exceed the so called cut-in speed. If this inequality is realized then regarding the wind-climatic features of Hungary the following conditions may occur: the wind turbine is operating with high probability, energy is generated; it is working in a regulated mode with low probability; it is not working with very low probability. Therefore in terms of continuous energy production by wind one question arises: are there any temporal and/or orographic shifts in different heights compared to the wind-climatic condition mentioned above. In this paper this question is analyzed on the basis of seven Hungarian meteorological stations that have hourly measured wind speed data considering the period between 1991 and 2000. The probability of wind speeds exceeding 3 m/s, statistics of wind speed intervals higher and lower than 3 m/s and statistics of average hourly wind speed intervals higher than 3 m/s were analyzed at the heights of 10, 30 and 60 m. A statistical parameter that is proportional to the average specific wind power of a day in a time period was defined and, its connection to the average length of those intervals that have higher or equal hourly average wind speeds more than 3 m/s in a given month was investigated. With the help of such parameters the value of monthly average specific wind power can be estimated. Published by Elsevier Ltd.
Keywords: Wind speed distribution Power law Daily run and hourly probability of wind speed Wind speed intervals Monthly mean specific wind power
1. Introduction 108 wind turbines worked in Hungary, in 32 points of the country, coming from 5 manufacturers, at the end of 2009 [1]. One of the most important parameters of these wind turbines is the cutin speed (vci), which is less than 4 m/s in more than 70% of the cases, according to the homepages and the different product catalogs of the manufactures. The values of the related (vr) and the cut-out (vco) wind speeds are found also in these sources. According to the power curve of wind turbines if wind speed (v) reaches or surpasses vci speed then energy production commences the quantity of which is proportional to the third power of wind speed until the nominal performance related wind speed (vr). The related wind speed is between 12 m/s and 14 m/s at Hungarian wind farms. Wind turbines operate when wind speed reaches the cut-in speed until the so called cut-out speed, which is usually vco ¼ 25 m/s. In this case the wind turbine operates on nominal performance (Pr), however, when winds reach the speed of vco the system stops working due to safety concerns. Statistical analysis of these wind speed domains (Table 1) is indispensable in terms of continuously operating wind farms. * Corresponding author. Tel./fax: þ36 52 512 927. E-mail address: [email protected] (K. Tar). 0960-1481/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.renene.2010.06.034
In order to simulate the electric power output of a wind turbine the following equations are used generally [2,3]:
P ¼ 0
if v < vci vk vkci P ¼ Pr if vci v vr vkr vkci P ¼ Pr if vr < v vco P ¼ 0 if v > vco
(1)
where v is wind speed and k is the shape-factor of the Weibull probability distribution function. At potential wind speed analysis, the frequency distribution of observed wind speeds is approximated by the Weibull distribution. The most obvious reason for this is if the two required parameters (k and c scale-parameter) are calculated from the measured data at a given altitude then having these outcomes these parameters (k and c) can be calculated to different altitudes as well [4]. Other examinations and researches confirm that this method is correct, in other words potential wind energy of given period is determined by distribution of wind speed [5e8]. If the distribution of wind speed is examined in a given altitude, Rayleigh or lognormal distribution can be used because the parameters of these distributions can be predicted easily.
K. Tar et al. / Renewable Energy 36 (2011) 510e518
Table 1 Important wind speed domains in terms of continuously operating wind farms.
Nomenclature v vci vco vr
a f l
h ha p3(t) p3(h) P3(t) kmax [k] R2 b Tac [I]
wind speed cut-in wind speed cut-out wind speed related wind speed Hellmann power law exponent geographical latitude geographical longitude altitude above sea level altitude above the ground of the anemometer average hourly probabilities of wind speeds higher than 3 m/s average probabilities of wind speed higher than 3 m/s continuously changing probabilities of wind speeds higher than 3 m/s maximum length of wind speed intervals higher/ lower than 3 m/s average length of wind speed intervals higher/lower than 3 m/s quadrant of the correlation index constant of gradient of the curve the area beneath the approximation function length of intervals that have v 3 m/s hourly average wind speeds
Measured wind speed values at the altitude of anemometer in a moment can be transformed to different altitudes by the Hellmann power law equation:
v1 ¼ v2
h1 h2
511
a (2)
According to our previous studies [9,10] the a average values for } 0.26, the selected sites in Hungary are the followings: Kékesteto Szombathely 0.26, Keszthely 0.32, Pécs 0.27, Budapest 0.28, Szeged 0.26, Debrecen 0.27. These values (except for the value at Keszthely) are rather close to the average a value (0.25) that is recommended for calculations for Hungary. By the virtue of SODAR examinations
Category
Explanation
v vci
Wind generator is operating and produces electricity Wind generator is operating and produces increasing electricity Wind generator is operating at maximum performance under control
vci v < vr vr v < vco
[11] in the case of those wind speeds that exceed 3 m/s this exponent is expected to be between 0.2 and 0.3 at Budapest and Szeged. There were examinations for momentary and average values of a depending on the roughness of the surface, atmospheric equilibrium and wind speed [5,8,12]. From the results of these papers it can be assessed that above flat and low roughness territories the value of a can be approximated well with 1/7 z 0.14 until the altitude of 100 m i.e. in range of 5e6 m/s wind speed. Although according to Ref. [6], a value of 0.25 is the standard value for Egyptian terrains and wind conditions. Nevertheless in other cases in Refs. [13,6] different equation was derived from (2) for transformation of vertical wind speeds.
2. Aim and database of the study The vci v < vco inequality can be considered as the windclimatic assumption for operation of wind farms. If this condition is accepted then due of the wind-climatic features of Hungary the following cases are possible: the wind turbine is operating with high probability, it is operating in a regulated mode with low probability, it is not operating with very low probability. In terms of continuous energy production by wind flow the following question arises: are there any temporal and/or orographic shifts in different heights in Hungary compared to the wind-climatic condition mentioned above. In this paper this question is analyzed on the basis of seven Hungarian meteorological stations that have hourly measured wind speed data from period between 1991 and 2000. In Fig. 1 the geographical position of the meteorological observatories can be seen. The used database was from these stations. Seven
Fig. 1. Geographical positions of the meteorological observatories comprising the whole database.
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K. Tar et al. / Renewable Energy 36 (2011) 510e518
Table 2 Geographic coordinates of the involved meteorological stations and the altitudes of anemometers from the ground. Met. station High land } Kékesteto Non-lowland Szombathely Keszthely Pécs Lowland Budapest-L. Szeged Debrecen
f
l
h (m)
ha (m)
47 520
20 010
1011
26
47 160 46 460 46 000
16 380 17 140 18 140
219 117 201
9 15 10
47 270 46 150 47 300
19 130 20 060 21 380
130 83 111
12 9 10
exceeded this chosen cut-in speed value. In those speed intervals that were determined by the other two options (see Table 1) the transformations (2) led to low case numbers that are not interpretable statistically. 3. Probability of wind speeds exceeding 3 m/s Probability of those wind speed values that are higher or equal to 3 m/s on a day at a given ‘t’ hour and ‘h’ altitude can be approached by this equation
p3 ðtÞ ¼ observatories were chosen where wind speed can be considered homogeneous. Geographic coordinates of these observatories and the altitude of their anemometer can be found in Table 2 grouped by orographic environment. It is rather certain that over the height of 60 m above the ground the daily run of hourly wind speeds is in reverse with converse extreme value at around 1 pme2 pm than below the height of 60 m [11,14,15]. Calculating without daily run i.e. constant exponent (a) we will not be able to get this phenomenon. According to some simulation results this 60 m is a special boundary altitude in Hungary, as above this altitude the surface has no significant impact on the wind field like beneath the height of 60 m [16e18]. Hence our examinations are limited to the heights of 10 m, 30 m and 60 m. The cut-in speed was chosen as 3 m/s and statistical analysis of the entire time interval were only performed when wind speeds
gðt=v 3Þ N
(3)
where numerator is the conditional frequency of these wind speed values at t time and N is the number of examined days of the season. Daily run of probabilities can be seen in Fig. 2 in three different altitudes that were calculated by the help of the position dependent Hellmann exponent. Daily runs can be seen in this figure that do not show significant orographic and altitude differences. Values are increasing in the }), between 1 pm and 2 pm morning from 6 am (except for Kékesteto } ) then values reach their maximum (the minimum is at Kékesteto } ) until 7 pm and values are decreasing (increasing at Kékesteto finally at night values are changing insignificantly at all heights and at all of the observatories. Some of the values, which belong to a particular time, indicate significant differences on the basis of geographic position and altitude. Most of the times at all altitudes the following descending order can be noticed: Szeged,
Fig. 2. Daily run of average hourly probabilities of wind speeds higher than 3 m/s (1991e2000).
K. Tar et al. / Renewable Energy 36 (2011) 510e518
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Table 3 Average probabilities (p3(h)) of wind speed higher than 3 m/s (1991e2000); a: stations in orographic grouping with the yearly average operation time (a.op.time), b: probabilities in descending order. a
10 m
30 m
60 m
p3(h)
a.op.time
p3(h)
a.op.time
p3(h)
a.op.time
Debrecen Szeged Budapest Szombathely Keszthely Pécs } Kékesteto
0.396 0.463 0.262 0.434 0.155 0.425 0.534
3469 4056 2295 3802 1358 3723 4678
0.509 0.609 0.446 0.560 0.272 0.566 0.696
4459 5335 3907 4906 2383 4958 6097
0.644 0.719 0.564 0.671 0.387 0.688 0.748
5641 6298 4941 5878 3390 6027 6552
b 10 m 0.534 0.463 0.434 0.425 0.396 0.262 0.155
30 m Kékes Szeged Szombathely Pécs Debrecen Budapest Keszthely
0.696 0.609 0.566 0.560 0.509 0.446 0.272
60 m Kékes Szeged Pécs Szombathely Debrecen Budapest Keszthely
0.748 0.719 0.688 0.671 0.644 0.564 0.387
Kékes Szeged Pécs Szombathely Debrecen Budapest Keszthely
} the Szombathely, Pécs, Debrecen, Budapest, Keszthely. At Kékesteto minimum values vary between 0.4 and 0.7 approximately around 12 ame13 pm in all altitudes. The daily mean values and the yearly mean operating times are shown in Table 3a, grouped by orographic environment (lowland, not lowland, highland) for the entire examined season. Table 3b consists of the probabilities in descending order. Of course, highest } and the above mentioned order of the values appeared at Kékesteto observatories is only true in the height of 10 m because at the other two heights the positions of Szombathely and Pécs was changed indicating the unutilized wind prospects of southern Hungary. Most of the old windmills were built there. According to some examinations, the positions of the old windmills locate precisely those areas where utilization of wind energy could be economic in all probabilities [19,20]. In Fig. 3 and Fig. 4 conditioned spatial geometry patterns of average probabilities of v 3 m/s wind speeds (1991e2000) were calculated and mapped with the help of the spline interpolation algorithm (ArcGIS) [21,22].
Fig. 4. Contingent map of average probabilities of v 3 m/s wind speeds at the height 60 m.
With 50 m of altitude difference, greatest change of average probabilities is experienced at Keszthely: at 60 m it is 2.5 times greater than at the height of 10 m. At most of the observatories this ratio (p3(60)/p3(10)) is the following: Budapest 2.2, Pécs, Debrecen } 1.4. and Szeged 1.6, Szombathely 1.5, Kékesteto Average values of the three examined altitudes are indicated in Fig. 5. Using approximating power function y ¼ axb intermediate values, that belong to various altitudes can be calculated. Values of the }). correlation index are between 0.999 (Keszthely) and 0.982 (Kékesteto By the help of fitting power functions a new equation, that is similar to the Hellmann formula, can be determined for the mean probability of height depending wind speeds that are higher than 3 m/s:
p3 ðh1 Þ ¼ p3 ðh2 Þ
h1 h2
a 3 (4)
Time depending (hour) probability of wind speeds that are higher than 3 m/s was defined by another method: the continuously changing (in time) probabilities were defined until the given time (P3(t)). Thus P3(t) probabilities are approached by the ratio of the frequency of v 3 cases occurred until t hour and the elapsed time:
p (h) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Debrecen
Szeged
Budapest
Szombathely
Keszthely
Pécs h (m)
Kékestető 0.0 10
Fig. 3. Contingent map of average probabilities of v 3 m/s wind speeds at the height of 10 m.
15
20
25
30
35
40
45
50
55
60
Fig. 5. Average probabilities of calculated wind speeds higher than 3 m/s at 10, 30, 60 m and approximation with power function.
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K. Tar et al. / Renewable Energy 36 (2011) 510e518
Fig. 6. Daily run of continuously changing probabilities.
Pt P3 ðtÞ ¼
i¼1
gði=v 3Þ Nt
(5)
Its daily run at all of the seven meteorological stations can be seen } ) that it in Fig. 6. It can be assessed (except for P3(t) at Kékesteto reaches its minimum at dawn and early in the morning and from this point on it reaches its maximum in a monotone increasing way in every altitude and at all of the stations at around 5 pme6 pm. Consequently, increasing energy production is anticipated until the maximum rate in a day, however, after this time decreasing energy } minima occurs at 5 pm production is expected. At Kékesteto therefore in this altitude the situation is reverse. Significant changes can be noticed in the average daily run of the temporally continuously changing probability. This oscillation (maximum-minimum) influences the average daily energy production and variability of electricity. According to Table 4 at Szeged, Pécs and Szombathely, e these are the non highland stations where probability of wind speeds higher than 3 m/s is high e the oscillation is decreasing by increasing altitude. At Keszthely where the average probability is the lowest oscillation is increasing with height. At the other observatories (in Debrecen, Budapest and in } ) maxima of the oscillation can be observed in 30 m. Kékesteto 4. Statistics of speed intervals higher and lower than 3 m/s wind speed With the help of hourly wind speed continuous time series, the length of those intervals that have higher, lower or the same speed as 3 m/s were determined for all the observatories and altitudes.
Our continuous time series consist of 24*N members where N is equal to the considered number of days in the examined period (1991e2000). If all of the hourly wind speed data is provided from all days of every month then our time scale has 3653 elements. In case of missing days (where some of the 24 data of a day are not available) determination of the elapsed time depending statistics is restarted. In Table 5 maximum and average length of the intervals that have wind speed higher, equal or lower than 3 m/s are indicated. From this table the following can be concluded: In the case of v 3 m/s at all of the considered observatories and } and the absolute heights, maximum values occurred at Kékesteto maximum appeared here at 60 m (kmax ¼ 334 h, [k] ¼ 14.9 h) as well. Considering average lengths at all three altitudes Szeged is the next. Nevertheless at the height of 30 m and 60 m Budapest and Keszthely close the order in every altitude. In a height of 50 m difference in the average lengths vary less than the proper average
Table 4 Ranges (maximum-minimum) in daily run of continuously changing probabilities depending on height.
Debrecen Szeged Budapest Pécs Keszthely Szombathely Kékes
10 m
30 m
60 m
0.135 0.156 0.121 0.100 0.068 0.146 0.113
0.140 0.138 0.146 0.092 0.114 0.135 0.115
0.137 0.128 0.139 0.089 0.156 0.130 0.112
K. Tar et al. / Renewable Energy 36 (2011) 510e518
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Table 5 Maximum (kmax in hours and days) and average ([k] in hours) length of intervals having wind speeds higher or lower than 3 m/s.
v 3 m/s 10 m
30 m
60 m
v < 3 m/s 10 m
30 m
60 m
Debrecen
Szeged
Budapest
Szombat-hely
Keszthely
Pécs
} Kékesteto
kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour)
102 4.3 6.2 164 6.8 7.3 170 7.1 8.5
134 5.6 6.6 166 6.9 8.0 311 13.0 10.0
90 3.8 4.9 109 4.5 5.9 135 5.6 6.8
139 5.8 6.2 146 6.1 6.7 146 6.1 7.6
102 4.3 4.6 109 4.5 5.0 112 4.7 5.7
96 4.0 5.5 137 5.7 7.1 197 8.2 8.5
228 9.5 10.2 243 10.1 13.1 334 13.9 14.9
kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour)
211 8.8 9.5 152 6.3 6.5 152 6.3 4.7
164 6.8 7.2 131 5.5 5.1 89 3.7 3.9
405 16.9 13.7 159 6.6 6.7 117 4.9 4.5
122 5.1 7.6 100 4.2 5.2 95 4.0 3.7
407 17.0 24.6 317 13.2 12.6 203 8.5 8.1
145 6.0 7.4 134 5.6 4.9 104 4.3 3.9
183 7.6 8.4 76 3.2 5.7 57 2.4 4.7
probabilities. Therefore the ratio is the following: Pécs, Szeged and }: 1.5, Budapest and Debrecen: 1.4, Keszthely and SzomKékesteto bathely: 1.2. In the case of v < 3 m/s, it is reasonable to examine some of the minima of the interval lengths. However, the situation is not as unified as in the previous case. At 10 m and 30 m the minimum of maximal length can be noticed at Szombathely, although at Szeged this minimum appears at 60 m that is the absolute minimum at the same time (kmax ¼ 89 h). In case of average lengths different orders are developed in all of the altitudes with the maximum at Keszthely. At the altitude of 50 m difference of the ratios is between 0.3 and 0.6. Distribution of the length (1, 2, 3, ., 24, >24 h) of the intervals that have hourly wind speeds higher than 3 m/s shows an interesting result. There are notable margins among the meteorological stations and various altitudes in the case of one or 2 h long sessions as well as in the case of the sessions longer than 24 h. The power function fits best in all cases for the distribution of 1e24 h long intervals. However, these intervals do not give the full probability back thus it can just be conjectured that the distribution of intervals, that have wind speeds higher or lower than 3 m/s follow Udistribution [23,24]. Distribution of interval lengths containing hourly wind speeds higher or equal to 3 m/s exceeding various thresholds (1, 2, 3, .,
24 h) is sharply different at various heights at all of the seven stations. However, there are some similarities in these distributions at some of the stations. The curves start around 0.6e0.7 everywhere hence the probability of the intervals longer than 1 h is approximately equal at all of the seven meteorological stations and at all heights. These curves can be approximated with an exponential function y ¼ a*ebx in every case. If logarithm of probabilities is taken into consideration then b gains expressive meaning hence gradient of linear function Y ¼ A þ bx can be expressed by b. In fact, the gradient of the curves at a point, that is equal to the slope of the tangent line of x, is a function of b. Comparing these, the run of the original curves is determined. In Table 6 the values of parameter b and quadrant of correlation indexes (R2), which were calculated by exponential function approximation, are indicated. According to this table, the gradient of the curves (to linear transformed) increase with height at all observatories. Order of observatories on the basis of parameter b is not the same at all heights: at 30 m and 60 m Keszthely, Budapest, Szombathely, Debrecen, Pécs, Szeged } . While at the altitude of 10 m just the first two and and Kékesteto the last places are the same. The distribution of different thresholds exceeding length of intervals that have lower hourly wind speed data than 3 m/s was also investigated. It can be noticed that these curves are different from each other according to altitude at all of the observatories. The
Table 6 Quadrants of correlation indexes (R2) that were calculated on the basis of the distribution of the length of intervals having hourly wind speeds higher or equal to 3 m/s, fit exponential function, typified constant of gradient of curves (b).
Table 7 Quadrants of correlation indexes (R2) that were calculated on the basis of the distribution of the length of intervals having hourly wind speeds lower than 3 m/s, fit exponential function, typified constant of gradient of curves (b).
Debrecen Szeged Budapest Pécs Keszthely Szombathely } Kékesteto
R2 b R2 b R2 b R2 b R2 b R2 b R2 b
10 m
30 m
60 m
0.989 0.113 0.995 0.116 0.990 0.143 0.988 0.124 0.978 0.147 0.982 0.114 0.982 0.077
0.991 0.100 0.991 0.093 0.987 0.116 0.983 0.098 0.985 0.130 0.988 0.110 0.979 0.066
0.990 0.089 0.990 0.077 0.989 0.103 0.978 0.086 0.992 0.125 0.991 0.102 0.975 0.061
Debrecen Szeged Budapest Pécs Keszthely Szombathely } Kékesteto
R2 b R2 b R2 b R2 b R2 b R2 b R2 b
10 m
30 m
60 m
0.995 0.090 0.996 0.109 0.993 0.068 0.992 0.100 0.986 0.042 0.996 0.112 0.992 0.092
0.996 0.127 0.996 0.142 0.997 0.119 0.995 0.145 0.992 0.070 0.998 0.162 0.998 0.142
0.997 0.164 0.996 0.193 0.993 0.161 0.996 0.190 0.986 0.109 0.997 0.229 0.999 0.182
516
K. Tar et al. / Renewable Energy 36 (2011) 510e518 [v(t)] (m/s)
Debrecen, May, 1991., 10 m
4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0
t (hour) 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Fig. 7. Daily run of hourly average wind speeds at Debrecen on 10th of May 1991 at the height of 10 m (wind speeds higher than 3 m/s are indicated by filled markers).
curves start from 0.6 to 0.7 except for Keszthely as here this interval starts from 0.7 to 0.8, thus probability of intervals longer than 1 h is highest at Keszthely. The curves end at all altitudes under 0.1 probability except for Budapest and Keszthely, thus probability of intervals longer than 24 h is lower than this. Furthermore this value is lower than 0.05 at 30 m and 60 m as well. While at Budapest at the height of 10 m and at Keszthely at the height 10 m and 30 m the probability of those intervals that are longer than 24 h and have lower hourly wind speed than 3 m/s is above 0.1. The curves can still be approximated by y ¼ a*ebx exponent function. According to Table 7, the gradient of the curves is decreasing by altitude at all observatories. Ascendant order of observatories according to }, b parameter at all altitudes: Szombathely, Szeged, Pécs, Kékesteto Debrecen, Budapest, Keszthely, therefore curves are flatter at those places that have high nominal wind performance. 5. Statistics of intervals of average hourly wind speed higher than 3 m/s Various statistical features of intervals of 3 m/s or higher hourly average wind speeds are analyzed monthly on the basis of distribution of length from January of 1991 till December of 2000. The problem is illustrated on the Fig. 7: length of the illustrated interval is 13 h.
Fig. 8. Values of trigonometric polynomial ([v3]fit) that was fit to the daily run of the hourly average of wind speed cubes ([v3]) and area under the curve (Tac) at Debrecen at the height of 10 m in May 1991.
In an optimal case these intervals belong to a time scale of 120 elements, at a given place and height. They are indicated by [I]i (i ¼ 1,2,3,.,120). Basic statistics of time scales are indicated in Table 8. According to this table, it can be concluded that the calculated average for the entire examined period increases with altitude. The descending order of the observatories is the same at }, Szombathely, Szeged, Pécs, Debrecen, all altitudes: Kékesteto Budapest, Keszthely. Consequently, at high energy places the average length of intervals, that have higher average wind speed than 3 m/s or equal average wind speed to 3 m/s is great. Greatest changes in the ratio of averages occur at the height of 50 m (16.5 times) and it changes least where the nominal wind performance is }, Szombathely, Szeged, Pécs). Variation of the significant (Kékesteto average (independent from volume and number of sample elements) value, coefficient of variation (relative deviation) decrease everywhere by altitude and this decrease shows different order at the three altitudes. The absolute maximum of the coefficient of variation is at Keszthely at the height of 10 m (2.88) and the } at absolute minimum of the coefficient of variation is at Kékesteto the height of 60 m (0.07). According to Table 8, these are strongly asymmetric and kurtosis distributions, hence maybe, this was the reason why it could not have been approximated by the known
Table 8 Basic statistics of intervals of hourly average wind speeds higher than 3 m/s (%: average length in % of length of day).
Debrecen
Szeged
Budapest
Pécs
Keszthely
Szombathely
} Kékesteto
10 30 60 10 30 60 10 30 60 10 30 60 10 30 60 10 30 60 10 30 60
m m m m m m m m m m m m m m m m m m m m m
Mean
%
St.dev.
Var.coeff.
Mode
Median
Skewness
Kurtosis
8.2 17.5 21.9 13.4 20.6 22.9 3.6 13.6 20.8 11.2 19.8 21.9 0.7 5.4 11.1 14.7 21.2 23.3 15.4 21.8 23.5
34.3 73.1 91.3 55.9 85.7 95.2 14.8 56.8 86.5 46.7 82.4 91.2 2.8 22.5 46.3 61.4 88.2 97.1 64.1 91.0 98.1
6.2 5.9 3.9 6.3 4.9 2.9 4.0 6.6 4.6 7.6 6.3 4.3 1.9 4.9 6.2 6.6 4.3 2.2 8.1 4.1 1.7
0.76 0.34 0.18 0.47 0.24 0.13 1.14 0.48 0.22 0.68 0.32 0.19 2.88 0.91 0.56 0.45 0.20 0.09 0.53 0.19 0.07
0 24 24 9 24 24 0 24 24 24 24 24 0 0 7 24 24 24 24 24 24
7 18 24 12 24 24 2 13 23 10 24 24 0 5 9 13 24 24 17 24 24
0.952 0.448 1.987 0.243 1.097 2.854 0.885 0.007 1.400 0.328 1.147 1.850 3.270 0.899 0.718 0.011 1.466 4.408 0.487 1.765 4.569
0.557 0.799 3.101 0.827 0.272 7.969 0.065 0.775 0.845 1.017 0.169 1.919 10.881 0.588 0.284 0.989 1.078 23.581 1.027 1.795 23.252
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Table 9 The area beneath the curve (Tac) that is proportional to the monthly average specific wind power and basic statistics of lengths of intervals that have v 3 m/s hourly average wind speeds ([I]) as well as parameters of assumed linear relationship.
Tac (m3/s3)
Mean St.dev. Var.coeff. [I] (hour) Mean St.dev. Var.coeff. correlation coefficient (Tac,[I]) determination coefficient (%) regression coefficient (Tac,[I])
Debrecen
Szeged
Budapest
Pécs
Keszthely
Szombathely
} Kékesteto
1252.1 619.8 0.50 8.2 6.2 0.76 0.812 66 80.7
1792.5 855.5 0.48 12.4 6.3 0.50 0.757 57 103.6
934.0 454.9 0.49 4.9 4.5 0.91 0.828 69 84.6
1612.0 898.1 0.56 11.2 7.6 0.68 0.818 67 96.1
832.5 654.5 0.79 1.7 3.1 1.87 0.675 46 143.2
3250.7 2178.3 0.67 14.0 6.7 0.48 0.794 63 258.2
3775.1 2021.5 0.54 21.4 4.6 0.22 0.620 38 272.0
distributions. The coefficient of skew decreases by altitude at Debrecen, Szeged, Budapest, Pécs and Szombathely: at 10 m it is positive (left-sided asymmetry) and at the other two altitudes it is negative (right-sided asymmetry). This means that at the height of 10 m smaller while at the other two heights higher values occur } the more frequently than the average. At Keszthely and Kékesteto standards of skewness decrease by altitude, however, at the previous station it is positive at every height and at the latter station it is negative at every height. Regarding the coefficient of kurtosis no regularity at all can be noted. However, it is revealed } and Szomthat this coefficient gains maximum both at Kékesteto bathely (the two places that have the biggest wind resources) at altitudes of 30 m and 60 m. In the following part of this paper the dependence of the monthly average specific wind power on the length of those intervals that have higher or equal hourly average wind speed than 3 m/s in a given month is discussed. Features of monthly average specific wind power were analyzed by a trigonometric polynomial that was fit to the average of hourly wind speeds on the power of three. This simple harmonic model was applied by [8] to determine the parameters of wind profiles. In our case the area beneath the curve (Tac) was calculated by definite integral of this trigonometric polynomial (Fig. 8) [9,25]. Linear correlation and regression of (Tac) and [I] monthly values at the height of the anemometer were analyzed. Most important statistical features, coefficients of correlation and constants of regression are presented in Table 9. According to this table the two averages have the same } , Szombathely, descending order regarding volume: Kékesteto Szeged, Pécs, Debrecen, Budapest, Keszthely suggesting a positive correlation. The coefficients of correlation are indicated in the seventh record. All of them are highly significant (r0,05 z 0.19) at Budapest, Pécs and Debrecen (higher than 0.8) followed by Szom} . Although bathely and Szeged and finally Keszthely and Kékesteto orographic difference cannot be noticed, it is surprising that the places of highest and lowest wind energy are the same. The explanation of this phenomenon at Keszthely is that there are numerous months when at the altitude of anemometer (15 m) } the number of those months when at the [I] ¼ 0 h and at Kékesteto altitude of anemometer [I] ¼ 24 h is high. These impair the tightness of stochastic connection. The order above does not concur with any other order even not with the order of regression coefficients. This latter order is: } , Szombathely, Keszthely, Szeged, Pécs, Budapest and Kékesteto Debrecen. Thus if the length of the interval that represents higher or equal hourly average wind speed as 3 m/s changes with 1 h then it has the smallest impact on specific wind power at Debrecen. This impact is 1.5 times higher at Szombathely and it is more than 3 } . On the basis of regression equations, times higher at Kékesteto linear connections can be detected at Szombathely (values are } (values are higher than higher than value [I] at 1 h) and Kékesteto value [I] at 7 h).
According to the determination coefficients the monthly average specific wind power is determined by of length of intervals of hourly average wind speed of 3 m/s or higher. The biggest dependence was determined at Budapest, Pécs and Debrecen (69, 67 and 66% respectively). At Szombathely, Szeged, and Keszthely moderate dependence was determined (63, 57 and 46% respec} this dependence proved to be the tively). Finally at Kékesteto lowest (38%). 6. Conclusions The most important results of this study can be summarized as follows. There are no orographic similarities, uniformities in the daily run of probabilities of v 3 m/s hourly wind speeds. The maximum value of this probability is around 1 pme2 pm. According to the daily run of continuously changing (cumulative in time) probabilities we can calculate with increasing energy production until 5 pme6 pm. There are no orographic similarities and differences by height in the order or by size of average length of time intervals with v 3 m/s hourly wind speed. There are different orographic orders depending on the height in the average length of time intervals with v < 3 m/s hourly wind speed. They are more disordered than the former ones. The length of time intervals with v 3 m/s hourly average wind speed by months has an effect on the monthly mean specific wind power between 38% and 69%. The monthly mean specific wind power responds more sensitively to the change of lengths of these intervals at the non-plain observatories than at the plain observatories. Acknowledgements The research on the wind climate of Hungary was supported by OTKA (Hungarian Scientific Research Fund, program: T 023765). The authors thank the Hungarian Meteorological Service for providing data for the analysis. References [1] Homepage of the Hungarian wind energy association, www.mszet.hu. [2] Torres JL, Prieto E, Garcia A, De Blas M, Ramirez F, De Francisco A. Effects of the model selected for the power curve on the site effectiveness and the capacity factor of a pitch regulated wind turbine. Solar Energy 2003;74:93e102. [3] Hrayshat ES. Wind resource assessment of the Jordanian southern region. Renewable Energy 2007;32:1948e60. [4] Justus CG, Hargaves WR, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology 1978;17:350e3. [5] Pérez IA, Garcia MA, Sánchez ML, De Torre B. Analysis and parameterization of wind profiles in the low atmosphere. Solar Energy 2005;78:809e21. [6] Cellura M, Cirrincione G, Marvuglia A, Miraoui A. Wind speed spatial estimation for energy planning in Sicily: a neural kriging application. Renewable Energy 2008;33:1251e66. [7] Shata ASA, Hanitsch R. Evaluation of wind energy potential and electricity generation on the coast of Mediterranean Sea in Egypt. Renewable Energy 2006;31:1183e202.
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[8] Nfaoui H, Buret J, Sayigh AAM. Wind characteristics and wind energy potential in Morocco. Solar Energy 1998;63:51e60. [9] Tar K. Energetic characterization of near surface windfield in Hungary. Renewable and Sustainable Energy Reviews 2008;12:250e64. [10] Tar K. Some statistical characteristics of monthly average wind speed at various heights. Renewable and Sustainable Energy Reviews 2008;12:1712e24. [11] Varga B, Németh P, Dobi I Magyarországi szél- és napenergia kutatás eredményei. Országos Meteorológiai Szolgálat/Hungarian Meteorological Society; 2006. pp. 7e20 [in Hungarian]. [12] Hussain M. Dependence of power law index on surface wind speed. Energy Conversion and Management 2002;43:467e72. [13] Voorspools K, D’haeseleer W. Impact assessment of using wind power. Solar Energy 2006;80:1165e78. [14] Radics K, Bartholy J. Estimating and modelling the wind resource of Hungary. Renewable and Sustainable Energy Reviews 2008;12:874e82. [15] Bíróné Kircsi A. Climatological aspects of utilization of wind energy. PhD thesis, Department of Meteorology, University of Debrecen; 2008. [16] Wieringa J. An objective exposure correction method for average wind speeds measured at sheltered location. Quarterly Journal of the Royal Meteorological Society 1976;1002:241e53.
[17] Wieringa J. Description requirements for assessment of non-ideal wind station e for example Aachen. Journal of Wind Engineering and Industrial Aerodynamics 1983;11:124e31. [18] Rozsavolgyi K. Spatial complex model for wind farm site assessment. Open Atmospheric Science Journal 2009;3:204e11. doi:10.2174/1874282300903010204. [19] Bárány I, Vörös E, Wagner R. The influence of the wind conditions of the Hungarian Alföld on the geographical distribution of mills. Acta Climatologica, Tom. IX., fasc 1970;1e4:73e81. [20] Keveiné Bárány I. A climatic background to the utilization of wind energy in the } , XL 1991;3e4:355e69 [in Hungarian]. Great Hungarian Plain. Földrajzi Értesíto [21] Kerseya S, Laib M-J. Convergence of local variational spline interpolation. Journal of Mathematical Analysis and Applications 2008;341:398e415. [22] Hancockand PA, Hutchinsona MF. Spatial interpolation of large climate data sets using bivariate thin plate smoothing splines. Environmental Modelling and Software 2005;21:1684e94. [23] Essenwanger O. Applied statistics in atmospheric science. AmsterdamOxford-New York: Elsevier Scientific Publishing Company; 1976. [24] Schönwiese CD. Praktische Statistik für Meteorologen und Geowissenschaftler. Berlin-Stuttgart: Gebrúder Borntraeger; 2000. [25] Tar K. Diurnal course of potential wind power with respect to the synoptic }járás 2007;111:261e79. situation. Ido
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Climatic conditions for operation of wind turbines in Hungary Károly Tar a, *, István Farkas b, Kornél Rózsavölgyi c a
Department of Meteorology, University of Debrecen, H-4010 Debrecen, P.O. Box 13, Hungary }, Hungary Department of Physics and Process Control, Szent István University, Gödöllo c Wind Science and Engineering Research Center, Texas Tech University, Texas, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 June 2009 Accepted 24 June 2010 Available online 14 August 2010
According to wind-climatic requirement of wind farms wind speed should exceed the so called cut-in speed. If this inequality is realized then regarding the wind-climatic features of Hungary the following conditions may occur: the wind turbine is operating with high probability, energy is generated; it is working in a regulated mode with low probability; it is not working with very low probability. Therefore in terms of continuous energy production by wind one question arises: are there any temporal and/or orographic shifts in different heights compared to the wind-climatic condition mentioned above. In this paper this question is analyzed on the basis of seven Hungarian meteorological stations that have hourly measured wind speed data considering the period between 1991 and 2000. The probability of wind speeds exceeding 3 m/s, statistics of wind speed intervals higher and lower than 3 m/s and statistics of average hourly wind speed intervals higher than 3 m/s were analyzed at the heights of 10, 30 and 60 m. A statistical parameter that is proportional to the average specific wind power of a day in a time period was defined and, its connection to the average length of those intervals that have higher or equal hourly average wind speeds more than 3 m/s in a given month was investigated. With the help of such parameters the value of monthly average specific wind power can be estimated. Published by Elsevier Ltd.
Keywords: Wind speed distribution Power law Daily run and hourly probability of wind speed Wind speed intervals Monthly mean specific wind power
1. Introduction 108 wind turbines worked in Hungary, in 32 points of the country, coming from 5 manufacturers, at the end of 2009 [1]. One of the most important parameters of these wind turbines is the cutin speed (vci), which is less than 4 m/s in more than 70% of the cases, according to the homepages and the different product catalogs of the manufactures. The values of the related (vr) and the cut-out (vco) wind speeds are found also in these sources. According to the power curve of wind turbines if wind speed (v) reaches or surpasses vci speed then energy production commences the quantity of which is proportional to the third power of wind speed until the nominal performance related wind speed (vr). The related wind speed is between 12 m/s and 14 m/s at Hungarian wind farms. Wind turbines operate when wind speed reaches the cut-in speed until the so called cut-out speed, which is usually vco ¼ 25 m/s. In this case the wind turbine operates on nominal performance (Pr), however, when winds reach the speed of vco the system stops working due to safety concerns. Statistical analysis of these wind speed domains (Table 1) is indispensable in terms of continuously operating wind farms. * Corresponding author. Tel./fax: þ36 52 512 927. E-mail address: [email protected] (K. Tar). 0960-1481/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.renene.2010.06.034
In order to simulate the electric power output of a wind turbine the following equations are used generally [2,3]:
P ¼ 0
if v < vci vk vkci P ¼ Pr if vci v vr vkr vkci P ¼ Pr if vr < v vco P ¼ 0 if v > vco
(1)
where v is wind speed and k is the shape-factor of the Weibull probability distribution function. At potential wind speed analysis, the frequency distribution of observed wind speeds is approximated by the Weibull distribution. The most obvious reason for this is if the two required parameters (k and c scale-parameter) are calculated from the measured data at a given altitude then having these outcomes these parameters (k and c) can be calculated to different altitudes as well [4]. Other examinations and researches confirm that this method is correct, in other words potential wind energy of given period is determined by distribution of wind speed [5e8]. If the distribution of wind speed is examined in a given altitude, Rayleigh or lognormal distribution can be used because the parameters of these distributions can be predicted easily.
K. Tar et al. / Renewable Energy 36 (2011) 510e518
Table 1 Important wind speed domains in terms of continuously operating wind farms.
Nomenclature v vci vco vr
a f l
h ha p3(t) p3(h) P3(t) kmax [k] R2 b Tac [I]
wind speed cut-in wind speed cut-out wind speed related wind speed Hellmann power law exponent geographical latitude geographical longitude altitude above sea level altitude above the ground of the anemometer average hourly probabilities of wind speeds higher than 3 m/s average probabilities of wind speed higher than 3 m/s continuously changing probabilities of wind speeds higher than 3 m/s maximum length of wind speed intervals higher/ lower than 3 m/s average length of wind speed intervals higher/lower than 3 m/s quadrant of the correlation index constant of gradient of the curve the area beneath the approximation function length of intervals that have v 3 m/s hourly average wind speeds
Measured wind speed values at the altitude of anemometer in a moment can be transformed to different altitudes by the Hellmann power law equation:
v1 ¼ v2
h1 h2
511
a (2)
According to our previous studies [9,10] the a average values for } 0.26, the selected sites in Hungary are the followings: Kékesteto Szombathely 0.26, Keszthely 0.32, Pécs 0.27, Budapest 0.28, Szeged 0.26, Debrecen 0.27. These values (except for the value at Keszthely) are rather close to the average a value (0.25) that is recommended for calculations for Hungary. By the virtue of SODAR examinations
Category
Explanation
v vci
Wind generator is operating and produces electricity Wind generator is operating and produces increasing electricity Wind generator is operating at maximum performance under control
vci v < vr vr v < vco
[11] in the case of those wind speeds that exceed 3 m/s this exponent is expected to be between 0.2 and 0.3 at Budapest and Szeged. There were examinations for momentary and average values of a depending on the roughness of the surface, atmospheric equilibrium and wind speed [5,8,12]. From the results of these papers it can be assessed that above flat and low roughness territories the value of a can be approximated well with 1/7 z 0.14 until the altitude of 100 m i.e. in range of 5e6 m/s wind speed. Although according to Ref. [6], a value of 0.25 is the standard value for Egyptian terrains and wind conditions. Nevertheless in other cases in Refs. [13,6] different equation was derived from (2) for transformation of vertical wind speeds.
2. Aim and database of the study The vci v < vco inequality can be considered as the windclimatic assumption for operation of wind farms. If this condition is accepted then due of the wind-climatic features of Hungary the following cases are possible: the wind turbine is operating with high probability, it is operating in a regulated mode with low probability, it is not operating with very low probability. In terms of continuous energy production by wind flow the following question arises: are there any temporal and/or orographic shifts in different heights in Hungary compared to the wind-climatic condition mentioned above. In this paper this question is analyzed on the basis of seven Hungarian meteorological stations that have hourly measured wind speed data from period between 1991 and 2000. In Fig. 1 the geographical position of the meteorological observatories can be seen. The used database was from these stations. Seven
Fig. 1. Geographical positions of the meteorological observatories comprising the whole database.
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K. Tar et al. / Renewable Energy 36 (2011) 510e518
Table 2 Geographic coordinates of the involved meteorological stations and the altitudes of anemometers from the ground. Met. station High land } Kékesteto Non-lowland Szombathely Keszthely Pécs Lowland Budapest-L. Szeged Debrecen
f
l
h (m)
ha (m)
47 520
20 010
1011
26
47 160 46 460 46 000
16 380 17 140 18 140
219 117 201
9 15 10
47 270 46 150 47 300
19 130 20 060 21 380
130 83 111
12 9 10
exceeded this chosen cut-in speed value. In those speed intervals that were determined by the other two options (see Table 1) the transformations (2) led to low case numbers that are not interpretable statistically. 3. Probability of wind speeds exceeding 3 m/s Probability of those wind speed values that are higher or equal to 3 m/s on a day at a given ‘t’ hour and ‘h’ altitude can be approached by this equation
p3 ðtÞ ¼ observatories were chosen where wind speed can be considered homogeneous. Geographic coordinates of these observatories and the altitude of their anemometer can be found in Table 2 grouped by orographic environment. It is rather certain that over the height of 60 m above the ground the daily run of hourly wind speeds is in reverse with converse extreme value at around 1 pme2 pm than below the height of 60 m [11,14,15]. Calculating without daily run i.e. constant exponent (a) we will not be able to get this phenomenon. According to some simulation results this 60 m is a special boundary altitude in Hungary, as above this altitude the surface has no significant impact on the wind field like beneath the height of 60 m [16e18]. Hence our examinations are limited to the heights of 10 m, 30 m and 60 m. The cut-in speed was chosen as 3 m/s and statistical analysis of the entire time interval were only performed when wind speeds
gðt=v 3Þ N
(3)
where numerator is the conditional frequency of these wind speed values at t time and N is the number of examined days of the season. Daily run of probabilities can be seen in Fig. 2 in three different altitudes that were calculated by the help of the position dependent Hellmann exponent. Daily runs can be seen in this figure that do not show significant orographic and altitude differences. Values are increasing in the }), between 1 pm and 2 pm morning from 6 am (except for Kékesteto } ) then values reach their maximum (the minimum is at Kékesteto } ) until 7 pm and values are decreasing (increasing at Kékesteto finally at night values are changing insignificantly at all heights and at all of the observatories. Some of the values, which belong to a particular time, indicate significant differences on the basis of geographic position and altitude. Most of the times at all altitudes the following descending order can be noticed: Szeged,
Fig. 2. Daily run of average hourly probabilities of wind speeds higher than 3 m/s (1991e2000).
K. Tar et al. / Renewable Energy 36 (2011) 510e518
513
Table 3 Average probabilities (p3(h)) of wind speed higher than 3 m/s (1991e2000); a: stations in orographic grouping with the yearly average operation time (a.op.time), b: probabilities in descending order. a
10 m
30 m
60 m
p3(h)
a.op.time
p3(h)
a.op.time
p3(h)
a.op.time
Debrecen Szeged Budapest Szombathely Keszthely Pécs } Kékesteto
0.396 0.463 0.262 0.434 0.155 0.425 0.534
3469 4056 2295 3802 1358 3723 4678
0.509 0.609 0.446 0.560 0.272 0.566 0.696
4459 5335 3907 4906 2383 4958 6097
0.644 0.719 0.564 0.671 0.387 0.688 0.748
5641 6298 4941 5878 3390 6027 6552
b 10 m 0.534 0.463 0.434 0.425 0.396 0.262 0.155
30 m Kékes Szeged Szombathely Pécs Debrecen Budapest Keszthely
0.696 0.609 0.566 0.560 0.509 0.446 0.272
60 m Kékes Szeged Pécs Szombathely Debrecen Budapest Keszthely
0.748 0.719 0.688 0.671 0.644 0.564 0.387
Kékes Szeged Pécs Szombathely Debrecen Budapest Keszthely
} the Szombathely, Pécs, Debrecen, Budapest, Keszthely. At Kékesteto minimum values vary between 0.4 and 0.7 approximately around 12 ame13 pm in all altitudes. The daily mean values and the yearly mean operating times are shown in Table 3a, grouped by orographic environment (lowland, not lowland, highland) for the entire examined season. Table 3b consists of the probabilities in descending order. Of course, highest } and the above mentioned order of the values appeared at Kékesteto observatories is only true in the height of 10 m because at the other two heights the positions of Szombathely and Pécs was changed indicating the unutilized wind prospects of southern Hungary. Most of the old windmills were built there. According to some examinations, the positions of the old windmills locate precisely those areas where utilization of wind energy could be economic in all probabilities [19,20]. In Fig. 3 and Fig. 4 conditioned spatial geometry patterns of average probabilities of v 3 m/s wind speeds (1991e2000) were calculated and mapped with the help of the spline interpolation algorithm (ArcGIS) [21,22].
Fig. 4. Contingent map of average probabilities of v 3 m/s wind speeds at the height 60 m.
With 50 m of altitude difference, greatest change of average probabilities is experienced at Keszthely: at 60 m it is 2.5 times greater than at the height of 10 m. At most of the observatories this ratio (p3(60)/p3(10)) is the following: Budapest 2.2, Pécs, Debrecen } 1.4. and Szeged 1.6, Szombathely 1.5, Kékesteto Average values of the three examined altitudes are indicated in Fig. 5. Using approximating power function y ¼ axb intermediate values, that belong to various altitudes can be calculated. Values of the }). correlation index are between 0.999 (Keszthely) and 0.982 (Kékesteto By the help of fitting power functions a new equation, that is similar to the Hellmann formula, can be determined for the mean probability of height depending wind speeds that are higher than 3 m/s:
p3 ðh1 Þ ¼ p3 ðh2 Þ
h1 h2
a 3 (4)
Time depending (hour) probability of wind speeds that are higher than 3 m/s was defined by another method: the continuously changing (in time) probabilities were defined until the given time (P3(t)). Thus P3(t) probabilities are approached by the ratio of the frequency of v 3 cases occurred until t hour and the elapsed time:
p (h) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Debrecen
Szeged
Budapest
Szombathely
Keszthely
Pécs h (m)
Kékestető 0.0 10
Fig. 3. Contingent map of average probabilities of v 3 m/s wind speeds at the height of 10 m.
15
20
25
30
35
40
45
50
55
60
Fig. 5. Average probabilities of calculated wind speeds higher than 3 m/s at 10, 30, 60 m and approximation with power function.
514
K. Tar et al. / Renewable Energy 36 (2011) 510e518
Fig. 6. Daily run of continuously changing probabilities.
Pt P3 ðtÞ ¼
i¼1
gði=v 3Þ Nt
(5)
Its daily run at all of the seven meteorological stations can be seen } ) that it in Fig. 6. It can be assessed (except for P3(t) at Kékesteto reaches its minimum at dawn and early in the morning and from this point on it reaches its maximum in a monotone increasing way in every altitude and at all of the stations at around 5 pme6 pm. Consequently, increasing energy production is anticipated until the maximum rate in a day, however, after this time decreasing energy } minima occurs at 5 pm production is expected. At Kékesteto therefore in this altitude the situation is reverse. Significant changes can be noticed in the average daily run of the temporally continuously changing probability. This oscillation (maximum-minimum) influences the average daily energy production and variability of electricity. According to Table 4 at Szeged, Pécs and Szombathely, e these are the non highland stations where probability of wind speeds higher than 3 m/s is high e the oscillation is decreasing by increasing altitude. At Keszthely where the average probability is the lowest oscillation is increasing with height. At the other observatories (in Debrecen, Budapest and in } ) maxima of the oscillation can be observed in 30 m. Kékesteto 4. Statistics of speed intervals higher and lower than 3 m/s wind speed With the help of hourly wind speed continuous time series, the length of those intervals that have higher, lower or the same speed as 3 m/s were determined for all the observatories and altitudes.
Our continuous time series consist of 24*N members where N is equal to the considered number of days in the examined period (1991e2000). If all of the hourly wind speed data is provided from all days of every month then our time scale has 3653 elements. In case of missing days (where some of the 24 data of a day are not available) determination of the elapsed time depending statistics is restarted. In Table 5 maximum and average length of the intervals that have wind speed higher, equal or lower than 3 m/s are indicated. From this table the following can be concluded: In the case of v 3 m/s at all of the considered observatories and } and the absolute heights, maximum values occurred at Kékesteto maximum appeared here at 60 m (kmax ¼ 334 h, [k] ¼ 14.9 h) as well. Considering average lengths at all three altitudes Szeged is the next. Nevertheless at the height of 30 m and 60 m Budapest and Keszthely close the order in every altitude. In a height of 50 m difference in the average lengths vary less than the proper average
Table 4 Ranges (maximum-minimum) in daily run of continuously changing probabilities depending on height.
Debrecen Szeged Budapest Pécs Keszthely Szombathely Kékes
10 m
30 m
60 m
0.135 0.156 0.121 0.100 0.068 0.146 0.113
0.140 0.138 0.146 0.092 0.114 0.135 0.115
0.137 0.128 0.139 0.089 0.156 0.130 0.112
K. Tar et al. / Renewable Energy 36 (2011) 510e518
515
Table 5 Maximum (kmax in hours and days) and average ([k] in hours) length of intervals having wind speeds higher or lower than 3 m/s.
v 3 m/s 10 m
30 m
60 m
v < 3 m/s 10 m
30 m
60 m
Debrecen
Szeged
Budapest
Szombat-hely
Keszthely
Pécs
} Kékesteto
kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour)
102 4.3 6.2 164 6.8 7.3 170 7.1 8.5
134 5.6 6.6 166 6.9 8.0 311 13.0 10.0
90 3.8 4.9 109 4.5 5.9 135 5.6 6.8
139 5.8 6.2 146 6.1 6.7 146 6.1 7.6
102 4.3 4.6 109 4.5 5.0 112 4.7 5.7
96 4.0 5.5 137 5.7 7.1 197 8.2 8.5
228 9.5 10.2 243 10.1 13.1 334 13.9 14.9
kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour) kmax (hour) kmax (day) [k] (hour)
211 8.8 9.5 152 6.3 6.5 152 6.3 4.7
164 6.8 7.2 131 5.5 5.1 89 3.7 3.9
405 16.9 13.7 159 6.6 6.7 117 4.9 4.5
122 5.1 7.6 100 4.2 5.2 95 4.0 3.7
407 17.0 24.6 317 13.2 12.6 203 8.5 8.1
145 6.0 7.4 134 5.6 4.9 104 4.3 3.9
183 7.6 8.4 76 3.2 5.7 57 2.4 4.7
probabilities. Therefore the ratio is the following: Pécs, Szeged and }: 1.5, Budapest and Debrecen: 1.4, Keszthely and SzomKékesteto bathely: 1.2. In the case of v < 3 m/s, it is reasonable to examine some of the minima of the interval lengths. However, the situation is not as unified as in the previous case. At 10 m and 30 m the minimum of maximal length can be noticed at Szombathely, although at Szeged this minimum appears at 60 m that is the absolute minimum at the same time (kmax ¼ 89 h). In case of average lengths different orders are developed in all of the altitudes with the maximum at Keszthely. At the altitude of 50 m difference of the ratios is between 0.3 and 0.6. Distribution of the length (1, 2, 3, ., 24, >24 h) of the intervals that have hourly wind speeds higher than 3 m/s shows an interesting result. There are notable margins among the meteorological stations and various altitudes in the case of one or 2 h long sessions as well as in the case of the sessions longer than 24 h. The power function fits best in all cases for the distribution of 1e24 h long intervals. However, these intervals do not give the full probability back thus it can just be conjectured that the distribution of intervals, that have wind speeds higher or lower than 3 m/s follow Udistribution [23,24]. Distribution of interval lengths containing hourly wind speeds higher or equal to 3 m/s exceeding various thresholds (1, 2, 3, .,
24 h) is sharply different at various heights at all of the seven stations. However, there are some similarities in these distributions at some of the stations. The curves start around 0.6e0.7 everywhere hence the probability of the intervals longer than 1 h is approximately equal at all of the seven meteorological stations and at all heights. These curves can be approximated with an exponential function y ¼ a*ebx in every case. If logarithm of probabilities is taken into consideration then b gains expressive meaning hence gradient of linear function Y ¼ A þ bx can be expressed by b. In fact, the gradient of the curves at a point, that is equal to the slope of the tangent line of x, is a function of b. Comparing these, the run of the original curves is determined. In Table 6 the values of parameter b and quadrant of correlation indexes (R2), which were calculated by exponential function approximation, are indicated. According to this table, the gradient of the curves (to linear transformed) increase with height at all observatories. Order of observatories on the basis of parameter b is not the same at all heights: at 30 m and 60 m Keszthely, Budapest, Szombathely, Debrecen, Pécs, Szeged } . While at the altitude of 10 m just the first two and and Kékesteto the last places are the same. The distribution of different thresholds exceeding length of intervals that have lower hourly wind speed data than 3 m/s was also investigated. It can be noticed that these curves are different from each other according to altitude at all of the observatories. The
Table 6 Quadrants of correlation indexes (R2) that were calculated on the basis of the distribution of the length of intervals having hourly wind speeds higher or equal to 3 m/s, fit exponential function, typified constant of gradient of curves (b).
Table 7 Quadrants of correlation indexes (R2) that were calculated on the basis of the distribution of the length of intervals having hourly wind speeds lower than 3 m/s, fit exponential function, typified constant of gradient of curves (b).
Debrecen Szeged Budapest Pécs Keszthely Szombathely } Kékesteto
R2 b R2 b R2 b R2 b R2 b R2 b R2 b
10 m
30 m
60 m
0.989 0.113 0.995 0.116 0.990 0.143 0.988 0.124 0.978 0.147 0.982 0.114 0.982 0.077
0.991 0.100 0.991 0.093 0.987 0.116 0.983 0.098 0.985 0.130 0.988 0.110 0.979 0.066
0.990 0.089 0.990 0.077 0.989 0.103 0.978 0.086 0.992 0.125 0.991 0.102 0.975 0.061
Debrecen Szeged Budapest Pécs Keszthely Szombathely } Kékesteto
R2 b R2 b R2 b R2 b R2 b R2 b R2 b
10 m
30 m
60 m
0.995 0.090 0.996 0.109 0.993 0.068 0.992 0.100 0.986 0.042 0.996 0.112 0.992 0.092
0.996 0.127 0.996 0.142 0.997 0.119 0.995 0.145 0.992 0.070 0.998 0.162 0.998 0.142
0.997 0.164 0.996 0.193 0.993 0.161 0.996 0.190 0.986 0.109 0.997 0.229 0.999 0.182
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K. Tar et al. / Renewable Energy 36 (2011) 510e518 [v(t)] (m/s)
Debrecen, May, 1991., 10 m
4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0
t (hour) 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Fig. 7. Daily run of hourly average wind speeds at Debrecen on 10th of May 1991 at the height of 10 m (wind speeds higher than 3 m/s are indicated by filled markers).
curves start from 0.6 to 0.7 except for Keszthely as here this interval starts from 0.7 to 0.8, thus probability of intervals longer than 1 h is highest at Keszthely. The curves end at all altitudes under 0.1 probability except for Budapest and Keszthely, thus probability of intervals longer than 24 h is lower than this. Furthermore this value is lower than 0.05 at 30 m and 60 m as well. While at Budapest at the height of 10 m and at Keszthely at the height 10 m and 30 m the probability of those intervals that are longer than 24 h and have lower hourly wind speed than 3 m/s is above 0.1. The curves can still be approximated by y ¼ a*ebx exponent function. According to Table 7, the gradient of the curves is decreasing by altitude at all observatories. Ascendant order of observatories according to }, b parameter at all altitudes: Szombathely, Szeged, Pécs, Kékesteto Debrecen, Budapest, Keszthely, therefore curves are flatter at those places that have high nominal wind performance. 5. Statistics of intervals of average hourly wind speed higher than 3 m/s Various statistical features of intervals of 3 m/s or higher hourly average wind speeds are analyzed monthly on the basis of distribution of length from January of 1991 till December of 2000. The problem is illustrated on the Fig. 7: length of the illustrated interval is 13 h.
Fig. 8. Values of trigonometric polynomial ([v3]fit) that was fit to the daily run of the hourly average of wind speed cubes ([v3]) and area under the curve (Tac) at Debrecen at the height of 10 m in May 1991.
In an optimal case these intervals belong to a time scale of 120 elements, at a given place and height. They are indicated by [I]i (i ¼ 1,2,3,.,120). Basic statistics of time scales are indicated in Table 8. According to this table, it can be concluded that the calculated average for the entire examined period increases with altitude. The descending order of the observatories is the same at }, Szombathely, Szeged, Pécs, Debrecen, all altitudes: Kékesteto Budapest, Keszthely. Consequently, at high energy places the average length of intervals, that have higher average wind speed than 3 m/s or equal average wind speed to 3 m/s is great. Greatest changes in the ratio of averages occur at the height of 50 m (16.5 times) and it changes least where the nominal wind performance is }, Szombathely, Szeged, Pécs). Variation of the significant (Kékesteto average (independent from volume and number of sample elements) value, coefficient of variation (relative deviation) decrease everywhere by altitude and this decrease shows different order at the three altitudes. The absolute maximum of the coefficient of variation is at Keszthely at the height of 10 m (2.88) and the } at absolute minimum of the coefficient of variation is at Kékesteto the height of 60 m (0.07). According to Table 8, these are strongly asymmetric and kurtosis distributions, hence maybe, this was the reason why it could not have been approximated by the known
Table 8 Basic statistics of intervals of hourly average wind speeds higher than 3 m/s (%: average length in % of length of day).
Debrecen
Szeged
Budapest
Pécs
Keszthely
Szombathely
} Kékesteto
10 30 60 10 30 60 10 30 60 10 30 60 10 30 60 10 30 60 10 30 60
m m m m m m m m m m m m m m m m m m m m m
Mean
%
St.dev.
Var.coeff.
Mode
Median
Skewness
Kurtosis
8.2 17.5 21.9 13.4 20.6 22.9 3.6 13.6 20.8 11.2 19.8 21.9 0.7 5.4 11.1 14.7 21.2 23.3 15.4 21.8 23.5
34.3 73.1 91.3 55.9 85.7 95.2 14.8 56.8 86.5 46.7 82.4 91.2 2.8 22.5 46.3 61.4 88.2 97.1 64.1 91.0 98.1
6.2 5.9 3.9 6.3 4.9 2.9 4.0 6.6 4.6 7.6 6.3 4.3 1.9 4.9 6.2 6.6 4.3 2.2 8.1 4.1 1.7
0.76 0.34 0.18 0.47 0.24 0.13 1.14 0.48 0.22 0.68 0.32 0.19 2.88 0.91 0.56 0.45 0.20 0.09 0.53 0.19 0.07
0 24 24 9 24 24 0 24 24 24 24 24 0 0 7 24 24 24 24 24 24
7 18 24 12 24 24 2 13 23 10 24 24 0 5 9 13 24 24 17 24 24
0.952 0.448 1.987 0.243 1.097 2.854 0.885 0.007 1.400 0.328 1.147 1.850 3.270 0.899 0.718 0.011 1.466 4.408 0.487 1.765 4.569
0.557 0.799 3.101 0.827 0.272 7.969 0.065 0.775 0.845 1.017 0.169 1.919 10.881 0.588 0.284 0.989 1.078 23.581 1.027 1.795 23.252
K. Tar et al. / Renewable Energy 36 (2011) 510e518
517
Table 9 The area beneath the curve (Tac) that is proportional to the monthly average specific wind power and basic statistics of lengths of intervals that have v 3 m/s hourly average wind speeds ([I]) as well as parameters of assumed linear relationship.
Tac (m3/s3)
Mean St.dev. Var.coeff. [I] (hour) Mean St.dev. Var.coeff. correlation coefficient (Tac,[I]) determination coefficient (%) regression coefficient (Tac,[I])
Debrecen
Szeged
Budapest
Pécs
Keszthely
Szombathely
} Kékesteto
1252.1 619.8 0.50 8.2 6.2 0.76 0.812 66 80.7
1792.5 855.5 0.48 12.4 6.3 0.50 0.757 57 103.6
934.0 454.9 0.49 4.9 4.5 0.91 0.828 69 84.6
1612.0 898.1 0.56 11.2 7.6 0.68 0.818 67 96.1
832.5 654.5 0.79 1.7 3.1 1.87 0.675 46 143.2
3250.7 2178.3 0.67 14.0 6.7 0.48 0.794 63 258.2
3775.1 2021.5 0.54 21.4 4.6 0.22 0.620 38 272.0
distributions. The coefficient of skew decreases by altitude at Debrecen, Szeged, Budapest, Pécs and Szombathely: at 10 m it is positive (left-sided asymmetry) and at the other two altitudes it is negative (right-sided asymmetry). This means that at the height of 10 m smaller while at the other two heights higher values occur } the more frequently than the average. At Keszthely and Kékesteto standards of skewness decrease by altitude, however, at the previous station it is positive at every height and at the latter station it is negative at every height. Regarding the coefficient of kurtosis no regularity at all can be noted. However, it is revealed } and Szomthat this coefficient gains maximum both at Kékesteto bathely (the two places that have the biggest wind resources) at altitudes of 30 m and 60 m. In the following part of this paper the dependence of the monthly average specific wind power on the length of those intervals that have higher or equal hourly average wind speed than 3 m/s in a given month is discussed. Features of monthly average specific wind power were analyzed by a trigonometric polynomial that was fit to the average of hourly wind speeds on the power of three. This simple harmonic model was applied by [8] to determine the parameters of wind profiles. In our case the area beneath the curve (Tac) was calculated by definite integral of this trigonometric polynomial (Fig. 8) [9,25]. Linear correlation and regression of (Tac) and [I] monthly values at the height of the anemometer were analyzed. Most important statistical features, coefficients of correlation and constants of regression are presented in Table 9. According to this table the two averages have the same } , Szombathely, descending order regarding volume: Kékesteto Szeged, Pécs, Debrecen, Budapest, Keszthely suggesting a positive correlation. The coefficients of correlation are indicated in the seventh record. All of them are highly significant (r0,05 z 0.19) at Budapest, Pécs and Debrecen (higher than 0.8) followed by Szom} . Although bathely and Szeged and finally Keszthely and Kékesteto orographic difference cannot be noticed, it is surprising that the places of highest and lowest wind energy are the same. The explanation of this phenomenon at Keszthely is that there are numerous months when at the altitude of anemometer (15 m) } the number of those months when at the [I] ¼ 0 h and at Kékesteto altitude of anemometer [I] ¼ 24 h is high. These impair the tightness of stochastic connection. The order above does not concur with any other order even not with the order of regression coefficients. This latter order is: } , Szombathely, Keszthely, Szeged, Pécs, Budapest and Kékesteto Debrecen. Thus if the length of the interval that represents higher or equal hourly average wind speed as 3 m/s changes with 1 h then it has the smallest impact on specific wind power at Debrecen. This impact is 1.5 times higher at Szombathely and it is more than 3 } . On the basis of regression equations, times higher at Kékesteto linear connections can be detected at Szombathely (values are } (values are higher than higher than value [I] at 1 h) and Kékesteto value [I] at 7 h).
According to the determination coefficients the monthly average specific wind power is determined by of length of intervals of hourly average wind speed of 3 m/s or higher. The biggest dependence was determined at Budapest, Pécs and Debrecen (69, 67 and 66% respectively). At Szombathely, Szeged, and Keszthely moderate dependence was determined (63, 57 and 46% respec} this dependence proved to be the tively). Finally at Kékesteto lowest (38%). 6. Conclusions The most important results of this study can be summarized as follows. There are no orographic similarities, uniformities in the daily run of probabilities of v 3 m/s hourly wind speeds. The maximum value of this probability is around 1 pme2 pm. According to the daily run of continuously changing (cumulative in time) probabilities we can calculate with increasing energy production until 5 pme6 pm. There are no orographic similarities and differences by height in the order or by size of average length of time intervals with v 3 m/s hourly wind speed. There are different orographic orders depending on the height in the average length of time intervals with v < 3 m/s hourly wind speed. They are more disordered than the former ones. The length of time intervals with v 3 m/s hourly average wind speed by months has an effect on the monthly mean specific wind power between 38% and 69%. The monthly mean specific wind power responds more sensitively to the change of lengths of these intervals at the non-plain observatories than at the plain observatories. Acknowledgements The research on the wind climate of Hungary was supported by OTKA (Hungarian Scientific Research Fund, program: T 023765). The authors thank the Hungarian Meteorological Service for providing data for the analysis. References [1] Homepage of the Hungarian wind energy association, www.mszet.hu. [2] Torres JL, Prieto E, Garcia A, De Blas M, Ramirez F, De Francisco A. Effects of the model selected for the power curve on the site effectiveness and the capacity factor of a pitch regulated wind turbine. Solar Energy 2003;74:93e102. [3] Hrayshat ES. Wind resource assessment of the Jordanian southern region. Renewable Energy 2007;32:1948e60. [4] Justus CG, Hargaves WR, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology 1978;17:350e3. [5] Pérez IA, Garcia MA, Sánchez ML, De Torre B. Analysis and parameterization of wind profiles in the low atmosphere. Solar Energy 2005;78:809e21. [6] Cellura M, Cirrincione G, Marvuglia A, Miraoui A. Wind speed spatial estimation for energy planning in Sicily: a neural kriging application. Renewable Energy 2008;33:1251e66. [7] Shata ASA, Hanitsch R. Evaluation of wind energy potential and electricity generation on the coast of Mediterranean Sea in Egypt. Renewable Energy 2006;31:1183e202.
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