Abstract—This paper studies the effect of a number of clo
wind farms, where there is a relationship among the farms. First of all, data are statistically analyd to check main relationships between farms.
The cond analysis goes further in the characterisation of wind farm relationships. Artificial Neural Networks (ANN) provide a powerful tool to classify data automatically. They are very uful in finding patterns of productions of a zone. The patterns are obtained only with data of the power of wind farms through competitive neural networks and lf-organizing feature maps (SOFM).
Time variations of wind farm output have been studied in the third analysis. Only hourly data is available, so only slow variations can be analyd (such as down and dusk variations). Two tools have been ud in the time study: correlogram and spectrogram of each wind farm.
In addition to this, tho patterns found by ANN have been compared in the forth analysis with meteorological data of a nearby station.
Index Terms— wind energy, wind farm, artificial neural network.
I. I NTRODUCTION
The following paper treats in deep about power generated in one year (registered each hour) in the wind farms in an area in Spain. The position of the wind farms is in the middle of a valley, and they are less of 170 km apart one to another. Becau of the short distances, their performance is suppod to have a good correlation.
Their powers are evaluated and averaged each hour, and all the wind farms are grouped in nine groups (some farms that are very near are considered to have only one value). In the final part of this study, data from a meteorological tower located in the middle of the valley are also ud.
We only have hourly data, so it is not possible to study neither fast fluctuations nor gusts in the power production. It is possible, however, to study the oscillations of veral hours of duration, as the diurnal/nocturnal variations in wind speed and the due to the meteorological evolution in the area.
So, the study prented here is very uful to study the stationary performance of wind farms in the power system (i.e. to calculate the power flow in a small number of cas type that can be considered as reprentatives of the most probable states in the wind farms). This study is also uful as a very first point of departure to estimate the power production of wind farms in order to plan the generation in an electrical power system.
面汤
The autors are with the Electrical Engineering Department of Zaragoza University and CIRCE Foundation, Spain, (Tfn 34 976 76 19 20, Fax 34 976 76 22 26, e-mail: joako@posta.unizar.es).
The authors also thank Miguel García, Juan Bautista Arroyo, Roberto Zapata and Daniel Romanos for their valuable comments.
II. S TATISTICAL ANALISYS
The analyd data are expresd in per unit, so the productions of all the wind farms are of the same magnitude. Some errors have been detected in the original data (outliers). The adopted solution consisted in eliminate this entries (8233 hourly data are left).
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Another difficulty in the study of the data is that some wind farms are been enlarged, and some are quite new (therefore, maintenance stops are more probable to happen). It is also necessary to consider that the stopping due to fails and maintenance can cau some distortion in the data. Nevertheless, some of the wind farms are going to prent bigger productions in relation with their nominal power. This can be en in the figure 1, in which one can obrve that the wind farms with less production in per unit are numbers 6, 7 and 8. This can be due to have a location with a greater wind resource, or to dispo of WT with larger energy production / rated power ratio. Other point is t
hat measured data are apparent power, not active power. However, wind farms in Spain operate with power factors very clo to 1, so all conclusions derived from apparent power can be assumed to be valid for the active power.
Wind farm number
Figure 1: Average of apparent power of wind farm in per unit
(with reference to rated power) .
Figure number 1 gives us an idea of the average productions. With the histogram of the figure numb
er 2, we can e the distribution of the productions en each wind farm (i.e. how much time the farm is not generating, with low production and with full generation).
For instance, looking at the figure number 2 we can conclude that the wind farms 6,7 and 8 are not generating the 30% of the time (besides, the farms are the ones that have less production). Wind farm number 9 is producing at 10% ± 5% of his nominal power during the 22% of the time.
Characterization of wind farm energy production in a zone by artificial neuronal networks
Joaquín Mur Ángel Antonio Bayod
However, the first wind farm is producing about 100% of its nominal power during the 10% of the time. One can obrve even that in certain periods, the wind farms 1, 4 and 9 produce slightly above their nominal power.
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Apparent power in p.u. Figure 2: Histogram of apparent power of wind farms.
We can also study the relationship between the productions in each wind farm. Every element of the correlation’s matrix shows how similar the productions of two wind farms are. If the productions of both parks are identical, the correlation will be the unity (100%, brownish red colour in figure 3), and i
f the productions are not
correlated at all, the factor will be zero (blue colour) –full colour version of the figures can be eing in the CD-ROM proceedings of ICREP ‘03–. That is why the elements in the main diagonal of the matrix are all one. The matrix is symmetrical becau of it is equivalent to compare the park A with the B or vice versa.
In the following figure we can e the correlation’s matrix. The squares with hot colours (the red ones) show that the relationship between the wind farms indicated by the row and the correspondent column have a high correlation. However, a cold colour indicates that the relationship between the
two farms is weak.
Correlation matrix of apparent power
Wind farm
W i n d f a r m
1
2
3 4 5 6 7
8
9
1
2 3 4 5 6 7 8 9
0 0.1 0.2 0.3
0.4 0.5 0.6 0.7 0.8 0.9 1
Colour Scale
Figure 3: Correlation matrix, codified by colors.
Attending to this graphic, we can classify the wind farms in two groups:
• The wind farms number 2 to 5 show a great similitude
between them, becau of in the interction of the correspondent rows and columns have hot colours, whereas in the rest of the rows the correlation is lower (colder colors). In this group, the most reprentative
wind farm are the third and the fourth ones, and the one that prent a more different performance is number 5. • The wind farms 6, 7, 8 and 7 show also a very good
similitude among them. The least reprentative wind farm in this group is number 9.
• The wind farm number 1 prents behaviour more
similar to farm 9. However, this wind farm is the less related to the rest.
Another conclusion that we can obtain from this data is that wind farm 1 and 5 are the ones that prent more different behaviour from the average.
III. S EARCH OF OPERATION PATTERNS
A. C LASSIFICATION IN 10 PATTERNS
If the relationship among the wind farms is linear, the statistical study is sufficient. However, ANN have been ud
to detect non-linear ways of functioning. In figure number 4
we can e the operation patterns obtained from clustering all
data in 10 patterns, codified by colours. Each row corresponds to one pattern and each column corresponds to
the production in each one of the nine farms analyd. So, if we e in one row that the correspondent column to one farm is red, that farm has a high production in this pattern. If we obrve the blue colour in the column of a farm, the production of this farm is very small in this pattern.
Although it is necessary to u the bias in the first pha of training to obtain a balanced network (each pattern with a similar occurrence frequency) an without “dead neurones”. After that, the bias is forced to zero and a cond pha of training has been realized to obtain a network with a lower error of classification (at dispen of that all the parameters
do not have the same relative frequency). Another advantage of having a bias zero is that the correspondent pattern to a production is that one that is nearer, i.e., the one that has a lower Euclidean –geometric– distance. Conquently, to have a bias zero is more intuitive.
After a first training with bias, a cond training without bias has been ud in order to check its effect. The patterns have no changed significantly in the cond training. The small differences are due to the fact that very similar patterns have evolved to situations of production slightly more specifics. As shown in figure 5, the first and last patterns are
now more frequents (without production and with high production in al the wind farms).
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Weight matrix of Competitive ANN
Wind farm
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10
Figure 4: Weight matrix of the Competitive ANN (patterns of wind
farm power).
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男士皮带25 Frequency of occurrence of patterns
Pattern F r e q u e n c y i n p e r c e n t a g e
Figure 5: Frequency of occurrence of patterns of the Competitive
ANN.
It is possible to measure the error committed for each wind farm in the classification (difference between the production of the nearer pattern and the real production). This value permits to know which farm is worst adjusted to the patterns (this can be ud to consider if a wind farm is independent of other ones). The total classification error will be the geometric distance (in a space of dimension N=9 wind farms) between the measured point and the nearest pattern. A.1 Low winds
The first conclusion that we can obtain is that the first four
patterns correspond to no production in the nine wind farms. This result can be foreen becau the greatest part of the time, the wind farms do not inject energy to the power system
(e Fig. 2).
As a curiosity, we can obrve that in the first four patterns, the wind farm with a lower production is usually
the number 8 becau the blue colour is darker (in the histogram, this one was the wind farm that showed a greater frequency in the bin 0,05-0,15% p.u. power and besides, it is the one that has a lower average production).
The three first patterns correspond to productions of every wind farm below 12%. As we have three patterns of a total of ten, we can assign a 3x10% = 30% of the time to calm or null production. The patterns would correspond to calm periods, of weak geostrophic wind (geostrophic wind is that that exists in the layer of the atmosphere that is not in contact with the terrestrial surface, but to a high height that is not strongly affected by the orography, for instance to one height of 800 kPa –approximately 1200 meters above the a level–). The fourth ca is surprising becau, in the conditions in
which the wind farms 6 to 9 are still, the number 5 prents a
production of the 33% (and in a lesr extent, the farms 2,3 and 4). Studying the matrix of correlation we saw that the farms could be divided in two groups: farms 2 to 5 in one hand, and farm
s 6 to 9 in the other). In this ca it would be necessary to verify if the WT installed in wind farm 5 can take advantage of lower winds or if there exist some
orographic characteristics that reinforce geostrophic wind
with a certain direction. A.2 High winds
The pattern 9 and 10 correspond to high production. The pattern 10 corresponds to the maximum production,
characterid by high productions in every farm. A remark: although the productions in pattern 10 are high, some farms are above 90% of rated production.
The wind farms that prent a higher production are the farm 1 and 9. This can be obrved in the histogram directly. For instance, the farm 1 stays during more than 1000 hours a year producing above 105% p.u. and wind farm 9 stays for more than 1000 hours above 85%. (The maximum power of the farms is lower than the nominal power. This can be due to the increa of the installed power in the farm without having updated the nominal power in the databa).
B. C LASSIFICATION IN 50 PATTERNS
Once classified the usual functioning of a group of farms, we are going to make a arch of a bigger number of patterns. This will permit us the visualization of some critic ca, that although is prented only a 2% of the time (some 44 hours of functioning type in one year), it has a special interest (for
instance, very high productions in every farm). In the ca of 50 patterns, the topology of the competitive neuronal network is no efficient enough and the process of learning is quite nsitive to the parameters. , the algorithm of training has some difficulties to choo a high number or patterns, increasing the number of neurones in the competitive network. As a conquence, the polarization or bias of the neurones increas significantly in order to not produce "dead neurones". Having a high bias, the
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classification is not so good. For the election of 50 patterns of functioning, we have cho to u lf-organid maps (SOFM). This solution is more logic, due to the fact that the types of networks are more appropriated to solve problems of automatic
classification when the number of pattern to extract is elevated.
We have decided to u the one-dimensional connection among the neurones. If the wind farms ana
lyzed corresponded to two or three meteorologically independent zones, a two-dimensional or a three-dimensional scheme
would have been more appropriate. To compensate the low connectivity of the one-dimensional network, a parameter of vicinity of 3 is ud instead of the usual 2. The result of the lf-organid map can be en in graphic number 6. Besides, one can obrve that using a linear connection, the patterns are organized. The average error of the classification of a production to a pattern is 0.0045 p.u. Weight matrix of SOFM with 50 neurons Wind Farm
P a t t e
r n
2345678915 10 15
20
25
30 35
40
45 50
0.1
0.20.3
0.40.5
0.6
0.7
0.80.91
Colour scale
Figure 6: Weight matrix of SOFM with 50 neurons
In figure 7 we can e the frequency of occurrence of each pattern (with a number as high of patterns is difficult to obtain that all of them have a similar frequency of occurrence).
Pattern
F r e q u e n c y i n p e r c e n t a g e
Figura 7: Frequency of occurrence of patterns of SOFM.
A remark: in figure 6 the wind farm 1 have been moved next to the farm 9 in order to produce a nicer scheme. This is due to the fact that the productions of both farms are relatively correlated.
IV. F
REQUENTIAL STUDY
In order to study the evolution of the power in each farm, a
joint time-frequency analysis has been ud, by means of the
spectrogram. This tool gives us, in each farm, the
distribution of the oscillations of the power as time varies.
The horizontal axis is the axis of time and the vertical axis is
读书好处the one of frequencies. A hot colour (red) indicates that in
that moment an oscillation of power have been produced,
with the frequency associated to the vertical axis. The colour
at a point indicates the amplitude (in dB) of the fluctuation
content of that frequency at that time.
To understand better this graphic, we are going to e
some examples. A frequency of 1 would indicate that a daily oscillation of power has been produced. This frequency appears in every farm becau of usually at dawn the wind speed is minimum and maximum at dusk due to the warm-up of the surface by the sun (for instance at 7 h. the power usually is lower and at 19h. the power is usually bigger). A frequency less than 1 would be associated to changes in
the meteorology. A frequency of 0.25 would indicate that in a period of 4 days the power has lowered and has incread again of vice versa. In the spectrogram one can obrve that
the slow fluctuation of power (daily oscillations) is frequent
becau they have red colours associated. You can also obrve in the spectrograph that the intraday oscillations (the ones that are produced veral times a day)
are very few frequents. This means that although the produc-tion of the wind farms is continuously changing, the hourly variations have a random character; they have no periodicity
nor a determined pattern. If the power oscillates veral
times a day during a significance period, this would be
probably due to a periodic disconnection in the machines
(disconnection by overheating in the gearbox with a high wind speed, etc.). The are the reasons why the superior part of the spectrograms has a colder colour (variations of some
hours of period rarely occur), whereas the bottom part has a
hotter colour (daily variations and meteorological changes). There can be also obrved that when
an abrupt change in the production of the farm (for instance due to a disconnection of the farm or to an erroneous data), this produces a column of hotter colours. This is due to the fact that a steep change in the power, no cyclic, generates a wide spectrum of frequencies.
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F l u c t u a t i o n s p e r d a y
Spectrogram of wind farm 9 output, in dB
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8
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Figure 8: Spectrogram of power of wind farm No. 9,
Given the characteristics of the ud data, it is not possible to study the fast oscillations of power due to gusts,
disconnections and sudden changes of production. To this
type of study it would be necessary data sampled veral
times by cond and the period of study could be diminished
proportionally.
To compare the variability of the power in veral farms is
preferable to obrve the spectrum averaged during all the
year. In figures 6 and 7 it is possible to obrve that all the
farms show a similar behaviour, although in some of them
the power is slightest more fluctuating that in others. For
instance, the daily modulation is lower in the farm 3 and it is
superior in 1 and 9.
Fluctuations per day F l u c t u a t i o n i n d B
Figure 9: Power Spectrum Density (one year modulus average) of farm outputs. A peak can be noticed in 1 fluctuation/day. V. S TUDY OF THE TEMPORAL CORRELATION The correlogram and the spectrogram give similar information and are related mathematically [1, 2]. Although
the spectrogram is more adequate for clearly periodic signals, the correlogram is more adequate for the study of random process and time ries. Another possibility to identify the system is to u parametric means to the identification of systems, but the have the disadvantage that it is necessary to make suppositions about the model of the system [3, 4]. The correlation coefficients have been ud in the graphics to compare the results in wind farms that has different vari-ance. Due to the fact that the average of power is not sub-tracted from the data, the correlogram is not nullified with increasing lag times. You can also obrve that the graphic prent some fluctuations every 12 hours due to a meteoro-logical cycle every 12 and 24 h (each two peaks of 12h there is other one more noticeable due to the daily variation).
In figure 10 one can obrve that the correlogram prents a sharp decrea in the first hours and th
en the decay is slower. This can be interpreted as the power in the farms varies between a 20 and a 28% of its variance in the first 5 hours (the correlation coefficient is between 0.8 an 0.72 depending of the farm). With a lag of 10 hours, the production has changed between a 28 and a 35% of its variance.熬夜脱发能恢复吗
As in the frequential study, the farm with bigger power variations is the number 1, and the one of the lower variations is number 8. However, this difference is clearer in the correlogram.
Auto-correlation of wind farm output
Lag hours
C o r r e l a t i o n c o e f f i c i e n t
Figure 10: Auto-correlogram of wind farm output.
To summarize, the power of a farm usually varies in the 5 first hours in an interval of ±20% to an ±28% of its variance (depending on the farm) with an confidence interval of 68% (supposing that the generated power by the farms is a random process that follows a normal distribution). From the 10 h, the intervals slowly increa. One can even obrve that the following day, to the same hour, the interval is of ±34% to ±50% of the variance of each farm, with the same confidence interval. To obtain a confidence interval of 95% in p.u. power, we must multiply the previous percentages by 1.96 and by the variance of each farm.
In figure 11 the correlation of the farm 1 is shown, with respect to the rest of the farms. The corresponding coefficient to zero lag hours corresponds to the first row of the matrix of correlation.
Lag hours
C o r
r e l a t i o n c o e f f i c i e n t
Figure 11: Correlogram of wind farm output respect wind farm 1.
The farm with a more similar behaviour to the 1 is the 9, and the more different is number 2. You can obrve, as in figure 10, that there is a fast decay of the correlation in the first 24 h. From this level, the correlation tends to the stationary value. The ripple due to the cyclic behaviour is noticeable: the production prents patterns that are reproduced every 12 and 24 h.
A.1 Additional considerations about the measurements The period of integration has a filtering effect on the power fluctuations. Fluctuations due to the tower shadow, gusts, etc. is studied from power measured at least at a sample rate of 10 Hz. However, in this work the data integrated each hour are treated and so the fluctuations (in the range of conds and milliconds) do not appear.
If the prediction of the production is desired, it is desirable to have in mind the meteorological prediction and the stopping for maintenance. Nowadays, there is a big effort in predicting the wind (for WT control) and the farm output (for electrical dispatch plan) [5, 6, 7, 8, 9].
VI. R ELATIONSHIP BETWEEN THE ENCOUNTERED PATTERNS
AND THE METEOROLOGICAL PARAMETERS ..
A meteorological station located approximately in the centre of the farms has been ud to study the meaning of the found production patterns. Although the wind speed is measured at some 10 m. above a roof, the data are valid enough to our aim.
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Figure 12: Wind direction ro of a nearby meteorological station.
2.4.6.9.11.1
3.16.H i s t o g r a m o f w i n d s p e e d
W i n d s p e e d i n m /s
F r e q u e n c y i n p e r c e n t a g e
Figure 13: Histogram of wind speed at the meteorological station.
A. P ATTERNS CHOSEN FOR THE METEOROLOGICAL STUDY
The patterns chon for the meteorological study are shown in figure 14. Basically, they are the same as tho of figure 4. The patterns 1 and 2 have been substituted here by a null production pattern and the pattern 10 has been added, corresponding to a 100% production in all farms.
This classification does not significantly increa the classification error and it is very natural to consider no 0
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Figure 14: Patterns of wind farm output utilized in the
meteorological study.
Frecuencia de aparición de los patrones en %
Figure 15: Frequency of occurrence of patterns. The relative frequency of patterns (e fig. 15) varies becau the bias has been nullified in the cond training, two patterns have been removed and other two patterns have been added.
Full production (1 p.u. production in all farms) is the least frequent pattern (4,4 %). Nevertheless, pattern 9, being very
similar to 10 but having less production in farms 2,3, 5 and 8, shows a high frequency (16.6 %). Although full production has a probability inferior to 5 %, it is worthy to study becau it can result in electric overload of some tie lines and transformers.
B. M ETEOROLOGICAL PARAMETERS
In order to obtain the relationship between the meteorological parameters and the patterns, the histogram of the meteorological parameters have been computed for every pattern. The vertical axes of the graphics are the relative frequency in % of the pattern minus the relative frequency in % of the whole data. In other words, vertical axes are the deviation of the histogram whereas the horizontal axes are the values of the meteorological variable under study.
On the one hand, if the histogram of a meteorological variable has the same frequency distribution than the average of data, then the variable is not related to the pattern. On the other hand, if the histogram deviates significantly from the average, then the variable is related to the pattern.
If the difference between the pattern histogram and the average of the data is positive in a range, the pattern will happen more likely if the meteorological parameter is in this range. Correspondingly, a negative difference means that the probability of this pattern to appear is lower when the meteorologi
cal variable is in this range.
B.1 Influence of wind speed
In order to study the wind speed associated to each of the patterns, the deviation with respect to the average has been calculated. The horizontal axis of figure 16 is wind speed and
Patterns 1 and 3 are associated with low winds and calms at the meteorological station becau there is a positive deviation in winds lower than 3,5 m/s. The null production pattern (1) is associated with the lowest wind speeds.
Patterns 2, 4 and 7 are associated to medium speeds, be-tween 5 and 7 m/s. Surprisingly, pattern number 7 is associated to moderate wind speed although the production is high. Pattern number 5 is related to winds in the 5 to 10 m/s range.
The patterns corresponding to the highest production (number 9 an 10) are associated to the strongest winds. Nevertheless, the full production pattern is associated to wind which are not as strong (9 to 11.5 m/s) as tho
associated to pattern 9 (8 to 14 m/s). This is due to the fact that fixed blades, fixed speed turbines yi
eld its maximum
