Google translation, not edited:
Correlation of the feed-in from wind turbines makes base load capacity in Germany impossible
by Dr. - Ing Detlef Ahlborn
When it comes to studies, to develop strategies to secure electricity supply of so-called renewable energies, one finds invariably only vague statements. In this paper it is shown why a strategy for achieving a secure electricity supply from wind turbines can not be developed, and in a country the size of Germany is not developable. Each of these strategies will fail to physical laws and fundamental principles of mathematical statistics. Below is this to be justified in a clear way.
With the current expansion are all wind and solar energy plants in Germany together not baseload. A corresponding popular scientific study was published by the author on the Internet at www.vernunftkraft.de/statistik/. There, the statement was made that "the secured capacity of all wind turbines is to be recognized in Germany together with zero." This case has now occurred, as the entire wind power on March 13, 2014, to 34 MW (which is one-thousandth of installed capacity or rated output of 34.000MW) has fallen. The practical total failure of wind power is therefore now occurred in Germany.
At this consensus among engineers and scientists can not be shaken, and finally the Einspeisekurven of all wind turbines in Germany are publicly available.
It is therefore not surprising that there is only "vague statements" in relevant studies here. To this fact, the lobby pushes gathered around with their subordinate institutions with semi-specific generalities.
Performs an expansion of wind power for smoothing the supply?
In the evaluation of the further expansion to an equalization of the supply, the estimates vary widely among scientists. The sense after about IWES in Kassel considers that a further expansion for smoothing and thus to equalize the supply leads. So it says in the verfertigten in Kassel on IWES "Agora short study of the development of wind energy in Germany" for example: "A large-scale distribution of plants consequently leads to a smoothing of supply."
Anyone who has ever dealt with mathematical statistics, sees "at first sight" that this thesis is mathematically unsustainable. The dispersion or variability of a random size, such as the number thrown eyes of a sequence of 50 tosses of a cube is "measured" in mathematics by the so-called variance. If one performs this cube experiment with 2 dice (and thus the expansion of wind power includes in this experiment, because the dice are rolled with more cubes) and forms the sum of the spots numbers and consider the scattering of this sum, it is found that the scattering ( and increases the variance!) the sum and does not sink. This statement is evident, because the numbers fluctuate in a cube 1-6, with two litters 2-12. Underlying this is the addition theorem for the variance of mathematical statistics.He says that the variance of a sum of random numbers as the sum of the variances of the individual random numbers.With each summand the variance and thus the scattering and, ultimately, the variability increases.
The conclusion at this point is beyond doubt:
An expansion of wind power increases the dispersion of the feed. The team fielded by IWES scientists claim for smoothing is in clear contradiction with unique sets of mathematical statistics. The claim is simply wrong!
If the infeed is perpetuated by the expansion of wind power?
Looking at the issue of complementarity of wind turbines to a "stabilization" of the feed, should be brought to see more detail. However, the deeper connections of mathematical statistics are "somewhat tricky" (new German: more sophisticated): The described dice experiment, we now want to carry with 3, 4, 5, and finally with a very large number of dice and the sum of the reflected eyes Numbers consider it. This sum we want to make in thought, because the feeds of all individual wind turbines are added in our grid completely analogous in every moment. If the following statements we perform this experiment with 50 cubes immediately clear:
- As the sum of the number is very rarely 50 or 300 shown because it is very unlikely that 50 times the number of eyes will fall 1 or 6,
- The number 175 is frequent, because there are many combinations of eyes figures that lead to the sum of 175.
Figure SEQ Figure \ * ARABIC 1 Total number of eyes at 50 cubes
If one evaluates the frequency distribution of this sum from, it can be seen that this sum is distributed approximately according to the known normal distribution Gaussian. This
Knowledge is the statement of a fundamental theorem of mathematical statistics, known as the "Central Limit Theorem". He states the following: If one forms the sum of a large number of random numbers, then this sum follows a normal distribution, the more accurate the larger the number of summands. In the described experiment cube ie the sum of the figures eyes to the value of 175 will vary, the minimum value can be 50, the maximum value may be 300. If one were to interpret the sum of the eyes numbers than the sum formed from 50 individual feeds the feed services, you can initially set the statement can be made that this imaginary random "performance" is baseload, because she never falls practically to zero and varies about a mean value. The course of 50 litters in succession formed the sum is shown in Figure 1. It can be seen that the sums eye number varies around a mean value, and practically never drops to small values.
Figure SEQ Figure \ * ARABIC 2 The actual supply of wind turbines in Germany
Now the electric grid in Germany is the sum of the feeds from 24,000 wind turbines. The number of these summands so statistically exceeds the number being used here of 50 cubes by orders of magnitude. Due to the aforementioned dice experiment is therefore to be expected that the sum of the sources leads to a smooth curve, which would resemble the one in Figure 1, at least.
This is without a doubt not the case: The course of the feed shows the known fluctuation behavior with the extreme fluctuations of injected power. In addition, the total supply of all wind turbines Germany does not follow the normal distribution Gaussian (Figure 3). Thus the course of the actual feed-in is initially very evidently contrary to the statements that would be expected of the central limit theorem of mathematical statistics for the fed wind power
The transfer of the results for the simple cube experiment on the total supply of the wind turbines is obviously unjustified.
Now what is the problem?
First, the injected power of a single windmill is distributed differently than the eyes number of dice. The latter is uniformly distributed, ie each eye number is equally likely = 1/6, corresponding to a probability of 16.67%. In a small wind turbine performance are much more likely than large ones. However, this is not the reason for the deviation of the curves, finally you can generalize the "central limit theorem" of statistics on any kind of distribution. 
The difference between the test cubes with 50 dice and adding the feeds from 24000 (!) Wind turbines is that the reflected eyes of each number cube "has nothing to do" with that of another cube. The values of all dices are thrown independently in the statistical sense. This statement does not apply to supplies, the individual wind turbines because the wind speed at various wind turbine locations are similar in virtually any weather conditions in large areas, ie the individual feeds are not statistically independent. When the wind blows strongly in the north of Hesse, which is virtually always in the south of Hesse the case. This statement is also obvious in the usual size of low pressure areas and apply mutatis mutandis to each state. This simple fact causes high as well as low feeds at the same time virtually always occur in large areas. It is said that the feeds are correlated with one another, ie, in large-scale environment of a randomly chosen reference system can be traced back the feeds of all plants in this a reference plant. If you know the power fed a reference system, so you can determine the capacities of all stations in the large-scale environment of the performance of the reference system with high probability. This fact, the content of the statistical correlation. For the entire area of Germany corresponds each reference system in a statistical sense just a cube from the cube experiment in which the question is asked, by how many reference systems shown feeding into Germany can be so understood. This number measures the intensity of the correlation. If this number is small, the correlation is strong, this number is large, the correlation is fairly weak. The cube experiment has shown: the larger the number, the better the feeds can be offset with each other. If this number is small, however, a mutual compensation of the feeds is possible in principle, benefits may but fall again and again to very small values, because it frequently occurs in less than 5 independent reference systems that supply all systems decreases to very small values. In this case, the total supply is in principle not baseload. In this context, wind turbines have another problem: low performance are very common, and are therefore very likely high performances are rare, and are therefore unlikely. This fact is then reflected in the frequency distribution of the total feed, which is shown in Figure 3.
Figure SEQ Figure \ * ARABIC 4 Frequency of actual and calculated from three reference plants feed
This distribution is not normally distributed without any doubt according to Gauss, from which it can be immediately concluded that their analysis to a small enough number of independent reference systems.
It can be shown that this "small number" is only at 3, ie the total sum feed in Germany can be traced back to only three reference plants. This relationship is shown in Figure 4. The feeds all plants are therefore among themselves highly correlated. Thus, although these three reference systems are not mutually correlated, all 23997 remaining plants can be traced back to these three reference systems. Published in the named Agora study on page 13 knowledge, "that plants can complement each other in different locations" is certainly correct, however it does not follow that the complementarity of the different feeds to a base load. As they say in mathematics, the condition of statistical independence of two power supplies for the base load capacity is necessary but not sufficient.
It does not matter whether individual plants can complement each other in different locations (that are statistically independent from each other), but how large is the number of facilities that are statistically independent from each other in different locations. If the total supply of all equipment can currently be traced back to only 3 statistically independent reference plants in Germany, can not reasonably be expected that the number of reference plants and thus statistically independent feeds will grow significantly due to the construction of facilities.
An expansion of wind power due to the proven strong dependence of the feeds themselves not help to stabilize the performance. The prepared by IWES on behalf of Agora claim would be desirable, but turns out to be incorrect and contrary to the central limit theorem, a fundamental theorem of mathematical statistics, which was proved in 1922 by the mathematician Lindenberg.
1 Because of the fundamental principles of mathematical statistics the summary feed-in from wind turbines in the area of Germany is in principle not baseload. The development of wind power in our country can not and will not change anything essential.
- 2 The power peaks will increase due to the expansion of wind power further and further exacerbate the known problems of overproduction of non-recyclable stream of evils such as the so-called negative prices in the stock market.3 There are no large technically available memory efficient technology for the use of the rising power peaks, so that the power supply without power plants in the background can not be operated. It does not matter whether they are operated with gas, lignite or hard coal. The exit from the nuclear power plants will force an expansion of conventional power plants. The costs associated with electricity production and carbon dioxide emissions will increase and not decrease.
 Those skilled in the art: In the mathematical literature, this message is known as a Lyapunov condition.
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