Onshore versus offshore capacity factor and reliability for wind energy production in Germany: 2010–2022

Similarities and differences between the features related to the productivity of onshore and offshore wind energy are developed with the aid of information theory techniques complemented by normal statistics. The data comes from the 13‐year period between 2010 and 2022 for the registered turbines in Germany (practically all). The information content of the generated power is dynamically measured by the mutability of the files storing the information. Monthly statistics show that in spite of the Summer months being relatively unproductive, the corresponding mutability shows the possibility of making use of short periods of intermediate productivity in the case of offshore plants. Favorable conditions for wind energy generation in Wintertime are reached for both onshore and offshore production, although the latter is favored. More homogeneity and stability in the data are still necessary to generalize algorithms, protocols, and criteria. This general study shows the success of the information theory techniques in describing wind ramps. Applications to specific zones could improve the efficiency and capacity factor of particular wind turbines depending on their exposure to wind streams or the blocking of nearby mountains and forestry. The information theory techniques presented here allow for a different and novel viewpoint to detect favorable and unfavorable wind energy periods.


| INTRODUCTION
Over 80% of the world's energy consumption is presently covered by chemical energy stored in fossil fuels (coal, oil, and gas). 1 Over longer time scales, their exploitation is limited by the finiteness of these resources and by the ever-increasing effort required to make them usable.International conflicts can also lead to the search for the independence of the fuel markets, favoring local sources of energy even at a higher cost or longer time for their development.In addition, CO 2 and other gases are released into the atmosphere when the energy of the fossil sources is converted into other energy forms, such as mechanical, chemical, electrical, or thermal energy.These are required to satisfy the ever-increasing needs of a global human community.It is assumed that this additional input of CO 2 into the atmosphere, increased by the burning of fossil fuels, can contribute to global climate changes on an average time scale of just a few decades. 2 The challenge of reducing the share of fossil sources and developing alternative strategies to provide energy in their place is being handled differently in different countries.Germany is pursuing the political goal of completely phasing out coal burning in power plants by 2038 as part of a national energy program: "Energiewende."It is assumed that a massive expansion of renewable energies can contribute to this goal, mainly based on wind turbines and photovoltaics.In 2021, the installed power of wind turbines onshore and offshore was 56 and 8 GW, respectively.They contributed 88 TWh (onshore) and 24 TWh (offshore) to the total generation of electrical energy. 3It is planned to double the onshore installed facilities by 2030.In addition, at the same time, the offshore installed capacity is expected to grow 2.5 times in 2021.
The share of wind energy in electricity generation in 2020 was 6% worldwide.This contribution increased to 7.2% in 2022.The specification of annual full load hours provided information on the total amount of electric energy fed in by wind turbines over a year.With the further increase in the share of electricity from wind energy, knowledge of these two parameters is no longer sufficient.More information about the volatility of generation is needed so that the feed-in of wind energy into the public grid can be realized.With the increase in the mean value, the fluctuation of the feed-in power around the mean value increases, too.One consequence of this is the occurrence of increasingly large and sudden power gradients.
In Germany, wind power contributed about 21.5% to the total electricity generated in 2022 (half of the total electricity generated from renewable sources 4 ).However, at some hours, the wind power was close to zero, while at other times, almost the entire grid load was close to being covered.The output of backup power plants must be continuously adjusted to the feed-in of volatile generators.So far, there is no automatic process that would guarantee efficient and safe use of the installed facilities, and human operators are needed.This requires prompt data access, appropriate processing, trained personnel, and alternative derivatives for the energy (directly to the lines or to a variety of storage mechanisms).
The knowledge of the behavior of wind ramps and the response of the installations is of prime importance here, and it is our primary objective for the present paper.Indications of incoming favorable conditions and their possible strength will be searched, separating onshore from offshore contributions.At this time, no further filtering of the data is attempted pointing to generalities in methodology rather than particular applications to a field in expansion.For the same reason, some lenience is needed to compare productivity over the years when technical conditions are changing.
Compared with the conventional generation of electrical energy based on fossil or nuclear energy sources via thermal power plants, the generation of electrical energy by wind turbines has at least two disadvantages: (1) Storage systems with gigantic capacity are required to balance the volatile and yet unpredictable energy generation.(2) Because of the small energy density of the mechanical primary energy source in wind turbines, which is several orders of magnitude lower than in fossil fuels, there is a large demand for land areas usually devoted to housing, social life, agriculture, industry, landscape, navigation, and others, which makes it a difficult political decision.
For onshore installations, possible conflicts come from regulations about the distance between turbines and residential areas and concerns about nature conservation and species protection.Offshore installations have different technical challenges: longer lines to the grid or storing centers and specialized maintenance.
There are also operational differences between these two installation systems.Thus, for instance, onshore wind turbines must fight against nearby mountains and forestry, while offshore generators require more sophisticated installation procedures and logistics.
A second objective for the present investigations is to gain insight into the energy productivity by these two methods.Thus, we separate the data for onshore and offshore turbines for Germany during the 13 years from 2010 to 2022.This is a prerequisite for optimizing the feeding of wind energy production (WEP) into the public grid, thus helping to save other sources of production.
Approaches to data handling in relation to optimizing WEP have varied over the years, and they continue to do so, being a field of active research.An early review was published in 2014. 5][10][11] Recently, a multiobjective optimization method has been proposed to cope with this goal. 12One shortcoming of all the methods based on meteorological variables is that normally these data are not recorded in situ, and landscape and nearby conditions can significantly affect the performance.
A different way to try to forecast favorable periods for WEP is through the power output time series itself.4][15] The protocols can become very complex, indeed like a multiparameter segmentation algorithm to detect wind power ramps. 16hese efforts are spread in the techniques as well as in the geography; thus, incorporating a huge amount of information on a field of rapid present expansion accelerated even more by the design of new turbines.Just to mention a couple of recent examples, we can mention a rather simple method based on wavelet transforms to detect wind ramps applied to data from Belgium and Sweden. 17A more sophisticated algorithm based on data analysis was proposed to combine power output data with wind speed data from South Korea to evaluate ramp events. 18The more advanced recent proposals on the ways of treating the variable wind volumes make use of artificial intelligence 19 A recent review article on the variety of mathematical models to deal with wind energy can help the interested reader to get deeper into this subject. 20So far, most of these efforts have focused on individual farms, which is a perfectly valid approach looking for local productivity.Our viewpoint is different since we try to find general features in the gross data for Germany, trying to find general standards by means of entropy approaches to energy productivity, which could be later refined for local uses. 21ur main technique is different also: we make use of information recognition through data compressor techniques. 22Of course, there are also hybrid methods combining meteorological and WEP data, but this is not the route of this paper. 23,24Even hydroelectric plants can lower productivity in extremely dry seasons.Solar energy is diurnal, seasonal, and weather-dependent.Wind energy is completely weather-dependent.This means that natural sources need some flexibility when mixing with other sources of energy. 25To achieve this level, knowledge of the way WEP works is fundamental, and one of the primary characteristics that arises is the two main components: onshore and offshore.They have differences in several respects, 26 but here, we will mainly concentrate on their capacity factor and their different entropic responses during the weak Summer season.
Wind turbine design evolves significantly in parallel with the data analyzed in the present study 27 : larger towers with smaller generators are becoming more efficient both onshore and offshore.This makes it difficult to compare year-to-year data since meteorological changes mix with the changes in technical developments.This is a reason to focus on the general tendencies of WEP at the moment.Additionally, gradients in productivity also become larger, so the search for efficient algorithms will continue to optimize the use of the produced energy either directly to the network or to storage.
The recent success of the information theory techniques in detecting premonitory signs in the sequence of magnitudes of seisms 28,29 is encouraging to attempt a similar approach for the sequence of WEP.However, this will have to wait until the conditions to produce electricity from wind reach geographical homogeneity and time stability.
This paper is organized in the following way.Section 2 refers to the methods, covering the data handling and the information theory method by examples; a sensible indicator is proposed to recognize the onset of favorable periods.Results are presented and discussed in Section 3. Conclusions follow in Section 4, followed by the appendix where the information theory method is displayed with the aid of a flowchart.In addition, the tuning process to recognize information content is explained.

| Data organization
WEP data are updated in Germany every 15 min: on the hour HH:00, then HH:15, HH:30, HH:45, (HH + 1):00, and so on. 30We will organize these data in yearly files beginning at 0:00 h of each year and ending at 24:00 on December 31 that same year.This last register is the first register of next year, and so on.Such sequence will be denoted by P(t) and it represents the total instant power produced by the contribution of all wind turbines connected to the generation of electricity in Germany.It is reported in megawatts (MW) with a production that reaches over ten thousand MW (10 GW) in the good periods.From the numeric point of view, P(t) is stored in registers comprising 6-8 digits.This is too many digits for a total where there is no guarantee that the measurement in the instrument of each wind turbine reaches such precision.So, we will restrict ourselves to the number of significant digits recommended by the tuning process depicted in the appendix.Examples are given in the third and fourth columns of Table 1, which will be fully explained below.
A first obvious filter is imposed: we separate onshore from offshore productivity since one goal of this paper is to compare the behavior, with similarities and differences, for these two sources of WEP.Just to present the data we deal with, Figure 1 reproduces the yearly average WEP in Germany from 2010 to 2022.Then, in Figure 2, we report the average capacity factor for P(t) along the 13 years; capacity factor F is defined as the dimensionless ratio of the power actually generated P(t) regarding the installed capacity C(t) for electricity generation: where P(t) varies mainly due to meteorological conditions but also due to technical aspects dealing with the performance of new turbines; the installed capacity C(t) varies exclusively due to human intervention because of the number of new turbines installed through Germany and also because of maintenance and replacement of old turbines by new ones.
In the present paper, F(t) will represent several different instances depending on the analysis: yearly averages (as in Figure 2, monthly averages when studying the seasonal variances, and also (8 h time windows) when analyzing the dynamic behavior of this parameter.

| Information recognizer
We apply the data compressor wlzip 22,[31][32][33] to the recognition of information in a file, creating a new file with the compressed information.The just cited papers discuss the details of using this technique.In this subsection, we summarize how this method applies to power generation; a flowchart illustrating the procedure is given in the appendix.In addition, interested readers Note: First column: sequential number or instant (t); second column: the original power data (in GW) for the first 24 quarters of an hour (6 h) for a portion of real data on a January day; third column: truncation to four digits counting from the first one (dot counts as a digit); fifth column: File P* as stored by wlzip.
F I G U R E 1 Average onshore and offshore wind power produced yearly in Germany from 2010 to 2022.
F I G U R E 2 Average onshore and offshore capacity factor (produced vs. installed) for energy produced in Germany during the period reported.Offshore for the years 2010-2013 is left out of the analysis.
can request by e-mail (eugenio.vogel@ufrontera.cl) a free copy of our wlzip manipulation program, complete with an instruction manual and examples.The starting point is the vector file containing the records with the series P(t) with registers every 15 min.Then the size of a time window, ν consecutive registers, is defined.This process is illustrated in Table 1, where the first column is just an enumeration of 24 consecutive measurements, namely, ν = 24 (6 h), for real data with descriptive purposes only (date is not important).The second column gives the instant power P(t) in GW (six digits, including a decimal point).These are too many digits, so they are truncated to only 4 in the third column.This will be labeled 1.4 truncations: four digits counting from position 1.Actually, this is the truncation we will use in the present article, as it will be justified in the appendix.So, from now on, we use the third column only, whose weight is bytes is w(t).
We will recognize information originating in column (3), storing it in the fourth column in a coded way.This new column keeps all the information of the third one in a more condensed or compressed way.We prepared a flowchart to aid in the presentation of how wlzip works.This flowchart can be used as an alternative or complement to the description given in the next paragraph.The flowchart is included in the appendix.
The new file P * (t) is represented by the fourth column, and it is formed in the following way: (a) The first record of P(t), which is 38.8, is new, and it is placed in P * in the first place, with a suffix 0, showing its position at a distance D = 0 from the start of the original file.(b) Next, we move to the following record P(2) = 39.5 and search for its previous presence in column (4).Since it is new, we write it as a new record in the fourth column with a suffix 1, indicating its distance as D = 1 from the start of the original file.(c) Moving on, P(3) is 39.5, which is the same as the previous record; to indicate an immediate repetition of a value, add a comma to the fourth column and specify the number of repetitions or length of the string; it is 2 in this example.(d) Next, we proceed to P(4) = 42.1, which is new and it appears three positions below the origin (D = 3); the same value is found again at P(10), six positions ahead; this is summarized by writing 42.1 3 6, in the fourth column.(e) We can skip to P(13) = 45.1, located 12 positions below the origin.It repeats immediately and will appear again 2 positions below its last location, with suffixes 12, 2 2.
Thus, the fourth column presents a shortened sequence of weight w * .We keep going until the first dynamic window is fully recognized.The dynamical process continues along the series P(t) considering the next window, going from register 2 (39.5) to register 25 (not shown), then from 3 to 26, all the way until the vector file is finished.It is possible to get the window weights w(t) in bytes for the P(t) sequence and also the corresponding weights w * (t) for the corresponding compressed sequence (fourth column).Then we can calculate the mutability for all the windows along the original file: In future applications, we shall omit ν and t for simplicity.
Thus, a shortened sequence of weight w * is created along the fourth column.We continue until the recognition of the first dynamic window is completed.
Then we repeat the process for the second window from time 2 to time 25, to time 3 to time 26, and so on until the end of the original file.For any WEP sequence P(t), we can get its successive window weights w(t) in bytes.Similarly, we can obtain the weight of the corresponding successive compressed windows w * (t), leading to dynamic mutability ζ(t) across an interval of ν instants.For the present series of 35,040 annual records, we used dynamic time windows with ν = 32 records (8 h) and a precision of 1.4.For fixed-time applications of wlzip (month or year), longer sequences are considered in a single pass, and the same precision of 1.4 is used.A tuning analysis that optimizes the recognition process for different numbers of significant digits is presented in the appendix.

| Indicator
A period of good production will begin with a substantial increase in power production (P(t)).Mutability measures activity: large values meaning a less compressible series like it is obtained during the changes in the intensity of winds.To make sure we deal with an increase in wind power, we will combine mutability with the time derivative of the P(t) series.
Let us begin by obtaining the dynamical mutability of the capacity factor µ E (t) for ν = 32 instants and a precision of 1.4 (see Section 2.2, Table 1, and the appendix).
Independently, we can calculate the A-points time derivative of the same capacity function defined as where q is the time displacement to define the derivative; we will consider q = 4 in the rest of this paper.Then, we can define an indicator I(t) for a 4-point (A = 4) time derivative in the following way: Thus, when the derivative of the capacity factor increases, this product is positive, and it gets amplified by the mutability of a nonmonotonic series under windy conditions.On the opposite, even if the derivative is positive, but the wind is calm, I(t) takes low values.Periods with negative derivatives and low capacity factors are revealed by low values of this indicator.

| RESULTS
The actual yearly wind power production in Germany is reported in Figure 1, while the corresponding capacity factor is reported in Figure 2. Onshore and offshore contributions are shown separately: different scales are necessary, and it should be noticed that offshore production is almost nil for 2010, 2011, 2012, and 2013, which is basically because of the very few offshore turbines available during those years.
Because of this negligible productivity before 2014, those years will be discarded from any comparative analysis between onshore and offshore WEP, which will be possible for the period 2014-2022 only.
Figure 2 presents the capacity factor of the WEP produced onshore and offshore.This is calculated daily as the percentage of generated power regarding the installed power; then, this is averaged along the days of the corresponding year.
Figure 3 gives the monthly average capacity factor for WEP during the period 2014-2022, comparing onshore and offshore sources.This is calculated daily, then averaged for a year, and then averaged over the 9-year period.The interpretation of this figure requires some precautions due to inequity between onshore and offshore data.Offshore data are still very poor as compared with onshore which is a first consideration.Only 12% of the turbines are presently installed at sea.Offshore installations are more recent, making use of all the learning processes provided by onshore facilities.Many of the onshore turbines are old equipment, inefficient, and not well located.This means a large dispersion in the productivity of machines installed inland.This is shown in Figure 4, where the more powerful machines are responsible for the larger share of full load hours. 34 similar dispersion is also appreciated if we plot the number of turbines with respect to their full load hours, grouped by the years when they were actually connected.This is presented in Figure 5, where it is clear that the old turbines produce less electricity than the modern ones and that a great dispersion of productivity is present in the onshore facilities in the year 2022. 34he main difference between onshore and offshore power outcomes is presented in Figure 6, which gives the monthly average mutability for WEP during the period 2014-2022.This is calculated daily, then averaged for each month, and then averaged over the 7-year period.It is clear that independent of the power produced or dispersion considerations, the offshore data presents a higher degree of variability at all months.The onshore facilities approach this behavior in Wintertime only.In the calm Summer months, the onshore productivity presents a monotonic behavior as indicated by the low mutability values in Figure 6.This is an important result because it opens the possibility of making use of offshore turbines even in Summertime if appropriate protocols are implemented for local farms where data are more homogeneous.
The indicator defined above will now be reported dynamically for both onshore and offshore data.As already said, strict comparison is not yet possible, but we can get some general trends.We pick two different years to contrast their responses: low WEP (2016) and high WEP (2019).For each of these years, we analyze Summer (July) and Winter (January) performances.This is a total of eight plots that will be presented in Figures 7-10.In all the plots, onshore indicators are presented to the left, while offshore indicators are presented to the right.To allow for comparisons, the scale is the same throughout all these plots, despite the maximum value of 60 for the indicator is clearly exceeded sometimes.
In a real operation, only when the capacity factor exceeds a certain level, wind energy will partially substitute other sources of energy in the grid.The threshold value is fixed by local conditions, and it is not universal.To proceed with the analysis using the entire data for Germany, we arbitrarily set a threshold value of I (t) = 20 as the minimum to begin mixing wind energy with other sources.This is represented by a red horizontal line in Figures 7-10.
Let us begin with the unproductive year 2016.Even for the Winter month of January (Figure 7), the onshore indicator is low, exceeding the threshold red line only at the end of the month, as shown in Figure 7.For the same period, the offshore indicator is higher but discontinuous for most of the month, except at the beginning and at the end of January 2016.These two separate periods are wellmarked and can contribute to producing electricity from wind, thus saving other sources of energy.The capacity factor is over 70% during these good periods lasting about a week each.
Figure 8 presents the same setup but for a poor Summer month (July 2016).Just once, the onshore indicator goes over the red line for a short period during F I G U R E 6 Average monthly mutability for both onshore and offshore WEP productivity 2010-2022.WEP, wind energy production.
F I G U R E 7 Analysis for WEP productivity during January 2016.Indicators for production and capacity factor are reported for onshore production (left) and offshore production (right).WEP, wind energy production.
F I G U R E 8 Analysis for WEP productivity during July 2016.Indicators for production and capacity factor are reported for onshore production (left) and offshore production (right).WEP, wind energy production.
F I G U R E 9 Analysis for WEP productivity during January 2019.Indicators for production and capacity factor are reported for onshore production (left) and offshore production (right).WEP, wind energy production.
F I G U R E 10 Analysis for WEP productivity during July 2019.Indicators for onshore production and capacity factor are reported for onshore production (left) and offshore production (right).WEP, wind energy production.the first week.Even then, the capacity factor reaches only 40%.At the same time, the offshore productivity of the first part of the month is good for a Summer month, with at least five short periods over the red line and capacity factors between 50% and 80%.The message is clear: even in a poor year, for the poorest month, it is possible to handle some good periods of offshore WEP.
The productive year 2019 presents a month of January with low onshore WEP, as presented in Figure 9.Even in a good year, the Winter months contribute very little to the onshore WEP, and such activity shows low chances for good forecasting since the indicator is under the reference line most of the time.Oppositely, offshore WEP shows high productivity during extended periods anticipated by rises of the indicator over the reference line.Actually, the indicator goes over the scale on several occasions, showing the sensitivity of this parameter when energy productivity increases.
Then in Figure 10, we present the situation for the Summer of the year 2019.The onshore productivity deserves almost no comments since both the indicator and the capacity factor stay low for almost the entire month of July.With offshore generation, there are few short periods that raise the indicator function, just over 60%.Thus, onshore is nearly impossible to predict during Summer and its contribution would be scarce; offshore productivity could be partially used, thus saving other sources of energy.In such cases, the reference red line should be tuned carefully for the local situations of the nearby turbines.

| CONCLUSIONS
The productivity gap between offshore and onshore lessens over time as they both become more efficient.Public data could assist by distinguishing the location and altitude of onshore installations.Separation by year of the turbine's fabrication can further inform about the efficiency of any installation.
Seasonal dependence is quite clear in general.Even for the Summer months, like, June, July, and August, when the average onshore capacity factor is about 12%, this parameter is near 27% for offshore generation.WEP is consistently low during Summer at the onshore locations, as shown by its low information content through the indicator function.The information content for the offshore series shows that even in months of low productivity, there are variations in the WEP.This could allow for combined use with other sources of energy or storage for future use.
Summer periods have little impact on onshore production, regardless of the year's overall behavior.It seems there is no way to expect significant periods of direct use of WEP from onshore turbines during Summer.However, even in Summer, there are short profitable periods for offshore productivity.January 2016 looks nearly non-existent for onshore generation.If we look at a more productive year like 2019, January is still very low in the indicator function and in capacity factor.We got a different result for offshore WEP, where these functions are extremely high for most of January 2019 and large enough for January 2016.
One important result reported here is that mutability offers a reliable characterization of the offshore time series independent of the season (see Figure 6).This indicator could render more stable and significant results if confined to specific areas and homogeneity in the installations, which is beyond the possibilities of the present article.
The indicator I(t) defined above shows instantaneous response stepping up to announce useful generation that has been started.When applying this technique to local turbine farms, one could adapt and better tune this function.The present analysis attempts to show a way of detecting promising periods of WEP in a general way.A potential task is to analyze productivity in zones with homogeneous wind energy installations.recognized file, w * which leads to the mutability through Equation ( 2).In the present paper we use the latter only.

A.2 | Tuning process
Figure A2 gives four different results for the mutability of the onshore WEP for the year 2018.This is calculated as the mutability of the daily sequence, which is then averaged over the month.
The original data sequence looks like the second column of Table 1: it is a register of two integers, a dot, and 3 decimal digits.This represents a total of 6 characters.If all are recognized, that compression is labeled (1.6): begins with the first character and goes for six characters in total.If truncation leaves out the third decimal (sixth register), that compression is labeled (1.5), and so on.It should be noticed that the vertical span is the same for the four vertical scales in Figure A2.Then we can observe that curves (1.5) and (1.4) give the largest contrast between months with high and low mutability values.
Figure A3 gives four different results for the mutability of the offshore WEP for the year 2018, obtained in a way similar to the previous figure.Again, tuning (1.5) and (1.4) represent better contrast for high and low mutability values; (1.4) has the additional advantage of handling shorter words.We will stick to (1.4) curves for the present calibration, meaning that we recognize the leading four digits in the WEP series, neglecting all the remaining digits that can be regarded as numerical noise.
F I G U R E A1 Flowchart guiding the process by which the fourth column in Table 1 is generated.
F I G U R E A2 Mutability with different tuning selections for onshore production.
F I G U R E A3 Mutability with different tuning selections for offshore production.

F
I G U R E 3 Average monthly capacity factor for both onshore and offshore WEP productivity 2014-2022.WEP, wind energy production.F I G U R E 4 Distributions of the number of turbines as a function of the full load hours for five different power ranges.F I G U R E 5 Distributions of the number of turbines as a function of the full load hours for five different time ranges (connection year of each turbine is considered here).
Illustration of data handling and the way wlzip works.
T A B L E 1