Modeling of the German Wind Power Production with High Spatiotemporal Resolution

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Article Modeling of the German Wind Power Production with High Spatiotemporal Resolution

Reinhold Lehneis 1,* , David Manske 1 and Daniela Thrän 1,2

1 Department of Bioenergy, Helmholtz Centre for Environmental Research GmbH—UFZ, Permoserstraße 15, 04318 Leipzig, Germany; [email protected] (D.M.); [email protected] (D.T.) 2 Bioenergy Systems Department, DBFZ Deutsches Biomasseforschungszentrum gGmbH, Torgauer Str. 116, 04347 Leipzig, Germany * Correspondence: [email protected]

Abstract: Wind power has risen continuously over the last 20 years and covered almost 25% of the total German power provision in 2019. To investigate the effects and challenges of increasing wind power on energy systems, spatiotemporally disaggregated data on the electricity production from wind turbines are often required. The lack of freely accessible feed-in time series from onshore turbines, e.g., due to data protection regulations, makes it necessary to determine the power generation for a certain region and period with the help of numerical simulations using publicly available plant and weather data. For this, a new approach is used for the wind power model which utilizes a sixth-order polynomial for the speciﬁc power curve of a turbine. After model validation with measured data from a single wind turbine, the simulations are carried out for an ensemble of 25,835 onshore turbines to determine the German wind power production for 2016. The resulting

hourly resolved data are aggregated into a time series with daily resolution and compared with measured feed-in data of entire Germany which show a high degree of agreement. Such electricity

Citation: Lehneis, R.; Manske, D.; generation data from onshore turbines can be applied to optimize and monitor renewable power Thrän, D. Modeling of the German systems on various spatiotemporal scales. Wind Power Production with High Spatiotemporal Resolution. ISPRS Int. Keywords: wind power; satellite-based weather data; spatiotemporal modeling; power generation J. Geo-Inf. 2021, 10, 104. https:// doi.org/10.3390/ijgi10020104

Academic Editors: Wolfgang Kainz 1. Introduction and Luis Ramirez Camargo Despite its volatility, renewable energy from wind turbines has become an essential pillar for the electricity supply in many countries around the world. During the past Received: 21 December 2020 decade, wind power continued its strong forward momentum with signiﬁcant advances in Accepted: 14 February 2021 Published: 23 February 2021 grid integration and cost reduction. For example, 60.4 GW of new wind turbine capacity was installed worldwide in 2019, the second highest value in history and close to the 2015

Publisher’s Note: MDPI stays neutral peak of 63.8 GW, leading to a total volume of 651 GW [1]. The German onshore capacity with regard to jurisdictional claims in has increased from 6.1 GW in the year 2000, when the German Renewable Energy Act published maps and institutional afﬁl- (EEG) was introduced, to 53.3 GW at the end of 2019 [2]. These numbers are expected to iations. rise in the future due to the decreasing levelized costs of electricity [3] and the needed further de-carbonization of the power sector to achieve the currently set climate targets in Germany, e.g., reducing greenhouse gas emissions by at least 55% below 1990 levels by 2030, according to the Federal Climate Change Act (KSG 2019). The rapid advancement of variable renewable energies like wind power not only has Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. an essential impact on the future development of power grids but on many other ﬁelds of This article is an open access article the energy sector as well, triggering the need for further research. Thus far, current energy distributed under the terms and studies for Germany often contain the electricity production from wind turbines with a high conditions of the Creative Commons spatial resolution, but lack a high temporal resolution, such as the energy transition analysis Attribution (CC BY) license (https:// of the power sector [4]. On the other hand, there are also wind power simulations available, creativecommons.org/licenses/by/ such as the potential analysis for hybrid renewable energy systems in Central Europe [5,6], 4.0/). which already provide a high spatiotemporal resolution using highly resolved weather

ISPRS Int. J. Geo-Inf. 2021, 10, 104. https://doi.org/10.3390/ijgi10020104 https://www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2021, 10, 104 2 of 18

data but cannot represent this information for existing wind turbines due to the lack of detailed plant datasets. In order to gain a better understanding of the effects and challenges caused by a growing share of variable renewables on energy systems, high spatiotemporal distributions of the power generation, e.g., down to municipal and hourly resolutions, will increasingly become a crucial factor for future research. Especially, energy studies on decentralized power systems with many renewable power plants can benefit from this information, e.g., to prevent possible power shortages induced by regional dark doldrums or local component failures [7]. However, the lack of disaggregated electricity production data for a certain region and period, e.g., due to strict data protection regulations, makes it difficult for decision makers and researchers to investigate the multiple effects of increasing wind power on a regional or local scale. This publication presents a new approach for creating power generation data of wind turbines with a high spatiotemporal resolution, which can help to close the previously mentioned gap. Up to now, energy transition maps have been developed to support decision makers and researchers with such data down to the municipal level [4], but only on the basis of an annual power production from onshore turbines. In order to be able to generate this information also for a shorter period of time, spatiotemporally resolved data are necessary, which are made possible with the presented model approach using publicly available plant and weather data. The remainder of this paper is organized as follows: Section2 introduces the used plant and weather data, as well as the information needed for calibration and validation of the simulations. The wind power model, which is a further development of our physical model presented in [8], and its implementation are described in Section3. In Section4, this simulation model is applied to a measured single turbine and, subsequently, to an ensemble of 25,835 onshore turbines located in Germany. Afterwards, the resulting time series from the numerical simulations are aggregated and compared with measured feed-in data for the validation. Section5 discusses the performed simulations and introduces the first utilization examples using the obtained results. Last but not least, this study ends with brief conclusions in Section6.

2. Data The following subsections describe all the data required for the simulation model including their origin and properties.

2.1. Plant Dataset The initial wind turbine dataset originates from the EE-monitor project [9], which is freely accessible via the data research portal (www.ufz.de/drp (accessed on 5 March 2020)) of the UFZ. This dataset, with detailed onshore turbine information including the geographical location, installed capacity, hub height, rotor diameter, and the year of commissioning until end of the year 2015, was compiled from official sources of the federal states of Germany [10]. As known from plant-related studies [10–12], wind turbine datasets for larger regions or an entire country are rarely complete due to the high number of plants with many specific parameters. That is why different procedures were developed to complete such turbine datasets as much as possible. For the turbine data of the EE-monitor project, the method of random forests was applied to generate the missing information [13], e.g., to reconstruct an unknown hub height of a certain turbine by the other available parameters. In order to extend this plant dataset to all federal states and update it to the year 2016, the wind turbines of the German city states and the onshore turbines erected in 2016 were inserted by using additionally requested data from official sources. Finally, all wind turbines of this dataset were compared with the Core Energy Market Data Register [14] by a spatial join. If the turbine locations were nearly identical in this operation, i.e., showing a spatial deviation smaller than 75 m in both data sources, the corresponding turbine data of the plant dataset were supplemented with information from the Core Energy Market Data Register. This join has often inserted the exact hub ISPRS Int. J. Geo-Inf. 2021, 10, 104 3 of 18

ISPRS Int. J. Geo-Inf. 2021, 10, 104 3 of 18 the corresponding turbine data of the plant dataset were supplemented with information from the Core Energy Market Data Register. This join has often inserted the exact hub height instead of the estimated value generated by the random forest method, the date of (de-)commissioning,height instead of the and estimated the turbine value type generated into th bye dataset. the random Thus, forests in many method, cases, thethe dateactual of date(de-)commissioning, of (de-)commissioning and the can turbine be used type instead into the of dataset. the less Thus, precise in manycommissioning cases, the actualyear, whichdate of enables (de-)commissioning the wind power can model be used to insteadconsider of the the intra-annual less precise plant commissioning changes. After year, thesewhich improvements enables the wind and powerfiltering model the data to considerby wind theturbines intra-annual operated plant in the changes. investigated After yearthese 2016, improvements the final plant and dataset filtering consists the data of by 25,835 wind onshore turbines turbines operated corresponding in the investigated to a totalyear capacity 2016, the of final 43.61 plant GW. dataset This value consists is in of good 25,835 agreement onshore turbineswith the correspondingofficially installed to a capacitytotal capacity of 45.28 of GW 43.61 of GW.all on Thisshore value turbines is in in good Germany agreement for 2016 with [2]. the The officially small deviation installed ofcapacity less than of 45.283.7% from GW of the all official onshore sum turbines indicates in Germany that most for wind 2016 turbines [2]. The are small included deviation in theof lessfinal than dataset. 3.7% from the official sum indicates that most wind turbines are included in the finalFor each dataset. turbine, the plant dataset contains the geographical position using the latitudeFor and each longitude turbine, the coordinates, plant dataset the contains associated the geographical local administ positionrative usingunit (LAU)-Id the latitude 1, 1 ratedand longitude power, hub coordinates, height, turbine the associated type, and local the administrative date of (de-)commissioning, unit (LAU)-Id ,as rated shown power, in Tablehub height,1. It should turbine be stated, type, andthat the rotor date ofdiameter (de-)commissioning, of a wind turbine as shownis not needed in Table for1. the It should be stated, that the rotor diameter of a wind turbine is not needed for the model model approach introduced in this study, and therefore all uncertainties regarding this approach introduced in this study, and therefore all uncertainties regarding this parameter parameter do not influence the simulation results. do not influence the simulation results. Table 1. Parameters of the turbine dataset used for the wind power model. Table 1. Parameters of the turbine dataset used for the wind power model. Parameter Usage Parameter Usage Latitude required LatitudeLongitude requiredrequired Longitude required 1 LAU-Id 1LAU-Id optional optional Rated powerRated power required required Hub heightHub height required required TurbineTurbine type type optional optional Commission date required DecommissionCommission date date optional required Decommission date optional 1 The LAU-Id is an eight-digit identifier which determines a municipal area or local administrative unit (LAU). 1 The LAU-Id is an eight-digit identifier which determines a municipal area or local administrative unit (LAU).

FigureFigure 1 showsshows the the installed installed capacity capacity of of the the wind wind turbines turbines at atthe the spatial spatial resolution resolution of LAU2of LAU2 in Germany in Germany for for 2016 2016 and, and, as as additional additional information, information, the the intra-annual intra-annual capacity capacity increase during this time. increase during this time.

MW MW 250 125 200 100 150 75 100 50 50 25

(a) (b)

Figure 1. (a) Installed wind turbine capacity and (b) intra-annual capacity increase at LAU2 level in Germany for 2016. In the grey areas no wind turbines are (a) installed or (b) have been added during this year. ISPRS Int. J. Geo-Inf. 2021, 10, 104 4 of 18

Figure 1. (a) Installed wind turbine capacity and (b) intra-annual capacity increase at LAU2 level in Germany for 2016. In ISPRSthe Int. grey J. Geo-Inf. areas2021 no, wind10, 104 turbines are (a) installed or (b) have been added during this year. 4 of 18

2.2. Calibration Data 2.2. CalibrationFor a reasonable Data calibration of the wind power model, further information is required, which is not included in the plant dataset shown in Table 1. For the presented For a reasonable calibration of the wind power model, further information is required, simulation model, the data of the specific power curve of a wind turbine, including its which is not included in the plant dataset shown in Table1. For the presented simulation characteristic cut-in, rated, and cut-out speed, are necessary. Such power curves, which model, the data of the speciﬁc power curve of a wind turbine, including its characteristic cut- show the relationship between the wind speed at hub height and the output power at a in, rated, and cut-out speed, are necessary. Such power curves, which show the relationship standardized air density of 1.225 kg/m3, are available in the technical datasheets of the between the wind speed at hub height and the output power at a standardized air density turbine manufacturer or can be found on internet platforms, e.g., at The Wind Power of 1.225 kg/m3, are available in the technical datasheets of the turbine manufacturer or can (www.thewindpower.net) [15]. be found on internet platforms, e.g., at The Wind Power (www.thewindpower.net)[15]. TheThe graph graph in in Figure 22 showsshows thethe typicaltypical powerpower curvecurve ofof aa pitch-controlledpitch-controlled windwind turbineturbine with with its its characteristic characteristic parameters.

0.6 Rated speed Cut-out speed

0.5 Rated power

0.4

0.3

0.2 Output power (MW) 0.1 Cut-in speed

0.0 0 4 8 1216202428 Wind speed (m/s)

FigureFigure 2. TypicalTypical power curve (blue line) of a wind tu turbinerbine using the example of an Enercon E-40 with 0.5 MW rated power. The black dots on the power curve mark the discrete values as given in thethe manufacturer’s manufacturer’s datasheet datasheet [16]. [16]. The The depicted depicted ch characteristicaracteristic parameters parameters of of the the power curve are explainedexplained in in the the following following text.

AtAt wind wind speeds speeds belo beloww the the cut-in cut-in speed speed (v (cut-invcut-in) there) there is insufficient is insufﬁcient torque torque exerted exerted by theby thewind wind stream stream on onthe the turbine turbine blades blades to to make make them them rotate. rotate. However, However, when when the the wind speedspeed increases, the turbine beginsstarts to to rotate rotate and and generates generates electricity. The The wind speed when the the turbine turbine begins starts toto deliverdeliver energyenergy intointo thethe powerpower gridgrid isis calledcalled cut-incut-in speed.speed. For mostmost wind turbines itit isis betweenbetween 22 and and 4 4 m/s. m/s. WhenWhen thethe wind wind speed speed rises rises above above this this cut-in cut- inspeed, speed, the the level level of of the the generated generated electricity electricityincreases increases rapidly.rapidly. Typically, somewheresomewhere in thethe range range of of 12 and 14 m/s, the the electrical electrical ou outputtput reaches reaches the the nominal nominal value value that that the wind turbineturbine is is designed for. This This value is called rated power ((PR)) and the concerning wind speedspeed is is the the rated rated speed speed (v (vratedrated). At). At higher higher wind wind speeds, speeds, the the turbine turbine is designed is designed to limit to limit the outputthe output to this to thislevel. level. How How this thisbehavior behavior is done is done depends depends on the on thetechnical technical design, design, but butfor mostfor most onshore onshore turbines, turbines, it is achieved it is achieved by adju bysting adjusting the blade the blade angles angles depending depending on the on wind the speedwind speedto keep to the keep electrical the electrical output output constant. constant. This kind This of kind power of power regulation regulation is called iscalled pitch control.pitch control. When When the wind the wind speed speed increases increases well well above above the the rated rated speed, speed, the the forces forces on on the turbineturbine structure structure continue to rise and, and, at at some some point, there is a risk of of damage. damage. As As a a result, result, aa switch-off and braking system is employed to bring the rotor to a standstill. The wind speedspeed required required for for a a switch-off switch-off is is called called cut-out cut-out speed speed (v (vcut-outcut-out) which) which is about is about of 25 of 25m/s m/s for manyfor many onshore onshore turbines. turbines. ForFor losses of wind turbines, which cannot be captured by calculations based on the power curve, an additional reduction of the pr producedoduced electricity has to be considered in thethe numerical numerical simulations. simulations. Such Such losses losses ar aree caused, e.g., by the following effects: 1. PowerPower losses losses due due to to mutual mutual shading shading of of adjacent adjacent turbines turbines (wake (wake effect). effect). 2. Switch-offs due to wind turbine revisions or bird and bat protection. 3. Feed-in interruptions due to energy surpluses in the power grids.

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Due to the lack of this information on each wind turbine, this kind of turbine losses is included in the wind power model as an averaged overall value for the entire plant ensemble.

2.3. Weather Database High-resolution weather data are a key requirement for modeling the power production from wind turbines and, herein, the data quality plays an important role for the accuracy of the performed simulations. For the region of Central Europe or Germany, various weather products with different spatiotemporal resolutions are freely accessible via the web interfaces of many meteorological services. So-called reanalysis products have emerged as a popular source of weather data for various electricity generation studies, especially for wind power modeling [11,17–20]. Such reanalysis weather data are calculated using numerical forecast models, re-running these weather models for a certain period in the past, and making corrections with existing meteorological measurements. In general, the spatial resolutions of global reanalysis data, e.g., the MERRA and MERRA-2 products with a resolution of about 50 km [21,22], are not sufﬁcient for the level of detail needed for this paper. In contrast to global weather products, regional reanalysis data have typically higher spatial resolutions, e.g., the COSMO-REA6 weather data covering Europe with a spatial resolution of about 6 km [23], and, therefore, would already allow detailed simulation results with our wind power model. This publication goes a step further and uses satellite-based weather data from the Satellite Application Facility on Climate Monitoring (CMSAF) collaboration [24] via the open-access web interface of the Photovoltaic Geographical Information System (PVGIS) [25]. The CMSAF database in PVGIS has a temporal resolution of an hour and a spatial resolution of about 2.5 km for the region of Germany according to [25]. The delivered hourly resolved time series for a required location and period contains the following information relevant for the simulation model: date and time in coordinated universal time (UTC), ground elevation, ambient temperature at 2 m, and the total wind speed at 10 m above ground level. Although the wind speed is only available at 10 m in PVGIS, which may reduce the accuracy of the wind speed extrapolation to the required hub height of the onshore turbines, the weather data are retrieved individually for each plant location. This circumstance avoids additional spatial interpolations of weather data to the speciﬁed turbine sites and, therefore, the uncertainties caused by such routines. Moreover, PVGIS also provides the ground elevation at the plant location needed for the calculation of air pressure as a function of the total height above sea level. Thus, the CMSAF weather product via PVGIS 5.1 was used for the simulation of the German wind power production. In addition, the wind power model and the already published photovoltaic model [26] can be used together with the same weather product in PVGIS, which improves the mutual combinability of the simulation results, e.g., because they have the same time base.

2.4. Validation Data The obtained results from numerical simulations have to be compared with measurements on real systems in order to validate the underlying model and assess its accuracy. For the validation of the wind-to-power conversion, measured time series of the output power and the corresponding wind speed from an onshore turbine with known specific parameters are required. Such measurements, which can be regarded as the most accurate data for validating a wind power model, are difficult to obtain from wind farm operators, e.g., due to data protection regulations. Through a cooperation with the Institute for Applied Geosciences of the TU Berlin concerning the influence of turbine noise on seismic recordings, measured wind speed and output power data of a single turbine are available for this study. The measurements were carried out on a General Electric GE 1.5sl with 1.5 MW rated power and 100 m hub height between 11 and 14 December 2015. The following diagram (Figure3) shows the time series of the output power and the corresponding wind speed at hub height. ISPRS Int. J. Geo-Inf. 2021, 10, 104 6 of 18

with 1.5 MW rated power and 100 m hub height between 11 and 14 December 2015. The ISPRS Int. J. Geo-Inf. 2021, 10, 104 6 of 18 following diagram (Figure 3) shows the time series of the output power and the corresponding wind speed at hub height.

1.6 20.0

1.2 15.0

0.8 10.0

0.4 5.0 Wind speed (m/s) Wind speed Output power (MW) 0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (h) FigureFigure 3. 3. MeasuredMeasured output power (black(black line)line) and and wind wind speed speed (blue (blue line) line) time time series series of aof wind a wind turbine tur- bineGeneral General Electric Electric GE 1.5slGE 1.5sl located located in Zodel in Zodel near near the the town town of Görlitz. of Görlitz. The The depicted depicted measurements measurements are areperformed performed every every 10 min10 min over over a period a period of 60of h.60 h.

Furthermore,Furthermore, the the developed developed simulation simulation model model includes includes not not only only physical physical algorithms algorithms forfor the the wind-to-power wind-to-power conversion conversion but but takes takes into into account account additional additional turbine turbine losses losses (de- (de- scribedscribed in in Section Section 2.2)2.2) and and intra-annual intra-annual changes changes of of the the wind wind turbines turbines for for the the determination determination ofof the the generated generated electricity. electricity. The The transformation transformation of of the the simulated simulated time time series series from from UTC UTC to to locallocal time time and and the the appropriate appropriate temporal temporal aggregation aggregation of of the the final ﬁnal results results are are also also performed performed byby the the wind wind power power model. model. Thus, Thus, the the time time series series from from the the simulations simulations should should be be validated validated withwith measured measured time time series series as as well. well. PowerPower production production data data of of variable variable renewables renewables like like wind wind power power are are only only available available for for largerlarger regions, regions, such such as as entire entire countries. countries. Hence, Hence, the the electricity electricity generation generation from from all all wind wind turbinesturbines of of the the dataset has toto bebe spatiallyspatially aggregatedaggregated toto compare compare it it with with measured measured feed-in feed- indata data for for the the whole whole of of Germany, Germany, provided provided by by the the internet internet platform platform SMARD SMARD of theof the Federal Fed- eralNetwork Network Agency Agency (www.smard.de (www.smard.de)[27].) From[27]. thisFrom platform, this platform, measured measured data of thedata German of the Germanwind power wind production power production were downloaded were downloaded for the entire for yearthe entire 2016. year It should 2016. be It mentionedshould be mentionedthat no measurement that no measurement data were availabledata were by av SMARDailable by on SMARD three different on three days different during days this duringperiod this and, period thus, the and, resulting thus, the zero resulting values arezero not values considered are not for considered the validation for the and valida- faded tionout inand the faded concerning out in the diagram concerning (Figure diagram 9). (Figure 9).

3.3. Model Model ThisThis section section describes describes our our simulation simulation model model for for the the electricity electricity generation generation from from wind wind turbines and on which physical laws it has been implemented. In general, power pro- turbines and on which physical laws it has been implemented. In general, power produc- duction data for energy studies can be determined either with statistical methods, e.g., tion data for energy studies can be determined either with statistical methods, e.g., auto- auto-regressive and Monte Carlo models, or with physical models [11,18]. Unlike statistical regressive and Monte Carlo models, or with physical models [11,18]. Unlike statistical models [28], the results of physical models, such as the wind power model presented herein, models [28], the results of physical models, such as the wind power model presented are based on high-resolution weather data from meteorological measurements or numerical herein, are based on high-resolution weather data from meteorological measurements or models. Therefore, an advantage of physical models compared to statistical methods is the numerical models. Therefore, an advantage of physical models compared to statistical possibility to provide electricity generation data on a highly resolved spatiotemporal scale. methods is the possibility to provide electricity generation data on a highly resolved spa- The complete development process from calibration to validation of the wind power tiotemporal scale. model is outlined in Figure4. In this ﬁgure, input and output data are symbolized as The complete development process from calibration to validation of the wind power containers and the arrows indicate the direction of the data ﬂow. model is outlined in Figure 4. In this figure, input and output data are symbolized as containers and the arrows indicate the direction of the data flow.

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Figure 4. Scheme of the development process of the wind power (WP) model. FigureFigure 4. Scheme 4. Scheme of the of development the development process process of the of wind the wind power power (WP) (WP) model. model. The internal structure of the simulation model is depicted in Figure 5. The plant and The Theinternal internal structure structure of the of simulation the simulation model model is depicted is depicted in Figure in Figure 5. The5. The plant plant and and weatherweather datadata inin thisthis ﬂowchartflowchart representrepresent thethe inputinput datadata forfor thethe calibratedcalibrated windwind powerpower weather data in this flowchart represent the input data for the calibrated wind power model.model. TheThe requiredrequired calculationcalculation stepssteps ofof thethe simulationsimulation modelmodel areare displayeddisplayed asas rectanglesrectangles model. The required calculation steps of the simulation model are displayed as rectangles andand allall thethe otherother symbolssymbols havehave thethe samesame meaningmeaning asas describeddescribed forfor FigureFigure4 .4. and all the other symbols have the same meaning as described for Figure 4.

FigureFigure 5.5. StructureStructure ofof thethe WPWP modelmodel shownshown asas aa flowchart.flowchart. Figure 5. Structure of the WP model shown as a flowchart. AccordingAccording toto FigureFigure5 ,5, the the wind wind power power model model can can be be divided divided into into the the following following main main According to Figure 5, the wind power model can be divided into the following main calculationcalculation steps,steps, whichwhich areare performedperformed forfor eacheach windwind turbineturbine ofof thethe plantplant dataset:dataset: calculation steps, which are performed for each wind turbine of the plant dataset: 1. 1.ExtrapolationExtrapolation of the of weather the weather data dataprovided provided for the for specified the specified plant plant location location to the to thehub hub 1. Extrapolation of the weather data provided for the specified plant location to the hub height.height. height. 2. 2.Wind-to-powerWind-to-power conversion conversion with the with help the of help the ofspecific the specific power powercurve of curve the wind of the tur- wind 2. Wind-to-power conversion with the help of the specific power curve of the wind turbine.turbine. bine. 3. 3.CorrectionCorrection of the of output the output power power using using the ai ther temperature air temperature and andpressure pressure at hub at hub height. height. 3. Correction of the output power using the air temperature and pressure at hub height. 4. 4.CalculationCalculation of the of produced the produced electricity electricity considering considering turbine additional losses and losses the andoperating the date of 4. Calculation of the produced electricity considering turbine losses and the operating time.(de-)commissioning. time. 5. 5.Temporal Temporal aggregation aggregation of the of simulat the simulateded time timeseries series and anddata datastorage. storage. 5. Temporal aggregation of the simulated time series and data storage. For the extrapolation of the wind speed to the required hub height the Hellmann’s For the extrapolation of the wind speed to the required hub height the Hellmann’s law is applied, which can be expressed by the following relationship: law is applied, which can be expressed by the following relationship:

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For the extrapolation of the wind speed to the required hub height the Hellmann’s law is applied, which can be expressed by the following relationship:

H α v ≈ v0· (1) H0

In Equation (1), v is the unknown wind speed at hub height H and v0 stands for the known wind speed at the height H0, which is 10 m above the ground and obtained from the weather data. The exponent α is called the friction coefficient or Hellmann exponent. This coefficient is a function of the topography at a specific location and frequently assumed as a value of 1/7 for open land [29,30], which corresponds well with the sites of most onshore turbines in Germany. Hence, this value is used for the simulations, but, if necessary and reasonable, other averaged values, e.g., 1/5 or 1/6, can be easily applied in the wind power model. The next step converts the calculated wind speed at hub height to the corresponding output power of the wind turbine. This operation is performed with the help of the power curve, which returns the output power at a standardized air density of 1.225 kg/m3. The main advantage of using the power curve is that no further information about the turbine technology, e.g., the specific rotor diameter or electrical losses of the power generator and converter electronics, has to be known to calculate the output power. Thus, in the presented simulation model, each wind turbine can be treated like a black box with the power curve as its transfer function. The nonlinear section of a typical power curve, as depicted in Figure6, is typically given by the manufacturer as a table of values. In order to integrate such a nonlinear and discrete relationship into the simulation model with high accuracy and without any additional interpolation routines for intermediate values, the specific power curve is divided into separate sections and these sections are developed to analytical functions. Moreover, to be able to assign the same power curve to similar wind turbines with a different rated power, it is beneficial to use normalized power curves for the wind power model. The specific power curve of most wind turbines, which are often pitch-controlled like the example given in Figure2, is implemented according to Equation (2). In this relationship, N(v) stands for the normalized output power as a function of the wind speed, i.e., N(v) = P(v)/PR ∈ [0, 1]:  0, v < vcut−in   f (v), v ≤ v ≤ v N(v) = cut−in rated (2)  1, vrated < v ≤ vcut−out  0, v > vcut−out

The expression ( ) = 6 i f v ∑i=0 aiv (3) is a sixth-order polynomial which has to be derived for each power curve used for the numerical simulations. The required coefficients ai of Equation (3) are determined by polynomial regression using the Excel software. It turns out, as shown in Figure6 for an Enercon E-40, that the development of the nonlinear section of the power curve, i.e., the range between the specific cut-in and rated speed, to a sixth-order polynomial results in precise approximations with coefficients of determination (R2) better than 0.99 and root-mean-square errors (RMSE) lower than 0.01. ISPRS Int. J. J. Geo-Inf. Geo-Inf. 2021,, 10,, 104 104 9 9of of 18

1,0

0,8 R² = 0.9998

0,6 RMSE = 0.0049

0,4

0,2 Normalized Normalized output power

0,0 02468101214 Wind speed (m/s)

FigureFigure 6. 6. ApproximationApproximation of of the the nonlinear nonlinear section section of ofthe the normalized normalized power power curve curve of ofan anEnercon Enercon E- 40E-40 to toa sixth-order a sixth-order polynomial polynomial (blue (blue line) line) with with the thecorresponding corresponding coefficient coefﬁcient of determination of determination (R2) and(R2) root-mean-square and root-mean-square error (RMSE). error (RMSE). The black The dots black on dots the onblue the line blue mark line the mark normalized the normalized values determinedvalues determined from the from discrete the discretevalues shown values in shown Figure in 2 Figureand given2 and in giventhe manufacturer’s in the manufacturer’s datasheet [16].datasheet [16].

ForFor wind turbines with a variable power level above the rated speed, e.g., turbines with a passive passive stall stall regulation, regulation, the range betw betweeneen the rated and cut-ou cut-outt speed is developed developed toto a a sixth-order sixth-order term byby polynomialpolynomial regressionregression as as well. well. After After deriving deriving such such analytical analytical repre- rep- resentationssentations of of the the speciﬁc specific power power curve, curve, the outputthe output power power can be can calculated be calculated straightforwardly straightfor- wardlyfor any for given any wind given speed, wind i.e., speed, without i.e., without any additional any additional effort for effort interpolation for interpolation routines. rou- This 3 tines.calculation This calculation step returns step the outputreturns powerthe outputPN at power a ﬁxed P airN at density a fixed of 1.225air density kg/m of, which 1.225 ◦ kg/mcorresponds3, which to corresponds an ambient to temperature an ambient of temperature 288.15 K (15 ofC) 288.15 at normal K (15 atmospheric°C) at normal pressure atmos- phericof 1.013 pressure bar. Hence, of 1.013 the obtainedbar. Hence, power the obta valueined has power to be correctedvalue haswith to be the corrected air temperature with the airand temperature pressure at and hub pressure height. For at hub this, height. the ambient For this, temperature the ambient provided temperature by the provided weather bydata the is weather extrapolated data is according extrapolated to the acco generalrding rule to the given general in [31 rule]: given in [31]:

T≈≈ T0−−0.0065 0.0065·(H ∙ (−− H0)) (4)

In this relationship, T describes the air temperature in K at hub height H and T0 stands In this relationship, T describes the air temperature in K at hub height H and T0 for the ambient temperature at height H0, which is 2 m above ground level. After estimat- stands for the ambient temperature at height H0, which is 2 m above ground level. After ingestimating the air temperature the air temperature at hub height, at hub assuming height, assuming an average an averagetemperature temperature gradient gradient over all weatherover all weatherconditions conditions of 0.0065 ofK/m 0.0065 [31], K/m the outp [31],ut the power output can power be corrected can be by corrected the following by the expressionfollowing expressionderived from derived the barometric from the barometricheight formula height and formula the power and thecurve power correction curve accordingcorrection to according [32]: to [32]:

288.15 ≈∙288.15 ∙− H (5) P ≈ P · ·exp − 8430T (5) N T 8430 In Equation (5), which also considers an exponential reduction of the air pressure with Inthe Equation total height, (5), P which stands also for considersthe corrected an exponential output power reduction at the air of temperature the air pressure and pressurewith the totalat hub height, height.P Thestands total for height the corrected HT is given output by the power sum at of the the air hub temperature height and andthe groundpressure elevation at hub height. above Thesea level, total heightand theH so-calledT is given scale by the height sum has of the a value hub heightof about and 8,430 the mground at an isothermal elevation above temperature sea level, of and 288.15 the K. so-called Since changes scale height in atmospheric has a value pressure of about caused 8430 m byat anthe isothermal weather are temperature not considered of 288.15 in these K. Since calculations, changes indue atmospheric to the lack pressureof highly caused resolved by airthe pressure weather data are not in PVGIS, considered this incorrection these calculations, of the output due power to the takes lack ofonly highly into resolvedaccount the air airpressure temperature data in at PVGIS, hub height this correction and the air of pressure the output as power a function takes of only the intototal accountheight. the air temperatureAfter the at correction hub height of andthe output the air pressurepower, th ase next a function calculation of the step total of height. the wind power modelAfter is to the determine correction the of generated the output electric power,ity the by next multiplying calculation the step output of the power wind by power the givenmodel time is to slot, determine which is the defined generated by the electricity temporal by resolution multiplying of the the used output weather power product by the mostlygiven time offering slot, whichan hourly is deﬁned resolution. by the This temporal step also resolution includes of additional the used weather losses of product wind turbines,mostly offering which cannot an hourly be covered resolution. by calculatio This stepns also based includes on the power additional curve, losses and ofthe wind date turbines, which cannot be covered by calculations based on the power curve, and the

ISPRS Int. J. Geo-Inf. 2021, 10, 104 10 of 18

of (de-)commissioning in order to consider intra-annual plant changes. Finally, the result- ingdate hourly of (de-)commissioning resolved time series in order is transformed to consider from intra-annual UTC to local plant time changes. and, if Finally, required, the convertedresulting hourly into an resolved additional time time series series, is transformed e.g., with from daily UTC resolution. to local timeAfter and, the ifdescribed required, stepsconverted are performed into an additional for each wind time turbine series, e.g.,of the with dataset, daily the resolution. time series After of the the entire described plant ensemblesteps are performedare stored foras comma-separated each wind turbine values of the for dataset, subsequent the time processing, series of the e.g., entire applying plant aensemble geographical are stored information as comma-separated system (GIS) or values a web-based for subsequent GIS application. processing, e.g., applying a geographical information system (GIS) or a web-based GIS application. 4. Results 4. Results The following subsections present the performed simulations using the previously describedThe following input data subsections and the wind present power the model. performed simulations using the previously described input data and the wind power model. 4.1. Simulation of a Single Wind Turbine 4.1. Simulation of a Single Wind Turbine For proof of concept and model validation, the output power of a wind turbine with For proof of concept and model validation, the output power of a wind turbine with known specific parameters is simulated and, afterwards, compared with a measured feed- known speciﬁc parameters is simulated and, afterwards, compared with a measured feed- in time series of this plant. The measurements were performed on a General Electric GE in time series of this plant. The measurements were performed on a General Electric GE 1.5sl with 1.5 MW rated power and 100 m hub height located in Zodel near the town of 1.5sl with 1.5 MW rated power and 100 m hub height located in Zodel near the town of Görlitz. As introduced in Section 2.4, the output power and wind speed were measured Görlitz. As introduced in Section 2.4, the output power and wind speed were measured every 10 min over a period of 60 h (Figure 3). For the calibration of the wind power model, every 10 min over a period of 60 h (Figure3). For the calibration of the wind power model, the power curve of this turbine, as shown in Figure 7, is developed into a sixth-order pol- the power curve of this turbine, as shown in Figure7, is developed into a sixth-order ynomial and implemented with its characteristic parameters, e.g., the specific cut-in and polynomial and implemented with its characteristic parameters, e.g., the speciﬁc cut-in rated speed. and rated speed.

1.8 Rated power 1.5 MW 1.5

Rated speed 15 m/s 1.2

0.9

0.6 Output power (MW) 0.3 Cut-in speed 3 m/s

0.0 0246810121416 Wind speed (m/s) Figure 7. RequiredRequired section section of of the the guaranteed guaranteed power curve (blue line) of the the General General Electric GE 1.5sl, which is givengiven byby thethe discretediscrete values values (black (black dots dots on on the the blue blue line) line) taken taken from from the the turbine turbine database database of ofThe The Wind Wind Power Power [15 [15].].

Moreover, thethe valuevalue for for additional additional turbine turbine losses losses and and the the Hellmann Hellmann exponent exponent were were set setto zeroto zero for for this this simulation, simulation, since since the windthe wind speed speed was was directly directly measured measured at hub at hub height. height. The Theground ground elevation elevation and ambient and ambient temperature temperatur requirede required for the calculationsfor the calculations were retrieved were forre- trievedthis turbine for this site turbine via PVGIS site via using PVGIS the CMSAFusing the weather CMSAF database. weather database. The following The following diagram diagram(Figure8 )(Figure shows the8) shows simulated the simulated and measured and measured time series time of the series output of the power output from power this fromsingle this turbine. single turbine.

ISPRS Int. J. J. Geo-Inf. Geo-Inf. 2021,, 10,, 104 104 1111 of of 18

1.6

1.2

0.8

0.4 Output power (MW) 0.0 0 4 8 12162024283236404448525660 Time (h) FigureFigure 8. 8. SimulatedSimulated (black (black line) line) and and measured measured (blue (blue line) line) output output power power of the the wind wind turbine turbine General ElectricElectric GE GE 1.5sl over a period of 60 h with a temporal resolution of 10 min.

AsAs depicted inin FigureFigure8 ,8, the the wind wind power power model model reproduces reproduces the the pattern pattern of the of measuredthe meas- uredtime seriestime series very well very over well the over whole the period. whole Theperiod. frequent The underestimationfrequent underestimation of the simulation of the simulationresults is mainly results caused is mainly by caused the fact by that the the fact model that the uses model the guaranteeduses the guaranteed power curve power of curvethe General of the ElectricGeneral GE Electric 1.5sl from GE 1.5sl the manufacturer, from the manufacturer, which may which often be may exceeded often be under ex- ceededreal conditions. under real The conditions. RMSE of The the RMSE 10 min of data the over10 min the data complete over the period, complete as a period, statistical as ameasure statistical for measure such deviations, for such deviations, reaches a value reaches of 84.8 a value kW. of Despite 84.8 kW. the Despite existing the deviations, existing deviations,the introduced the introduced wind power wind model power leads model to realistic leads results to realistic with results a sufficient with accuracy.a sufficient In accuracy.addition, aIn Pearson addition, correlation a Pearson between correlation the firstbetween differences the first of differences the simulated of andthe simulated measured andtime measured series shows time a series strong shows positive a strong linear posi relationshiptive linear with relationship a correlation with coefficient a correlation (R- coefficientvalue) of 0.96, (R-value) indicating of 0.96, that indicating the value that pattern the value of the pattern two time of the series two vary timein series the samevary indirection the same and direction magnitude. and magnitude. Hence, this Hence, simulation this simulation model can model be used can tobe determineused to deter- the mineoutput the power output and power the corresponding and the corresponding electricity electricity production production from wind from turbines. wind turbines. 4.2. Simulation of the Plant Ensemble 4.2. Simulation of the Plant Ensemble Given the lack of freely accessible electricity production data of wind turbines with Given the lack of freely accessible electricity production data of wind turbines with a high spatiotemporal resolution, which was the chief motivation for the wind power a high spatiotemporal resolution, which was the chief motivation for the wind power model presented in this study, it is not possible to benchmark the performance of the whole model presented in this study, it is not possible to benchmark the performance of the turbine ensemble on a spatially resolved scale. However, if the simulation results are whole turbine ensemble on a spatially resolved scale. However, if the simulation results spatially aggregated over Germany, they can be compared with a publicly available feed-in aretime spatially series from aggregated all German over onshore Germany, turbines, they can provided be compared by SMARD with [ 27a publicly]. available feed-inIn time this series subsection, from all the German wind poweronshore model turbines, was provided used to determineby SMARD the [27]. electricity generationIn this fromsubsection, 25,835 windthe wind turbines power in model Germany was for used the to year determine 2016. For the these electricity simulations, gen- erationeach wind from turbine 25,835 of wind the plant turbines ensemble in German is calculatedy for the individually year 2016. and For the these required simulations, weather eachand groundwind turbine elevation of datathe areplant retrieved ensemble via is the calculated PVGIS web individually interface for and each the turbine required site, weatherusing its and geographical ground elevation position. Sincedata theare turbineretrieved type via is the often PVGIS not given web ininterface the plant for dataset, each turbinedue to missingsite, using information its geographical from official position. sources Since [8 ],the the turbine turbines type are is assigned often not to differentgiven in thepower plant classes dataset, with due typical to missing power information curves. These from power official classes sources with [8], the the corresponding turbines are assignedranges and to thedifferent applied power turbine classes types with are showntypical inpower Table 2curves.. For example, These power for wind classes turbines with thewith corresponding a rated power ranges in the rangeand the between applied 0.25 turb andine 0.75 types MW, are the shown normalized in Table power 2. For curve exam- of ple,an Enercon for wind E-40 turbines with a with rated a powerrated power of 0.5 MW in the was range used between in the simulation 0.25 and model.0.75 MW, the normalized power curve of an Enercon E-40 with a rated power of 0.5 MW was used in the simulation model.

Table 2. Power classes with the corresponding ranges of rated power (PR) and the applied turbine types.

Power Class (MW) Power Range (MW) Turbine Type 0.1 PR ≤ 0.15 Fuhrländer FL100 0.2 0.15 < PR ≤ 0.25 Enercon E-30 0.5 0.25 < PR ≤ 0.75 Enercon E-40 1 0.75 < PR ≤ 1.50 Vestas V52

ISPRS Int. J. Geo-Inf. 2021, 10, 104 12 of 18

Table 2. Power classes with the corresponding ranges of rated power (PR) and the applied turbine types.

Power Class (MW) Power Range (MW) Turbine Type ISPRS Int. J. Geo-Inf. 2021, 10, 104 12 of 18 0.1 PR ≤ 0.15 Fuhrländer FL100 0.2 0.15 < PR ≤ 0.25 Enercon E-30 0.5 0.25 < PR ≤ 0.75 Enercon E-40 1 0.75 < PR ≤ 1.50 Vestas V52 2 1.50 < PR ≤ 2.50 Enercon E-82 2 1.50 < PR ≤ 2.50 Enercon E-82 R 33 2.502.50 <

> 3.50 EnerconE-126 E-126

Nevertheless, the the plant plant location, location, rated rated powe power,r, hub hub height height and and the the date date of of (de-)commissioning were considered individually for each turbine. For additional turbine losses, e.g., caused byby thethe effectseffects described described in in Section Sectio n2.2 2.2,, an an overall overall value value of 16%of 16% was was used used for thefor theentire entire plant plant ensemble. ensemble. This This value, value, which which typically typically ranges ranges from from 5 to 30% 5 to for30% onshore for onshore wind windprojects projects according according to [33], to has [33], been has proven been prov by manyen by simulations many simulations to be a reasonableto be a reasonable average averagefor the considered for the considered turbine ensemble.turbine ensemble. After carrying out the numerical simulation simulationss for 25,835 wind turbines, the hourly resolvedresolved data data of of the plant ensemble were aggregated into a time series to compare the simulation results results with measured power genera generationtion data data of onshore turbines for all of Germany. The The simulated simulated and and me measuredasured time time series, series, which which were were converted converted into intodaily daily res- olutionsresolutions for fora better a better comparability, comparability, are are shown shown in Figure in Figure 9. 9.

0.9

0.6

0.3

Generatedpower (TWh) 0.0 0 40 80 120 160 200 240 280 320 360 Time (d) Figure 9. Simulated electricity production (black line) and measured feed-in data (blue line) from wind turbines in Germany fo forr 2016 with a daily resolution.

ItIt can be seen from Figure9 9 that that thethe simulated simulated electricityelectricity productionproduction followsfollows thethe measured feed-in data well throughout the ye year.ar. The deviations are mainly caused by the followingfollowing effects, which are not coveredcovered by the wind power model: 1. DeviationsDeviations through through the the Hellmann’s Hellmann’s expone exponentialntial law law with with wind wind speeds speeds at at 10 10 m. m. 2. TheThe uncertainties uncertainties of of the the weather weather data data and and the the fact fact of of hourly hourly averaged averaged values. values. 3. Weather-relatedWeather-related changes changes in air pressure are not considered in the model. 4. TheThe assignment assignment of of wind wind turbines turbines to to the the corresponding corresponding power power classes. classes. Nevertheless, with with an an RMSE RMSE of of 45.6 45.6 GWh GWh de determinedtermined forfor thethe daily daily resolved resolved data, data, the obtainedthe obtained results results show show a good a good agreement agreement with withthe measured the measured feed-in feed-in time timeseries. series. In com- In parisoncomparison to the to annual the annual power power generation generation of 64.0 ofTWh, 64.0 produced TWh, produced from all fromonshore all turbines onshore inturbines Germany in Germany for the year for 2016 the year according 2016 according to SMARD, to SMARD,the RMSE the shows RMSE a value shows of a 0.07%. value In of addition,0.07%. In a addition, Pearson acorrelation Pearson correlation between the between first differences the ﬁrst differences of both time of bothseries time results series in anresults R-value in an of R-value 0.97, indicating of 0.97, indicating that the trends that the of the trends time of series the time vary series in the vary same in direction the same anddirection magnitude. and magnitude. There are Therefurther are statistical further statisticalmethods to methods compare to comparetwo time twoseries time more series in- depth,more in-depth, e.g., by applying e.g., by applyingautoregressive autoregressive (AR) or autoregressive-moving (AR) or autoregressive-moving average (ARMA) average models(ARMA) to models the time to series. the time Since series. the similarity Since the of similarity the simulated of the and simulated measured and time measured series istime visually series obvious, is visually such obvious, models such were models not performed were not for performed this study. for In this the study. near future, In the when the German Core Energy Market Data Register, which also contains the specific turbine types, is fully completed, it will be possible to assign the exact power curve to each wind turbine of the plant dataset. This circumstance should improve the accuracy of the simulation results further.

ISPRS Int. J. Geo-Inf. 2021, 10, 104 13 of 18

near future, when the German Core Energy Market Data Register, which also contains the speciﬁc turbine types, is fully completed, it will be possible to assign the exact power curve to each wind turbine of the plant dataset. This circumstance should improve the accuracy of the simulation results further.

5. Discussion The main objective of this study was to generate high-resolution electricity production data of onshore turbines in Germany for a longer period, e.g., an entire year, using publicly available data. For this, the year 2016 was chosen because the applied plant and weather data were only available until the end of 2016 at the writing of this paper. A further reason for this year was the continuation of the energy transition maps of 2015 [4] with power generation data of wind turbines in Germany for 2016. For these energy transition maps, a spatial resolution at LAU2 level is needed. Hence, the introduced simulation model in combination with the CMSAF weather database in PVGIS [25], which provides a high spatial resolution, is well suited for the generation of such maps. The freely available web tool of renewables.ninja (www.renewables.ninja)[34], which also provides electricity generation data of wind turbines for a certain region and period, only applies MERRA-2 weather data with a lower resolution of about 50 km [22], which is not sufficient for the level of detail required for the energy transition maps of 2016. Understanding the variable power generation of existing onshore turbines on a spatiotemporal scale is a precondition for the successful integration of future renewable power plants into increasingly decentralized power systems. Figure 10 shows, as a first utilization example regarding this topic, the monthly electricity production from wind turbines at the spatial resolution of LAU2 based on the performed simulations. Hence, regional advances of the energy transition towards higher shares of wind power can be reliably monitored with the help of such maps. Moreover, these simulation results can be used in combination with the existing values of the installed capacity, as shown in Figure1, to determine spatiotemporal capacity factors of onshore turbines in order to investigate their efficiency depending on the specified region and period. For wind turbines, a spatiotemporal capacity factor CFst can be calculated according to Equation (6): Ewt CFst = × 100% (6) T·Cwt

In this expression, T stands for the speciﬁed period of time, Cwt is the wind turbine capacity installed in the considered region, and Ewt is the produced electricity from wind turbines in this region and period. Figure 11 shows the monthly capacity factors at the spatial resolution of LAU2 in Germany for the year 2016. ISPRSISPRS Int. Int. J. J. Geo-Inf. Geo-Inf. 20212021,, 1010,, 104 104 1414 of of 18 18

Jan Feb Mar Apr

May Jun Jul Aug

GWh 60 40

Sep Oct Nov Dec

Figure 10. Aggregated monthly electricity production from onshore turbines at LAU2 level in Germany for 2016. In the Figure 10. Aggregated monthly electricity production from onshore turbines at LAU2 level in Germany for 2016. In the grey areas no wind turbines are installed. grey areas no wind turbines are installed.

Moreover, these simulation results can be used in combination with the existing values of the installed capacity, as shown in Figure 1, to determine spatiotemporal capacity factors of onshore turbines in order to investigate their efficiency depending on the specified region and period. For wind turbines, a spatiotemporal capacity factor CFst can be calculated according to Equation (6):

= × 100% (6) ∙

In this expression, T stands for the specified period of time, Cwt is the wind turbine capacity installed in the considered region, and Ewt is the produced electricity from onshore turbines in this region and period. Figure 11 shows the monthly capacity factors at the spatial resolution of LAU2 in Germany for the year 2016.

ISPRS Int. J. J. Geo-Inf. Geo-Inf. 2021,, 10,, 104 104 1515 of of 18

Jan Feb Mar Apr

May Jun Jul Aug

CF st

60%

40%

20%

Sep Oct Nov Dec

Figure 11. Determined monthly capacity factors of wind turbines at LAU2 level in Germany for 2016. In the grey areas no Figure 11. Determined monthly capacity factors of wind turbines at LAU2 level in Germany for 2016. In the grey areas no wind turbines are installed. wind turbines are installed. From this ﬁgure, it can be easily deduced that the determined capacity factors of wind From this figure, it can be easily deduced that the determined capacity factors of turbines were much higher from November till February than in the remaining months of wind turbines were much higher from November till February than in the remaining 2016. In February, the spatiotemporal capacity factors reached averaged values above 30% months of 2016. In February, the spatiotemporal capacity factors reached averaged values almost nation-wide, with a peak value of 64% in Stedesdorf near the town of Wittmund, above 30% almost nation-wide, with a peak value of 64% in Stedesdorf near the town of which also had the annual peak of 72% in January. It is also noteworthy that the northern Wittmund,part of Germany, which especiallyalso had the the annual coastal peak regions, of 72% have in theJanuary. highest It capacityis also noteworthy factors during that thethe entirenorthern year. part In Juneof Germany, till September, especially the lowest the coastal monthly regions, capacity have factors the highest can be foundcapacity for factorsGermany during with the averaged entire year. values In around June till 10%. September, the lowest monthly capacity factors can beFrom found the for numerical Germany simulations with averaged in Section values4, itaround could be10%. clearly seen that, with the help of theFrom developed the numerical wind power simulations model, sufﬁcientlyin Section 4, precise it could results be clearly can be seen achieved that, both with for the a helpsingle of windthe developed turbine and wind a large power plant model, ensemble. sufficiently For the precise German results wind can power be achieved production both forin 2016,a single 25,835 wind onshore turbine turbines and a large were plant taken ensemble. into account For in the the German simulations wind in power which pro- the ductionpower generation in 2016, 25,835 of each onshore wind turbine turbines was were calculated taken into individually. account in The the obtained simulations results in whichreach athe spatial power resolution generation on of turbine each wind site level turbine and was have calculated an hourly individually. time resolution. The ob- To tainedthe best results of our reach knowledge, a spatial such resolution highly resolvedon turbine power site level production and have data an ofhourly wind time turbines resolution.considering To the almost best allof onshoreour knowledge, plants in such Germany highly [ 2resolved], which power receive production guaranteed data power of

ISPRS Int. J. Geo-Inf. 2021, 10, 104 16 of 18

feed-in prices according to the EEG, has never been shown before. Furthermore, a new approach was used for the simulation model, in which the nonlinear sections of the speciﬁc power curve of a wind turbine are developed into sixth-order polynomials, to simplify and improve the numerical simulations.

6. Conclusions This paper has shown new ideas for generating high-resolution power production data of onshore turbines in Germany applying a physical model. It was also an objective of this publication to develop a wind power model, in which the focus was set on a very transparent, easy to imitate, and sufficiently precise model approach. To contribute to such an approach, the plant and weather data required for the numerical simulations should be publicly available to give potential users the opportunity to create their own model based on the introduced ideas. It was clearly shown in this study that the developed wind power model can be a promising alternative to obtain highly resolved power generation data of wind turbines using publicly available plant and weather data. Thus, based on the presented model approach and applying an open-source pro- gramming language, such as R or Python, it is possible to generate spatiotemporal power production data of onshore turbines for all of Germany. Such spatiotemporally resolved time series can also help to investigate the electricity generation from wind turbines during extreme weather events, e.g., long periods of calm wind or extended and severe storms. Furthermore, the developed simulation model can be used for other countries or geographical areas without any changes, if all the needed plant and weather data are available for these regions. Furthermore, other applications, e.g., site assessment studies for future wind farms [35] or the influence of wind turbine noise on seismic recordings [36], can benefit from high-resolution electricity generation data delivered by the presented wind power model.

Author Contributions: Conceptualization, Reinhold Lehneis; Methodology, Reinhold Lehneis and David Manske; Software, Reinhold Lehneis and David Manske; Validation, Reinhold Lehneis; Formal Analysis, Reinhold Lehneis and David Manske; Investigation, Reinhold Lehneis; Resources, David Manske and Reinhold Lehneis; Data Curation, David Manske; Writing—Original Draft Preparation, Reinhold Lehneis; Writing—Review and Editing, Reinhold Lehneis, David Manske, and Daniela Thrän; Visualization, David Manske and Reinhold Lehneis; Supervision, Daniela Thrän; Project Administration, Daniela Thrän; All authors have read and agreed to the published version of the manuscript. Funding: This research received general funding from the Helmholtz Association of German Re- search Centres. Informed Consent Statement: Not applicable. Acknowledgments: The authors gratefully acknowledge Hortencia Flores Estrella (TU Berlin) for providing measurement data on a wind turbine General Electric GE 1.5sl. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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