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Research ArticleComparison and Optimization of Neural Networks and Network Ensembles for Gap Filling of Wind Energy Data

Andres Schmidt1 and Maya Suchaneck 2

Department o Forest Ecosystems and Society, Oregon State University, Corvallis, OR , USA Department o Geography, Ruhr University Bochum, Bochum, Germany

Correspondence should be addressed to Andres Schmidt; [email protected]

Received January ; Revised April ; Accepted April ; Published May

Academic Editor: Shuhui Li

Copyright © A. Schmidt and M. Suchaneck. Tis is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Wind turbines play an important role in providing electrical energy or an ever-growing demand. Due to climate change driven by anthropogenic emissions o greenhouse gases, the exploration and use o sustainable energy sources is essential with wind energy covering a signicant portion. Data o existing wind turbines is needed to reduce the uncertainty o model predictions o utureenergy yields or planned wind arms. Due to maintenance routines and technical issues, data gaps o reerence wind parks areunavoidable. Here, we present real-world case studies using multilayer perceptron networks and radial basis unction networks toreproduceelectrical energy outputso windturbines at differentlocations in Germany coveringa range o landscapes with varyingtopographic complexity. Te results show that the energy output values o the turbines could be modeled with high correlationsranging rom . to .. In complex terrain, the RBF networks outperormed the MLP networks. In addition, rare extreme valueswere better captured by the RBF networks in most cases. By using wind meteorological variables and operating data recorded by the wind turbines in addition to the daily energy output values, the error could be urther reduced to more than %.

1. Introduction

Te Combination o climate change and the dependenceon ossil uels slowly cause changes in energy policy andtrigger an increasing demand or sustainable energy sources.Global carbon dioxide emissions are ever increasing and the

associated consequences or the climate are widely scienti-cally recognized [–]. Over the last decade and in particularsince the release o the report o the Intergovernmental Panelon Climate Change (IPCC) in , public and politicalawareness o renewable energy technologies has increasedconsiderably. Tis is notat least due to the large andast grow-ing economies and the associated increase o numbers o carsandenergyconsumption, andthereore o CO2 emissions [].Wind energy has the potential to be a vital contributor torenewable energy technologies that will substitute more andmore or gas and coal [].

In order to decrease the uncertainty o wind energy yieldpredictions during the planning o a single turbine or wind

arm, data o nearby existing wind turbines are ofen used asreerence or model evaluation.

In Germany, the legislation that grants priority to renew-able energy sources (Renewable Energy Resources Act, EEG)states that only wind turbines in areas with sufficient windenergy potential are qualied to receive compensation or the

electrical power provided or the power grid [].Moreover, according to the EEG, power grid owners are

not required to connect turbines to the grid that does notmeet or exceed % o the turbine type-specic reerence

value calculated based on reerence wind conditions.Because o these restrictions, a correct prediction or

expected wind energy yield is an indispensable economiccriterion or most wind arm projects. However, becauseo technical malunctions, maintenance routines, or otherproblems, the availability o valuable comparison data romexisting turbines nearby is limited. Such data limitationaffects the statistical saety o model predictions o utureenergy yields.

Hindawi Publishing CorporationJournal of Renewable Energy Volume 2014, Article ID 986830, 15 pageshttp://dx.doi.org/10.1155/2014/986830

http://dx.doi.org/10.1155/2014/986830http://dx.doi.org/10.1155/2014/986830


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Journal o Renewable Energy

Articial neural networks are able to approximate nonlin-ear relationships between individual data series by adjustingnetwork parameters in a purely data-driven, and, in our case,supervised learning process.

Here, we present a method to model the data o nearby wind turbines using different types o neural networks and

network ensembles to llin gaps in time series o wind energy outputs. Real-world operating data o six exemplary windarms in Germany were available or this purpose.

2. Data and Methods

o provide a high planning dependability, the potentialannual wind energy yields have to be estimated careully during the planning process o a wind turbine. Te accuracy o predictions becomes even more crucial when wind armsare planned due to the substantially increased nancial risk.Several microscale and mesoscale wind ow models basedon computational uid dynamics are available to calculate

uture wind energy yields o single turbines and wind arms.ypically, terrain data such as surace roughness, orography,and existing wind obstacles or a radius o km around theproposed location o the wind turbine is considered or themodel o computations in combination with long-term windstatistics.

One widely used model, or instance, that has passedseveral stages o development over the last decades is WAsP (Wind Atlas Analysis and Application Program) []. WAsP was developed by the RISØ National Laboratory, Roskilde,Denmark, and is approved among others by the GermanFederal Research Ministry.

Te various specic models that account or wind obsta-

cles, orography, wake effects, and surace roughness wereassembled in the model suite o WAsP . A detailed descriptiono the model and its algorithms can be ound in therespectiveliterature [].

In order to validate the predicted long-term average windenergy yields based on the model results considering theenvironmental conditions, the geometry o the turbine andits power curve [] data o existing, nearby turbines are usedas a reerence. For that purpose, energy output values o existing wind turbines are corrected or technical availability.In addition, the wind conditions and the correspondingobserved electrical energy output values o a certain yearare compared and scaled to long-term data or the area o

interest []. Afer correcting the observed values throughlinear regression to % long-term averages, the values canbe compared to the model results that are based on long-term wind statistics and thereore also represent long-termaverages [].

.. Articial Neural Networks. Articial neural networksprovide a method to map input variables on target vari-ables by using a combination o nonlinear unctions and alearning procedure that can be supervised or unsupervised[, ]. Te ability to nd mathematical unctions withoutprior knowledge o the unctional relationship makes neuralnetworks a powerul tool to solve problems or which no

analytical solution exists or i the unction that relates variables to each other is unknown [–]. Articial neuralnetworks have ound a growing range o applications in recentyears including the eld o wind energy research [, ]. Teability to sel-adjust its parameters makes neural networks asuperior tting method compared to classical data-tting and

prediction methods [–].Te most popular network architecture currently used isthe so-called multilayer perceptron (MLP) topology, whichwas presented comprehensively rst by Rumelhart et al. [].

Within this study we compare the perormance o MLPnetworks to the perormance o radial basis unction (RBF)neural networks. Compared to MLP networks, the param-eters o RBF networks can be adjusted aster to the datapresented to the network during the training process. Inaddition, RBF networks are less affected by the problem o local minima []. MLP networks use the scalar product o the input data vector consisting o input variables and aweight vector to calculate the neuron output usually applyinghyperbolic activation unctions. In contrast to that, RBFnetworks use the distance between the input vector and thecenter o the radial basis unction to determine the activation

value within an RBF neuron. Te most commonly usedactivation unction type with a radial basis is the Gaussianunction that was also deployed in the networks used orthis study. Te -dimensional vectors that determine theshape o each neuron’s -dimensional Gauss unction in theinput space are dened by the center vector and the -dimensional variance vector .

Te central values o have been optimized within thiswork using the -means clustering algorithm. Te input

vectors were separated into clusters and the center valueso the RBF neurons were set to represent all considered input

vectors while minimizing the number o clusters by ndingthe centers or each cluster with the smallest mean squareddistance to all points in the cluster. According to Hestenes[], this can be calculated by minimizing the unction asgiven in (() and ()). Consider

= ∑=1

∑

− 2, ()with

= 1∑. ()Here, is the mean o subsample which the cluster iscomposed o . Te index is the index over the subsample .At the end o the procedure, each input vector is assignedto the cluster center (i.e., RBF network node) to which it hasthe least Euclidean distance. Te closer an input vector to theRBF center o a neuron is, the higher the activation value o that neuron is. Hence, the parameters o all RBF unctionsare adjusted during the network learning phase so that every input can be assigned to one o the RBF neurons in the hiddenlayer and the weighted sum o the activation unctions canbe transormed to satisyingly match the target values. Moredetails about the large eld o learning algorithms or neuralnetworks can be ound in the literature [, , ].


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For the network training and evaluation process, eachavailable learning dataset was divided into different datasetsections: training data, test data, and validation data. Tetraining data is transormed by the network unctions. Aferthe output o the network is compared to the real availablemeasured outputs, the error is determined. Te error value

used or this perormance check is the nal RMSE (root o the mean squared error) summing up the differences betweenmodeled output and known measured output according to

= √ 1 ∑=1

− 2. ()Here, is the measured result within the available learningdataset (i.e., data that contains all values or all input variablesandmeasured samples o the corresponding target value) and is the value estimated by the neural network. is thenumber o data records used to determine the error or thetraining data and test or validation data, respectively.

Te parameters o the network are, then, iteratively adjusted applying the conjugate gradient descent method orthe training algorithm [, ] until an acceptable error isreached.

In a second step the test data is used. est data wasnot used or the network parameter adjustment during thetraining. Te trained network is now applied to the testdataset and the RMSE is determined again.

I the error or the training data is small and the erroror the test data is large, this indicates that the network parameters have been over adjusted to the training data.Hence, the training has to be started again until minima orboth, the training error and the test error, have been reached.

Once the optimal balance between training data errorand test data error is reached, the network has the ability to sufficiently generalize the unctional relationship betweeninput and target variable well and is not over-tted to aspecic training dataset.

Te third dataset section, the validation data, hasnot beenused or the learning process o the network at all and isprocessed with the adjusted neural network in a nal step.Hence, the validation error is the only o the three error

values that is admissible to assess the goodness o a neuralnetwork model. Te division o the data into the trainingdata, test data, and validation data was conducted accordingto values presented in the literature [, ]. Te validationerror indicates the nal perormance o the trained network

when applied on new data and is thereore given in the resultspresented.

In order to scale all input variables to values between and in a preliminary step we applied min-max normaliza-tion to prevent the network results rom being biased by thestronger numerical inuence o a variable measured in unitswith larger numbers than a variable that is limitedto a smallerscale by deault []. For each dataset, we trained specicneural networks and determined the three best networks.For that purpose, a batch algorithm was conducted to test, networks or each dataset while varying the numbero neurons, number o input variables, network type, andactivation unctions in the nodes.

o demonstrate the potential o the method, three pairso turbine sites were selected with different large-scale windconditions, whereupon the wind conditions amongst thepairs are similar due to the relative spatial adjacency.

.. Real-World Case Studies with Operating Data o Exem-

plary Wind Farms. Te daily energy output o existingwind turbines provide important inormation and are usedas input data or the neural networks. Also, the mean

values, minima and maxima o wind speed, wind direc-tion, instantaneous power, and number o rotor revolutionsrecorded by the operating and surveillance sofware weretaken into account or the neural network calculation. Tethree exemplary test areas are located in Germany wherethe prevailing wind conditions are dominated by the globalWest wind drif o the temperate latitudes in the Northernhemisphere.

Te locations were selected with respect to their differentorographic eatures to validate the robustness o the method

presented.It is a coastal location, a site in the Muensterland lowland

area in Northwest Germany, and an area located in themountainous orested uplands o West central Germany (Figure ).

Overall, the data rom modern gearless wind turbineso the manuacturer Enercon (ENERCON GmbH, Aurich, Germany) recorded over a period o our years wereavailable or the calculations.

3. Results and Discussion

In the ollowing section the results or case studies are

presented, consecutively with increasing topographic com-plexity. In each case, we provide detailed inormation aboutturbine types, wind conditions, and topographic circum-stances that affect the local wind elds or the distinct typeso terrain.

In each case, specic neural networks were trained toreproduce the electrical energy output using the data o existing wind turbines with various distances to the respectivetarget turbines and wind arms. Te perormances o the besttrained networks are presented and errors values are givenand compared.

.. Te Coastal Sites. Due to the at landscape with no

signicant changes in elevation, orographic effects on thewind speed are negligible around the coastal siteso Hinte and

Jennelt .Te site belongs to the district o the city o Aurichin the

East Frisia region in Lower Saxony, Germany. Te North Seais located in a distance o about km to the West o thesite Hinte. Te nearest city Emden is located at a distance o . km South o the wind arm Hinte. Te immediate vicinity o the site is characterized by meadows and agriculturally used land. Te terrain is atand mostly ree o windobstacles.

Te wind arm is located . km Northwest o Hinte. Tewind arm consists o a total o wind turbines operated by different companies with an average annual energy output o


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Kiel

Hamburg

Hannover

Erfurt

Munich

Stuttgart

Saarbrucken

Mainz

Bonn

EssenDuisburg

N

E

S

W

Dusseldorf Cologne

Wiesbaden

Leipzig

Dresden

Magdeburg

BerlinPotsdam

Bremen

Bremerhaven Schwerin

0 100 20050

(km)

14∘

0

0E12∘ 0 0E10∘ 0 0E8∘ 0 0E6∘ 0 0E

54∘

0

0N

52∘

0

0N

50∘

0

0N

48∘

0

0N

Elevation (m a.s.l.)

2937

0

Olpe

Wenden

Jennelt

Hinte

CoesfeldSuedlohn

F : Shaded relie overview map o the incorporated wind arm sites in Germany. Te elevations shown are based on the NASA ShuttleRadar opography Mission data.

: Coordinates and data o the wind turbines at the site Hinte.

urbine ype Hub height [m] Rotor Ø [m] Nominal power [kW] Longitude Latitude

Elevation (m a.s.l.)(WGS )

HI E /. . . .E .N

HI E /. . . .E .N

HI E /. . . .E .N

: Coordinates and data o the wind turbines at the site Jennelt .



JE E /. . . .E .N

JE E /. . . .E .N

JE E /. . . .E .N

JE E /. . . .E .N

JE E /. . . .E .N

GWh. Te specications and geographical coordinates o the turbines used or the calculations are given in ables and, respectively.

Due to ongoing expansions and changes, the wind arminormation given in this study always reer to the turbines

with data incorporated in the analyses and do not necessarily represent the current total number o installed turbines.

Te wind arm Jennelt is located at . km to the North-west o the wind arm Hinte. Te North Sea lies West o thesite in a distance o . km.


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4% 8% 12% 16% 20%

0

45

90

135

180

225

270

315

Hinte

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(a)

4% 8% 12% 16%

0

45

90

135

180

225

270

315

Jennelt

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(b)

F : Average wind conditions at thecoastal sites in Hinte (target site) and Jennelt (input site) during the observation period rom January to January .

Te data collection period or the site pair Hinte/ Jennelt istwo years, rom January , , to December , . Tus, data records were available or the two sites.

Te wind conditions at the sites Hinte and Jennelt mea-sured by anemometers on the nacelle o the wind turbines(i.e., m above ground level) were similar with regard tothe wind speeds and the distribution o wind directionsduring the data collection period (Figure ). Even thoughthe wind measurements on the nacelle o the plants aresubjected to certain errors by ow distortions, they are stillsufficiently accurate to capture the speed and direction ormost applications [].

Comparisons between the wind speeds measured on thenacelle anemometer and an undisturbed measurement o wind in ront o the rotor show only minor deviations o %and less [].

daily data records were used or the training o theneural networks. Te remaining records were used to thesame parts or the test dataset and the validation dataset.

Te nonparametric Spearman rank correlation coefficient was used or the comparison o the measured electricalenergy output and the results reproduced by the neuralnetworks. Te RMSE values given reer to the validationdata set that was composed o values that were randomly distributed over the entire dataset. In able , the resultsor the three best networks are shown, that is, the networkswith the lowest validation errors and highest correlationcoefficients.

: Summary o results or the energy output o the targetturbines at the coastal site Hinte.

arget

variable

Input

variables

Network

type

Network

topology

RMSE

(kWh)

HI (JE –JE ) MLP -- .HI (JE –JE ) RBF -- .HI (JE –JE ) RBF -- .HI (JE –JE ) MLP -- .HI (JE –JE ) RBF -- .HI (JE –JE ) RBF -- .HI (JE –JE ) MLP -- .HI (JE –JE ) RBF -- .HI (JE –JE ) RBF -- .All correlations given are signicant on a % condence

level ( ≤ 0.05). Te network topology reers to the numbero input variables, the number o hidden nodes, and thenumber o output nodes o the neural networks used. Tenumber o hidden neurons within RBF networks is usually higher than or the MLP type networks to accomplish thesame ability o generalization [, ].

Te differences in network perormance are overall small.All networks achieved very high correlations o . and .and the statistics or the measured and reproduced poweroutput data are similar (ables and ).

Figure shows the observed and network reproducedrequency distributions o the daily values o

or the


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Measured

MLP (5-6-1)RBF (5-44-1)RBF (5-80-1)

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

3 5 0 0 0

4 0 0 0 0

4 5 0 0 0

Upper bin limit (kWh)

0

5

10

15

20

25

30

F

r e q u e n c y

W (24 h) HI 1

(a)

Measured

MLP (5-6-1)

RBF (5-44-1)

RBF (5-80-1)

14 115 232 473 6 14 679

Case number

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

W ( k W h )

W (24 h) HI 1

(b)

Measured

MLP (5-10-1)

RBF (5-51-1)

RBF (5-53-1)

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

3 5 0 0 0

4 0 0 0 0

4 5 0 0 0


0

5

10

15

20

25

30

F r e q u e n c y

W (24 h) for HI 2

(c)

Measured

MLP(5-10-1)

RBF (5-51-1)

RBF (5-53-1)

13 162 228 359 548 662 716

Case number

0

5000

10000

15000

20000

25000

30000

35000

40000

4500050000

W ( k W h )

W (24 h) of HI 2

(d)

Measured

MLP (5-6-1)

RBF (5-42-1)

RBF (5-80-1)

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

3 5 0 0 0

4 0 0 0 0

4 5 0 0 0


0

5

10

15

20

25

F r e q u e n c y

W (24 h) of HI 3

(e)

Measured

MLP (5-6-1)

RBF (5-42-1)

RBF (5-80-1)

8 114 197 291 435 615

Case number

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

W ( k W h )

W (24 h) of HI 3

()

F : Results or the best networks or the dataset o the coastal wind arms Hinte and Jennelt . Te case numbers in the right panelsrepresent individual data records o the complete time series available that were chosen randomly and assigned to the validation dataset.


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: Descriptive statistics o the measured MES time series and the time series modeled by the best articial neural network ANNcalculated over all available daily values.

arget variable Average Standard deviation Maximum Minimum

Measured ANN Measured ANN Measured ANN Measured ANNHI (kWh) HI (kWh) HI (kWh)

validation data set by the three best neural networks orthe three target turbines H (a), H (c), and H (e). Terequency distributions show that all networks produce asimilar value range o the energy output or the three turbinesindicating that the unctional relationships between the inputand output variables are well captured by all best networks(able ). It is noteworthythat, or the rarepeak valueso over MWh o turbine HI , the RBF networks exhibit smallerdifferences to the measured data than the MLP networks

(Figures (a) and (b)). Tese extreme values are not outliersin the statistical sense but rare, yet physically meaningul,

values.Te act that RBF networks outperorm MLP net-

works while generalizing the underlying unctional relationbetween input and output also covering extreme values hasalso been observed in other studies [, ].

Also the direct comparisons o individualnonconsecutivesamples o the validation dataset (Figures (b), (d), and ())show that the twoRBF networks estimate valueson eithersideo the end o the scale are the best. Te rst and second orderstatistic moments o the measured and modeled data are ingood agreement (able ).

Prior to the learning process, three continuous periodso approximately three weeks each were extracted romthe dataset. Tis data was then calculated with the bestneural network or each turbine o the target wind arm(Figure ). In contrast to the actual validation data (Figure )that were also excluded rom the training processes, thisarticially created data gap simulates real-world situationswhen continuous gaps in the records or several days dueto technical problems or or several hours due to machinemaintenance may occur. Te energy output values o thesystem o wind turbines could be reproduced closely with theneural networks.

One reason or the very reliable and accurate calculation

(0.98 ≤ ≤ 0.99) is given by the similarity o the data.Te wind conditions at the locations o the wind turbines arenot compromised by a complex terrain or large topographicelements. Furthermore, the turbines o both wind arms areo the same type with the same hub height. Tis assumptionabout the initial similarity o the data o the two wind armsis supported by the linear regression matrix or the measureddata o the two wind arms (Figure ).

.. Sites in the Westphalian Basin. With regard to the orog-raphy, the Muensterland lowland area around the sites o Coeseld and Suedlohn can be classied as a transitionallandscape between the at area in the very Northwest o

0 3 / 0 3 / 2 0 0 6

0 5 / 0 3 / 2 0 0 6

0 7 / 0 3 / 2 0 0 6

0 9 / 0 3 / 2 0 0 6

1 1 / 0 3 / 2 0 0 6

1 3 / 0 3 / 2 0 0 6

1 5 / 0 3 / 2 0 0 6

1 7 / 0 3 / 2 0 0 6

1 9 / 0 3 / 2 0 0 6

2 1 / 0 3 / 2 0 0 6

2 3 / 0 3 / 2 0 0 6

2 5 / 0 3 / 2 0 0 6

2 7 / 0 3 / 2 0 0 6

2 9 / 0 3 / 2 0 0 6

0

5000

10000

15000

20000

25000

30000

35000

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W ( k W h )

(a)

1 3 / 1

1 / 2 0 0 6

1 5 / 1

1 / 2 0 0 6

1 7 / 1

1 / 2 0 0 6

1 9 / 1

1 / 2 0 0 6

2 1 / 1

1 / 2 0 0 6

2 3 / 1

1 / 2 0 0 6

2 5 / 1

1 / 2 0 0 6

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2 / 2 0 0 6

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2 / 2 0 0 6

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30000

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W ( k W h )

(b)

0 2 / 0 1 / 2 0 0 7

0 4 / 0 1 / 2 0 0 7

0 6 / 0 1 / 2 0 0 7

0 8 / 0 1 / 2 0 0 7

1 0 / 0 1 / 2 0 0 7

1 2 / 0 1 / 2 0 0 7

1 4 / 0 1 / 2 0 0 7

1 6 / 0 1 / 2 0 0 7

1 8 / 0 1 / 2 0 0 7

2 0 / 0 1 / 2 0 0 7

2 2 / 0 1 / 2 0 0 7

2 4 / 0 1 / 2 0 0 7

0

10000

20000

30000

40000

50000

W ( k W h )

(c)

F : Comparison o the measured (blue continuous line) andnetwork reproduced (red dashed line) daily energy values o theturbines at the coastal site.

Germany close to the North Sea and the low mountain rangeto the Southeast.

Despite some slight elevations with weak slopes, thelandscape is relatively at as typical or the WestphalianBasin in the Southern marginal area o the North German


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HI 1 HI 2 HI 3

JE 1

JE 2

JE 3

JE 4

JE 5

R = 0.96

R = 0.96

R = 0.96 R = 0.96

R = 0.98

R = 0.98

R = 0.98

R = 0.98

R = 0.98 R = 0.97

R = 0.97

R = 0.97

R = 0.95

R = 0.95

R = 0.95

F : Graphic correlation matrix with linear regression coefficients or the daily energy yields at the coastal sites or the entire dataperiodrom thebeginningo throughthe endo . Te requency distributions are equally divided into classes or all distributions.

Plain. Te surace roughness is generally higher comparedto the coastal sites Hinte and Jennelt due to many smalltowns and some small orests that disrupt the predominantly agricultural region.

Te wind arm in Coeseld consisting o ve wind turbinesis located at a distance o km South-East o the townCoeseld . Te arm is composed o two different types o wind turbines, two turbines o the type E-/., and threelarger turbines o the type E-/.. Te topography in

the immediate vicinity around the wind arm is slightly undulating. Te specications and geographical coordinateso the turbines in the Westphalian Basin area used or thecalculations are given in ables and , respectively.

Te target wind arm Suedlohn is located at a distance o about . km East o the border to the Netherlands. Te windarm is located Southwest o the community o Suedlohn, km away rom the wind arm Coeseld . As or the windarm Coeseld, the topography in Suedlohn is expected to havesome effects on the wind regime due to upwind obstructioneffects at hills [, ]. Te near surrounding o the site isdominated by arable land, pasture, and widespread armbuildings.

At the site Suedlohn, noise emissions restrictions producelegal reasons to reduce the sound level o the turbinesaffecting the arm houses in the vicinity o the turbinesduring nighttime. Tereore, the turbines SU and SU are operated with sound reduced perormance characteristicsrom : to : which reduces the nominal power outputrom kW to kW.

Te data collection period or the two sites in theWestphalian Basin covers two years rom January , , to

January , , providing daily data records. Te wind isdominated by winds rom West and Southwest at both windarms because no larger topographic structures are affectingthe superimposed West wind drif.

However, the Southwesterly wind directions exhibit aslightly higher requency at the site Coeseld (Figure ). Inorder to achieve the best comparability anemometer datarom turbine CO was used or the comparison o the windconditions as the hub height o . m is closest to the hubheight o . o the turbines at the target site Suedlohn.

Te correlation coefficients (able ) indicate that thecombination o increased topographic structure and thedistance o km between the wind arm delivering the input


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0

45

90

135

180

225

270

315

Suedlohn

4% 8% 12% 16% 20%

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(a)

4%

0

45

90

135

180

225

270

315

Coesfeld

8% 12% 16% 20%

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(b)

F : Average wind conditions at the locations Suedlohn (target site) and Coeseld (input site) during the data collection period romJanuary to January .

: Coordinates and data o the wind turbines at the site Coeseld .



CO E-/. . . .E .N CO E /. . . .E .N

CO E /. . . .E .N

CO E /. . . .E .N

CO E-/. . . .E .N

: Coordinates and data o the wind turbines at the site Suedlohn.



SU E /. . . .E .N

SU E /. . . / .E .N

SU E /. . . / .E .N

: Correlation matrix or the daily energy output at thelocations o Coeseld and Suedlohn or the analyzed period.

CO CO CO CO CO

SU . . . . .

SU . . . . .

SU . . . . .

All correlations shown are signicant on a % condence level.

data (Coeseld ) and the target wind arm (Suedlohn) lead toa unctional relation between, then, input and target variablesthat cannot be described well by a simple linear approach.

Tus, due to their ability to emulate any nonlinearunctions, neural networks provide an ideal tool or suchsituations. Te available energy output data were dividedrandomly in the training data, test data, and validation data( training data records, test data records, and

validation data records).


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: Summary o the results or the target site Suedlohn in the Westphalian Basin within the area o the North German Plain.

arget variable Input variables Network type Network topology RMSE (kWh) SU (CO –CO ) MLP -- .SU (CO –CO ) MLP -- .

SU

(CO –CO ) RBF -- .

SU (CO –CO ) RBF -- .SU (CO –CO ) RBF -- .SU (CO –CO ) MLP -- .SU (CO –CO ) MLP -- .SU (CO –CO ) RBF -- .SU (CO –CO ) RBF -- .

: Descriptive statistics o the measured MES time series and the time series modeled by the best articial neural network ANNcalculated over all available daily values.

arget variable Average Standard deviation Maximum Minimum

Measured ANN Measured ANN Measured ANN Measured ANNSU (kWh) SU (kWh) SU (kWh)

Te neural network modeling results or the energy yield values o the turbines SU to SU are given in able considering all results o the respective three best networks.

Only the power output values o all ve turbines wereused as input vectors or all neural networks.

Te correlations o the network reproduced values with

the corresponding measured values are all high and statisti-cally signicant ( = 0.95, ≤ 0.05) or the validation datasets o all target turbines (able ).

Since turbine SU was affected most by the noisereduction restrictions, the absolute RMSE values are smallestor that turbine which has to be taken into account whileinterpreting the relatively low RMSE values. Nevertheless, theassociated Spearman rank correlation coefficient shows that,despite altering operating conditions during nighttime, theneural networks produce satisactory results (ables and ).Nevertheless, the scattering o differences between modeledand observed values when considering multiple networks isan unwanted effect.

Since the accumulated RMSE is calculated rom thesquared residual values, the direction o deviation is not con-sidered when constraining the length o the network learningprocess as shown in (). Network ensembles provide a way to reduce these variations among a group o neural networkstrained or the same purpose.

By weighted averaging o the output values o individualnetworks, the variations are smoothed and deliver improvedresults [, ]. Te weight actors or the averaging weredetermined using the RMSE values o the incorporatednetworks.

It is noteworthy in the context o the present work thatthe results rom the individual networks are satisactory. For

the application in practice, there is at least no urgent needor improvement. Nevertheless, since this study outlines theuseulness o neural networks or energy output modeling orwind turbines in order to close data gaps, the perormance o a network ensemble was analyzed or turbine SU .

As shown in able , the results could be improved using

an ensemble composed o three neural networks. In com-parison to the values gained through the best single RBFnetwork (able ), improved rom . to ., while theRMSE could be reduced by kWh.

Te distance between the two wind arms in the Muen-sterland lowland area is more than km. Moreover, themore complex topography leads to a relationship between thepower output values o the two wind arms that can hardly becaptured by simple linear unctions (able ). Nevertheless,the results show that the neural network approach deliverssound results using data that were collected over a period o years only.

.. Mountainous Sites with Complex opography. Te regionaround the third pair o sites is located in the mountainousarea within the Rhine Massi near the Southern rim o theEbbe Mountains in central Germany (Figure ) in the densely orested Sauerland region.

Accordingly, the topographic and in particular the oro-graphic conditions will have a signicant inuence onregional scale and local scale wind elds []. Caused by the vast orested areas with different stand ages and scat-tered towns, the surace roughness is signicantly highercompared to the previously presented sites causing highershear stress on the airmass. Tese topographic conditionsmake the wind eld modeling challenging and make a simple


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Olpe

8% 12% 16%

0

45

90

135

180

225

270

315

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(a)

Wenden

8% 12% 16% 20%

0

45

90

135

180

225

270

315

Wind (m/s)

>3–6

>6–9

>9–12

>15

≤3

(b)

F : Average wind conditions at the sites Olpe and Wenden during the period rom January through January .

: Summary o the results or the calculation o the incomeo investment.

arget

variable

Input

variables Network type

RMSE

(kWh) SU (CO –CO ) Ensemble( × MLP + ×RBF)

.

SU using an ensemble rom the previously optimized individual networks.

spatial interpolation o wind velocities and wind energy yields, respectively, uneasible. Te technical specicationsand geographical coordinates o the turbines used or thecalculations or the mountainous site are given in ables and , respectively.

Te area is mostly used or orestry and grazing. Tewind arm Wenden is located . km South o the villageWenden. Te wind arm Olpe delivering the input data orthe neural network training and calculations is located kmNorth-Northeast o the wind arm Wenden and about . kmNortheast o the town Olpe. Te topography in the vicinity o both wind arms is undulating.

Te data collection period or the turbines in Olpe andWenden exceeds our years rom January , , until April, . However, because the input vector is mathematically mapped on the output value by the neural networks, thenumber o variables in the input vector cannot be alteredrom the dimensionality used or the training and adjustment

procedure when applying the trained network to new data.Hence, daily records that contain the synchronal oper-ating data o all ve wind turbines were available.

Te wind conditions measured at m above groundshow signicant differences between the two wind armsites. At both locations the Southwestern wind directionsexhibit the highest wind speeds. Te West-Southwesterly and South-Southwesterly wind directions are more requentin Olpe compared to the site in Wenden (Figure ). Tedistributions o the wind direction indicate the effect o the orography in the complex terrain creating pronouncedlocal scale wind elds with distinct distributions o wind

velocity and direction at the two sites.

A training dataset o data records was used or thecalculations on the site pair Olpe/Wenden. Te test datasetand the validation dataset consisted o data records each.

Te Spearman rank correlation coefficients are lowercompared to the coastal sites and the sites in the WestphalianBasin area presumably caused by the more complex, nonlin-ear relationship between wind energy yields o the two windarms. Nevertheless, correlations are still high reaching valuesrom . to . (able ).

Te comparison o the requency distributions show thatthe energy output values in the most occupied class o lessthan kWh per day are better captured by the RBFnetworks in both cases (Figure ). Also, or the other bins,the requencies calculated by the best RBF agree best withthe measured requencies with the exception o a single valueabove kWh calculated by the RBF (topology --) that


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1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0


0

5

10

15

20

25

F r e q u e n c y

Measured

RBF (3-22-1)RBF (3-23-1)MLP (3-9-1)

W (24 h) WE 1

(a)

0

5

10

15

20

25

30

F r e q u e n c y

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0


Measured

MLP (3-7-1)RBF (3-24-1)RBF (3-21-1)

W (24 h) WE 2

(b)

F : Te requency distributions or the measured data and the data calculated by the respective best networks or the turbines WE (a) and WE (b).

: Coordinates and data o wind turbines at the site Olpe.


Elevation (m a.s.l.)

(WGS )OL E /. . . . .

OL E /. . . . . .

OL E /. . . . . .

: Coordinates and data o wind turbines at the site Wenden.



WE E /. . . .E .N

WE E /. . . .E .N

: Summary o results rom the best neural networks out o iteratively tested networks or the target turbines in the complexterrain o the Sauerland region.

arget variable Input variables Network type Network topology RMSE (kWh) WE (OL –OL ) MLP -- .WE (OL –OL ) RBF -- .WE (OL –OL ) RBF -- .WE (OL –OL ) MLP -- .WE (OL –OL ) RBF -- .

WE

(OL –OL ) RBF -- .


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was not observed in the corresponding validation dataset(Figure (a)).

o account or the more complex topographic conditions,we tested the addition o more input variables that potentially carry the inormation needed to better map the input valuesonto the energy yields o the target turbines. While choosing

additional input variables, one must avoid that redundant variables are chosen as an increased number o variables willaffect the ability to nd the global minimum o the errorunction during the network training process [, ]. Tiseffect is also known as the “curse o dimensionality” andaffects all multivariate optimization algorithms [].

Sensitivity analyses are one method to ensure that only variables are used as input that are important to map the input vectors on the target values. Sensitivity analyses determinethe inuence o each variable on the minimum o RMSE by,rst, determining the minimal error, while taking all input

variables into account. In the next steps, the values o theinput variables will be partially replaced by random values,

while the other input variables remain unchanged. Tisis done consecutively through all variables. Te minimumerror applying the random valuesis then compared tothe original minimum error (0) achieved with the original

values o the respective variable. Tis is done by simply calculating the ratio = /0. Tus,an error ratio equalto or less indicates that the variable does not add additionalinormation. In that case, the variable can be considereddisruptive or at least redundant and should not be used asinput variable.

In able , the error ratios or the network that wasoptimized or the reproduction o the energy output values o the turbine WE are shown using the operating data recorded

by the three turbines o the Olpe wind arm.Te ranks reect the inuence o each input variable

on the result. Te higher a specic variable is ranked, themore it contributes to the error minimization. Only variablesthat exhibit an error ratio > 1.1 were used or theneural networks during urther analyses []. Te error ratiosconrm that the energy output values have a large impacton the quality o the results. It is also shown that additionalwind meteorological variables and operating data such asthe instantaneous power contain important inormation tomodel the target variable. Te act that the wind directionexhibits an error ratio o . also underlines the importanceo the topographic effects on the wind energy yields in

complex terrain. Since the dimensionality o the input vectorwas increased, more neurons in the hidden layers wereneeded or the two RBF networks used [].

Trough application o the additional important variablesthe perormance o the neural network could be increased(able ). Te correlation between the energy output calcu-lated with the neural network utilizing the additional input

variables and the measured energy output could be increasedrom a maximum o . (able ) to . (able ). Fur-thermore, Te RMSE accumulated over validation datarecords was reduced by .% rom on kWh. Usingan RBFnetwork ensemble didnot increase thecorrelation butslightly reduced the RMSE by another .% (able ).

: Ranked error ratios or available input variables o thewind arm Olpe.

Rank Variable (OL ) .

(OL ) .

Average wind direction (OL ) . Average instantaneous power (OL ) .

(OL ) . Average instantaneous power (OL ) .

Minimum instantaneous power (OL ) .

Daily hours o operation (OL ) .

Minimum instantaneous power (OL ) .

Maximum instantaneous power (OL ) .

Maximum wind speed (OL ) .

Average o wind speed (OL ) .

Average o wind speed (OL ) .

Minimum wind speed (OL ) .

Minimum number o revolutions (OL ) .

Only the variables with > 1 are shown.

4. Conclusion

We presented a neural network approach to model the daily energy yields o wind turbines by training neural networksusing the data o other wind arms. Te method was deployedon three examples with different spatial setups and distancesbetween the input sites and the target sites in exemplary regions covering a variety o topographic complexity. Teresults show that articial neural networks provide a capablemathematical tool to deliver reliable results. Te data mod-eled by the trained neural networks are highly correlatedto the corresponding data measured by the operating andsurveillance system o the turbines with coefficients o .andhigher.

Differences between the predictions o the best networksare small or the coastal sites as well as or the sites in themostly at region o the Westphalian Basin. Both network types tested allow a sound and accurate lling o the datagaps. However, the RBF networks turned out to bettercapture extreme values compared to the respective best MLPnetworks.

Te biggest advantage o the method o articial neural

networks to ll data gaps is the act that no inormationabout the relationships between the variables or the statisticaldistributions o the individual quantities must be assumedprior to the network training.

In combination with the ast learning procedure or RBFnetworks, this makes them a suitable approach or windenergy yield predictions in practice.

Te operating data o wind turbines are recorded today by deault with high temporal resolution and many importanttechnical parameters as well as basic wind meteorologicalmeasurements.

Our results show that these additional measurements cansignicantly increase the perormance o the neural networks


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: Summary o results or the modeled energy output o turbine WE using input variables rom the site Olpe.

Destination variable

Input variables Network type

and topology RMSE (kWh)

Correlation()

WE

(OL )average instantaneous power (OL )

Minimum instantaneous power (OL )Average wind direction (OL )Maximum wind speed (OL )(OL )Daily hours o operation (OL )Minimum instantaneous power (OL )Average instantaneous power (OL )Maximum instantaneous power (OL )Average wind speed (OL )(OL )Average wind speed (OL )

Ensemble × RBF(--)

(--)

.

RBF (--) .

RBF (--) .

especially in areas with complex topography. Tereore, theapproach presented helps to reduce the uncertainty o uturewind energy predictions conducted with wind ow models.Te work presented delivers the methodical ramework tobe deployed anywhere on the globe where input and relatedoutput data is available to train the articial neural networks.

Due to the increasing demand or energy the applicationo specically trained networks or turbines in complexterrain is o great interest in practice. Distances betweenwind turbines used as input and the target locations canbe signicantly larger than the distances considered in ourcase studies. Modeled power output values could be used asinput or a different ANN that is applied on turbines evenurther away rom the turbines that deliver the primary input

values. Exploring the capability o the ANN approach to work on larger spatial scales by using consecutive stages o inputand output datasets is a goal or uture research in order toutilize the inherent exibility o articial neural networks andincrease the planning dependability or wind energy projects.

Conflict of Interests

Te authors declare that there is no conict o interestsregarding the publication o the paper.

Acknowledgments

Te operating data o the wind turbines was kindly providedby ENERCON GmbH, SOLVEN GmbH, and SL-windenergy GmbH. Te authors thank these companies or theirsupport. Te authors also wouldlike to thank Joshua Baur orediting the language o the manuscript.

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