energies
Article Analysis of Wind Turbine Aging through Operation Data Calibrated by LiDAR Measurement
Hyun-Goo Kim * and Jin-Young Kim
Korea Institute of Energy Research, Daejeon 34129, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-42-860-3376
Abstract: This study analyzed the performance decline of wind turbine with age using the SCADA (Supervisory Control And Data Acquisition) data and the short-term in situ LiDAR (Light Detection and Ranging) measurements taken at the Shinan wind farm located on the coast of Bigeumdo Island in the southwestern sea of South Korea. Existing methods have generally attempted to estimate performance aging through long-term trend analysis of a normalized capacity factor in which wind speed variability is calibrated. However, this study proposes a new method using SCADA data for wind farms whose total operation period is short (less than a decade). That is, the trend of power output deficit between predicted and actual power generation was analyzed in order to estimate performance aging, wherein a theoretically predicted level of power generation was calculated by substituting a free stream wind speed projecting to a wind turbine into its power curve. To calibrate a distorted wind speed measurement in a nacelle anemometer caused by the wake effect resulting from the rotation of wind-turbine blades and the shape of the nacelle, the free stream wind speed was measured using LiDAR remote sensing as the reference data; and the nacelle transfer function, which converts nacelle wind speed into free stream wind speed, was derived. A four-year analysis of the Shinan wind farm showed that the rate of performance aging of the wind turbines was estimated Citation: Kim, H.-G.; Kim, J.-Y. to be −0.52%p/year. Analysis of Wind Turbine Aging through Operation Data Calibrated Keywords: performance aging; normalized capacity factor; nacelle transfer function (NTF); LiDAR; by LiDAR Measurement. Energies 2021, 14, 2319. https://doi.org/ Shinan wind farm 10.3390/en14082319
Academic Editors: Davide Astolfi and Francesco Castellani 1. Introduction According to IEC 61400-1, which explains the design condition of wind turbines, the Received: 12 March 2021 design life-span of wind turbines should be more than twenty years [1]. Since a wind Accepted: 17 April 2021 turbine is a machine that operates continuously under repetitive fatigue load conditions, Published: 20 April 2021 its performance inevitably deteriorates as a result of aging during its twenty-year life cycle (blade erosion, efficiency reduction of gearbox, bearing, generator, etc.) [2]. Publisher’s Note: MDPI stays neutral The results of a comprehensive analysis of 5600 wind turbines in the UK and 7600 wind with regard to jurisdictional claims in turbines in Denmark [3] verified that performance due to aging deteriorated to a significant published maps and institutional affil- extent. Nonetheless, performance aging has not been taken into consideration during iations. evaluations of the economic feasibility of wind farm projects due to a lack of reliable estimation data. According to the results of another study on thirty years of operational records of 3200 wind turbines in Denmark [4], the rate of reduction of their capacity was calculated Copyright: © 2021 by the authors. to be −0.32%p (percent point) per year, but the report did not specify whether this rate Licensee MDPI, Basel, Switzerland. was due purely to a deterioration of the wind turbines or to variations in the annual wind This article is an open access article resources. The results of an analysis of wind farms located in Ontario, Canada, for five distributed under the terms and years [5] showed that if the annual wind speed change is calibrated every year, the rate conditions of the Creative Commons of reduction of their capacity was −1.0%p per year, which is a much higher rate than Attribution (CC BY) license (https:// that reported in Denmark. The estimation by Hughes (2012) [3] and that by Staffell and creativecommons.org/licenses/by/ Green (2014) [6], who calibrated wind resource variability using MERRA (Modern-Era 4.0/).
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(2014) [6], who calibrated wind resource variability using MERRA (Modern-Era Retro- Retrospectivespective analysis analysis for Research for Research and Applications) and Applications) reanalysis reanalysis data, showed data, showed that the that normal- the normalizedized load factor load (or factor capacity (or capacity factor) factor)in onshore in onshore wind farms wind in farms the UK in thehad UK fallen had steadily fallen steadilyby −0.48%p by − per0.48%p year for per a year decade. for aHere, decade. the normalized Here, the normalized load factor load is the factor total ispower the total out- powerput over output a certain over period a certain of periodtime divided of time by divided the maximum by the maximumpotential power potential output power ad- outputjusted for adjusted monthly for variations monthly variations of wind speed. of wind speed. ByrneByrne etet al. (2020) (2020) [7] [7 ]and and Astolfi Astolfi et etal. al.(2020) (2020) [8] demonstrated [8] demonstrated the wind the wind turbine turbine aging agingof Vestas of Vestas V52 using V52 usingthe support the support vector vector machin machinee regression regression of operation of operation curves, curves, and found and foundthat the that performance the performance decline decline over overten years ten years was about was about 5%. Hamilton 5%. Hamilton et al. et (2020) al. (2020) [9] ana- [9] analyzedlyzed fleet-wide fleet-wide performance performance with with age age with with 917 917 wind wind farms farms installed installed before 20082008 inin thethe USUS andand showedshowed thethe performanceperformance decline decline of of− −0.54%p per year. InIn SouthSouth Korea, Korea, the the rate rate of of deterioration deterioration in in the the capacity capacity of of Sungsan Sungsan wind wind farm farm in in Jeju Jeju waswas reportedreported toto be be− −0.12%p0.12%p perper yearyear forfor fivefive yearsyears [[10],10], butbut thethe reliabilityreliability ofof thethe resultresult is is suspicioussuspicious becausebecause itit waswas obtainedobtained byby aa trendtrend analysisanalysis thatthat usedused onlyonly fivefive values values for for the the annualannual averageaverage capacitycapacity factor.factor. MostMost previousprevious studies studies have have estimated estimated the the deterioration deterioration of wind of wind farm farm capacity capacity by con- by ductingconducting a trend a trend analysis analysis of the of normalized the normaliz capacityed capacity factor, factor, which waswhich calibrated was calibrated according ac- tocording monthly to windmonthly speed wind variability. speed va However,riability. However, according accordin to one analysisg to one of analysis wind resource of wind variabilityresource variability off the western off the coast western of South coast Korea of South [11 ],Korea the uncertainty [11], the uncertainty of the yearly of the capacity yearly factorcapacity decreased factor decreased to 0.7% when to 0.7% the when analysis the an periodalysis was period set was to ten set years to ten or years longer, or longer, while thewhile monthly the monthly capacity capacity factor fell factor to 2.7% fell whento 2.7% the when analysis the period analysis was period set to 36was months set to or36 longer.months This or longer. implies This that, implies since the that, uncertainty since the of uncertainty the capacity of factor the capacity due to wind factor resource due to variabilitywind resource is comparable variability or is higher comparable than that or higher of the windthan that turbine of the deterioration wind turbine rate, deteriora- a long- termtion trendrate, a analysis long-term of moretrend than analysis ten years of more would than be ten needed years to would obtain be a reliableneeded qualitativeto obtain a estimatereliable qualitative of the rate ofestimate deterioration of the rate by a of monthly deterioration trend analysis.by a monthly trend analysis. ForFor windwind farmsfarms whosewhose totaltotal operatingoperating periodperiod isis short, short, any any estimate estimate of of performance performance agingaging would be be unreliable unreliable since since the the uncertainty uncertainty of wind of wind resource resource variability variability is more is more dom- dominantinant than than the wind the wind farm farmdeterioration deterioration rate. The rate. cumulative The cumulative installation installation capacity capacity of MW- ofclass MW-class wind turbines wind turbines in South in Korea South is Korea1512 MW is 1512 (as of MW the (asend of of the2019), end and of 2019),the cumulative and the cumulativenumber of installations number of installationsis over 600 turbines, is over 600around turbines, half of around which halfhave of a whichtotal operating have a totalperiod operating of less than period five of years less (Figure than five 1) years[12]. Thus, (Figure even1)[ if12 the]. Thus,monthly even wind if the speed monthly varia- windtion is speed calibrated variation in the is case calibrated of wind in turbines the case in of South wind Korea, turbines few in of South the available Korea, few cumu- of thelative available operational cumulative data cover operational a long enough data cover peri aod long to enable enough a reliable period toestimate enable of a reliable the rate estimateof wind ofturbine the rate deterioration of wind turbine using deterioration only the normalized using only capacity the normalized factor. capacity factor.
FigureFigure 1.1.Total Total wind wind turbine turbine installation installation capacity capacity in in South South Korea. Korea.
ThisThis studystudy aimsaims toto proposepropose aa newnew methodmethod ofof calculating calculating purelypurely mechanicalmechanical windwind turbineturbine performance performance aging aging rate rate using using SCADA SCADA data data whichwhich isis thethe rawestrawest windwind turbineturbine data.data. InIn other other words, words, a theoreticala theoretical prediction prediction of power of power generation generation is calculated is calculated through through the wind the turbine power curve based on the free stream wind speed, which is incident to a wind
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wind turbine power curve based on the free stream wind speed, which is incident to a wind turbine, and is then compared with the actual power generation data contained in theturbine, SCADA and record. is then compared with the actual power generation data contained in the SCADAThe record.deficit in power output between the predicted power generation and the actual The deficit in power output between the predicted power generation and the actual power generation is attributable to turbulence effects due to wake, site conditions such as power generation is attributable to turbulence effects due to wake, site conditions such wind shear caused by climate or terrain, operating effects such as the inflow angle and as wind shear caused by climate or terrain, operating effects such as the inflow angle and yaw misalignment, and the mechanical aging of the wind turbines among other factors yaw misalignment, and the mechanical aging of the wind turbines among other factors [6]. [6]. Although most of these are caused by stochastic effects, the dominant long-term cu- Although most of these are caused by stochastic effects, the dominant long-term cumulative mulative factor is wind turbine aging. Thus, the rate of mechanical deterioration of wind factor is wind turbine aging. Thus, the rate of mechanical deterioration of wind turbines turbines can be estimated by conducting a trend analysis of the power output deficit. can be estimated by conducting a trend analysis of the power output deficit. In addition, a LiDAR, a ground-based remote sensing device, was deployed and a In addition, a LiDAR, a ground-based remote sensing device, was deployed and a short-term campaign was conducted to accurately measure the free stream wind speed short-term campaign was conducted to accurately measure the free stream wind speed toward the wind turbines. The accuracy of the predicted power output calculation can be toward the wind turbines. The accuracy of the predicted power output calculation can be improved by calibrating the nacelle wind speed to the free stream wind speed. To that improved by calibrating the nacelle wind speed to the free stream wind speed. To that end,end, a a correlation correlation equation equation was was derived derived between between the the free free stream stream wind wind speed speed measured measured at at thethe hub hub height height of of a a wind wind turbine turbine by by LiDAR, LiDAR, and and the the nacelle nacelle wind wind speed speed measured measured by by the the nacellenacelle anemometer mountedmounted in in the the wind wind turbine. turbine. The The results results from from applying applying the proposedthe pro- posedmethod method to the Shinanto the Shinan wind farm, wind which farm, has which been has in commercial been in commercial operation sinceoperation 2009, since were 2009,compared were withcompared those with obtained those using obtained the conventional using the conventional method. method.
2.2. Analysis Analysis Data Data 2.1.2.1. Shinan Shinan Wind Wind Farm Farm TheThe Shinan Shinan wind wind farm farm is a is small-scale a small-scale wind wind farm farm (3 MW) (3 MW) that was that built was on built the onsandy the northernsandy northern shore shoreof Bigeumdo of Bigeumdo Island, Island, locate locatedd in the in thesouthwestern southwestern sea sea of of South South Korea Korea ◦ 0 00 ◦ 0 00 (34°46(34 46′33.833.8″ NN 125°56 125 56′15.315.3″ E).E). In In the the Shinan Shinan wind wind farm, farm, three three IEC IEC Class Class IIA IIA 1 1 MW MW wind wind turbinesturbines (Mitsubishi (Mitsubishi MWT-1000A MWT-1000A of of Japan), Japan), each each with with a cut-in a cut-in wind wind speed speed of 3 of m/s, 3 m/s, a hub a heighthub height of 69 ofm, 69and m, a androtor a rotordiameter diameter of 61.4 of m, 61.4 are m, arranged are arranged in line inin linethe east-west in the east-west direc- tiondirection (Figure (Figure 2). This2). study This study analyzed analyzed four years four years of SCADA of SCADA data datataken taken from fromFebruary February 2009 (i.e.,2009 the (i.e., farm’s the farm’s start of start commercial of commercial power powergeneration) generation) to April to 2013 April such 2013 as such wind as speed, wind windspeed, direction, wind direction, power poweroutput, output, yaw misalignme yaw misalignment,nt, ambient ambient temperature, temperature, etc. During etc. During the operationthe operation period, period, there there was was no nopower power curtailm curtailment,ent, and and the the Weibull Weibull distribution distribution of of wind wind speedspeed measured measured at at the nacelle-mounted anemomet anemometerer was the scale factorfactor ofof cc == 6.776.77 m/sm/s andand the the shape shape factor factor of of kk == 1.66. 1.66.
FigureFigure 2. 2. LocationLocation ( (leftleft)) and and layout layout ( (rightright)) of of the the Shinan Shinan wind wind farm farm (the (the wind wind turbines turbines and and the the LiDAR). LiDAR).
2.2.2.2. LiDAR LiDAR Measurement Measurement Campaign Campaign TheThe remote remote sensing sensing campaign campaign was was conduct conducteded from from November November 2009 2009 to toMarch March 2010 2010 (4 (4 months) using the Leosphere WindCube LiDAR which uses a pulsed erbium-doped fiber months) using the Leosphere WindCube LiDAR which uses a pulsed erbium-doped fiber laser at 1.54 µm wavelength and heterodyne detection. The vertical measurement heights laser at 1.54 μm wavelength and heterodyne detection. The vertical measurement heights were designed to include the wind turbine rotor area and the hub height (40 m, 70 m, 100 m, 130 m, ... above ground level). The sampling rate of SCADA and LiDAR is 1 Hz
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were designed to include the wind turbine rotor area and the hub height (40 m, 70 m, 100 werem, 130 designed m, ... above to include ground the level). wind Theturbine sampling rotor area rate andof SCADA the hub and height LiDAR (40 m, is 701 Hz m, and100 m,andthe 130 data the m, datawere ... above were converted converted ground into level). intoa 10 amin The 10 minaverage. sampling average. The rate Theaccuracy of accuracySCADA of the ofand WindCube the LiDAR WindCube is LiDAR 1 Hz LiDAR and has thehasbeen data been verified were verified convertedthrough through ainto comparative a comparativea 10 min average. verifi verificationcation The accuracywith with SODAR SODAR of the WindCube(SOnic (SOnic Detection LiDAR And has beenRanging) verified underunder through variousvarious a terrains terrainscomparative such such as asverifi plain, plain,cation hilly hilly terrain,with terrain, SODAR and and urban urban(SOnic [13]. [13]. ADetection measurement A measure- And Ranging)algorithmment algorithm under of the variousof LiDAR the LiDAR andterrains a correctionand such a correction as methodplain, hillymethod in complexterrain, in complex and terrain urban terrain using [13]. computationalusing A measure- compu- mentfluidtational dynamicsalgorithm fluid dynamics (CFD)of the areLiDAR (CFD) well andare described wella correction described in Kim method and in Kim Meissner in and complex Meissner (2017) terrain [14 (2017)]. using [14]. compu- tationalThe fluid LiDAR LiDAR dynamics was was deployed deployed (CFD) are between between well described wind wind turbines turbinesin Kim #2 and and #2 Meissner and #3 at #3 the at (2017)Shinan the Shinan [14]. wind windfarm farmin orderThe in order LiDARto measure to was measure deployedthe sea the breeze, sea between breeze, which wind which is turbines a ismain a main #2wind, and wind, without#3 at without the interruption Shinan interruption wind of farm the of intheterrain order terrain features to featuresmeasure (Figure (Figurethe 2). sea Due2 ).breeze, Due to the to which conica the conical isl scanninga main scanning wind, setup setup withoutof WindCube of WindCube interruption [14], [the14 of ],scan- the terrainscanningning plane features plane at the at(Figure thehub hub height 2). height Due of to the of the the wind conica wind turbine turbinel scanning (the (the yellowsetup yellow of circle circleWindCube in in Figure Figure [14], 22)) mightthemight scan- bebe interfered partiallypartially byby the the blade blade rotation rotation (the (the white white circle circle of #2).of #2). To preventTo prevent this, this, the LiDARthe Li- ning plane at◦ the hub height of the wind turbine (the yellow circle in Figure 2) might be interferedisDAR rotated is rotated 35partiallyclockwise 35° clockwiseby the so thatblade so the that rotation scanning the scanni (the points whiteng points (four circle yellow(four of #2). yellow dots) To dopreventdots) not do overlap this, not overlapthe in theLi- DARrotorin the is plane. rotor rotated plane. 35° clockwise so that the scanning points (four yellow dots) do not overlap in theThe rotor comparison plane. of wind speed at the hubhub heightheight betweenbetween thethe SCADASCADA andand LiDARLiDAR data is depicted in Figure3. The frequency distribution of wind direction measured by data Theis depicted comparison in Figure of wind 3. The speed frequency at the hu distributionb height between of wind the direction SCADA measured and LiDAR by LiDAR during the campaign period revealed that the excellent north-northwest sea breeze dataLiDAR is depictedduring the in campaign Figure 3. periodThe frequency revealed distribution that the excellent of wind north- directionnorthwest measured sea breeze by with the mean wind speed of 10 m/s is the main wind as shown in Figure4a. Figure4b LiDARwith the during mean the wind campaign speed ofperiod 10 m/s revealed is the mainthat the wind excellent as shown north- innorthwest Figure 4a. sea Figure breeze 4b shows the wind rose of the third-generation reanalysis data, MERRA-2 at the same period withshows the the mean wind wind rose ofspeed the third-generationof 10 m/s is the mainreanalysis wind data, as shown MERRA-2 in Figure at the 4a. same Figure period 4b of the campaign. They share very similar characteristics with the LiDAR measurements. showsof the thecampaign. wind rose They of theshare third-generation very similar ch reanalysisaracteristics data, with MERRA-2 the LiDAR at the measurements. same period Figure4c shows the wind rose of MERRA-2 for the last ten years, in which southeasterly ofFigure the campaign. 4c shows theThey wind share rose very of MERRA-2similar ch aracteristicsfor the last tenwith years, the LiDARin which measurements. southeasterly winds blew in summer but north-northwesterly winds were dominant throughout the year, Figurewinds 4cblew shows in summer the wind but rose north-northweste of MERRA-2 forrly the winds last ten were years, dominant in which throughout southeasterly the and the frequencies of easterly and westerly winds where the wake effect occurred were windsyear, and blew the in frequencies summer but of north-northwesteeasterly and westerlyrly winds winds were where dominant the wake throughout effect occurred the very few. year,were andvery the few. frequencies of easterly and westerly winds where the wake effect occurred were very few.
Figure 3. Comparison of the daily-mean wind speed betweenbetween SCADA andand LiDARLiDAR datadata atat thethe hubhub height.height. Figure 3. Comparison of the daily-mean wind speed between SCADA and LiDAR data at the hub height.
(a) (b) (c) Figure 4. Wind frequency(a) roses at the Shinan wind farm from(b) 30 November 2009 to 17 March 2010.( c()a ) LiDAR measure- ment (dashed line: mean wind speed at 70 m above ground); (b) MERRA-2; (c) MERRA-2 over a period of 10 years. Figure 4. Wind frequency rosesroses atat the the Shinan Shinan wind wind farm farm from from 30 30 November November 2009 2009 to 17to March17 March 2010. 2010. (a) LiDAR(a) LiDAR measurement measure- ment (dashed line: mean wind speed at 70 m above ground); (b) MERRA-2; (c) MERRA-2 over a period of 10 years. (dashed line: mean wind speed at 70 m above ground); (b) MERRA-2; (c) MERRA-2 over a period of 10 years.
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For reference, MERRA-2 refers to third-generation reanalysis data (1 h average) that extensively assimilates satellite-based remote sensing data, showing a highly accurate es- timate for the southwest offshore of South Korea [15]. The MERRA-2 and LiDAR meas- urements showed a high correlation of the coefficient of determination, R2 = 0.78 and 0.95 for wind speed and wind direction respectively.
3. Analysis Methods
Energies 2021, 14, 2319 The method of calculating the rate of deterioration of the capacity factor from5 of 12the SCADA data of the wind farm and sort-term LiDAR measurements is presented in Figure 5 in the form of a schematic diagram. First, the free stream wind speed was measured through the short-term LiDAR meas- urementFor reference, campaign, MERRA-2 and the refersnacelle to transfer third-generation function (NTF; reanalysis the correlation data (1 h average)between thatwind extensivelyspeeds measured assimilates at the satellite-based upstream of remotewind tu sensingrbine using data, a showingremote sensing a highly device accurate and a estimatenacelle foranemometer the southwest on a offshorewind turbine) of South was Korea derived [15]. by The analyzing MERRA-2 the and correlation LiDAR mea- with 2 surementsregard to showed the nacelle a high wind correlation speed of ofthe the SCADA coefficient data. of determination, R = 0.78 and 0.95 for windSecond, speed the and nacelle wind directionwind speed respectively. of the SCADA was calibrated to the free stream wind speed using the derived NTF, and the calibrated speed was substituted into the wind tur- 3. Analysis Methods bine power curve to calculate the predicted power output. TheThird, method the difference of calculating between the ratethe actual of deterioration power output of the and capacity the predicted factor power from the out- SCADAput was data calculated, of the wind and farm the andrate sort-termof deterioration LiDAR of measurements the performance is presented of the wind in Figure turbine5 inwas the formestimated of a schematicby a monthly diagram. trend analysis.
FigureFigure 5. 5.Schematic Schematic diagram diagram of of analysis analysis of of rate rate of of deterioration deterioration of of performance performance of of a winda wind turbine. turbine.
3.1.First, Derivation the free of the stream Nacelle wind Transfer speed Function was measured through the short-term LiDAR mea- surementSince campaign, a nacelle andanemometer the nacelle is transferinstalled function in the rear (NTF; side the of correlationthe blade roots between on the wind wind speedsturbine’s measured nacelle, at itthe measures upstream wind of windspeedturbine that is deformed using a remote by the sensing nacelle devicegeometry and and a nacellethe wake anemometer caused byon the a blades’ wind turbine) rotation; was ther derivedefore, the by higher analyzing the wind the correlationspeed, the greater with regardthe deficit. to the In nacelle this regard, wind speed IEC 61400-12-2 of the SCADA [16], data.which recommends the guideline for wind Second, the nacelle wind speed of the SCADA was calibrated to the free stream wind turbine power performance, provides a rule on the creation of the NTF to calibrate the speed using the derived NTF, and the calibrated speed was substituted into the wind nacelle wind speed to the free stream wind speed. Kim et al. (2015) [17] verified various turbine power curve to calculate the predicted power output. types of NTFs according to the type of wind turbine, blades, nacelle geometry, and sensor Third, the difference between the actual power output and the predicted power output position via an analysis of the literature (Figure 2 of Kim et al., 2015 [17]). They defined was calculated, and the rate of deterioration of the performance of the wind turbine was estimated by a monthly trend analysis.
3.1. Derivation of the Nacelle Transfer Function Since a nacelle anemometer is installed in the rear side of the blade roots on the wind turbine’s nacelle, it measures wind speed that is deformed by the nacelle geometry and the wake caused by the blades’ rotation; therefore, the higher the wind speed, the greater the deficit. In this regard, IEC 61400-12-2 [16], which recommends the guideline for wind turbine power performance, provides a rule on the creation of the NTF to calibrate the nacelle wind speed to the free stream wind speed. Kim et al. (2015) [17] verified various types of NTFs according to the type of wind turbine, blades, nacelle geometry, and sensor position via an analysis of the literature (Figure2 of Kim et al., 2015 [ 17]). They defined the Energies 2021, 14, 2319 6 of 12 Energies 2021, 14, x FOR PEER REVIEW 6 of 12
NTF as a function of wind speed as well as turbulence intensity, thereby improving the functionthe NTF fitnessas a function [18]. of wind speed as well as turbulence intensity, thereby improving the functionAssuming fitness that the[18]. variations of wind flow passing through the wind turbine can be expressedAssuming with the that blades’ the variations aerodynamic of wind characteristics, flow passing that through is, thepower the wind coefficient turbine ( CcanP) orbe thrustexpressed coefficient with the (CT blades’). This studyaerodynamic conducted characteristics, a regression that analysis is, the of power the NTF coefficient using the (CCPP) -equationor thrust (Equationcoefficient (1)), (CT).C TThis-equation study conducted (Equation (2)), a regression and non-linear analysis function of the (NTFEquation using (3) the). NoteCP -equation that Equations (Equation (1) (1)), and C (2)T -equation are derived (Equation empirically (2)), [and19,20 non-linear]. function (Equation (3)). Note that Equations (1) and (2) are derived√ empirically [19,20]. 3 a1 − CP Vcorrected,1 = Vnacelle + a3 (1) 𝑎 a 𝐶 𝑉 2 𝑉 𝑎 (1) , 𝑎 q Vcorrected,2 = b1 (1 − CT) Vnacelle + b2 (2) 𝑉 , 𝑏 1 𝐶 𝑉 𝑏 (2) V = c V3 + c V2 + c V + c (3) corrected𝑉 , ,3 𝑐1 nacelle𝑉 𝑐2 nacelle𝑉 𝑐3 nacelle 𝑉 𝑐4 (3) where a , a , a , b , b , c , c , c , c are the fitting coefficients determined by the maximum where 1𝑎 ,𝑎2 ,𝑎3 ,𝑏1 ,𝑏2 ,𝑐 1,𝑐 2,𝑐 ,𝑐3 4 are the fitting coefficients determined by the maximum likelihood estimation. (a = 4.60, a2 = 3.84, a3 = 0.35, b = 1.06, b2 = 3.65, c = 0.0008, likelihood estimation. (𝑎 1 = 4.60, 𝑎 = 3.84, 𝑎 = 0.35, 𝑏1 = 1.06, 𝑏 = 3.65, 𝑐1 = 0.0008, c2 = 0.0538, c3 = 0.3025, c4 = 2.8041). 𝑐 = 0.0538, 𝑐 = 0.3025, 𝑐 = 2.8041). TheThe powerpower coefficientcoefficient isis defineddefined asas thethe ratioratio betweenbetween rotorrotor powerpower andand freefree streamstream windwind power,power, which which refers refers to to the the fraction fraction of of wind wind power power that thatis is absorbedabsorbed byby thethe rotor.rotor. TheThe thrustthrust coefficientcoefficient isis defineddefined as the the ratio ratio betw betweeneen the the thrust thrust force force and and the the dynamic dynamic force force of of free stream wind, which refers to the fraction of wind energy that is absorbed by the free stream wind, which refers to the fraction of wind energy that is absorbed by the rotor rotor [21]. The power and thrust coefficients of the Mitsubishi MWT-1000A wind turbine [21]. The power and thrust coefficients of the Mitsubishi MWT-1000A wind turbine are are shown in Figure6. shown in Figure 6.
FigureFigure 6.6. PowerPower curve,curve, powerpower andand thrustthrust coefficientcoefficientof ofthe theMitsubishi Mitsubishi MWT-1000A. MWT-1000A.
3.2.3.2. TrendTrend AnalysisAnalysis ofof Wind Wind Turbine Turbine Deterioration Deterioration TheThe differencedifference betweenbetween actualactual powerpower generationgenerationand and predictedpredicted power powergeneration generation can can bebe calculatedcalculated usingusing thethe followingfollowing sequence.sequence.
(1)(1) The nacelle wind wind speed speed (V (Vnacellenacelle) is) calibrated is calibrated to free to free stream stream wind wind speed speed (Vcorrected (Vcorrected) using) usingthe NTF the derived NTF derived in Section in Section 3.1. 3.1. (2)(2) The effectiveeffective windwind speedspeed ((VVeffeff) is calculatedcalculated toto compensatecompensate thethe effecteffect ofof airair densitydensity whenwhen thethe performanceperformance curve is applied as follows. In the equation below, below, ρ𝜌o refersrefers to the standard standard air air density density when when the the wind wind turbine turbine performance performance curve curve is derived. is derived. The ◦ Theseasonal seasonal temperature temperature change change in Korea in Korea is about is about26 °C, 26so accurateC, so accurate air density air densitycalcula- calculationtion is essential is essential for wind for resource wind resource assessment. assessment. In this Instudy, this study,air density air density was calcu- was lated using SCADA data and the nearby weather station data (located 2.5 km behind) such as air temperature, air pressure, and humidity.
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1/3 Ve f f = Vcorrected(ρ/ρo) (4)