Validation of a Quasi-Steady Wind Farm Flow Model in the Context of Distributed Control of the Wind Farm

Validation of a quasi-steady wind farm flow model in the context of distributed control of the wind farm

A.J. Brand J.W. Wagenaar

Presented at: Torque 2010, 28-30 June 2010, Crete, Greece

ECN-M--10-058 JULY 2010

2 ECN-M-10-058 Validation of a quasi-steady wind farm flow model in the context of distributed control of the wind farm

A J Brand J W Wagenaar ECN Wind Energy ECN Wind Energy P.O. Box 1, NL 1755 ZG Petten, P.O. Box 1, NL 1755 ZG Petten, Netherlands Netherlands [email protected] [email protected]

wind farm flow model, and presents load Abstract quantifiers calculated by the model. First, the research objectives of the FP7 project This work presents validation of an Aeolus are described (section 2) and the intermediate version of a quasi-steady quasi-steady wind farm flow model is wind farm flow model which will be part of introduced (section 3). Next, a comparison distributed control of a wind farm. In is presented between model output for and addition power and three load quantifiers measured data from the ECN Wind turbine as calculated by the model are Test site Wieringermeer EWTW (section demonstrated. It is concluded that 4). In addition power and three short-term differences between measurement and load quantifiers as calculated for the prediction are smaller than 2 m/s (wind considered cases are presented (section speed) and 200 kW (power), measured 5). Finally, a summary of the work and an minimum in wind speed and aerodynamic outlook to future work are given (section power at second or third turbine is not 6). predicted, and main differences originate from un-modelled spatial variations in wind speed and too gradually modelled decay 2. Objectives and approach of wind speed. The general objectives of the FP7 project Keywords: Model predictive control, Aeolus are to develop models that allow Wind farms, Offshore wind energy real-time predictions of flow in a wind farm and incorporate data from a network of 1. Introduction sensors, and to develop control paradigms that acknowledge the uncertainty in the In Europe wind farms are being developed modelling and dynamically manage the at a large scale. These installations are flow resource in order to optimize specific expected to operate similar to control objectives. conventional power plants and to provide Specific objectives of the project, quality power at the lowest possible cost. contained in the two flow modelling work During operation this is achieved by packages, include the development of a addressing three control objectives at wind quasi-steady and a dynamic flow model. farm level: maximum power production, The quasi-steady flow model relates single minimum structural loads and optimal turbine production and loading to a map of integration into the power system. wind speeds [4, 5, 6], in contrast to the The EU project FP7-ICT STREP dynamic flow model which describes 22548 / Aeolus is aimed at the deviations from the steady model due to development of distributed control of large rapidly changing flow effects [7]. offshore wind farms [1, 2]. In this context a quasi-steady wind farm flow model is The quasi-steady flow model is derived developed, which is to be part of the from fluid dynamics principles and is supervisory control algorithm [3]. based on a database of meteorological This paper addresses validation of an and wind turbine related measurements. It intermediate version of the quasi-steady is developed in two stages: first a preliminary version (finished April 2009 theory the aerodynamic state of a wind and reported separately [4, 5, 6]) and next turbine is expressed in terms of an axial the final version (finished February 2010, induction factor. Relations for the mean also reported separately [8, 9] and partly and the standard deviation of the axial covered in this paper). induction factor both bring the effect of In fact the quasi-steady flow model is turbulence into account. Subsequently a model of the control object "wind farm"; aerodynamic power, tower bending where "model" means a mathematical moment, blade bending moment and rotor map/function in the form of equations (or shaft torque are calculated. In addition initially look-up tables) which relates farm velocity deficit and extra turbulence due to output (power and load quantifiers) to the single wind turbine are calculated. measured quantities (e.g. rotor speed, The model treats a cluster of wind blade pitch angle, wind speed), references turbines by linking individual wind turbines (e.g. power set point) and disturbances via their wakes. For the given wind (unmodelled system inputs). Figure 1 direction, for all wind turbines in the cluster shows the basic structure. The model is the streamwise and the spanwise distance steady in the sense that it is valid over downstream each wind turbine is averaging periods of 10 minutes, in determined. Subsequently, this infomation contrast to the dynamic flow model which is employed in order to calculate all local is dynamic in the sense that it describes values of velocity deficit and added deviations from the mean. The model is turbulence by using decay laws. quasi steady because it gives mean as 3.2 Load quantifiers well as standard deviation of a quantity, and by doing so provides information on The quasi-steady wind farm flow model variations which are translated into load translates wind speed mean values and quantifiers. standard deviations into mean values and standard deviations of mechanical loads. 3. Quasi steady wind farm Subsequently the model translates this information into load quantifiers. In this flow model section the approach is presented. 3.1 Flow model First, as described in preceding The quasi-steady wind farm flow model publications [4, 8], it is assumed that load allows the wind farm controller to calculate mean μL as well as load standard deviation in real time maps of wind, loads and σL depend on wind speed mean μU and energy, or to be more specific, wind speed wind speed standard deviation σU: at each turbine in a wind farm plus tower bending moment, blade bending moment,     ,  and     , . rotor shaft torque and aerodynamic power L L U U L L U U of each turbine as a function of "ambient" This crucial assumption is motivated by wind speed, wind direction and turbulence experimental and modelling based intensity. The corresponding flow chart is identification of the parameters that shown in figure 2. influence equivalent loads [14, part 1, sub B, section 5.4]. The conclusions in the The structure and the details of the flow referred work are that: model, which are described in preceding publications [5, 6], are summarized in this  The primary fatigue load parameter is the standard deviation of the longitudal section. 1 Apart from sub-models based on wind speed component , and classic momentum theory [10], inspired by  The equivalent load is a function of the the literature on wind turbine wakes [11, wind speed standard deviation σU and, 12, 13, 14 part 1 sub A section 2.4, 15, because at higher wind speeds a 16], this model includes specially constant value of the turbulence developed sub-models for creation and intensity may be assumed, the mean decay of velocity deficit, creation and wind speed μU. decay of added turbulence, impact of turbulence on average values, and standard deviation of all quantities. The model treats individual wind 1 The second important parameter is yaw turbines separately. By using momentum misalignment, and the third important parameter is turbulence structure Secondly, it is assumed that loads are normally distributed. This assumption is Section 5 demonstrates the equivalent fair in a short-term assessment of wind load concept on basis of measured data. turbine components because: Future work is aimed at relating equivalent  In a short time period (10 minutes) the load to fatigue load. number of observations or revolutions is high (600 resp. ~200), and 4. Model output versus  Under normal operation during a 10- minute period wind turbine loads have measured data comparison experimentally been found to vary with 4.1 Overview well-defined mean and standard deviation. In this section output from an intermediate version of the quasi-steady flow model is The load quantifier selected is the compared to measured data from the ECN Wind turbine Test site Wieringermeer equivalent load Leq [e.g. 17, page 80] of a EWTW. (The EWTW consists of a row of series of loads Lj (j = 1, 2, 3, …, N): five 2.5 MW wind turbines plus a meteo 1 1 mast.) Various wind speed and direction m m m cases are presented and discussed, see Leq  niLi  L j N i N j figure 3 for a definition sketch, and = m-th raw moment of the observed loads. modelling issues are identified in the light of the modelling objective. Here L indicates the load, m is the slope of the SN-curve of the material and N is the 4.2 Inflow perpendicular to turbine row number of load observations in the time In this section inflow perpendicular to the period. Furthermore ni is the number of row of turbines (wd2) together with four loads with value Li, whereas j indicates an wind speed cases is considered. This wind individual load in the series Lj. direction case is relevant because it shows to what extent the state of each turbine is If the load is a moment (e.g. tower bending predicted if all turbines have the same moment, or blade bending moment), ni is inflow. The wind speed cases are relevant the number of load observations of level Li because they correspond to near cut-in in the time period and N = Σi ni is the (ws1), halfway nominal power (ws2), near number of load observations in that period nominal power (ws3) and constant power [e.g. 17, page 80]. (ws4). The wind speed cases have been If, on the other hand, the load is a set on basis of the 10-minute averaged shaft load (e.g. rotor shaft torque), m is 3, wind speed as measured at the meteo ni is the number of revolutions at shaft load mast and correspond to an upstream Li and N = Σi ni is the number of turbulence intensity of 9-11%. Figure 4 revolutions [e.g. 17, pages 136-137]. shows a comparison between calculated and measured mean values, and figure 5 Under the assumption that observed loads shows a comparison between calculated are normally distributed with mean μL and and measured standard deviations. standard deviation σL, the m-th raw First it should be noted that even over moment, and for that reason the the small separation distances between equivalent load, is expressed in terms of the wind turbines in the EWTW there is μL and σL: some spatial variation in the mean inflow wind speed. For example, there are 1 differences of the order of 1 m/s between Lm  f  , .  j  L L  the mean wind speed at the meteo mast N j and the individual wind turbines, and even For example, the 4-th order (m = 4) larger differences between the wind speed equivalent load is [18]: standard deviations. As another example all wind speeds at the high wind speed

1 case (ws4) should be equal to the meteo 4 2 2 4 4 Leq  L  6LL  3L  . mast reading 17-18 m/s. However in fact these vary between 16 m/s and 18 m/s. Methods to find the raw moment for other These variations, which have not been integer and even non-integer values of m taken into account in the modelling, cause can be found in the literature [18]. variations in the calculated power between the wind turbines, and to a smaller extent good agreement for power standard in the tower bending moment and the deviation of turbines T1, T4 and T5. blade bending moment. However the agreement for power of the In addition, between the wind turbines other turbines and for all bending there is a clear variation in the standard moments is poor. deviation of the inflow wind speed. This variation is caused by the IJsselmeer, 5. Demonstration of power where turbulence intensity is lower than over land. Nevertheless calculated and load quantifiers standard deviations are of the correct In this section power and three short-term order of magnitude. load quantifiers, as calculated by the 4.3 Inflow aligned with turbine row intermediate version of the quasi-steady flow model, are presented for the cases In this section inflow aligned with the row introduced in section 4. The motivation is of turbines (wd1) together with the four that these quantities, together with for wind speed cases is considered. This wind example rotor speed and blade pitch direction case is relevant because it shows angle, are the primary quantities that are to what extent the state of each turbine is considered by the supervisory control predicted if all but one turbine is in the algorithm. wake of another turbine. Again the wind The short-term load quantifiers are speed cases have been set on basis of the equivalent tower bending moment (m=4), 10-minute mean of the wind speed as equivalent blade bending moment (m=12), measured at the meteo mast, and and equivalent rotor-shaft torque (m=3). correspond to an upstream turbulence Figure 8 shows calculated power and intensity of 9-11%. Figures 6 and 7 show calculated load quantifiers as a function of the various quantities as a function of wind speed in the case of inflow distance along the row of turbines, plus, in perpendicular to the row of five wind the case of wind speed, upstream wind turbines in the EWTW. Clearly, since all speed as measured at the meteo mast. turbines have the same inflow (mean wind First it is checked whether the speed and turbulence intensity of 9-11%), upstream wind turbine (T1) has the same the options to control the wind farm via the inflow as the meteo mast (T0). This is the turbine wakes under these conditions are case for the mean wind speed (figure 6), few. but not for the wind speed standard Figure 9, on the other hand, shows that deviation as there are differences up to 1 power and load quantifiers differ between m/s (figure 7). The latter hampers the the individual wind turbines when inflow is assessment of the impact of turbulence. along the row of wind turbines. This Figure 6 compares calculated and illustrates the options to control the power measured 10-minute mean values. Here it of and the loads in the wind farm via the is found that, apart from the high wind wakes of the turbines. Note however that speed case, the predicted mean wind in this case the coupling via the wakes is speed in the wake is within a meter per strong because of the short distance of 3.8 second of the measured wind speed. On rotor diameters between the turbines in the other hand predicted decay of wind the EWTW. speed deficit is too gradual, and measured wind speed minimum at second or third turbine is not calculated. This picture also 6. Summary and outlook emerges form power, tower bending The intermediate version of a quasi-steady moment, and blade bending moment. wind farm flow model has been compared Figure 7 compares calculated and to data from the ECN Wind turbine Test measured 10-minute standard deviations. site Wieringermeer EWTW, and various As to calculated and measured wind modelling issues have been identified. In speed standard deviation it must be noted addition power and three load quantifiers that these can not be compared because have been demonstrated. It is concluded the latter is measured at the hub, in the that differences between measurement centre of the rotor disc, where turbulence and prediction are smaller than 2 m/s is higher due to the hub. Anyway, there is (wind speed) and 200 kW (power), a good agreement between calculated and measured minimum in wind speed and measured decay of turbulence. In addition, aerodynamic power at second or third there is a reasonable although not very turbine is not predicted, and main differences originate from un-modelled Conference 2010, Warsaw, Poland, spatial variations in wind speed and too April 2010 gradually modelled decay of wind speed. [7] Knudsen T, Soltani M and Bak Th, "Prediction models for wind speed at The modelling issues that have been turbines in a farm with application to identified include: control", Euromech Colloquium 508  The value of the constants in the "Wind turbine wakes", Madrid, Spain, velocity deficit decay law. October 2009  The value of the constants in the added [8] Brand A J and Wagenaar J W, FP7- turbulence decay law. ICT STREP 22548 / Aeolus  The inhomogeneity of the inflowing Deliverable D1.4a, "Scale wind farm wind speed. flow model improvements Part 1: These modelling issues will be addressed Quasi-steady wind farm flow model - by applying the model to the ECN Scale Model description", confidential, Wind Farm. (The ESWF consists of ten 10 February 2010 kW wind turbines and fourteen meteo [9] Brand A J and Wagenaar J W, FP7- masts.) In addition the equivalent loads ICT STREP 22548 / Aeolus will be related to fatigue load. Deliverable D1.4b, "Scale wind farm Subsequently, the final version of the flow model improvements Part 2: quasi-steady wind farm flow model will be Quasi-steady wind farm flow model - developed. User's manual", confidential, February 2010 [10]Manwell J F, McGowan J G and Rogers A L, Wind energy explained, Acknowledgements John Wiley and Sons, ISBN 0 471 This work was performed in the framework 49972 2, 2002 of the EU project FP7-ICT STREP 22548 / [11]Barthelmie R et al., "Efficient Aeolus "Distributed control of large-scale Development of Offshore Windfarms offshore wind farms". (ENDOW)", Report Risø-R-1407(EN), 2003 [12]Barthelmie R et al., "Modelling the References impact of wakes on power output at [1] Aeolus - Distributed control of large- Nysted and Horns Rev", European scale offshore wind farms, http://ict- Wind Energy Conference 2009, aeolus.eu, 2008-2010 (17 February Marseille, France, April 2009 2010) [13]Cleve J, "Wake flow model for large [2] Knudsen T, Bak Th and Soltani M, wind farms", Euromech Colloquium "Distributed control of large-scale 508 Wind Turbine Wakes, Madrid, offshore wind farms", European Wind Spain, October 2009 Energy Conference 2009, Marseille, [14]Dekker J W M and Pierik J T G (ed.), France, April 2009 European Wind Turbine Standards II [3] Spudić V, Baotić M, Jelavić M and ECN-C--99-073, 1999 Perić N, "Hierarchical wind farm [15]Elliott D L, "Status of wake and array control for power/load optimization", loss research", Windpower91, Palm Torque 2010, Heraklion, Greece, June Springs, California, 1991 2010 [16]Milborrow D J, "The performance of [4] Brand A J, FP7-ICT STREP 22548 / arrays of wind turbines", J. Industrial Aeolus Deliverable D1.3, "Preliminary Aerodynamics, 5 (1980), pp. 403-430 maps of wind, loads and energy", [17]Guidelines for Design of Wind confidential, April 2009 Turbines (1st ed.), Det Norske Veritas [5] Brand A J and Wagenaar J W, "A wind and Risø National Laboratory, ISBN farm model in the context of 87-550-2870-5, 2001 distributed control", Euromech [18]Weisstein E.W., Normal Distribution, Colloquium 508 "Wind turbine wakes", From MathWorld - A Wolfram Web Madrid, Spain, October 2009 Resource, [6] Brand A J and Wagenaar J W, "A http://mathworld.wolfram.com/Normal quasi-steady wind farm flow model in Distribution.html (17 February 2010) the context of distributed control of the wind farm", European Wind Energy model based control control object = = farm control wind farm

reference: total farm power Controller System

power produced power & speed disturbances fatigue measures references to wind field

Figure 1 Basic structure of the quasi-steady wind farm flow model

upstream wind speed turbine wake turbine wake wake wake upstream turbulence model model model model etc model model T1 T1 - T2 T2 T2 - T3 T1 - T3 T2 - T4 upstream wind direction

separation distances T1 and T2 separation distances T2 and T3 separation distances T1 and T3 separation distances T2 and T4

cluster coordinates T1, T2, ... ,Tn model

Figure 2 Flow chart of the quasi-steady wind farm flow model

wind power

T5 T6 T7 T8 T9

wd1

wd3

wd2 wind speed

ws1 ws2 ws3 ws4

Figure 3 Description of the wind speed ranges (left) and the wind direction ranges (right) in the EWTW 25 3000

2500 20

2000 15 meas, ws1 meas, ws1 meas, ws2 1500 meas, ws2 meas, ws3 meas, ws3 10 meas, ws4 1000 meas, ws4 calc, 5 m/s calc, 5 m/s Power ave [kW] 5 calc, 9 m/s 500 calc, 9 m/s Wind speed ave [m/s] calc, 13 m/s calc, 13 m/s calc, 18 m/s calc, 18 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

20000 5000

4000 15000

meas, ws1 3000 meas, ws1 10000 meas, ws2 meas, ws2 [kNm] meas, ws3 [kNm] 2000 meas, ws3 meas, ws4 meas, ws4 5000 calc, 5 m/s calc, 5 m/s calc, 9 m/s 1000 calc, 9 m/s calc, 13 m/s calc, 13 m/s Tower bending moment ave calc, 18 m/s Blade bending moment ave calc, 18 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

Figure 4 Calculated and measured means of wind speed, power, tower bending moment and blade bending moment in the case of inflow parallel perpendicular to the row of five wind turbines

5 1000

4 800

3 meas, ws1 600 meas, ws1 meas, ws2 meas, ws2 meas, ws3 meas, ws3 2 400 meas, ws4 meas, ws4 calc, 5 m/s calc, 5 m/s Power std [kW] 1 calc, 9 m/s 200 calc, 9 m/s Wind speed std [m/s] calc, 13 m/s calc, 13 m/s calc, 18 m/s calc, 18 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

5000 1000

4000 800

3000 meas, ws1 600 meas, ws1 meas, ws2 meas, ws2 meas, ws3 meas, ws3 [kNm] [kNm] 2000 400 meas, ws4 meas, ws4 calc, 5 m/s calc, 5 m/s 1000 calc, 9 m/s 200 calc, 9 m/s calc, 13 m/s calc, 13 m/s

Blade bending moment std calc, 18 m/s Tower bending moment std calc, 18 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

Figure 5 Calculated and measured standard deviations of wind speed, power, tower bending moment and blade bending moment in the case of inflow parallel perpendicular to the row of five wind turbines 25 3000

2500 20

Turbine number [-] Turbine number [-]

20000 5000

4000 15000

meas, ws1 3000 meas, ws1 10000 meas, ws2 meas, ws2 [kNm] meas, ws3 [kNm] 2000 meas, ws3 meas, ws4 meas, ws4 5000 calc, 5 m/s calc, 5 m/s calc, 9 m/s 1000 calc, 9 m/s calc, 13 m/s calc, 13 m/s Tower bending moment ave calc, 20 m/s Blade bending moment ave calc, 20 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

Figure 6 Calculated and measured means of wind speed, power, tower bending moment and blade bending moment in the case of inflow aligned with the row of five wind turbines

5 1000

4 800

Turbine number [-] Turbine number [-]

5000 1000

4000 800

3000 meas, ws1 600 meas, ws1 meas, ws2 meas, ws2 meas, ws3 meas, ws3 [kNm] [kNm] 2000 400 meas, ws4 meas, ws4 calc, 5 m/s calc, 5 m/s 1000 calc, 9 m/s 200 calc, 9 m/s calc, 13 m/s calc, 13 m/s

Blade bending moment std calc, 20 m/s Tower bending moment std calc, 20 m/s 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6

Turbine number [-] Turbine number [-]

Figure 7 Calculated and measured standard deviations of wind speed, power, tower bending moment and blade bending moment in the case of inflow aligned with the row of five wind turbines 3.0E+03 2.0E+04 T1 1.8E+04 T1 T2 2.5E+03 T2 1.6E+04 T3 T3 T4 2.0E+03 T5 1.4E+04 T4 1.2E+04 T5 1.5E+03 1.0E+04 8.0E+03 1.0E+03 Power [kW] 6.0E+03 4.0E+03 5.0E+02 Tower bottom (m=4) 2.0E+03Equivalent load [kNm] 0.0E+00 0.0E+00 0 5 10 15 20 25 0 5 10 15 20 25 Wind speed [m/s] Wind speed [m/s]

4.0E+03 1.6E+03 T1 T1 3.5E+03 T2 1.4E+03 T2 T3 T3 3.0E+03 1.2E+03 T4 T4 2.5E+03 T5 1.0E+03 T5

2.0E+03 8.0E+02

1.5E+03 6.0E+02

1.0E+03 4.0E+02 Blade root (m=12) Rotor shaft (m=3)

5.0E+02Equivalent load [kNm] 2.0E+02Equivalent load [kNm]

0.0E+00 0.0E+00 0 5 10 15 20 25 0 5 10 15 20 25 Wind speed [m/s] Wind speed [m/s]

Figure 8 Calculated power and load quantifiers for the turbine tower, the blade and the rotor shaft as a function of wind speed in the case of inflow perpendicular to the row of five wind turbines and a turbulence intensity of 9%

3.0E+03 2.0E+04 T1 T1 1.8E+04 2.5E+03 T2 T2 T3 1.6E+04 T3 T4 2.0E+03 1.4E+04 T4 T5 1.2E+04 T5 1.5E+03 1.0E+04 8.0E+03

1.0E+03Power [kW] 6.0E+03 4.0E+03 5.0E+02 Tower bottom (m=4) 2.0E+03Equivalent load [kNm] 0.0E+00 0.0E+00 0 5 10 15 20 25 0 5 10 15 20 25 Wind speed [m/s] Wind speed [m/s]

4.0E+03 1.6E+03 T1 T1 3.5E+03 T2 1.4E+03 T2 T3 T3 3.0E+03 1.2E+03 T4 T4 2.5E+03 T5 1.0E+03 T5

2.0E+03 8.0E+02

1.5E+03 6.0E+02

1.0E+03 4.0E+02 Blade root (m=12) Rotor shaft (m=3)

5.0E+02Equivalent load [kNm] 2.0E+02Equivalent load [kNm]

0.0E+00 0.0E+00 0 5 10 15 20 25 0 5 10 15 20 25 Wind speed [m/s] Wind speed [m/s]

Figure 9 Calculated power and load quantifiers for the turbine tower, the rotor blade and the rotor shaft as a function of wind speed in the case of inflow aligned with the row of five wind turbines and a turbulence intensity of 9% Validation of a quasi-steady wind farm flow model in the context of distributed wind farm control

Arno J. Brand Jan Willem Wagenaar

FP7-ICT STREP 224548 / Aeolus Outline

Motivation & Objectives

Method

Results

Summary & Outlook

Motivation & Objectives - Method - Results - Summary & Outlook

2 FP7-ICT STREP 224548 / Aeolus Motivation and objectives

Quasi-steady flow model basic structure

Motivation & Objectives - Method - Results - Summary & Outlook

3 FP7-ICT STREP 224548 / Aeolus Method

Wind farm flow model

Motivation & Objectives - Method - Results - Summary & Outlook

4 FP7-ICT STREP 224548 / Aeolus Method

Wind turbine model

Motivation & Objectives - Method - Results - Summary & Outlook

5 FP7-ICT STREP 224548 / Aeolus Method

Wind turbine wake model

Motivation & Objectives - Method - Results - Summary & Outlook

6 FP7-ICT STREP 224548 / Aeolus Method

Cluster model

Motivation & Objectives - Method - Results - Summary & Outlook

7 FP7-ICT STREP 224548 / Aeolus Method

Model output

External conditions: Wind speed, Wind direction, Turbulence intensity

State of all turbines: Hub wind speed, Blade pitch angle, Rotor speed

Output of all turbines: Power, Loads

Motivation & Objectives - Method - Results - Summary & Outlook

8 FP7-ICT STREP 224548 / Aeolus Method

Model output

Forward

({ {WS, BPA, RS}iklm, {Power, Loads}iklm) = f( {WSk, WDl, TIm} ) state output external conditions Inverse

({WSk, WDl, TIm}, {WS, BPA, RS}iklm, {Loads}iklm) = g( {Power}iklm ) external conditions state loads power reference

WS = Ambient wind speed WD = Ambient wind direction TI = Turbulence intensity BPA = Blade pitch angle RS = Rotor speed

Motivation & Objectives - Method - Results - Summary & Outlook

9 FP7-ICT STREP 224548 / Aeolus Method

Assumptions

Momentum theory for wind turbine states and wakes

Ten minute wind speed normally distributed

(),N:U σμ UU

Derived quantities normally distributed

= ()Ufx (μ ,N:x σ xx ) μ = (μ ,g σUU1x ) σx = (μ ,g σ UU2 )

Load quantifier depending on μx and σx

Motivation & Objectives - Method - Results - Summary & Outlook

10 FP7-ICT STREP 224548 / Aeolus Method

Wind turbine state

Motivation & Objectives - Method - Results - Summary & Outlook

11 FP7-ICT STREP 224548 / Aeolus Method

Wind turbine production and loading

Motivation & Objectives - Method - Results - Summary & Outlook

12 FP7-ICT STREP 224548 / Aeolus Method

Velocity deficit

D = 80 m a = 1/3

Motivation & Objectives - Method - Results - Summary & Outlook

13 FP7-ICT STREP 224548 / Aeolus Method

Added turbulence

D = 80 m a = 1/3

Motivation & Objectives - Method - Results - Summary & Outlook

14 FP7-ICT STREP 224548 / Aeolus Method

Load quantifier

Equivalent load Leq 1 1 Lm ≡ Ln m m (),fL σμ== eq ii ∑∑ j LL N i N j

Equivalent tower bottom bending moment 1 4 2 2 4 4 L eq ()L L L 36 σ+σμ+μ= L

Equivalent blade root bending moment

1 12 10 2 8 4 6 6 4 8 2 10 12 12 L eq ( L 66 L L 1485 L L 13860 L L 51975 L L 62370 L L 10395σ+σμ+σμ+σμ+σμ+σμ+μ= L )

Equivalent rotor shaft torque

1 3 2 3 L eq ()L 3 σμ+μ= LL

Motivation & Objectives - Method - Results - Summary & Outlook

15 FP7-ICT STREP 224548 / Aeolus Results

Measurements: Research Wind Turbines in EWTW

Nominal power: 2.5 MW Hub height: 80 m Rotor diameter: 80 m Turbine separation: 3.8D

Motivation & Objectives - Method - Results - Summary & Outlook

16 FP7-ICT STREP 224548 / Aeolus Results

Wind speed and wind direction cases

Motivation & Objectives - Method - Results - Summary & Outlook

17 FP7-ICT STREP 224548 / Aeolus Results

Perpendicular inflow: averages

Motivation & Objectives - Method - Results - Summary & Outlook

18 FP7-ICT STREP 224548 / Aeolus Results

Perpendicular inflow: standard deviations

Motivation & Objectives - Method - Results - Summary & Outlook

19 FP7-ICT STREP 224548 / Aeolus Results

Parallel inflow: averages

Motivation & Objectives - Method - Results - Summary & Outlook

20 FP7-ICT STREP 224548 / Aeolus Results

Parallel inflow: standard deviations

Motivation & Objectives - Method - Results - Summary & Outlook

21 FP7-ICT STREP 224548 / Aeolus Results

Load quantifier versus fatigue quantifier

Equivalent load Leq

Fatigue equivalent load range ΔLeq

Motivation & Objectives - Method - Results - Summary & Outlook

22 FP7-ICT STREP 224548 / Aeolus Results

Conclusion

Main difference measurements and predictions due to: * Un-modelled spatial variations in wind speed, and * Too gradually modelled decay of wind speed

Equivalent load: * Promising load quantifier

Motivation & Objectives - Method - Results - Summary & Outlook

23 FP7-ICT STREP 224548 / Aeolus Summary and outlook

Quasi-steady wind farm flow model

Model output comparison with data from EWTW

Various modelling issues

Model output to be compared to data from ESWF

Modelling issues to be addressed: * Decay of velocity deficit and added turbulence * Loads and load quantifier * Power reference

Motivation & Objectives - Method - Results - Summary & Outlook

24 FP7-ICT STREP 224548 / Aeolus Contact

Arno J. Brand

ECN Wind Energy Wind turbine rotor and Wind farm Aerodynamics

M: P.O. Box 1, NL 1755 ZG Petten, Netherlands E: [email protected] T: +31 224 56 4775 F: +31 224 56 8214 I: linkedin.com/in/arnobrand

Motivation & Objectives - Method - Results - Summary & Outlook

25 FP7-ICT STREP 224548 / Aeolus