10.2514/6.2014-0874 AIAA SciTech Forum 13-17 January 2014, National Harbor, Maryland 32nd ASME Wind Energy Symposium Sizing and Control of Trailing Edge Flaps on a Smart Rotor for Maximum Power Generation in Low Fatigue Wind Regimes Jeroen Smit∗ and Lars O. Bernhammer † Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, The Netherlands Sachin Navalkar ‡ Mechanical Engineering, Delft University of Technology, Mekelweg 2, 2628CD Delft, The Netherlands Leonardo Bergami§ and Mac Gaunaa¶ DTU Wind Energy, Frederiksborgvej 399, 4000 Roskilde, Denmark In this paper an extension of the spectrum of applicability of rotors with active aerodynamic devices is presented. Besides the classical purpose of load alleviation, a secondary objective is established: power capture optimization. As a first step, wind speed regions that contribute little to fatigue damage have been identified. For these regions the turbine energy output can be increased by deflecting the trailing edge (TE) flap as a function of local, instantaneous speed ratios. For this purpose, sizing of TE flap configuration for maximum power generation is established using blade element momentum theory. The investigation then focuses on operation in non-uniform wind field conditions. Firstly, the deterministic fluctuation in local tip speed ratio due to wind shear was evaluated. The second effect is associated with delays in adapting the rotor speed to time varying inflow. The increase of power generation due to wind shear has been demonstrated with an increase of energy yield of 1%. Finally a control logic based on inflow wind speeds has been devised. Keywords: wind energy, smart rotor, fatigue, trailing edge flaps, power generation I. Introduction For the last two decades a strong increase in wind turbine size has been observed. One of the main drivers behind the upscaling is an effort to reduce the cost of energy. A limiting factor in this process are fatigue loads on rotor blades. Ashuri1 has determined that upscaling of classical wind turbines will not be cost effective when considering 10 or 20 MW turbines. To enable further growth of rotor diameter the smart rotor concept has been developed. Smart rotors alleviate fluctuating loads using active aerodynamics devices mounted on the blades. This results in lower fatigue damage on the turbine, thereby enabling further upscaling using the same materials. From previous studies by Bergami2 and Baek3 the hypothesis is formed that fatigue damage at the blade root in the flapwise direction is mainly caused at and above rated wind speed. Wind turbine operations below rated speed only contribute to a small extent to the total fatigue damage. This allows the use of aerodynamic devices on a smart rotor for a secondary purpose: increasing energy capture for wind speeds below rated. ∗ MSc, Wind Energy, Delft University of Technology, The Netherlands Student, Aircraft Structures and Computational Mechanics / Wind Energy, l.o.bernhammer@tudelft.nl ‡ PhD Student, Delft Center for Systems and Control § Postdoc, DTU Wind Energy, Denmark ¶ Senior Scientist, DTU Wind Energy, Denmark † PhD 1 of 17 American Institute of Aeronautics and Astronautics Copyright © 2014 by J. Smit, L.O. Bernhammer, S. Navalkar, L. Bergami, M. Gaunaa. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 This paper presents an approach for sizing and control of trailing edge flaps for maximum power capture on a wind turbine with a smart rotor in low fatigue damage wind regimes. Wind turbine control aims to maximize power generation for below rated wind speeds and control of the aeroelastic loads in region 3. Controllers are designed with the rotor shaft speed and the generated power as input parameter. For controller region 2, the generator torque is selected such that the rotor operates at optimal tip speed ratio. Due to the rotor inertia and the time varying inflow, the actual tip speed ratio sees strong fluctuations. Additionally, local speed ratios along the blade span fluctuate even more due to turbulence in the wind field, wind shear and tower shadow. Smart rotors, which are traditionally used for load alleviation, are investigated to harvest these unsteady aerodynamic effects to maximize energy yield. All analyses and simulations in this study are executed using the NREL 5MW reference turbine.4 In section II in a first step, fatigue damage is further quantified as a function of wind speed regimes. The loads on the rotor blade root are found using aeroelastic simulations in GH Bladed.5 From this analysis, wind speed regions were identified that could be used for power optimization purposes. For the remaining part of the study an unsteady blade element momentum (BEM) tool has been developed and validated. Using this BEM tool, it is shown that the possible power increase using flaps consists of a steady part and a cyclic part. A study on the effects of the sizing and placement of the flaps on (the steady part) of the increase in power has been conducted. Using the results from this study an optimal flap configuration is proposed. Through system linearization, the plant for controller design is found with the input being local wind speed measurements and flap deflections and the output being power generation. In simulation environment, the reference wind speed at the hub can be exactly known, whereas for the physical implementation this wind speed needs to be estimated, e.g. through LIght Detection And Ranging (LIDAR) measurements. II. Fatigue Damage Quantification Previous research has shown that fatigue loads in wind turbines can be efficiently alleviated using Smart rotors.6, 7 The main contribution to the overall fatigue damage is only cased by a fraction of the load cycles that a turbine encounters. To further quantify the fatigue damage accumulation, a sequence of fatigue analyses have been carried out. For these fatigue analyses, a set of 10 minute turbulent aeroelastic simulations are performed in GH Bladed for wind speeds from 3 to 25 m/s. The turbulence intensity varies per wind speed according to the IEC61400 standards for a wind turbine with turbulence class B.8 The simulations include tower shadow and wind shear. The blade root moments in flapwise and edgewise direction are measured. The fatigue damage analysis is done using rainflow counting and the Palmgren-Miner’s rule. This results in a distribution of the number of load cycles, nj , over a set of load ranges, ∆Mj , for each wind speed bin, V0,i . Using these cycles per load range the equivalent load Meq,i per wind speed is calculated using Equation (1). To find the relative fatigue damage per wind speed di Equation (2) is used. P m 1/m j=1 nj,lif e · ∆Mj (1) Meq,i = Tlif e Ti Meq,i m (2) Tlif e Meq,lif e m With m as the Wöhler exponent for composites equal to 10. The variable Ti represents the time the turbine operates in the corresponding wind speed bin, according to a Weibull distribution with scale parameter 10.85 and shape parameter 2.15. In Figure 1(a) the cumulative fatigue damage due to the flapwise bending moment is plotted versus the wind speed. Wind speeds below 12 m/s contribute less then 2% to the total lifetime fatigue damage due to flapwise root bending moment, while this region accounts for 60% of the load cycles. This means that practically all fatigue damage for the blade root bending moment is accumulated above the rated wind speed of 11.4 m/s. Increasing this envelope to wind speeds up to 15 m/s , the damage increases to 20% of the total damage, while including 75% of the load cycles. For edgewise loading the fatigue damage is dominated by the gravity driven fatigue cycles. Figure 1(b) displays the corresponding edgewise damage equivalent root moments. The gravitational loads can not be alleviated by the use of aerodynamic devices. Unlike the deterministic gravitational loads, the stochastic part of the blade root flapwise moment can be effectively addressed by trailing edge flaps, as they have high control authority on the lift coefficient. Fatigue damage in flapwise and edgewise direction for wind speeds below rated wind speed damage is negligible compared to damage caused at wind speeds above rated wind speed. Using flaps on a smart rotor di = 2 of 17 American Institute of Aeronautics and Astronautics 1 d and n [-] (normalized & cumulative) d and n [-] (normalized & cumulative) Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 1 d 0.9 n 0.8 0.7 ← d ≤20% 0.6 0.5 ← d ≤2% 0.4 0.3 0.2 0.1 0 d 0.9 n 0.8 0.7 ← d ≤20% 0.6 0.5 0.4 ← d ≤2% 0.3 0.2 0.1 0 5 10 15 20 25 5 10 V0 [m/s] 15 20 25 V0 [m/s] (a) Flapwise root bending moment (b) Edgewise root bending moment Figure 1. Cumulative fatigue damage generation due to equivalent root bending moment and number of load cycles vs wind speeds in this wind regime can only have very limited contribution to the reduction of the total fatigue damage. Using flaps for secondary purposes like maximization of power generation below rated wind speed is therefore expected to have little impact on the total fatigue damage. III. Modeling of unsteady power generation using blade element momentum theory To carry out the remaining work presented in this paper an unsteady blade element momentum (BEM) tool is developed. This tool has been created to perform both, fast steady as well as unsteady analyses with built-in optimization capabilities. Blade element momentum theory is widely used in industry and science for wind turbine analyses and design. The BEM tool used for this work is built according to the framework described by Hansen.9 This framework allows for time varying inflow conditions resulting in dynamic loading on the turbine blades. In each time step the following 6 calculation steps are executed. Step 1 allows for changes in wind velocity over time. However, for the sizing of the flap configuration presented in the first part of this paper only steady inflow conditions are considered. Step 2 applies a correction to the wind speed profile to model the wind shear caused by the boundary layer of the earth. The wind speed V0 can be described as a function of height x and the wind speed at hub height V0 (Hhub ), as prescribed by the IEC61400 Standards8 see Equation 3. In all simulations a wind shear factor, ν = 0.2, is used. ν x V0 (x) = V0 (Hhub ) (3) Hhub In step 3 the quasi steady axial and tangential inductions factors a and a0 are calculated for each blade element as described by Hansen10 using Equations 4 and 5 with the normal and tangential coefficients according to Equations 6, the local solidity, σ = cB/2πr and the Prandtl tip loss factor F according to Equation 7. In this paper the notationas are used as in the referenced literature. The lift and drag coefficients in Equation 6 are obtained from static steady airfoil data tables. For highly loaded blade elements (a > ac with ac = 0.326)) simple momentum theory is not valid and an 3 of 17 American Institute of Aeronautics and Astronautics empirical relation is used to calculate axial induction as given in Equations 8. a= a0 = 4F sin2 φ +1 σcn −1 (4) −1 4F sin φ cos φ −1 σct (5) cn = cl (φ, θ, β) cos φ + cd (φ, θ, β) sin φ Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 ct = cl (φ, θ, β) sin φ − cd (φ, θ, β) cos φ 2 B R−r F = cos−1 exp − π 2 r sin φ a= 1 2 2 + K(1 − 2ac ) − q (6) (7) 2 (K(1 − 2ac )) + 4(Kac 2 − 1) K= 4F sin2 φ σcn (8) In step 3 the induction factors are calculated as if the turbine adapts instantaneously to a new loading situation (e.g. due to a change in wind speed, change in pitch angle or flap deflection). In reality the induction does not adapt instantly to new aerodynamics forces hence a time delay is present before Equations (4-6) do converge. This time delay is modeled using a dynamic wake model proposed by S. Øye11 and is applied in step 4. In step 4 steady aerodynamic properties of the 2D airfoils are used. However, with continuous changes in flow conditions (e.g. due to wind shear, tower shadow) and/or airfoil properties (e.g. blade pitch, flap angle) steady aerodynamic airfoil properties only give an approximation of the induction properties, depending on the timescale of these dynamics. In step 5 the dynamic lift, drag and moment coefficients are found using the ATEFlap model.12 The model combines the effects of shed vorticity and dynamic flow separation by merging a thin airfoil potential flow model with a dynamic stall model of the Beddoes-Leishmann type. In step 6 the dynamic aerodynamic load is calculated using unsteady aerodynamic coefficients from step 6 and inductions resulting from step 5. The aerodynamic forces are integrated over the blade assuming linear variation of the loads between calculation points to obtain aerodynamic thrust and power. The code has been benchmarked against the aerodynamic module of HAWC213 and found to be in very good agreement for a range of wind speeds from 5m/s to 11m/s and flap angles from -8 degree to 8 degree. The maximum occurring error was less than 1.5% as shown in Figure 2. IV. Steady state power optimization using flaps and pitch The starting assumption is that trailing edge flaps on a smart rotor can increase power generation by altering the aerodynamic properties of the blade. The BEM tool described above was used to simulate the NREL reference turbine with a single trailing edge flap per blade spanning 10% of the chord length at 0.78 ≤ r/R ≤ 0.98. Deflections have been limited to 10 degrees. The steady aerodynamic data has been obtained using Xfoil. The sizing simulations are steady state (constant wind fields, no wind shear, no tower shadow, without dynamic wake model and without ATEFlap model). For tip speed ratios λ between 4 and 14 the flap angle is varied between -10 and 10 degree. Figure 3(a) shows the resulting power curves (CP − λ curve). The stars represent the baseline setting with no flap deflection. The optimal flap setting depends on the tip speed ratio. While the tip speed ratios above maximum power capture require negative flap deflections, positive flap deflections increase the power capture when operating below the optimal tip speed ratio. Still the baseline setting achieves the highest overall power coefficient, when operating at the design tip speed ratio. However, when the turbine is operating at suboptimal tip speed ratios the power coefficient can be increased by using the trailing edge flap. The optimal flap angle βopt per tip speed ratio resulting in the highest power coefficient was determined and is shown in Figure 4 with the corresponding maximal achievable power curve. The same procedure has been followed to determine the optimal pitch angle θopt of the blade. The results for the optimal pitch angle 4 of 17 American Institute of Aeronautics and Astronautics 3 0.48 β = -8 deg 2.5 β = 0 deg 2 0.46 β = 8 deg 0.44 1.5 CP [-] 0.5 0 0.4 0.38 HAWC2 β = -8 deg BEM β = -8 deg 0.36 −0.5 HAWC2 β = 0 deg 0.34 −1 −1.5 0.32 −2 0.3 BEM β = 0 deg HAWC2 β = 8 deg BEM β = 8 deg 4 5 6 7 8 9 10 4 11 5 6 7 8 9 10 11 V0 [m/s] V0 [m/s] (a) Power coefficient vs wind speed (b) Difference in power coefficient vs wind speed Figure 2. Power coefficient below rated wind speed for 3 flap angles and constant, uniform inflow 0.45 0.4 β = -10 deg β = -8 deg CP [-] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 ∆CP [%] 0.42 1 β = -6 deg 0.35 β = -4 deg β = -2 deg 0.3 β = 0 deg β = 2 deg β = 4 deg 0.25 β = 6 deg β = 8 deg 0.2 β = 10 deg 4 5 6 7 8 9 10 11 12 13 14 15 λ [-] Figure 3. Power coefficient vs tip speed ratio for various flap angles and a zero pitch angle and constant, uniform inflow 5 of 17 American Institute of Aeronautics and Astronautics 10 θ for optimal pitch β for optimal flap θoptimal & βoptimal [deg] 8 0.5 7 m/s 6 m/s 8-10 m/s 11 m/s 0.45 5 m/s CP [-] 0.4 4 m/s 0.35 0.3 Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 baseline: θ = 0 & β = 0 optimal pitch: θopt & β = 0 0.25 6 7 8 9 10 11 12 13 4 2 0 −2 −4 −8 optimal flap & pitch: θopt & βopt 0.2 5 β for optimal flap & pitch −6 optimal flap: θ = 0 & βopt 4 θ for optimal flap & pitch 6 4 6 14 10 12 14 λ [-] λ [-] (a) Power curves 8 (b) Corrsponding optimal pitch and flap angles Figure 4. Baseline and improved power curves using flaps and/or blade pitch and corresponding control settings, with circles representing tip speed ratios for wind speeds below rated and constant, uniform inflow are also given in Figure 4. The fourth power curve in Figure 4 represents the combined power optimization using flap deflections and full span pitch. As already concluded from Figure 3(a) the global maximum power coefficient is not increased with the use of flaps or pitch, however for suboptimal tip speed ratios the use of flaps is beneficial, and the power coefficient can be increased. A combination of optimal flap and pitch angle results in the highest power coefficients. When comparing the effectiveness of the flaps and the pitch mechanism flaps outperform blade pitch for tip speed ratios above 5. The operation points of the NREL reference turbine as a function of the wind speed at hub height are displayed by circles in Figure 4(a). The turbine operates at suboptimal tip speed ratios for significant amounts of time as for wind speeds below 5 m/s a clear increase in power coefficient can be achieved by flaps. One should also notice that in the entire range of design tip speed ratios up to rated wind speed the pitch controller power optimization is outperformed by trailing edge flaps. Therefore the trailing edge flaps are able to increase power production below rated wind speed more than the pitch mechanism. The optimal flap and pitch angle for maximum power is described as a function of the tip speed ratio and shown in Figure 4(b). V. Unsteady state power optimization using flaps The simulations for Figures 3(a) and 4 were performed with constant wind fields without wind shear and tower shadow. The local speed ratio λr , defined in Equation 9, on the blade is thus constant during a rotation. r Ω·r Ω·R = =λ (9) λr = V0 V0 (R/r) R However a turbine operating in real life conditions experiences time-varying wind velocities on the blade, resulting in time-varying instantaneous (local) speed ratios. The time fluctuations in the wind velocity (and correspondingly speed ratio) can be separated into a stochastic and a deterministic part. The stochastic fluctuations result from the turbulence present in a wind field. The deterministic fluctuations can be caused by wind shear, tower shadow, tilt angle or yaw angle. These deterministic variations in velocity and local speed ratio can often be described as a function of azimuth angle and the radial location. The deterministic nature of these fluctuations makes them particularly suitable for power maximization. 6 of 17 American Institute of Aeronautics and Astronautics 2 0.09 excl. shear incl. shear 1.5 0.08 0.07 ∆AEP [%] ∆P [%] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 Steady simulations including wind shear but no tower shadow or turbulence are performed for wind speeds between 4 and 11 m/s. For each azimuthal position of the blade the flap angle that returns the highest Cp has been determined in section IV. This information was used to set the flap angles of the blades. Figure 5(a) shows the average increase in power for a given wind speed bin if the flaps are used as described above, both for the case where wind shear is included and excluded. Figure 5(b) combines the percentage increase in Figure 5(a) with the Weibull wind speed distribution and shows the increase of the Annual Energy Production (AEP) contribution as a function of the wind speed at hub height. To obtain the overall increase in AEP, one needs to sum all wind speed bins resulting in an increase of AEP of 0.19% excluding wind shear and 0.27% including wind shear. While the highest increase in terms of power percentage can be reached for low wind speeds, the contribution to the increase of AEP is higher for wind speeds close to the rated speed of the wind turbine. The larger increase in energy capture in the case of shear can be explained by the fact that wind shear induces changes in the local speed ratio on a blade. These changes lead to more time spent in suboptimal speed ratio conditions. In these conditions the positive effect of flap-use has already been demonstrated in Figure 4. 1 0.5 0.06 0.05 0.04 0.03 0.02 0.01 0 4 5 6 7 8 9 10 11 4 5 6 7 8 9 10 11 V0 [m/s] V0 [m/s] (a) Increase in power vs wind speed (b) Increase in annual energy production vs wind speed Figure 5. Increase in power and annual energy production vs wind speed using optimal flap angle including and excluding wind shear VI. Flap sizing and location The effects of the sizing of the flap configuration on the possible energy yield increase is investigated. First the optimum location of the flaps is determined, followed by the span and the number of flaps. During the optimization, the chordwise length of the flap is fixed at 10%. In this section all analyses are performed considering steady aerodynamic models and a uniform wind field, with speeds ranging from 4-11 m/s. The authors are aware that power performance optimization is a secondary purpose of flaps on a smart rotor. Because of that the actual sizing of the flaps will always be a trade off between possible fatigue reduction, possible energy yield increase, installation & operational costs and complexity. However the goal here is to investigate what flap size and location would be beneficial for power optimization. The results presented here should be incorporated in the design process of flaps on smart rotors. A. Effect of spanwise location of flaps One flap with a length Sf lap = 1 m in spanwise direction and 10% chord c length is placed at 17 different locations along the blade, between r/R = 0.74 and 0.99. For all combinations of wind speeds and 17 locations, the optimal flap angle, corresponding to the highest power coefficient, is found with a precision of 0.1 deg. The increase in power coefficient, expressed as a percentage of its original value, is plotted in Figure 6(a). The plot shows that the increase in power coefficient is highest at low wind speeds. In Figure 6(b) the curves 7 of 17 American Institute of Aeronautics and Astronautics 1 0.6 V0 = 4 m/s λ = 11.835 0.9 V0 = 5 m/s λ = 9.895 0.5 0.8 V0 = 6 m/s λ = 8.724 V0 = 8 m/s λ = 7.543 0.4 ∆CP [%] ∆CP (normalized) [-] V0 = 7 m/s λ = 7.974 V0 = 9 m/s λ = 7.54 V0 = 10 m/s λ = 7.535 0.3 V0 = 11 m/s λ = 7.125 0.2 0.7 0.6 0.5 0.4 0.3 0.2 Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 0.1 0.1 0 0 0.75 0.8 0.85 0.9 0.75 0.95 0.8 0.85 0.9 0.95 r/R [-] r/R [-] (a) Increase in power coefficient (b) Increase in power coefficient normalized Figure 6. Increase in power coefficient due to a 1 meter span flap at various flap locations for various wind speeds from Figure 6(a) are divided by their maximum value such that the peaks of the curves reach unity. For low wind speeds (and high tip speed ratios) the optimum flap position shifts towards the root compared to its optimum position at higher wind speeds (and near optimal tip speed ratios). To find the location where the application of flaps is most effective and hence where the largest increase in AEP (∆E) can be achieved, Equation 10 is used. P11 CP,i,flap · 12 ρV0,i 3 Arotor Ti ∆E = P11i=4 (10) 3 1 i=4 CP,i,no flap · 2 ρV0,i Arotor Ti The power (P = CP 12 ρV0 3 A) at each wind speed is multiplied by a probability factor Ti . This probability factor corresponds to the time of occurrence per wind speed for a Weibull distribution with a scale parameter 10.85 and shape parameter 2.15. The energy yield increase per flap location is shown in Figure 7. The distinctive peak in Figure 7 results from peaks in Figure 6(b) located at r/R = 0.95 for wind speeds 7-11 m/s. The effect of the high increase in the power coefficient, for flaps closer to the root, at low wind speeds shown in Figure 6(a) is not visible in Figure 7 because the power produced at those wind speeds is much lower. Additionally, the Weibull distribution favors outboard flaps as the majority of the probability density function corresponds to cases where the optimum flap placement is outboard of 95% span. In order to maximize the energy yield increase the location of the flap should be chosen in such a way that the area under the curve in Figure 7 is maximized. For a flap with length equal to or larger than 3 m one can conclude that the flap should be placed from r/R=0.97 extending towards the root of the blade. The effect of flap length on energy yield is determined in a next step. B. Ideal length of flaps In previous subsection it was concluded that flaps should start from r/R =0.97 and run towards the blade root. In Figure 8(a) the energy increase was calculated for flap lengths ranging from 1 to 16 m, using Equation 10. From Figure 8(a) the conclusion can be drawn that a longer flap enlarges the possible energy increase. However, adding extra flap length becomes less and less effective for larger flap lengths. The local increase in the curve in Figure 8(b) between 2 and 4 meters can be explained by two peaks for optimal flap location depending on the wind speed (or tip speed ratio) shown in Figure 6. For flap lengths of 15 meters an increase in energy yield of 0.5% can be achieved. If the cost of installation of flaps is known a trade off can be made on the actual size of the flap by determining if the increase in energy production outweighs 8 of 17 American Institute of Aeronautics and Astronautics ∆E [%] 0.04 0.03 0.02 0.01 0.8 0.85 0.9 0.95 r/R [-] Figure 7. Increase in yield vs flap location ∆(∆E)/ ∆Sf lap [%/m] 0.5 0.4 ∆E [%] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 0.75 0.3 0.2 0.1 5 10 0.045 0.04 0.035 0.03 0.025 5 15 10 15 Sf lap [m] Sf lap [m] (a) Flap span vs increase in energy yield (b) Effect of adding 1 m Sf lap at Sf lap Figure 8. Effect of the size of the flap, Sf lap , on increase in yield, ∆E, with flap located at: 0.73 ≤ r/R = 0.97 the increase in production costs. The energy used for operating the flap is expected to be low for this case because the flap angle is only changed for a change in average wind speed which is a gradual change. C. Number of flap elements The location and size of the flaps can be determined using Figure 7 and 8. In this section a third design variable is addressed, namely the number of flap elements that can be individually controlled. In this example a total flap length of 12m is used to study the effect of the number of flap elements, that can be controlled separately, on the energy yield. In Figure 9 the energy increase is plotted versus the number of equally sized flap element. Increasing the number of flap elements from 1 to 4 has a larger effect than increasing the number of flaps from 4 to 12. However 1 flap element already reaches 95% of the attainable increase in energy yield of 12 flap elements. Increasing to 2 elements captures 98% of the energy gain. From these results it is suggested to use one flap to keep the complexity of the system minimal. It is noted that this suggestion arises from analyses using uniform steady wind fields. In real life operation the turbine 9 of 17 American Institute of Aeronautics and Astronautics experiences a variation in local speed ratios along the blade. How to cope with these effects is considered in a next step. 0.45 ∆E [%] 0.445 0.44 Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 0.435 0.43 2 4 6 8 10 12 nf laps [-] Figure 9. Effect of number of controllable flaps, nf laps , on yield, E, for a flap with Sf lap = 12 m located at: 0.78 ≤ r/R ≤ 0.97 D. Final design of flap configuration In Figure 10(a) the optimal flap angle for a 1-meter flap at various location (as in section A) is plotted. It can be seen that the variation in optimal flap angle is larger towards the tip than towards the root of the blade. To obtain more insight into this effect the gradient of the optimal flap angle is calculated for each location on the blade. This is done for all wind speeds and averaged using the probability factor Ti , described previously; the results of these calculation are plotted in Figure 10(b). These figures suggest that uniform flap spacing results in a suboptimal design because the size of the individually controllable flaps should be relatively small near the tip and large towards the root. VII. Controller design In previous sections, the rotor speed has been prescribed as a function of wind speed according to the NREL documentation . However to model the rotor speed more realistically in time-varying wind conditions, a baseline generator torque controller is included as is described in NREL documentation.4 Using this expanded BEM Tool, two controllers for the flap angles have been created, a Lookup Table Controller (LTC) and a Model Predictive Controller (MPC), described in the two following subsections. A. Lookup Table Controller The first control input, rotor speed, is a conventional control input for wind turbine controllers. The second control input, wind speed along the blade, is less standard. In a simulation environment it is easy to ‘measure’ the wind speed on the blade, in real life operation this is less easy. The control scheme consists of 5 consecutive steps shown in Figure 12. First the local speed ratio is calculated using the incoming wind speed and predicted rotor speed. Then the local TSR is limited to the range of the lookup table: if the ratio is below 3 its value is set to 3, if the ratio is above 18 its value is set to 18. Then the table lookup procedure is executed: the optimal flap angle is found using linear interpolation. The optimal flap angles in the lookup table are found using the same method as described in section IV, where the optimal flap angle was determined for steady state operation at TSRs between 3 and 18, with a 10 of 17 American Institute of Aeronautics and Astronautics βoptimal [deg] V0 =4 m/s λ =11.835 4 V0 =5 m/s λ =9.895 V0 =6 m/s λ =8.724 2 V0 =7 m/s λ =7.974 0 V0 =8 m/s λ =7.543 −2 V0 =9 m/s λ =7.54 −4 V0 =10 m/s λ =7.535 −6 V0 =11 m/s λ =7.125 0.75 0.8 0.85 0.9 0.95 r/R [-] (a) Optimal flap angle, βoptimal , for a flap (Sf lap = 1 m) at various location on the blade 0.6 ∆β/∆r [deg/m] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 6 0.5 0.4 0.3 0.2 0.75 0.8 0.85 0.9 0.95 r/R [-] (b) Averaged gradient of optimum flap angle in spanwise direction Figure 10. Variations in optimal flap angle for various location and various wind speeds 11 of 17 American Institute of Aeronautics and Astronautics B. 1. Model Predictive Controller Linearized model To further investigate the power generation, a more complex controller has been implemented, namely a Model Predictive Controller, which maximizes aerodynamic torque over a prediction horizon. It has been assumed that torque can be described as a combination of a static and dynamic response. The static part depends on the local speed ratio and flap angle. The dynamic part can be seen as a history term containing the previous states, which influence the current state. A physical interpretation of the latter is the convection of shed and trailed vorticity. The static part represents the steady state torque corresponding to the instantaneous conditions on the blade. The torque is proportional to the product of the square of the wind speed and the torque coefficient: dyn Q ∝ CQ · V02 (11) dyn It has been assumed that the torque coefficient, CQ , is a linear combination of the steady torque coefficient, st of previous and current time step, and the torque coefficient of the two preceding time steps according CQ to: dyn st C CQ,i−1 dyn CQ,i+1 = A Q,i−1 + B dyn st CQ,i CQ,i (12) In a simulation environment it is easy to extract the dynamic torque coefficient, on a real turbine this is less easy but could be achieved by means of a combination of measurement of wind speed (using LIDAR) and reconstruction of the torque using strain gauges. During the study on this concept the physical implementation of the controller was of no concern as the goal was in the first place to create a controller capable of maximizing the power. 15 10 β [deg] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 minimum and maximum flap angle of ±15 degree. The resulting flap angles are shown in Figure 11. In a final step the flap angle is set for the next time step in the simulation. This procedure is repeated for all blades in each time step. The LTC has been implemented in the BEM Tool and tested with a 10 minute simulation with time varying wind speed. The turbulent wind speed history was created using Turbsim and wind shear was included. Figure 13 shows the time history for such a simulation. It can be seen that during phases of increasing wind speed the LTC controller increases the power output, while in cases of decreasing wind speed, a reduction in generated power is observed. The rotor inertia hereby serves as low-pass filter in the system such that the aerodynamic power as shown in Figure 13(b) exhibits significantly more vibrations than the generator power as displayed in Figure 13(a). In Figure 14 the increase in energy is shown for a square wave in the wind speed signal. The square marking correspond to step increases in wind speed, while the circles represent step decreases. The diamonds are the sum of a step increase and a step decrease and therefore represent the effective energy gain. For 1/32 and 1/16 Hz, a very large overshoot in the power response can be seen. This holds true for the decrease in power when decreasing the wind speed. This loss is more than compensated by the power gain for increasing wind speeds such that a net gain in generated power is achieved. 5 0 −5 −10 4 6 8 10 12 14 λ [-] Figure 11. Optimal flap angle vs TSR 12 of 17 American Institute of Aeronautics and Astronautics 16 18 V̄flap,i+1,j Ωi+1 calculate λr,i,j limit 3 < λr < 18 j≤3 set flap βi+1,j = βopt lookup table βopt = β(λr ) end Figure 12. Lookup table controller (LTC) Paero,no flap Paero,flap 5 Paero [MW] 3.5 3 2.5 2 without flap deflection with flap deflection 1.5 335 340 345 350 355 360 4 3 2 1 335 365 340 345 350 355 360 t [s] t [s] (a) Generator power vs time (b) Aerodynamic power vs time Figure 13. Part of time histories for turbulent simulation with average wind speed of 8 m/s ∆E∆V =+1 ∆E∆V =−1 ∆E 1.2 1 0.8 0.6 ∆E [%] Pgenerator [MW] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 start 0.4 0.2 0 −0.2 −0.4 −0.6 10−2 10−1 100 F∆V [Hz] Figure 14. Energy gain and loss due to flap use vs frequency of a square wave in wind speed 13 of 17 American Institute of Aeronautics and Astronautics 365 The steady torque coefficient depends on local speed ratio and the flap angle. This dependency was determined using steady state analysis in the BEM Tool. For the steady torque coefficient one can write: st st CQ = CQ (λr , β) (13) A VAF of 100% means that the two compared signals are the same. Figure 15 shows the VAF achieved for different prediction horizons with the linearized model, as in Equation 12. Especially with a prediction horizon of 1 time step the model is very capable of predicting the torque coefficient, a VAF> 99% was found. In the considered prediction horizons of 0.5s and 2.5s, the VAF stays above 80%. 100 95 VAF [%] Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 Linear regression was applied on the results of a set of simulation to find the vectors A, B. Those simulations were done for a 1D turbulence spectrum and wind shear combined with a random flap deflection. If the steady torque coefficient is known the recurrence relation in Equation 12 provides the opportunity dyn to predict the torque coefficient, ĈQ , over an prediction horizon, thoriz . To check the quality of the linear model, A, B, the variance accounted for, VAF, was determined: dyn dyn var CQ − ĈQ,i+1 · 100% (14) VAF = 1 − dyn var CQ 90 85 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 thoriz [s] Figure 15. Variance accounted for versus the prediction horizon 2. Optimization procedure The rotor speed is assumed to be constant and the wind speed can be measured. Consequently the local speed ratio can be estimated over the prediction horizon. This leaves the flap angle as the only variable in linear prediction model that is not fixed. Goal of the MPC is to maximize aerodynamic torque over a time span, the prediction horizon. Using the linearized model the torque can be expressed as a function of the steady torque coefficient. In order to achieve maximum torque the following cost function has to minimized: Cost = 1 ihoriz P n=i = Qn 1 ihoriz P n=i dyn CQ,n (15) · 2 V0,n In the MPC this minimization is done through optimization of the steady torque coefficients over the prediction horizon. The range of possible steady torque coefficients is limited. Therefore, optimization is constrained as follows. Goal of the MPC is to control the flap angle in such a way that steady state optimum flap deflection is reached via an optimal path. Because of that the following constraint is introduced: at the prediction horizon the steady torque coefficient must be the maximum steady torque coefficient possible for the local speed ratio at that time step. This fixes the flap angle at the prediction horizon, βhoriz . To avoid large flap commands, the flap angle is only allowed to vary in the range between current flap angle and the flap angle at the prediction horizon. Combining this range of flap angles with the local speed ratios (known via LIDAR measurements) over the prediction horizon limits the path that the steady torque coefficient can follow. The limits of the steady torque coefficients are found using the table described by Equation 13. This MPC controller has been implemented and first been tested in a series of steps in the wind speed of 0.5m/s at 0.2Hz and a baseline wind speed of 9m/s. Figure 16 shows a time window of this simulation. 14 of 17 American Institute of Aeronautics and Astronautics The baseline case is a simulation without flap activity. For the current simulation a prediction horizon of 2.5 seconds has been chosen. While the LTC controller increases the power during increasing wind speed, the MPC controller shows a more complicated reaction. Initially, during increasing wind speed, a increase in power can be seen. However, this increase is quickly turned into a decrease compared to the control free case. When the wind speed is stepped down, a strong initial dip in the power response is seen, however this transitions into a significant increase directly after recovering from this dip. The power integral over one positive and negative step in wind speed is positive such that this controller also yields a higher energy output. Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 Qaero [MNm] 2.7 2.6 2.5 2.4 2.3 2.2 72 74 76 78 80 82 84 t [s] baseline LTC MPC thoriz = 2.5s Figure 16. Aerodynamic torque using the MPC and LTC for a time window between 72 and 92s, with a prediction horizon of 2.5 s The performance of the LTC and MPC are compare in Table 1. For the MPC controller two different prediction horizon were used: 0.5s and 2.5s. One should note that the 2.5s case is purely academic as the computation time, even when only using a very simple BEM model was much higher than real time and can therefore not be applied in wind turbine control. The increase in energy capture for the simple LTC controller is 0.31, while the more complex MPC performs more poorly when considering the low prediction horizon case. Only when the prediction horizon is significantly increased, the LTC can be outperformed. Table 1. Increase in energy from LTC and MPC, corresponding to simulations in Figure 16 LTC ∆Eaero [%] ∆Egenerator [%] 3. 0.30 0.31 MPC thoriz = 0.5s thoriz = 2.5s 0.25 0.40 0.21 0.42 Power production simulations using LTC As a final step, time domain simulations have also been performed for the LTC controller. This controller was chosen despite the potentially higher gains of the MPC controller because of the computational requirements that make an implementation of the MPC in a field test very challenging. Two different turbulence models have been used, namely the Mann and the Kaimal turbulence spectra to create 1D turbulent wind speed histories. As before, wind shear was included in the simulations. 10 minutes of turbine operation were simulated with wind speeds between between 7-11 m/s. Figure 17 shows the energy increase as a function of wind speeds. One can see that the resulting differences in generator power between the 2 turbulence models are less than 5% for all wind speeds and will therefore not be decisive for the evaluation of the controller performance. As shown in Figures 5(a) and 17, the addition of turbulence to the simulations increases the energy capture of the LTC from 0.5% to 0.9%. Combining this power performance increase with the Weibull distribution, an increase in annual energy production of 0.4% is obtained. VIII. Conclusions An approach for the sizing and control of trailing edge flaps for maximum power capture on a wind turbine with a smart rotor in low fatigue damage wind regimes has been presented. 15 of 17 American Institute of Aeronautics and Astronautics 0.92 ∆Egenerator [%] 0.91 0.9 0.89 0.88 Mann: ∆Egenerator Kaimal: ∆Egenerator 0.87 0.86 7 8 9 10 11 Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 V0 [m/s] Figure 17. Increase in energy vs wind speed: 10 minute simulations with 1D turbulence and wind shear Wind speeds below rated wind speed contribute less than 2% to the fatigue damage equivalent load flapwise root bending moment. Therefore, trailing edge flaps can be used for secondary purpose below rated wind speeds without negative impact on the fatigue damage. An unsteady BEM tool has been developed and validated against HAWC2Aero. With this tool, it has been shown that trailing edge flaps cannot increase the maximum power coefficient of the investigated turbine, when operating at optimal tip speed ratio. However, for suboptimal tip speed ratios, flaps are able to increase the power coefficient. Although the pitch mechanism is also capable of increasing the power coefficient, the investigated setup of the flaps outperform the pitch mechanism over the entire range of design tip speed ratios below rated wind speed. A turbine operating in a physical wind field experiences great variations of local speed ratios. Part of these variations are deterministic. The predictability of these variations makes them suitable for power optimization using trailing edge flaps, as the flap angle for maximum power can be described as a function of local speed ratio. Taking into account the possibilities for increasing the energy yield using trailing edge flaps, the size and location of the flaps has been analysed. A design study aiming for optimal flap location and length for maximizing power has been carried out. It is concluded that flap elements near the blade tip are most effective. Accordingly flaps should be placed from 0.97 r/R running towards the blade root. The length of the flap can be determined after a trade off between the possible power increase and the extra costs and complexity of installing extra flap length. Multiple flap segments only show a small benefit over a single flap, therefore it is recommended to only use one element. An aerodynamic simulation has been performed of the NREL 5MW reference turbine. Two different control schemes have been studied in a simulation with steps in the wind speed. A look-up table controller based on the local instantaneous speed ratio increased the energy production of the wind turbine by 0.31%, while a more complex model predictive controller only increased this value when a sufficiently long prediction horizon was implemented. Consequently, the LTC has been used in time domain simulations with a 1D turbulence field and wind speeds between 7-11 m/s. The controller was able to achieve an increase of 0.4% in annual energy production. References 1 Ashuri, T. (2012), “Beyond Classical Upscaling: Integrated Aeroservoelastic Design and Optimization of Large Offshore Wind Turbines,” PhD Thesis, Delft University of Technology, The Netherlands (ISBN: 9789462032101) 2 Bergami, L., Gaunaa, M., “Analysis of aeroelastic loads and their contributions to fatigue damage,” The Science of Making Torque from Wind, 9.-11. October 2012, Oldenburg, Germany 3 Baek, P. (2011), “Unsteady Flow Modeling and Experimental Verification of Active Flow Control Concepts for Wind Turbine Blades,” PhD Thesis, Risø-DTU, Denmark 4 Jonkman, J., Butterfield, Musial, Scott (2009), “Definition of a 5MW reference wind turbine for offshore system development,”Technical Report, National Renewable Energy Laboratory, Colorado, USA (NREL/TP-500-38060) 5 Bossanyi, E.A. (2003), “GH bladed theory manual,”Technical Report, Garrad Hassan and Partners Ltd. (282/BR/009) 16 of 17 American Institute of Aeronautics and Astronautics Downloaded by UNIVERSITY OF ADELAIDE on October 26, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2014-0874 6 Bernhammer, L.O., De Breuker, R., van Kuik, G.A.M., Berg, J., van Wingerden, J.-W., “Model Validation and Simulated Fatigue Load Alleviation of SNL Smart Rotor Experiment,” 51st AIAA Aerospace Sciences Meeting, 7.-10. January 2012, Grapevine, USA 7 Bernhammer, L.O., De Breuker, R., van Kuik, G.A.M., “Assessment of fatigue and extreme load reduction of HAWT using smart rotors,” 9th Phd Seminar on Wind Energy in Europe, 18.-20.September 2013, Visby, Sweden 8 International Electrotechnical Commission,“IEC61400” 9 Hansen, M.O.L. (2008),“Aerodynamics of Wind Turbines - Chapter 9 Unsteady BEM Model,” Earthscan LLC (ISBN: 9781849770408) 10 Hansen, M.O.L. (2008),“Aerodynamics of Wind Turbines - Chapter 6 The Classical Blade Element Momentum Method,” Earthscan LLC (ISBN: 9781849770408) 11 Schepers, J. G., Snel, H., van Bussel, G.J.W., (1995),“Dynamic Inflow: Yawed Conditions and Partial Span Pitch Control,” Technical Report, ECN Petten, The Netherlands (ECN-C–95-056) 12 Bergami, L., Gaunaa, M. (2012), “ATEFlap Aerodynamic Model, a dynamic stall model including the effects of trailing edge flap deflection,”Technical Report, Risø-DTU, Denmark (Risø-R-1792(EN)) 13 Larsen, T.J., Hansen, A.M., (2012), “How 2 HAWC2, the user’s manual,” Technical Report, Risø-DTU, Denmark (RisøR-1597(ver. 4.3)(EN)) 17 of 17 American Institute of Aeronautics and Astronautics

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