A new simulation method for turbines in wake—applied to extreme response during operation推荐

A New Simulation Method for Turbines in Wake—Applied toExtreme Response during OperationKenneth Thomsen and Helge Aagaard Madsen *,Risø National Laboratory, PO Box 49, DK-4000Roskilde, DenmarkThe work focuses on prediction of load response for wind turbines operating in wind farms using a newly developed aeroelastic simulation method.The traditionally used concept is to adjust the free flow turbulence intensity to account for increased loads in wind farms—a methodology that might be suitable for fatigue load simulation.For extreme response during operation the success of this simplified approach depends significantly on the phys-ical mechanism causing the extremes.If the physical mechanism creating increased loads in wake operation is different from an increased turbulence intensity,the resulting extremes might be erroneous.For blade loads the traditionally used simplified approach works better than for integrated rotor loads—where the instantaneous load gradient across the rotor disc is causing the extreme loads.In the article the new wake simulation approach is illus-trated with flapwise blade loads and yaw loads as examples.In this method it is assumed that the wind speed deficit moves transversally depending on the free turbulence transver-sal components,and it is used as inflow for the actual turbine.It is shown that the new method si multaneously predi cts power reducti on and load response characteri sti cs for these loads in wake conditions in good agreement with measurements.The results are com-pared with the traditionally used simplified method,and this approach seems conservative for some loads,e.g.the extreme blade moments,and non-conservative for others,e.g.the extreme yaw moments.Copyright © 2004 John Wiley &Sons,Ltd.WIND ENERGYWind Energ. 2005; 8:35–47 (DOI:10.1002/we.130)Research Article*Correspondence to: K. Thomsen, Risø National Laboratory, PO Box 49, DK-4000 Roskilde, Denmark E-mail: kenneth.thomsen@risoe.dkContract/grant sponsor: Danish Ministry of Energy; contract/grant number: UVE 511117/00-0040IntroductionUsually, different methods for prediction of power loss and load response for wind turbines in wind farms are used. For the estimation of production, models describing the average deficit for a specific turbine are used (e.g. References 1), while turbulence equivalent models are used to predict the increased loading (e.g. Refer-ences 2). The simplicity is an advantage of both types of models and usually the computational work is small.If there is a need for more detailed response prediction (both power and loads), it can be difficult to combine these two types of methods.One example can be the prediction of extreme response of an operating turbine or cases where simultane-ous analysis of production and load responses is carried out, e.g. as a basis for establishing an operational strat-egy based on the trade-off between loads and power production. For such cases a more physically detailed modelling is needed, and this is the background for the present work. Another example is when advanced indi-vidual pitch control is used to reduce rotor loads in wake operation.The method presented here differs from previous work 3in being a more detailed physical modelling of the wind speed deficit in the wake of the upwind turbine. The region with reduced wind speed movesKey words:wind farms;wakes; extremes36K. Thomsen and H. Aa. Madsen–––Figure 2.Shear profile for different downwind positions. A k–e model is used in the CFD simulation of the actuatordisc flowtransversally depending on the free turbulence transversal components, and it is used as inflow for the actual turbine. Thus this turbine will experience periods with varying shear profile across the rotor disc in combina-tion with the free turbulence field.Traditionally, the wake phenomenon has been modelled as increased free turbulence intensity, without taking the time-varying shear profile into account. The new method is implemented in the aeroelastic model HAWC,4 and the results illustrate that it is possible to model details in the response that have not been seen in simula-tions previously.The physical basis of the new method enables a more correct response simulation than using the traditional simplified ‘equivalent’methods. This means that the load characteristics are simulated more correctly, hence both load statistics, fatigue and extreme characteristics, are computed simultaneously.The advantages of the new method are illustrated in terms of extreme response of a turbine operating in a severe wake condition. The results are compared with measurements and with the current IEC61400-1 requirements.5Description of the MethodThe new method is based on two parts: a prediction of the deficit field in the wake of an upstream turbine, and the meandering of the deficit field due to transversal turbulence (Figure 1).The first part is a calculation of the wake deficit of the upwind turbine in steady flow. The full flow field for the upwind turbine is calculated, in this case with a three-dimensional actuator disc model in the CFD code FIDAP. Turbulence is modelled with a k–e model. The calculation (Figure 2) is carried out for different rotor loadings (wind speeds), and the deficit field is determined from this flow field in the correct downwind posi-tion for the turbine operating in wake and for the actual loading on the upwind turbine. Using the actuator discconcept to model the rotor flow, the tip vortices are not modelled, but the turbulence generated in the shear layer of the deficit will cause a spreading of the deficit region downstream as seen in Figure 2.In the method we now assume the simplification that each volume of air passing the upwind turbine is trans-ported downwind in the turbulent atmospheric boundary layer with a velocity corresponding to the mean wind speed U . Thus during a small time step D T the deficit moves U D T in the longitudinal direction. At the same time we assume a transversal movement of the wake centreline as a result of the cross-turbulence components.At the time t i the transversal movement (y - and z -direction) is calculated as the accumulated movement in two directions:where u c and w c are the characteristic lateral and vertical turbulence components respectively. These quanti-ties are calculated as the lowpass filtered transversal turbulence components, where the filtering in the current implementation is chosen to correspond to the upstream turbine rotor diameter.The movement is accumulated during time, and the resulting movement corresponding to one point in a ‘movement’series is later used in the full aeroelastic simulation. An example of the large turbulence field is plotted in Figure 3 and the time series of the horizontal movement are given in Figure 4. Since the wake moves and the characteristic lateral and vertical turbulence components are calculated in the actual position, it is nec-essary to use a large turbulence field for calculation of the movement.It should be noted that no time shift is seen for the largest movements for the different downstream posi-tions. This is due to the fact that, when a disc of air passes the upstream turbine and feels transversal turbu-lence components, it tends to move continuously in the initial direction. This is a characteristic of the turbulence field.y t y t t T z t z t t Ti i c i i i c i ()=()()()=()()--11u w D D Extreme Response of Turbines in Wake 3750100150200250the turbulence field plotted in Figure 3. The simultaneous vertical motion is not illustrated38K. Thomsen and H. Aa. Madsen More details concerning the dynamic wake model are given in Reference 6.The shear deficit from the three-dimensional actuator disc model now moves as illustrated in Figure 4, and it is used as wake inflow for an aeroelastic simulation.A normal turbulence field, tower shadow and normal shear are added to this time-varying shear profile. In the present implementation it is thus an assumption that the primary load-increasing mechanism for a turbine operating in wake is the time-varying wake deficit—leading to periods with full-wake, half-wake and no-wake operation within one period of time, e.g. 10min.Comparison with MeasurementsThe new method is validated by measurements from the low-turbulence Tjæreborg wind farm.7A3·3D wake configuration was selected for the two NEG Micon pitch/variable speed turbines of 80m diameter. The cen-treline (full wake) corresponds to a direction of 205°and half wake corresponds to approximately 195°and 215°.The actual turbine was instrumented with many load sensors and a rotating pitot tube for inflow angle mea-surements. The wind speed was determined by the nacelle anemometer.Comparison of statisticsIn Figure 5 the statistics (mean and standard deviation) are compared for three measured and simulated sensors. The sensors are electrical power, flapwise root bending moment and tower top yaw moment. Two sets of measurements are illustrated: one with free wind speeds between 7 and 9m s-1and one with free wind speeds between 9 and 11m s-1. All measured and simulated loads are 10min statistics.Large reductions in the power and flapwise moment are seen for the full-wake direction (205°), while the mean value of the yaw moment increases significantly in half-wake conditions and is unchanged in full wake. The standard deviation of the flapwise moment and yaw moment increases by more than a factor of two in half-wake conditions, while the increase is less in full-wake conditions. It should be noted that another wake condition occurs at 245°.The increase in dynamic loads in half-wake conditions is due to the blades passing in and out of the reduced wind speed region in the wake created by the upstream turbine. For full-wake conditions the load increase is less than for half wake. This is due to the more coherent wind field observed by the rotating blades. Some increase compared with free flow exists, however, and this is due to the fact that the statistics are calculated during a 10min period. During this period the average condition is full wake, but the meandering process causes the turbine to experience some periods with half-wake conditions too. The ratio of full-wake and half-wake periods experienced depends on the transversal turbulence components.For both wind speed intervals the simulations fit well with the measurements. The relative load increase in half-wake and full-wake conditions is predicted well with the model, and this indicates that the meandering process has the correct characteristics.Detailed comparisonFor a more detailed comparison of the predicted and the measured response, a specific time series in a half-wake situation is selected. The measurement is illustrated in Figure 6 and the simulation in Figure 7.The wake condition corresponds to half wake on average during the time series, but during the time series both periods with half-wake and free flow conditions are seen.For the measured time series (Figure 6), free flow is experienced at 210s, resulting in a limited period with small variations in angle of attack and flapwise moment. At the same time the mean level of the yaw moment is close to zero. At t=440s the turbine operates in a half-wake situation. This drives the loading towards large variations in angle of attack and flapwise load, and the mean level of the yaw moment increases significantly. The same tendencies are seen in the simulated response at t=180 and 300s respectively.Extreme Response of Turbines in Wake39Figure 5.Measured and simulated loads at 8m s(full lines and crosses) and 10m s(broken lines and squares)In Figure 8 the azimuthal variation of the binned angle of attack is illustrated. Rotor position 180°corre-sponds to the blade pointing downwards, and a small variation due to tower shadow occurs. However, the vari-ation in mean angle of attack due to wake operation is much larger. At azimuth angles of 200°–300°the wind speed is reduced (wake region) and the mean angle of attack reduces.As seen in the sample time series (Figures 6 and 7), the meandering process of the wake region results in a variation in wake degree during the full period of 600s. Thus the rotating blade experiences periods with more or less 1p variation due to wake operation. For a half-wake situation (on average) this will be reflected in the azimuthal binned standard deviation of the blade responses. In the lower plot of Figure 8 the standard deviation of the angle of attack is illustrated. For the part of the rotor disc which is unaffected by wake operation (50°–150°), the standard deviation is small, while it is significantly larger for the wake-affected part of the rotor disc. This characteristic depends directly on the meandering process.The same tendency is seen in the azimuthal binned flapwise signal (Figure 9). The overall characteristics are similar in measurements and simulations, but the azimuthal variation of the measured stan-dard deviation of the flapwise signal is less than in the simulation. This could be due partly to different flap-wise damping and partly to statistical variation.40K. Thomsen and H. Aa. MadsenThe results in the previous subsection indicate that the new model works well in a qualitative manner, and now the same model is used to predict extreme responses during operation.In Figures 10 and 11 the extreme responses (10min periods) for the 3·3D wake are illustrated. The maximum values of the flapwise moment are almost unaffected by wake operation, while the minimum values are reduced to close to zero. The reason is that the flapwise load is a result of instantaneous wind speed, and the maximum wind speed is experienced in the free flow periods—which in turn means that the maximum load is similar to the free flow maximum, since the meandering process causes the blades to operate in (at least a few) periods with free flow. The minimum wind speed is experienced in the wake region, resulting in a deloading of the flapwise moment.For the yaw moment—which is an integrated rotor load—the wake operation results in a very different response. Half-wake operation results in changes in both mean values and extreme values, because the yaw moment is created from the load variation across the rotor.The comparison of extreme response between simulations and measurements illustrates again that the quali-tative characteristics are well reflected in the new model.Comparison with Other Methods for Load PredictionTraditionally, wake effects are accounted for by increasing the turbulence intensity of a free flow situation.2,5 Considering the different characteristics of different loads in wake operation illustrated in the previous section, it is necessary to investigate the change in different load signals for different levels of turbulence intensity.In Figures 12 and 13 the sensitivity to turbulence intensity at a mean wind speed of 10m s-1is illustrated for the flapwise moment and yaw moment respectively. Both loads increase monotonically with turbulence intensity. In the same plots the extreme values from wake operation are given, see also Figures 10 and 11. The extreme load equivalent turbulence for the flapwise moment is similar to the free flow turbulence intensity,Extreme Response of Turbines in Wake41approximately 8%, while it is approximately 25% for the yaw moment. Thus the equivalent turbulence inten-sity approach cannot be applied directly to extremes during operation.If the equivalent intensity suitable for flapwise moments was used for the yaw moment, the resulting extreme yaw moment would be non-conservative with a factor of three. If, on the other hand, the equivalent intensity suitable for the yaw moment was used for the flap moment, the extreme flap moment would be conservative with 30%. These differences would probably increase if the extreme values were extrapolated—as introduced in the latest draft of the IEC61400-1 standard.In Figures 14 and 15 the fatigue loads simulated with the new wake model are compared with simulations with increased turbulence intensity.Depending on the wind directional probability distribution, a reasonable level of a fatigue equivalent tur-bulence intensity is 15%–20%. The IEC high turbulence level is 23% at 8m s-1. Thus the equivalent turbu-lence intensity approach seems to be suitable for fatigue, and the level specified in the IEC standard is of a suitable order of magnitude.ConclusionA newly developed method for aeroelastic response simulations for wind turbines operating under wake condi-tions has been presented. The new method is implemented in the aeroelastic model HAWC, and the results illus-trate that it is possible to model details in the response which have not been seen in the previously used methods. Simulated extreme loads during normal operation have been compared with measured response and with simulations carried out using the well-known equivalent turbulence intensity approach. The conclusion is that the new method predicts the extremes well, whereas the traditionally used method underestimates rotor loads but overestimates blade loads. The equivalent turbulence intensity approach seems to predict fatigue well for the investigated sensors, however.For many load sensors the design-driving extreme value occurs in a special load case: standstill, stopping or gust cases, etc. However, the extrapolation method for loads during operation introduced in the current draft of42K. Thomsen and H. Aa. Madsenare illustrated. Azimuthal position 180°is downwardsthe IEC61400-1 standard increases the importance of the normal operation loads. For a proper extrapolation of extreme loads in these situations a physically based model which predicts the load characteristics well is needed. The new method gives a more realistic simulation of the loading on a turbine operating in wake, but some crude simplifications have been made in some submodels. Some of these will be modified in the future. ItExtreme Response of Turbines in Wake43might be necessary to change the characteristics of the turbulence in the wake so that the meandering process can be modelled more correctly.A central assumption of the method is that the meandering process is controlled by large-scale turbulence structures. Medici and Alfredsson8have carried out wind tunnel investigations and studied the wake charac-teristics in detail. They concluded that the transversal transportation of the wake was primarily controlled by vortex shedding—similar to that of a solid disc. H owever, several diffierences exist between those44K. Thomsen and H. Aa. MadsenExtreme Response of Turbines in Wake45Figure 13.Extremes of yaw moment versus turbulence intensity46K. Thomsen and H. Aa. MadsenExtreme Response of Turbines in Wake47 investigations and the full-scale measurements used in the present article. The loading of the rotor seems rather high in the wind tunnel experiment. In the case of a very high rotor loading in the wind tunnel experiment, recirculation will occur and the wake will become unstable, which also is seen in actuator disc simulations at high loading. Furthermore, it is questionable whether the large-scale turbulence structure which dominates the wake movement in the full-scale experiments is present in the wind tunnel experiments. Full-scale measure-ments from the Tjæreborg site at very low turbulence intensity7illustrate a highly stable wake situation, and no indication of vortex shedding is observed for these measurements.It is expected that the new method can be used in cases where detailed response analysis is necessary, e.g. in establishing operational strategies for turbines in farms, in calibration of more simplified methods and for simulation of advanced individual pitch control systems to reduce rotor loads in wake operation.AcknowledgementsThe measurements were carried out by the Test and Measurement Group at Risø under contracts with NEG Micon A/S (load measurements) and SEAS (inflow measurements). The inflow measurements were funded by the Danish Ministry of Energy through the UVE programme 511117/00-0040 under the name ‘Measurement Project Middelgrunden Offshore Wind Farm’. The authors thank Torben J. Larsen and Gunner Larsen from Risø for valuable discussions and ideas on the specific formulation of the meandering process. References1.Sanderhoff P. PARK—user’s guide. A PC-program for calculation of wind turbine park performance. Risø-I-1668(EN),Risø National Laboratory, Roskilde, 1993.2.Frandsen S, Chacón L, Crespo A, Enevoldsen P, Gómez-Elvira R, Hernández J, Højstrup J, Manuel F, Thomsen K,Sørensen P. Final report on measurements on and modelling of offshore wind farms. Risø-R-903(EN), Risø National Laboratory, Roskilde, 1996.3.Thomsen K, Madsen HAa, Larsen GC. A new method can predict detailed response for turbines in wind farms. FactSheet AED–RB–16(EN), Risø National Laboratory, Roskilde, 2003.4.Petersen JT. The aeroelastic code HAWC—model and comparisons. Proceedings of 28th IEC Expert Meeting ‘Stateof the Art of Aeroelastic Codes’, Lyngby, 1996; 129–135.5.IEC. Wind Turbine Generator Systems—Part 1: Safety Requirements(2nd edn). IEC61400-1:1999(E), 1999.rsen GC, Thomsen K, Madsen HAa. Wake meandering—a pragmatic approach. Risø National Laboratory, Roskilde.To be published.7.Madsen HAa, Thomsen K, Petersen SM. Wind turbine wake data from inflow measurements using a five hole pitottube on a NM80 wind turbine rotor in the Tjæreborg wind farm. Risø-I-2108(EN), Risø National Laboratory, Roskilde, 2003.8.Medici D, Alfredsson PH. Measurements on a wind turbine wake: 3D effects and bluff-body vortex shedding. In WindTurbine Wakes—Control and Vortex Shedding. Technical Report from KTH Mechanics, Medici D (ed.) Royal Institute of Technology: Stockholm, 2004; 77–95.。