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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'How does the wind blow behind wind turbines and in wind farms?' taking place on Tuesday, 11 March 2014 at 16:30-18:00. The meet-the-authors will take place in the poster area.

George Sieros Centre for Renewable Energy Sources and Saving, Greece
Co-authors:
John Prospathopoulos (1) F P George Sieros (1) Panagiotis Chaviaropoulos (1)
(1) Centre for Renewable Energy Sources and Saving, Pikermi, Greece

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Abstract

NUMERICAL ESTIMATION OF POWER DEFICIT AND EFFICIENCY IN LARGE OFFSHORE WIND FARMS

Introduction

A preliminary evaluation of the main wind farm models in the context of the UpWind project indicated the CFD models over-predict wake losses in the narrow sectors [1]. The existing wind farm models are further assessed in the context of the EERA-DTOC project using detailed measurements from the Horns Rev and Lillgrund offshore wind farms. Evaluation of the power deficit predictions of the CRES-flowNS [2] RANS solver is presented in this paper. Furthermore, predictions of the park efficiency for the whole wind rose are given with the engineering model GCL [3] calibrated with the CFD predictions for certain wind directions.

Approach

CRES-flowNS model: CRESflow-NS [2] is an in-house RANS solver using the k-ω turbulence model for closure and the actuator disk theory for the simulation of the embedded wind turbines. The k-ω turbulence model has been suitably modified for atmospheric conditions [4]. Stratification is considered through an additional production term added to each one of the k and ω transport equations to account for the buoyancy effect [5]. According to the actuator disk approach, the rotor of each wind turbine is simulated as a disk discretized by a number of control volumes. Each control volume acts as a momentum sink through the actuator force (thrust). The reference velocity required for the thrust calculation is estimated at the position of each wind turbine as if the specific turbine was absent. In offshore wind farms wind turbines are mostly installed in parallel rows, so turbine rows can be considered instead of single turbines. A parabolic procedure activating successively the wind turbine rows is applied: The run starts ignoring the presence of the turbines to estimate the reference velocities at the positions of the first row. When a certain convergence criterion is fulfilled for the velocities at those positions, the actuator disks are activated at the first row. The simulation continues and the reference velocities are estimated at the second row. This procedure is repeated until all turbine rows are added.

GCL model: The GCL model [3] encompasses a semi–analytical description of the wake deficit and a set of simple empirical relations providing the relevant characteristics for the turbulence field in the wake. GCL model was developed for the estimation of the velocity deficit and the turbulence level within the wake of a single wind turbine. In the case of a wind farm, a wind turbine is subject to the effect of multiple wakes. To calculate the incoming speed on the rotor of one wind turbine due to the wake effects of the neighboring turbines, the sum of the squared induced velocity deficits is considered.


Main body of abstract

a) Power deficit: In the case of the Horns Rev wind farm [6] 12 sub-sectors of 2.5° are considered for the simulation of the western wind directions (270°±15°). For each one of the sub-sectors the mean wind direction is simulated, e.g. for the sub-sector 270°-2.5°, the simulated mean wind direction is 268.75°. Next, two sub-domains, marked with blue lines in Figure 1, are considered. The first one including rows 1-3 is used for the simulation of the wind directions 268.75°-283.75° and the second one including rows 6-8 is used for the simulation of the wind directions 256.25°-266.25°. Simulation of one sub-domain instead of the whole wind farm is found to be acceptable and saves significant computational cost. Three cases are defined to evaluate the influence of the flow sector size for western wind directions: 270°±2.5°, 270°±7.5° and 270°±15°. Numerical simulations are performed with a step of ±2.5° starting from 270°±1.25°. In order to estimate the power output for the flow sector 270°±2.5°, the average of the 270°+1.25° and 270°-1.25° simulations is calculated. It is observed that the agreement between the predicted and measured mean power deficit is improved as the flow sector size increases (Figure 2). For a size of ±15° predictions well agree with the measurements.





In the case of the Lillgrund wind farm [7], the 222±15° and 120±15° wind direction sectors are simulated considering 12 sub-sectors of 2.5° for each one of the wind sectors and simulating the mean wind direction. 2x7 principal cases are defined to evaluate the influence of the flow sector. The first set of 7 cases refers to the 120±15° sector, each case corresponding to a 2.5° sub-sector. The power deficit is estimated along a single complete row of 8 turbines (Figure 3) or a single incomplete row of 5 turbines (two “missing” turbines, see Figure 4), with an internal spacing of 3.3D. The second set of 7 cases refers to the 222±15° sector, each case corresponding to a 2.5° sub-sector. The power deficit is estimated along a single complete row of 7 turbines (Figure 3) or a single incomplete row of 6 turbines (one “missing” turbine, see Figure 4), with an internal spacing of 4.3 D. CFD predictions over the 2.5° sub-sectors show a larger variation of the power deficit in comparison to the measurements. When averaging is performed over the wider sector of ±15°, the agreement between predictions and measurements is quite satisfactory (Figure 5), which is similar to what was found in the Horns Rev wind farm case. As expected, the effect of the 2 missing wind turbines is the significant power increase of the turbine (≈80%) which is located 9.9 D behind its neighbouring upstream machine (Figure 6a). In the case of 1 missing wind turbine (4.3 D internal spacing, Figure 6b), the effect of the absent wind turbine is a power increase of almost 35% in its downstream turbine.









b) Efficiency polar: The power efficiency of the Horns Rev wind farm for 0 - 360° inflow is calculated using the amended GCL engineering model, calibrated with the CRES-flowNS predictions for the 270°, 221° and 312° wind directions. According to the standard procedure, the velocity deficit at each wind turbine of the farm is estimated by summing up the inductions of the neighboring turbines using the Euclidean norm. An alternative is to use the maximum velocity deficits. Comparison with both CFD results and measurements shows that this alternative performs better at those wind directions, where the maximum shadowing between the wind turbines occur, but worst elsewhere. Therefore, a combined method is adopted: the maximum velocity deficit approach is used when the ambient flow is aligned with the turbine rows, whereas the Euclidean norm approach is used elsewhere. Comparison of the calibrated GCL predictions with measurements is shown in Figure 7.



In the Lillgrund wind farm, the distances between the wind turbines are much smaller in comparison to the Horns Rev wind farm resulting in a higher degree of shadowing. As a consequence, the maximum velocity deficit approach of the amended GCL model performs better than the Euclidean norm approach at all wind directions and not only at the 221° and 120° directions of maximum shadowing. The comparison of the GCL predictions using the maximum velocity deficit approach with measurements is shown in Figure 8. It can be investigated if the wind turbine distance can be inserted as a parameter to the GCL model, in order to determine the choice of the proper approach at each wind direction.




Conclusion

The performance of the CRES-flowNS CFD model in large offshore wind farms was evaluated using experimental datasets from the Horns Rev and the Lillgrund wind farms. The comparisons indicated that predictions significantly overestimate the power deficit when the wind sector is narrow (±2.5°). As the size of the sector increases the agreement between predictions and measurements becomes better and for the wide sectors of ±15° it can be considered quite satisfactory. There is a possibility that part of these large differences is attributed to the uncertainty in the measurement of the wind direction. It should be further investigated if such an uncertainty produces artificially low power losses in the wake centre because of direction variability. Both predictions and measurements predict a high power increase in the cases of incomplete wind turbine rows, but only for the single wind turbine which is located in a larger spacing due to the absence of the missing turbines. The increase in power is more than doubled in the case of two missing turbines in comparison to that of one missing turbine.

The estimation of the wind farm efficiency for the whole wind rose was performed using the amended GCL model calibrated with the CRES-flowNS predictions. In the Horns Rev wind farm, the maximum velocity deficit approach was used when the ambient flow is aligned with the turbine rows and the maximum shadowing between the wind turbines occur, whereas the Euclidean norm summation of velocity deficits was used for the rest of wind directions. In the Lillgrund wind farm, the higher shadowing resulting from the smaller distances between the wind turbines, suggests the usage of the maximum velocity deficit approach for all wind directions. The comparison with measurements was satisfactory and encouraged the prospect that the combination of fast engineering models with advanced CFD solvers can be used for the prediction of efficiency polar, reducing significantly the computational cost.




Learning objectives
In large offshore wind farms, CFD predictions and measurements of power deficit are in good agreement when they both refer to mean values over wide sectors of ±15°. The differences over narrow sectors may be attributed to the uncertainty in the measurement of the wind direction. Fast engineering models can be used for the prediction of efficiency polar when properly calibrated with the predictions of advanced CFD models in certain wind directions.


References
[1] Barthelmie, R.J., Hansen, K, Frandsen, S.T., Rathmann, O., Schepers, J.G., Schlez, W., Phillips, J., Rados, K., Zervos, A., Politis, E.S., and Chaviaropoulos, P.K., “Modelling and Measuring Flow and Wind Turbine Wakes in Large Wind Farms Offshore”, Wind Energy, Vol. 12, No. 5, pp. 431-444, 2009
[2] Chaviaropoulos, P. K. and Douvikas, D. I., “Mean-flow-field Simulations over Complex Terrain Using a 3D Reynolds Averaged Navier–Stokes Solver,” Proceedings of ECCOMAS ’98, 1998, Vol. I, Part II, pp. 842-848
[3] Dekker, J.W.M, Pierik, J.T.G. (Editors), "European Wind Turbine Standards II", ECN-C--99-073, 1999
[4] Prospathopoulos, J.M., Politis, E.S., Chaviaropoulos, P.K., "Modelling Wind Turbine Wakes in Complex Terrain", Proceedings of EWEC 2008, Brussells, Belgium, pp. 42-46
[5] Schepers, J.G., ENDOW: Validation and Improvement of ECN’s Wake Model. ECN:ECN-C-03-034: Petten, The Netherlands, 2003: 113
[6] Hansen, K. ”WP1.1 Wake model performance validations for Horns Rev offshore wind farm” Technical Report: Eera-Dtoc, 2013
[7] Hansen, K. ”WP1.1 Wake model performance validations for Lillgrund offshore wind farm” Technical Report: Eera-Dtoc, 2013.