RESOURCE DECREASE BY LARGE SCALE WIND FARMING

Transcription

1 ECN-RX RESOURCE DECREASE BY LARGE SCALE WIND FARMING G.P. Corten A.J. Brand This paper has been presented at the European Wind Energy Conference, London, -5 November, 4 NOVEMBER 4

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3 Resource Decrease by Large Scale Wind Farming dr.ir. G.P. Corten dr.ir. A.J. Brand ECN Wind Energy - Wind Farm Design - The Netherlands Wind resource estimates, especially offshore, are based on the situation without the presence of the planned farms. We show that the wind resource will drop by 5-14% when we account for roughness increase that will occur when large farms are installed offshore. In the Netherlands 6 GW of wind power is to be installed on the North Sea in an area of approximately 5 by kilometres. We modelled this situation by distributing 1 turbines of 6 MW uniformly over this area. Using Lettau's relation this corresponds to a roughness increase from. m to.5 m. Calculating the new wind resource based on this roughness change, we found that the average wind speed decreases from 1 m/s to 9 m/s. This corresponds to a production loss of about 14%. A roughness increase from. m to.3 m would increase the shear stress in the atmospheric boundary layer by precise the amount added by the axial forces on the turbines. Using this roughness estimate we find a production loss of 5%. We formulated a hypothesis which clears up this inconsistency: The mechanic turbulence generated by the turbines increases the shear of the sea surface and thereby introduces a parasitic axial force. The wind speed therefore is reduced by the axial force of the turbine and by the parasitic axial force from the sea surface. Key words: offshore wake effects, wind farm roughness, inter farm losses. 1. Introduction Several Nations have plans for large scale (offshore) wind farming. For example by in the Netherlands the policy aims at 6 GW installed power in a North Sea area of approximately by 5 kilometres, see figure 1. Many other countries have similar plans. The remarkable aspect of those plans is that the wind resource estimates are based on the situation without the presence of the actual farms. It is common practice to account for wake losses inside a farm, however this paper deals with the inter farm losses. We show that the wind resource may drop significantly when we take into account the increase of the surface roughness accompanied with the future farms. Returning to the situation in the Netherlands, in the sea area of by 5 kilometres about 5 farms with considerable inter spacing are being considered. The estimated production of these farms is based on the undisturbed wind resource at each farm. In this paper we estimate the average reduction of the wind resources. Much literature can be found on the wakes of wind turbines. However, not much literature is available on inter farm effects. A good overview of several approaches is given by Milborrow [1]. This paper from 198 only deals with wake effects within farms, but the same theory can be used to calculate inter farm effects. The calculations are based on roughness models in infinite arrays of wind turbines. For spacings of 1 diameters an array efficiency of 75% is found, or in other words 5% is lost due to wake effects. In 199 the same approach is followed by Frandsen []. Here for wind farms with a spacing of 1 diameters installed at sea it is found that the wind speed will decrease by a factor of.74. The corresponding production loss would be in the order of 5%. A different approach was

4 published by Rooijmans [3] in September 3. Here, the roughness increase due to the installation of wind farms at sea was estimated by Lettau's relation and the resulting new area characteristics were fed into the meteorological model MM5. It was assumed that in an area of 9 km 45 GW of wind power was installed. This would increase the roughness to.5m. The decrease of the production was 5%. Roy and Pacala [4] presented an analysis similar to that of Rooijmans, although no estimates for production losses or wind speed reductions are given in this paper. This paper does confirm that large effects on the microclimate may be expected. km 5 km 9 m/s 8 m/s 7 m/s 6 m/s. Method We first estimate the wind speed reduction by a qualitative method in section.1. Then we follow a more qualitative approach similar to that of Milborrow [1] and Frandsen []. New in our approach is first that we calculate the wind speed reduction for a large number of wind speeds separately and that we apply the results to an actual power curve of a wind turbine. This gives more accurate results since the added roughness (depending on the axial force coefficient of the turbine) is depending on the wind speed. Secondly we calculate the practical values for the forces exerted by the sea surface, by the turbines and by the shear in the atmosphere. These values show that there is an inconsistency in the roughness approach. Thirdly we come up with a prior explanation for the inconsistency. We finally present some trends that are predicted by our roughness model. An interesting result is that the inter farm efficiency increases when the capacity factor of the turbines increases..1 Qualitative Estimate Figure 1: This roughness change due to offshore wind farms is comparable to the roughness change when moving from sea to flat land.therefore we expect that due to large scale wind farming the wind resources will reduce approximately by the same amount as when changing from sea to land. It is common practice to assume a certain vertical wind profile as a function of the surface roughness. By fitting this profile to the known geostrophic wind at high altitude (15 metres) the wind resources can be estimated at other heights, such as the hub height. The roughness of open sea is about. metres and this changes to a value of about.5 m in the case of large scale wind farming. The value of.5 m was calculated for a farm of 6 GW in an area of 5 by kilometres. This roughness change is comparable to the roughness change when moving from sea to flat land such as the Netherlands. Typical land values of the roughness range from.3 to.3 meter. Therefore we expect that due to large scale wind farming the wind resources will reduce approximately by the same amount as when changing from sea to land. The latter change is in the order of 1 to m/s at 1 m altitude when moving from 5 km offshore to 5 km onshore perpendicular to the coast line. In short

5 we think that the effect of large wind farms in the area shown by figure 1 will be comparable to a shift of the coast line by about 75 kilometres in the South-West direction. The geostrophic wind also decreases by moving from offshore regions to the continents. This is partly due to the different thermal properties of sea and land, but also partly due to roughness effects: more roughness means that the wind is directed more from high pressure to low pressure areas. This flow of course vanishes the pressure gradient, which is the driver of the geotropic wind. We estimated the gradient of the geostrophic wind as it is given by the European Wind Atlas when going from NW to SE. It was found to be in the order of 1 m/s per 5 km of which we assume that 5% is due to roughness. Using this result we estimate that large scale wind farming in the North Sea in an area of 5 by kilometres corresponds to moving 75 km from NW to SE and thus will result in an reduction of the geostrophic wind speed at 15 metres by.75 m/s. At 1 m altitude (our hub height) this increases the wind by about.55 m/s.. Quantitative estimate We quantify the inter farm effects by calculating the reduction of the wind speed in an area of 5 by kilometres wherein 6 GW of wind power is installed. We assume that this farm is so large that only the shear force of the planetary boundary layer drives the flow through the farm. So the momentum transport takes place in vertical direction only. The 6 GW of wind power consists of 1 turbines of 6 MW rated power each. The turbines have a hub height of 1 metres and a diameter of 15 metres. Turbines of this geometry reach nominal power (6 MW) at a wind speed of 11.3 m/s assuming a power coefficient C p of.44. We will explain our method for a single wind speed: the average undisturbed wind speed of 1. m/s at hub height. This speed is valid for the undisturbed case, so the surface roughness is. m which is the usual value for open water. Assuming a logarithmic velocity profile we can estimate the friction velocity. Once the friction velocity is known we calculate the geostrophic wind speed. This is the speed at the geostrophic height where it is assumed that the influence of the surface roughness can be neglected. So when we now change the surface roughness to the value for wind farms, the geostrophic wind speed remains unchanged. However the logarithmic velocity profile backwards to the surface is different. As a result of the higher roughness we will find a lower wind speed at hub height. This speed is used as the estimated wind speed in the real situation with the wind farms installed...1 Roughness Model To estimate the inter farm effects we assumed that 1 turbines of 15 m diameter and a rated power of 6 MW each, are installed uniformly in an area of 5 times km. Using the Lettau's formula we find: z 1 8 h S h π D N C 1 1 4, D ax π F = = =.55 [m], (1) A A 5, = in which z,f is the estimated roughness with wind farms, h is the turbine height, S is the total swept area times the drag coefficient C Dax, N is the number of turbines and A is the ground area of the farm. For the undisturbed offshore situation we use the value recommended in the European Wind Atlas [5] so that z is. m. Assuming a logarithmic velocity profile we find for the friction velocity u * : U k 1.4 m u * = = =.35, 1 s () h ln ln z. wherein U is the undisturbed wind speed at hub height and k is the von Karman constant (.4).

6 Using the friction velocity we can transform the wind speed at hub height upwards to the geostrophic wind speed U G at 15 m. U G = u * z ln k z (3) G = 1.6 m, s wherein z G is the corresponding height of 15 m. Now we again calculate the friction velocity using the roughness of the wind farm. With equation () wherein z is replaced by z,f and U by U G we find for the friction velocity in the farm u *F =.47 m/s. The next step is to transform the geostrophic wind speed backwards to hub height level using relation (3). We have to replace z by z,f and u * by u *F. We find for the disturbed speed at hub height U,F = 8.8 m/s, which is a reduction of 1.18 m/s with respect to the undisturbed wind speed. In literature the production loss factor is often estimated by the cube of the wind speed reduction. We would find a production loss by a factor (.88) 3 =.69. In the next section we show that this value is too pessimistic...3 Effect on Production The wind speed distribution at the locus of the farm in figure 1 is approached by a Weibull distribution with shape parameter 11.3 m/s and form parameter.. With these parameters the average wind speed is 1. m/s at hub height (1m). Subsequently we follow the procedure of section... For every wind speed we calculate the generated power by assuming a turbine efficiency of 75% so that the electric power coefficient is.44 for a turbine operating at the Betz limit. The turbines start at 4 m/s and operate up to a cut out wind speed of 35 m/s. The turbine has an efficiency (aerodynamic/electric) of =.75 for all wind speeds, and it produces a power of 6 MW between rated and cut out. Since the aerodynamic power coefficient C p =.59 for this case, the axial induction factor a is 1/3 and the axial force coefficient C Dax = 4a(1-a) = 8/9. If the electric power reaches 6 MW, which occurs for a wind speed of 11.4 m/s, then the axial induction factor is adapted so that the electric power does not exceed the 6 MW. For the total farm of 1 turbines the axial induction factor follows from (4). 3 3 ρ U N η C = 6[GW] with C = 4a(1 ). (4) 1 a, F p p Above nominal wind speed a and thus C Dax decreases with increasing wind speed. Since the roughness is a function of C Dax, also the farm roughness decreases above nominal wind speed. This more accurate way of estimating the production losses yields smaller losses. For the actual wind farm of 1 turbines we find a production loss of 14%. This is about half the loss of 31% which was found in section.. when only a single wind speed was evaluated. The main reason that explains the difference is that the turbines produce over 5% of the time above rated wind speed at maximum power. In that situation the wind speed reduction does not have a yield penalty. Using our model we calculated the production loss for our simulated farm for both the offshore and the land situation. For the latter case we used a surface roughness of.1 m. Figure shows the relation as a function of the number of turbines expressed in installed power per square km. In all cases the turbines are of the 6 MW type with 15 m diameter and 1 m hub height. In figure 3 we show how the inter farm losses change with the capacity factor of the turbines. The capacity factor was changed by increasing the rotor diameter while the rated power remained 6 MW, the number of turbines was fixed at 1 and the hub height was fixed to 1 m.

7 3 Inconsistency The approach of Milborrow [1] and Frandsen [] that we used here seems to have an inconsistency. The force balance is not in equilibrium. In an infinite array the momentum inflow from the flow comes only from above. The momentum inflow equals the shear stress of the atmospheric boundary layer. This shear stress is given by relation 5. τ = ρu *, (5) in which ρ is the density of air which is approximately 1. kg/m 3. Inter farm losses [%] Inter Farm Losses sea, z=. land, z= Installed power / surface [MW/km] Figure : Inter farm losses as a function of installed power per unit of surface. 6 GW installed power in an area of 5by km corresponds to a loss of 14 %. By substitution of the friction velocity for the undisturbed situation we find for the shear stress of the sea surface when the wind speed is 1 m/s at hub height: =.113 N/m. This is the force per unit of surface exerted by the sea on the atmosphere for the situation that the turbines are not present. To find the additional shear exerted by the turbines we divide the axial force exerted by all 1 turbines of section.. by the total farm area of 5 by km. We find: T =.67 N/m. We are not yet at the inconsistency, however we see that the turbines have a minority share in the total shear force on the planetary boundary layer. Of course this depends on the spacing of the turbines in the farm (5 diameters for this case), but it is IF losses [%] / Vnom [m/s] Inter Farm Losses Inter Farm Losses % Vnom Rotor diameter Capacity factor Figure 3: Inter farm losses as a function of capacity factor. Up to a cap. factor of.3 the losses increase to a maximum of 17%, at higher cap. factors the losses decrease since the turbines operate dominantly above Vnominal, when farm losses vanish. remarkable that the shear of the flat sea surface is at least of the same order of magnitude as the shear due to the turbines. Now we come back to the equilibrium constraint which will lead to the inconsistency. We can calculate the shear in the atmospheric boundary layer ABL also for the situation Rotor diameter [m]

8 that the farm is present. By substituting u *,F =.497 m/s in eq. (5) we find ABL =.31 N/m. So the downward flow of momentum is.31 N/m and the upward flow of momentum (the sum of the shear force acting on the atmosphere) is + T =.179 N/m. Since we assumed that the farm is an infinite array and thus that the situation is entirely steady this is an inconsistency. 3.1 Decreasing the surface roughness of the Farm We made the force balance described above consistent by decreasing the roughness of the farm we used in our model. Equilibrium was reached when the farm roughness was decreased to.3 m, while Lettau's relation gave us the value of.54 m. If we use the value of.3 m for the roughness, then the shear stresses are balancing, but of course the wind speed reduction will be much less in this case. Following the method of section..3 to estimate the loss of production for z,f =.3 m we find a loss of 5% for the situation of 1 turbines of 6 MW installed in an area of 5 times km. We used this value as an estimate for the minimum loss to be expected. At this point we cannot say if a deviation in Lettau's relation by a factor of is plausible. Nevertheless we have a second explanation. 3. Parasitic Axial Force From measurements in wind farms it is known that the turbulence increases by even more than 1 percent close to turbines, but still by a few percent much further away. We assume that the turbulence at sea is 6% at 1 m height and that this value increases inside our hypothetical farm to 9%. Those values correspond to values measured in wind tunnel experiments with model farms. The turbulence is related to the friction velocity by U =.5 u *, so u * increases by the same factor of 3 / as U. From relation (5) it follows that the shear increases by a factor ( 3 / ) =.5. This would imply that the shear of the sea surface may increase by about a factor of. If we correct the shear stress exerted by the sea surface with this factor we find =.6 N/m. The shear caused by the turbines remains the same: T =.67 N/m. When we add those two shear values we find the shear exerted by the farm (including sea surface) on the atmosphere: + T =.87 N/m. This corresponds satisfactory to the downward momentum flux calculated from the friction velocity based on Lettau's roughness: ABL =.31 N/m. This is a new hypothesis and we have not yet experimental data to support it. If the hypothesis is correct this would mean that by extracting energy from the wind by wind turbines, there will be a large parasitic additional energy extraction originating from an increase of the shear on the ground area of the farm. Perhaps this can be validated in offshore farms: if the hypothesis is correct it would imply that waves become higher in offshore farms while the classical thought is the opposite. 4. Conclusion and Discussion We conclude that regarding the wind resources the sea characteristics may change in land characteristics to some extent. In this analysis we find losses in the order of 5% to 14% for the Dutch situation of installing 6 GW in an area of 5 by kilometres. Those numbers are Weibull weighted averages including the turbine property that V nominal was reached at 11.4 m/s. Values of up to 3% such as found in literature are based on analyses at a single wind speed. We showed that a 3% loss for a single wind speed reduces by about a factor when a realistic wind speed distribution and realistic turbine properties are used in the model. Still the magnitude of the loss is reason to reduce the uncertainty in the models and to think of ways to reduce the inter farm losses. We suggest to implement the following model improvements and to study the following option to reduce the losses.

9 Model improvements: The model should include the increase of kinetic energy in the flow by the atmospheric pressure gradient. This is a large input of energy when the wind has a component in the direction of the gradient. The model should include the effect of reduction of pressure gradients in the atmosphere due to the additional drag force (including possible parasitic drag) of the turbines. Due to this drag the wind turns into the direction of the negative pressure gradient so that air flows faster from high to low pressure areas, thereby vanishing the pressure gradient. The model should include the decrease of momentum in the atmospheric boundary layer when the boundary layer slows down in a large area of wind farming. Even for a farm of 5 times kilometres this is an important contribution of momentum. Thermal effects should be included in the model. The hypothesis on the parasitic axial force should be validated. This may be possible by means of wind tunnel measurements. Option to reduce inter farm losses: Orientating the farm with respect to one another so that the losses are minimal. Controlling upwind farms differently: in such a way that the total production is optimised and not the production of individual farms. References [1] Milborrow DJ, 'The Performance of Arrays of Wind Turbines', Jounal of industrial Aerodynamics, 5, [] Frandsen S, 'On the Wind Speed Reduction in the Centre of Large Clusters of Wind Turbines', Jounal of Wind Engineering and Industrial Aerodynamics, 39, 199, [3] Rooijmans P, 'Impact of a Large Scale Offshore Wind Farm on Meteorology', master thesis, January 4, Univ. Utrecht. [4] Baidya Roy S, Pacala SW, 'Can Large Wind Farms Affect Local Meteorology?', Journ. of Geophys. Res. Vol 19, 4. [5] Troen I, Petersen EL, 'European Wind Atlas', Riso National Laboratory, Roskilde, Denmark, ISBN , 656pp., 1989.