Energy harvesting via co-locating horizontal- and vertical-axis wind turbines
EEnergy harvesting via co-locating horizontal- andvertical-axis wind turbines
M. Hansen , P. Enevoldsen and M. Abkar Department of Engineering, Aarhus University, Denmark Department of Business Development and Technology, Aarhus University, DenmarkE-mail: [email protected]
Abstract.
Co-locating horizontal- and vertical-axis wind turbines has been recently proposedas a possible approach to enhance the land-area power density of wind farms. In this work, weaim to study the benefits associated with such a co-location using large-eddy simulation (LES)and analytical wake models. In this regard, small-scale vertical-axis wind turbines (VAWTs)in triangular clusters are deployed within a finite-size wind farm consisting of horizontal-axiswind turbines (HAWTs). Wake flow within the wind farm and the effect of VAWTs on theoverall wind-farm efficiency are investigated and quantified. The results show that the optimaldeployment of small-scale VAWTs has a negligible impact on the performance of HAWT arrayswhile increasing the total power production. For the particular cases considered here, the poweroutput of the co-located wind farm increases up to 21% compared to the baseline case in whichonly the HAWTs are present. Also, by comparing to the LES results, it is shown that theanalytical framework proposed here is able to accurately predict the power production of windfarms including both HAWTs and VAWTs. Next, as a real-world application, potential benefitsof deploying small-scale VAWTs inside the Horns Rev 1 wind farm are explored for variouswind directions using the calibrated wake model. The results show potential for about an 18%increase in the wind-farm power production, averaged over all wind directions, for a particularVAWT layout investigated in this study. The levelized cost of energy (LCoE) for the co-locatedwind farm is also assessed. The simulations finds that meanwhile the installation of VAWTsincreases the annual energy production of the wind farm, it also increases the LCoE, which iscaused by a) lack of operational data, and b) a low technology readiness level for VAWTs andfloating foundations.
1. Introduction
Wind-turbine wakes require a relatively large distance to be fully recovered. Hence, when windturbines are deployed in clusters, the performance of waked turbines significantly decreasescompared to wind turbines in the free stream (see the review of Ref. [1]). One possible approachto mitigate the power defect due to the wake interaction is to install wind turbines as faras possible from one another [2], which is further enforced by the development of rotor sizesthroughout the past decades [3]. However, this approach requires significant amounts of landwhich in practice is not always feasible for several reasons ranging from the costs of aquiring theland to increased likelyhood of social opposition [4, 5].Historically, wind farms were assumed to consist of identical horizontal-axis wind turbines(HAWTs). Recent studies have proposed a paradigm shift in which size and type of turbinesis also a decision variable in the farm-design process [6–10]. Feng and Shen [8] investigated the a r X i v : . [ phy s i c s . f l u - dyn ] A ug enefits of wind farms consisting of HAWTs with multiple types using analytical wake models.They showed a lower energy cost for a wind farm with different sizes compared to a uniform-sized wind farm. Vasel-Be-Hagh and Archer [9] assessed the impact of hub-height optimizationon wind-farm energy extraction. They found that a wind farm with variable hub heights canproduce >
2% more energy annually compared to the wind farm with a uniform hub height.The benefits of vertically staggered wind farms by varying HAWT hub heights were also studiedrecently by Zhang et al. [10]. Using large-eddy simulation (LES), they showed that verticalstaggering enhances the energy production of turbines in the entrance/developing region of thefarm. However, this approach does not improve the power output in the fully developed regime.A different approach is to fill the gap between large-scale HAWTs by deploying smallervertical-axis wind turbines (VAWTs) [11]. VAWTs are a class of turbines with rotational axesperpendicular to the free stream, and have received a great deal of attention in recent years (seefor instance Refs. [12–16], among others). VAWTs offer several advantages and opportunitiesover conventional HAWTs. In particular, they can produce power from any wind direction,thereby obviate the need of any yaw control mechanism [11]. They have also lower installationand maintenance costs as their drive train systems can be mounted close to the ground/seasurface [17]. Recently, Xie et al. [18] performed LES of an infinite wind farm (i.e., numericallysubjected to periodic boundary conditions) consisting of co-located HAWTs and VAWTs. Theyshowed that the small-scale VAWTs enhance the vertical momentum exchange within the farmleading to a significant increase (up to 32%) in the total wind-farm power. Despite the promisingfindings reported in that study, the aerodynamic interaction of co-located HAWTs and VAWTsin a finite-size wind farm is unknown and has not been studied so far. Note that for a smallnumber of wind turbines or at the leading edge of a large wind farm, the energy is mainlyextracted from the incoming wind due the horizontal flux of kinetic energy [19]. Given the finitesize of existing farms, investigating the impact of co-locating HAWTs and VAWTs on the overallperformance of wind farms is valuable and is the central focus of this work.The present work aims at exploring wake flow and generated power from a finite-size windfarm consisting of co-located HAWTs and VAWTs using LESs and analytical wake models.Section 2 provides a brief description of the LES and analytical frameworks for modeling wakeflow through HAWTs and VAWTs. In Section 3, the impact of co-location on the wake flowand the total power production of the farm is examined, and the results are compared to thebaseline case in which only HAWTs are present. Finally, the power enhancement by addingsmall-scale VAWTs to the Horns Rev 1 wind farm, as an existing wind farm, is investigated forvarious wind directions. In Section 4, a summary and concluding remarks are given.
2. Modelling
The previously-validated LES framework presented here (see for instance Refs. [20–23]) solvesthe filtered continuity and NavierStokes equations for incompressible turbulent flow, ∂ ˜ u i ∂x i = 0 , ∂ ˜ u i ∂t + ∂ (˜ u i ˜ u j ) ∂x j = − ρ o ∂ ˜ p∂x i − ∂τ ij ∂x j − f i ρ o , (1)where ˜ u i and ˜ p are the filtered velocity and pressure fields, respectively. x i indicates the Cartesiancoordinates. t is time. ρ o is the fluid density. τ ij = (cid:103) u i u j − ˜ u i ˜ u j denotes the kinematic subfilterstress tensor. f i is a body force and accounts for the effect of wind turbines on the flow.The code employs a pseudo-spectral discretization in horizontal directions, and a central finitedifference method in the vertical direction. The second-order Adam-Bashforth scheme is appliedfor time advancement. The molecular viscous forces are neglected away from the wall, hence theflow is at nominally infinite Reynolds number. The subfilter turbulent motions are modeledvia the scale-dependent Lagrangian dynamic approach [24]. The actuator-disk model with .5 1 1.5 U/U hub z / D -2 k z -2 E u ( k ) u * - z - -1 -5/3 I u = σ u /U hub (b) Figure 1: (a) Vertical profiles of the normal-ized mean streamwise velocity
U/U hub andthe turbulence level I u = σ u /U hub for theincoming free stream. Horizontal black andred dot-lines show the HAWT and VAWTextents, respectively. (b) Normalized re-solved streamwise velocity spectra. Here, u ∗ is the friction velocity, and the normalizedheight z/D increases from 0.03 to 2.85. rotation [20] and the actuator swept-surface model [13] are respectively used to parameterizethe forces induced by HAWTs and VAWTs. Through these approaches, the aerodynamic forceson the rotors are determined using the blade airfoil geometry, the relative wind velocity, andthe lift-drag force characteristics of the blades. The inflow condition is generated through aprecursor method and by simulating a turbulent flow over a rough surface. The computationaldomain size is 4800m × × x ), lateral ( y ) and wall-normal ( z )directions, respectively, and it is broken uniformly into 480 × ×
96 grid points. An imposeduniform pressure gradient drives the boundary-layer flow in the streamwise direction. Theeffective ground roughness ( z o ) is 0 . U hub is about 7 . I u = σ u /U hub at the same height is about 7 . σ u is the standarddeviation of the streamwise velocity. Figure 1b illustrates the normalized spectra of the simulatedstreamwise velocity field obtained from the precursor simulation. As can be seen in this figure,the normalized power spectra depict the expected collapse for the small resolved scales ( k z > − /
3. In the wake-flowsimulation, a fringe zone is implemented to adopt the flow from the wake state downstream tothat of a fully turbulent boundary-layer inflow condition [21, 26].The HAWTs used in the simulations are Vestas V80 turbines with the rotor diameter ( D ) of80m and the hub height ( z h ) of 70m. Details of the Vestas V80 wind turbine such as distributionsof twist angle and chord length along the blades, and lift-drag coefficients as a function of angleof attack can be found in Ref. [20]. The VAWTs immersed in the flow are 200kW T1-turbines,which are the three- and straight-bladed VAWTs with the rotor diameter ( D v ) of 26m, theblade span ( H v ) of 24m, and the equator height ( z hv ) of 40m. The blades of VAWTs consistof the standard NACA 0018 airfoil with the chord length of 0 . . The reduction of the mean wind velocity inside the wake is described by the normalized velocitydeficit as ∆
U /U ∞ = ( U ∞ − U w ) /U ∞ , where U ∞ is the turbine inflow velocity, and U w is thewind velocity at a given position inside a wake. In this study, we use the recently-introducedGaussian wake model for both HAWTs [27, 28] and VAWTs [22, 29]. The Gaussian wake modeldescribes the wake velocity deficit as igure 2: A schematic of a HAWT (left), and a three-and straight-bladed VAWT (right). ∆ UU ∞ = C ( x ) × exp (cid:32) − (cid:34)(cid:18) yσ y (cid:19) + (cid:18) z − z h σ z (cid:19) (cid:35)(cid:33) , (2)where C is the maximum velocity deficit, and σ y and σ z are respectively the spanwise andwall-normal standard deviations of velocity deficit distribution. The maximum velocity deficitin the wake is given by C = 1 − (cid:112) − C t / [2 π ( σ y σ z /A p )]. Here, the turbine thrust coefficient isdenoted by C t . A p is the turbine projected area, and is equal to πD / D v H v for HAWTsand VAWTs, respectively. As shown in the earlier studies [27, 29], for wind turbines in theturbulent free stream, a linear growth of the wake with downwind distance can be assumed, σ y = k ∗ x + (cid:15)L y and σ z = k ∗ x + (cid:15)L z , where k ∗ denotes the wake expansion rate, and thecharacteristic turbine dimensions in the y and z directions are respectively labeled as L y and L z . In particular, L y = L z = D for HAWTs, and L y = D v and L z = H v for VAWTs [29]. Thewake expansion rate k ∗ is estimated based on the empirical formula suggested in Ref. [30] as k ∗ = 0 . I u . (cid:15) in the equation above characterizes the wake standard deviation at the rotor, andit is defined as (cid:15) = 0 . √ β , where β = 0 . √ − C t ) / √ − C t [27]. Note that in the veryfar-wake region, where k ∗ x (cid:29) (cid:15)L y,z , the velocity deficit distribution by definition asymptotes toa circular shape from an elliptic shape as σ y /σ z →
1. To account for multiple wake interactionswithin a wind farm, rotor wakes can be superposed in either linear or nonlinear manner [31, 32].Based upon the linear superposition , the wake velocity within the farm can be estimated as U i = U ∞ − (cid:80) k ( U k − U ki ) where U i is the velocity at turbine i , U k is the incoming velocityat turbine k , and U ki is the wake velocity caused by turbine k at downstream turbine i . Thevelocity field emerged from multiple wake interactions can be alternatively modeled using thenonlinear superposition method as U i = U ∞ − (cid:113)(cid:80) k ( U k − U ki ) . In the following section, theperformance of the above-mentioned superposition methods is assessed using the LES data.The generated power by turbine i is determined as P i = 0 . ρ o C p A p U i , where C p is the powercoefficient of the turbine.It should be mentioned that the wake model for HAWTs has been validated using wind-tunnel measurements and LES data [27], as well as field experiments of wind-turbine wakes [30].The wake model for VAWTs has been recently assessed using the LES data as well as fieldmeasurements of VAWT wakes [29]. The derivation of the analytical wake model for bothHAWTs and VAWTs is based on assuming a two-dimensional Gaussian shape for the wakevelocity deficit, and assuming a linear growth rate for the wake expansion downstream ofthe turbine. Hence, the accuracy of the analytical models is sensitive to the validity of theaforementioned assumptions. Besides, selecting the magnitude of the wake expansion rate k ∗ ,as a tuning parameter, together with the employed superposition model can cause uncertaintiesin the prediction of wake flows and power output in wind farms. naccessible wind by HAWTs Figure 3: Wind-farm layout: Case (0):baseline (top) and Case (1): VAWTclusters between HAWTs (bottom).
Figure 3 illustrates the schematic of the wind-farm layout for the two cases considered in thisstudy. Case (0) is the baseline case with no VAWT. The HAWTs are arranged in six columnsand three rows in the streamwise and lateral directions, respectively. The distance among theHAWTs in the streamwise and lateral directions is 7 D and 5 D , respectively. As mentionedbefore, deployment of wind turbines as far apart is required to mitigate the wake loss in windfarms. However, the available energy passing through the gap between large HAWTs is notaccessible by them. In order to increase the land-area power density of wind farms, the gapbetween large HAWTs can be filled by the smaller VAWTs [4]. There are different ways tofill the gap between HAWTs using VAWTs, and several design parameters such as geometry,number, and exact location of VAWTs can be essentially optimized in order to maximize thebenefits of wind-farm co-location. In this study, we consider one particular case to show thepotential benefits of this approach in improving the power production of an existing wind farm.Case (1) represents a layout in which VAWTs are installed in triangular clusters in the free spaceamong HAWTs. Here, the center of VAWT cluster is placed between each row and column ofHAWTs in order to minimize the interaction between them. Each VAWT cluster consists ofthree turbines with center-to-center distance among them of about s v D v = 5 D v . The selectedconfiguration for the VAWT clusters is motivated by the recent study by Hezaveh et al. [33]who showed that the performance of VAWTs can be increased using synergetic clustering. Inparticular, by optimizing the VAWT numbers and the distance among them, they showed thatsuch a configuration results in higher power production over a wide range of wind direction. Ascan be visually acknowledged in Fig. 3, the distance between VAWT clusters in the streamwiseand lateral direction is 7 D (cid:39) . D v and 5 D (cid:39) . D v , respectively, and the first column ofVAWT clusters is placed 3 . D downstream of the first HAWT column.
3. Results
Here, we present the results obtained from the LES and the analytical wake model. In particular,we focus on analyzing the mean wake flow through the wind farm as well as the generated powerby wind turbines for the two scenarios described in Section 2.3. igure 4: Instantaneous (top) andtime-averaged (bottom) streamwisevelocity field at HAWT hub heightobtained from LES for Case (0).
LES HAWTWM HAWT
Nonlinear SP
WM HAWT
Linear SP k* 10% errorbar
Figure 5: Power efficiency as afunction of turbine columns forCase (0) obtained from LES andwake model (WM) with differentsuperposition (SP) methods.
Figure 4 illustrates contour plots of the normalized instantaneous and time-averaged streamwisevelocity at the HAWT hub height obtained from LES. As expected, the waked turbines encountera reduced wind velocity and, consequently, produce less power compared to the turbines in thefirst column. Figure 5 represents the power efficiency as a function of turbine columns. Here,the power efficiency of each column is calculated as η c = P c /P c,free , where P c is the poweroutput of all turbines in each column, and P c,free is the power output of all HAWTs in the firstcolumn operating in the free stream. The first column has all the turbines in the free streamand, hence, η c = 1. Due to the wake effect, the efficiency drops by around 50% for turbinesin the downstream columns. In this figure, the predictions obtained from the analytical wakemodel with linear and nonlinear superposition methods are also provided for comparison. Ascan be seen, the linear addition of the wake velocity defects leads to an underestimation of thepower output for the downwind wind turbines. On the other hand, there is a good agreementbetween LES and the analytical model with nonlinear wake superposition. These results areconsistent with previous studies that show the nonlinear superposition method can provide amore accurate prediction for the power production of wind turbines subjected to multiple wakeinteractions (see for instance the review of Refs. [34, 35], among others). In the analytical wakemodel, we also investigate the uncertainty in estimating the wake growth rate, k ∗ , as it is theonly empirically-tuned parameter in the wake model. Here, we present the results with 10%uncertainty in the estimation of this parameter. It is found that 10% uncertainty in the wakegrowth rate leads to about 2.3% uncertainty in the power prediction of waked wind turbines.Since the analytical model with the nonlinear wake superposition provides a relatively accurateprediction for the power output in the baseline case, this method is used in the rest of the paper. In this case, HAWTs are kept in the same position as Case (0), and VAWT clusters are placedin the gap among them. Figure 6 show the contours of the normalized mean flow at HAWT and igure 6: Time-averaged stream-wise velocity field at HAWT (top)and VAWT (bottom) hub heightsobtained from LES for Case (1).
VAWT hub heights, respectively, obtained from LES. At the HAWT hub height, VAWT wakesappears far downstream of the farm, since the wake behind VAWTs needs to grow sufficientlyin the vertical direction before being visible at the HAWT hub height. It can be also realizedfrom these figures that the wakes of VAWT clusters are almost fully recovered before the nextcolumn since the relative distance between the two columns of VAWT clusters is relatively large(around 21 . D v ).The average turbine power efficiency for the turbines in each column is plotted in Fig. 7.The total power efficiency of the co-located wind farm is also plotted in this figure to illustratethe gain potential due to the presence of VAWTs. In order to better quantify the effect ofVAWTs on the performance of HAWTs and on the total power output of the farm, we definethe gain/loss factor as follows. The gain/loss factor in the power production of HAWTs due tothe presence of VAWTs is defined as ζ HAW T,n = (cid:80) P HAW T,n / (cid:80) P −
1, where (cid:80) P HAW T,n isthe total power of HAWTs in Case (n) and (cid:80) P is the total power of HAWTs in the baselinecase (i.e., Case 0). We also define the gain factor for VAWTs as ζ V AW T,n = (cid:80) P V AW T,n / (cid:80) P ,where (cid:80) P V AW T,n is the total power of VAWTs in Case (n). Then, the net gain/loss factor isdefined as ζ net,n = ζ HAW T,n + ζ V AW T,n . Note that, based on the definitions above, the gain/lossfactor for Case (0) is zero. The gain/loss factor for the co-located wind farm is provided in Table1. As can be noticed, the VAWTs have a relatively small impact on the performance of HAWTsby decreasing the HAWT farm efficiency by 0 . .
1% compared to thebaseline case. Note that optimizing the design and placement of VAWTs can further reducetheir negative impacts on HAWTs, and thus it can be addressed in future works. Also, similarto the previous results, a relatively good agreement between the LES data and the wake modelis observed in predicting power efficiency for both the HAWTs and VAWTs.In this study, in order to assess the effect of HAWTs on VAWTs, we also considered anothercase in which only VAWTs are present (not shown here). We found that the power output ofVAWT only farm is slightly less (about 8%) than the VAWTs in HAWT+VAWT case. Thereason is mainly related to the fact that in aligned HAWT farms, there is a high-speed channelsbetween the turbine rows. In particular, the wind speed slightly increase in the channels amongthe HAWT rows due to the blockage induced by the turbines. In the co-located wind farm, sincethe VAWTs are located between the HAWTs in the high-speed channels, the power output fromthe VAWTs is slightly more than the one from the VAWT only farm.
LES HAWTLES VAWTLES HAWT + VAWT
WM HAWTWM VAWTWM HAWT + VAWT k* 10% errorbar
Figure 7: Power efficiency as afunction of turbine columns for Case(1) obtained from LES and wakemodel (WM).Table 1: Gain/loss factor for Case (1) obtained from LES. I u ζ HAW T ζ V AW T ζ net . − .
7% 21 .
8% 21 .
160 200 320 360240
Wind direction [°]
HAWT+VAWT WMHAWT WMHAWT LESk*
Figure 8: Left: Layout of the Horns Rev 1 wind farm. The HAWTs and VAWTs are respectively shownwith blue squares and red circles. Right: Power efficiency distribution of the Horns Rev 1 wind farm withVAWT clusters. The ambient turbulence level is 7 . As a real-world application, the benefits of co-locating HAWTs and VAWTs are investigatedin the Horns Rev 1 wind farm under different wind directions. To do so, the analytical wakemodel, calibrated in the previous section, is employed. The Horns Rev 1 wind farm consistsof 80 Vestas V80 HAWTs in 8 rows by 10 columns grid with a minimum distance among twoturbines ( s ) of 7 HAWT rotor diameter. Columns are turned 7 ◦ from the North-South axis. Aschematic of the wind farm is shown in Fig. 8. The type of turbines is the same as the ones usedin previous cases. The incoming wind velocity at the HAWT hub height is 8m/s. To assess theeffect of atmospheric turbulence on the results, three different values for the ambient turbulenceintensity are considered as I u = 5%, 7 .
7% and 15%. VAWTs are deployed based on the samelayout concept as Case (1), i.e., VAWT triangular clusters in the gap between the HAWTs. Inorder to provide a more complete picture of the effect of VAWTs on the HAWT array, wind-farmefficiency in all wind directions is investigated. Due to the symmetry of the wind-farm layout,it is sufficient to investigate wind directions ranging over 180 ◦ . Here, we define the efficiency ofthe entire wind farm as η = (cid:80) P / (cid:80) P free , where (cid:80) P is the sum of power output from all windturbines, and (cid:80) P free is the total power output from HAWTs calculated as if they were placedin the free stream.Figure 8 shows the wind-farm power efficiency, η , for wind directions ranging from 173 ◦ − ◦ obtained from wake model with 10% uncertainty in the wake growth rate. The wind-farm poweroutput obtained from LES in the absence of VAWTs [36] is also included for comparison. As able 2: Gain/loss factor for the Horns Rev 1 case averaged over all wind directions. I u ζ HAW T ζ V AW T ζ net − .
4% 17 .
9% 16 . − .
0% 18 .
3% 17 . − .
6% 18 .
8% 18 . . .
3% and 18 .
2% for the ambient turbulence intensity of 5%, 7 .
7% and 15%,respectively. It is interesting to observe that the ambient turbulence level has a relatively smalleffect on power enhancement due to the turbine co-location. In addition, it is found that 10%uncertainty in the wake growth rate yields about 1% uncertainty in estimating the total powerproduction averaged over all wind directions which is much smaller than the gained power dueto the presence of VAWTs. This result reveals the potential to enhance the wind-power densityof wind farms by co-locating VAWTs and HAWTs.
The levelized cost of energy (LCoE) is measured as $/MWh and is an important parameterfor benchmarking the competitiveness of any energy technology [37]. The LCoE is estimatedfollowing equation,
LCoE = (cid:80) nt =1 (cid:104) CAP EX t + (cid:80) nt =1 (cid:16) OP EX t (1+ r ) t + DECEX (1+ r ) t (cid:17)(cid:105)(cid:80) nt =1 E t (1+ r ) t , (3)where CAPEX describes the capital expenditures with hardware as the greatest cost, OPEXdescribes the operational expenditures such as service and maintenance, and finally DECEXdescribes the expenditures related to decommissioning of the wind turbine.The expected LCoE for European offshore wind in 2028 is 51 $/MWh for fixed-bottomfoundations [38]. For the studied wind farm, Horns Rev 1, the mean annual energy production(AEP) is 577.64 GWh/year estimated over the past eleven years (2009-2019) , which have beenused to estimate the potential impact of combining VAWT and HAWT in Table 3. Havingestimated the corresponding energy outputs, Equation 3 can be applied to determine the impacton LCoE of an offshore wind farm with and without the installation of VAWTs. Table 4 providesan overview of such.The expected European offshore LCoE for 2028 from [38] has been applied to determine thebaseline for Horns Rev 1. The results indicate that even though VAWTs increase the wind Data obtained from https://ens.dk/service/statistik-data-noegletal-og-kort/data-oversigt-over-energisektoren. able 3: The mean AEP (GWh) for Horn Rev 1 has been estimated for the different scenarios with 7.7%as the baseline ambient turbulence intensity. I u HAWT (GWh) VAWT (GWh) Net (GWh)5% 575 .
33 103 . . .
64 105 . . .
95 108 . . Table 4: LCoE of an offshore wind farm with and without the installation of VAWTs. I u LCoE
HAWT
LCoE
VAWT
LCoE
Net
Change in LCoE
Net ($/MWh) ($/MWh) ($/MWh) (%)5% 50 . . .
65 +17 . .
17 +18 . . . .
34 +19 . .
4. Conclusion
The benefits associated with co-locating HAWTs and VAWTs in a finite-size wind farm areinvestigated in this study. In this regard, LES together with the analytical wake model isemployed. Small-scale VAWTs in triangular clusters are deployed within a finite-size wind farmconsisting of conventional HAWTs. For the particular cases studied here, the potential powergain in the wind farm with both HAWTs and VAWTs is up to 21% compared to a baselinecase in which only HAWTs are present. It is also shown that the impact of small-scale VAWTson the performance of HAWTs is relatively small if the VAWTs are deployed properly amongHAWTs. Furthermore, the performance of the analytical framework is evaluated using the LESdata, and it is found that the presented analytical framework is able to accurately predict thepower output from wind farms consisting of both HAWTs and VAWTs.The calibrated analytical wake model is used to investigate the potential power enhancementin the Horns Rev 1 wind farm by adding small-scale VAWTs over a wide range of wind directions.It is shown that by adding the small-scale VAWTs to the wind farm, the power productioncan increase by up to 18% (averaged over all wind directions). We conclude that co-locatingconventional HAWTs and small-scale VAWTs is a promising approach to increase the land-areapower density in existing wind farms.The LCoE for the co-located wind farm is also addressed. It is shown that having access toreal CAPEX numbers for bottom-fixed foundations for VAWT would have reduced the LCoEsignificantly. It is further expected that floating wind turbines and VAWTs will undergo thesame technological innovation patterns [41] and reductions in LCoE as what have been seen foroffshore HAWTs in the past decades [42] making it an interesting asset for increasing the outputdensity for offshore wind.Despite the promising results presented in this study future research is required (a) to evaluatehe impact of atmospheric thermal stability on the performance of co-located wind farms, (b) toextend the validation of both LES and analytical wake models to different atmospheric regimesand different wind-farm layouts, (c) to assess the effect of a realistic wind rose in the calculationof LCoE in co-located wind farms, and (d) to optimize the design and placement of clusteredVAWTs within HAWT arrays to maximize the power production of co-located wind farms.
Acknowledgments
The work is financially supported by Aarhus University.
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