WIND ARRAY PERFORMANCE EVALUATION MODEL FOR LARGE WIND FARMS AND WIND FARM LAYOUT OPTIMIZATION

Transcription

1 WIND ARRAY PERFORMANCE EVALUATION MODEL FOR LARGE WIND FARMS AND WIND FARM LAYOUT OPTIMIZATION by SIMENG LI Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Department of Mechanical and Aerospace Engineering CASE WESTERN RESERVE UNIVERSITY August, 2014 i

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Simeng Li candidate for the degree of Doctor of Philosophy in Mechanical Engineering Committee Chair J. IWAN D. ALEXANDER Committee Member JAIKRISHNAN R. KADAMBI Committee Member PAUL BARNHART Committee Member DAVID H. MATTHIESEN Date of Defense July 2, 2014 *We also certify that written approval has been obtained for any proprietary material contained therein ii

3 Contents Chapter 1 Introduction Background Wake measurements and wake model Wind farm layout optimization Dissertation Outline... 7 Chapter 2 Literature Review Wake models Analytical Wake models Numerical Wake model Multiple wake models Wind farm performance evaluation models Wind farm layout optimization problem Chapter 3 Objectives Wind array performance evaluation Wind farm layout optimization Chapter 4 Wake models Kinematic Wake Models Jensen wake model Larsen model Frandsen analytical model Field Wake Models Ainslie wake model Three-dimensional field model Wake added turbulence models Chapter 5 Methodology Large wind array performance evaluation model (LWAP) Multiple wake model Effect of the wind array on the atmospheric boundary layer Wind array layout optimization model (WALOM) Wind array configuration set up Wind data and distribution iii

4 5.2.3 Cost function Turbine power Wake effect evaluation Genetic Algorithm (GA) Chapter 6 Results: wind farm layout evaluation model Wind speed evaluations at Horns Rev when wind direction is along turbine rows Turbine power evaluations at Horns Rev: wind direction parallel to turbine rows Power output predictions for turbines in the row at the Horns Rev and Nysted for a representative wind speed and variable wind directions Chapter 7 Results: wind farm layout optimization Extension of Mossetti s approach Case 1: Constant unidirectional wind Case 2: Constant wind speed with an equal probability variable wind direction Case 3: Variable Wind Speed with Variable Wind Direction Different Spacing Limits for Unidirectional Wind Different Area Sizes for Unidirectional Wind Constant Wind Speed with Variable Wind Direction and a circular site area Comparison of optimized layouts using Jensen wake model and Ainslie wake model Horns Rev wind farm layout optimization Weibull data for 12 wind direction sectors Wind data for 16 wind direction sectors Wind data for 72 wind direction sectors Chapter 8 Conclusions and future work Bibliography iv

5 Tables TABLE 5.1 WIND DATA EXAMPLE 51 TABLE 5.2 WEIBULL FACTORS FOR DIFFERENT WIND DIRECTIONS [77]. 54 TABLE 6.1 MAPE OF THE COMPUTED NORMALIZED WIND VELOCITY USING OBSERVED DATA FOR TWO WIND DIRECTIONS AND TWO WIND SPEEDS REPORTED IN [60] AT HORNS REV. 69 TABLE 6.2 MAPE OF THE COMPUTED NORMALIZED TURBINE POWER USING COMPUTED PREDICTIONS AND ACTUAL OBSERVATIONS AT HORNS REV [58]: WIND DIRECTION PARALLEL TO TURBINE ROWS. 72 TABLE 6.3 RMSD OF THE COMPUTED NORMALIZED POWER FOR VARIOUS WIND DIRECTIONS AND A WIND SPEED OF 8 M/S AT HORNS REV WIND FARM [60] 78 TABLE 6.4 RMSD OF COMPUTED NORMALIZED POWER FOR VARIOUS WIND DIRECTIONS AND A WIND SPEED OF 8 M/S AT NYSTED WIND FARM [60] 78 TABLE 7.1 RESULTS FROM PREVIOUS STUDY AND CURRENT STUDY: REPORTED AND RECOMPUTED 83 TABLE 7.2 RESULTS FROM PREVIOUS STUDY AND CURRENT STUDY: REPORTED AND RECOMPUTED 86 TABLE 7.3 RESULTS FROM PREVIOUS STUDY AND CURRENT STUDY: REPORTED AND RECOMPUTED 89 TABLE 7.4 TURBINES DISTRIBUTIONS IN OPTIMIZED LAYOUTS FOR ISOTROPIC WIND AND ROUND AREA 96 TABLE 7.4 VESTAS V80 THRUST COEFFICIENT AND POWER AS A FUNCTION OF WINS SPEED 101 TABLE 7.5 WIND DISTRIBUTION FOR HORNS REV 102 TABLE 7.6 TURBULENCE INTENSITIES FOR VARIABLE WIND SPEEDS 102 TABLE 7.7 LAYOUT PERFORMCANCE OF OPTIMIZATION RESULTS 109 v

6 Figures FIGURE 1.1 AERIAL VIEW FROM THE SOUTHEAST OF WAKE CLOUDS AT HORNS REV ON FEBRUARY 12, 2008 [11]. 2 FIGURE 4.1 WAKE PROFILE DOWNSTREAM A TURBINE 21 FIGURE 4.2 TURBINES TAKEN INTO CONSIDERATION WHEN CALCULATING ADDED TURBULENCE 32 FIGURE 5.1 OVERLAPPED WAKES WHERE s1=7d 38 FIGURE 5.2 WAKE DECAY CONSTANT, k, AS A FUNCTION OF UPSTREAM TURBINE WIND SPEED DEFICIT 39 FIGURE 5.3 COMBINATION COEFFICIENT, C, AS A FUNCTION OF NORMALIZED DOWNSTREAM DISTANCE 40 FIGURE 5.4 NORMALIZED WIND VELOCITY CALCULATED USING MULTIPLE WAKE MODEL AND THE JENSEN WAKE SINGLE MODEL. 41 FIGURE 5.5 PREDICTED FREE STREAM WIND SPEEDS AT TURBINE HEIGHT FOR THE HORNS REV WIND FARM LAYOUT 45 FIGURE 5.6 WIND FARM BOUNDARY SET UP 47 FIGURE 5.7 HORNS REV ARRAY TURBINE LAYOUT COORDINATES 48 FIGURE 5.8 HORNS REV TURBINES RANKING FOR NORTH WIND 48 FIGURE 5.9 HORNS REV TURBINES RANKING FOR WEST WIND 49 FIGURE 5.10 MEAN WIND SPEED FREQUENCY DISTRIBUTION (WEIBULL SHAPE FACTOR, K, AND SCALE 52 FIGURE 5.11 WIND DIRECTION ROSE 53 FIGURE 5.12 COST OF WIND FARM VS. NUMBER OF TURBINES 55 FIGURE 5.13 VESTAS V80 2MW TURBINE POWER OUTPUT AND THRUST COEFFICIENT VS. WIND SPEED [78] 57 FIGURE 5.14 GENETIC ALGORITHM PROCESS 61 FIGURE 5.15 FLOWCHART OF GENETIC ALGORITHM OPTIMIZATION PROCESS 62 FIGURE 6.1 HORNS REV LAYOUT: CASE 1 OF 270 AND 7D SPACING, CASE 2 OF 222 AND 9.4 D SPACING 64 FIGURE 6.2 HORNS REV EVALUATION WIND DIRECTION 270 AND WIND SPEED 8.5 M/S +/- 0.5 M/S 65 FIGURE 6.3 HORNS REV EVALUATION WIND DIRECTION 270 AND WIND SPEED 12 M/S +/- 0.5 M/S 66 FIGURE 6.4 HORNS REV EVALUATION WIND DIRECTION 222 AND WIND SPEED 8.5 M/S +/- 0.5 M/S 67 FIGURE 6.5 HORNS REV EVALUATION WIND DIRECTION 222 AND WIND SPEED 12 M/S +/- 0.5 M/S 68 FIGURE 6.6 POWER CURVE FOR THE TURBINE AT HORNS REV 70 FIGURE 6.7 TURBINES POWER AT CASE 1 FOR WIND SPEED AT 8M/S AND DIRECTION 270 AT HORNS REV 70 FIGURE 6.8 TURBINES POWER AT CASE 1 FOR WIND SPEED AT 10M/S AND DIRECTION 270 AT HORNS REV 71 FIGURE 6.9 TURBINES POWER AT CASE 2 FOR WIND SPEED AT 8M/S AND DIRECTION 222 AT HORNS REV 71 FIGURE 6.10 HORNS REV ARRAY. EXACT ROW (ER=270 ) OF TURBINES [60] 74 FIGURE 6.11 NYSTED ARRAY. EXACT ROW (ER=278 ) OF TURBINES [60] 74 FIGURE 6.12 NORMALIZED POWER AT HORNS REV FOR THE FREE STREAM WIND SPEED OF 8 ± 0.5 M/S: COMPARISON OF MODELS WITH OBSERVATIONS 75 FIGURE 6.13 NORMALIZED POWER AT NYSTED FOR THE FREE STREAM WIND SPEED OF 8 ± 0.5 M/S: COMPARISON OF MODELS WITH OBSERVATIONS 76 FIGURE 7.1 WIND FARM AREA 82 FIGURE 7.2 WIND DISTRIBUTION FOR CASE 3 82 FIGURE 7.3 FITNESS VALUE OF DIFFERENT NUMBER OF TURBINES FOR CASE FIGURE 7.4 TURBINES PLACEMENT OF FOUR STUDIES FOR CASE 1: (A) MOSSETTI ET AL. [25] (B) GRADY ET AL. [27] (C) MARMIDIS ET AL. [28] (D) MITTAL ET AL. [29] (E) WALOM 84 FIGURE 7.5 FITNESS VALUE OF DIFFERENT NUMBER OF TURBINES FOR CASE 2 85 FIGURE 7.6 TURBINES PLACEMENT FOR CASE 2: (A) MOSSETTI ET AL. [25] (B) GRADY ET AL. [27] (C) MITTAL ET AL. [29] (D) WALOM 86 vi

7 FIGURE 7.7 FITNESS VALUE OF DIFFERENT NUMBER OF TURBINES FOR CASE 3 87 FIGURE 7.8 TURBINES PLACEMENT FOR CASE 3: (A) MOSSETTI ET AL. [25] (B) GRADY ET AL. [27] (C) MITTAL ET AL. [29] (D) WALOM 88 FIGURE 7.9 FITNESS VALUES OF DIFFERENT SPACING LIMITS 90 FIGURE 7.10 EFFICIENCIES OF DIFFERENT SPACING LIMITS 90 FIGURE 7.11 OPTIMAL PLACEMENTS OF FOUR SPACING LIMITS FOR 40 TURBINES 91 FIGURE 7.12 FITNESS VALUES OF DIFFERENT AREA SIZES 93 FIGURE 7.13 EFFICIENCIES OF DIFFERENT AREA SIZES 93 FIGURE 7.14 OPTIMAL PLACEMENT OF FOUR AREA SIZES FOR 40 TURBINES 94 FIGURE 7.15 FITNESS VALUE AS A FUNCTION OF TURBINE NUMBER 95 FIGURE 7.17 OPTIMAL TURBINES LAYOUTS FOR A CIRCULAR SITE AREA 96 FIGURE 7.18 OPTIMAL TURBINES LAYOUTS FOR 48 TURBINES WITH CASE 1 UNIFORM ONE DIRECTION (FROM NORTH TO SOUTH) WIND USING JENSEN WAKE MODEL AND AINSLIE WAKE MODEL. 98 FIGURE 7.19 OPTIMAL TURBINES LAYOUTS FOR 48 TURBINES WITH CASE 2 FOR VARIABLE WIND DIRECTION AND A CONSTANT WIND SPEED USING JENSEN WAKE MODEL AND AINSLIE WAKE MODEL. 99 FIGURE 7.20 OPTIMAL TURBINES LAYOUTS FOR 48 TURBINES WITH CASE 3 FOR VARIABLE WIND DIRECTION USING THE JENSEN WAKE AINSLIE WAKE MODELS. 99 FIGURE 7.21 WIND DIRECTION DISTRIBUTION FOR 12 DIRECTION SECTORS 103 FIGURE 7.22 OPTIMIZED LAYOUT FOR CASE FIGURE 7.23 ANNUAL WIND POWER ROSE WITH 12 DIRECTION SECTORS 104 FIGURE 7.24 WIND DIRECTION DISCRETIZATION FOR 16 DIRECTION SECTORS 106 FIGURE 7.25 ANNUAL POWER COMPARISON OF 16 DIRECTION SECTORS 106 FIGURE 7.26 WIND DIRECTION DISCRETIZATION FOR 72 DIRECTION SECTORS 107 FIGURE 7.27 OPTIMIZED LAYOUT FOR 72 DIRECTION SECTORS 108 vii

8 Nomenclature A Rotor disc area A n The n th wake area A rn Rotor area of the n th turbine A c The Weibull scale factor A j The Weibull scale factor of the j th wind direction a Turbine induction factor b Wake lateral width C Combination factor C T Wind turbine thrust coefficient C t The distributed thrust coefficient c 1 Constants in Larsen wake model c mw The relative mean wind speed in the wake c wf The flow speed deficit in the infinitely large wind farm cost Total cost of the wind farm D Turbine rotor diameter D eff The effective rotor diameter D M Centerline velocity deficit D mi The initial centerline velocity deficit D r The expanded downstream rotor diameter D s Empirical distance constant D w Wake width h Height of the internal boundary layer h H Turbine hub height I a The ambient turbulence intensity I a The ambient turbulence intensity in a turbine wake I T Maximum center wake turbulence intensity I w Turbulence intensity in the wake K The Weibull shape factor K j The Weibull shape factor of the j th wind direction k Wake decay constant k Wake decay coefficient N Number of turbines in the wind farm P Power output of a turbine P avail Power available from the wind P observed Observed turbine power P prediected Predicted turbine power Total wind farm power P total viii

9 R 9.5 R w s s i s c s d s f U U 1 U c U initial U 0 U 0j U U u u i u i u observed u predicted u 0 u 1 x 0 z 0 z 00 α β ε v θ j κ ρ σ U σ y σ z The wake radius at 9.5 rotor diameters downstream the turbine Rotor wake radius Normalized downstream distance by turbine rotor diameter Normalized downstream distance from the i th turbine Crosswind turbine spacing Downwind turbine spacing Turbine spacing The relative wake velocity deficit Free stream velocity at turbine height in the internal boundary layer Normalized centerline velocity deficit The initial wake velocity deficit Free stream wind velocity Free stream wind velocity of the j th wind direction The mean wind speed Velocity deficit in the wake Wind velocity in a turbine wake Wind velocity calculated by the wake model in the i th turbine wake Wind velocity calculated by the single wake model in the i th turbine wake Observed wind speed Predicted wind speed Friction velocity in the atmospheric boundary layer Friction velocity in the internal boundary layer The position of the rotor respected to the applied coordinate system Offshore roughness Wind farm roughness Constant related to the trust coefficient Wake expansion parameter Eddy viscosity The j th wind direction Von Karman Constant Air density The standard deviation of the wind speed in the wake Standard deviation of wind velocity in y direction Standard deviation of wind velocity in z direction ix

10 Abbreviations CFD Computational Fluid Dynamics ENDOW EfficieNt Development of Offshore WindFarms ECN ER EWTS FLaP GA GH IBL KAMM LWAP MAPE MC NTUA RGU RMSD SAR SODAR WALOM WAsP WFOG Energy Research Centre of the Netherlands Exact Row European Wind Turbine Standards Farm Layout Program Genetic Algorithms Garrad Hassan Internal Boundary Layer Karlsruhe Atmospheric Mesoscale Model Large Wind Array Performance Evaluation Model Mean Absolute Percentage Error Monte Carlo National Technical University of Athens Robert Gordon University Root Mean Square Deviation Synthetic Aperture Radar Sonic Detection and Ranging Wind Array Layout Optimization Model Wind Atlas Analysis and Application Program Wind Farm Optimization using a Genetic Algorithm x

11 Acknowledgements Many people have contributed in one way or another to the completion of this work and, while I cannot name them all, I wish to express my deep gratitude to each of them. My first gratitude must go to my advisor, Dr. J. Iwan D. Alexander. He patiently provided the vision, encouragement and advice necessary for me to proceed through the doctoral program and complete my dissertation. I want to thank Iwan for his unflagging encouragement and serving as a role model to me as a junior member of academia. He has been a strong and supportive adviser to me throughout my graduate school career. In addition, he has always given me a great freedom to work independently. Special thanks to my committee, Professors Jaikrishnan R. Kadambi, Paul Barnhart and David H. Matthiesen for their support, guidance, helpful suggestions and patience throughout the course of my research. Their guidance has served me well and I owe them my great appreciation. I am heartily thankful to Hui Yi, for her help, support and encouragement throughout my pursuit for the doctoral degree. I feel fortunate to have met you and cherish the time we spent together in US. Also, thanks to Professor Joseph Prahl for his constant help and encouragement on my study and research. Thank you, Professor Bo Li, for your advice on my dissertation and journal papers. I would also like to thank my colleagues, Yng-Ru Chen, Ying Chen, Xinyou Ke and department assistant Sheila Campbell. I enjoy the time studying and working with you. Finally, I would also like to express my gratitude to my parents for their care and support. Also thanks to my friends Jinxia Guo, Hua Zhou, Lin Chen and Zhe Yang for their support and encouragement. This work was partially supported by the Department of Energy (Award Numbers EE and DE-EE ). I would also like to acknowledge support from Case Western Reserve University s Great Lake Energy Institute. xi

12 WIND ARRAY PERFORMANCE EVALUATION MODEL FOR LARGE WIND FARMS AND WIND FARM LAYOUT OPTIMIZATION Abstract by SIMENG LI The grouping of wind turbines in arrays introduces two major issues: (1) reduced power production caused by wake wind speed deficits and (2) increased dynamic loads on the blades caused by higher turbulence levels. Depending on the layout and local wind conditions, the drop in power production of downstream turbines can easily reach 40% of the upstream turbines in fully developed wake conditions. These power drops across arrays arise due to wake wind speed deficits. Even when averaged over different wind directions, drops in power production of 8% (onshore arrays), and 12% (offshore arrays) have been recorded. In this dissertation, a large wind array performance evaluation model (LWAP) to evaluate wake effects in large wind farms is developed. The model accounts for multiple wake interactions and the effect on the vertical wind profile in the atmosphere boundary layer by the wind farm itself. The model predicts wind speed deficits at each turbine and for specific turbine power curves and assesses power for individual turbines and for the entire wind farm. The calculation method converges within seconds for a large wind farm evaluation. To assess the efficacy of the wake model, measured wind speed deficits and turbine power deficits along two wind directions and wind turbine rows in the Horns Rev xii

13 wind farm were compared with deficits calculated using the model. The mean absolute percentage error is around 2% on average in wind speed evaluation and around 4% on average in wind turbine power evaluation. Case studies predicting row-wise power deficits of turbines arrays in Horns Rev and Nysted wind farms on multiple wind directions were compared to observations. LWAP exhibits the same accuracy on power deficit evaluation as with the CFD based models such as WindFarmer, WakeFarm and NTUA and performs better than the WAsP Park model. The computing time to process an entire full wind farm (e.g., Horns Rev) is on the order of a few seconds, significantly less than the CFD based models. In addition, a wind array layout optimization model (WALOM) is proposed to simulate, evaluate and optimize wind array performance for real wind farm site. Results of optimized wind array layouts are obtained and analyzed on case studies of multiple wind distributions conditions and site conditions. It is found that the optimized results are affected by factors such as wind distribution, wind data resolution, wake model and wind farm site conditions. xiii

14 Chapter 1 Introduction 1.1 Background Wind energy is the fastest growing source of electricity and one of the fastest growing markets in the world. At the end of 2011, worldwide wind power capacity reached 238 GW, doubled in three years [1, 2]. Wind power is renewable, clean, worldwide and using little land [3]. In the year of 2010, it was reported that 430 TWh was generated by wind power, which is about 2.5% of worldwide electricity usage [4, 5]. It is expected to reach 3.35% by 2013 and 8% by 2018 [6, 7]. For the U.S. to reach 54 GW of offshore wind energy by 2030 [8], 1000 s of wind turbines (typical offshore array sizes today range from turbines) will need to be installed along the Atlantic, Pacific, and Great Lakes coasts. The cost of these developments must be competitive with traditional on-shore generation, requiring new and optimized designs now. Wind turbines, which transform wind power into electricity, are usually grouped into large wind farms, also called wind arrays, for reason of economies, such as lower transportation, installation, maintenance and land costs. However, grouping turbines causes a reduction of the power produced due to wake effects. When wind turbine extracts energy from the wind, it produces a wake of wind velocity deficit downwind the turbine, so that the power extracted by downstream turbines is reduced. Nowadays, a large wind farm may consist of several hundred wind turbines, so that wake effects are unavoidable. Recent studies found that the average power losses due to wake in a wind array are in the order of 1

15 10-20% [8]. In addition, the effect of increased fatigue loads of wind turbines operating in wakes leads to a shorter turbine lifetime [9, 10]. Figure 1.1 Aerial view from the Southeast of wake clouds at Horns Rev on February 12, 2008 [11]. Figure 1 shows a famous photograph of the Horns Rev wind farm in Denmark. It illustrates the wake by wind turbines and wake interactions in the large wind farm. During a 2

16 previous study [12] for this wind case, power losses of wind turbines downstream in the wind farm reach 40%. The ability to accurately quantify power losses associated with wind turbine wakes is an important aspect of wind farm design analysis. One source of uncertainty in estimating these losses is the effects of interacting wakes within the wind farm. Flow in the wake from a wind turbine is characterized by momentum or velocity deficits and increased turbulence levels that can adversely affect the performance of wind turbines situated downstream. Accurate prediction of wind velocity deficit and wind turbine power deficit downstream of wind turbines is crucial to the evaluation of wind farm layout. Specifically this reduction in performance is manifested by subpar power output due to decreased wind speeds as well as decreased efficiency due to fluctuating loads on the blades and tower. It is also important that a detailed understanding is developed of the relevant aspects of turbine placement within a wind farm and how that placement affects the wakes and, thus, the expected power losses from a given wind distribution. Reducing wake losses, or even reduce uncertainties in predicting power losses from wakes, contributes to the overall goal of reducing the cost of wind-farm operation while maximizing power produced. Accurate prediction of wind velocity deficit downstream of the wind turbines is crucial to the estimation of the power output and loading of a wind farm. The spatial configuration of wind turbines in a large scale wind power plant will affect the overall performance of the plant and, thus, be an important contributing factor to cost-effectiveness over the long-term. The grouping of turbines in arrays introduces two major issues: (1) reduced power production caused by wake velocity deficits and (2) 3

17 increased dynamic loads on the blades caused by higher turbulence levels. Depending on the layout and local wind conditions, the drop in power production of downstream turbines can easily reach 40% of the upstream turbines in fully developed wake conditions. These power drops across arrays arise due to wake velocity deficits. Even when averaged over different wind directions, drops in power production of 8% (onshore arrays), and 12% (offshore arrays) have been recorded (Barthelmie et al. [13]). The land requirement for wind turbines is roughly 10 hectares (2.78 acres) per MW. To date, with a few exceptions, most of the rationale behind spacing is intuitive, e.g., Patel [14] proposed 8-12 rotor diameters windward diameters crosswind. This was suggested to be inefficient by Ammara [15] who proposed a denser staggered siting scheme that would produce the same power but use less land. The placement of wind turbines in large wind turbine arrays or wind fields will, thus, affect the overall power generation characteristics of the wind field. If turbines in large arrays are not sited to attempt to maximize performance while keeping within other practical site-particular constraints that may be imposed (for example, with respect to wake interference between turbines and with respect to the prevailing winds) then sub-par performance of the individual turbines within the field may result. A good example of this is the Horns Rev (160 MW) wind field off the coast of Denmark. Certainly, one of the most heavily studied wind field Horns Rev has exposed limitations of current methods that are employed to determine turbine placement in large wind turbine arrays [16-18]. 4

18 1.2 Wake measurements and wake model The measurement and characterization of wind turbine wakes, while relatively straight forward under certain controlled laboratory conditions, i.e., scaled wind turbine models in wind tunnels or small turbines in large wind tunnels is more complicated in the field as wakes are spatio-temporally variable phenomena shifting with the direction of the wind and not amenable to meteorological measurements on a long term basis without excessive instrumentation [19]. Erection and maintenance of meteorological towers offshore is costly and so wake measurements are typically limited to measurements downstream of the prevailing wind direction. The Danish wind turbine group at RISO has made the most advances in wake measurements. Three meteorological towers erected in the vicinity of eleven turbines at the Vindeby offshore farm have permitted simultaneous measurements of wind speed in the free stream and wake for several wind directions [20]. Measurements of velocity profiles at different distances downstream from the turbines were also obtained by Barthelmie et al. [21] using ship-borne Sonic Detection and Ranging (SODAR). Types of wake measurements were also discussed by Barthelmie et al. [8]. Wake measurements have also been obtained from satellite SAR measurements by Christiansen and Hasager [22]. Wind turbine wakes have been studied for two decades and various models have been developed. These models can be divided into two main categories, namely, analytical wake models and computational or numerical wake models. An analytical wake model characterizes the velocity in a wake by a set of analytical expressions whereas in computational wake models, fluid flow equations, whether simplified or not, must be solved 5

19 to obtain the wake velocity field. Analytical models have advantages from the viewpoint of evaluating and designing wind farm performance because of its simplicity and computational speed [17]. As wakes develop downstream, they interact with the atmospheric boundary layer as well as with other wakes and are also affected by variable surface terrain. The extent of the wake and the way in which the wake evolves is dependent on a number of factors. These include the wind conditions (speed and turbulence intensity) entering the wind field (the so-called inlet conditions), the terrain, the interaction of the wake with the atmospheric boundary layer [23], the turbulence developed in the wake (wake-added turbulence) and the characteristics of the turbine (size, blade design, hub height, etc.). 1.3 Wind farm layout optimization At present, in existing wind arrays, turbines are often organized in identical rows that are separated by a convenient spacing, normally of 6-10 rotor diameters [24]. As the spacing between turbines increases, the wake losses decrease, but results in higher interturbine cabling and land costs. The problem then is to balance these competing effects by determining the distance from shore and the turbine spacing that results in lowest possible wake effects. Several attempts have been made to optimize turbine placement in wind arrays and showed that irregular arrays result in a higher energy layout than regular grids [25-37]. One of the earliest was by Mossetti et al. [25] who developed optimal placing schemes based on Genetic Algorithms (GA). It seems to be a good way to go and could be optimized to 6

20 constrain placement to maximize power output, minimize surface area occupied by the wind farm and minimize cost or maximize asset lifetimes as well as factoring in spatially variable operating points for individual or groups of turbines. Mossetti [25] also applied Jensen wake model [26] to evaluate the turbine wake. Many relevant researchers that used the similar method to optimize this problem in the wind array can be found in the literature [27-31]. However, the models in these studies for optimal wind turbine placement proposed to date are strikingly simple and lack a robust wake model capable of accounting for inter-turbine interactions. In addition, changes in operating points on the turbines power curves according to turbulence intensity etc., are not accounted for. 1.4 Dissertation Outline The dissertation is organized as follows: A review of previous work on wind turbine wake modelling and wind farm layout optimization is presented in Chapter 2. A brief review of optimization methods is also given. Chapter 3 defines and discusses the objectives of this dissertation. Wind turbine wake and wind farm related models form the core part of the work and the optimization modeling and are discussed in Chapter 4. Chapter 5 describes the methodology of the wind array performance modeling. In Chapter 6, the wind array performance evaluation model is verified against actual data obtained from Horns Rev wind array and Nysted wind array. The application of the optimization model to two wind farm layout case studies is described in Chapter 7. In addition, factors affecting the optimization are analyzed. Finally, the conclusions and ideas for future work are presented in Chapter 8. 7

21 Chapter 2 Literature Review This chapter provides the literature review and relevant background for this dissertation. Section 2.1 reviews wake models that have been widely used in wind turbine and wind farm researches. In section 2.2, models for wind farm performance evaluation and wind farm design analysis are reviewed. Section 2.3 provides the background for the wind farm layout optimization problem. 2.1 Wake models Wake models can be divided into two main categories, namely, analytical wake models and computational or numerical wake models. An analytical wake model characterizes the velocity in a wake by a set of analytical expressions whereas in computational wake models, fluid flow equations, whether simplified or not, must be solved to obtain the wake velocity field Analytical Wake models Analytical models are first introduced by Lanchester and Betz [38, 39], who derived the principles of conservation of mass and momentum of the wind flow through an idealized actuator disk that extracts energy from the wind. Jensen wake model [26] treated the wake behind the wind turbine as a turbulent wake which ignores the contribution of vortex shedding that is significant only in the near wake region. The wake model is thus derived by conserving momentum downstream of 8

22 wind turbine. The velocity in the wake is given as a function of downstream distance and it is assumed that the wake expands linearly downstream of the wind turbine. Jensen also proposed that when two wakes interact, the resultant kinetic energy deficit is equal to the sum of the kinetic energy deficits of the individual wakes at that point. The work of Katic et al. [40] expanded the previous work of Jensen and assumes the wake velocity profile is constant or a top hat profile. This assumption is justified by the fact that the purpose of the model is to estimate the energy content within the wind field as seen by downwind turbines rather than accurately describing the spatial variation velocity field. Notably, the Katic model is currently the basis of the wake model used in WAsP [41]. WAsP is a wind climate and turbine power prediction software developed by Risø and is widely used. Frandsen s kinematic model based on work completed by Larsen et al. [42], and currently included in the European Wind Turbine Standard II, is based on the classical wake theory outlined by Schlichting [43]. This model proposes a semi-analytical solution for predicting the velocity deficit within a wake in which a set of simple empirical relations are used to predict the turbulence intensity and the turbulence length scale. It assumes an axisymmetric wake within which the velocity deficit decays with downstream distance to the power of 2/3 and the turbulence intensity decays to the power of 1/3. It also suggests that the wake width increases with the downstream distance to the power of 1/3. Ishihara et al. [44] developed an analytical wake model by taking the effect of turbulence on the rate of recovery into account. They used similarity theory for the velocity profile and defined wake recovery as a function of ambient turbulence and turbine 9

23 generated turbulence. They calculated results for both offshore and onshore conditions and also at both high loading and low loading of wind turbine. These results compared well with experimental data obtained using a 1/100 scale model of Mitsubishi MWT-1000 wind turbine in a wind tunnel. The scale model used surface roughness models upstream of the wind turbine to simulate onshore conditions and a smooth upstream surface to simulate offshore conditions. Werle [45] proposed a three part wake model: an exact model for the inviscid near wake region; Prandtl s turbulent shear layer mixing solution for the intermediate wake and a far wake model based on the classical Prandtl/Swain axisymmetric wake analysis. No comparisons of the model with actual data have been published to date. Lissaman s kinematic wake model [46] predicts the effects of individual turbine wakes, based on self-similar velocity deficit profiles. The work involved both experimental and theoretical components related to co-flowing jets. The results give a full definition of the velocity profile within a wake and facilitate the prediction of the velocity deficit for a given wake radius. The growth of the wake depends on the ambient, free stream turbulence, the shear generated turbulence and the turbulence created by the turbine. The maximum velocity deficit at each downwind position is found via a control volume momentum balance, with the initial velocity deficit calculated using the thrust coefficient of the turbine Numerical Wake model There are a number of numerical wake models that range in complexity, and are used by the wind turbine industry. Early work by Templin [47] and Newman [48] described 10

24 the effects of turbines as distributed roughness elements and were developed further by Bossanyi et al. [49], Frandsen [50] and Emeis and Frandsen [51]. These models are useful when predicting the effects of large wind farms on wind flow [52]. In another type of wake model wind turbines are modeled as roughness elements [50, 52]. Frandsen combined the drag from turbine with surface drag to get the total drag. The limitation of these types of models is that the calculated total roughness is independent of wind direction and these models are best suited for predicting overall effects of large wind farms on wind characteristics. Crespo et al. [52] carried out an extensive survey of different modeling methods for wind turbine wakes. Apart from surveying various analytical wake models (discussed above) she reported the computational wake model UPMWAKE to be one of the best after comparing various models with wind tunnel measurements. Field models (also known as implicit models), in contrast to kinematic models, calculate the flow at every position throughout the wake field. The original work of this type was completed by Sforza et al. [53] and describes a wake using the linearized conservation of momentum equation in the direction of the free stream flow. The wake is assumed to have constant advective velocity, constant eddy diffusivity and a wake shape described by a parabolic approximation. Other field models have been developed by Taylor [54], Liu et al. [55], Crespo et al. [56], Ainslie [57] and, more recently, Magnusson [58]. These models involve solution of a simplified version of the Reynolds averaged Navier Stokes flow equations. They employed 11

25 an eddy viscosity turbulence model to model the turbulent mixing contributions from the shear layer and the ambient free stream turbulence Multiple wake models One multiple wake calculation method was described by Mossetti et al. [25]. Multiple wakes were accounted for by simply assuming that the kinetic energy deficit of a mixed wake was equal to the sum of energy deficits. The velocity downstream of n turbines was then calculated using the following expression 1 u 2 = (1 u i ) 2 U 0 U 0 n i=1 2.1 where u is the wind velocity for the turbine in the wake, U 0 is the free stream wind velocity, and u i is the wind velocity calculated in the i th turbine wake. This approach to accounting for multiple wakes was also applied in other studies [27-31]. However, Li et al. [32] showed that predictions with this method were not in agreement to the measured wind speed deficits at Horns Rev array. Another method was developed by Frandsen et al. [15] who presented a wake expansion model developed by taking the control volume analysis of the momentum flow. This model was used in WAsP engineering model for the wake evaluation [41]. The wind speed at the n+1 downwind turbine can be found from U n+1 = 1 A n A n+1 1 U n 1 C T 2 A rn A n+1 A n

26 where C T is the thrust coefficient, A n is the n th wake area and A rn is the rotor area of the n th turbine. The limitation of this model is that it applies only to a single row of equally spaced turbines aligned parallel to the wind direction. To describe real wind farms an extension of the approach to account for an irregular wind array layout is needed. In addition, any evaluation of multiple wake effects on the performance of the wind farm needs to consider a representative description of the distribution of expected wind speeds and directions for a given geographic location, i.e., a large number of discrete wind directions and wind speeds. Finally, the required computational time must to be sufficiently low to allow for efficient computation of wind farm layout optimizations. 2.2 Wind farm performance evaluation models In this section, four models for the wind farm performance evaluation model are introduced. They are the Wind Atlas Analysis and Application Program (WAsP), the GH WindFarmer, the ECN s WAKEFARM and the NTUA model [41, 59-65]. WAsP is based on a linearized model used in the European Wind Atlas. The WAsP program [41] is a series of models that developed from site measured wind data at a generalized wind climate and hence is restricted to location specific descriptors of the flow climate. In terms of wind farm modelling, the Park wake model [40] is used in the commercial version. A new wake model with Mosaic tile is being developed for use within WAsP which is described by Rathmann et al. [59]. The program utilizes the observed wind data by fitting it to a two parameter Weibulll distribution. The main advantage of the WAsP 13

27 program is that it is fast and robust. It is reported that for running a full wind farm simulation as Horns Rev wind farm, WAsP takes the order of minutes [60]. However, in the model, turbulence is not specifically treated for the wind farm. Garrad Hassan (GH) WindFarmer is a CFD based model [61]. It applies an empirical representation of the wind turbine wake developed by Ainslie [57]. Empirical expressions are applied to model turbulence intensities in the turbine wake and the superposition of multiple wakes. Multiple wakes are determined by a consecutive downstream modelling of individual wakes. In addition, for very large wind farms, the change of the vertical wind profile as a result of the presence of wind turbines is modeled [62]. The computation time for a full wind farm simulation for this model was reported as minutes [60]. ECN s WAKEFARM model is developed from the UPMWAKE code and was developed by the Universidad Polytecnica de Madrid [63]. This model is similar to the GH WindFarmer model, but is extended to 3D. The wake model is computed using a 3D parabolized Navier- Stokes code and applies a k-epsilon turbulence model. The parabolisation of equations leads to an efficient calculation procedure, but for the near wake, an empirical velocity profile is required to for initialization. The axial pressure gradients are assumed as external forces and enforce the flow to decelerate. Because it computes a 3D flow filed for the simulation of wind farms such as Horns Rev, several hours are needed to converge [60]. The NTUA CFD model is developed by National Technical University of Athens and is based on the 3D Reynolds averaged incompressible Navier-Stokes equations [64, 65]. The model applies the k-epsilon turbulence closure model and accommodates wind turbines embedded in the grid as momentum sinks representing the thrust force applied on the 14

28 rotor disk. This model needs much more computation than models discussed above. It is reported that it requires a time scale of days for the Horns Rev wind farm simulation [60]. 2.3 Wind farm layout optimization problem The spatial configuration of wind turbines in a large scale wind power plant will affect the overall performance of the plant and, thus, be an important contributing factor to its cost-effectiveness over the long-term. The placement of wind turbines in large wind turbine arrays or wind fields will affect the overall power generation characteristics of the wind field. If turbines in large arrays are not sited to attempt to maximize performance while keeping within other practical site-particular constraints that may be imposed (for example, with respect to wake interference between turbines and with respect to the prevailing winds) then sub-par performance of the individual turbines within the field, and, thus, the field itself, may result. The land requirement for wind turbines is roughly 10 hectares (2.78 acres) per MW. To date, with a few exceptions, most of the rationale behind spacing is intuitive e.g., Patel [17] proposed 8-12 rotor diameters windward diameters crosswind. This was suggested to be inefficient by Ammara [18] who proposed a denser staggered siting scheme that would produce the same power but use less land. Most approaches to placement of wind turbine within large arrays are based on simplified wake models that account for different levels of interaction between turbines. In recent work, particularly that by Frandsen, there have also been attempts to bring in more meteorological based models [15] (in this case the Karlsruhe Atmospheric Mesoscale Model, 15

29 KAMM) to assist in assessing the efficacy of given wind turbine array configurations. When compared to Horns Rev data, this was found to lead to improvements in predictive ability but the reader is cautioned that that this approach may not translate well to different locations and conditions. Other researchers have attempted to optimize the placement of wind turbines in wind farms. The first (published) attempt was made by Mossetti [25] who used genetic algorithm for optimization. Mossetti s idea was to develop optimal placing schemes based on genetic algorithms. This seems to be a good way to go and could be optimized to constrain placement to maximize power output, minimize surface area occupied by the wind farm and minimize cost or maximize asset lifetimes as well as factoring in spatially variable operating points for individual or groups of turbines. The key physical ingredient in Mossetti s model was the wake model. He used utilized Jensen s model [26]. Three different cases were analyzed. The same problem was tackled by Grady et al. [27] who improved upon Mossetti s analysis by accounting for non-uniform and variable winds. From their study it is apparent that there is great sensitivity to the assumptions made in the analysis. Grady showed that Mossetti s results were not optimum and gave improved results. However, there are some inconsistencies in the reported results. Marmidis [28] attempted the problem of optimal placement using a Monte Carlo (MC) method for optimization. He analyzed only one case out of three cases analyzed by Mossetti and Grady. The biggest problem with his adaptation of the MC approach is the size of the parameter space to be scanned and the slow approach to a minimum. 16

30 Wan et al. [34] improved previous works by using a Weibull function to describe the probability of wind speed distribution and an improved turbine speed-power curve to estimate turbine power output. Kusiak et al. [30] extended this problem by using a multi-objective evolutionary strategy algorithm. They achieved the optimization problem which maximized the expected energy generation, and also minimizes the constraint violations. Mittal et al. [29] developed a code Wind Farm Optimization using a Genetic Algorithm (WFOG) for optimizing the placement of wind turbines in large wind farms by using Jensen wake model [26] and the Fuga wake model developed by Ishihara et al. [44]. Mittal also used a refined grid for the possible turbine position. It allowed more flexibility in the placement of wind turbines. It was reported that the Fuga wake model estimated the velocity in the wake more accurately than the Jensen model. Chen et al. [37] focused on optimizing the wind farm layout of turbines with different hub height and under the uncertainty with landowner s financial and noise concerns. Their work improved transparency-of-information that can potentially affect the negotiation process between developers and landowners during early wind farm planning for the onshore site. 17

31 Chapter 3 Objectives The overall objective of this research is to create a simulation tool suitable for characterization of the in-situ operating environment within an offshore wind farm. The tool will supply quantitative information necessary for wind turbine and wind farm design, and power production estimates, and also optimize wind array layout to maximize power production. 3.1 Wind array performance evaluation Accurately predicting the wind and is a necessary part of assessing the power production potential of a given layout of turbines in the wind array area and is crucial for the success of any wind farm project. For multi-turbine arrays, this includes modeling of wind distribution, power curve and wake losses caused by one or more upwind turbines. Reducing wake losses, or even reduce uncertainties in predicting power losses from wakes, contributes to the overall goal of reducing the cost of wind-array operation while maximizing power produced. In this dissertation the goal is to develop a wind array performance evaluation model which is fast and suitable for the large wind farm design. A multiple wake model was developed by only considering the wake of the nearest upstream turbine and its operating conditions which are affected by other upstream turbine wakes. The model was developed from the flow momentum theory of the Jensen wake model [26], see also Chapter 4. This approach requires much less calculation than two multiple wake models discussed above 18

32 and can be easily applied to regular or irregular wind array layout for multiple wind directions. 3.2 Wind farm layout optimization The models for optimal wind turbine placement proposed to date are strikingly simple and lack a robust wake model capable of accounting for the effects of wakes from neighboring turbines. In addition, changes in operating points on the turbine power curve according to turbulence intensity etc. are also not accounted for. The wind distribution forwarded by Mossetti et al. [25] only considered three different wind speeds and assumed an oversimplified angular distribution. The potential for improvement is high if only by applying actual observed wind data with different real site and applying simultaneous consideration of how factors such as wind distribution, wake model, optimization algorithms and site area limitation will affect optimization results. The wind farm layout optimization analyzes turbine positioning, power production, turbine layout and installation and operating costs in a wind array. The goal is to maximize the power per unit cost. In this study, a comprehensive model will be developed in which turbines positioning is optimized, evaluated and analyzed under simulated various real wind farm circumstance. Factors affecting the optimization and evaluation such as wind distribution resolution, wake model, wind farm site limitation and turbine type will be analyzed to improve the reliability of the program. The objective is to provide an offshore wind array optimization tool suitable for characteristic of any offshore array site. It analyzes the performance of wind turbines within 19

33 the array for given external wind distributions and optimizes the array layout to maximize array power production per unit cost. It is expected to find some patterns of turbine placement that can obtain more power on various wind farm sites. 20

34 Chapter 4 Wake models As wakes develop downstream, they interact with atmospheric boundary layer as well as with other wakes and are also affected by variable surface terrain. The extent of the wake and the way in which the wake evolves is dependent on a number of factors. These include the wind conditions (speed and turbulence intensity) entering the wind field (the socalled inlet conditions), the terrain, the interaction of the wake with the atmospheric boundary layer [15, 66], the turbulence developed in the wake (wake-added turbulence) and the characteristics of the turbine (size, blade design, hub height, etc.). Figure 4.1 Wake profile downstream a turbine As wind passes through the region swept by the blades, over the nacelle and past the tower, the energy extracted by the wind turbine reduces the wind speed. Figure 4.1 shows an idealization of the turbine wake. The near wake behavior is different from the far wake region. 21

35 The wind speed measured immediately downstream of a turbine is significantly lower than the free stream velocity. At near hub-height, the air in the wake is more turbulent. This wake is characterized by the relative velocity deficit [26] U = U 0 U(x) U where U(x) is the velocity in the wake at a distance x downstream from the originating turbine and U 0 is the free-stream velocity. The wake velocity U(x) and U 0 are obtained from meteorological data measured at fixed points in and around the wind field. Another significant characteristic of the wake is its turbulence intensity [66] I w = σ U U 4.2 where U is the mean wind speed (in the wake) and U is the standard deviation of the wind speed in the wake. Turbulence intensity will affect wind turbine performance and different I w can result in different wind turbine power curve characteristics for the same wind speed [66]. Compressibility as wind moves through the plane of the rotor is negligible and the velocity reduction across the rotor plane results in a downstream conically expand wake. The wake continues to expand downstream and, for flat terrain, interacts with the ground when the wake radius equals the turbine hub height. Frandsen et al. [15] reported that this occurs at a typical distance of ten rotor diameters downstream. Turbulent diffusion of momentum from the free stream occurs due to the initially large velocity gradient and as the air moves downstream the velocity deficit diminishes. 22

36 Wind turbine wakes have been studied for two decades and various models have been developed. These models can be divided into two main categories, namely, kinematic wake models (analytical wake models) and field wake models (computational or numerical wake models). A kinematic wake model characterizes the velocity in a wake by a set of analytical expressions whereas in field wake models, fluid flow equations, whether simplified or not, must be solved to obtain the wake velocity field. In what follows past work on wake models relevant to wind turbines is discussed. The models range from simple linear wake models that simply account for downstream attenuation of wind speed in the near wake region to reattainment of the free stream speed in the far wake, to more sophisticated computational fluid dynamics based models that can account for wake turbulence and in some cases uneven topography. 4.1 Kinematic Wake Models Kinetic wake models are developed from the momentum equation to model the velocity deficit in the wake behind a turbine. The wake descriptions usually do not consider the near wake region (less than two turbine diameters distance downwind a turbine). They also do not account for the change in turbulence intensity in the wake. Thus they have to be combined with a turbulence model if it is required to account for values of the turbulence intensity throughout the wind farm. Kinetic wake models are simple and computationally economic in that they can be easily implemented within large scale for calculations of large wind farm performance. 23

37 4.1.1 Jensen wake model The so-called Jensen model is one of the oldest and simplest wake models and developed by N.O. Jensen [26]. It has been used in several studies that employ a wake model in algorithms that attempt to optimize the cost per unit power by seeking the optimizing placement of wind turbines within a given area. He treated the wake behind the wind turbine as a turbulent wake which ignores the contribution of vortex shedding that is significant only in the near wake region. The wake model is thus derived by conserving momentum downstream of wind turbine The velocity in the wake is given as a function of downstream distance and it is assumed that the wake expands linearly downstream of the wind turbine. The width of the wake is given by D w = D r (1 + 2ks) 4.3 and the velocity in the wake u is given by u = U 0 [1 1 1 C T (1 + 2ks) 2 ] 4.4 where C T is turbine thrust coefficient, k is Wake Decay Constant and s=x/d is relative downstream distance. The value of k is generally taken to be for land cases, and 0.05 is recommended for offshore cases [41]. D r is expanded downstream rotor diameter of turbine diameter D of the form D r = D 1 a 1 2a 4.5 Katic et al. [40] expanded the previous work by Jensen, describes the wake velocity profile as constant or top hat profile which is justified by the fact that the purpose of the 24

38 model is to estimate the energy content within the wind field as seen by downwind turbines rather than accurately describing the spatial variation velocity field. Notably, the Katic model is currently the basis of the wake model used in WAsP. WAsP is a wind climate and turbine power prediction software developed by Risø. It is also included in Garrad Hassan WindFarmer and WindPRO [59-61] Larsen model The model developed by G.C. Larsen [42], also known as the EWTS-II model (used in WindPRO), is based on the Prandtl turbulent boundary layer equations. A self-similar velocity profile is assumed and Prandtl s mixing length theory [43] is used to get a closed form solution. The flow is further assumed to be incompressible, stationary and of no wind shear, and thus the flow is axisymmetric. Larsen showed both a first-order and a second-order approximate solution to the boundary layer equations [67], of which the last one is capable of resolving the double dip in the velocity deficit profile of the near wake. The following equations for the, rotor wake radius R w and the axial velocity deficit in the wake ( U) 1 are obtained R w (x) = π 5 (3c1 2 ) 1 5(C T A(x + x 0 )) ( U) 1 (x, r) = U 9 (C TA(x + x 0 ) 2 ) 1 3[r 3 2 3c 2 1 C T A(x + x 0 ) π 10 (3c1 2 ) 1 5]

39 Two unknown constants, c 1 is respectively related to the Prandtl mixing length and x 0 is the position of the rotor which respect to the applied coordinate system. Following relations are given by Larsen [42], c 1 = D 5 1 eff π 2 (CT A x 0 ) x 0 = 9.5D ( 2R 9.5 D eff ) Where the effective rotor diameter D eff is calculated by from [30] D eff = D C T 2 1 C T 4.10 And R 9.5 is the wake radius at 9.5 rotor diameters downstream the turbine is taken With an empirical relation [42] R 9.5 = 0.5[R nb + min (H, R nb )] 4.11 R nb = max (1.08D, 1.08D D(I a 0.05)) Frandsen analytical model Frandsen s model, also known as Riso s analytical model [15], is designed to estimate wake behavior across an entire wind farms rather than individual turbines. It is based on conservation of the momentum deficit in the wake. The model distinguishes three different wake regimes: a single wake regime, two neighboring interacted wake flow regimes and a wake flow regime that is in balance with the atmospheric boundary layer. 26

40 In single wake case, the velocity deficit is determined as u = 1 2 U 0 ± U 0 2 A 0 A C T 4.13 where A 0 is the turbine rotor swept area immediately downstream of the rotor, and A is the area of the wake. The expansion of the area of the wake for the single wake case is given by where D 1 = D 0 (β 3/ αs f ) 1/3 β = C T 1 C T 4.15 and α is a constant related to the thrust coefficient, which describes the initial wake expansion and s f is the turbine spacing. In the case of multiple wakes, the wakes are divided in several sections each having a constant but different velocity deficit. In order to calculate the mean wind speed over the rotor area, a semi-linear method is applied. For details see the paper by Rathmann et al. [59]. 4.2 Field Wake Models Field models (also known as implicit models), in contrast to kinematic models, calculate the flow at every position throughout the wake field, by solving the Reynoldsaveraged Navier-Stokes equations with a turbulence model for closure. The following are two best known field models. 27

41 4.2.1 Ainslie wake model The Ainslie wake model is a two-dimensional field model [57]. The model assumes that the wake profile is axisymmetric and assumes a Gaussian profile at the two rotor diameters downstream from the turbine. The flow is considered to be incompressible with no external forces. Beyond the first two diameters, the gradients of mean quantities in the axial direction are neglected as they will be much less than the gradients in the radial direction [57]. The flow can then be described with a two-dimensional Reynolds equation in the thin shear-layer approximation without viscous terms, as following U U V + V x r = ε v r ( U r + r 2 U r 2 ) 4.16 U x = 1 V r + V 4.17 r r here ε v is the eddy-viscosity and used for closure. These two equations are solved numerically starting from the near wake with an empirical wake profile. The initial centerline velocity (at x = 2D) deficit D mi is given by equation D mi = C T 0.05 (16C T 0.5) 1000 I a 4.18 where C T is the wind turbine s thrust coefficient (a function of the upstream wind speed) and I a is the free stream turbulence intensity. The wake width b which increases with downstream distance is related to the thrust coefficient C T and centerline velocity deficit D M 3.56C T b = 8D M (1 0.5D M )

42 the form Given a wake width b and a Gaussian shape by the wind velocity in the wake U is of 1 U U 0 = D M e 3.56(r/b) here U 0 is the free stream velocity and r is the distance from the centerline. The effects of turbulence and turbine operation (described in C T ) are included in the model. A lower turbulence intensity leads to a slower wake recovery. Higher C T leads to a stronger near wake. Software packages that apply the Ainslie wake model include WindPRO, GH WindFarmer, FLaP. The Ainslie model was adapted by Anderson [68] who developed a simplified solution. He substituted equation (4.17) and equation (4.20) into equation (4.16) and obtained here the normalized centerline velocity is du c dx = 16ε v(u 3 c U 2 c U c + 1) 4.21 U c C t U c = (1 D M ) 4.22 The system (4.16) - (4.17) now reduces to a first order differential equation (4.21) which can be solved efficiently by a simple numerical integration scheme. In our study, we applied this simplifying method and decreased computing time two orders of magnitude Three-dimensional field model ECN Wakefarm model 29

43 The ECN model is based on the UPMWAKE model developed by Crespo et al. [69]. The model is a 3D parabolized Navier-Stokes code for the far wake using a k-ε turbulence model. The near wake model is solved by momentum theory and some empirical corrections. The increase of momentum at infinity is subtracted from the undisturbed wind profile. The near wake profile is u(z) = (1 2a)U 0 (z) 4.23 where a is designated to the axial induction factor in the rotor plane. Similar to Jensen wake model, the velocity decrease is assumed to be constant with the expanded rotor diameter D r D r = D 1 a 1 2a 4.24 The near-wake velocity deficit is defined as Gaussian in shape initial at 2.25D U initial (z) = 1.3(1 1 C T )U 0 (e 0.5(y/rσ y) 2 e 0.5((z H)/rσ z) where the factors σ z and σ y are defined as σ z,y = D r 2D Elliptic field models Researchers at Robert Gordon University (RGU) have developed a fully elliptic turbulent three-dimensional Navier-Stokes numerical solver with k-ε turbulence closure during the ENDOW project [63] based on a previous axisymmetric model by Magnusson et al. [64]. Initial data required to start the 3D-NS calculations are the velocity and turbulence 30

44 intensity profiles in the atmospheric boundary layer upstream of the rotor. The computational domain includes the rotor of the wind turbine, which is approximated by means of a semipermeable disk to simulate the pressure drop across a real rotor disk. The computational time is much longer for this model compare to other model [70]. 4.3 Wake added turbulence models As mentioned earlier, some wake models have to be combined with turbulence intensity when used for wake calculations. In our work, we used the Frandsen model/iec standard [71] to calculated added turbulence in wakes. The model assumes the following: if the distance separation between two wind turbines in a wind farm is more than 10 rotor diameters, wake effects on turbulence intensity can be neglected. If the separation is less than 10 rotor diameter, the wake effects on the added turbulence have to be calculated following equations. Wake added turbulence intensity, which Frandsen calls effective turbulence, is given by I eff = (1 p w N)I m a + p w N I m T (s i ) N 1 m 4.27 i=1 where m is the Wohler curve exponent depending on the material of the structural component under consideration N is the number of neighboring turbines (nearest and next nearest neighbors) p w is the wake probability and is taken to be 0.04 s i is the distance to the neighboring turbine i 31

45 I a depends on the considered load case and the maximum center wake turbulence intensity I T is given by 1 I T = + I2 a s i U 0 The wake of a turbine that is upstream another turbine from the point of view of the turbine in consideration is not taken into account. So in a rectangular array configuration, the possible number of nearest and next nearest neighboring turbines is 8, see also Figure 4.2. Figure 4.2 Turbines taken into consideration when calculating added turbulence Inside large wind farms, the wind turbines tend to generate their own ambient turbulence. Thus, when (a) the number of wind turbines from the considered unit to the 32

46 edge of the wind farm is more than 5, or (b) the spacing in the rows perpendicular to the predominant wind direction is less than 3 rotor diameters from each other, a different value for ambient turbulence intensity, I a, is calculated by I a = 1 2 I w 2 + I a 2 + I a 4.29 I w = s rs f C T 4.30 The values s r and s f are the relative spacings in the rows and between the rows of turbine in wind array 33

47 Chapter 5 Methodology This chapter describes the Wind farm performance evaluation and layout optimization model used in subsequent chapters. The motivation for developing the model is to enable the characterization of the in-situ operating environment within an offshore wind array to supply quantitative information necessary to determine optimal turbine array layout and even guide wind plant control/operation and power production estimates. In previous chapters, the development of model approach that can provide quantitative characterization of the in-situ operating environment throughout the array with sufficient resolution to capture the essential dynamics within the array to quantify performance have been presented and discussed. In the chapter, the wind array configurations are simulated, wind data or wind distribution is processed to describe the annual average wind condition and wake models are used to evaluate wake losses. In addition, a new multiple wake model and a wind farm roughness model were developed by measured data from Horns Rev wind farm and Nysted wind farm. It only needs a simple computation scheme for any complex multiple wakes case, but its result is promising. An optimization model is also created in a Matlab code and applies Matlab Global Optimization Toolbox to optimized wind array turbine placement layout. 5.1 Large wind array performance evaluation model (LWAP) In this section, a new model for large wind array performance evaluation to evaluate wake effects in large wind farms is developed. To distinguish it from other models it is 34

48 referred to as the LWAP or the LWAP model. The LWAP applies a single wake model such as the Jensen wake model or the Ainslie wake mode, and accounts for multiple wake interactions and the effect on the vertical wind profile in the atmosphere boundary layer by the wind farm itself. The LWAP predicts wind speed deficits at each turbine and for specific turbine power curves and assesses power for individual turbines and for the entire wind farm. The calculation method converges within seconds for a large wind farm evaluation. The calculation scheme of the model comprises the following steps: Apply wind data (speed, direction and turbulence intensity) over the wind farm site. Place the wind turbines in the wind farm and calculate the new free stream wind velocity due to the increased surface roughness in the atmospheric boundary layer caused by the presence of the wind farm. Input this new free stream velocity into a combination of a single wake model and a multiple wake model to evaluate the wake deficits in the wind farm. The single wake models are introduced in Chapter 4. Here the multiple wake model and the model for the evaluation of the effect by the wind array on the atmospheric boundary layer are developed. A Matlab code was developed for this simplified model that is suitable for wind farm evaluation. In order to save computational time for the Ainslie implicit model, a simplified solution for the model by Anderson [68] was used, and wind speed deficits in the field of the single wake were calculated and saved as a data base for using for wake deficits evaluation. The code requires much less computational time than 35

49 CFD based wind farm evaluation models, but the accuracy is not sacrificed. For comparative purposes both the Jensen wake model and the Ainslie wake model were used as the single wake model to predict wind speed deficits and turbine power deficits that were compared to observations from the Horns Rev and Nysted wind farm Multiple wake model A simplified multiple wake model is developed by considering the wake of only the nearest upstream turbine and its operational condition (wind speed, thrust coefficient and turbulent intensity). The following assumptions were made: The nearest upstream turbine always dominates in multiple wake effects. Wind turbine operating conditions and the extra flow momentum exchange between multiple wakes and with the free stream will affect or contribute to downstream wake recovery. The effect of overlapped wakes was a combination of momentum flow from a single turbine wake and interaction with the free stream which can be attributed to the higher momentum exchange. Thus the wind speed in the i th overlapped wake, u i, is u i = Cu i + (1 C)U where U 0 is the free stream velocity, u i is the velocity calculated in the wake of the upstream turbine by a single wake model, and C is a combination coefficient having the value from 0 to 1. The combination coefficient C is a function of turbine downstream distance s i in that C 0 for small s i and C 1 for very large s i. 36

50 When the upstream turbine is in the wake of another turbine, the wind entering the rotor area has a lower wind velocity than the free stream. Thus, if momentum exchange with the atmospheric boundary layer is ignored the wind velocity will at most only recover to the wind speed at the upstream turbine. However, because of interactions with the atmospheric boundary layer, it should eventually recover to the free stream velocity as the distance from the turbine gets large. To determine the value for the combination coefficient C, the contribution of the free stream velocity was assessed as shown in Figure 3. The wake in this case was produced by a wind turbine in the free stream with a thrust coefficient, C T, equal to 1. This means that no free stream momentum flow could pass through the turbine. The wake velocity, (1 C)U 0, is then be calculated using equation (4.4) and gives C = 1 (1 + 2k s) where k is the wake decay coefficient for this case. Its value should be less than which is chosen for a normal wake, because there is a lower velocity gradient between the inner wake and the free stream as shown in Figure 5.1. The wake decay constant, k, shown in Figure 4, is a function of the ratio of upstream turbine velocity deficit to the free stream velocity as following k = u 1.4 i 1 U 0 and k = < u i 1 U 0 1 u i 1 U where u i 1 is wind speed at the location of upstream turbine. 37

51 Figure 5.3 shows the combination coefficient, C, calculated using equation (5.2) with different k versus normalized downstream distance s. Figure 5.4 shows the wind speed recovery calculated using the multiple wake model and the Jensen single wake model. The wind velocity in the wake(s) caused by the wind turbine will finally recover to the free stream velocity. Figure 5.1 Overlapped wakes where s 1 =7D 38

52 k' The ratio of wind velocity at upstream turbine to free stream velocity Figure 5.2 Wake decay constant, k, as a function of upstream turbine wind speed deficit Figure 5.2 shows the relationship between coefficient k and wind speed at upstream turbine. When upstream turbine is in free stream, k is zero and will increase with decreasing wind speed ratio to freestream which means higher wake effects on the turbine. 39

53 C k'=0.030 k'=0.053 k'= Normalized downstream distance Figure 5.3 Combination coefficient, C, as a function of normalized downstream distance Figure 5.3 shows C calculated by equation (5.2), relating to upstream turbine wind speed deficit and downstream distance. C is zero when downstream distance is zero, because there is no space where the wake can interact with free stream. With downstream distance increasing, C is increasing as the wake accumulates more free stream kinetic energy. In addition, if the upstream turbine is under higher wake effects, it can be considered to produce higher turbulence intensity. Then the increasing rate of C by the downstream distance will be higher because higher turbulence intensity means more energy exchanges. 40

54 Normalized wind velocity Turbine in freestream u1/uo=0.81 u2/uo=0.85 u3/uo= Normalized downstream distance Figure 5.4 Normalized wind velocity calculated using multiple wake model and the Jensen wake single model. Blue: turbine in the free stream. Red: Second turbine with an incident wind velocity of 0.81 of the free stream. Green: Second turbine with an incident wind velocity of 0.85 of the free stream. Purple: Second turbine with an incident wind velocity of 0.9 of the free stream. Figure 5.4 shows wind speed recovery calculated by our new multiple wake model. Wind speed recovers slower than turbine wake in the free stream especially in the near wake region. However, with downstream distance increasing (more than 3 to 4 D), the recovery rate is similar to that from single wake model and will finally recover to free stream wind speed. 41

55 5.1.2 Effect of the wind array on the atmospheric boundary layer Investigations by Frandsen [15, 66] show that standard wake models under predict wake effects. He states that the reason is that the effect a large wind farm has on the atmospheric boundary layer is not taken into account. This effect was modeled as an extended wind farm and resembles an increase in local surface roughness which results in a change in vertical wind profile. According to this theory, the infinite wind farm equivalent roughness z 00 is calculated by κ z 00 = h H exp c t + (κ/ln(h H/z0 )) where h H is the hub height, κ is the von Karman constant, z 0 is the local roughness without wind farm, and c t is the distributed thrust coefficient defined by c t = π 8s d s c C T 5.4 where C T is turbine thrust coefficient and s d and s c are the mean downwind and crosswind spacing in rotor diameters. The wind farm roughness of 0.56 will be calculated for the Horns Rev layout and 0.40 for the Nysted layout. As the wind reaches the wind farm, an internal boundary layer (IBL) is modeled by Sempreviva et al. [72] using an increase in roughness. The effect on the wind speed at the hub height for the turbine within the array is estimated from meteorological theory under the assumption that the upstream wind flow and the IBL flow are neutral logarithmic 42

56 profiles. In the model the free stream speed, U 0, for a known height, z, above the internal boundary layer height, h, can be calculated by U 0 = u 0 κ ln z z Below the internal boundary layer, h, the free stream speed, U 1, is by U 1 = u 1 κ ln z z where u 0 and u 1 are the friction velocity for the free stream above and below the internal boundary layer. And combine equation (5.5) and (5.6), it is obtained U 1 U 0 = u 1 u 0 ln (z/z 00) ln (z/z 0 ) 5.7 same, hence At the height h the wind speed above and below the internal boundary layer are the u 0 u 1 = ln (h/z 00) ln (h/z 0 ) 5.8 It follows then that when the height of the IBL grows higher than turbine hub height, the new wind speed u at turbine hub height can be calculated from equations (5.7) and (5.8) and is U 1 (h H ) U 0 (h H ) = ln (h/z 0) ln (h/z 00 ) ln (h H/z 00 ) ln (h H /z 0 ) 5.9 Frandsen et al. [15] developed a model of the growth of the internal boundary layer for the overlapped wake case in the wind farm as following h x = c mw c 1 c t h = c mw c mw 1 c t (x x o ) + h mw 43

57 where c mw is the relative flow speed in the wake, x is the downstream distance in the wind farm and x o and h 0 are to be determined. Frandsen et al. [15] suggested that the value of c mw could first approximated by the flow speed deficit in the infinitely large wind farm, c wf. Kristensen et al. [73] showed a relationship between the friction velocity before and after the roughness change as following u 1 z u 0 z Hence the flow speed deficit in the infinitely wind farm, c wf, can be calculated by c wf = U 1 = z ln (h H/z 00 ) U 0 z 0 ln (h H/z0 ) 5.12 However, Frandsen s model on the growth of internal boundary layer was developed from a wind direction that is along turbine rows. In order to account for other orientations this model is extended. Based on observed data at Horns Rev [8, 60] the following assumptions were made for our model of large wind farms: Offshore roughness height z 0 is equal to without the wind farm [66]. When a turbine is located downwind the array with a specified distance, D s, the height of the internal boundary layer reaches turbine hub height. This distance is empirically assumed of 7 turbine rotor diameters, hence the integration constant x o in equation (20) is equal to D s = 7D. Frandsen s model on the growth rate of the internal boundary layer for the wind parallel to wind turbine rows is extended for all other wind directions. 44

58 Based on these assumptions, the following empirical formula was developed for the growth of the internal boundary layer for the wind farm h x = c wf c 1 c t h(x) = c wf c wf 1 c t (x D s ) + h H 5.13 wf Figure 5.5 shows the calculated free stream speed at turbine hub height for the Horns Rev farm layout. Normalized freestream speed at turbine height Distance (m) Figure 5.5 Predicted free stream wind speeds at turbine height for the Horns Rev wind farm layout 45

59 5.2 Wind array layout optimization model (WALOM) In this section, the wind array layout optimization model is described. To distinguish it from other models it is referred to as the WALOM or the WALOM model. It uses the LWAP model to evaluate the turbine and wind farm power output. However, the multiple wake model is simplified and effect on the wind profile in atmospheric boundary by the wind farm is not considered in WALOM. Simulations of wind distribution, wind array layout and turbine properties such as power curve were demonstrated. The Genetic Algorithm method is also introduced and applied in the Matlab in which turbines positioning is optimized, evaluated and analyzed under given simulated various wind farm circumstance Wind array configuration set up The area occupied by the wind array is generally taken to be a rectangular area with Cartesian coordinate system, see Figure 5.6. No matter whatever wind array site boundary is, we can always find an appropriate rectangular to include all turbines locations. An x coordinate and a y coordinate are given to each turbine to describe its location. Note that all coordinates must be positive in our model for codes calculating wake effects. For any given wind array, all wind turbine coordinates are then determined and normalized ranging from 0 to 1. For example for Horns Rev array, turbine coordinates are shown in Figure 5.7. In this way, we can create a general code which is suitable for wake loss evaluation of any wind array configurations. 46

60 When evaluating wake effects, we first give each turbine a ranking arranged by upwind location to downwind location order. For examples, when wind is from the north direction, this ranking is ascending from north location turbine to south location turbine. However, in East wind case, the ranking starts at east location turbine and ends at most west location turbine, see Figures 5.8 and 5.9. Figure 5.6 Wind farm boundary set up 47

61 Figure 5.7 Horns Rev array turbine layout coordinates Figure 5.8 Horns Rev turbines ranking for North wind 48

62 Figure 5.9 Horns Rev turbines ranking for West wind Wind data and distribution The measurement and characterization of wind turbine wakes, while relatively straight forward under certain controlled laboratory conditions, i.e., scaled wind turbine models in wind tunnels or small turbines in large wind tunnels by Larwood [74], is more complicated in the field because wakes are spatio-temporally variable phenomena shifting with the direction of the wind and not amenable to meteorological measurements on a long term basis without excessive instrumentation [21]. Erection and maintenance of meteorological towers offshore is costly especially offshore and so wake measurements are typically limited to measurements downstream of the prevailing wind direction. The Danish 49

63 wind turbine group at RISO has made the most advances in wake measurements. Three meteorological towers erected in the vicinity of eleven turbines at the Vindeby offshore farm have permitted simultaneous measurements of wind speed in the free stream and wake for several wind directions by Frandsen et al. [20]. Measurements of velocity profiles at different distances downstream from the turbines were also obtained by Barthelmie et al. [23], using ship-borne Sonic Detection and Ranging (SODAR). Wake measurements are also discussed by Barthelmie et al., in a recent paper [8]. Wake measurements have also been obtained from satellite synthetic aperture radar (SAR) measurements by Christiansen et al. [22] Original wind data In planning wind farms, shot-time wind data plays an important role in estimating various engineering parameters, such as wake effect, power output, extreme wind load and fatigue load. Raw data (including wind speed, wind direction etc.) will be tested for validation and then be analyzed. Recording an average wind speed and wind direction of 10 minutes period is widely used. Table 5.1 is a recording sample 10 minutes average wind data measured on Lake Eire by the US Army Corps of Engineers [75]. This first wind data input method is to direct applying wind data into our program. However, tens of thousands data are created even only for one year period wind recording. Evaluating wake effects with this large number of wind cases need a lot of CPU time 50

64 Table 5.1 Wind data example Time Period Station number Wind direction Wind speed

65 Weibull wind distribution The wind variation for a site can be statistically described using a Weibull distribution [76]. Wind speed data in our study is discretized by 1m/s. Wind orientation (angular) distributions is also discretized by different direction sectors. The probability density function of the wind speed for a direction θ j sector is f(θ j, U 0j, A cj, K i ) = K j ( U 0j ) Kj 1 e (U K 0j/A cj ) j 5.14 A cj A cj where the direction-dependent Weibull parameters are K, the shape factor, A c the scale factor. Figure 5.10 Mean Wind Speed Frequency Distribution (Weibull shape factor, K, and scale factor, A c, was 2.10 and 8.33 respectively) 52

66 Figure 5.10 shows an example of the Weibull wind distribution. The wind data is from a 50m height anemometer. It shows a maximum frequency of 5.57% for the bin 6.5 to 7.0 m/s (14.5 to 15.7 mph). This is the modal point of the distribution. The average was reported earlier to fall within the bin 7.0 to 7.5 m/s (15.7 to 16.8 mph) which occurs at a frequency of 5.37%. Figure 5.11 Wind Direction Rose 53

67 Figure 5.11 is a wind direction distribution rose for wind data from Lake Erie. Prevailing winds come primarily from around southwest at nearly 45%. Southwest is the most prevalent sector of the 16 with a frequency of 10.49%. Like the overall wind speed frequency distribution, a direction wind rose cannot tell the whole story as about the wind speed distribution. For each wind direction, Weibull factors and probabilities are calculated from wind data and shown in Table 5.2. Table 5.2 Weibull factors for different wind directions [77]. Sector A c K % Mean N NNE ENE E ESE SSE S SSW WSW W WNW NNW

68 5.2.3 Cost function The cost function is needed when optimizing wind array layout problem for a given site information while number of wind turbine is also not determined. A cost function related to number of wind turbines was chosen that was also used in previous studies [27-31]. The total cost is only dependent on the number of wind turbines, N, installed in the wind farm. The non-dimensional cost of wind farm is cost = N( e N2 ) 5.15 The cost function is based on that a maximum discount of 1/3 is available when large number wind turbines are purchased. Figure 5.12 shows the total cost of wind farm based on number of turbines. Figure 5.12 Cost of wind farm vs. number of turbines 55

69 5.2.4 Turbine power Wind turbine extract kinetic energy from the wind. According to wind turbine momentum theory, the available power from the wind crossing a wind turbine for a wind speed, u, is P avail = 1 2 ρau Where A is turbine swept area and ρ is air density The turbine power output is by equation P = 2ρAu 3 a(1 a) Where a is the induction factor which is relate to turbine thrust coefficient C T C T = 4a(1 a) 5.18 Figure 5.13 shows power curve and correlated thrust coefficient for turbines installed on Horns Rev wind farm. Note that turbine cut in speed is 4m/s and cut out speed is 25m/s. When determining a turbine power output in a wind array, first effect on atmospheric boundary layer by existing wind array will be evaluated and an affected new free stream field at the turbine hub height will be calculated. Then wind turbines are checked in the upstream to downstream order that whether they are operating in the wake of any other wind turbine. If this is not the case, then power is calculated using the atmospheric boundary layer considered free stream velocity. Otherwise wind velocity at the point where the wind turbine placed is determined by applying wake model discussed earlier. 56

70 Figure 5.13 Vestas V80 2MW turbine power output and thrust coefficient vs. wind speed [78] Wake effect evaluation In WALOM model, the LWAP model is used to evaluate wake effects and predict turbine power output and the whole wind farm performance with a given array configuration. However the LWAP model used in WALOM was modified: (1) the multiple wake model was simplified that only the wake by nearest upstream turbine were calculated; (2) the effect on the wind profile in atmospheric boundary layer by wind farm itself is not considered. 57

71 5.2.6 Genetic Algorithm (GA) The so called genetic algorithm has been a popular approach so far although it is not the only option. The genetic algorithm is a stochastic global search method that evolves transformations of a coded configuration [79, 80]. Genetic information is initially stored in a chromosomal string that represents say, two individuals, and is used to create the genetic code of a new individual with its own code. During the reproduction phase, each individual is assigned a fitness value derived from its raw performance measure given by the objective function. This value is used in the selection to bias towards more fit individuals. Genetic operators manipulate the genes of the chromosomes between parent pairs by crossover and mutation, producing child generation. After recombination and mutation, the individual strings of new generation are then decoded, assigned with fitness values, and then compared. The process continues through subsequent generation. Figure 5.14 shows a simple GA operation in the optimization of wind array problems. A wind farm layout evaluation code is developed in MATLAB which calculates the power produced and the cost of a wind farm. The code is coupled with the genetic algorithm solver (referred as ga solver), available in MATLAB s genetic algorithm toolbox for optimization process. In our code, wind turbine position coordinates was developed. The number of turbines N must be fixed first, and there are 2N variables represent X and Y coordinates. In this algorithm, turbine can be placed any location compare to center of cells in previous one. Information of turbines location coordinates is initially stored in chromosomal strings that represent individuals, and is used to create the genetic code of a new individual with their own codes. For given number of turbines, the placement of 58

72 these turbines is described in the genetic string. Evolution and adaptation of the individual strings representing turbines placement will be applied and guarantee best placement individuals with higher power output for a given wind distribution. In GA judgment of better turbine placement is by the objective function, also referred to as the fitness value Objective = cost P total 5.19 The flowchart in Figure 5.15 demonstrates the process through of the code and the ga solver operates to find an optimal solution. The optimization process starts with the initialization in the genetic algorithm ga solver. In the initialization step, following parameters are specified. Number of variables: The number of variables is twice the number of wind turbines because two variables are required to specify the position of a wind turbine in a two dimensional coordinates. Population size: The population size is the total number of individual solutions that represent wind farm layouts in one evolution generation. Constraints: The constraints in the ga solver are specified as bounds i.e., lower and upper limits for the variables. The area size of the wind farm is specified in constraints so that wind turbines cannot be placed outside the wind farm region. Optimization criteria: The optimization criteria are referred to as stopping criteria in the ga solver. It include maximum number of iterations which is also referred as generations, stall generations (i.e., if average change in objective 59

73 function value over stall generations is less than function tolerance than algorithm stops) and function tolerance. After the initialization process, random set of solutions is created taking into account the constraints. All the solutions created are analyzed by the wind farm layout evaluation model. Estimated power production and the cost of the wind farm are calculated and objective function value (cost per unit power) of each solution is returned to ga solver. In the next step, the optimization criteria are checked if they are satisfied or not. When the optimization criteria are not met, all the solutions are ranked based on their objective function values. A solution with small objective function value is better as its cost per unit power is smaller and is placed before other solutions with larger objective function value. After ranking is completed, a number of solutions are selected and some new solutions are created (reproduced). This selection of solutions is affected by the ranking done in previous step and a solution with good ranking has a better chance of being selected. New solutions are created while some solutions are copied from original set of solutions to the new set of solutions. These selected a few solutions are one of the best in terms of the ranking and are called elite count. The last step before new set of generations (new population) is ready is called Mutation. In this step some random changes are made in a few solutions. This step is very important as it helps in maintaining diversity in the solution set. This new solution set is analyzed by the wind farm performance evaluation code and this iterative procedure continues until one of the optimization criteria is satisfied. 60

74 With application of a large number of evolutionary iterations, the sequential placement configurations of turbines are iterated toward an optimal. Figure 5.15 shows a flowchart of the optimization process of our work. Figure 5.14 Genetic Algorithm process 61

75 Figure 5.15 Flowchart of Genetic Algorithm optimization process 62

76 Chapter 6 Results: wind farm layout evaluation model Matlab codes for the LWAP model were developed to apply the Jensen wake and Ainslie wake models to predict wake losses at the Horns Rev wind array and Nysted wind arrays. Wind array configurations for wind farm and site information, wind distribution and offshore conditions are taken into account. Power curves and parameters corresponding to the Vestas V MW turbines located in Horns Rev and the Siemens 2.3 MW turbines located in the Nysted Array are used in the calculations. Results of wind speed deficits and turbine power deficits from multiple wind cases are evaluated and compared to observation data by Rathmann et al. [59] and Barthelmie et al. [8, 60]. Evaluations made using the model developed here are also compared to other wind farm analyzing tools such as WAsP, WindFarmer and NTUA etc. Compared to other models, our model applies simple computational schemes. For example, with a given wind Weibull distribution on 72 wind direction sectors, an overall evaluation of wind array efficiency will be processed in 2 seconds using the Jensen wake model and 10 seconds with the Ainslie wake model. 6.1 Wind speed evaluations at Horns Rev when wind direction is along turbine rows In this case, two wind directions along wind turbine rows in the Horns Rev Array are taken into consideration, shown in Figure 6.1. Wind turbine spacing is 7D in the 270 case and 9.4D in the 222 case. Wind speed deficits at turbine locations in the row are evaluated with two free stream speeds (8.5 m/s and 12m/s) and compared to observation data by 63

77 Rathmann et al. [60]. There are two groups of observation data, respectively from internal row located in the interior of the wind farm and external row located at the edge of wind farm. At these low to moderate wind speeds, the thrust coefficient is relatively high, and thus the wake effects shown are likely to be severe. Figure 6.1 Horns Rev layout: Case 1 of 270 and 7D spacing, Case 2 of 222 and 9.4 D spacing 64

78 1 Wind velocity deficit Observation Jensen model Ainslie model Turbine number Figure 6.2 Horns Rev evaluation wind direction 270 and wind speed 8.5 m/s +/- 0.5 m/s In Figure 6.2, evaluation of wind speed deficits at each turbine location from wind direction of 270 and wind speed of 8.5 m/s is obtained and compared to observation data. Results show that evaluation by Ainslie model in general under predicted wind speed deficit by about 0.01 to 0.02 of free stream velocity. The Jensen model seems to have a better prediction in this case. 65

79 Observed int. row Observed ext. row Jensen model Ainslie model Wind velocity deficit Turbine number Figure 6.3 Horns Rev evaluation wind direction 270 and wind speed 12 m/s +/- 0.5 m/s In Figure 6.3, evaluation and observation data of wind speed deficits are from wind case of 270 and 12m/s. Observations are from both internal turbine row and external turbine row. Wind speed deficits at internal turbine are less than those at external turbine. This may be because there is a more complex wake effect well inside the array, so that turbulence intensity will be higher. This means that more energy is exchanged between the turbine wakes and free stream wind. Clearly, the Jensen and Ainslie models generally over predict the wind speed deficit in the wake. Predictions are better correlated to observations 66

80 from l turbine rows on the outside of the array. The Ainslie model appears to yield better predictions than the Jensen model in this case Wind velocity deficit Observed int. row Observed ext. row Jensen model Ainslie model Turbine number Figure 6.4 Horns Rev evaluation wind direction 222 and wind speed 8.5 m/s +/- 0.5 m/s In Figure 6.4, wind speed deficits are evaluated with a wind direction of 222 and wind speed of 8.5 m/s. As discussed in Figure 6.3, observed wind speed deficits from interior turbine rows are less than those from exterior rows. This may also because of higher turbulence intensity inside the wind farm. Predictions by our model are not as good as in the 270 wind direction case. Wind speed deficits are over predicted for the first three turbines and under predicted for last two. 67

81 Wind velocity deficit Observed int. row Observed ext. row Jensen model Ainslie model Turbine number Figure 6.5 Horns Rev evaluation wind direction 222 and wind speed 12 m/s +/- 0.5 m/s In Figure 6.5, it shows that predictions for wind speed of 12m/s on 222 wind direction compared to observation. To provide a quantitative evaluation of model performance versus the observations, the mean absolute percentage error (MAPE) of the wind velocity was calculated using MAPE = 100% n n u predicted u observed i=1 u observed 6.1 where u is the wind velocity at each turbine (observed or predicted) and n is the number of turbines. 68

82 The MAPE for the predictions by the LWAP using the Jensen wake model and the Ainslie wake model versus observation data of mean wind speed are calculated in Table 6.1. It shows that observations by the LWAP using both single wake models have MAPE less than 2.2%. Predictions from exterior turbines are better correlated to observation data (i.e., exhibit lower MAPE) than interior turbines. In addition, predictions for 270 wind direction cases have lower MAPE than 222 wind direction cases. Table 6.1 MAPE of the computed normalized wind velocity using observed data for two wind directions and two wind speeds reported in [60] at Horns Rev. Wind case LWAP Jensen (%) LWAP Ainslie (%) Interior row Exterior row Interior row Exterior row 270 and 8.5 m/s and 12 m/s and 8.5 m/s and 12 m/s Average Turbine power evaluations at Horns Rev: wind direction parallel to turbine rows Wind turbine power can be predicted by evaluating the wind velocity at all turbine locations within the array and then calculating the predicted output power using a wind turbine power curve [32]. The curve shown in Figure 6.6 illustrates the one used in the model and represents a Vestas-V80 2 MW wind turbine in Horns Rev. Two wind direction cases (the 270 case and 7D spacing, the 222 case and 9.4D spacing) along wind turbine rows in the Horns Rev Array were examined. 69

83 2.5 x 106 Turbine power (w) Wind velocity (m/s) Figure 6.6 Power curve for the turbine at Horns Rev Normalized power Observation Jensen model Ainslie model Turbine number Figure 6.7 Turbines power at Case 1 for wind speed at 8m/s and direction 270 at Horns Rev 70

84 Normalized power Observation Jensen model Ainslie model Turbine number Figure 6.8 Turbines power at Case 1 for wind speed at 10m/s and direction 270 at Horns Rev Normalized power Observation Jensen model Ainslie model Turbine number Figure 6.9 Turbines power at Case 2 for wind speed at 8m/s and direction 222 at Horns Rev 71

85 Figures 6.7 and 6.8 show results of wind turbine power calculated for a wind direction of 270 and wind speeds of 8 m/s and 10 m/s. The second case is the wind direction of 222 and a wind speed of 8 m/s (chosen because there is a real data set to compare with). Results are shown in Figure 6.9. In this case, Barthelmie et al. [8] reported data of the first 5 turbines because there was a large uncertainty in the measurements due to small number of observations. The mean absolute percentage error of the normalized turbine power was calculated for each case using MAPE = 100% n n P predicted P observed i=1 P observed 6.2 where P is the normalized power to turbine power at the free stream at each turbine (observed or predicted), and n is the number of turbines. The MAPE for the turbine power are shown in Table 2. Predictions using the Ainslie single wake model have a higher MAPE in 270 wind direction cases than those using Jensen single wake model. Table 6.2 MAPE of the computed normalized turbine power using computed predictions and actual observations at Horns Rev [58]: wind direction parallel to turbine rows. Wind LWAP Jensen (%) LWAP Ainslie (%) 270 and 8m/s and 10m/s and 8m/s Average

86 6.3 Power output predictions for turbines in the row at the Horns Rev and Nysted for a representative wind speed and variable wind directions Detailed case studies of turbine power losses due to wakes at the Horns Rev and Nysted wind farms were analyzed. The major difference between the two wind farms is the turbine spacing, with 7 7D at Horns Rev and D at the Nysted. The average power at each turbine was calculated for seven wind directions: a wind direction where the flow is down an exact row (ER) including observations within ± 2.5 (270 ± 2.5 at Horns Rev, 278 ± 2.5 at Nysted), and six directions of ER + 5, + 10, + 15, - 5, - 10 and - 15, as shown in Figures 6.10 and The observed data were reported by Barthelmie et al. [60] and results by wind farm layout evaluation models such as WAsP, WindFarm, WakeFarm and NTUA were also reported and analyzed. As shown in Figure 6.12 and 6.13, results from Horns Rev and Nysted illustrated an acceptable agreement between predictions and observations in most directions except 255 in Horns Rev and ER ± 5 in both Horns Rev and Nysted arrays. It was reported that in 255 wind direction at Horns Rev the asymmetry in the observations may not reflect real case and it could be a data issue due to insufficient observations [60]. 73

87 Figure 6.10 Horns Rev Array. Exact Row (ER=270 ) of turbines [60] Figure 6.11 Nysted array. Exact Row (ER=278 ) of turbines [60] 74

88 Figure 6.12 Normalized power at Horns Rev for the free stream wind speed of 8 ± 0.5 m/s: comparison of models with observations 75

89 Figure 6.13 Normalized power at Nysted for the free stream wind speed of 8 ± 0.5 m/s: comparison of models with observations 76

90 In order to compare predictions by the model to reported results of other wind farm layout evaluation models, the root mean square deviation (RMSD) of the normalized turbine power was calculated for each case using [60] RMSD = n P observed P predicted ) 2 i=1 n 6.3 The RMSD of the turbine power predictions by models versus observation data of the mean turbine power by various wind directions and wind speed of 8 m/s at Horns Rev and Nysted wind farms are given in Tables 3 and 4. In general, predictions in by the LWAP using either the Jensen and Ainslie single wake model have the same accuracy, with the overall RMSE of 0.08 by using the Jensen model compare to 0.07 by the Ainslie model in Horns Rev case. The overall RMSE for Nysted wind farm are 0.05 computed using the Jensen model and 0.04 b using the Ainslie model. However, results computed using the Jensen model show that there are large discrepancies between predictions and observations at Horns Rev for a 265 and 275 wind direction cases and also for the Nysted 283 wind direction case. This is likely due to the uniform wind velocity distribution in Jensen wake model which tends to desensitize the sensitivity of this model to wind direction. Compare to the RMSD by other wind farm layout evaluation models, the LWAP performs better (i.e., exhibit lower RMSD) than WAsP. These predictions also have little RMSD difference compare to CFD based models such as WindFarmer, WakeFarm and NTUA. However, the run times for the LWAP applied to a full wind farm simulation like Horns Rev wind farm is only a few seconds. This is significant less than reported time for running in the CFD based WindFarmer, WakeFarm and NTUA [60]. 77

91 Table 6.3 RMSD of the computed normalized power for various wind directions and a wind speed of 8 m/s at Horns Rev wind farm [60] Horns Rev: 8.0 ± 0.5 m/s Direction( ) WindFarmer WakeFarm WAsP NTUA LWAP - Jensen LWAP - Ainslie All Table 6.4 RMSD of computed normalized power for various wind directions and a wind speed of 8 m/s at Nysted wind farm [60] Nysted: 8.0 ± 0.5 m/s Direction( ) WindFarmer WakeFarm WAsP LWAP - Jensen LWAP - Ainslie All

92 Chapter 7 Results: wind farm layout optimization In this chapter, the wind array layout optimization model (WALOM) is applied with Genetic Algorithm method to the wind farm layout optimization problem. Wind turbine layout is optimized by a given site information and wind distribution, while wake effects are minimized and therefore the expected power production is maximized. Two approaches were implemented. One approach is an extension of the previous work started by Mossetti et al. [25], in which a 2km 2km square wind farm site area is considered. Mossetti also assumed a simple wind distribution with a higher frequency for some directions and applied the Jensen wake model in the calculation. In this work the Mossetti approach was extended by developing a new turbine placement coordinates and considering effect on the results by factors as turbine spacing limit, area size and wake models. Results from this approach are shown in section 7.1. Section 7.2 describes the second approach which is from the view point of the existing or potential wind farm layout design. Unlike the approach discussed in section 7.1, the wind data, site area, turbine properties etc., from a real wind farm site were used. Weibull distributions were applied and turbulence intensities of wind were also factored into the model. A real wind turbine power curve was used to convert wind speeds to power. 7.1 Extension of Mossetti s approach Three cases for an area of 2 km 2 km square were investigated from section to section Case 1 is a simple example for a uniform wind direction with a free stream velocity of 12 m/s, shows in Figure 7.1. There are two reasons for looking at this, one is to 79

93 compare and validate against previous work and two, understand the effects of parameter variation in the model. For Case 2 the wind direction is variable and the free stream velocity is constant at 12 m/s. There is an equal probability that wind blows from any direction. The wind direction is discretized in 36 segments each measuring 10. Case 3 is variable wind direction and variable wind speed case. Figure 7.2 shows the wind distribution in this case. Three wind speeds are possible, 17, 12 and 8 m/s. The probability is higher for wind directions between 270 o to 350 o. The optimization for wind Case 1 (uniform one speed wind) was also applied for different wind turbine spacing limits (the smallest distance between two turbines) and area sizes (2 km 2, 4 km 2, 8 km 2 and 16 km 2 ). Results are shown in sections and In section 7.1.6, the optimization was applied to wind Case 2 (equal probability variable wind direction with a constant wind speed) with a round shape wind farm site area. The reason for studying on this is that it is expected to find some optimized layout pattern for the turbine layout under isotropic wind distribution and isotropic site shape area. In section 7.1.7, optimized turbines layouts using the Jensen and Ainslie wake models were calculated and compared for the model three wind cases presented above Case 1: Constant unidirectional wind The optimization was carried out for different numbers of turbines (N). For each N, there is an optimal configuration. The space limit between two turbines is such that two turbines should not occupy the same 100m 100m square. Figure 7.3 shows optimal fitness values for different N. The limiting value of fitness is the situation when there is no wake 80

94 effect for all turbines so that a maximum power is produced. It is noted that when N increases, the difference between the optimal fitness value and the limiting value increases. The optimal result is when N=48 and is compared with previous studies in Table Figure 7.4 shows the computed optimal distributions of wind turbines from previous studies and this study. All were configured under the same parameters except that in the present study two turbines cannot occupy the same 100m 100m square. The grid is sufficiently refined following Mittal s approach [29] that turbines can be placed anywhere outside of the spacing limit. In the Figure 7.4 (E), it shows that turbines trend to be positioned at upstream area and downstream area. This is because in upstream area, there is no wake affect and downstream area has better wake recovery. This is unlike the optimized layouts by other works, shown in Figure 7.4. It may because of a different multiple wake model used in WALOM. It is also noted that placement of diamond shape is preferred in the distribution as it reduces the possibility that wind speeds will be lowered at the turbine because of the velocity deficit in the wake. Table 7.1 compares the number of turbines, the total power produced, fitness value and efficiency for the results of previous studies and the present study. The optimal placements of previous studies were also recomputed by our model. The power outputs of previous configurations were reduced in the recomputed results. 81

95 Figure 7.1 Wind farm area Figure 7.2 Wind distribution for case 3 82

96 Figure 7.3 Fitness value of different number of turbines for case 1. Table 7.1 Results from previous study and current study: reported and recomputed Mossetti et al. Grady et al. Reported Recomputed Reported Recomputed Number of turbines Total power (km) Fitness value Efficiency (%) Marmidis et al. Mittal et al. WALOM Reported Recomputed Reported Recomputed Report Number of turbines Total power (km) Fitness value Efficiency (%) N/a

97 A B C D E Figure 7.4 Turbines placement of four studies for case 1: (a) Mossetti et al. [25] (b) Grady et al. [27] (c) Marmidis et al. [28] (d) Mittal et al. [29] (e) WALOM 84

98 7.1.2 Case 2: Constant wind speed with an equal probability variable wind direction In this case, several optimal layout configurations were obtained. Figure 7.5 shows the fitness values for different number of turbines. When N=32, the fitness value reduces to a minimum of The optimized placement of the turbines for this case and those obtained by previous study are shown in Figure 7.6. Figure 7.5 Fitness value of different number of turbines for case 2 85

99 A B C D Figure 7.6 Turbines placement for case 2: (a) Mossetti et al. [25] (b) Grady et al. [27] (c) Mittal et al. [29] (d) WALOM Table 7.2 is a comparison for the results of previous studies and the present study. Even though the optimal configuration obtained does not have highest efficiency the fitness value is lowest. Table 7.2 Results from previous study and current study: reported and recomputed Mossetti et al. Grady et al. WALOM Reported Recomputed Reported Recomputed Report Number of turbines Total power (km) Fitness value Efficiency (%)

100 7.1.3 Case 3: Variable Wind Speed with Variable Wind Direction In this case, the optimal configuration was obtained when N=35. Figure 7.7 shows optimal fitness values for different number of turbines. The optimal wind farm layout configuration of previous studies and that obtained using the model described earlier are showed in Figure 7.8. Figure 7.7 Fitness value of different number of turbines for case 3 In comparison to the previous optimal configurations, it has been shown that optimal wind turbine location will tend to be positioned in the edges of the turbine array area. Presumably this is an attempt to maximize the distance between turbines and to 87

101 eliminate the effects of wakes, like what had been discussed in section It is worth noting that, because the proximity exclusion rule has been relaxed in comparison to the restrictions in previous models which did not allow turbines to occupy the same 200m 200m square, turbines at the edges cluster in a zigzag fashion along the edge direction. This is to reduce wake effects when the wind blows along the edge of the square. Table 7.3 compares the results obtained in previous studies and this study. It shows that the efficiencies recomputed of previous configurations were reduced. The optimal configuration by present study has a lower fitness value. A B C D Figure 7.8 Turbines placement for case 3: (a) Mossetti et al. [25] (b) Grady et al. [27] (c) Mittal et al. [29] (d) WALOM 88