wind array performance evaluation model for large wind farms and wind farm layout optimization PDF
Preview wind array performance evaluation model for large wind farms and wind farm layout optimization
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 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 Contents Chapter 1 Introduction ......................................................................................................................... 1 1.1 Background ............................................................................................................................. 1 1.2 Wake measurements and wake model .................................................................................. 5 1.3 Wind farm layout optimization .............................................................................................. 6 1.4 Dissertation Outline ................................................................................................................ 7 Chapter 2 Literature Review ................................................................................................................. 8 2.1 Wake models .......................................................................................................................... 8 2.1.1 Analytical Wake models ................................................................................................. 8 2.1.2 Numerical Wake model ................................................................................................ 10 2.1.3 Multiple wake models .................................................................................................. 12 2.2 Wind farm performance evaluation models ........................................................................ 13 2.3 Wind farm layout optimization problem .............................................................................. 15 Chapter 3 Objectives .......................................................................................................................... 18 3.1 Wind array performance evaluation .................................................................................... 18 3.2 Wind farm layout optimization ............................................................................................ 19 Chapter 4 Wake models ..................................................................................................................... 21 4.1 Kinematic Wake Models ....................................................................................................... 23 4.1.1 Jensen wake model ...................................................................................................... 24 4.1.2 Larsen model ................................................................................................................ 25 4.1.3 Frandsen analytical model ............................................................................................ 26 4.2 Field Wake Models ............................................................................................................... 27 4.2.1 Ainslie wake model ....................................................................................................... 28 4.2.2 Three-dimensional field model .................................................................................... 29 4.3 Wake added turbulence models .......................................................................................... 31 Chapter 5 Methodology ...................................................................................................................... 34 5.1 Large wind array performance evaluation model (LWAP) ................................................... 34 5.1.1 Multiple wake model .................................................................................................... 36 5.1.2 Effect of the wind array on the atmospheric boundary layer ...................................... 42 5.2 Wind array layout optimization model (WALOM)................................................................ 46 5.2.1 Wind array configuration set up ................................................................................... 46 5.2.2 Wind data and distribution........................................................................................... 49 iii 5.2.3 Cost function ................................................................................................................ 55 5.2.4 Turbine power .............................................................................................................. 56 5.2.5 Wake effect evaluation................................................................................................. 57 5.2.6 Genetic Algorithm (GA) ................................................................................................ 58 Chapter 6 Results: wind farm layout evaluation model ..................................................................... 63 6.1 Wind speed evaluations at Horns Rev when wind direction is along turbine rows ............. 63 6.2 Turbine power evaluations at Horns Rev: wind direction parallel to turbine rows ............. 69 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 ................................................................ 73 Chapter 7 Results: wind farm layout optimization ............................................................................. 79 7.1 Extension of Mossettiβs approach ........................................................................................ 79 7.1.1 Case 1: Constant unidirectional wind ........................................................................... 80 7.1.2 Case 2: Constant wind speed with an equal probability variable wind direction ........ 85 7.1.3 Case 3: Variable Wind Speed with Variable Wind Direction ........................................ 87 7.1.4 Different Spacing Limits for Unidirectional Wind ......................................................... 89 7.1.5 Different Area Sizes for Unidirectional Wind ............................................................... 92 7.1.6 Constant Wind Speed with Variable Wind Direction and a circular site area .............. 95 7.1.7 Comparison of optimized layouts using Jensen wake model and Ainslie wake model 97 7.2 Horns Rev wind farm layout optimization .......................................................................... 100 7.2.1 Weibull data for 12 wind direction sectors ................................................................ 103 7.2.2 Wind data for 16 wind direction sectors .................................................................... 105 7.2.3 Wind data for 72 wind direction sectors .................................................................... 107 Chapter 8 Conclusions and future work ........................................................................................... 110 Bibliography ........................................................................................................................................ 113 iv 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 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 =7D 38 FIGURE 5.2 WAKE DECAY CONSTANT, β², AS A FUNCTION OF UPSTREAM TURBINE WIND SPEED DEFICIT 39 π¬π FIGURE 5.3 COMBINATION COEFFICIENT, C, AS A FUNCTION OF NORMALIZED DOWNSTREAM DISTANCE 40 π 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 Β° Β° FIGURE 6.3 HORNS REV EVALUATION WIND DIRECTION 270 AND WIND SPEED 12 M/S +/- 0.5 M/S 66 Β° FIGURE 6.4 HORNS REV EVALUATION WIND DIRECTION 222 AND WIND SPEED 8.5 M/S +/- 0.5 M/S 67 Β° FIGURE 6.5 HORNS REV EVALUATION WIND DIRECTION 222 AND WIND SPEED 12 M/S +/- 0.5 M/S 68 Β° FIGURE 6.6 POWER CURVE FOR THE TURBINE AT HORNS REV 70 Β° 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 Β° FIGURE 6.9 TURBINES POWER AT CASE 2 FOR WIND SPEED AT 8M/S AND DIRECTION 222 AT HORNS REV 71 Β° FIGURE 6.10 HORNS REV ARRAY. EXACT ROW (ER=270 ) OF TURBINES [60] 74 Β° FIGURE 6.11 NYSTED ARRAY. EXACT ROW (ER=278 ) OF TURBINES [60] 74 Β° FIGURE 6.12 NORMALIZED POWER AT HORNS REV FOR THE FREE STREAM WIND SPEED OF 8 Β± 0.5 M/S: Β° COMPARISON OF MODELS WITH OBSERVATIONS 75 FIGURE 6.13 NORMALIZED POWER AT NYSTED FOR THE FREE STREAM WIND SPEED OF 8 Β± 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 1. 83 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 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 1 104 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 Nomenclature Rotor disc area The nth wake area π΄ Rotor area of the nth turbine π΄π The Weibull scale factor π΄ππ The Weibull scale factor of the jth wind direction π΄π Turbine induction factor π΄π Wake lateral width π Combination factor π Wind turbine thrust coefficient πΆ The distributed thrust coefficient πΆπ Constants in Larsen wake model πΆπ‘ The relative mean wind speed in the wake π1 The flow speed deficit in the infinitely large wind farm πππ€ cost Total cost of the wind farm ππ€π Turbine rotor diameter The effective rotor diameter π· Centerline velocity deficit π·πππ The initial centerline velocity deficit π·π The expanded downstream rotor diameter π·ππ Empirical distance constant π·π Wake width π·π Height of the internal boundary layer π·π€ Turbine hub height β The ambient turbulence intensity βπ» The ambient turbulence intensity in a turbine wake πΌπ β² Maximum center wake turbulence intensity πΌπ Turbulence intensity in the wake πΌπ The Weibull shape factor πΌπ€ The Weibull shape factor of the jth wind direction πΎ Wake decay constant πΎπ Wake decay coefficient π Number of turbines in the wind farm πβ² Power output of a turbine π Power available from the wind π Observed turbine power πππ£πππ Predicted turbine power ππππ πππ£ππ Total wind farm power πππππππππ‘ππ ππ‘ππ‘ππ viii The wake radius at 9.5 rotor diameters downstream the turbine Rotor wake radius π 9.5 Normalized downstream distance by turbine rotor diameter π π€ Normalized downstream distance from the ith turbine π Crosswind turbine spacing π π Downwind turbine spacing π π Turbine spacing π π The relative wake velocity deficit π π β² Free stream velocity at turbine height in the internal boundary layer π Normalized centerline velocity deficit π1 The initial wake velocity deficit ππ Free stream wind velocity πππππ‘πππ Free stream wind velocity of the jth wind direction π0 The mean wind speed π0π Velocity deficit in the wake ποΏ½ Wind velocity in a turbine wake βπ Wind velocity calculated by the wake model in the ith turbine wake π’ Wind velocity calculated by the single wake model in the ith turbine wake π’π β² Observed wind speed π’π Predicted wind speed π’πππ πππ£ππ Friction velocity in the atmospheric boundary layer π’πππππππ‘ππ Friction velocity in the internal boundary layer π’β0 The position of the rotor respected to the applied coordinate system π’β1 Offshore roughness π₯0 Wind farm roughness π§0 Constant related to the trust coefficient π§00 Wake expansion parameter πΌ Eddy viscosity π½ The jth wind direction Ξ΅π£ Von Karman Constant ππ Air density π The standard deviation of the wind speed in the wake π Standard deviation of wind velocity in y direction ππ Standard deviation of wind velocity in z direction ππ¦ ππ§ ix Abbreviations CFD Computational Fluid Dynamics ENDOW EfficieNt Development of Offshore WindFarms ECN Energy Research Centre of the Netherlands ER Exact Row EWTS European Wind Turbine Standards FLaP Farm Layout Program GA Genetic Algorithms GH Garrad Hassan IBL Internal Boundary Layer KAMM Karlsruhe Atmospheric Mesoscale Model LWAP Large Wind Array Performance Evaluation Model MAPE Mean Absolute Percentage Error MC Monte Carlo NTUA National Technical University of Athens RGU Robert Gordon University RMSD Root Mean Square Deviation SAR Synthetic Aperture Radar SODAR Sonic Detection and Ranging WALOM Wind Array Layout Optimization Model WAsP Wind Atlas Analysis and Application Program WFOG Wind Farm Optimization using a Genetic Algorithm x
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