Assessment of the Lillgrund Windfarm

Transcription

1 Assessment of the Lillgrund Windfarm Power Performance Wake Effects Lillgrund Pilot Project September 2009

2 Dokumenttyp Dokumentidentitet Rev. nr. Rapportdatum Uppdragsnummer REPORT 6_1 LG Pilot Report 1.0 September 10, Författare Uppdragsnamn Jan-Åke Dahlberg Lillgrund Pilot Project Beställare Vattenfall Vindkraft AB Granskad av Jan Norling, Göran Loman, Sven-Erik Thor Godkänd av The Reference Group Delgivning Antal sidor Antal bilagor The Swedish Energy Agency 28 0 PREFACE Vattenfall s Lillgrund project has been granted financial support from the Swedish Energy Agency and Vattenfall will therefore report and publish experiences and lessons learned from the project. This report is compiled in a series of open reports describing the experiences gained from the different aspects of the Lillgrund Wind Farm project, for example construction, installation, operation as well as environmental, public acceptance and legal issues. The majority of the report authors have been directly involved in the Lillgrund project implementation. The reports have been reviewed and commented by a reference group consisting of the Vattenfall representatives Sven-Erik Thor (chairman), Ingegerd Bills, Jan Norling, Göran Loman, Jimmy Hansson and Thomas Davy. The experiences from the Lillgrund project have been presented at two seminars held in Malmö (4 th of June 2008 and 3 rd of June 2009). In addition to those, Vattenfall has presented various topics from the Lillgrund project at different wind energy conferences in Sweden and throughout Europe. All reports are available on In addition to these background reports, a summary book has been published in Swedish in June An English version of the book is foreseen and is due late The Lillgrund book can be obtained by contacting Sven-Erik Thor at sven-erik.thor@vattenfall.com. Although the Lillgrund reports may tend to focus on problems and challenges, one should bear in mind that, as a whole, the planning and execution of the Lillgrund project has been a great success. The project was delivered on time and within budget and has, since December 2007, been providing households with their yearly electricity demand. Sven-Erik Thor, Project Sponsor, Vattenfall Vindkraft AB September 2009 DISCLAIMER Information in this report may be used under the conditions that the following reference is used: "This information was obtained from the Lillgrund Wind Farm, owned and operated by Vattenfall." The views and judgment expressed in this report are those of the author(s) and do not necessarily reflect those of the Swedish Energy Agency or of Vattenfall. 1(28)

3 Power Performance Assessment of the Lillgrund Windfarm SUMMARY In this report, an assessment of the power performance of individual turbines, as well as for the whole wind farm, Lillgrund, is presented. By using the nearby meteorological mast, a power performance assessment, in line with international standards, has been carried out for three turbines located close to the met mast, as well as for the whole farm. The derived power curves for the single turbines are almost identical, and slightly better than, the power curves given in WindPro. The assessment of the power performance of the whole wind farm resulted in an average power curve that is significantly lower than the power curve for an undisturbed turbine. The overall energy efficiency of the farm, calculated from the measured wind farm power curve and assuming a Rayleigh distributed wind speed with an annual average value of 8.0 m/s, gives an efficiency value of about 77%. The losses are relatively high, which is not surprising, for such a dense wind farm configuration. The Lillgrund wind farm is considered to have a very dense configuration and it is, therefore, of great interest to investigate how shading effects (wake effects) will influence the production. The main objective of the project has been to analyze the power output of the whole wind farm for different wind directions and wind speeds and thus identify and quantify the wake effects. Shading effects are defined as the power ratio between the power output of one or more selected object turbines and the power levels of one or more reference turbines, located up front. Shading effects have been identified for a number of cases and can be clearly demonstrated. Significant wake effects occur when the wind is blowing along a row of turbines. The maximum peak loss occurs for the second turbine in the row and is, for inter row spacing of 4.4xD, typically 70%, and for row spacing of 3.3xD, typically 80%. One assumption that has been adopted is that power reduction only occurs for production below rated wind speeds, i.e. when the turbines strive to extract as much energy out of the wind as possible. For above rated wind speeds, the turbines reduce the energy extraction in order to limit the power output, and consequently allow more wind to pass by. An attempt to estimate the power losses for the entire wind farm has also been made by dividing the wind rose in sectors and select different undisturbed turbines. These undisturbed turbines are located up front and used as reference turbines. Combining the relative power levels from all sectors gives the whole rose. The turbine production efficiency rate for the entire wind farm has been found to be 67% if only below rated wind speeds are considered. If 70% of the energy is assumed to be produced with below rated wind speeds, and thus influenced by wake losses, the overall wind farm efficiency, for an assumed isotropic wind distribution, becomes the same (77%), as derived from the wind farm power curve, in a narrow wind direction sector, and assumed wind statistics. The analysis is based on all available data. The temperature is measured at only one level, so it has not been possible to investigate how the wake effects vary with various atmospheric stability. However, since the data covers roughly a whole year of observation, the results can be considered representative for the Lillgrund site. 2(28)

4 TABLE OF CONTENTS PREFACE... 1 DISCLAIMER INTRODUCTION Background Objectives DESCRIPTION OF THE LILLGRUND WINDFARM History Turbines Meteorology mast Measured data POWER PERFORMANCE ASSESSMENT Power Performance Assessment of undisturbed turbines Power Performance Assessment of the whole farm INVESTIGATION OF WAKE EFFECTS Approach Sector width for binning of relative power Power losses for different power levels Power losses for turbines in a row with 4.4D separation Power losses for turbines in a row with 3.3D separation Power losses for different wind directions Power losses for the whole farm DISCUSSION AND CONCLUSIONS FIGURES (28)

5 1 INTRODUCTION 1.1 Background Vattenfall AB has received a financial grant from the state for the construction of the Lillgrund wind farm in Öresund. The overall objective of the support is to promote the development and to make offshore wind energy more cost-effective. Vattenfall will, therefore, report knowledge and experience generated from the Lillgrund project. This activity is conducted within the Lillgrund Pilot Project, which runs until the second half of Objectives The Lillgrund wind farm, see Figure 1, is considered to have a dense turbine configuration and it is, therefore, of great interest to investigate how shading effects (wake effects) will influence the production in the farm. The main objective of the project is to analyze the power output of the whole wind farm for different wind directions and wind speeds and thus identify the wake effects. 2 DESCRIPTION OF THE LILLGRUND WINDFARM 2.1 History Vattenfall acquired the Lillgrund project from Eurowind AB in the autumn of The area is bordered, on the west and on the northwest by the navigational fairways to Drogden and Flintrännan, on the east by the navigational fairway Lillgrundsrännan. The water protected area Bredgrund borders the area to the south, but for practical reasons the border between the Malmö and Vellinge communities was defined as the limit. The original permit application requested permission for the construction of MW turbines within the above specified area. There was a requirement that the turbines in the farm should be arranged in rows, such that these rows could be used as a support for navigation. However, the long permit turnaround times led to a situation where the intended wind turbine size was no longer available when permission was finally given. After discussions with the authorities, the 1.5 MW limit was removed, and a more up-to-date turbine model could be chosen. A turbine with a 92.6 meter rotor diameter, 65 meter hub height and a rated power output of 2.3 MW was chosen by Vattenfall. With these larger turbines, the spacing between the turbines became very close. It would have been possible for Vattenfall to remove some turbines to optimise the layout. A decision was made to continue with the originally planned layout and, consequently, prioritise maximum production instead of maximum profitability. 4(28)

6 2.2 Turbines The wind farm consists of 48 turbines, which are placed in rows. Original labelling of each turbine in Lillgrund project is a combination of a letter designation (rows A-D) and number designation (rows 1-8). For convenience, the turbines have also been numbered from 1 to 48 as shown in Figure 1. Both labelling conventions will be used in this report. The separation between the turbines in the row is 3.3xD (D = diameter of the turbine) and the separation between the rows is 4.3xD. Note the opening in the centre of the farm, due to shallow water at this location, which made turbine placement impossible. The turbines are Siemens SWT , Figure 2, with a 92.6 meter rotor diameter, 65 meter hub height and a rated power output of 2.3 MW. This power level is reached with wind speeds at around 12 m/s (rated wind speed). The turbines in the wind farm were installed in the autumn of 2007 and were all connected to the grid in the end of December Meteorology mast A meteorological mast, Figure 3, is located approximately 250 meters southwest of turbine 23 and 30. The mast is 65 meters high, and has anemometers and wind direction sensors at several levels. 2.4 Measured data Data from all the turbines and from the met tower are stored data in a database. From this database, data as 1-min averages has been extracted according to the tables below. The channels, which are used in this study, are shown in bold. Tabell 1 Data from the Substation 0 Time stamp 1 WLG-GMS-ION7650-ActiveEnergyExport 2 WLG-GMS-ION7650-ActiveEnergyImport 3 WLG-GMS-ION7650-ActivePower 4 WLG-GMS-ION7650-Date 5 WLG-MET-M01-Pressure 6 WLG-MET-M01-RelativeHumidity 7 WLG-MET-M01-Temperature 8 WLG-MET-M01-Winddirection 9 WLG-MET-M01-Windspeed 10 WLG-MET-M01-WpsStatus 11 WLG-Site-ActivePowerSetpoint 12 WLG-Site-TurbineActivePower 13 WLG-Site-TurbineActivePowerCurtail 14 WLG-Site-TurbineReactivePower 15 WLG-Site-TurbineWindSpeed 16 WLG-TurbineInError 17 WLG-TurbineInRun 18 WLG-TurbineProduction 5(28)

7 Tabell 2 Data from each turbine 0 Time Stamp 1 WLGA01-ActiveEnergyExport 2 WLGA01-ActiveEnergyExportSub 3 WLGA01-ActiveEnergyImport 4 WLGA01-ActiveEnergyImportSub 5 WLGA01-ActivePower 6 WLGA01-AlarmTxt 7 WLGA01-BladeAngleA 8 WLGA01-BladeAngleB 9 WLGA01-BladeAngleC 10 WLGA01-BladeAngleRef 11 WLGA01-Downtime 12 WLGA01-PossiblePower 13 WLGA01-Production 14 WLGA01-ReactiveEnergyExport 15 WLGA01-ReactiveEnergyExportSub 16 WLGA01-ReactiveEnergyImport 17 WLGA01-ReactiveEnergyImportSub 18 WLGA01-ReActivePower 19 WLGA01-RotorRPM 20 WLGA01-WindSpeed 21 WLGA01-WindSpeedSecondary 22 WLGA01-WPSStatus 23 WLGA01-WTOperationState 24 WLGA01-YawDirection The met mast was connected to the database as late as March 13, 2008, and, therefore, covers a little less than a year of data. Turbine data is stored from the October 4, 2007,when the first turbine was connected. The last of the 48 turbines were connected to the database December 21, The data that this study covers is the period from December 21, 2007 and February 19, 2009 when all the turbines were connected. In Figure 4 and Figure 5, the hourly distribution of wind directions and power levels, from the whole measurement period, are shown. As will be shown later on, the data from the met mast has only been used for the power performance assessment of the three individual turbines closest to the met mast. The analysis of wake effects has been based on SCADA data from the turbines. From the very extensive 1-min average database, the following channel readings were chosen for each turbine: power output, nacelle wind speed, nacelle direction, rotational speed and timestamp (minutes). The following data were selected from the met mast measurements: Hub height, wind speed (at 65 meters high), wind direction, temperature, air pressure and relative humidity. These data were synchronised in time and saved in a single data file (about 1.8 Gb). 6(28)

8 3 POWER PERFORMANCE ASSESSMENT The method to assess the power performance follows the standard procedure according to IEC The deviation from the standard is that the analyses in this study are based on 1-minute average values instead of the stated 10-minute average values. 3.1 Power Performance Assessment of undisturbed turbines According to the standard, a met mast should be located about 2.5xD, preferably upstream and within the measurement sector. In the Lillgrund wind farm, only two or perhaps three turbines fulfil these requirements. To determine the power curve, the scattered data of power output and wind speed, as measured by the mast in the 190 to 240 degrees sector, presented in Figure 6, was stored in bins. Bins with a width of 1 m/s were used in this study. The results of the binning for turbine B08 is presented in Figure 7. In Figure 8 to Figure 11, the corresponding graphs for turbine C08 and D08 are presented. A comparison of the derived power curves for the three turbines is presented in Figure 12, and in Figure 13, a comparison between the average of the three curves and the power curve given by WindPro for the Siemens 2.3 MW turbine, is shown in Figure 14. As can be seen in the graph, the measured power curve is very close or slightly above the power curve taken from WindPro. 3.2 Power Performance Assessment of the whole farm The method to assess the power performance of the whole farm was carried out in a similar way as for the single turbines. The wind speed was taken from the undisturbed met mast, (except for plant blockage, which not is considered here), in the wind direction sector of 170 to 230 degrees. Instead of using the average values in each bin, median values were used. This was done in order to minimize the contamination of data when individual turbines, for whatever reason, were not fully operating. The derived power curve for the selected wind direction sector, expressed as average or median values of the whole wind farm, is presented in Figure 14 together with the average of the three power curves from the undisturbed turbines. The shadowing effects are evident. It is also evident from the graph that shadowing effects are no longer visible in the power curve for wind speeds above 13.5 m/s. The explanation is, of course, that when the rated power level for the generator is reached, the turbines limit the extraction of power from the wind flow and, thereby, allow more flow to pass the turbine. This benefits the turbines further downstream. If a Rayleigh distributed wind speed with an annual average value of 8.0 m/s is assumed, the power curve derived, as an average of the 48 turbines (red), yields a production level of 77.6 % for a turbine not affected by wakes. The corresponding value for median power curve (blue), yields a production level of 76 % for a turbine not affected by wakes. These losses are as predicted in the planning phase of the Lillgrund project. 7(28)

9 4 INVESTIGATION OF WAKE EFFECTS 4.1 Approach A number of Fortran programs have been developed to enable effective management of the data. At each execution the program reads selected data from the data file, for further processing, binning and storing of new values. The data from the turbines contains neither wind speed (wind sensor on the nacelle roof is disturbed and can not be used) or wind direction, so other methods must be used. To overcome this lack of information, another approach was chosen namely to use the nacelle direction of each turbine as the wind direction indicators. The method requires that the turbines be aligned with the wind. This has been investigated, and a comparison between the wind direction measured on the mast and the nacelle direction for the nearest turbine shows a good match. A primary interest was to examine how the turbines are affected when they operate in the wake of other turbines. Shading effect, on an arbitrary turbine in the wind farm, can be expressed as the ratio between the power from the turbine of interest (object turbine), and the power of undisturbed turbines (reference turbines) located up front. To minimize the risk of using an erroneous wind direction, the average or the median (the value in the middle) value is used for the direction of the reference turbines. The reference power output, from the undisturbed turbine upfront, is determined in the same manner, as a mean or median value of the power from one or more reference turbines. For the selection of data from a sample of turbines, (for example a row of turbines) a requirement has been, that all the turbines in the sample must meet certain criteria, e.g. have a nacelle direction that falls within a given wind direction sector or produce power that falls within a specific range. 4.2 Sector width for binning of relative power In order to distinguish the detailed shape of the wake, it is necessary to use sufficiently narrow wind direction bins. The shape of the wake, as a result of using different bin widths, is evident from the curves in Figure 16. From the graph, it is evident that bin widths less than or equal to 5 is necessary to use in order to clearly distinguish the shape of the wake. 4.3 Power losses for different power levels The influence from the power level on the relative power is presented in Figure 18. From the graph, it is evident that the relative power is essentially independent of the power level. This implies that the turbines are operating efficiently, with a constant thrust coefficient over 8(28)

10 a wide wind speed range. Therefore most of the data taken at below rated wind speed has been used in this study. 4.4 Power losses for turbines in a row with 4.4D separation The predominant wind direction comes from the southwest direction, i.e. the winds blow along the rows with 4.4D downstream separation between turbines. The relative power levels for the turbines in row B; C and D are presented in Figure 20, Figure 21 and Figure 22 respectively. The second turbine in the row experiences the largest loss, whereas the third turbine in the row experiences the lowest loss. The peak losses for the subsequent turbines are relatively equal and levels out at around 70%. 4.5 Power losses for turbines in a row with 3.3D separation Figure 25 presents the power loss as an average of all the turbines in row B, when they are operating in the wakes from the turbines in row A. The inter turbine spacing in the row is 3.3D and the peak loss for the second turbine in the row reaches 80%. The relative power levels for the turbines in row 1, 3 and 5 are presented in Figure 27, Figure 28 and Figure 29 respectively. The wake effects are, according to the figures, clearly different when there is a gap in the row. 4.6 Power losses for different wind directions By selecting different reference turbines and object turbines, various wake configurations can be studied. Figure 32 shows, for example, relative power levels for the turbines 47, 43 & 44. The distance between the turbines varies between 3.3 and 6.0xD. 4.7 Power losses for the whole farm The relative power for the whole wind farm has been studied by selecting suitable reference turbines in different sectors. Figure 34 presents the compiled result for the entire wind farm when all turbines are operating below rated wind speed. The overall farm efficiency for power levels below rated wind (the knee) is about 67%. If approximately 70% of the energy is produced below rated wind speed, the total farm efficiency, for an assumed isotropic wind distribution will be about 77%. This corresponds rather well with the assumptions of power losses that were assumed in the design phase. 9(28)

11 5 DISCUSSION AND CONCLUSIONS The analysis is based on all available data. The temperature is measured at only one level, so it has not been possible to investigate how the wake effects vary with changing atmospheric stability. However, since the data covers almost a whole year of observation, the results can be considered to be representative for the Lillgrund site. The efficiency of the farm is calculated with the assumption that shadowing effects only occur below rated wind. When the wind is so high that the turbines are operating above rated wind speed, i.e. with power control/limitation, no losses are assumed. This means that the magnitude of wake losses will depend on the wind conditions at the site. For the Lillgrund site the overall farm efficiency for power levels below rated wind (the knee) is about 67%. If 70% of the energy is produced at below rated wind speeds the total farm efficiency is about 77%. 10(28)

12 6 FIGURES 3.3 x D 4.3 x D Figure 1 - The picture shows the location of the 48 turbines in Lillgrund. The turbines have been numbered from 1 to 48 according to the figure. The meteorology mast is located approximately 250m southwest of the turbines 23 and 30. Figure 2 - A picture of a Siemens SWT in Lillgrund. Note the dark triangle in the rear of the nacelle, on which the wind speed and wind direction sensors are mounted. (Photo: Richard Larsson, VPC October 2007) 11(28)

13 Figure 3 - Pictures of the 65-meter high met mast. (Photo: Richard Larsson, VPC October 2007) Wind direction Hours Figure 4 The graph shows the distribution of hourly wind direction averages from the whole measurement period. The concentration of values around southwest is obvious. 12(28)

14 Power (kw) Hours Figure 5 The graph shows the distribution of hourly average power values (of the 48 turbines) from the whole measurement period. 13(28)

15 Power kw Pow-B08 B08_ave Wind Speed m/s Figure 6 Scatter plot of 1-minute data showing power versus wind speed for turbine B08. Power kw B08_ave Wind Speed m/s Figure 7 Binned power versus wind speed for turbine B08. The vertical bars represent +/- one standard deviation. 14(28)

16 Power kw Pow-C08 C08_ave Wind Speed m/s Figure 8 Scatter plot of 1-minute data showing power versus wind speed for turbine C08. Power kw C08_ave Wind Speed m/s Figure 9 Binned power versus wind speed for turbine C08. The vertical bars represent +/- one standard deviation. 15(28)

17 Power kw Pow-D08 D08_ave Wind Speed m/s Figure 10 Scatter plot of 1-minute data showing power versus wind speed for turbine D08. Power kw D08_ave Wind Speed m/s Figure 11 Binned power versus wind speed for turbine D08. The vertical bars represent +/- one standard deviation. 16(28)

18 Power kw B08_ave 1600 C08_ave D08_ave Wind Speed m/s Figure 12 Comparison of binned power versus wind speed for the three turbines. Power kw B08_ave 600 C08_ave D08_ave 400 WindPro-Siemens 2.3MW, Level 0, 107,0 db Wind Speed m/s Figure 13 Comparison of binned power versus wind speed for the three turbines and for the power curve derived from WindPro. The agreement between the measured power curves and the WindPro curve is very good. 17(28)

19 Power kw Average of the three turbines in row 8 (BCD) Average of all 48 turbines Median of all 48 turbines Wind Speed m/s Figure 14 - The graph shows a comparison of the average power curve, from the three undisturbed turbines in row 8, and the power curve, average and median, of all of the 48 turbines. Wind Direction Wind Direction from Mast Nacelle Direction 30_D08 Nacelle Direction 23_C08 Nacelle Direction 15_B Minutes Figure 15 The graph shows a comparison between the wind direction measured by the wind vane in the met mast and the wind direction measured by the nacelle direction for the turbines in row 8. 18(28)

20 1,2 1,0 Relative Power 0,8 0,6 0,4 0,2 22_C07-ActivePow_2 22_C07-ActivePow_3 22_C07-ActivePow_5 22_C07-ActivePow_10 22_C07-ActivePow_20 22_C07-ActivePow_30 Fr_15_To_14, X/D= 4.3, Dir= , Wind Direction Figure Shadow effects on turbine 22 due to the wake from turbine 23, as derived with different bin widths (according to the number in the end of the label). From the graph it is evident that bin widths less than or equal to 5 is necessary to use in order to clearly distinguish the shape of the wake. Power kw Wind Speed m/s Figure 17 The graph highlights the four power level ranges that were selected for special wake studies. 19(28)

21 Relative Power 1,2 1,0 0,8 0,6 0,4 P P P P ,2 0, Wind Direction Figure 18 Derived relative power of the turbines in row 7, (14, 22 and 29) for different power levels according to Figure 17. Figure 19 Map to highlight the conditions presented in Figure 20, Figure 21 and Figure (28)

22 1,2 1,0 0,8 0,6 15_B08-ActivePow 14_B07-ActivePow 13_B06-ActivePow 12_B05-ActivePow 11_B04-ActivePow 10_B03-ActivePow 09_B02-ActivePow 08_B01-ActivePow 0,4 0,2 0, Figure 20 - Relative power levels for the turbines in row B. The second turbine in the row (14) experiences the largest peak loss, whereas the third turbine in the row experiences lowest peak loss. The losses for the following turbines are relatively equal and levels out around 70%. 1,2 1,0 0,8 0,6 23_C08-ActivePow 22_C07-ActivePow 21_C06-ActivePow 20_C05-ActivePow 19_C04-ActivePow 18_C03-ActivePow 17_C02-ActivePow 16_C01-ActivePow 0,4 0,2 0, Figure 21 - Relative power levels for the turbines in row C. The picture is similar as for row B. 21(28)

23 1,2 1,0 0,8 0,6 30_D08-ActivePow 29_D07-ActivePow 28_D06-ActivePow 27_D04-ActivePow 26_D03-ActivePow 25_D02-ActivePow 24_D01-ActivePow 0,4 0,2 0, Figure 22 - Relative power levels for the turbines in row D. The picture is similar as for row B, except for the fourth turbine in the row (27), which reaches a higher level due to the gap in the row (between turbine 27 and 28). 1,2 Relative power 1,0 0,8 0,6 0,4 Row_B_WD_219,1 Row_C_WD_219,0 Row_D_WD_219,1 0,2 0,0 Row_1 Row_2 Row_3 Row_4 Row_5 Row_6 Row_7 Row_8 Row_number Figure 23 - Relative power levels for the turbines in row B; C and D when the wind is blowing along the rows. Note the markedly increased power for the turbine behind the gap in the row. 22(28)

24 Figure 24 Map to highlight the conditions presented in Figure 25. 1,2 1,0 0,8 0,6 0,4 15_B08-ActivePow 14_B07-ActivePow 13_B06-ActivePow 12_B05-ActivePow 11_B04-ActivePow 10_B03-ActivePow 09_B02-ActivePow 08_B01-ActivePow Average of (8-14) 0,2 0, Figure 25 - Relative power levels for the turbines in row B due to the wakes from the turbines in row A. The distance is 3.3xD and the maximum power loss is about 80%. 23(28)

25 Row 1 Row 3 Row 5 Figure 26 Map to highlight the conditions presented in Figure 27, Figure 28 and Figure 29. 1,2 1,0 0,8 0,6 01_A01-ActivePow 08_B01-ActivePow 16_C01-ActivePow 24_D01-ActivePow 31_E01-ActivePow 0,4 0,2 0, Figure 27 - Relative power levels for the turbines in row 1. The second turbine in the row (8) experiences the largest peak loss. The reason for the phase shift of turbine 31 is not known, and needs to be investigated. 24(28)

26 1,2 1,0 0,8 0,6 0,4 03_A03-ActivePow 10_B03-ActivePow 18_C03-ActivePow 26_D03-ActivePow 33_E03-ActivePow 38_F03-ActivePow 43_G03-ActivePow 47_H03-ActivePow 0,2 0, Figure 28 - Relative power levels for the turbines in row 3. 1,2 1,0 0,8 0,6 05_A05-ActivePow 12_B05-ActivePow 20_C05-ActivePow 40_F05-ActivePow 45_G05-ActivePow 0,4 0,2 0, Figure 29 - Relative power levels for the turbines in row 5. The picture is similar as for row3, except for the fourth turbine in the row (40), which reaches a significantly higher level due to the gap in the row (between turbine 20 and 40). 25(28)

27 1,2 Relative power 1,0 0,8 0,6 0,4 Row_1_WD_129,0 Row_3_WD_129,0 Row_5_WD_129,1 0,2 0,0 Row_A Row_B Row_C Row_D Row_E Row_F Row_G Row_H Row_number Figure 30 - Relative power levels for the turbines in row 1; 3 and 5 when the wind is blowing along the rows. Note the markedly increased power for the turbine behind the gap in the row. 26(28)

28 Figure 31 Map to highlight the conditions presented in Figure 32. 1,2 1,0 Relative power 0,8 0,6 0,4 0,2 Fr_48_To_47, X/D= 4.3, Dir=222.4 Fr_48_To_43, X/D= 6.0, Dir=255.2 Fr_48_To_44, X/D= 3.3, Dir= , Wind direction Figure 32 - Relative power levels for the turbines 47, 43 & 44. The distance varies between 3.3 and 6.0xD. 27(28)

29 Figure 33 Map to highlight the conditions presented in Figure 34 Relative Power 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0, Wind Direction Figure 34 - The graph shows the relative power level of the entire wind farm when all the turbines are operating below rated wind speed. If an isotrop wind direction distribution is assumed, the overall farm efficiency, for power levels below rated wind speed can be calculated as the average of the curve, and yields about 67%. 28(28)