PERFORMANCE ASSESSMENT OF THE CASE WESTERN RESERVE UNIVERSITY WIND TURBINE AND CHARACTERIZATION OF WIND AVAILABILITY CHUNG Y. WO

Transcription

1 PERFORMANCE ASSESSMENT OF THE CASE WESTERN RESERVE UNIVERSITY WIND TURBINE AND CHARACTERIZATION OF WIND AVAILABILITY by CHUNG Y. WO Submitted in partial fulfillment of the requirements for the degree of Master of Science Thesis Adviser: Iwan Alexander January, 214

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Chung Y. Wo candidate for the Master of Science degree*. (signed) (chair of the committee) Dr. Jaikrishnan Kadambi Dr. Iwan Alexander Dr. Paul Barnhart (date) 9/6/213 *We also certify that written approval has been obtained for any propriety material contained therein

3 To my friends and family For science i

4 Table of Contents List of Tables...v List of Figures...vi List of Symbols...ix Acknowledgments...xi Abstract...xii 1 Introduction Wind Turbines Background/Literature Review Objective Experimental Design Wind Turbine System and Anemometers Remote Terminal Unit (RTU) Data Collection Data Manipulation Redundant Data Elimination Data Organization Wind and Power Frequency Plots Rayleigh Distribution of Wind Speed Theoretical Power Output and Turbine Efficiency Calculating Power Curve Calculating Power Coefficient Curve...11 ii

5 4 Statistics Overview Wind Speed and Energy Production Details Fall Winter Spring Summer Year Long (Sept 211 Aug 212) Data Plots and Experimental Results Wind Speed Frequency Plots and Rayleigh Distributions Power Output Frequency Plots Seasonal and Year Long Empirical Power Curves Theoretical vs. Actual Power Output Plots Compiled Efficiency Curves Compiled Coefficient Curves Discussion Statistical Results and Energy Output Wind Speed Frequencies Probability Distributions Empirical Power Curves Theoretical vs. Actual Power Output and Efficiency Curves Power Coefficient Curves Economic Feasibility Conclusion and Recommendations...55 iii

6 7.1 Conclusion Recommendations...58 Appendix A: Plots of Turbine Output Data...6 Appendix B: Seasonal and Year Long Efficiency Curves...63 Appendix C: Seasonal and Year Long Power Coefficient Curves...66 Appendix D: Bin Resolution Plots...69 Appendix E: Uncertainty in Efficiency Plots...72 References...74 iv

7 List of Tables Table 1: Seasonal and Year-Long Data Points...6 Table 2: Wind Speed and Power Output Summary...13 Table 3: Fall second Wind Speed Data...15 Table 4: Fall second Power Output and Energy Data...15 Table 5: Fall minute Averaged Wind Speed Data...15 Table 6: Fall minute Averaged Power Output and Energy Data...15 Table 7: Winter second Wind Speed Data...16 Table 8: Winter second Power Output and Energy Data...16 Table 9: Winter minute Averaged Wind Speed Data...16 Table 1: Winter minute Averaged Power Output and Energy Data...16 Table 11: Spring second Wind Speed Data...17 Table 12: Spring second Power Output and Energy Data...17 Table 13: Spring minute Averaged Wind Speed Data...17 Table 14: Spring minute Averaged Power Output and Energy Data...17 Table 15: Summer second Wind Speed Data...18 Table 16: Summer second Power Output and Energy Data...18 Table 17: Summer minute Averaged Wind Speed Data...18 Table 18: Summer minute Averaged Power Output and Energy Data...18 Table 19: Sept 211- Aug second Wind Speed Data...19 Table 2: Sept 211- Aug second Power Output and Energy Data...19 Table 21: Sept 211- Aug minute Averaged Wind Speed Data...19 Table 22: Sept 211- Aug minute Averaged Power Output and Energy Data...19 v

8 List of Figures Figure 1: Fall second Normalized Wind Speed Distribution...2 Figure 2: Fall minute Averaged Normalized Wind Speed Distribution...21 Figure 3: Fall 211 Wind Speed Rayleigh Cumulative Density Function...21 Figure 4: Winter second Normalized Wind Speed Distribution...22 Figure 5: Winter minute Averaged Normalized Wind Speed Distribution...22 Figure 6: Winter 211 Wind Speed Rayleigh Cumulative Density Function...23 Figure 7: Spring second Normalized Wind Speed Distribution...24 Figure 8: Spring minute Averaged Normalized Wind Speed Distribution...24 Figure 9: Spring 212 Wind Speed Rayleigh Cumulative Density Function...25 Figure 1: Summer second Normalized Wind Speed Distribution...26 Figure 11: Summer minute Averaged Normalized Wind Speed Distribution...26 Figure 12: Summer 212 Wind Speed Rayleigh Cumulative Density Function...27 Figure 13: Sept Aug second Normalized Wind Speed Distribution...28 Figure 14: Sept Aug minute Avg Normalized Wind Speed Distribution...28 Figure 15: Sept Aug 212 Wind Speed Rayleigh Cumulative Density Function...29 Figure 16: Fall second Normalized Power Output Distribution...3 Figure 17: Fall minute Averaged Normalized Power Output Distribution...3 Figure 18: Winter second Normalized Power Output Distribution...31 Figure 19: Winter minute Averaged Normalized Power Output Distribution...31 Figure 2: Spring second Normalized Power Output Distribution...32 Figure 21: Spring minute Averaged Normalized Power Output Distribution...32 Figure 22: Summer second Normalized Power Output Distribution...33 vi

9 Figure 23: Summer minute Averaged Normalized Power Output Distribution...33 Figure 24: Sept Aug second Normalized Power Output Distribution...34 Figure 25: Sept Aug minute Avg Normalized Power Output Distribution...34 Figure 26: Fall 211 Empirical Power Curve...36 Figure 27: Winter 211 Empirical Power Curve...37 Figure 28: Spring 212 Empirical Power Curve...38 Figure 29: Summer 212 Empirical Power Curve...39 Figure 3: Sept Aug 212 Empirical Power Curve...4 Figure 31: Fall 211 Theoretical vs. Actual Power Output Plot...41 Figure 32: Winter 211 Theoretical vs. Actual Power Output Plot...41 Figure 33: Spring 212 Theoretical vs. Actual Power Output Plot...42 Figure 34: Summer 212 Theoretical vs. Actual Power Output Plot...42 Figure 35: Sept Aug 212 Theoretical vs. Actual Power Output Plot...43 Figure 36: Compiled Efficiency Curves...44 Figure 37: Compiled Power Coefficient Curves...45 Figure 38: Fall second Wind Speed vs. Power Output Data Plot...6 Figure 39: Winter second Wind Speed vs. Power Output Data Plot...6 Figure 4: Spring second Wind Speed vs. Power Output Data Plot...61 Figure 41: Summer second Wind Speed vs. Power Output Data Plot...61 Figure 42: Sept Aug second Wind Speed vs. Power Output Data Plot...62 Figure 43: Fall 211 Efficiency Curve...63 Figure 44: Winter 211 Efficiency Curve...63 Figure 45: Spring 212 Efficiency Curve...64 vii

10 Figure 46: Summer 212 Efficiency Curve...64 Figure 47: Sept Aug 212 Efficiency Curve...65 Figure 48: Fall 211 Power Coefficient Curve...66 Figure 49: Winter 211 Power Coefficient Curve...66 Figure 5: Spring 212 Power Coefficient Curve...67 Figure 51: Summer 212 Power Coefficient Curve...67 Figure 52: Sept Aug 212 Power Coefficient Curve...68 Figure 53: Fall 211 Wind Speed 1m/s Bin Resolution Plot...69 Figure 54: Fall 211 Wind Speed.75m/s Bin Resolution Plot...7 Figure 55: Fall 211 Wind Speed.5m/s Bin Resolution Plot...7 Figure 56: Fall 211 Wind Speed.25m/s Bin Resolution Plot...71 Figure 57: Efficiency Plot with Varying Air Densities...73 viii

11 List of Symbols A Area swept by turbine blades, assuming disc and ignoring nacelle [m 2 ] a CSV C p F(U) LiDAR MATLAB MySQL TM N i P P Betz P i P i,j p(u) RTU R T U U V i V i,j η Axial induction factor Comma separated variable Power Coefficient Rayleigh cumulative density or frequency function for wind speed Light Detection And Ranging Numerical computing environment and programming language Database management system Number of data points in bin i Recorded power output [kw] Betz Limit power output [kw] Averaged power within bin i [kw] Power of data point j in bin i [kw] Rayleigh probably density or frequency function for wind speed Remote Terminal Unit Universal Gas Constant for air, 287 J/kg*K Temperature [K] Recorded Wind Speed [m/s] Mean wind speed [m/s] Averaged wind speed within bin i [m/s] Wind speed of data point j in bin I [m/s] Turbine efficiency relative to Betz Limit ix

12 ρ Air density [kg/m 3 ] x

13 Acknowledgements First and foremost I would like to thank my advisor Dr. Iwan Alexander for his patience, guidance, assistance, and encouragement throughout my graduate career. I would also like to thank Dr. David Matthiesen and John Yingling for their guidance in conducting this research and assistance in gathering turbine data. Writing this thesis would not have been possible without the following people: Mr. Jim Henning for an extraordinary amount of guidance throughout the thesis writing and defense process, Alison O Brien for her unsurpassable love and for motivating me to write harder than I ever thought possible, and Dr. Paul Barnhart for assuring me that my Master s thesis does not need to change the world. I would also like to thank the countless many who have helped and struggled alongside me throughout my time at Case Western Reserve University. Though I cannot name you all individually, be assured that without you all my college experience would have been significantly less awesome. The following organizations have also assisted or otherwise contributed positively to my life as a student: The Ohio Space Grant Consortium for funding and providing the first opportunity to publicly speak about my research, Monster Energy for their wide assortment of research and thesis writing juice, and the Department of Mechanical and Aerospace Engineering at Case Western Reserve University for existing. xi

14 Performance Assessment of the Case Western Reserve University Wind Turbine and Characterization of Wind Availability Abstract by CHUNG Y. WO To better understand the behavior of wind turbines placed in an urban environment, a study was performed to characterize the wind availability and performance of a 1-kilowatt Northern Power Systems wind turbine installed at Case Western Reserve University. It was found that the annual average wind speed was 4.m/s, generating net energy of 67MWh at a rate of 8.kW. It was also found that the winds rarely reach the required 15m/s for the turbine to output at its rated capacity. The winds that do reach 15m/s or faster exist only in short gusts, prevalently during the Winter 211 and Spring 212 months. Additionally, in studying the turbine performance, it was found that the turbine has a maximum efficiency of 65-7% relative to the Betz Limit, at a wind speed of approximately 6.75m/s. xii

15 1. Introduction 1.1 Wind Turbines In response to the dwindling supply of fossil fuels and the ever increasing demand for power, alternative energy methods have been a prevalent research topic in recent years. Alternative energy sources include solar, hydroelectric, and wind energy, with each requiring a method of conversion to usable electrical energy. In the case of wind power, a wind turbine is used. A wind turbine is a device that converts available wind power to useable electricity through the use of a generator connected to a rotating shaft that is torqued by a rotor due to aerodynamic forces of incoming wind. 1.2 Background and Literature Review In the late 21, Case Western Reserve University installed a 1-kilowatt horizontal axis wind turbine originally intended to power a portion of the student athletic center, and provide a means of conducting alternative energy research. Since wind turbines are typically placed in large open plains or large bodies of water, the performance of a wind turbine in an urban setting has not been researched in depth. Among the topics proposed for research include the existence and efficacy of the Venturi effect on the wind turbine installed at Case Western Reserve University. The Venturi effect is a phenomenon in which wind speed is increased between passages of buildings parallel to the flow direction. Blocken et al. (27) found through CFD simulation that beyond the pedestrian level, defined as 2m, the increase in wind velocity within building passages is negligible. This is due to the wind-blocking effect found in unconfined flows around buildings where the majority of the air flow to avoids the passage in favor of going around or over the buildings. (Blocken et all. 28). At 1

16 a hub height of 37m, the wind turbine is well above the effective height (2m) of the Venturi effect. Nakayama et al. (211) characterized the effect of surface roughness due to densely packed buildings typically found in large urban areas. Nakayama et al. used wind tunnel measurements and large eddy simulations to conclude that in the presence of building arrays, there exists a vertical power law velocity profile with complete velocity recovery at approximately 1 building heights from ground level and significant wind speed loss up to 1.5 time average building height. This is significant to studying the performance of an urban wind turbine as the research by Nakayama et al. suggests that potential for wind power is reduced by the presence of buildings upstream of the wind turbine. 1.3 Objective Few studies have reported on the performance of wind turbines in an urban setting. To assess the performance of the wind turbine installed at Case Western Reserve University, raw wind speed and power output data from the turbine will be analyzed and manipulated using MATLAB code. The recorded wind speed data over a large span of time used in this study will be used to characterize the wind. Statistics regarding wind availability are usually considered when siting a turbine to determine the power generation potential of a site (Manwell et al., 29). Useful statistics include the wind probability density function (PDF), wind cumulative density function (CDF), mean wind speed, and wind availability. Of particular interest is the frequency with which the speeds are below cut-in speed, the minimum wind speed that allows for net power production. At speeds below cut-in, there is negative power produced by the turbine, indicating that there is parasitic power draw by the turbine. 2

17 With knowledge of past wind availability and actual power production from the turbine, an efficiency assessment may be conducted by comparing the theoretical power output calculated from the available wind with the actual power output reported by the turbine. Additionally, power curves may be generated from the accumulated wind speed and power data using the International Electrotechnical Commission (IEC) standard IEC The calculated power curve may then be compared to the theoretical power curve published by Northern Power to evaluate the power production behavior of the turbine through a range of wind speeds. Power coefficient curves may be found through the use of reported wind speed and power output data. Similar to comparing the actual to theoretical power outputs, examining the power coefficient curve would reveal the wind speed effects on turbine efficiency as well as the speeds at which the turbine is best suited for operation. With the performance assessment complete the economic feasibility of the turbine may also be determined. 2. Experimental Design In this section, the design and layout of the experiment will be discussed, including a description of the wind turbine and data collection systems. 2.1 Wind Turbine System and Anemometers The wind turbine installed at Case Western Reserve University is a Northern Power Systems 1-21, a 21m diameter 1-kilowatt horizontal axis wind turbine with hub height of 37m and cut-in speed of 3.5m/s. The turbine is outfitted with an array of sensors that monitor parameters such as rotor speed, wind speed, power output, ambient temperature, cab temperature, inverter phase power, and the general health of the wind turbine in 1- second intervals. Surrounding the turbine are three cup anemometers to measure the 3

18 surrounding wind speed and direction. These anemometers, as well as a Light Detection and Ranging (LiDAR) system were used for a period of time for siting purposes prior to turbine installation. The data gathered by the cup anemometers and LiDAR system when used for siting purposes was aimed at determining wind characteristics such as wind availability, prevailing direction and speed all factors that are used to make performance predictions. Since the construction of the turbine, the LiDAR system was removed, with only the cup anemometers remaining as the sole method for upstream and downstream wind monitoring. These cup anemometers send data to a central data recorder which then transmits the data to a third party host, Adcon Telemetry, who in turn make the data available for viewing and download via their secured website. Unlike the wind turbine sensor data, the cup anemometer data is unavailable in 1-second intervals. Rather, the data is taken as 1-minute averages before being made available on the Adcon Telemetry website. For the purposes of this study, only the turbine cup anemometer will be used, as the surrounding cup anemometers were found to have unreliable data. 2.2 Remote Terminal Unit (RTU) System The wind turbine is monitored by a Remote Terminal Unit (RTU), which is a Windowsbased personal computer that is located inside of a locked server closet and is connected to suite of sensors on the turbine. The RTU monitors data such as wind speed, wind direction, power output, ambient temperature, and rotor speed. The RTU is capable of reporting and recording the data in 1-second intervals. The 1-second data is stored in the system for one week then 1-minute averages are automatically taken of the weekly data while the 1-second data is discarded. However, 1-second data is required for much of the wind turbine 4

19 performance analysis. Therefore, a protocol for weekly 1-second data collection was developed. 2.3 Data Collection To conserve hard drive space, the RTU automatically records 1-minute averages for the monitored data and discards the 1-second data. However, much of the turbine performance is dependent upon intermittent gusts of wind that last no more than a few seconds. The existence and performance impact of the wind gusts would not be easily detectable if the data were averaged over 1-minutes. Therefore, a protocol for weekly manual data collection of the 1-second data was developed. Parameters of interest are power output, wind speed, wind direction, and yaw angle. The program used to collect the data from the turbine is MySQL TM Query browser, which for each parameter collects the weekly 648 data points. The weekly data is then exported as a comma separated file (CSV file) and saved in the RTU with the date as the filename. 3. Data Manipulation This section will discuss the data processing procedure used for each weekly set of data, including elimination of redundant data, organization into seasonal data, and data presentation. 3.1 Redundant Data Elimination The data collected from the RTU to be used for this study spanned from September 211 through August 212. This data includes the wind speed data collected by an anemometer immediately downstream of the blades and the resulting power output generated by the turbine. Although efforts were made to collect the data every week at approximately the same time to avoid redundant data being recorded, the 1-second resolution of the data 5

20 coupled with holidays, human error and schedule conflicts prevented perfectly continuous data from one week to the next. As a result, the raw data sets often repeated data that were already captured from the previous week or there would be gaps in time were no data would be collected because the time between collections would exceed 168 hours. To mitigate the effects of redundant or overlapping data, each new data set would be searched for time points that were already included within the previous set. The redundant data points in the new set would be deleted, making each time point exist in only the earlier set. Unfortunately, because the RTU automatically produces 1-minute averages for data older than 168 hours and discards the 1-second data, there is no way to recover the 1-second data in the gap between collection times longer than 168 hours. 3.2 Data Organization After eliminating redundant data, each weekly set of data points were concatenated using MATLAB code to create monthly data, which in turn were concatenated to create seasonal data. The seasonal data sets were then concatenated to create a year-long data set. The data presented in the body of this performance study will be limited to the seasonal and year-long data. Seasonal and year-long plots of the wind speed and power output data can be found in Appendix A. Seasonal data is concatenated from weekly data as follows: Season Dates Included Data Points Fall 211 8/3/211-11/28/ Winter /28/211-2/27/ Spring 212 2/27/212-5/29/ Summer 212 5/29/212-9/4/ Sept 211 Aug 212 8/3/211-9/4/ Table 1: Seasonal and Year-Long Data Points 6

21 3.3 Wind Speed and Power Frequency Plots From the seasonal and year-long data sets, normalized frequency plots for the wind speed and turbine power output were created. The data used for these plots included both the raw, 1-second data, as well as 1-minute averaged data. Averaging the data over a 1-minute span mitigates the effects of intermittent and low duration outlier data, such as infrequent wind gusts. Additionally, comparing the averaged data and 1-second data would reveal the prevalence of intermittent low or high wind speeds and power outputs interspersed throughout the data. 3.4 Rayleigh Distribution of Wind Speeds To further characterize the wind available at the turbine site, probability distributions may be developed using the reported wind speeds. The probability distributions include the probability density function and the cumulative density function. A probability density function can be used to estimate the probability (or frequency) with which a range of wind speeds occurs, and is useful when extensive empirical data is unavailable, such as data at exceptionally high wind speeds. The cumulative density function is used to measure the frequency of a maximum wind speed. In other words, the cumulative density function is used to measure the occurrence frequency of all wind speeds up to a particular speed. Two types of probability distributions typically used to characterize wind speeds are the Weibull distribution and the Rayleigh distribution. (M.T. Alodat et al., 211). The Rayleigh distribution requires only the mean wind speed to be known to create the probability distribution, whereas a Weibull distribution uses two parameters: the scale factor and shape factor. (Manwell et al., 29) For the purposes of this study, only the Rayleigh distributions will be used. From the turbine reported wind data, the seasonal and year-long mean wind 7

22 speeds are easily found. With the mean wind speeds known, the Rayleigh probability density function and cumulative density function are given by: 2 π U π U p( U) = exp 2 2 U 4 U Equation 6: Rayleigh Probability Density Function 2 π U F( U) = 1 exp 4 U Equation 7: Rayleigh Cumulative Density Function Where pu ( ) F( U ) U is the probability density function of wind speed U is the probability of wind speeds ( < U) occurring is the mean wind speed Because wind speed is a continuous data set (as opposed to discreet), the probability of a particular wind speed occurring is zero. Rather it is useful to find the probability of a range of speeds occurring. To do this, probability density function is integrated over the range of wind speeds to estimate the probability with which that range of speeds occur. Equivalent to integrating the probability density function is to take the difference of the cumulative distribution function at the ends of the wind speed ranges in question. This is because cumulative density function is the integral of the probability density function from to speed U. 8

23 3.5 Theoretical Power Output Theoretical power output may be calculated from known wind speed then used to compare with the actual power output to evaluate turbine performance. The theoretical power output calculated from the wind speed data employs the One-dimensional Momentum Theory, a simple model developed by Albert Betz used for predicting power output (Manwell et al., 29). Calculating the maximum available power output for a given wind speed requires the assumption that the turbine operates with a complete mechanical efficiency as well as a uniform axial induction factor that is optimized to yield maximal turbine efficiency, and is only a function of the wind speed given a set rotor diameter. This induction factor,a, is a = 1/3, yielding a Power Coefficient equal to that of the Betz Limit, 59.26%, or the maximum amount of power extracted from upstream wind. From the One-dimensional Momentum Theory, power output may be calculated from the following: 1 P= ρ ( ) 2 3 AU a a Equation 1: One-dimensional Momentum Theory Power Output Where P is power output, ρ is air density, A is area swept by turbine blades, U is wind velocity, and a is axial induction factor. For lack of recorded air density or air temperature data, the air density for the purposes of calculating the theoretical power output will be assumed to be sea-level air density, 1.225kg/m 3. This assumption is a potential source of error and is addressed in Appendix E, as well as in Figure 36. The One-dimensional Momentum Theory assumes an actuator disk model for the wind turbine, making the swept area simply the circular area with diameter equal to the rotor diameter. For the Northern Power Systems 1-21 turbine, the rotor diameter is 21m, making the swept area m. 9

24 The wind velocity used to calculate the theoretical power is the wind velocity reported by the turbine, as measured by the cup anemometer atop the nacelle. The axial induction factor is fixed at an optimal a =1/3 to assume a Betz Limit efficient turbine. With the Betz Limit efficient power output known, the turbine efficiency may be found by normalizing the actual power output with the Betz Limit efficient power output. This may be done for a wide range of wind speeds to find turbine efficiency as a function of wind speed. Using the theoretical Betz Limit power output given by Equation 1 and an optimal a=1/3 induction factor, the turbine efficiency is then found by: η turb P = = P Betz 8 27 P ρau 3 Equation 2: Turbine Efficiency Relative to Betz Limit Where η turb is turbine efficiency relative to the Betz Limit, P is the measured (actual) power output, P Betz is the theoretical Betz Limit efficient power output ρ is air density, A is area swept by turbine blades, U is wind velocity 3.6 Calculating Power Curve A power curve shows the expected relationship between power output and wind speed. As part of the turbine specifications, Northern Power Systems has made readily available the theoretical power curve on their website ( From the wind speed and power output data reported by the turbine, an empirical power curve may be found by following the procedure set forth by IEC for wind turbine power performance 1

25 measurement. IEC requires that the recorded wind speed and power output dataset should meet the following criteria to be used for power curve generation: Minimum of 18 hours of continuous data Minimum of 3 minutes at each wind speed Range of wind speeds should include 1m/s below cut-in speed, up to 1.5x the wind speed that corresponds to 85% of rated power Additionally, the wind speed should be captured by a cup anemometer placed on a metrological tower 2-4 rotor diameters from the turbine, sampled at a rate of 1Hz or faster. Air pressure and temperature should also be recorded for the purposes of calculating normalized air density if air density at turbine site is not within +/-.5kg/m 3 of ISO standard atmosphere (1.225 kg/m 3 ). After obtaining the raw wind data, IEC employs a procedure known as method of bins to generate the power curve: 1. Raw data is averaged over 1-minute intervals 2. 1-minute averaged data is binned according to wind speed in.5m/s bins 3. Within each bin, the arithmetic average of wind speed and power are taken: P V i j= 1 N i, j i Where 1 Ni = 1 Ni = P V i j= 1 N i, j i Equation 3: Method of Bins for Power Output Equation 4 Method of Bins for Wind Speed V i P i is the averaged wind speed within the bin is the averaged power within the bin 11

26 N i V,i,j P,i,j is the number of data points in the bin is the wind speed of data point j in bin i is the power of data point j in bin i 4. The averaged power output of each bin is then plotted with the corresponding averaged wind speed to create the power curve. 3.7 Calculating Power Coefficient Curve A parameter known as the Power Coefficient (C p ) is typically used when evaluating wind turbine performance (Manwell et al., 29). After applying the method of bins to the raw wind turbine data to calculate the power curve, the averaged power output data is nondimenionalized by the available wind power within each bin to find the Power Coefficient as a function of wind speed. A power coefficient curve shows the wind speeds at which the turbine extracts the largest proportion of available energy, with the maximum allowable quantity being the Betz Limit (59.26%). C p = 1 2 P ρau 3 Equation 5: Calculating Power Coefficient Where P is power output, ρ is air density, A is area swept by turbine blades, U is wind speed. 12

27 4. Statistics This section will discuss the statistics derived from the turbine output data. Statistical parameters of interest include the average wind speeds, average power, total energy production, frequency of wind speeds and frequency of power output. Each of these parameters will be examined on a seasonal as well as a year-long basis. 4.1 Overview The following is a summary of the seasonal and year-long statistics gathered from the one-second data reported by the turbine, including average wind and power output, as well as total net energy. The net energy is calculated as the gross energy produced by the turbine, less the energy lost due to parasitic consumption by the turbine when the available wind is below cut in speed. Data Set Average Wind Speed (m/s) Std Dev. Wind Speed Average Power (kw) Std. Dev Power Output Fall Winter Spring Summer Sept 211 Aug 212 (year-long) Total Net Energy (MWh) Table 2: Wind Speed and Power Output Summary 13

28 4.2 Wind Speed and Energy Production Details The following sections further analyze the statistical details of the wind and power output data. Both 1-second and 1-minute averaged data are analyzed and tabulated. To characterize the wind availability, the wind speeds are categorized into three ranges: Below Cut-in (Speeds < 3.5m/s), Between Cut-in and Rated (3.5 < Speed < 15m/s) and Between Rated and Cut-out (15 < Speed < 25m/s). For each range of speed, the number of occurrences and corresponding normalized frequency are shown, as well as the expected frequency as given by the Rayleigh cumulative density function. For the purposes of evaluating the turbine performance, a similar approach is taken to categorize the power output data: power produced by the turbine and power consumed by the turbine in the form of parasitic energy consumption. 14

29 4.2.1 Fall 211 Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized E-5 Frequency Expected Cum. Frequency E-5 Table 3: Fall 2111-second Wind Speed Data Criteria Power Produced Power Consumed Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 4: Fall 2111-second Power Output and Energy Data Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized Frequency.4.6 Table 5: Fall 2111-minute Averaged Wind Speed Data Criteria Power Produced Power Consumed Downtime Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 6: Fall 2111-minute Averaged Power Output and Energy Data 15

30 4.2.2 Winter 211 Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized E-4 Frequency Expected Cum. Frequency E-4 Table 7: Winter 2111-second Wind Speed Data Criteria Power Produced Power Consumed Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 8: Winter 2111-second Power Output and Energy Data Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized Frequency Table 9: Winter 2111-minute Averaged Wind Speed Data Criteria Power Produced Power Consumed Downtime Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 1: Winter 2111-minute Averaged Power Output and Energy Data 16

31 4.2.3 Spring 212 Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized E-4 Frequency Expected Cum. Frequency E-5 Table 11: Spring 2121-second Wind Speed Data Criteria Power Produced Power Consumed Net Energy (MWh) Occurrences Normalized.6.4 Frequency Energy (MWh) Table 12: Spring 2121-second Power Output and Energy Data Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized Frequency Table 13: Spring 2121-minute Averaged Wind Speed Data Criteria Power Produced Power Consumed Downtime Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 14: Spring 2121-minute Averaged Power Output and Energy Data 17

32 4.2.4 Summer 212 Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized E-5 Frequency Expected Cum. Frequency E-7 Table 15: Summer 2121-second Wind Speed Data Criteria Power Produced Power Consumed Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 16: Summer 2121-second Power Output and Energy Data Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized Frequency Table 17: Summer 2121-minute Averaged Wind Speed Data Criteria Power Produced Power Consumed Downtime Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 18: Summer 2121-minute Averaged Power Output and Energy Data 18

33 4.2.5 Year Long (Sept 211 Aug 212) Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized E-4 Frequency Expected Cum. Frequency E-5 Table 19: Sept Aug 2121-second Wind Speed Data Criteria Power Produced Power Consumed Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 2: Sept Aug 2121-second Power Output and Energy Data Criteria Below Cut-In Between Cut-In and Between Rated and Rated Cut-Out Wind Speeds (m/s) Speed < < Speed <15 15< Speed <25 Occurrences Normalized Frequency Table 21: Sept Aug 2121-minute Averaged Wind Speed Data Criteria Power Produced Power Consumed Downtime Net Energy (MWh) Occurrences Normalized Frequency Energy (MWh) Table 22: Sept Aug 2121-minute Averaged Power Output and Energy Data 19

34 5. Data Plots and Experimental Results This section will provide a graphical representation of the turbine recorded data for wind speed and power output. Additionally, this section will also present calculated graphical results such as Rayleigh distributions for wind speed, empirical power curves, theoretical and actual power outputs comparisons, efficiency curves and power coefficient curves. 5.1 Wind Speed Frequency Plots and Rayleigh Distributions Fall 211 One Second Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 1 2

35 Fall 211 Ten Minute Averaged Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure Fall 211 Wind Speed Rayleigh Cumulative Frequency Distribution Cum. Freq. Distribution Cut In Speed, 3.5m/s.8 Cumulative Frequency X: 3.5 Y: Wind Speed (m/s) Figure 3 Figures 1-3 are a graphical representation of the wind speed data for Fall

36 Winter 211 One Second Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 4 Winter 211 Ten Minute Averaged Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 5 22

37 1.9 Winter 211 Wind Speed Rayleigh Cumulative Frequency Distribution Cum. Freq. Distribution Cut In Speed, 3.5m/s.8 Cumulative Frequency X: 3.5 Y: Wind Speed (m/s) Figure 6 Figures 4-6 are a graphical representation of the wind speed data for Winter

38 Spring 212 One Second Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 7 Spring 212 Ten Minute Averaged Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 8 24

39 1.9 Spring 212 Wind Speed Rayleigh Cumulative Frequency Distribution Cum. Freq. Distribution Cut In Speed, 3.5m/s.8 Cumulative Frequency X: 3.5 Y: Wind Speed (m/s) Figure 9 Figures 7-9 are a graphical representation of the wind speed data for Spring

40 Summer 212 One Second Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 1 Summer 212 Ten Minute Averaged Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 11 26

41 1.9 Summer 212 Wind Speed Rayleigh Cumulative Frequency Distribution Cum. Freq. Distribution Cut In Speed, 3.5m/s.8 Cumulative Frequency X: 3.5 Y: Wind Speed (m/s) Figure 12 Figures 1-12 are a graphical representation of the wind speed data for Summer

42 Sept Aug 212 One Second Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 13 Sept Aug 212 Ten Minute Averaged Normalized Wind Speed Distribution.3 Actual Frequency Rayleigh Distribution Expected Frequency.25 Normalized Frequency Wind Speed (m/s) Figure 14 28

43 Sept Aug 212 Wind Speed Rayleigh Cumulative Frequency Distribution Cum. Freq. Distribution Cut In Speed, 3.5m/s Cumulative Frequency X: 3.5 Y: Figure 15 Figures are a graphical representation of the wind speed data for the year-long data set that encompasses all data points used in this study. Figure 15 shows that an estimated 44% of winds encountered throughout the year fall below the cut in speed of 3.5m/s while the likelihood of encountering wind speeds at the rated speed (15m/s) or faster is infinitesimally small Wind Speed (m/s) 29

44 5.2 Power Output Frequency Plots Fall 211 One Second Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 16 Fall 211 Ten Minute Averaged Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 17 3

45 Winter 211 One Second Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 18 Winter 211 Ten Minute Averaged Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 19 31

46 Spring 212 One Second Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 2 Spring 212 Ten Minute Averaged Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 21 32

47 Summer 212 One Second Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 22 Summer 212 Ten Minute Averaged Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 23 33

48 Sept Aug 212 One Second Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 24 Sept Aug 212 Ten Minute Averaged Normalized Power Output Distribution.5 Normalized Frequency Power Output (kw) Figure 25 34

49 Figures are graphical representations of the normalized power output. In each instance there is a high frequency of power measured outputs around-1 to 1kW with the frequency rapidly trailing off for increasing power outputs. This indicates that the turbine spends much of the time consuming energy or producing energy a lower power, possibly due to the high frequency of low wind speeds, as shown in Figures

50 5.3 Seasonal and Year Long Empirical Power Curves 12 Fall 211 Power Curve 1 8 Power (kw) Published Power Curve Empirical Curve Wind Speed (m/s) Figure 26 The Fall 211 empirical power curve shows good agreement with the published power curve wherever there is available data. At speeds beyond ~11m/s there is an insufficient amount of data to create an empirical power curve. 36

51 12 Winter 211 Power Curve 1 8 Power (kw) Published Power Curve Empirical Curve Wind Speed (m/s) Figure 27 Figure 27 shows the Winter 211 empirical power curve, which like the Fall 211 power curve has good agreement at speeds below 1m/s. Unlike the Fall 211 empirical power curve, the Winter 211 curve contains sufficient data to extend the curve into ~13m/s. However, at these high speeds the empirical curve shows significant deviation from the published curve, possibly due to a relatively low number of data points and high influence of outlier data. 37

52 12 Spring 212 Power Curve 1 8 Power (kw) Published Power Curve Empirical Curve Wind Speed (m/s) Figure 28 The Spring 212 empirical power curve has similar wind speed range as the Winter 211 power curve. However the Spring 212 power curve is in much better agreement with the published curve, with relatively small deviation at higher wind speeds. 38

53 12 Summer 212 Power Curve 1 8 Power (kw) Published Power Curve Empirical Curve Wind Speed (m/s) Figure 29 Like the Fall 211 empirical power curve, the Summer 212 curve shows good agreement where there is sufficient data to form a power curve. For the Summer 212 data set, there is sufficient data for speeds up to ~9m/s, where at the last wind speed bin there is very slight deviation from the published curve. 39

54 12 Sept Aug 212 Power Curve 1 8 Power (kw) Published Power Curve Empirical Curve Wind Speed (m/s) Figure 3 The year-long data set has a larger range of wind speeds than the other data sets. This is due to the accumulation of data from each set that allows for high wind speed bins to satisfy the minimum sampling time set forth by IEC As with the empirical power curves generated by other data sets, there is good agreement up to ~1m/s with deviations from the published curve at higher wind speeds. These deviations are less extreme due to the larger sample mitigation of outlier effects. 4

55 5.4 Theoretical vs. Actual Power Output Plots 25 Fall 211 Theoretical Power vs Actual Power Output 2 Power (kw) Theoretical Published Power Curve Actual Wind Speed (m/s) Figure Winter 211 Theoretical Power vs Actual Power Output 2 Power (kw) Theoretical Published Power Curve Actual Wind Speed (m/s) Figure 32 41

56 Spring 212 Theoretical Power vs Actual Power Output 25 2 Power (kw) Theoretical Published Power Curve Actual Wind Speed (m/s) Figure Summer 212 Theoretical Power vs Actual Power Output 2 Power (kw) Theoretical Published Power Curve Actual Wind Speed (m/s) Figure 34 42

57 35 Sept Aug 212 Theoretical Power vs Actual Power Output 3 25 Power (kw) Theoretical Published Power Curve Actual Wind Speed (m/s) Figure 35 Figures 31, 32, 33, 34, and 35 are plots of the theoretical Betz Limit power output (as calculated by Equation 1) along with empirical and published power curves. The plots are done for each data set over the range of wind speeds for which there are bins to generate an empirical power curve. In every instance the Betz Limit power output is greater than both published and actual power curves by increasing magnitude with wind speed, suggesting that as designed the turbine has losses that prevent the turbine efficiency from reaching the Betz Limit. 43

58 5.5 Compiled Efficiency Curves Turbine Efficiency Relative to Betz Limit Fall 211 Winter 211 Spring 212 Summer 212 Sept Aug 212 Efficiency /- 6% uncertainty Wind Speed (m/s) Figure 36 Figure 36 is a compilation of all data sets efficiency plots over the range of wind speeds for which there was sufficient data to generate a power curve. The efficiency at each wind speed was calculated using Equation 2, with the binned wind speed and corresponding power output as the incoming wind speed and actual power output, respectively, in Equation 2. The resulting collection of efficiency curves indicates that relative to the Betz Limit, the turbine operates a peak efficiency of ~65-7% at a wind speed of ~6.75m/s. The error in the data, given by variations in the air density affect the efficiency by up to 5% (See Appendix E) Individual data sets efficiency curve can be found in the Appendix B. 44

59 5.6 Compiled Power Coefficient Curves Compiled Power Coefficient.5.4 Fall 211 Winter 211 Spring 212 Summer 212 Sept Aug 212 Cp Wind Speed (m/s) Figure 37 Figure 37 is a compilation of power coefficient curves where the power coefficient is calculated from Equation 5 and plotted as a function of binned wind speeds for every data set. As with the turbine efficiency curve, the power coefficient curve indicates that at ~6.75m/s the power coefficient peaks at ~ with the Winter 211 having the highest peak coefficient, and Summer 212 the lowest. This indicates that at 6.75m/s the turbine converts the highest proportion (35-4%) of available wind energy to electrical energy output. By comparing Equation 5 and Equation 2, it would be expected that the power coefficient and efficiency curves should peak at the same wind speed. Note that individual data sets power coefficient curve can be found in Appendix C. 45

60 6. Discussion This section will use the wind speed and power production statistical data and calculations to characterize the seasonal and yearly wind speeds, as well as the resulting power output of the turbine. Comparing with the annual energy output with the expected energy output as published by Northern Power Systems would allow the turbine efficiency to be found. Turbine performance will also be characterized by comparing the calculated empirical power curves with the published power curve and analyzing the efficiency and power coefficient curves. Additionally, the effects of wind gusts will be examined by comparing the results calculated 1-second data with those calculated the 1-minute averaged data. 6.1 Statistical Results and Energy Output The average wind speeds vary by season, ranging from 3.4m/s for Summer 212 to 4.7m/s for Winter 211, with a yearly wind speed average of 4.m/s. Within each data set the wind fluctuations, as measured by the wind speed standard deviation, correspond in magnitude to the average wind speed. That is, along with having the lowest average wind speed, Summer 212 also had the lowest standard deviation at 1.6m/s. Conversely, Winter 211 experienced the greatest fluctuation in wind speeds with a standard deviation of 2.3m/s. The seasonal wind speeds are an indicator of average power output, but only relative to outputs of other seasons. As expected by examining the relative average wind speeds, Winter 211 had the highest average power output at 13kW and Summer had the lowest average power output at 3.8kW. Though the difference in average wind speeds is small, only 1.33m/s, the difference in average power output between the two extreme seasons is large at 8.767kW. From Equation 1, it can be seen that the power output varies with the cube of velocity. By normalizing the cube of the Winter 211 average wind speed with that of the 46

61 Summer 212, the Winter 211 average power output should be about greater by a factor of approximately 2.2. However, the actual difference in power output is a factor of approximately 3.3. This may be due to the turbine response to wind speeds. Although the available energy in the Winter 211 wind is greater by a factor of 2.2, the turbine power output behavior is not directly predictable by the amount of available power. Rather, the behavior is best predicted by analyzing the turbine power curve and noting the cut-in speed. As the Summer 212 average wind speed is below the cut-in speed for the turbine, with relatively low variation from the average wind speed, it would be expected that the Summer 212 power output of the turbine would be smaller than that of Winter 211 by a factor greater than 2.2. With the power output for known for the time period spanning September 211 to August 212, it was possible to find a total net energy output that takes into account the periods of low wind speed and turbine maintenance. The gross energy production was found to be 68MWh, with a consumption of.74mwh. giving a total net energy output to be 67MWh, which is slightly lower than the predicted completely efficient turbine energy output value published in the Northern Power Systems turbine specification sheet. With an annual average wind speed of approximate 4 m/s, Northern Power predicted that a no-loss turbine with complete operating availability would output 77MWh. Relative to the published energy output as a theoretical quantity, the Case Western Reserve University wind turbine generates 87.7% of the theoretical annual energy output. Using an estimated cost of electricity provided by the Bureau of Labor Statistics at $.129/kWh, the turbine has generated approximately $87 worth of electricity. 47

62 6.2 Wind Speed Normalized Frequencies To characterize the seasonal and annual wind speeds encountered by the wind turbine, the wind speeds were categorized into speeds below cut-in (speeds below 3.5m/s), speeds between cut-in and rated (speeds between 3.5m/s and 15m/s), and between rated and cut-out (between 15m/s and 25m/s). The number of occurrences observed within each category was then normalized by the total number of data points within the data set. Analyzing the normalized frequency for each category allows for a comparison of wind behavior between the seasons. With the lowest average wind speed, Summer 212 was also observed to have the highest proportion of wind speeds below cut-in, at 57% and 54% for 1-second data and 1- minute averaged data, respectively. By contrast, Winter 211 had the lowest proportion of below cut-in speeds, at 34% and 31% for 1-second data and 1-minute averaged data, respectively. The Fall 211 and Spring 212 data sets have below cut in speed frequencies falling between the Winter 211 and Summer 212 observations, but not correlating with their respective average seasonal energy outputs. That is, Fall 211 with 42% and 4% of 1- second and 1-minute averaged speeds below cut in has slightly less total energy output than Spring 212, despite Spring 212 having higher proportion of below cut in wind speeds (48% and 45%). This may be due to the fact that the Spring 212 data set contains significantly more data points at the higher wind speeds, with an accumulated 486s of high wind speeds for Spring 212, and 68s for Fall 211. It should be noted that the high wind speeds only appear in the 1-second data sets. The 1-minute averaged data sets do not contain any speeds beyond the rated speed, 15m/s. This suggests that while the turbine does experience high speed winds, high speed winds exist 48

63 only as short duration gusts. In addition, the differences found in low (below cut in) wind speed frequencies between the 1-second and 1-minute averaged data sets suggest the presence intermittent breaks of low wind speeds between longer gusts at moderate (between cut in and rated) speeds. 6.3 Probability Distributions The normalized wind speed frequency plots tend to follow a Rayleigh distribution, as observed in the wind speed frequency plots. While the frequency plots follow the Rayleigh probability density function closely in shape and center, the frequency plots are not expected to follow it exactly. Since the Rayleigh distribution relies only on the mean wind speed to produce the probability density function without other means of influencing the shape of the probability curve, the observed data may show some discrepancies when compared to the expected. The most prevalent discrepancy is a higher than expected observed frequency of the mean bin speed, and lower than expected frequencies of the adjacent bins. The observed one-second data tends to deviate more than the 1-minute averaged data from the expected, suggesting that intermittent gusts have wind speeds that tend towards the mean value. To find the expected probability that wind speed falls within a specified wind speed range, the Rayleigh Probability Density function is integrated over that range of speeds. This is done because wind speed is a continuous function where the probability of any one particular speed occurring is zero, which also necessitates displaying the actual wind speed normalized occurrences as ranges, or bins. Although plotting with smaller bins would result in a finer histogram plot, as the bins approached an infinitesimally small size, their frequencies tend towards zero (See Appendix D for a graphical representation). Therefore bin sizes were chosen to be 1m/s. 49

64 The Rayleigh cumulative frequency distribution plot shows the frequency with which wind speeds up to a particular speed are expected to appear. The actual normalized frequency with which certain speed ranges appear can be used to compare with the expected frequency based on the Rayleigh distribution. Similar to the probability density plot, the cumulative frequency plot provides an estimated range of wind speeds most likely to occur. The cumulative frequency plots are in good agreement with the actual data, as shown by comparing Figure 3, Figure 6, Figure 9, Figure 12, and Figure 15 with the respective seasonal one-second data tabulated in Table 3, Table 7, Table 11, Table 15, and Table 19. Using Equation 7 and the seasonal mean wind speeds tabulated in Table 2, the expected frequency of encountering winds at or greater than the 15m/s rated turbine speed were found to be small. This suggests that the turbine very rarely has sufficient wind speed to output power at its rated capacity. This is corroborated by the empirical power curves. 6.4 Empirical Power Curves To gauge performance over a range of wind speeds, empirical power curves were created in accordance to IEC standard IEC using the wind speed and output power reported by the wind turbine. These power curves were then plotted alongside the published power curve provided by Northern Power Systems (Figures 26-3). As with the other components of this study, power curves were created for each season, as well as for the yearlong compilation of data. For every data set the empirical power curve closely follows the published power curve until approximately 1m/s. The deviations thereafter are range from slight, as with the Fall 211 power curve (Figure 26) to extreme, as seen with the Winter 211 power curve (Figure 27). In every instance the deviations from the theoretical published power curve occur only at 5

65 the higher wind speeds, at 1m/s and beyond. The Winter 211 power curve shows the most deviations at higher speeds, with unexpected dips in power output at the faster wind speeds. This may be attributed to several factors, such as a relatively large presence of high speed wind gusts where the wind turbine does not adequately respond in power production to the very brief increase in wind speed. This is supported by the large wind speed standard deviation found in the Winter 211 data. Another potential source of deviation from the theoretical power curve at high wind speeds may be the relatively low number of available data points at the higher speed regions. This would allow for outliers to strongly affect the resulting power curve. At the three highest speed bins, there are only 4, 1-minute averaged data points binned under the highest speed bin for the Winter 211 data set. While there are bins with as little as 1, 1-minute averaged data point, any bins with 2 or less 1-minute averaged data points are discarded as per the minimum 3 minute requirement per bin in IEC It should be noted from the empirical power curves that there is no data to show turbine behavior reaching the rated output. This is expected, as statistical analysis of the observed wind speeds has shown a very low frequency of wind speeds reaching the rated output speed (15m/s) or faster. Therefore, the requirement for wind speed range used for creating a power curve imposed by IEC has not been met, as the required range must include 1.5 times the speed at which the turbine is at 85% capacity. For the turbine under consideration the required wind speed upper bound is approximately 18m/s. The highest binned wind speed is 14m/s found in the Sept 211 Aug 212 power curve (Figure 3). With the lack of upper range wind speed data, the actual turbine performance under these conditions remains unknown. 51

66 6.5 Theoretical vs. Actual Power Output and Efficiency Curves The theoretical power output as determined by Equation 1 using the turbine reported wind speed assumes complete efficiency and conversion wind energy to electrical energy as allowed by the Betz Limit. As shown by Figures 31-35, the actual and designed power outputs fall short of the theoretical for all wind speeds, suggesting that there are inherent losses associated with the wind turbine as designed. These losses may include aerodynamic as well as mechanical losses. The turbine efficiency as defined by the actual output normalized by theoretical power output is wind speed dependent, as shown by Equation 2. For every data set the efficiency peaks at approximately 6.75m/s, ranging from ~65-7% efficiency, suggesting that the turbine is designed to operate at wind speeds near 6.75m/s. From the compiled efficiency curve in Figure 36 it can be seen that the Winter 211 data set has the highest peak efficiency, and the Summer 212 data set has the lowest peak efficiency. In addition to the efficiency peaking at the same speed for all data sets, the shape of the efficiency curves are similar at moderate speeds. At low speeds there are deviations, as most evident by the Spring 212 data set. This may be due to the relatively low power output at these speeds and even the slightest variations in power lead to large variations in efficiency. As encountered with the empirical power curves, there is a limited amount of data available for higher wind speeds, therefore limiting the availability and reliability calculated efficiencies. For the summer data set, there is no efficiency information known beyond ~9.5m/s, and for other data sets there is poor consistency beyond 1m/s. The shape of the curves suggest that at speeds lower than the peak 6.75m/s the efficiency drops quickly with every incremental decrease in wind speed. By contrast, at speeds higher than the peak, the 52

67 efficiency drops much slower, suggesting that this turbine is tuned to best operate at speeds slightly slower than the most frequently observed speeds, which for this turbine is 5-8m/s. 6.6 Power Coefficient Curves Power coefficient curves for each seasonal and yearly data set were created by calculating the power coefficients using Equation 4 with binned data then plotting the resulting power coefficients with the corresponding wind speeds bins. The resulting curve shows over a range of wind speeds the proportion of available wind energy successfully harnessed by the turbine as useful power output. While individual curves for each seasonal and year-long data set is useful for characterizing turbine power output behavior over a range of wind speeds, a compilation plot of power coefficient curves for all seasons as well as the year-long data set can also be used easily to evaluate the turbine performance over all seasons. Figure 37 shows the compilation of power coefficient curves over all seasons and the year-long data set. The seasonal and yearly power coefficient curves all exhibit similar behavior at low speeds up to where all curves peak at a wind speed of approximately 6.75m/s. At this peak wind speed, the Cp ~.4, suggesting that the turbine extracts at most, 4%, of power from the incoming wind at ~6.75m/s. Similar in shape to the Turbine Efficiency curves found in Figure 36, the Power Coefficient curves suggest that the turbine is turned for wind speeds 5-8m/s, with a steep drop in performance, as measured by Power Coefficient at wind speeds below the peak speed (6.75m/s). The Cp curves for Fall 211 and Spring 212 decrease and uniformly with each other, while the Summer 212 curve stops shortly after the peak for lack of data at higher wind speeds and the Winter 211 curve exhibits an unexpected increase after decreasing for all speeds post peak C p. 53

68 6.7 Economic Feasibility Based on an annual net energy output of 67MWh, a simple study may be done to determine the economic feasibility of the turbine. Using an estimated $17/kW installed cost of a turbine in 27 and 2-year operational period (Manwell et al., 29), the installed cost for the 1-kilowatt turbine would be $17. With an assumed 2-year operational period, the break even annual energy cost savings would be $85. That is, the turbine must generate a net cost savings of $85 for it to be economically feasible. The net cost savings must take into account the costs of maintenance and operations, which are the costs associated with blade cleaning, turbine tests, checks, and maintenance. As the turbine ages, the cost of maintenance and operations increases from ~2% of the installed cost for the first two years of operation to ~7% of the installed cost for the last four years of operation (Manwell et al. 29). Using an operational life time average 4.5% of installed cost for the annual operations and maintenance costs of the turbine, the operations and maintenance costs would be approximately $765 annually. Therefore, the turbine must produce $162 worth of energy annually to offset the $77 cost of maintenance in order to produce the net $85 cost savings to break even with the installed cost. To generate a $162 worth of electricity from the annual 67MWh energy output, the cost of electricity must be approximately $.24/kWh for the turbine to break even. This would be approximately double the 212 cost of electricity currently provided by the Bureau of Labor Statistics for Cleveland, Ohio. Therefore, the turbine is not economically feasible unless the cost of electricity doubles. Otherwise, the turbine produces approximately half of the energy required for it to break even with the installed and annual maintenance costs. In 54

69 order for the turbine to break even by doubling its energy output, the annual average wind speed would need to be approximately 6m/s, as shown by the power curves in Figures Conclusions and Recommendations A year-long study was successfully conducted to analyze the wind power available at Case Western Reserve University, as well as the performance characteristics of the 1-kilowatt wind turbine. 7.1 Conclusions Based on the results of this study, the following conclusions can be made regarding the wind availability: 1. As seen in Table 2, the winter months (December 211 February 212) have the highest average wind speed and wind variance at 4.7m/s and 2.3m/s, respectively. The summer months (June 212 August 212) have the lowest average wind speed and variance at 3.4m/s and 1.6m/s, respectively. 2. From Table 9 and 17, the frequency of 1-minute averaged wind speeds below cut-in speed varies between 31% for the winter months and 54% for the summer months. This suggests that while there is wind available for producing power, a significant portion of the observed wind speeds falls below the minimum required for power production. 3. From the year-long accumulated data in Table 19 and Table 21, wind speeds at or above the rated 15m/s speeds are rarely encountered, and only in the 1-second data. 55

70 Therefore, the minimum required wind speed for the turbine to operate at its rated capacity exists only in rarely occurring gusts. 4. The wind speed frequencies follow a Rayleigh distribution. This can be seen by applying a plot of the Rayleigh probability density function over the wind speed plots (Figures 1 through 15). Additionally the Rayleigh cumulative density function successfully approximated the expected frequencies with which certain wind speed ranges were observed, as shown in Tables 3, 7, 11, 15, and 19. The following conclusions can be made to characterize the performance of the Northern Power Systems kilowatt wind turbine: 1. As shown in Table 2, the total net energy production between September 211 and August 212 is 67MWh, at an average power of 8.kW. 2. From the accumulated year-long 1-second power production data found on Table 2 it can be seen that between September 211 and August 212, the turbine produced power 64% of the year while consuming power 36% of the year. The turbine produced a gross energy output of 68MWh and consumed.74mwh, which gives an annual net energy output of 67MWh. 3. Based on an average annual wind speed of 4m/s, Northern Power specifies that the annual energy output be 77MWh assuming no losses and complete turbine availability to produce power. With a net actual energy output of 67MWh, the turbine is produces 88% of the expected annual energy output. At a rate of $.129 per kwh, 56

71 the turbine produced approximately $87 worth of electricity between September 211 and August The empirical power curves found in Figures 26, 27, 28, 29, and 3 indicate that the turbine performs as expected at lower speeds. The empirical power curves show good agreement with the published curve at speeds up to approximately 1m/s. However, beyond 1m/s the amount of data available to reliably determine performance is inadequate, as indicated by deviations from the expected curve as well as the low frequency of wind speeds beyond 1m/s in Figures 1, 2, 4, 5, 7, 8, 1, 11, 13, and Recorded power output across all wind speeds fall well below the theoretical power available. As shown in Figure 36, the turbine efficiency relative to the Betz Limit varies according to wind speed, but is consistent across all data sets, peaking at a wind speed of ~6.75m/s at value ranging from 65 7%. 6. The power coefficient curves for all seasons appear to be similar and show a peak at approximately 6.75 m/s wind speed, with a value of Cp ~.4 as shown by Figure 37. This suggests the turbine produces the most power relative to the amount available in the wind at 6.75 m/s, with ~4% of available wind power converted to useful electrical output. 7. From the above conclusions, it can be seen that the turbine is designed to best operate at 5-8m/s, or circa 6.75m/s the speed where the power coefficient is maximized. Based on the shape of the turbine efficiency and power coefficient plots in Figures 36 and 37 respectively, the performance drops off quickly to the left of the curve peaks 57

72 where wind speeds are less than 6.75m/s. In contrast, at wind speeds higher than the curve peaks, the corresponding efficiency decrease is more gradual by comparison. 8. For improved efficiency with the available winds, the site would be better suited for a turbine tuned for speeds with the highest frequency and slightly slower, which Figures 13,14,15 is 3-5m/s. 9. The turbine as it is currently installed is not economically feasible. With operational and maintenance costs estimated to be 4.5% annually of the installed cost (~$17) and an operational life of 2 years, the turbine would need for the cost of electricity to maintain a rate twice is current value in order for the investment to break even over the 2 year operational life. That is, the turbine currently outputs half of the required energy required to break even. 7.2 Recommendations To better characterize the wind available to the turbine a LiDAR system or other well maintained system used to for monitoring the hub-height wind speed could be used over an extended period with the turbine operational. Despite the IEC requirements for a met tower placed 2-4 diameters upstream of the turbine to measure wind speed, this study relied entirely upon the wind speed reported by the nacelle mounted cup anemometer mounted behind the turbine blades. Therefore, wind speeds downstream of the blades were taken to be equal that of the upstream, disregarding any potential effects of wakes downstream of the blades. Although the findings in the wind characterization portion of this 58

73 study corroborate well with the findings in the performance analysis, the results can be validated by repeating the study using reliable upstream wind speeds. Along with improperly measuring wind speed for power curve generation, there is a lack of higher wind speed data available to fully study the turbine performance at or beyond the speed for which it outputs its rated power. The IEC standard for power curve generation calls for an upper range of at least 1.5 times the speed at which the turbine operates at 85% of capacity or 18m/s for this turbine, while the maximum binned wind speed is 14m/s. To properly generate a power curve from empirical data would require the turbine to be relocated to a region with a wider range of wind speeds. However, this study is to analyze performance of the turbine as it is currently installed. The data collection should be automated to ensure that each data set would be continuous with the previous set by having a consistent collection time each week. This would eliminate the need to manually erase redundant overlapping data points. There would also be no risk of lost data due to more than 168 hours passing between data weekly collection during holidays or times of busy schedules that only affect human data collectors. Measuring other parameters such as temperature and air pressure can eliminate the need to make assumptions in some of the calculations, such as air density in Equation 1, Equation 2, and Equation 5. Using air pressure and temperature data gathered from nearby site to calculate minimum and maximum air density result in values that exceed the allowable kg/m 3 range for assuming ISO standard air density equal to kg/m 3. 59

74 Appendix A: Plots of Turbine Output Data Figure 38 Figure 39 6

75 Figure 4 Figure 41 61