MCP-Based Wind Farm Site Selection Using Variance Ratio Algorithm

Transcription

1 MCP-Based Wind Farm Site Selection Using Variance Ratio Algorithm Devin A. Kasper Department of Physics and Astronomy, Minnesota State University Moorhead Department of Industrial and Manufacturing Engineering, North Dakota State University Abstract The Measure-Correlate-Predict approach, using the Variance Ratio algorithm, was utilized to correlate two wind observation sites. The target site had a full set of wind speed data, but half of it was ignored and predicted. Using a discretized power vs wind speed curve, the real power (and therefore revenue) were computed for the predicted and observed wind data. The error in the predicted wind data was determined to be less than or equal to 10.3%. Distance between sites and length of data were the predominant sources of increased error. Introduction Around the US there are many sites with observed wind speed data. In order for wind data to be useful to wind power companies, private investors, etc., it is necessary to be able to predict wind speed at other sites. If a company is able to get a good price on land that is 20 miles away from a wind speed test site, it is not cost effective for them to construct permanent wind speed testing equipment and wait for a year, or more, in order to determine whether or not they ought to purchase the land and build a wind farm at that location. In order to get reliable wind forecasts, the measure-correlate-predict (MCP) approach can be used. The MCP approach begins with measuring the wind speed as a function of time for an extended period of time. This portion is already occurring at the aforementioned wind speed observation sites. The wind speed values are given and used as exact values. Next, a correlation algorithm is necessary to link two geographically separated sites. This requires some limited wind speed data at the target site. Once the two geographic sites are correlated, a prediction can be made. This prediction of the wind speed as a function of time will give the necessary long-term wind speed data required for a business to determine whether or not it is cost effective to purchase/lease a plot of land and build a wind farm. This study was performed as a case-study. In this study, a fictitious Company X has approached the author and has told him that there are two parcels of land available for purchase. The company has a set cost for the land, building of the wind farm, etc. 1

2 Company X also has a Minimum Attractive Rate of Return (MARR) for any projects considered. Company X has hired the author to perform a study and find the revenue at the two sites so that they can determine if the projects meet their MARR. The two projects are not mutually exclusive. Company X is willing to pay for wind speed analysis for up to 2 months, but requires at least 4 months of revenue analysis. This study used two wind observation sites (Petersburg and Alfred) as the two parcels of land available for purchase. The two sites are imagined to have limited wind speed data from Company X s wind speed analyses. Theory In their 2005 publication, Rogers et al. compared the performance of four correlation algorithms (1). Their study included three different geographical locations and six different performance metrics. They found that the so-called Variance Ratio gave the most reliable results for predicting wind speed. Based on their conclusions, the Variance Ratio was the correlation algorithm used for this study. The following is the derivation of the Variance Ratio. This is the equation of a line where m is the slope of the line and b is the y-intercept of the line. The wind speed at the two sites are assumed to have a linear relationship. This is the equation for the standard deviation where N is the total number in a population and is the mean of the population. Given the above, then: 2

3 If we set as the unknown wind speed at the target site, then: This is the equation for the Variance Ratio where: = the standard deviation of the known wind speed data at the target site. = the standard deviation of the wind speed data at the test site. = the mean wind speed of the known wind speed data at the target site. = the mean wind speed of the wind speed data at the test site. Methods The study began by writing a MATLAB program to calculate the predicted wind speed. This program used the previously derived Variance Ratio algorithm. Wind speed data, collected each hour, for two separate sites was acquired. As previously mentioned, the wind speeds were taken as exact values as no uncertainty was stated. Next, one site was taken as the test site and the other data was taken to be the target site. Then, each data set was split in half. The program was given as an input three sets of known data: X1, X2 and Y1. X1 and X2 were first and second half of the wind speed data at the test site. Y1 was the first half of the wind speed data at the target site. The second half Y2 was removed from the data set to simulate a real-world situation of not having a complete set of wind 3

4 speed data. The missing piece became. This represents one iteration of the program. The first iteration of this procedure used Alfred as the test site and Green River as the target site (see fig. 1). Figure 1 Wind monitoring sites within North Dakota. Diagram taken from: The data used was hourly wind speed data observed from 09/01/1995 through 09/30/1995 at 10 m. If any observations were missing from either station, it was removed from both sets. The data was split so that the predicted portion of the data was from 09/16/1995 through 09/30/1995. The resulting wind speed predictions were plotted as a function of time and compared to the observed wind speed data (see fig. 2 & Appendix 1). 4

5 Figure 2 Observed, predicted wind speed vs time for Alfred (test) vs Green River (target). Next, the same process was used for Alfred (test) vs Olga (target) for 09/01/1995 through 09/27/1995 (fig. 3). Figure 3 Observed, predicted wind speed vs time for Alfred (test) vs Olga (target). The data from the first two runs, shown in figs 2 & 3, was reviewed. It was decided to examine data at sites that are closer, for more than one elevation and for a longer period of time. As such the next set of data was run for Olga (test) vs Petersburg (target) from 09/01/1995 through 09/27/1995 at 10 m, 25 m, 40 m and 55 m. The plots from this data set are shown in Appendix 1. These same two sites were used with data from 10/04/1995 through 01/31/1996 at 10 m, 25 m, 40 m and 55 m. The plots from this data set are shown in Appendix 1. The final set of sites tested were Valley City (test) vs Alfred (target). The wind speed data used was from 11/01/1995 through 03/31/1996 at 10 m, 25 m, 40 m. These plots are shown in Appendix 1. 5

6 Results The initial error analysis was performed simply by looking at the percentage difference between the observed wind speed (Y2) and the predicted wind speed ( ). This gave a value for each hour and did not make clear what the overall trend was. The same issue was true when the wind speed vs time plots shown above were examined. What looked like a good (or bad) prediction could be the opposite. In order to quantify the error, a theoretical power output was used (2): where is the density of air, A is the area swept out by the blades of the wind turbine, is the wind velocity and the wind power coefficient is assumed to be 1 (not shown). A constant value for was assumed to be (kg/m 3 ) (3). The radius of the wind turbine was assumed to be 25 (m) and was used to calculate the area A, a circular region swept out by the turbine (4). The units of power are Watts. The power was calculated using the wind speed measurement for each hour. Then, each power calculation was multiplied by 1 hour giving an energy value. Once the energy was calculated for each hour the sum total of all of the energy for the test period was found. Finally, a set price per unit energy (assumed to be $0.10/kW*hr) was multiplied with the energy resulting in a total revenue calculation. The total revenue was calculated for the observed and predicted wind velocities. The percentage difference between the two values was found, as well as the absolute dollar differences. For Olga (test) vs Petersburg (target) over a period of 1 month, the following was the revenue analysis: 1- Month Elevation (m) Total Actual Revenue ($) Total Calculated Revenue ($) Energy Error (%) 10 $58, $51, $92, $82, $112, $100, $168, $151, Table 1 Revenue analysis for 1 month calculations at Olga (test) vs Petersburg (target). Actual revenue values are those calculated using the observed wind speeds; calculated revenue values are those using the predicted wind speeds. The revenue data was also plotted using a bar-graph: 6

7 Figure 4 Revenue comparison of actual revenue (using observed wind speeds) and calculated revenue (using predicted wind speeds). For the same two sites over a period of 4 months, the following was the revenue analysis: 4- Month Elevation (m) Total Actual Revenue ($) Total Calculated Revenue ($) Energy Error (%) 10 $807, $1,149, $1,058, $1,042, $1,314, $1,252, $1,731, $1,641, Table 2 Revenue analysis for 4 month calculations at Olga (test) vs Petersburg (target). Actual revenue values are those calculated using the observed wind speeds; calculated revenue values are those using the predicted wind speeds. Again, the revenue data was also plotted using a bar-graph: 7

8 Figure 5 Revenue comparison of actual revenue (using observed wind speeds) and calculated revenue (using predicted wind speeds). The analysis of Valley City (test) vs Alfred (target) was performed only for a five-month period. The following was the revenue analysis: Valley City vs Alfred Elevation (m) Total Actual Revenue ($) Total Calculated Revenue ($) Energy Error (%) 10 $1,556, $1,394, $2,214, $1,933, $2,606, $2,322, Table 3 Revenue analysis for 5 month calculations at Valley City (test) vs Alfred (target). Actual revenue values are those calculated using the observed wind speeds; calculated revenue values are those using the predicted wind speeds. Again, the revenue data was also plotted using a bar-graph: 8

9 Figure 6 Revenue comparison of actual revenue (using observed wind speeds) and calculated revenue (using predicted wind speeds). Notice in this data set there were measurements at hub heights of 10 m, 25 m and 40 m, but not at 55 m. Using the theoretical power equation was useful, but was ultimately not a reflection of the true power output from a wind turbine. As such, the more accurate, discretized power vs wind speed curve from a GE 900 wind turbine was obtained (5): 9

10 Figure 7 Discretized power vs wind speed curve. A MATLAB algorithm was written to read in the power vs velocity data. Next, the observed wind speed data (Y2) was read in. Finally, the correct equivalent power output was written out. This same procedure was used for the predicted wind speed data ( ). The above procedure was used for Olga (test) vs Petersburg (target) with the 4-month data. Just like before, power data was converted to energy and then revenue using 1 hour and a constant price of $0.10/kw*hr. The following is the revenue analysis from that procedure: Olga vs Petersburg- Real Power Curve Elevation (m) Total Actual Revenue ($) Total Calculated Revenue ($) Energy Error (%) 10 $21, $26, $27, $29, $34, $35, $43, $41, Table 4 Revenue analysis for 4 month calculations at Olga (test) vs Petersburg (target). Actual revenue values are those calculated using the observed wind speeds; calculated revenue values are those using the predicted wind speeds. Again using the empirical power vs wind speed curve Valley City (test) vs Alfred (target) were analyzed. The following is the revenue analysis for those sites: 10

11 Valley City vs Alfred- Real Power Curve Elevation (m) Total Actual Revenue ($) Total Calculated Revenue ($) Energy Error (%) 10 $49, $45, $65, $58, $74, $67, Table 5 Revenue analysis for 5 month calculations at Valley City (test) vs Alfred (target). Actual revenue values are those calculated using the observed wind speeds; calculated revenue values are those using the predicted wind speeds. Conclusions It became immediately obvious that using two sites very far away geographically (such as Green River and Alfred) produced unreliable predictions. Furthermore, examining only one month worth of data, that is two weeks of prediction, caused error. This is in agreement with Rogers, et al. who claimed that the longer the concurrent data length is, the smaller the standard deviation of the metric is (1). When two sites closer geographically were used, the 10 m hub height was a factor in the prediction error, at least for Olga vs. Petersburg. This seemed reasonable as it was thought that topographical effects on the wind speed would be greatest closer to the ground. However, the large difference between the error on the 10 m hub height and that of the other heights, as well as the fact that the other set of sites did not show this trend, suggests that there could have also been a calculation error. All of these facts led to the decision that this error should be rejected until its source is found. Using the real power curve the energy error percentage was between 1.8% and 10.3%. Therefore, the upper-limit of the error found in this study was 10.3%. Further study should focus on longer data sets. Also, several more sets of sites should be examined. It would also be useful to find out how the distance between sites affects the prediction error. This study was able to use the MCP approach and the Variance Ratio correlation algorithm to predict the wind speed at the two target sites (Petersburg and Alfred). Using the upper-limit percentage error (10.3%), the minimum, mean and maximum revenue were easily calculable. This revenue, then, was reported to Company X in order to determine which, if any, of the two projects should be undertaken. Acknowledgements Special thanks to Gong Li and Dr. Jing Shi in the Industrial & Manufacturing Engineering Department at North Dakota State University. 11

12 Appendix 1 Figure 8 Alfred (test) vs Green River (target) from 09/01/1995 through 09/30/1995 at 10 m. Figure 9 Alfred (test) vs Olga (target) from 09/01/1995 through 09/27/1995 at 10 m. 12

13 Figure 10 Olga (test) vs Petersburg (target) from 09/01/1995 through 09/27/1995 at 10 m. Figure 11 Olga (test) vs Petersburg (target) from 09/01/1995 through 09/27/1995 at 25 m. 13

14 Figure 12 Olga (test) vs Petersburg (target) from 09/01/1995 through 09/27/1995 at 40 m. Figure 13 Olga (test) vs Petersburg (target) from 09/01/1995 through 09/27/1995 at 55 m. 14

15 Figure 14 Olga (test) vs Petersburg (target) from 10/04/1995 through 01/31/1996 at 10 m. Figure 15 Olga (test) vs Petersburg (target) from 10/04/1995 through 01/31/1996 at 25 m. 15

16 Figure 16 Olga (test) vs Petersburg (target) from 10/04/1995 through 01/31/1996 at 40 m. Figure 17 Olga (test) vs Petersburg (target) from 10/04/1995 through 01/31/1996 at 55 m. 16

17 Figure 18 Valley City (test) vs Alfred (target) from 11/01/1995 through 03/31/1996 at 10 m. Figure 19 Valley City (test) vs Alfred (target) from 11/01/1995 through 03/31/1996 at 25 m. 17

18 Figure 20 Valley City (test) vs Alfred (target) from 11/01/1995 through 03/31/1996 at 40 m. Works Cited 1. Comparison of the performance of four measure correlate predict algorithms. Rogers, Anthony L., Rogers, John W and Manweel, James F. 2005, Journal of Wind Engineering and Industrial Aerodynamics, pp Computer Aided Investigation towards the Wind Power Generation Potentials of Guangzhou. Yang, Gang, Du, Yongxian and Chen, Ming. 2008, Computer and Informational Science, pp Shelquist, Richard. An Introduction to Air Density and Density Altitude Calculations. [Online] Shelquist Engineering, 08 02, [Cited: 09 17, 2010.] 4. Wind Farm Resources. 750 kw Wind Turbines. [Online] Wind Farm Resources, [Cited: 09 17, 2010.] 5. Idaho National Laboratory. Idaho Wind Data. Idaho National Laboratory. [Online] 01 31, [Cited: 10 11, 2010.] 18

19 Additional Resources 1. Wind speed spatial estimation for energy planning in Sicily: A neural kriging application. Cellura, M, et al. 2008, Renewable Energy, pp Wind resource assessment of an area using short term data correlated to a long term data set. Bechrakis, D A, Deane, J P and McKeogh, E J. 2004, Solar Energy, pp Bechrakis, D A, Deane, J P and McKeogh, E J. 2004, Solar Energy, pp Wind Farm Power Prediction: A Data-Mining Approach. Kusiak, Andrew, Zheng, Haiyang and Song, Zhe. 2009, Wind Energy, pp Uncertainty in wave energy resource assessment. Part 1: Historic data. Mackay, Edward B.L., Bahaj, AbuBakr S and Challenor, Peter G. 2010, Renewable Energy, pp Uncertainty analysis of wind energy potential assessment. Kwon, Soon-Duck. 2009, Applied Energy. 7. The round robin site assessment method: A new approach to wind energy site assessment. Lackner, Matthew A, Rogers, Anthony L and Manwell, James F. 2008, Renewable Energy, pp Wan, Yih-huei. Summary Report of Wind Farm Data. Oak Ridge : National Renewable Energy Lab, Statistical Wind Power Forecasting Models: Results for U.S. Wind Farms. Milligan, M, Schwartz, M and Wan, Y. Austin : National Renewable Energy Laboratory, Windpower. pp Short-term wind power forecasting using evolutionary algorithms for the automated specification of artificial intelligence models. Jursa, Rene and Rohrig, Kurt. 2008, International Journal of Forecasting, pp Short-term prediction of wind energy production. Sanchez, Ismael. 2006, International Journal of Forecasting, pp Short-term prediction of the power production from wind farms. Landberg, L. 1999, Journal of Wind Engineering and Industrial Aerodynamics, pp SHORT-TERM FORECASTING OF WIND SPEED AND RELATED ELECTRICAL POWER. ALEXIADIS, M C, et al. 1998, Solar Energy, pp

20 14. Short term wind speed forecasting for wind turbine applications using linear prediction method. Riahy, G H and Abedi, M. 2008, Renewable Energy, pp Review of design conditions applicable to offshore wind energy systems in the United States. Manwell, J F, et al. 2007, Renewable and Sustainable Energy Reviews, pp Sloughter, J McLean, Gneiting, Tilmann and Raftery, Adrian E. Probabilistic Wind Speed Forecasting using Ensembles and Bayesian Model Averaging. Seattle : University of Washington, Power optimization of wind turbines with data mining and evolutionary computation. Kusiak, Andrew, Zheng, Haiyang and Song, Zhe. 2010, Renewable Energy, pp On comparing three artificial neural networks for wind speed forecasting. Li, Gong and Shi, Jing. 2010, Applied Energy, pp Neural Network for Wind Power Generation with Compressing Function. Li, Shuhui, et al. 1997, IEEE, pp Linear and nonlinear models in wind resource assessment and wind turbine micrositing. Palma, J M.L.M., et al. 2008, Journal of Wind Engineering and Industrial Aerodynamics, pp Joint segmentation of wind speed and direction using a hierarchical model. Dobigeon, Nicolas and Tourneret, Jean-Yves. 2007, Computational Statistics & Data Analysis, pp Improvements in wind speed forecasts for wind power prediction purposes using Kalman filtering. Louka, P, et al. 2008, Journal of Wind Engineering and Industrial Aerodynamics, pp Nnadili, Christopher Dozie. Floating Offshore Wind Farms- Demand Planning and Logistical Challenges of Electricity Generation. Cambridge : s.n. 24. Badran, Omar, Abdulhadi, Emad and Mamlook, Rustum. Evaluation of parameters affecting wind turbine power generation. Amman : s.n. 25. Evaluation of Correlation the Wind Speed Measurements and Wind Turbine Characteristics. Kadar, Peter. Budapest : s.n. 8th International Symposium of Hungarian Researchers on Computational Intelligence and Informatics. pp

21 26. Saint Francis University Renewable Energy Center. Electricity Generation Estimates for Small to Large Turbines in a Class 2 Wind Resource in Pennsylvania. Pennsylvania : s.n. 27. Critical evaluation of methods for wind-power appraisal. Voorspool, Kris R and D haeseleer, William D. 2007, Renewable and Sustainable Energy Reviews, pp Comprehensive evaluation of wind speed distribution models: A case study for North Dakota sites. Zhou, Junyi, et al. 2010, Energy Conversion and Management, pp Comparison of Wind Power Estimates from the ECMWF Reanalyses with Direct Turbine Measurements. Kiss, Peter, Varga, Laszlo and Janosi, Imre M. 2009, JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY. 30. Comparison of bivariate distribution construction approaches for analysing wind speed and direction data. Erdem, E and Shi, J. 2010, Wind Energy. 31. Application of Bayesian model averaging in modeling long-term wind speed distributions. Li, Gong and Shi, Jing. 2009, Renewable Energy, pp Application of artificial neural networks for the wind speed prediction of target station using reference stations data. Bilgili, Mehmet, Sahin, Besir and Yasar, Abdulkadir. 2007, Renewable Energy, pp Application of a control algorithm for wind speed prediction and active power generation. Flores, P, Tapia, A and Tapia, G. 2005, Renewable Energy, pp Advanced Short-term Forecasting of Wind Generation - Anemos. Kariniotakis, G N, et al. 2006, IEEE Trans. on Power Systems. 35. A two-site correlation model for wind speed, direction and energy estimates. Salmon, James R and Walmsley, John L. 1999, Journal of Wind Engineering and Industrial Aerodynamics, pp A review on the young history of the wind power short-term prediction. Costa, Alexandre, et al. 2008, Renewable and Sustainable Energy Reviews, pp A review on the forecasting of wind speed and generated power. Lei, Ma, et al. 2009, Renewable and Sustainable Energy Reviews, pp