Empirical Analysis of Wind Power Potential at Multiple Heights for North Dakota Wind Observation Sites

HOU Yong, PENG Yidong, A. L. Johnson, SHI Jing


Wind speed is the most critical factor that determines wind power potential and generation. In this paper, the wind speed data of multiple years from various observation sites in North Dakota, U.S. was analyzed to assess the wind power potential. The study first applied probability density functions (PDFs) to characterize the wind speed data and fit the distributions at various heights for each observation site. The fitted distributions were then used to estimate the wind power potential based on the theoretical cubic power relationship between energy potential and wind speed. Due to the complexity of functions, the numerical integration approach was employed. The following major findings were obtained from this empirical study: (1) Weibull distribution is not always the best function to fit wind speed data, while gamma and lognormal distributions produce better fitting in many occasions; (2) For different height levels at one observation site, the best performing distributions may be different; (3) The estimation accuracies of wind energy potential based on the fitted wind speed distributions range from -4% to 3.8%; (4) The rank of energy potential estimation accuracies is not always consistent with that of goodness-of-fit for wind speed distributions. In addition, a simplified approach that only relies on the hourly mean wind speed to estimate wind power potential is evaluated. Based on the theoretical cubic relationship for wind power estimation, it was found that the simplified approach may provide significantly lower estimates of wind power potential by 42-54%. As such, this approach will become more practical if this amount of difference is to be compensated.

Key words: Wind speed; Distribution; Goodness-of-fit; Wind power potential; North Dakota


Wind speed; Distribution; Goodness-of-fit; Wind power potential; North Dakota

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[1] Al-Abbadi, N. M. (2005). Wind energy resource assessment for five locations in Saudi Arabia. Renewable Energy, 30(10), 1489–1499.

[2] Annaert, J., Deelstra, G., Heyman, D., & Vanmaele, M. (2007). Risk Management of a Bond Portfolio Using Options. Insurance: Mathematics and Economics, 41(3), 299-316.

[3] Arias, A., Forquin, P., Zaera, R., & Navarro, C. (2008). Relationship Between Static Bending and Compressive Behaviour of Particle-Reinforced Cement Composites. Composites Part B: Engineering, 39(7-8), 1205-1215.

[4] Askari, H., & Krichene, N. (2008). Oil Price Dynamics (2002-2006). Energy Economics, 30(5), 2134-2153.

[5] Brabady, J., & Kumar, U. (2008). Reliability Analysis of Mining Equipment: A Case Study of a Crushing Plant at Jajarm Bauxite Mine in Iran. Reliability Engineering & System Safety, 93(4), 647-653.

[6] Celik, A.N. (2004). A Statistical Analysis of Wind Power Density Based on the Weibull and Rayleigh Models at the Southern Region of Turkey. Renewable Energy, 29(4), 593-604.

[7] Chang, T.P. (2011). Estimation of Wind Energy Potential Using Different Probability Density Functions. Applied Energy, 88(5), 1848-1856.

[8] Elamouri, M., & Amar, F. B. (2008). Wind Energy Potential in Tunisia. Renewable Energy, 33(4), 758-768.

[9] Gupta, A., Mukherjee, B., & Upadhyay, S.K. (2008). Weibull Extension Model: A Bayes Study Using Markov Chain Monte Carlo simulation. Reliability Engineering & System Safety, 93(10), 1434-1443.

[10] Jaganathan, S., Tafreshi, H.V., & Pourdeyhimi, B. (2008).Modeling Liquid Porosimetry in Modeled and Imaged 3-D Fibrous Microstructures. Journal of Colloid and Interface Science, 326(1), 166-175.

[11] Kamarianakis, Y., Feidas, H., Kokolatos, G., Chrysoulakis, N., & Karatzias, V. (2008). Evaluating Remotely Sensed Rainfall Estimates Using Nonlinear Mixed Models and Geographically Weighted Regression. Environmental Modelling & Software, 23(12), 1438-1447.

[12] Lu, W., & Tsai, T-R. (2009). Interval Censored Sampling Plans for the Gamma Lifetime Model. European Journal of Operational Research, 192(1), 116-124.

[13] NIST/SEMATECH. (2006). E-Handbook of Statistical Methods. Retrieved from http://www.itl.nist.gov/div898/handbook/

[14] ND Division of Community Service. (2000). North Dakota Wind Resource Assessment Study. Retrieved from http://www.communityservices.nd.gov/energy/energy-resources/archived-publications/wind/

[15] Ramirez, P., & Carta, J.A. (2005). Influence of the Data Sampling Interval in the Estimation of the Parameters of the Weibull Wind Speed Probability Density Distribution. Energy Conservation and Management, 46(15-16), 2419-2438.

[16] Safari, B., & Gasore, J. (2010). A Statistical Investigation of Wind Characteristics and Wind Energy Potential Based on the Weibull and Rayleigh Models in Rwanda. Renewable Energy, 35(12), 2874-2880.

[17] Stansell, P. (2004). Distributions of Freak Wave Heights Measured in North Sea. Applied Ocean Research, 26(1-2), 35-48.

[18] Synowiec, D. (2008). Jump-Diffusion Models with Constant Parameters for Financial Log-Return Processes. Computers & Mathematics with Applications, 56(8), 2120-2127.

[19] Tar, K. (2008). Some Statistical Characteristics of Monthly Average Wind Speed at Various Heights. Renewable and Sustainable Energy Reviews, 12(6), 1712-1724.

[20] U.S. Department of Energy. (2008). Energy Efficiency and Renewable Energy, 20% Wind Energy by 2030- Increasing Wind Energy’s Contribution to U.S. Electricity Supply. Retrieved from http://www.nrel.gov/docs/fy08osti/41869.pdf

[21] Van der Heide, C.M., Van den Bergh, C.J.M., Van Lerland, E.C., & Nunes, P.A.L.D. (2008). Economic Valuation of Habitat Defragmentation: A Study of the Veluwe, the Netherlands. Ecological Economics, 67(2), 205-216.

[22] Veber, B., Nagode, M., & Fajdiga, M. (2008). Generalized Renewal Process for Repairable Systems Based on Finite Weibull Mixture. Reliability Engineering & System Safety, 93(10), 1461-1472.

[23] Vogiatzis, N., Kotti, K., Spanomitsios, S., & Stoukides, M. (2004). Analysis of Wind Potential and Characteristics in North Aegean Greece. Renewable Energy, 29(7), 1193–1208.

[24] Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. J. Appl. Mech.-Trans. ASME, 18(3), 293-297.

[25] Zhou, J., Erdem, E., Li, G. & Shi, J. (2010). Comprehensive Evaluation of Wind Speed Distribution Models: A Case Study for North Dakota. Energy Conversion and Management, 51(7), 1449-1458.

[26] Zhou, X.P., Wang, F.H., Qian, Q.H., & Zhang, B.H. (2008). Zonal Fracturing Mechanism in Deep Crack-Weakened Rock Masses. Theoretical and Applied Fracture Mechanics, 50(1), 57-65.

DOI: http://dx.doi.org/10.3968/j.est.1923847920120401.289

DOI (PDF): http://dx.doi.org/10.3968/g2827


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