Research Papers: Energy Systems Analysis

Application of the Maximum Entropy Method for Determining a Sensitive Distribution in the Renewable Energy Systems

[+] Author and Article Information
Gholamhossein Yari

School of Mathematics,
Iran University of Science and Technology,
Tehran 16846-13114, Iran
e-mail: Yari@iust.ac.ir

Zahra Amini Farsani

School of Mathematics,
Iran university of Science and Technology,
Tehran 16846-13114, Iran
e-mails: Z_aminifarsani@iust.ac.ir;

National Oceanic and Atmospheric Administration.

1Present address: Department of Statistics, Ludwig-Maximilians-University of Munich, Ludwigstr. 33, Munich 80539, Germany.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received August 18, 2014; final manuscript received March 26, 2015; published online May 8, 2015. Assoc. Editor: Reza H. Sheikhi.

J. Energy Resour. Technol 137(4), 042006 (Jul 01, 2015) (7 pages) Paper No: JERT-14-1259; doi: 10.1115/1.4030268 History: Received August 18, 2014; Revised March 26, 2015; Online May 08, 2015

In the field of the wind energy conversion, a precise determination of the probability distribution of wind speed guarantees an efficient use of the wind energy and enhances the position of wind energy against other forms of energy. The present study thus proposes utilizing an accurate numerical-probabilistic algorithm which is the combination of the Newton’s technique and the maximum entropy (ME) method to determine an important distribution in the renewable energy systems, namely the hyper Rayleigh distribution (HRD) which belongs to the family of Weibull distribution. The HRD is mainly used to model the wind speed and the variations of the solar irradiance level with a negligible error. The purpose of this research is to find the unique solution to an optimization problem which occurs when maximizing Shannon’s entropy. To confirm the accuracy and efficiency of our algorithm, we used the long-term data for the average daily wind speed in Toyokawa for 12 yr to examine the Rayleigh distribution (RD). This data set was obtained from the National Climatic Data Center (NCDC) in Japan. It seems that the RD is more closely fitted to the data. In addition, we presented different simulation studies to check the reliability of the proposed algorithm.

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Fronk, B. M., Neal, R., and Garimella, S., 2010, “Evolution of the Transition to a World Driven by Renewable Energy,” ASME J. Energy Resour. Technol., 132(2), p. 021009. [CrossRef]
Prasad, B. G. S., 2010, “Energy Efficiency, Sources, and Sustainability,” ASME J. Energy Resour. Technol., 132(2), p. 020301. [CrossRef]
Rocha, J. E., and Sanchez, W. D. C., 2012, “The Energy Processing by Power Electronics and Its Impact on Power Quality,” Int. J. Renewable Energy Dev., 1(3), pp. 99–105. [CrossRef]
Merzic, A., Music, M., and Rascic, M., 2012, “First Aspect of Conventional Power System Assessment for High Wind Power Plants Penetration,” Int. J. Renewable Energy Dev., 1(3), pp. 107–113. [CrossRef]
Siddall, J. N., 1983, Probabilistic Engineering Design, 1st ed., Marcel Dekker, Basel, New York.
Ramı´rez, P., and Carta, J. A., 2006, “The Use of Wind Probability Distributions Derived From the Maximum Entropy Principle in the Analysis of Wind Energy: A Case Study,” Energy Convers. Manage., 47(15–16), pp. 2564–2577. [CrossRef]
Mathew, S., Pandey, K. P., and Kumar, V., 2002, “Analysis of Wind Regimes for Energy Estimation,” J. Renewable Energy, 25(3), pp. 381–399. [CrossRef]
Boccard, N., 2009, “Capacity Factor of Wind Power Realized Values vs. Estimates,” Energy Policy, 37(7), pp. 2679–2688. [CrossRef]
Lu, L., Yang, H., and Burnett, J., 2002, “Investigation on Wind Power Potential on Hong Kong Islands—An Analysis of Wind Power and Wind Turbine Characteristics,” Renewable Energy, 27(1), pp. 1–12. [CrossRef]
Wong, K. V., and Bachelier, B., 2013, “(A Review) Carbon Nanotubes Used for Renewable Energy Applications and Environmental Protection/Remediation,” ASME J. Energy Resour. Technol., 136(2), p. 021601.
Cheng, C., and Kewen, L., 2014, “Comparison of Models Correlating Cumulative Oil Production and Water Cut,” ASME J. Energy Resour. Technol., 136(3), p. 032901. [CrossRef]
Pastor, J., and Liu, Y., 2014, “Power Absorption Modeling and Optimization of a Point Absorbing Wave Energy Converter Using Numerical Method,” ASME J. Energy Resour. Technol., 136(2), p. 021207. [CrossRef]
Elia, S., Gasulla, M., and Francesco, A. D., 2012, “Optimization in Distributing Wind Generators on Different Places for Energy Demand Tracking,” ASME J. Energy Resour. Technol., 134(4), p. 041202. [CrossRef]
Carta, J. A., Ramı´rez, P., and Vela´zquez, S., 2009, “A Review of Wind Speed Probability Distributions Used in Wind Energy Analysis Case Studies in the Canary Islands,” Renewable Sustainable Energy Rev., 13(5), pp. 933–955. [CrossRef]
Dorini, F. A., Pintaude, G., and Sampaio, R., 2014, “Maximum Entropy Approach for Modeling Hardness Uncertainties in Rabinowicz's Abrasive Wear Equation,” ASME J. Tribol., 136(2), p. 021607. [CrossRef]
Wang, L., Yeh, T., Lee, W., and Chen, Z., 2009, “Benefit Evaluation of Wind Turbine Generators in Wind Farms Using Capacity-Factor Analysis and Economic-Cost Methods,” J. IEEE Trans. Power Syst., 24(2), pp. 692–704. [CrossRef]
Abdelaziz, A. R., and Salameh, Z. M., 1998, “A New Statistical Distribution Function Sensitive to Renewable Energy System,” J. Electr. Mach. Power Syst., 26(6), pp. 659–667. [CrossRef]
Habtezion, B. L., and Buskirk, R. V., 2012, “Numerical Simulation of Wind Distributions for Resource Assessment in Southeastern Eritrea, East Africa,” ASME J. Sol. Energy Eng., 134(3), p. 031007. [CrossRef]
Walker, A., 2011, “Estimating Reliability of a System of Electric Generators Using Stochastic Integration of Renewable Energy Technologies (SIRET) in the Renewable Energy Optimization (REO) Method,” Proceedings of ASME 54686, 5th International Conference on Energy Sustainability, pp. 1425–1431.
Borowy, S. B., and Salarneh, Z. M., 1996, “Methodology of Optimally Sizing the Combination of a Battery Bankand PV Array in a Windipv Hybrid System,” IEEE Trans. Energy Convers., 11(2), pp. 367–375. [CrossRef]
Salameh, Z., Borowy, B., and Amin, A., 1995, “Photovoltaic Module-Site Matching Based on Capacity Factor,” IEEE Trans. Energ. Conver., 10(2), pp. 326–332. [CrossRef]
Tchler, M., Singer, A. C., and Koetter, R., 2002, “Minimum Mean Squared Error Equalization Using a Priori Information,” J. IEEE Trans. Signal Process., 50(3), pp. 673–683. [CrossRef]
Raphan, M., and Simoncelli, E. P., 2011, “Least Squares Estimation Without Priors or Supervision,” J. Neurol. Comp., 23(2), pp. 374–420. [CrossRef]
Chow, G. C., and Lin, A., 1976, “Best Linear Unbiased Estimation of Missing Observations in an Economic Time Series,” J. Am. Stat. Assoc., 71(355), pp. 719–721. [CrossRef]
Dong, S., Liu, W., Zhang, L., and Soares, C. G., 2009, “Long-Term Statistical Analysis of Typhoon Wave Heights With Poisson-Maximum Entropy Distribution,” Proceedings ASME 43420; Structures, Safety and Reliability, pp. 189–196.
Ommi, F., Movahednejad, E., Hosseinalipour, S. M., and Chen, C. P., 2009, “Prediction of Droplet Size and Velocity Distribution in Spray Using Maximum Entropy Method,” Proceedings of the ASME Fluids Engineering Division Summer Meeting, Vol. 1, pp. 1009–1015.
Janes, E. T., 1957, “Information Theory and Statistical Mechanics,” J. Phys. Rev., 106(4), pp. 620–630. [CrossRef]
Pougaza, D. B., and Djafari, A. M., 2011, “Maximum Entropy Copulas,” AIP Conference Proceeding, American Institute of Physics, pp. 329–339.
Ebrahimi, N., Soofi, E. S., and Soyer, R., 2008, “Multivariate Maximum Entropy Identification, Transformation, and Dependence,” J. Multivari. Anal., 99(6), pp. 1217–1231. [CrossRef]
Shannon, C. E., 1948, “A Mathematical Theory of Communication,” Bell Syst. Tech. J., 27(3), pp. 379–423. [CrossRef]
Casella, G., and Berger, R. L., 2002, Statistical Inference, 2nd ed., Duxbury, Pacific Grove.
Thomas, J. A., and Cover, T. M., 2006, Elements of Information Theory, Wiley, Hoboken.
Golan, A., Judge, G., and Miller, D., 1996, Maximum Entropy Econometrics: Robust Estimation With Limited Data, Wiley, New York.
Djafari, A. M., 1992, Maximum Entropy and Bayesian Methods, Springer, Dordrecht, pp. 221–233.
Kuncir, G. F., 1962, “Algorithm 103: Simpson’s Rule Integrator,” Commun. ACM, 5(6), p. 347. [CrossRef]
Singla, N., Jain, K., and Sharma, S. K., 2012, “The Beta Generalized Weibull Distribution: Properties and Applications,” Reliab. Eng. Syst. Saf., 102, pp. 5–15. [CrossRef]


Grahic Jump Location
Fig. 1

The simulated HRD in comparison with the ME estimation of HRD (R2=0.9286)

Grahic Jump Location
Fig. 2

The simulated BGWD in comparison with its ME estimation (R2=0.8803)

Grahic Jump Location
Fig. 3

ME estimation of the BRD in comparison with the joint BRD (R2=0.8565)

Grahic Jump Location
Fig. 4

Wind-speed model via ME method (R2=0.774)



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