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.

References

References
1.
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
.10.1115/1.4001574
2.
Prasad
,
B. G. S.
,
2010
, “
Energy Efficiency, Sources, and Sustainability
,”
ASME J. Energy Resour. Technol.
,
132
(
2
), p.
020301
.10.1115/1.4001684
3.
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
.10.14710/ijred.1.3.99-105
4.
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
.10.14710/ijred.1.3.107-113
5.
Siddall
,
J. N.
,
1983
,
Probabilistic Engineering Design
,
1st ed.
,
Marcel Dekker, Basel
,
New York
.
6.
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
.10.1016/j.enconman.2005.10.027
7.
Mathew
,
S.
,
Pandey
,
K. P.
, and
Kumar
,
V.
,
2002
, “
Analysis of Wind Regimes for Energy Estimation
,”
J. Renewable Energy
,
25
(
3
), pp.
381
399
.10.1016/S0960-1481(01)00063-5
8.
Boccard
,
N.
,
2009
, “
Capacity Factor of Wind Power Realized Values vs. Estimates
,”
Energy Policy
,
37
(
7
), pp.
2679
2688
.10.1016/j.enpol.2009.02.046
9.
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
.10.1016/S0960-1481(01)00164-1
10.
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
.
11.
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
.10.1115/1.4026459
12.
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
.10.1115/1.4027409
13.
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
.10.1115/1.4007656
14.
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
.10.1016/j.rser.2008.05.005
15.
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
.10.1115/1.4026421
16.
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
.10.1109/TPWRS.2009.2016519
17.
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
.10.1080/07313569808955849
18.
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
.10.1115/1.4006267
19.
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
.
20.
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
.10.1109/60.507648
21.
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
.10.1109/60.391899
22.
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
.10.1109/78.984761
23.
Raphan
,
M.
, and
Simoncelli
,
E. P.
,
2011
, “
Least Squares Estimation Without Priors or Supervision
,”
J. Neurol. Comp.
,
23
(2), pp.
374
420
.10.1162/NECO_a_00076
24.
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
.10.1080/01621459.1976.10481554
25.
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
.
26.
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
.
27.
Janes
,
E. T.
,
1957
, “
Information Theory and Statistical Mechanics
,”
J. Phys. Rev.
,
106
(
4
), pp.
620
630
.10.1103/PhysRev.106.620
28.
Pougaza
,
D. B.
, and
Djafari
,
A. M.
,
2011
, “
Maximum Entropy Copulas
,”
AIP Conference Proceeding
,
American Institute of Physics
, pp.
329
339
.
29.
Ebrahimi
,
N.
,
Soofi
,
E. S.
, and
Soyer
,
R.
,
2008
, “
Multivariate Maximum Entropy Identification, Transformation, and Dependence
,”
J. Multivari. Anal.
,
99
(
6
), pp.
1217
1231
.10.1016/j.jmva.2007.08.004
30.
Shannon
,
C. E.
,
1948
, “
A Mathematical Theory of Communication
,”
Bell Syst. Tech. J.
,
27
(
3
), pp.
379
423
.10.1002/j.1538-7305.1948.tb01338.x
31.
Casella
,
G.
, and
Berger
,
R. L.
,
2002
,
Statistical Inference
,
2nd ed.
,
Duxbury
,
Pacific Grove
.
32.
Thomas
,
J. A.
, and
Cover
,
T. M.
,
2006
,
Elements of Information Theory
,
Wiley
,
Hoboken
.
33.
Golan
,
A.
,
Judge
,
G.
, and
Miller
,
D.
,
1996
,
Maximum Entropy Econometrics: Robust Estimation With Limited Data
,
Wiley
,
New York
.
34.
Djafari
,
A. M.
,
1992
,
Maximum Entropy and Bayesian Methods
,
Springer
,
Dordrecht
, pp.
221
233
.
35.
Kuncir
,
G. F.
,
1962
, “
Algorithm 103: Simpson’s Rule Integrator
,”
Commun. ACM
,
5
(
6
), p. 347.10.1145/367766.368179
36.
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
.10.1016/j.ress.2012.02.003
You do not currently have access to this content.