Suitable error evaluation criteria selection in the wind energy assessment via the K-means clustering algorithm

ABSTRACT

In this paper, wind energy potential of four locations in Xinjiang region is assessed. The Weibull distribution as well as the Logistic and the Lognormal distributions are applied to describe the distributions of the wind speed at different heights. In determining the parameters in the Weibull distribution, four intelligent parameter optimization approaches including the differential evolutionary, the particle swarm optimization, and two other approaches derived from these two algorithms and combined advantages of these two approaches are employed. Then the optimal distribution is chosen through the Chi-square error (CSE), the Kolmogorov–Smirnov test error (KSE), and the root mean square error (RMSE) criteria. However, it is found that the variation range of some criteria is quite large, thus these criteria are analyzed and evaluated both from the anomalous values and by the K-means clustering method. Anomaly observation results have shown that the CSE is the first one should be considered to be eliminated from the consequent optimal distribution function selection. This idea is further confirmed by the K-means clustering algorithm, by which the CSE is clustered into a different group with KSE and RMSE. Therefore, only the reserved two error evaluation criteria are utilized to evaluate the wind power potential.

KEYWORDS:

• Anomalous value
• K-means clustering algorithm
• parameter optimization
• wind energy
• wind power classification

Acknowledgments

The authors are grateful to Mrs. Jan Pope for her assistance in editing the language of this paper. The authors also gratefully acknowledge the editors and anonymous reviewers for their valuable comments and suggestions.

Funding

The work was supported by the Fundamental Research Funds for the Central Universities of Northwest University for Nationalities (Grant No. 31920160057) and the Research Project Funds for the Introduction of Talents of Northwest University for Nationalities (Grant No. xbmuyjrcs201608).

Nomenclature

	=	availability factor, dimensionless
	=	scale parameter of Weibull function, m/sec
()	=	cognitive constant
	=	cluster center
	=	crossover probability constant
	=	fitness value of the best particle
()	=	differential variation rate
	=	height, m
	=	random index chosen from
	=	shape parameter of Weibull function, dimensionless
	=	classification number
	=	sample size, dimensionless
	=	CDF values obtained by the actual data
	=	Air pressure, Pa or N/m2
()	=	random value selected from the range
	=	specific gas constant for air, 287.053 J/(kg·K)
	=	CDF values obtained by the selected function
	=	air temperature, K
	=	wind speed, m/sec
	=	cut-in speed of turbine, m/sec
	=	cut-off speed of turbine, m/sec
	=	wind speed at the height of 10 m, m/sec
	=	mean wind speed, m/sec
	=	velocity of the particle
	=	probability data series obtained by the selected PDF
	=	probability data series obtained by the observed data
	=	position with the best fitness value sought by the total particles
	=	position of the particle
	=	position with the best fitness value sought by the th particle

Greek symbols

	=	roughness factor
	=	inertia weight
	=	air density, kg/m3
	=	standard deviation of the wind speed
	=	mean of natural logarithm of the wind speed
	=	standard deviation of natural logarithm of the wind speed

Abbreviations

CDF	=	cumulative density function
CSE	=	Chi-square error
DE	=	differential evolutionary
DE-WPSO	=	Algorithm by carrying out the DE algorithm at the odd generation and the WPSO algorithm at the even generation
KSE	=	Kolmogorov–Smirnov test error
PDF	=	probability density function
PSO	=	particle swarm optimization
RMSE	=	root mean square error
WPSO-DE	=	Algorithm by carrying out the WPSO approach at the odd generation and the DE algorithm at the even generation

Additional information

Funding

The work was supported by the Fundamental Research Funds for the Central Universities of Northwest University for Nationalities (Grant No. 31920160057) and the Research Project Funds for the Introduction of Talents of Northwest University for Nationalities (Grant No. xbmuyjrcs201608).