Wind characteristics and wind energy assessment in the Barents Sea based on ERA-Interim reanalysis

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Four extreme value distribution functions

Distribution type	Probability density distribution function f(x)	Parameters
GEV	1α[ 1-β(v−μα) ]1/β-1exp{ -[ 1-β(v−μα) ]1/β } $\frac{1}{\alpha }{{\left[ 1\text{- }\!\!\beta\!\!\text{ }\left( \frac{v-\mu }{\alpha } \right) \right]}^{{1}/{\text{ }\!\!\beta\!\!\text{ -1}}\;}}\exp \left\{ \text{-}{{\left[ 1\text{- }\!\!\beta\!\!\text{ }\left( \frac{v-\mu }{\alpha } \right) \right]}^{{1}/{\text{ }\!\!\beta\!\!\text{ }}\;}} \right\}$	μ-location parameter α-scale parameter β-shape parameter
Gumbel	1αexpμ[ −(v−α)−expμ(−v−α) ] $\frac{1}{\text{ }\!\!\alpha\!\!\text{ }}\overset{\text{ }\!\!\mu\!\!\text{ }}{\mathop{\exp }}\,\left[ -\left( \frac{v-}{\text{ }\!\!\alpha\!\!\text{ }} \right)\overset{\text{ }\!\!\mu\!\!\text{ }}{\mathop{-\exp }}\,\left( -\frac{v-}{\text{ }\!\!\alpha\!\!\text{ }} \right) \right]$	μ-location parameter α-scale parameter
Weibull	αβ(v−μ)α−1exp[ −(v−μ)αβ ]x≥μ $\frac{\text{ }\!\!\alpha\!\!\text{ }}{\text{ }\!\!\beta\!\!\text{ }}{{\left( v-\text{ }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ }-1}}\exp \left[ -\frac{{{\left( v-\text{ }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ }}}}{\text{ }\!\!\beta\!\!\text{ }} \right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ge \text{ }\!\!\mu\!\!\text{ }$	μ-location parameter β-shape parameter α-scale parameter
P-III	βαΓ(α)(v- μ)α-1e-β(x−μ)v3μ,α>0 $\frac{{{\text{ }\!\!\beta\!\!\text{ }}^{\text{ }\!\!\alpha\!\!\text{ }}}}{\Gamma \left( \text{ }\!\!\alpha\!\!\text{ } \right)}{{\left( v\,\text{- }\!\!\mu\!\!\text{ } \right)}^{\text{ }\!\!\alpha\!\!\text{ -1}}}{{e}^{\text{- }\!\!\beta\!\!\text{ }\left( x-\text{ }\!\!\mu\!\!\text{ } \right)}}\,\,\,{{v}^{3}}\text{ }\!\!\mu\!\!\text{ , }\!\!\alpha\!\!\text{ }\,\text{}\,\text{0}$	μ-location parameter β-shape parameter α-scale parameter

Comparisons of the K-S test and RMSE between GEV, Gumbel, Weibull and P-III distributions

Distributions	K-S test	Mean	Maximum	Minimum
		RMSE	RMSE	RMSE
GEV	99.97%	0.0484	0.1700	0.0210
Gumbel	99.96%	0.0591	0.1353	0.0174
Weibull	98.56%	0.0473	0.2957	0.0191
P-III	100%*	0.0434*	0.1061*	0.0153*

Different return values of extreme wind speeds (m s−1) based on Gumbel and P-III distributions from P1 to P7 for 50-year and 100-year return periods; higher extreme speeds are marked with *

Points	Distribution	5-year	10-year	25-year	50-year	100-year
P1	Gumbel P-III	22.62 22.59	23.17 23.39	24.32 24.27	25.18* 24.85	26.03* 25.38
P2	Gumbel P-III	22.35 22.47	23.41 23.27	24.75 24.15	25.74* 24.73	26.73* 25.26
P3	Gumbel P-III	22.43 22.86	23.33 23.73	24.48 24.68	25.33* 25.30	26.17* 25.88
P4	Gumbel P-III	21.89 22.16	22.73 22.97	23.78 23.87	24.57* 24.49	25.34* 25.06
P5	Gumbel P-III	21.57 21.78	22.45 22.58	23.56 23.49	24.38* 24.11	25.20* 24.68
P6	Gumbel P-III	21.65 21.76	22.62 22.58	23.85 23.52	24.76* 24.16	25.67* 24.76
P7	Gumbel P-III	22.26 22.71	23.26 23.66	24.52 24.71	25.46* 25.40	26.39* 26.03

Locations of the selected points and 100 m annual average wind speeds, wind power density (WPD) and net electric energy output from P1 to P7

Points	Longitude (N)	Latitude (E)	Mean speed (m s−1)	WPD (W m−2)	Electric energy (MWhy)
					CCWE3000D	SL500
P1	22	74	10.23	1108	14 384	23 534
P2	22	72	9.99	1041	14 002	22 855
P3	32	74	10.26	1097	14 535	23 776
P4	35	72	10.10	1046	14 312	23 390
P5	42	73	9.91	985	14 011	22 873
P6	42	71	9.95	991	14 121	23 064
P7	37	70	9.96	1002	14 118	23 079

Parameters of model wind turbine generators for CCWE3000D and SL500

WTGs	Rated power (kW)	Hub height (m)	Rotor diameter (m)	Cut-in wind speed (m s−1)	Rated wind speed (m s−1)	Cut-out wind speed (m s−1)
CCWE3000D	3000	100	103	3	12	25
SL500	5000	100	128	3.5	12.5	25