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Wind turbines new criteria optimal site matching under new capacity factor probabilistic approaches

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Abstract

This paper introduces a novel methodology for determining wind turbines' optimal site matching. Our framework's key component is establishing four new probabilistic models to model wind turbines' capacity factors. First, we used the sum square of errors (SSE) and the determination coefficient (R2) to assess the accuracy of the proposed models. The developed models were then generalized to estimate wind farm capacity factors. After that, the proposed methodology's validity is tested by applying it to a known wind data site. We modeled the available wind data using Weibull distribution. Five different methods were used to determine Weibull parameters. The equivalent energy method combined with the invasive weed optimization algorithm yields the optimal values for these parameters. Finally, under the support of the presented models, the novel methodology is applied to a pool of 24 commercial turbines to choose the optimal ones. A comparison is made between the obtained capacity factor curves using the suggested models and other previous models for the selected wind turbines. When the presented models are utilized, the capacity factor of commercial wind turbines with non-ideal electrical power curves is more precisely predicted.

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Abbreviations

PDF:

Probability density function

CDF:

Cumulative density function

SDM:

Standard deviation method

MOM:

Method of moment

EPM:

Energy pattern method

LSM:

Least square method

EEM:

Equivalent energy method

IWO:

Invasive weed optimization

RMSE:

Root mean square of errors

SSE:

Sum square of errors

f(v) :

Weibull probability density function

F(v) :

Weibull cumulative density function

k :

Weibull shape factor

c :

Weibull scale factor (m/s)

v, v avg :

Wind speed, and average wind speed, respectively, (m/s)

v i :

The measured wind speed value for the ith data point (m/s)

σ :

Wind speed standard deviation

n :

Sample size

\(\widehat{{m}_{n}}\) :

The nth origin moment

E pf :

Energy pattern factor

F(v i ) :

Weibull cumulative density function value for measured wind speed vi

Q(v) :

Probability of wind speed occurrences greater than a specific value v

P(V) :

Probability of having wind speed V within a specified interval (vi-1,vi)

ε :

Stochastic error term

P v :

Probability density function considering stochastic error

P vi :

Probability of having wind speeds for the ith bin of wind speed histogram

l :

Total number of histogram bins of wind speed

iter, iter max :

Iteration number, and maximum number of iterations, respectively

σ initial , σ final :

Iteration initial and final standard deviation, respectively

o :

Nonlinear modulation index

σ iter :

Iteration standard deviation

C.f. :

Wind turbine capacity factor

u(v) :

The proper probability density function describing wind data

P f (v) :

Wind turbine generated electrical power at wind speed v (MW)

P rated :

Rated wind turbine power (MW)

v in , v r , v o :

Wind turbine cut-in speed, rated speed, and cut-out speed, respectively, (m/s)

c s, k s :

Site scale and shape factors, respectively

c t , k t :

Wind turbine scale and shape factors, respectively

a 0 , a 1 , a 2 :

Fitting models first, second, and third term coefficients

R 2 :

Determination coefficient

c R :

The ratio between site and wind turbine scale factors

k R :

The ratio between site and wind turbine shape factors

∆c s :

Rate of scale factor (m/s)

∆k s :

Rate of shape factor

∆c R :

Relative rate of scale factor

∆k R :

Relative rate of shape factor

h, h i :

Hub-height and initial hub-height, respectively (m)

c i , k i :

Site wind speed scale and shape factors, respectively, at height hi

N :

Number of interconnected turbines at the site

k ti , c ti :

Shape and scale factors of wind turbine number i, respectively

zi :

Wake effect of turbine number i

P i-rated :

Rated power of wind turbine number i (MW)

c ti-e :

Effective scaling factor

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Author information

Authors and Affiliations

  1. Physics and Engineering Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo, 11517, Egypt

    Othman A. M. Omar & Reda A. Elbarkouky

  2. Higher Institute of Engineering, El-Shorouk Academy, P.O. 3, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

  3. Egyptian Chinese University, Cairo, 11725, Egypt

    Reda A. Elbarkouky

Authors
  1. Othman A. M. Omar
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  2. Hamdy M. Ahmed
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  3. Reda A. Elbarkouky
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Corresponding author

Correspondence to Othman A. M. Omar.

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Appendices

Appendix A: Wind Atlas of Egypt at specified sites [35]

Region

Site ID

Site name

Site data

Lat. \(({\mathrm{N}}^{\mathrm{o}})\)

Long. \(({\mathrm{E}}^{\mathrm{o}})\)

\({h}_{i}\) (m)

\({c}_{i}\) (m/s)

\({k}_{i}\)

Avg. (m/s)

North Coast

1

Sidi Barani (62,301)

31.47

25.87

24.5

7

2.16

6.2

2

El-Mathany

31.35

26.88

24.5

6.4

2.33

5.7

3

Ras El-Hekma

31.25

27.86

24.5

7.2

2.23

6.4

4

El-Galaa

31.08

26.7

24.5

6.7

2.41

5.9

5

Alexandria (62,318)

31.2

29.92

10

5.2

2.42

4.6

6

Port Said

31.27

32.3

24.5

5.3

2.32

4.7

7

El- Arish (62,337)

31.13

33.8

8.5

3

1.44

2.8

Gulf of Aqaba

8

Nuweiba

28.97

34.65

24.5

6.2

2.58

5.6

9

Nabq

28.04

34.43

24.5

7.7

2.04

6.8

Gulf of Suez

10

Katamaya

29.92

31.82

24.5

6

2.66

5.4

11

El-Suez (62450)

29.97

32.55

10

6.2

3.17

5.5

12

Ras Sedr

29.6

32.67

24.5

8.5

3.06

7.6

13

Abu Darag NW

29.47

32.45

47.5

9.6

3.34

8.6

14

Abu Darag

29.47

32.45

24.5

10.1

3.5

9.1

15

Zafarana M7

29.22

30.82

47.5

11.1

3.57

10

16

Zafarana

29.12

32.66

24.5

10.2

3.19

9.1

17

Saint Paul

28.78

32.78

24.5

9.4

3.25

8.5

18

Ras Ghareb

28.35

33.08

24.5

11

3.4

9.9

19

Gulf of El-Zayt NW

28.00

33.30

24.5

11.8

3.7

10.7

20

Gulf of El-Zayt

27.77

33.61

24.5

11.5

3.29

10.3

Red Sea

21

Hurghada WETC

27.26

33.81

24.5

7.6

2.23

6.7

22

Hurghada (62,463)

27.18

33.8

10

7.6

2.66

6.7

23

Kossier (62465)

26.43

34.07

10

5.1

2.03

4.6

24

Kossier

26.11

34.27

24.5

6.5

2.32

5.8

Western Desert

25

Farafra (62423)

27.06

27.97

10

3.9

1.79

3.5

26

Kharga

25.44

30.56

24.5

7.4

2.57

6.6

27

Dakhla South

23.99

29.19

24.5

7.3

3.31

6.6

28

Shark El—Ouinat

22.72

28.11

24.5

7.2

3.29

6.5

29

Asswan (62412)

24.09

32.9

10

5.4

2.61

4.8

30

Abu Simbel

24.08

32.9

24.5

6.4

2.76

5.4

Appendix B: Commercial wind turbines data [17]

Turbine ID

Turbine name

Turbine data

Rating (KW)

\(v_{in}\)(m/s)

\(v_{r}\)(m/s)

\(v_{out}\)(m/s)

\(c_{t}\) (m/s)

\(k_{t}\)

1

Vestas (V80)

2000

4.0

16.0

25.0

9.6420951

4.5786415

2

Siemens (S82)

2300

4.0

13.5

25.0

10

4.1929594

3

Repower (RE82)

2050

3.5

14.5

25.0

9.4212791

4.557548

4

Nordex (N90)

2300

3.0

12.0

25.0

9.9995814

4.1613744

5

Siemens (S107)

3600

3.0

13.0

25.0

9.6739173

4.6331647

6

Vestas (V164)

6995

4.0

13.0

25.0

9.4674353

4.3835995

7

An-Bonus (1000/54)

1000

3.0

15.0

25.0

10.1682039

3.51399081

8

Enercon (E53)

810

3.0

12.0

34.0

9.11191916

3.50978311

9

Leitwind (LTW77–1000)

1000

3.0

11.0

25.0

7.91437529

3.75144762

10

Leitwind (LTW80–850)

850

3.0

10.0

25.0

7.21305636

5.08338348

11

Leitwind (LTW90–1000)

1000

3.0

9

25.0

6.86532481

4.77729061

12

Vestas (V47)

660

4.0

15.0

25.0

9.66602728

4.04811810

13

Wind Tech Windane (DWT34)

400

5.5

14

25.0

10.9005567

5.07686715

14

Enercon (E40/5.4)

500

2.5

12.0

25.0

9.61051239

5.08680599

15

Turbowinds (T400–34)

400

3.0

14.0

25.0

9.96184430

5.44584277

16

Vestas (V39)

500

4.0

15.0

25.0

10.1185051

3.95460524

17

Wespa (500/47)

500

4.0

14.5

25.0

8.47204202

5.30386838

18

Windflow (45–500)

500

4.5

11.5

25.0

9.44318401

3.75527729

19

Leitwind (LTW42–250)

250

3.0

9.0

25.0

7.3715829

4.0697689

20

Windmaster (Hmzwm 300/25)

300

5.0

15.0

25.0

11.9992984

3.56446705

21

Vergnet (C275/30)

275

3.5

12.0

25.0

9.44229627

4.73408344

22

Vestas (V27)

225

3.0

15.0

25.0

9.71250815

3.93238423

23

Wespa (200/31)

200

4.0

13.5

25.0

9.4369866

5.2200093

24

Norwin (29-STALL-225)

225

4.0

14.0

25.0

11.004852

4.0108782

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Omar, O.A.M., Ahmed, H.M. & Elbarkouky, R.A. Wind turbines new criteria optimal site matching under new capacity factor probabilistic approaches. Energy Syst 14, 419–444 (2023). https://doi.org/10.1007/s12667-021-00463-7

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