Authors
Abstract
A time series study of the electrical energy generated by wind turbines and solar cells shows that the energy produced has a lot of fluctuations due to the geographic conditions. These ups and downs have caused not only the share of these sources to be marginal, but also they lead to the volatility of electric power plants. By examining several different data from different countries and regions with the frequency of second and minute, we show that different scale behaviors exist at different time intervals and reveal their other random and nonlinear characteristics. We also compare the non-Gaussian behavior of these regions together, showing that studying the properties of such data helps us to better measure the incidence of these energies
Keywords
1. A Schavan, Germanyffs Energy Research Plan, Science (2010) 330295.
2. P Milan, M Wächter, and J Peinke, Phys. Rev. Lett. 110 (2013) 138701.
3. A Woyte, R Belmans, and J Nijs, Analysis and Statistics, Sol. Energy, 81 (2007) 195.
4. A Madanchi, M Absalan, G Lohmann, M Anvari and M R Rahimi Tabar, Solar Energy, 144 (2017) 1.
5. M Anvari et al., New J. Phys., 18 (2016) 063027.
6. http : //entsoe.eu/
7. G Andersson., Modeling and analysis of electric power systems ETH Zurich (2008) (http://eeh.ee.ethz.ch)
8. German TSOs Internet platform for control reserve tendering, 2015ff (https://regelleistung.net/)
9. Data can be downloaded under http://unioldenburg.de/fileadmin/
10. www.tennettso.de/site/Transparenz/veroeffentlichungen/netzkennzahlen/tatsaechlicheund-prognostiziertewindenergieeinspeisung.
11. www.eirgridgroup.com/operations/systemperformancedata/windgeneration/.
12. M Sengupta and A Andreas, Oahu Solar Measurement Grid (1-Year Archive):1-Second Solar Irradiance DA-5500- 56506 Oahu, Hawaii (Data); NREL(2010), (http://dx.doi.org/10.5439/1052451).
13. The data set are available atffftp://ftp.bsrn.awi.de/ see alsoffhttp://bsrn.awi.de/data/data-retrievalvia-ftp.html
14. H G Beyer, A Hammer, J Luther, J Poplawska, K Stolzenburg, and P Wieting, Sol. Energy, 52 (1994) 379.
15. R Friedrich, J Peinke, M Sahimi and M R Rahimi Tabar, Phys. Rep. 506 (2011) 87.
16. P Ineichen, Solar Energy 80 (2006) 468.
17. A Hammer, D Heinemann, A Westerhellweg, H G Beyer, and C Reise, 9th Conf. on Satellite Meteorology and Oceanography No. 2 (1998).
18. U Frisch, “Turbulence: The Legacy of A. N. Kolmogorov Cambridge”, Cambridge University Press (1996).
19. B Castaing, Y Gagne, and E Hopfinger, Physica D, 46 (1990) 177
20. F Chilla, J Peinke, and B Castaing, J. Phys. II 6 (1996) 455.
21. L Chevillard and C Meneveau, Phys. Rev. Lett. 97 (2006) 174501.
22. K R Sreenivasan, Rev. Mod. Phys. 71 (1999) S383.
23. G Falkovich, K Gawedzki, and M Vergassola, Rev. Mod. Phys. 73 (2001) 913.
24. J Apt, J. Power Sources, 169 (2007) 369.
25. M R Rahimi Tabar, M Anvari, G Lohmann, D Heinemann, M Wächter, P Milan, E Lorenz, and J Peinke, Eur. Phys. J. Spec. Top. 223 (2014) 2637.
26. R Calif and F G Schmitt, J. Wind Eng.Ind. Aerodyn. 109 (2012) 1.
27. A E Curtright and J Apt, Res. Appl. 16 (2008) 241.
28. O Kamps, “Characterizing the Fluctuations of Wind Power Production by Multi-Time Statistics Wind Energy—Impact of Turbulence”, ed M Hölling et al., Berlin: Springer (2014).
29. R Baïle and J-F Muzy, Phys. Rev. Lett. 105 (2010) 254501
30. R Wood and P R Field, J. Clim. 24 (2011) 4800
31. C Tsallis, J. Stat. Phys. 52 (1988) 479.
32. J W Kantelhardt, “Mathematics of Complexity and595 Dynamical Systems”, New York, Springer (2011) 463.
33. A Eke, P Herman, L Kocsis, L R Kozak, Physiol. Meas. 23 (2002) R1-38
34. C K Peng, S V Buldyrev, S Havlin, M Simons, H E Stan- ley, A L Goldberger, Phys. Rev. E 49 (1994) 1685.
35. L Xu, P C h Ivanov, K Hu, Z Chen, A Carbone, H E Stan- ley, Phys. Rev. E 71 (2005) 051101.
36. Z Chen, P C h Ivanov, K Hu, H E Stanley, 567 Phys. Rev. E 65 (2002) 041107.
37. K Hu, P C h Ivanov, Z Chen, P Carpena, H E Stanley, 583 Phys. Rev. E 64 (2001) 011114.
38. J W Kantelhardt, S A Zschiegner, E Koscielny-Bunde, 601 S Havlin, A Bunde, and H E Stanley, Physica A 316, 87 (2002) 441.
39. S M Ossadnik, S B Buldyrev, A L Goldberger, S Havlin, R N Mantegna, C K Peng, M Simons, and H E Stanley, Biophys. J. 67(1994) 64.
40. M S Taqqu, V Teverovsky, and W Willinger, Fractals 3 (1995) 785.
41. A Bunde, S Havlin, J W Kantelhardt, T Penzel, and J H Peter, Phys. Rev. Lett. 85, 564 (2000) 3736.
42. J Feder, “Fractals”, Plenum Press, New York (1988).
43. H O Peitgen, H Jurgens, and D Saupe, “Chaos And Fractals”, Springer-Verlag, New York (1992) 659.
44. M S Movahed, G Jafari, F Ghasemi, S Rahvar, and M R Rahimi, J. Stat. Mech. Theory (2006) P02003.
45. J W Kantelhardt, E Koscielny-Bunde, and H H A Rego, Physica A 599295 (2001) 441.
46. Y Ashkenazy, D R Baker, H Gildor, and S Havlin, Geophys. Res. Lett. 30 (2003) 2146.
47. A Biswas, T B Zeleke, and B C Si, Nonlin. Processes Geophys. 19 (2012) 227.
48. D Sornette, Phys. Rep. 378 (2003) 1.
49. V S L’vov, A Pomyalov, and I Procaccia, Phys. Rev. E 63 (2001) 056118.
50. D Sornette, Int. J. Terraspace, Sci. Eng. 2 (2009 ) 1.
51. Ł Czarnecki and D Grech, Acta, Phys. Pol. A 117 (2010) 623.
52. W X Zhou, Europhys. Lett. 88 (2009) 28004.
53. G Oh, C Eom, S Havlin, W S Jung, F Wang, H E Stanley, and S Kim, Eur. Phys. J. B 85 (2012) 214.
2. P Milan, M Wächter, and J Peinke, Phys. Rev. Lett. 110 (2013) 138701.
3. A Woyte, R Belmans, and J Nijs, Analysis and Statistics, Sol. Energy, 81 (2007) 195.
4. A Madanchi, M Absalan, G Lohmann, M Anvari and M R Rahimi Tabar, Solar Energy, 144 (2017) 1.
5. M Anvari et al., New J. Phys., 18 (2016) 063027.
6. http : //entsoe.eu/
7. G Andersson., Modeling and analysis of electric power systems ETH Zurich (2008) (http://eeh.ee.ethz.ch)
8. German TSOs Internet platform for control reserve tendering, 2015ff (https://regelleistung.net/)
9. Data can be downloaded under http://unioldenburg.de/fileadmin/
10. www.tennettso.de/site/Transparenz/veroeffentlichungen/netzkennzahlen/tatsaechlicheund-prognostiziertewindenergieeinspeisung.
11. www.eirgridgroup.com/operations/systemperformancedata/windgeneration/.
12. M Sengupta and A Andreas, Oahu Solar Measurement Grid (1-Year Archive):1-Second Solar Irradiance DA-5500- 56506 Oahu, Hawaii (Data); NREL(2010), (http://dx.doi.org/10.5439/1052451).
13. The data set are available atffftp://ftp.bsrn.awi.de/ see alsoffhttp://bsrn.awi.de/data/data-retrievalvia-ftp.html
14. H G Beyer, A Hammer, J Luther, J Poplawska, K Stolzenburg, and P Wieting, Sol. Energy, 52 (1994) 379.
15. R Friedrich, J Peinke, M Sahimi and M R Rahimi Tabar, Phys. Rep. 506 (2011) 87.
16. P Ineichen, Solar Energy 80 (2006) 468.
17. A Hammer, D Heinemann, A Westerhellweg, H G Beyer, and C Reise, 9th Conf. on Satellite Meteorology and Oceanography No. 2 (1998).
18. U Frisch, “Turbulence: The Legacy of A. N. Kolmogorov Cambridge”, Cambridge University Press (1996).
19. B Castaing, Y Gagne, and E Hopfinger, Physica D, 46 (1990) 177
20. F Chilla, J Peinke, and B Castaing, J. Phys. II 6 (1996) 455.
21. L Chevillard and C Meneveau, Phys. Rev. Lett. 97 (2006) 174501.
22. K R Sreenivasan, Rev. Mod. Phys. 71 (1999) S383.
23. G Falkovich, K Gawedzki, and M Vergassola, Rev. Mod. Phys. 73 (2001) 913.
24. J Apt, J. Power Sources, 169 (2007) 369.
25. M R Rahimi Tabar, M Anvari, G Lohmann, D Heinemann, M Wächter, P Milan, E Lorenz, and J Peinke, Eur. Phys. J. Spec. Top. 223 (2014) 2637.
26. R Calif and F G Schmitt, J. Wind Eng.Ind. Aerodyn. 109 (2012) 1.
27. A E Curtright and J Apt, Res. Appl. 16 (2008) 241.
28. O Kamps, “Characterizing the Fluctuations of Wind Power Production by Multi-Time Statistics Wind Energy—Impact of Turbulence”, ed M Hölling et al., Berlin: Springer (2014).
29. R Baïle and J-F Muzy, Phys. Rev. Lett. 105 (2010) 254501
30. R Wood and P R Field, J. Clim. 24 (2011) 4800
31. C Tsallis, J. Stat. Phys. 52 (1988) 479.
32. J W Kantelhardt, “Mathematics of Complexity and595 Dynamical Systems”, New York, Springer (2011) 463.
33. A Eke, P Herman, L Kocsis, L R Kozak, Physiol. Meas. 23 (2002) R1-38
34. C K Peng, S V Buldyrev, S Havlin, M Simons, H E Stan- ley, A L Goldberger, Phys. Rev. E 49 (1994) 1685.
35. L Xu, P C h Ivanov, K Hu, Z Chen, A Carbone, H E Stan- ley, Phys. Rev. E 71 (2005) 051101.
36. Z Chen, P C h Ivanov, K Hu, H E Stanley, 567 Phys. Rev. E 65 (2002) 041107.
37. K Hu, P C h Ivanov, Z Chen, P Carpena, H E Stanley, 583 Phys. Rev. E 64 (2001) 011114.
38. J W Kantelhardt, S A Zschiegner, E Koscielny-Bunde, 601 S Havlin, A Bunde, and H E Stanley, Physica A 316, 87 (2002) 441.
39. S M Ossadnik, S B Buldyrev, A L Goldberger, S Havlin, R N Mantegna, C K Peng, M Simons, and H E Stanley, Biophys. J. 67(1994) 64.
40. M S Taqqu, V Teverovsky, and W Willinger, Fractals 3 (1995) 785.
41. A Bunde, S Havlin, J W Kantelhardt, T Penzel, and J H Peter, Phys. Rev. Lett. 85, 564 (2000) 3736.
42. J Feder, “Fractals”, Plenum Press, New York (1988).
43. H O Peitgen, H Jurgens, and D Saupe, “Chaos And Fractals”, Springer-Verlag, New York (1992) 659.
44. M S Movahed, G Jafari, F Ghasemi, S Rahvar, and M R Rahimi, J. Stat. Mech. Theory (2006) P02003.
45. J W Kantelhardt, E Koscielny-Bunde, and H H A Rego, Physica A 599295 (2001) 441.
46. Y Ashkenazy, D R Baker, H Gildor, and S Havlin, Geophys. Res. Lett. 30 (2003) 2146.
47. A Biswas, T B Zeleke, and B C Si, Nonlin. Processes Geophys. 19 (2012) 227.
48. D Sornette, Phys. Rep. 378 (2003) 1.
49. V S L’vov, A Pomyalov, and I Procaccia, Phys. Rev. E 63 (2001) 056118.
50. D Sornette, Int. J. Terraspace, Sci. Eng. 2 (2009 ) 1.
51. Ł Czarnecki and D Grech, Acta, Phys. Pol. A 117 (2010) 623.
52. W X Zhou, Europhys. Lett. 88 (2009) 28004.
53. G Oh, C Eom, S Havlin, W S Jung, F Wang, H E Stanley, and S Kim, Eur. Phys. J. B 85 (2012) 214.
)