METHOD FOR THE CALCULATION OF PROBABILITY DENSITY FUNCTION OF THREE-PARAMETER GAMMA DISTRIBUTION OF RIVER FLOW DISCHARGE RELATED TO HYDROPOWER TASKS


  • M. Ibragimova Institute for Renewable Energy of NASU, Kyiv, 20A, Hnata Khotkevycha Str., Phone/fax: +38-044-206-28-09, e-mail: hydro@ive.org.ua http://orcid.org/0000-0003-1732-4477
Keywords: flow discharge, probability, interpolation, probability density function, availability, distribution.

Abstract

Hydrocarbon deficit, increasing pressure on the environment and problems of resource availability are the major triggers for the transformation of energy industry worldwide. The development of small hydropower also should conform to the principles of rational use of water resources, river conservation and restoration, reducing the human impact, etc. The article focuses on a pressing issue of construction of small hydroelectric power plant with operation modes that comply sustainable water use taking into account environmental constraints on the use of water for electricity generation. The author presents the advantages of density function of probability distribution of river flow discharge over its cumulative probability as a means of analyzing performance indicators of small hydroelectric power plants. The review of previous studies of probability density function showed the absence of summarized results required for further practical applications of this function. There have been developed, for the first time, a method for the calculation of the probability density function of three-parameter Gamma distribution of river flow discharge at random coefficients of variation and asymmetry by cubic spline interpolation in the vicinity of the poles of Gamma function. The article contains the results of a study of probability Gamma distribution of river flow discharge in tabular form of relevant density function values.  These tables are recommended for hydropower engineering and design services when performing hydrological and hydrotechnical calculations. Ref. 18, tab. 3, fig. 3.

References

1. Vasko P.F., Moroz A.V. Zakonodatelnye stimuly i prirodookhrannye ogranicheniya ispolzovaniya gidroenergeticheskikh resursov malykh rek Ukrainy. [Legislative Incentives and Environmental Restrictions on the Use of Hydropower Resources of Small Rivers of Ukraine]. International Scientific Journal for Alternative Energy and Ecology (ISJAEE). 2014. No. 15. Pp.82-92. [in Russian].

2. Vasko P.F. Suchasnyi stan, potentsiini mozhlyvosti ta peredumovy podalshoho rozvytku maloi hidroenerhetyky v Ukraini. [Сurrent state, potential opportunities and prerequisites for the further development to smallhydropower in Ukraine]. Vidnovluvana energetika. 2006. No. 1. Рр. 60-66. [in Ukrainian].

3. Vasko P.F., Moroz A.V. Potencial vykorystannja ghi-droenerghetychnykh resursiv osnovnykh malykh richok Ukrajiny. [The potential use of hydropower resources of main small rivers of Ukraine]. Vidnovluvana energetika. 2016. No. 3. Pp. 50-56. [in Ukrainian].

4. Vasko P.F., Ibragimova M.R. Osnovni polozhennja stvorennja «zelenykh» malykh GhES. [Basic regulations for con-struction of "green" small hydropower plants]. Abstracts of IV Scientific-practical Conf. “Optimal Control of Electrical Installa-tions - OKEU'2017”. Vinnytsia. 2017. [Electronic resource]. URL: https://conferences.vntu.edu.ua/ index.php/okeu/okeu/ paper/viewFile/3520/2979 (Applying date: 06.05.2019). [in Ukrainian].

5. Vasko P.F., Ibragimova M.R. Jenergeticheskaja jeffektivnost maloj gidrojelektrostancii pri jekologicheskih ogranichenijah na ispolzovanie stoka vody reki dlja proizvodstva jelektrojenergii. [Energy efficiency of small hydropower plant through environmental restrictions on water use for power genera-tion]. International Scientific Journal for Alternative Energy and Ecology (ISJAEE). 2017. No. 04-06(216-218). Pp. 103-115.

ISSN 1608 – 8298. [in Russian].

6. Ibragimova M.R. Vyznachennja proektnykh parametriv maloji GhES za reghuljuvannja potuzhnosti po vodotoku. [Determination of design parameters of a small hydroelectric power plant for capacity regulation by water flow]. Vidnovluvana energetika. 2016. No. 1. Pp. 55-60. [in Ukrainian].

7. Malynyn N.K. Teoretycheskye osnovы ghydroэnerghetyky. [Theoretical basics of hydropower]. Moscow. Energhoatomyzdat. 1985. 312 p. [in Russian].

8. Vasko P.F., Bril A.O., Moroz A.V., Ozorin D.F. Raschet teoreticheskogo znacheniya gidroenergeticheskogo po-tentsiala malykh rek s uchetom obespechennosti stoka vody. [Cal-culation of the theoretical value of the hydropower potential of small rivers, taking into account the availability of water flow]. International Scientific Journal for Alternative Energy and Ecolo-gy (ISJAEE). 2012. No. 7. Pp.126-132. [in Russian].

9. Blokhinov E.G. Raspredelenye verojatnostej velychyn rechnogho stoka. [Probability distribution of river runoff values]. Moscow. Science. 1974. 169 p. [in Russian].

10. Druzhynyn V.S., Sykan A.V. Metody statystycheskoj obrabotky ghydrometeorologhycheskoj ynformacyy. [Methods of statistical processing of hydrometeorological information]. St. Petersburg. RGGMU ed. 2001. 170 p. [in Russian].

11. DBN B.2.4-8:2014 Vyznachennja rozrakhunkovykh ghidrologhichnykh kharakterystyk. [DBN B.2.4-8: 2014 Determination of calculated hydrological characteristics]. Kyiv. Ministry of Regional Development of Ukraine. 2015. 107 p. [in Ukrainian].

12. Rechnoj stok y egho kharakterystyky. [The river flow and its characteristics]. Repair Construction Interior. 2015. [Elec-tronic resource]. URL: http://industrial-wood.ru/transport-lesa/6199-rechnoy-stok-i-ego-harakteristiki.html (Applying date: 06.05.2019). [in Russian].

13. Guiding Principles. Sustainable Hydropower Develop-ment in the Danube Basin. International Commission for the Pro-tection of the Danube River, 2013. [Electronic resource]. URL: http://www.icpdr.org/main/activities-projects/hydropower (Apply-ing date: 24.04.2018). [in English].

14. Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. Metody splajn-funkcyj. [Methods of spline functions]. Moscow. The main edition of the physical and mathematical literature. 1980. 352 p. [in Russian].

15. Shikin E.V., Plis L.I. Kryvye y poverkhnosty na ekrane kompjjutera. Rukovodstvo po splajnam dlja poljzovatelej. [Curves and surfaces on a computer screen. Spline guide for users]. Mos-cow. DIALOGUE-MIFI. 1996. 240 p. [in Russian].

16. Zavyalov Yu.S., Leus V.A., Skorospelov B.A. Splajny v ynzhenerghoj gheometryy. [Splines in engineering geometry]. Moscow. Engineering. 1985. 222 p. [in Russian].

17. Yatsik A.V., Byshovets L.B., Rich E.O. and others. Mali richky Ukrajiny: Dovidnyk. [Small Rivers of Ukraine: Hand-book]. Kyiv. Urozhaj. 1991. 296 p. [in Ukrainian].

18. Streljc B.Y. Spravochnyk po vodnym resursam. [Hand-book of Water Resources]. Kyiv. Urozhaj. 1987. 304 p. [in Rus-sian].

Author Biography

M. Ibragimova, Institute for Renewable Energy of NASU, Kyiv, 20A, Hnata Khotkevycha Str., Phone/fax: +38-044-206-28-09, e-mail: hydro@ive.org.ua

Ibragimova.jpgAuthor information: junior research fellow at Hydropower Department, Institute for Renewable Energy of National Academy of Sciences of Ukraine.
Education: National Technical University of Ukraine «Kyiv Polytechnic Institute»;
Specialty «Non-traditional and renewable energy sources».
Research area: alternative energy, conversion of renewable energy, small hydropower, energy conservation and efficiency.
Publications: 20.


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Published
2019-09-25
How to Cite
Ibragimova, M. (2019). METHOD FOR THE CALCULATION OF PROBABILITY DENSITY FUNCTION OF THREE-PARAMETER GAMMA DISTRIBUTION OF RIVER FLOW DISCHARGE RELATED TO HYDROPOWER TASKS. Vidnovluvana Energetika, (3(58), 58-66. https://doi.org/https://doi.org/10.36296/1819-8058.2019.3(58).58-66