Keywords: angle of rotation, hydropower, moment, power, programming, turbine.


The power equipment of small hydropower plants, namely hydro turbines, must operate reliably in continuous operation, have a high efficiency and be able to maintain high steady power over a longer life cycle. As a result of continuous improvement of structures, a number of types of hydroturbines have been created the best in these requirements. However, the workflows of hydroturbines remain under-researched, taking into account the possible natural and technical impacts. It is also quite difficult to take into account the sudden change in river flow velocity, the presence of vortices at the outlet of the turbine, etc.

In this work are explored the possibilities of using modern software for simulation of operating modes and energy characteristics of small hydroelectric power plants using experimental and reference data.

There are different types of characteristics of hydromachines, which are obtained during laboratory tests and graphically depict the dependence of some operating parameters on others. The most widespread in the hydropower industry are the given universal characteristics, which are built for single values ​​of certain values: D = 1m and H = 1m. Modeling of non-stationary electromechanical processes of a hydropower unit is based on the solution of the differential equation of motion of components using the mechanical characteristics of a turbine, generator and electrical load. The use of a set of nonlinear characteristics in the process of solving the differential equation of motion requires their representation by a continuous surface, which can be effectively implemented with the help of three-dimensional 3D graphs and approximate spline functions included in the Matlab software package.

In this article are provides an example code and a description of the main commands that enable the construction and analysis of various hydromechanical and power characteristics of units for conducting studies of the operating modes of small hydroelectric power plants. Finding the quantitative values of the curves formed at the intersection of two surfaces makes it possible to study and substantiate the laws of control of hydropower turbines, taking into account the natural features of the river flow, which could not be done so far. Ref. 14, fig. 9.

Author Biography

A. Moroz, Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20A Hnata Khotkevycha St., Kyiv, Ukraine.

moroz.jpgAuthor information: Candidate of Tech-nical Sciences in the field of «Renewable Energy Transformation», Senior Researcher in the Institute for Renewable Energy of the National Academy of Sciences of Ukraine.
Education: National Technical University of Ukraine «Kyiv Polytechnic Institute». Specialty «Non-traditional sources of energy».
Research area: alternative energy, energy saving, renewable energy transformation, small hydropower.
Publications: 24.


1. 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 of small hydropower in Ukraine]. Vidnovluvana energetіka. 2006. No. 1. Рр. 60-65. [in Ukrainian].
2. Bryl A.A., Vasko P.F., Moroz A.V., Ibragimova M.R. Ekolohichni aspekty rozvytku hidroenerhetyky v Ukrayini. [Ekolohichni aspekty rozvytku hidroenerhetyky v Ukrayini]. Vidnovluvana energetіka. 2018. No. 2. Pp. 57-69. [in Ukrainian].
3. 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]. Alternative energy and ecology]. 2014. No. 15. Pp. 82-92. [in Russian].
4. Vasko P.F., Ibragimova M.R. Energeticheskaya effektivnost maloy gidroelektrostantsii pri ekologicheskikh ogranicheniyakh na ispolzovanie stoka vody reki dlya proizvodstva elektroenergii. [Energy efficiency of small hydropower plant through environmental restrictions on water use for power generation]. Alternative energy and ecology. 2017. No. 04-06(216-218). Pp. 103-115. ISSN 1608-8298. [in Russian].
5. Vasko P.F., Moroz A.V. Potentsial vykorystannya hidroenerhetychnykh resursiv osnovnykh malykh richok Ukrayiny. [The potential use of hydropower resources of main small rivers Ukraine]. Vidnovluvana energetіka. 2016. No. 3. Pp. 50-56. [in Ukrainian].
6. Vasko P.F., Vasko V.P., Ibragimova M.R. Mala hidroenerhetyka v strukturi elektroenerhetychnoyi haluzi Ukrayiny. [Small hydropower in the structure of the electric power industry of Ukraine]. Vidnovluvana energetіka. 2015. No. 3. Pp. 53-61. [in Ukrainian].
7. Bryl A.A., Vasko P.F., Moroz A.V. Ekspress otsenka gidroenergeticheskogo potentsiala malykh rek Ukrainy s uchotom prirodookhrannykh ogranicheniy. [Express assessment of hydropower potential of the small rivers in ukraine with account of environmental restrictions]. Alternative energy and ecology. 2018. No. 25-27(273-275). Pp. 86-95. [in Russian].
8. Krivchenko G.I., Arshenevsky N.N., Kvyatkovskaya E.V., Klabukov V.M. Gidromekhanicheskiye perekhodnyye protsessy v gidroenergeticheskikh ustanovkakh. [Hydromechanical transients in hydropower plants]. M. Energiya. 1975. 367 p. [in Russian].
9. Bryl A.A., Vasko V.P., Vasko P.F., Soloviev P.B. Matematicheskoye modelirovaniye puskovykh rezhimov sinkhronnykh i asinkhronnykh generatorov malykh GES. [Mathematical modeling of starting modes of synchronous and asynchronous generators of small hydro power plants]. Alternative Energy and Ecology. 2013. № 3. Pp. 143-150. [in Russian].
10. Shchaveleva D.S. Gidroenergeticheskiye ustanovki. [Hydropower installations]. L. Izd. Energoizdat. 1981. 520 p. [in Russian].
11. Informatsiia shchodo MATLAB. [Information about MATLAB]. [Electronic resource]. URL: https://uk.wikipedia.org/wiki/MATLAB (Applying date: 10.10.2019). [in Ukrainian].
12. Kvasov B.I. Metody izogeometricheskoy approksimatsii splaynami. [Methods of isometric approximation by splines]. M. Fizmatlit publishing. 2006. 360 p. [in Russian].
13. Zavyalov Y.S., Kvasov B.I., Miroshnicenko V.L. Metody splayn-funktsiy. [Methods of spline functions]. M. Science publishing. 1980. 352 p. [in Russian].
14. Kvasov B.I. Chislennyye metody analiza i lineynoy algebry. [Numerical methods of analysis and linear algebra]. Novosibirsk. 2012. 262 p. [in Russian].

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How to Cite
Moroz, A. (2020). 3D SIMULATION OF HYDROMECHANICAL CHARACTERISTICS OF SMALL HYDROPOWER PLANTS. Vidnovluvana Energetika, (2(61), 70-79. https://doi.org/10.36296/1819-8058.2020.2(61).70-79