USE OF LOGRANGE EQUATIONS OF THE SECOND GENERAL FOR OBTAINING STATIC CHARACTERISTICS OF THE CENTRIFUGAL REGULATION

Keywords: wind turbine, differential equations of wind turbine motion, centrifugal angular velocity regulator.

Abstract

Low power wind turbines have a high value of the angular velocity of the rotor. In addition, it is also necessary to take into account the randomness of the nature of the wind flow and changes in its magnitude in a wide range. All these features require that low-power wind turbines, especially wind-driven wind turbines, be equipped with rotor angular speed control systems. Due to the fact that the main owners of wind turbines are individuals with limited territorial resources, wind turbines are mostly located in close proximity to buildings. Thus, among the many requirements for wind turbines, safety in operation comes to the fore, in addition to simplicity and low cost. Among the large number of control systems for low-power wind turbines, systems using centrifugal regulators of various designs meet these requirements to the greatest extent. Known means of their calculation require the choice of the appropriate general theorem of dynamics. In the case of systems with several degrees of freedom, the solution of problems is much more complicated, because it requires the combined application of some general theorems and other relations of dynamics, the choice of which sometimes causes considerable difficulties. When designing new control systems, design engineers need simplified methods for calculating the parameters of the regulator to determine the main mass and size indicators of the future design. In this paper we propose a system of differential equations of motion of the elements of the centrifugal regulator of the original design using Lagrange equations of the second kind. The solution of this system of equations at steady state allowed to obtain expressions for determining the parameters of the controller to ensure the nominal rotor speed and select the spring stiffness to ensure the required range of deviations of the rotor speed from the nominal value in a given range of control angles. These expressions can be used for similar in design centrifugal regulators of wind turbine rotors. Ref. 8, fig. 5.

Author Biographies

М. Shykhailov, Institute of Renewable Energy of NAS of Ukraine, 02094, 20A, Hnat Khotkevich Str., Kyiv, Ukraine

img12.pngAuthor information: researcher at Institute of Renewable Energy, National Academy of Sciences of Ukraine.
Education: graduated from the Kyiv Polytechnic  Institute in 1979 with the specialty "Hydropneumatic and Hydraulic Drive".
Research area: wind power systems, small capacity wind units, control systems.
Publications: 222

V. Golovko, Institute of Renewable Energy of the National Academy of Sciences of Ukraine, 02094, 20А Hnata Khotkevycha St., Kyiv, Ukraine

holovko1.jpgAuthor information: chief researcher at Institute of Renewable Energy, National Academy of Sciences of Ukraine.
Education: graduated from the Ukrainian Agricultural Academy in 1977 with the degree of "Electrification of Agriculture".
Research area: renewable sources of energy, wind power systems, small capacity wind units, autonomous power systems.
Publications: 168

V. Kokhanievych, Institute of Renewable Energy of NAS of Ukraine, 02094, 20A, Hnat Khotkevich Str., Kyiv, Ukraine

kokhanievych.jpgAuthor information: senior researcher at Institute of Renewable Energy, National Academy of Sciences of Ukraine.
Education: graduated from the Kyiv Polytechnic  Institute in 1979 with the specialization "Technology of Machine-Building, Metal Cutting Machines and Tools".
Research area: power systems, converting types of energy, automation and modeling processes. wind po-wer systems, small capacity wind units, control systems and protect.
Publications: 147

References

1. Shykhaylov N.A., Shevchenko YU.V., Kovalenko V.I. Regulyator chastoty vrashcheniya vetrokolesa. [Wind wheel speed regulator]. A. s. USSR №1038541. Оpubl. 30.08.1983 g., byul. No. 32. [in Russian].
2. Bat M.I., Dzhanelidze G.Yu., Kelzon A.S. Teoreticheskaya mekhanika v primerakh i zadachakh. [Theoretical mechanics in examples and problems]. M. Gos. izd-vo fiziko-matematicheskikh nauk. 1961. 616 p. [in Russian].
3. Tsukernyk L.M. Teoriya i raschet tsentrobezhnogo regulyatora. [Theory and calculation of a centrifugal regulator]. Moskow. Mashgiz. 1951. 110 p. [in Russian].
4. Sabinin G.H. Teoriya regulirovaniya bystrokhodnykh vetrodvigateley povorotom lopastey tsentrobezhnym regulyatorom. [Theory of regulation of high-speed wind turbines by turning blades by a centrifugal regulator]. Industrial aerodynamics. 1957. Sb. No. 8. Pp. 5-77. [in Russian].
5. Sabinin G.H. Teoriya regulirovaniya bystrokhodnykh vetryakov tsentrobezhnym regulyatorom s pomoshch'yu povorota lopastey. [The theory of regulation of high-speed windmills by a centrifugal regulator by means of rotation of blades]. Energy issues. 1959. Pp. 37-49. [in Russian].
6. Kokhanyevich V.P. Statyka rehulyuvannya rotoriv vitrodvyhuniv vidtsentrovymy rehulyatoramy pry antyflyuhernomu rehulyuvanni. [Static characteristics of the centrifugal regulator at weather vane regulation of the rotor of the wind turbine]. Vidnovlyuvana enerhetika. 2009. No. 3(18). Pp. 18-24. [in Ukrainian].
7. Mkhitaryan A.M., Ushakov V.V., Baskakova A.G. i dr. Aerogidromekhanika. [Aerogidromekhanika]. Pod red. prof. A.M. Mkhitaryana. Moskow. Mashinostroyeniye. 1984. 352 p. [in Russian].
8. Fateyev Ye.M. Vetrodvigateli i vetroustanovki. [Vetrodvigateli i vetroustanovki]. Moskow. Gosselkhozizdat. 1957. 536 p. [in Russian].

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Published
2021-12-25
How to Cite
ShykhailovМ., Golovko, V., & Kokhanievych, V. (2021). USE OF LOGRANGE EQUATIONS OF THE SECOND GENERAL FOR OBTAINING STATIC CHARACTERISTICS OF THE CENTRIFUGAL REGULATION. Vidnovluvana Energetika, (4(67), 60-68. https://doi.org/10.36296/1819-8058.2021.4(67).60-68