**Authors: **Shkolnyy E. P.

**Year: **2017

**Issue: **20

**Pages: **5-17

**Abstract**

It is impossible to organize wind energy systems without studying of wind speed regime at the surface layer of the atmosphere within a specific area and at climatic scales. Such studies are often accompanied by approximations of probabilities of wind speed performed in the form of normal law of a system of random values presented by a zonal u and a meridional which are components of a wind speed vector. It is suggested that, for the purposes of wind energy, display of a wind speed vector in polar coordinates (r,a) r – where is a module of wind speed and a – is a polar angle appears to be more preferable. The article shows a transform from a normal law of distribution of probabilities with density ф(u,v) to a normal law distribution with density ф(r,a) completed by means of functional transformation with elliptic dispersion in place. Based on a normal law of distribution ф(r,a) and through integration with respect to corresponding variables (r,a) individual distributions of probabilities ф(r) and ф(a) as well as conditional distributions of probabilities ф(r/a)and ф(a/r)were obtained in the areas of their existence. The article shows individual distributions in case of circular and elliptic dispersion of a wind speed vector. It shows that an individual distribution of a wind speed probability in case of circular

dispersion and in the absence of correlated dependence turns into the Rayleigh’s distribution and a conditional distribution of a polar angle degenerates in an even distribution. The cases of distributions with dispersions of a wind speed module having elliptic properties subject to availability of correlated connection between wind speed components were also studied. Calculation of probabilities of a polar angle being within different sections of the area 0≤α≤2π with set values of a wind speed module also took place. Numerical experiments proved the advantage of such modeling of distributions of wind speed vector.

**Tags: **dispersion; Fisher criterion; individual and conditional distribution; probability density; wind speed; дисперсія; критерій Фішера; частковий та умовний розподіли; швидкість вітру; щільність ймовірностей

**Bibliography**

- Obuhov S. G., Plotnikov I.’ A., Sarsikeev E. Z. Dynamic model of the longitudinal component of the wind speed.
*Sovre**mennye problemy nauki i obrazovaniya – Current problems of science and education,*2013, no. 5, pp. 139 – 145. (In Russian) - Van Der Hoven I. Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour.
*Meteor*., 1957, no. 14, pp. 160-164. - Shkol’nyy E. P.
*Fіzyka atmosfery*[Physics of the atmos- phere]. Kyiv: KNT, 2007. 508 - Laykhtman D. L. (Ed.)
*Dinamicheskaya meteorologiya (Teoreticheskaya meteorologiya).*[Dynamic Meteorology (The- oretical Meteorology)]. Leningrad: Gidrometeoizdat, 607 p. - Kaplya E. V. Statistical model of the dynamics of wind speed and direction.
*Meteorologiya i gidrologiya – Meteorology and Hydrology*, 2014, no. 12, pp. 29 – 34. (In Russian) - Kaplya E. V. Finite drive control system windmill blades finite drive control system windmill blades. Avtomatizatsiya i sovremennye tekhnologii – Automation and modern technology, 2013, no. 5, pp. 13 – 17. (In Russian)
- Mahrt L. Surface wind direction variability.
*J. Appl. Meterol and Clim., 2011, no. 50, pp. 144-152.* - Kobysheva N. V., Stepanskaya G. A., Chmutova Z. E. Assessment of potential wind energy resources on the territory of the USSR.
*Trudy GGO – Proc. of the Main Geophysical Observatory, 1983, vol. 475, pp. 7–12. (In Russian)* - Sapickiy K. A., Kobysheva N. V. Potential hydropower resources of Georgia.
*Trudy GGO — Proc. of the Main Geophysical Observatory*, 1983, vol.375, pp. 12 – 15. (In Russian) - Guterman I. G.
*Raspredelenie vetra nad severnym polushariem*[Wind distribution over the Northern Hemisphere]. Leningrad: Gidrometeoizdat, 1965. 252 - Yushkov V. P. Synoptic wind velocity fluctuations in the atmospheric boundary layer.
*Meteorologiya i gidrologiya – Meteorology and Hydrology*, 2012, no. 4, pp. 17 – 28. (In Russian) - Vencel E. S.
*Teoriya veroyatnostey*[Theory of probability]. Moscow, 1958. 464 - Gnadenko B. V.
*Kurs teorii veroyatnostey*[The course in probability theory]. Moscow: Fizmatlit, 1961. 396 - Smirnov N. V., Dunin-Barkovskiy I. V.
*Kurs teorii veroyatnostey i matematicheskoy statistiki dlya tekhnicheskikh prilozheniy*[The course of the theory of probability and mathematical statistics for technical applications]. Moscow: Nauka, 1969. 511 - Mitropol’skiy A. K.
*Tekhnika statisticheskikh vychisleniy*[Technique statistical calculations]. Moscow: Nauka, 1971. 576 p. - Kapustin S. N, Chervonyj A. A., Kolinichenko B. A.
*Te**oriya veroyatnostey, matematicheskaya statistika i metody issledovaniya operatsiy*[Probability theory, mathematical statistics and operations research techniques]. Moscow, 1961. 594 p. - Levin B. R.
*Teoreticheskie osnovy statisticheskoy radio*Engineering. Book 1]. Moscow, 1966. 728 p.*tekhniki*.*Kniga 1*[Theoretical Foundations of Statistical Radio