Geodesic
Relaxation oscillations in the Darie wind power plant model
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 31-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article discusses the mathematical model of the Daria small wind power plant. This installation is a type of vertical axis wind turbine named after its inventor, Georges Jean Marie Darrieux. The design consists of a vertically oriented shaft with curved blades or airfoils attached to it, forming a shape similar to an egg whisk. In today's world, against the backdrop of climate change and steadily increasing energy demand, wind energy acts as a critical pillar of the transition to renewable energy sources. This technology helps reduce carbon emissions and mitigate humanity's impact on the environment. In this context, wind energy is emerging not only as a means of supplying electricity, but also as a powerful catalyst for building a more sustainable and energy-efficient future. The equation of stationary modes is studied at the value of the external resistance of the dynamic model specified by the simplest equation. Conditions have been found under which relaxation oscillations are observed in the system.
Keywords: mathematical modeling, dynamic models, wind power plant, function approximation, invariant manifolds, differential equations.
Mots-clés : relaxation oscillations, singular perturbations 
@article{VSGU_2024_30_1_a2,
     author = {A. S. Kirsanova},
     title = {Relaxation oscillations in the {Darie} wind power plant model},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {31--39},
     year = {2024},
     volume = {30},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a2/}
}
TY  - JOUR
AU  - A. S. Kirsanova
TI  - Relaxation oscillations in the Darie wind power plant model
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2024
SP  - 31
EP  - 39
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a2/
LA  - ru
ID  - VSGU_2024_30_1_a2
ER  - 
%0 Journal Article
%A A. S. Kirsanova
%T Relaxation oscillations in the Darie wind power plant model
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2024
%P 31-39
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a2/
%G ru
%F VSGU_2024_30_1_a2
A. S. Kirsanova. Relaxation oscillations in the Darie wind power plant model. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 31-39. http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a2/

[1] Klimina L.A., Dosayev M.Z., Selyutski Yu.D., “Dynamics of a Wind Turbine with the Working Element Based on an Antiparallel Link Mechanism”, Mekhatronika, Avtomatizatsiya, Upravlenie, 17:8 (2016), 536–540 (In Russ.) | DOI

[2] Andronov P.R., Dosaev M.Z., Dynnikova G.Y., Selyutskii Y.D., Strekalov S.D., “Modeling of oscillating wind turbine”, Journal of Machinery Manufacture and Reliability, 38:4 (2009), 383–387 | DOI

[3] Dosaev M.Z., Lin C.H., Lu W.L., Samsonov V.A., Selyutskii Y.D., “A qualitative analysis of the steady modes of operation of small wind power generators”, Journal of Applied Mathematics and Mechanics, 73:3 (2009), 259–263 (In English; original in Russian) | DOI | MR | Zbl

[4] Dosaev M.Z., Samsonov V.A., Seliutski Yu.D., “On the dynamics of a small-scale wind power generator”, Doklady Physics, 52:9 (2007), 493–495 (In English; original in Russian) | DOI | Zbl

[5] Dosaev M.Z., Samsonov V.A., Selyutskii Y.D., Lu W.-L., Lin C.-H., “Bifurcation of operation modes of small wind power stations and optimization of their characteristics”, Mechanics of Solids, 44:2 (2009), 214–221 (In English; original in Russian) | DOI

[6] Kirsanova A.S., “Bifurcations of stationary regimes in the model of a wind power plant”, Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya / Vestnik of Samara University. Natural Science Series, 27:4 (2021), 92–98 (In Russ.) | DOI

[7] Kirsanova A., “Critical Phenomena in the Darrieus Wind Turbine Model”, 16th International Conference Management of large-scale system development (MLSD) (Moscow, Russian Federation), IEEE, 2023, 1–4 | DOI | MR

[8] Kobrin A.I., Dosaev M.Z., Lokshin B.Ya., Samsonov V.A., Selyutski S.Y., Constructive theory of small-scale wind power generators, Chapters I-II, v. I, Izd-vo Moskovskogo Universiteta, M., 2007, 76 pp. (In Russ.)

[9] Kobrin A.I., Dosaev M.Z., Lokshin B.Ya., Samsonov V.A., Selyutski S.Y., Constructive theory of small-scale wind power generators, Chapter III, v. II, Izd-vo Moskovskogo Universiteta, M., 2007, 88 pp. (In Russ.)

[10] Voropaeva N.V., Sobolev V.A., Geometric decomposition of singularly perturbed systems, FIZMATLIT, M., 2009, 256 pp. (In Russ.)

[11] Kurina G.A., Kalashnikova M.A., “Singularly Perturbed Problems with Multi-Tempo Fast Variables”, Automation and Remote Control, 83 (2022), 1679–1723 (In English; original in Russian) | DOI | DOI | MR | Zbl

[12] Mishchenko E.F., Rozov N.H., Differential equations with small parameters and relaxation oscillations, Nauka, M., 1976, 248 pp. (In Russ.)

[13] Sobolev V.A., Shchepakina E.A., Reduction of models and critical phenomena in macrokinetics, FIZMATLIT, M., 2010, 320 pp. (In Russ.)