PROBLEMS OF AERODYNAMIC STABILITY AND A MATHEMATICAL MODEL OF A WIND POWER PLANT OF TURBOGENERATOR TYPE
DOI:
https://doi.org/10.32782/KNTU2618-0340/2020.3.2-1.7Keywords:
wind power plant; mathematical model; stability; method of equivalent transformationsAbstract
An approach to obtaining a mathematical description of the dynamics of a multiplier turbine generator of wind power plant in a dimensionless normalized form is proposed, as well as an estimation of the available aerodynamic stability reserves for various wind conditions based on the proposed mathematical model. The approach is based on the initial formation of the equations for the rotational motion dynamics of the screw groups using the laws of conservation and equilibrium, taking into account the aerodynamic characteristics of the wind wheel and turbomachines. On the basis of the method of equivalent transformations of mathematical models, the equations of a wind power plant dynamics were obtained in a normalized form with respect to the speed of the wind wheel and each of the turbomachines. The equations of dynamics of a wind power plant in normalized form are a system of nonlinear parametric differential equations, the parameters of which depend both on the design features of the wind power plant and on the parameters of the wind flow. The proposed equations of the wind power plant dynamics in normalized form have a symmetrical form and can be used at the design stage for various construction schemes. The most important result of the study is the established dependence of the nonlinear equations parameters of the wind power plant dynamics on the gradient of wind speed. The study of the dependence of aerodynamic stability reserves on the speed of the wind flow and the gradient of this speed has been carried out by the method of computer simulation. It was found that in the presence of a positive gradient of the wind flow velocity, the aerodynamic stability reserves of a wind power plant at a constant load are reduced. A positive gradient in wind speed can be caused, for example, by wind gusts or by wind shear. The effect of reducing the aerodynamic stability reserves of a wind power plant is more significant at lower wind flow velocities. The proposed equations of the wind power plant dynamics in a normalized form can be used to solve a wide range of design problems and study the dynamic modes of wind power plants for conditions of variable wind flow.
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