Abstract—

The movement of a small wind power plant with a vertical axis of rotation in a stationary air flow is considered. The plant consists of two coaxial Darrieus rotors rotating in opposite directions. On the shaft of one of them, the rotor of the generator is rigidly fixed, on the shaft of the other, the stator is placed. A closed few parametric mathematical model of a wind turbine is constructed by taking into account the aerodynamic effect on the rotors and the electrical load in the local circuit of the generator. The corresponding dynamic system is dual frequency. The system is averaged over two angles under the assumption that the value of each of the frequencies is non-zero. Attracting fixed points of the averaged system are considered as a first approximation to describe the operating modes of a wind turbine. Bifurcation diagrams that describe the evolution of fixed points of the averaged system when changing the model parameter, which characterizes the value of external resistance in the local circuit of the generator of the plant, are constructed. A parametric analysis of stability conditions for fixed points is carried out. By numerically integrating equations with different initial conditions and parameter values, estimates for the deviation of the solutions of the averaged system from the slow variables of the complete system are obtained. The conditions for maintaining the resonance frequency ratio in the system are considered separately.

中文翻译：

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双转子达里乌斯风轮机的自转模式

摘要-

考虑了具有垂直旋转轴的小型风力发电厂在固定气流中的运动。该设备由两个沿相反方向旋转的同轴Darrieus转子组成。在其中一个的轴上，发电机的转子被牢固地固定，在另一个的轴上，定子被放置。通过考虑对转子的空气动力学影响以及发电机本地电路中的电负载，构建了一个风力涡轮机的封闭式几个参数数学模型。相应的动态系统是双频。在每个频率的值都不为零的假设下，在两个角度上对系统进行平均。吸引平均系统的固定点被视为描述风力涡轮机运行模式的第一近似值。构造了分叉图，该分叉图描述了平均模型系统固定点在更改模型参数时的演变，该变化表征了工厂发电机本地电路中的外部电阻值。对固定点的稳定性条件进行了参数分析。通过对具有不同初始条件和参数值的方程进行数值积分，可以得出平均系统解与完整系统慢变量之间的偏差估计值。单独考虑保持系统中谐振频率比的条件。对固定点的稳定性条件进行了参数分析。通过对具有不同初始条件和参数值的方程进行数值积分，可以得出平均系统解与完整系统慢变量之间的偏差估计值。单独考虑保持系统中谐振频率比的条件。对固定点的稳定性条件进行了参数分析。通过对具有不同初始条件和参数值的方程进行数值积分，可以得出平均系统解与完整系统慢变量之间的偏差估计值。单独考虑保持系统中谐振频率比的条件。