磁悬浮飞轮储能系统机电耦合非线性动力学研究

针对磁悬浮飞轮储能系统的"磁悬浮飞轮-发电机"机电耦合非线性动力学特性进行研究.通过推导磁悬浮飞轮储能系统在偏心条件下的动能、势能、发电机系统的磁场能以及系统的耗散函数,由Lagrange-Maxwell方程建立磁悬浮飞轮系统和两相四极永磁发电机系统的机电耦合动力学方程.采用数值法对0.6MW磁悬浮飞轮储能系统进行了仿真分析,研究结果表明,系统机电耦合非线性方程存在稳定的与转速同频的基频和三倍频周期运动解,且基频振动幅值比三倍频振动幅值大.对于稳定的磁悬浮储能飞轮机电耦合系统,飞轮转速增大,或磁轴承系统刚度减小或阻尼增大,或磁场能(电枢反应磁场能或永磁励磁磁场能)减小,可使系统的非线性振动幅值减小.而增大磁轴承系统的刚度,或减小磁轴承系统的阻尼,或增大系统的磁场能有可能破坏机电耦合系统的稳定性,使飞轮失稳.

Study on nonlinear dynamics of electromechanical coupling in flywheel energy storage system based on active magnetic bearings

This paper studied the nonlinear dynamics of electromechanical coupling between the flywheel and the generator in the flywheel energy storage system (FESS) based on active magnetic bearings (AMBs). By deducing the functions of the kinetic energy, the potential energy, the magnetic field energy in the air gap of the generator and the energy dissipation of the whole system with rotor eccentricity, the dynamical equations of the coupled system between the flywheel system with AMBs and the two phase four pole permanent magnet generator were established by using the Lagrange Maxwell equation. Then, the numerical method was adopted to analyze the nonlinear dynamical characters of the 0.6MW FESS based on AMBs, and the analytical results of the example show that the stable rotating synchronous harmonic solution and triple harmonic solution exist in the nonlinear equations of the coupled system, and the amplitude of the synchronous vibration is higher than that of triple harmonic vibration. Furthermore, when the FESS based on AMBs is stable, the nonlinear vibration can be weakened by increasing rotational speed of flywheel, the damping of AMBs or by decreasing the stiffness of AMBs, the magnetic field energy which includes the armature reaction energy and the permanent magnet excitation energy. As for decreasing the damping of AMBs or by increasing the stiffness, magnetic field energy, the flywheel may get unstable.