永磁同步风力发电机随机分岔现象的全局分析

Global analysis of stochastic bifurcation in permanent magnet synchronous generator for wind turbine system

永磁同步风力发电机在运行过程中不可避免地会受到风能的随机干扰,本文建立了在输入机械转矩存在随机干扰情况下永磁同步风力发电机的数学模型,采用胞映射方法分析了随机干扰强度变化时系统全局结构的演化行为,并通过数值模拟对理论分析进行验证.研究结果表明,随着随机干扰强度的增大,系统中会出现随机内部激变和随机边界激变,即由于随机吸引子与其吸引域内的随机鞍发生碰撞而产生的随机分岔现象和由于随机吸引子与其吸引域边界发生碰撞而产生的随机分岔现象.研究结果揭示了随机干扰对永磁同步风力发电机运行性能影响的机理,为永磁同步风力发电系统的运行和设计提供了理论依据.

The permanent magnet synchronous generator（PMSG） for wind turbine system operating under inevitable stochastic disturbance from wind power is a nonlinear stochastic dynamical system. With the random interaction and nonlinearity, the intense nonlinear stochastic oscillation is likely to happen in such a system, causing the system to be unstable or even collapse. However, the PMSG is usually considered as a deterministic system when analyzing its nonlinear dynamic behaviors in the past researches. Such a simplification can lead to wrong predictions for the system stability and reliability. This paper aims to discuss the effect of the stochastic disturbance on the nonlinear dynamic behavior of the PMSG. Based on the derived PMSG model considering the stochastic disturbance from the input mechanical torque, the evolution of the system global structure with the stochastic intensity is investigated using the generalized cell mapping digraph method. Meanwhile, the occurrence process and development process of the stochastic bifurcation are illustrated. Based on this global analysis, the intrinsic mechanism for the effect of the stochastic disturbance on the operating performances of the PMSG is revealed. Finally, the numerical simulations based on the Euler-Maruyama algorithm are carried out to validate the results of the theoretical analysis. The results present that as the intensity of the stochastic disturbance increases, two kinds of stochastic bifurcations can be observed in the PMSG system according to the definition of a sudden change in characteristic of the stochastic attractor. One is the stochastic interior crisis that occurs when a stochastic attractor collides with a stochastic saddle in its attraction basin interior, leading to the abrupt increase of the attractor and the disappearance of the saddle. This kind of bifurcation results in the intense stochastic oscillation and instability of the PMSG system. Another stochastic bifurcation is the stochastic boundary crisis which occurs when a stochastic attractor collides with the boundary of its attraction basin and results in the disappearance of the attractor. This sudden change of the number of stochastic attractors induces the stable solution set to vanish and thus the PMSG system to collapse. In a word, even the stochastic disturbance with small intensity may lead to the complete destruction of the stable structure of the PMSG, inducing the system to suffer a strong disordered oscillation or the operation to collapse. The results of this paper can provide significant theoretic reference for both practically operating and designing the PMSG for wind turbine systems.