无刷双馈风电系统最大李氏指数计算及混沌分析

Calculation of the largest Lyapunov exponents and chaos analysis of brushless doubly-fed wind power system

为研究无刷双馈风电系统(BDFWPS)的非线性动力学行为,根据电机dq轴下的电压、磁链方程,导出非线性微分方程组。通过引入转速PD控制项,建立了发电机的七阶非线性自治系统。以功率绕组、控制绕组与转子绕组间的扩散系数σrp、σrc为变量,采用Wolf算法计算最大Lyapunov指数三维谱,提出风电系统可能出现的分岔和混沌运动状态。通过数值仿真法从时序图、相图等方面研究BDFWPS经倍周期分岔、Hopf分岔进入混沌的转迁过程,验证了系统分岔和混沌现象的存在,相关结论,为提高BDFWPS复杂工况下的安全稳定运行性能,提供切实可靠的理论依据。

The nonlinear differential equations of the brushless doubly-fed wind power system (BDFWPS) were derived to study the nonlinear dynamical behavior based on voltage and flux equations under d-q axis. A order nonlinear autonomous system was constructed with the PD control of the speed. The three dimensional spectrum of the largest Lyapunov exponents was calculated by Wolf algorithm, in which the diffusion coefficient σ rp and σ rc were selected as variables between the power winding and control winding with rotor winding. The bifurcation phenomenon and chaos operation status possible existed in wind power system for the spectrum. The transition process from period-doubling bifurcation and Hopf bifurcation into chaos operation was studied in brushless doubly-fed machine (BDFM) by sequence diagram and phase diagram with numerical simulation. The bifurcation and chaos phenomenon existing in BDFM was proved. The practical and reliable theoretical basis is provided to enhance secure and stable operation performance of BDFM in complex condition.