高维网机系统失稳振荡的分岔研究

STUDY ON BIFURCATION OF UNSTABLE OSCILLATION OF HIGH-DIMENSIONS POWER SYSTEM

应用机电耦联动力学理论和电路理论,建立了统一的发电机组并网发电的数学模型.该模型为27维非线性微分动力系统,包括机械扭振方程、同步发电机瞬变过程基本方程、原动机力矩分配及调速控制方程、励磁调节控制方程和并网线路串补电容方程5大部分.本文选择线路串补电容的容抗、线路电阻作为分岔参数,计算并得到了失稳参数区域图.对满足两对纯虚特征值的参数点,利用中心流形定理对原系统方程做了降维.再利用多参数稳定性理论及归一化技术,对约化方程进行求解,得到了分岔方程.由此得到分岔参数图、4个参数区的动力学特性,并得到了数值验证.

On the basis of eletro-mechanical dynamics and electrical theory, we established a uniform mathematic model for a generator set power network. This model was a nonlinear differential dynamic system that had 27 dimensions. It consisted of the following 5 parts: the mechanical torsional equations, the synchro generator transient process equations, the prime motor torsion allocating and speed modulation control equations, and the field excitation modulation control equations. We used the series capacitor Xc and the resistance R of the transportation line as the bifurcation parameters and derived the area figure of destabilizing parameters from computing. At the point where two pairs of pure imaginary eigenvalues occured, we reduced the dimensions of the system through central manifold theory. Then, using the multi-parameter stability theory and unification technique, we solved the reduced equation and obtained the bifurcation equations and their solution. Finally, we obtained the diagram of bifurction parameters, dynamic characters in four parametric areas, and the result was verified by numerical calculation.