基于Lyapunov分解聚合法的汽轮发电机组轴系扭振稳定性分析

STABILITY ANALYSIS OF THE SHAFT TORSIONAL OSCILLATION BASED ON LYAPUNOV DIRECT METHOD

应用 Lyapunov分解聚合法研究电力系统轴系扭振现象 ,将电力系统分解为机械系统和电气系统两个子系统 ,将机械系统转化为鲁里叶型系统 ,构造了一类鲁里叶型 Lyapunov函数 ,对电气子系统也构造了一种 Lyapunov函数 ,然后应用聚合的方法同时考虑两个子系统间的耦合作用 ,构造了整个机电系统的 Lyapunov函数 ,并验证了其有效性。利用所构造的 Lyapunov函数 ,在对该非线性系统在平衡位置稳定性所进行的详细分析结果的基础上 ,讨论了其稳定运行域。并用 IEEE第1基准模型的时域仿真结果验证了所提出的 Lyapunov函数的有效性。

The Lyapunov decomposition and aggregation method is proposed to analyze the shaft torsional oscillation. The power system including the turbine-generator shaft, flux decay and voltage regulator is decomposed to two isolated subsystems: mechanical subsystem and electrical subsystem. The mechanical subsystem is converted to a standard Lure control system that is analyzed by an improved Lure Lyapunov function. A Lyapunov function for the electrical sub-system is also proposed. Combining the two Lyapunov functions and taking the interaction between the two sub-systems into consideration, a new Lyapunov function for the overall system is proposed. The effectiveness of the proposed Lyapunov function is proven. The stability of the power system at the equilibrium points is discussed in detail. The stable operation region of the system is obtained by use of the proposed Lyapunov function. The validity of the proposed method is also verified by simulation results for an IEEE First benchmark for SSR. This study has shown the potential benefits and validity of Lyapunov direct method in the shaft torsional oscillation analysis.