自励异步发电机带载稳态的解析计算

从自励异步发电机的暂态等效电路出发,基于其在两相静止坐标系上的状态空间数学模型,对其带载建压暂稳态过程提出了应用Lyapunov稳定性理论的整体性分析方法.依据理论分析方法分析得到了带载自励建压达到稳态的过程之应用暂态数学模型表示的稳态条件.解极限环条件得出了定子频率和转子转速的解析计算式,以及确保自励建压的负载取值范围和电机磁路过度饱和稳态励磁电感的解析关系式;为求解稳态运行点条件,提出了一种基于物理背景的等价转化解析计算方法,解得了稳态运行点的解析计算式.算例分析检验了稳态条件的唯一组解析解.实测值与计算结果相互吻合,验证了稳态条件解析计算式的正确性、科学性和有效性,表明了通用性和工程参考价值,解决了长期以来对异步发电机暂稳态运行性能无法解析计算的难题.理论分析方法适用于具有动力学特性的其他类型电力系统运行分析.

Analytic computation for steady states of loaded self-excited induction generators

Based on the state-space mathematic model obtained from the transient equivalent circuits in two-phase stationary reference frame of the loaded self-excited induction generator, a holistic analysis approach using Lyapunov stability theory was proposed for the whole of transient and steady state process of self-excitation buildup. According to the approach, it was obtained the steady-state conditions for self-excitation buildup represented by the transient mathematic model. The limit cycle condition was solved to get analytic formulas of the stator frequency and rotor speed, as well as the load ranges and analytic relationship of the magnetizing inductance for self-excitation buildup. In order to solve the steady-state operating point condition, an equivalent transformation method based on the physical occasion was presented to analytically compute all the points. The example analysis tested and confirmed only a set of analytic formulas. Good agreement between measured and computed results verified correctness, scientificalness and high validity of the steady-state conditions analytic formulas, showing universality and referenced value in engineering. It was solved the problem of the transient and steady state operating performance of induction generators unable to be analytically computed for a long time. The approach could be applicable to performance analysis of other power systems of dynamics.