水电站过渡过程计算中水轮机模型单点迭代求解方法及其收敛性研究

水力机组过渡过程计算中水轮机模型最为复杂,常需要采用迭代的方法进行求解,但迭代不收敛现象时有发生。针对该问题本文采用单点迭代的方法研究了水轮机模型迭代收敛性,并提出了一种新的求解流程,从数学层面上严格推导了该流程需要满足的最大允许计算步长。在此基础上分析了求解过程中水轮机各参数对计算收敛性的影响规律及影响程度。进而大大减少了水轮机模型迭代计算的不收敛现象,为工程计算和科学研究中求解水轮机模型提供了可靠的理论指导。

A single-point iterative method and its convergence for simulating hydropower station transient process

Hydraulic turbine models are the most complicated in the simulation of hydraulic transient process. They are typically solved with an iterative method, but numerical divergence frequently occurs in the calculation. To overcome this problem, this paper describes a new single-point iterative procedure that is optimized to improve the convergence of hydraulic turbine models. A maximum step size has been analytically derived for numerical iteration, and the influence of various parameters of the hydraulic turbine on convergence analyzed. Results show that this new method can greatly reduce the numerical divergence and would provide a reliable theoretical basis for modeling hydraulic turbines.