弹性模型下基于稳定性的水电站调压室设置条件

Setting conditions of surge chambers at hydropower station in elastic model based on operation stability

调压室设置条件是水电站初步设计的重要判据之一,引水道较长的电站水流弹性对设置条件有明显影响。本文根据模型的频域特性简化了水击弹性模型,运用拉普拉斯变换理论建立水电站运行稳定性的数学模型。根据霍尔维之稳定性判据推导出简化弹性水击方程下基于稳定性的调压室设置判别条件。并给出了不同调速器参数下的稳定边界,探讨了波动发散程度与水流弹性的关系。通过对数学模型的主导极点分析,求解出转速波动的简化解析表达式,并与数学模型数值计算结果对比,验证了其正确性。根据解析表达式进一步推导出满足不同调节品质的调压室设置判别条件。结合工程实例,得出了考虑弹性时的最大水流惯性常数,对比先前的判别条件可得出水流弹性的重要影响。

The setting condition of surge chamber is a key criterion in primary designs of hydropower stations, and in the case of long conduits it depends on the elasticity of water significantly. This paper describes a simplified water hammer elastic model based on frequency domain characteristics and a mathematical model of operational stability using Laplace transform theory. We derive a surge chamber stability setting criterion by applying simplified elastic water hammer equations and Hurwitz criterion, and analyze the stability limits corresponding to different governor parameters and the dependence of divergent fluctuations on the elasticity of water. An analytical equation of speed fluctuations is derived by identifying the dominant poles of the equation system, and verified by comparison with numerical results, and then it is used in formulation of the setting conditions for different governing qualities. Application of the theoretical procedure to practical cases shows the maximum inertia time constant of water with compressibility in effect as well as the significance of compressibility by comparison with common setting criterions.