Hydraulic oscillation is a fluctuating phenomenon of pressure and discharge in pipes, which can threaten the safety of hydropower, pumping and water conveyance systems. To analyse the associated problems, new methods with simple form and clear physics are needed. This paper presents a water-hammer reflection coefficient-based criterion for stability evaluation of free-vibration of hydraulic systems. The stability (or attenuation) condition for a single pipe system is that the modulus of the product of the reflection coefficients at the inlet and outlet should be smaller than 1. For a complex pipe system, the condition necessary for stability is that every single pipe system is stable. To apply this new criterion to stabilizing the reservoir-single pipe-constant power turbine system by adding a head loss valve in the pipe, a formula for the critical head loss is proposed and verified. This new method is theoretically consistent with conventional methods, but more convenient in application.

水力振荡是管道内压力和流量的波动现象，可威胁水电、抽水和输水系统的安全。为了分析相关问题，需要形式简单、物理清晰的新方法。本文提出了一种基于水锤反射系数的液压系统自由振动稳定性评价准则。单管系统的稳定（或衰减）条件是入口和出口处的反射系数乘积的模应小于1。对于复杂的管道系统，稳定的必要条件是每根单管系统稳定。为了应用这一新准则通过在管道中增加水头损失阀来稳定水库-单管道-恒功率涡轮系统，提出并验证了临界水头损失的公式。这种新方法在理论上与传统方法一致，但应用上更加方便。