This paper presents a mathematical model of hydro power units, especially the governor system model for different operating conditions, based on the basic version of the software TOPSYS. The mathematical model consists of eight turbine equations, one generator equation, and one governor equation, which are solved for ten unknown variables. The generator and governor equations, which are different under various operating conditions, are presented and discussed in detail. All the essential non-linear factors in the governor system (dead-zone, saturation, rate limiting, and backlash) are also considered. Case studies are conducted based on one Swedish hydro power plant (HPP) and three Chinese plants. The simulation and on-site measurements are compared for start-up, no-load operation, normal operation, and load rejection in different control modes (frequency, opening, and power feedback). The main error in each simulation is also discussed in detail. As a result, the model application is proved trustworthy for simulating different physical quantities of the unit (e.g., guide vane opening, active power, rotation speed, and pressures at volute and draft tube). The model has already been applied effectively in consultant analyses and scientific studies.

On the basis of the state–space method (SSM), a novel linear mathematical model of the unsteady flow for the tailrace system with an open channel is proposed. This novel model is an elastic linearized model of water hammer. The validity of the model has been verified by several examples of numerical simulation, which are based on a finite difference technique. Then, the complete mathematical model for the hydro-turbine governing system of hydropower station with an open tailrace channel, which is used for simulating the transient process of the hydro-turbine governing system under load disturbance, is established by combining the models of hydro-turbine, generator, governor and open tailrace channel. Finally, according to the complete model, the regulation quality for hydro-turbine governing system with an open tailrace channel under load disturbance is studied, and the effects of open tailrace channel and tailrace surge tank on regulation quality are analyzed. The results indicate that: The open tailrace channel has a strong influence on the regulation quality by observing the water level fluctuations in tailrace surge tank. The surge shows a piecewise periodical change along with the variation in the length of an open channel. The open tailrace channel can be used to improve the regulation quality of hydro-turbine governing system.

A model for simulating vertical water level fluctuations with coupled liquid and gas phases is presented. The Preissmann implicit scheme is used to linearize the governing equations for one-dimensional transient flow for both liquid and gas phases, and the linear system is solved using the chasing method. Some classical cases for single liquid and gas phase transients in pipelines and networks are studied to verify that the proposed methods are accurate and reliable. The implicit scheme is extended using a dynamic mesh to simulate the water level fluctuations in a U-tube and an open surge tank without consideration of the gas phase. Methods of coupling liquid and gas phases are presented and used for studying the transient process and interaction between the phases, for gas phase limited in a chamber and gas phase transported in a pipeline. In particular, two other simplified models, one neglecting the effect of the gas phase on the liquid phase and the other one coupling the liquid and gas phases asynchronously, are proposed. The numerical results indicate that the asynchronous model performs better, and are finally applied to a hydropower station with surge tanks and air shafts to simulate the water level fluctuations and air speed.

Hydraulic systems may involve both pipelines and open channels, which challenges the hydraulic transient analysis. In this paper, a method of characteristics (MOC)-finite volume method (FVM) coupling method has been developed with the pipeline modelled using the MOC and the open channel modelled using the FVM. The coupling boundaries between these two simulation regions are developed based on Riemann invariants. The simulated parameters can be transmitted from the MOC region to the FVM region and in the reverse direction through the coupling boundaries. Validation of the method is conducted on a simple tank-pipe system by comparing the simulated result using 3D computational fluid dynamics (CFD) analysis. The new method is then applied to a prototype hydropower station with a sand basin located between the upstream reservoir and the turbines. The sand basin is modelled as an open channel coupled with the pipes in the system. The transient processes are also simulated by modelling the sand basin as a surge tank. The comparison with the results by the MOC-FVM coupling method shows the new coupling method can provide more reliable and accurate results. This is because the flow velocity in the horizontal direction in the sand basin is considered in the coupling method but neglected when the sand basin is modelled as a surge tank in the MOC.

Smart isolation devices (SIDs) are commonly used in pressurized subsea pipelines that need to be maintained or repaired. The sudden stoppage of the SID may cause large water hammer pressures, which may threaten both the pipeline and the SID. This paper proposes a simulation method by using a coupled dynamic mesh technique to simulate water hammer pressures in the pipeline. Unlike other water hammer simulations, this method is the first to be used in the simulation in pipelines with a moving object. The implicit method is applied to model the moving SID since it has the mutual independence between the space step and the time step. The movement of the SID is achieved by updating the size of the computational meshes close to the SID at each time step. To improve the efficiency of the simulation and the ability of handling complex boundary conditions, the pipe sections far away from the SID can also be simulated by using the explicit Method of Characteristics (MOC). Verifications were conducted using the simulated results from the Computational Fluid Dynamics (CFD) numerical simulation. Two scenarios have been studied and the comparisons between the simulated results by using the dynamic meshes in 1D methods and those by the CFD simulation show a high correlation, thus validating the new method proposed in this paper.

The authors wish to make the following corrections to the published paper [1].