Effects Of S-shaped Characteristics On Transient Process Of Pumped-hydro Energy Storage Station

Pumped storage stations are the inevitable products of modern power gird, which play an irreplaceable role in the power system. Especially due to the large-scale development of green energy, it seems to become more and more clear that pumped storage stations have many roles and advantages in electric system, such as peak-clipping, valley-filling, frequency and phase modulation, spinning reserve, improving quality, flexibility and reliability. The guaranty calculation of regulation is one of the key contents in design and operation of the pumped storage stations. During the early design stage, without prototype curves, the calculation of regulation guarantee can only apply the existing pump-turbine characteristic curves with similar head, capacity and specific speed. However, even the applied characteristic curves has the same head, capacity, specific speed, as well as a similar characteristic in turbine operating range with the designed units, the difference between the S-shaped characteristics is likely to lead transient parameters exceed the control requirements. Then the design organization will revise the water delivery system for several times and come to a relatively conservative conveyance system. Also in the unit bidding stage, without explicit requirements according to the characteristics of hydraulic system, the turbine manufacturers usually need to design several model units and optimize them according to the numerical results of transient process, until get a suitable units. It's undoubtedly caused the waste of human resources and economic resources. So it's important to study the relationship between S-shaped and transient parameters. Based on previous research, this dissertation deeply discusses the relationship between S-shaped and water hammer pressure. The main contents include the following aspects:1. Based on the solving process of a simplified differential equations of the rigid water hammer model, this paper deduced the analytical expression of the rising rate of water hammer pressure during load rejection in pumped storage power station and illustrated the intrinsic relation between the water hammer pressure rise rate and the slope of the characteristic curve of the pump turbine. According to the signs of the slope of the operating point on the S-shaped characteristic curve of the pump turbine, the characteristic curve is divided into three regions and we can come to the conclusion:the larger the absolute value of the slope in the first region, the greater the pressure of water hammer is; the larger the slope value in the second region, the greater the pressure of water hammer is. The maximum value of the water hammer must occur before the lower singular point and next to it. In the first region, the water inertia time constant is the dominant factor that impacts the water hammer, while in the second region, the dominant factor is the slope of the curves.2. For the curve before the runaway point, analytical method can be used to solve the head of runaway point and speed increasing time. For the curve after the runaway point, take the braking zone as the study subject. First, by linearizing the curve of braking zone, the problem can be simplified as the influence of the slope of the braking area on water hammer maximum value. Then we transform the characteristic curve into a new form and insert it into the differential equations of the rigid water hammer, and yield an nonlinear planar quadratic systems. There is a stable extreme value (a limit cycle) when the nonlinear system is instability at the equilibrium point (runaway point). By changing the slope of braking zone, when the nonlinear system is instability, this paper analyzes the relationship between the maximum water hammer and parameters of the nonlinear system and get a fitting formula. The formula with an uncertainty coefficient is validated by examples and the uncertainty coefficient can be determined by numerical calculation with a risky slope of braking zone.3. According to the effect of the pump characteristic curves in different regions on water hammer, this paper presents an water hammer analysis method based on different regions of S-shaped region. This paper statistics S-shaped characteristic parameters of 27 groups datum of synthetic characteristic curves of pump turbines in China and gets formulas to describe the variations with specific speed and opening degree. The formulas have been worked out through Gauss-Newton method, and the prediction intervals have been figured out. According to the prediction intervals, the ranges of S-shaped characteristic parameters are determined. Combined with the fitting formula between braking zone and head maximum, further analysis of the influence of runaway point coordinates'changes on head extreme values is adopted. A common method to estimate the extreme value of the head according to braking zone parameters is proposed.4. Combining with the relationship between the S-shaped parameters and the extreme value of the head, this paper proposes a surge chamber setting criterion based on regulation guarantee which takes account of the S-shaped characteristic. It can amend the calculation error caused by the estimate of the time when discharge's change slowly during load rejection and is validated by examples. 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 validated 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. For the high and medium-head hydropower station, the conditions determining whether a surge chamber is regulation guarantee, while low-head station is governing qualities.