Wencheng Guo

Runaway Instability of Pump-Turbines in S-Shaped Regions Considering Water Compressibility

Pump-turbine characteristics greatly affect the operational stability of pumped-storage plants. In particular, the S-shaped region of the characteristic curves leads to severe instability during runaway conditions with servomotor failure. Thus, this paper aims to investigate the runaway stability criterion by considering all of the important effects in the hydromechanical system. The criterion also helps to judge the S-characteristics of pump-turbines and can provide a guide for plant design and turbine optimization. First, the pump-turbine characteristic curves are locally linearized to obtain formulae for the relative changes of discharge and torque, which depend on the relative changes of rotational speed and water head. Control theory is then applied to analyze the high-order system, by importing the transfer function of the conduits in the elastic mode. Two different kinds of oscillation are found, associated with water inertia and elasticity, based on the established theoretical mathematical model. New stability criteria for the inertia wave in both rigid and elastic modes are developed and compared. The comparison reveals the effect of the water elasticity on runaway instability, which has often been neglected in the previous work. Other effects, such as friction loss and the timescales of water flow and machinery, are also discussed. Furthermore, the elastic wave, which often has a higher frequency than the inertia wave, is also studied. The stability criterion is deduced with analyses of its effects. Based on the stability criteria for the inertia wave and elastic wave, the unstable regions for two waves of the S-shaped curves are plotted. The results are applied to explain the development from inertia wave to elastic wave during transient behavior at runaway conditions. Model tests of runaway conditions were conducted on a model pumped storage station and the experimental data show good agreement with the theoretical analyses regarding the instability of the inertia wave. Further analyses and validations are made based on transient simulations. The simulation software topsys, which uses the method of characteristics (MOC) and a unit boundary represented by a spatial pump-turbine characteristic surface, was applied to analyze the elastic wave. This also supports the conclusions of the theoretical research.

Time response of the frequency of hydroelectric generator unit with surge tank under isolated operation based on turbine regulating modes

Abstract Aiming at studying the regulation quality of isolated turbine regulating systems under load disturbance and different regulation modes, the complete mathematical model of a turbine regulating system under three regulation modes is established. Then, based on dominant poles and null points, the method of order reduction for a high-order system of time response of the frequency is proposed. By this method, the complete high-order systems are solved and the regulation quality for time response of the frequency is studied. The results indicate that (1) the tail wave, which is the main body of time response of the frequency and the principal factor that determines the regulation quality, is mainly determined by the dominant poles; (2) for the three regulation modes, by deleting the high-order terms, the three equivalent overall transfer functions are fourth order, third order, and third order, respectively, and can be solved; (3) the analytical fluctuation equations of time response of the frequency solved from low-order equivalent overall transfer functions accurately simulate the fluctuation characteristics of time response; and (4) based on damped vibrations decomposed from analytical fluctuation equations, the regulation qualities of three regulation modes are analyzed.

Effect Mechanism of Penstock on Stability and Regulation Quality of Turbine Regulating System

This paper studies the effect mechanism of water inertia and head loss of penstock on stability and regulation quality of turbine regulating system with surge tank or not and proposes the construction method of equivalent model of regulating system. Firstly, the complete linear mathematical model of regulating system is established. Then, the free oscillation equation and time response of the frequency that describe stability and regulation quality, respectively, are obtained. Finally, the effects of penstock are analysed by using stability region and response curves. The results indicate that the stability and regulation quality of system without surge tank are determined by time response of frequency which only depends on water hammer wave in penstock, while, for system with surge tank, the time response of frequency depending on water hammer wave in penstock and water-level fluctuation in surge tank jointly determines the stability and regulation quality. Water inertia of penstock mainly affects the stability and time response of frequency of system without surge tank as well as the stability and head wave of time response of frequency with surge tank. Head loss of penstock mainly affects the stability and tail wave of time response of frequency with surge tank.

Frequency Stability of Isolated Hydropower Plant with Surge Tank Under Different Turbine Control Modes

Abstract Currently, the Thoma criterion is often violated to diminish the cross-section of the surge tank; therefore, the surge fluctuation is aggravated and the frequency stability becomes more deteriorative. The focus of this article is on stabilizing the low-frequency oscillation of an isolated hydropower plant caused by surge fluctuation. From a new perspective of hydropower plant operation mode, frequency stability under power control is investigated and compared with frequency control by adopting the Hurwitz criterion and numerical simulation. In a theoretical derivation, the governor equations of frequency control and power control are introduced to the mathematical model. For numerical simulation, a governor model with a control mode switch-over function is built. The frequency oscillations under frequency control, power control, and control mode switch-over are simulated and investigated, respectively, with different governor parameters and operation cases. The result shows that the power control has a better performance on frequency stability at the expense of rapidity compared with the frequency control. Other recommendations regarding worst operation cases and choice of control modes are also developed.

Formulae for the intersecting curves of pump-turbine characteristic curves with coordinate planes in three-dimensional parameter space

Pump-turbine characteristics are important boundary conditions for simulating hydraulic transients in pumped-storage hydroelectric power stations. However, the changing laws of the characteristics of different pump turbines are not well understood. Here, two-dimensional characteristic curves are converted into three-dimensional forms, and the intersecting curves, defined by the intersection of the characteristic curves with the coordinate planes in a parameter space defined by the unit rotational speed, unit discharge, and unit torque, are determined to clarify these changing laws. Basic pump-turbine theory of the flow characteristics and idealizations of the “hump” and “S” regions of the characteristic curves are considered to determine formulae for each intersecting curve. Each formula consists of two unknown coefficients that are obtained from fits to measured data. The dependence of the coefficients on specific speed values is clarified to obtain general formulae governed by specific speed. The nonlinear changing laws of the characteristic curves and their relationship with the flow and operating conditions are analyzed and clarified. This work provides a theoretical basis for predicting the characteristic curves of any pump turbine without model-measured characteristics.

Research on Critical Stable Sectional Area of Surge Chamber Considering the Fluid Inertia in the Penstock and Characteristics of Governor

According to the fact that the existing critical stable sectional area of surge chamber does not consider the effect of the fluid inertia in the penstock and characteristics of governor, mathematical model of hydraulic and governor system considering those two factors is established. Critical stable sectional area criterion is equivalent to that the first derivative term of homogeneous differential equation is greater than zero, and the analytical formula of critical stable sectional area is deduced. The analytical formula is composed of diversion tunnel term, penstock term and governor term, diversion tunnel term is Thoma’s formula, penstock term is positive and governor term is negative. Finally, the mathematics essence of the governor parameters’ effect on critical stable sectional area is revealed: the effect of temporary droop bt and damping device time constant Td exist critical values, but the critical value is only meaningful in mathematics and would not appear in actual engineering. Critical stable sectional area is a monotone decreasing function of bt and Td.Copyright

Bifurcation analysis of hydro-turbine regulating system with saturation nonlinearity for hydropower station with upstream and downstream surge chambers

A nonlinear mathematical model of hydraulic turbine regulating system is applied to describe hydropower stations with upstream and downstream surge chambers. This model features saturation nonlinearity including pipeline system and turbine regulating system used in stability analysis. First, the existence conditions and direction of Hopf bifurcation are obtained. Second, based on the algebraic criteria for the occurrence of Hopf bifurcation, the stability domain is drawn in a coordinate system, where the proportional gain Kp is the abscissa and the integral gain Ki is the ordinate. Third, the nonlinear dynamic behaviour of a regulating system with different state parameters are analyzed, and the variations of the system stability around the two sides of the bifurcation point are numerically calculated. Based on this work we conclude that the Hopf bifurcation of system is supercritical. The bifurcation parameters that are far from the bifurcation point would be advantageous to the rapid system regulation needed to sustain equilibrium. Furthermore, it is established that using a PID controller is more conducive to stability than a PI controller. The unit stability regulation gets worse by taking into account the saturation nonlinearity.