Setting Condition And Critical Stable Section Area Of Surge Tank Of Hydropower Station Considering Complex Hydraulic Characteristics Of Flow Tunnel

With the development of hydropower industry,the layout and operation requirements of hydropower stations are more and more complicated.The layout of complex diversion power generation system and the special type of hydropower station with surge tank are gradually rising and introduced.Among them,the super long diversion tunnel hydropower station and hydropower station with sloping ceiling tailrace tunnel have become important types of hydropower energy development.No matter what type of hydropower station,as for the joint transition process of the water and electromechanical system of the diversion power generation system,it is necessary to set up a surge tank whether from the requirements of regulation guarantee,or from the requirements of stability and regulation quality to meet the requirements of safe and stable operation and power supply quality of the power station.The two most important aspects of the study of the surge tank are the setting conditions of the surge tank and the critical stable section area(CSSA)of the surge tank.On the one hand,about previous studies on the setting conditions and critical stable section area of surge tank,the basic equation and mathematical model are mainly linear,which simplifies the model,so it cannot fully reflect the characteristics and problems of the hydropower station with surge tank.On the other hand,the formulas of critical stable section area of surge tank are mostly based on Thomas formula,which contains many assumptions.The predecessors put forward the improved formulas on the basis of it,but all of them are almost based on the conventional pressurized tailrace tunnel hydropower station.Today's complex types of hydropower stations,such as super long diversion tunnel hydropower station or hydropower station with sloping ceiling tailrace tunnel(SCTT),contain the strong nonlinear characteristics of the hydro-turbine governing system(HTGS)and the complex water electromechanical coupling characteristics.In particular,the joint action of the hydropower station with SCTT and the downstream surge tank,in the tail-water system,the pressurized flow and free surface flow of SCTT and the flow oscillation of the downstream surge tank are involved at the same time,and the stability of the hydropower station system becomes more complicated.Therefore,it is of great significance to study the setting condition of surge tank,the critical sectional area of surge tank based on stability of HTGS considering complex hydraulic characteristics of flow tunnel,the setting condition and critical stable sectional area of downstream surge tank of hydropower station with SCTT.In this paper,based on the stability of HTGS,starting from the basic equations of hydropower station,established on the analysis of summarizing predecessors'work,the setting condition of surge tank based on stability of HTGS considering nonlinear penstock head loss,the critical sectional area of surge tank considering nonlinearity of head loss of diversion tunnel and steady output of turbine,the setting condition and CSSA of downstream surge tank of hydropower station with SCTT are carried on the thorough research.The main contents of the paper include the following three aspects:1 The study on the setting condition of surge tank based on stability of hydro-turbine governing system considering nonlinear penstock head lossFirstly,the mathematical model of the HTGS considering nonlinear penstock head loss is established.Then the setting condition of surge tank is derived by using Hopf bifurcation theory.The characteristics effects of setting condition of surge tank are analyzed.The effect mechanism of nonlinear penstock head loss on setting condition of surge tank is revealed by the comparative analysis of different setting conditions of surge tank based on stability.It indicates that there are three inequality criterions for the setting condition of surge tank,and the third one is the controlling inequality criterion with the highest requirement and acts as a dominant role.The value of flow inertia time constant of penstock T_wt0 corresponding to the endpoint of inequality interval is the allowable value of T_wt0 that the surge tank is not necessary to set,i.e.[T_wt0].When the T_wt0 of hydropower station is less than[T_wt0],it is not necessary to set surge tank;otherwise,it is necessary to set surge tank.2 The study on the critical sectional area of surge tank considering nonlinearity of head loss of diversion tunnel and steady output of turbineFirstly,four mathematical models for the derivation of critical section area(CSA)of surge tank are constructed.Then the stability of hydropower station with surge tank is analyzed by Hopf bifurcation.Then the formulas for the CSA of surge tank are derived.Finally,the verification and comparison of different CSAs are conducted.The results indicate that,under load increase operation condition,both the nonlinearity of head loss of diversion tunnel and nonlinearity of steady output of turbine can reduce the value of CSA of surge tank and are favorable for the stability of hydropower station.Under load decrease operation condition,the rules are opposite.Under both load increase and load decrease operation conditions,the effect of the nonlinearity of head loss of diversion tunnel on CSA of surge tank is much more significant than that of the nonlinearity of steady output of turbine.The formula for CSA of surge tank considering both the nonlinearity of head loss of diversion tunnel and nonlinearity of steady output of turbine can be expressed as an amplification coefficient times of the Thoma formula.That formula has a higher precision than Thoma formula.3 The study on the setting condition of downstream surge tank of hydropower station with sloping ceiling tailrace tunnel based on stabilityFirstly,the mathematical model of hydro-turbine governing system(HTGS)with SCTT is established and a third order nonlinear state equation is obtained.Then,the stability of HTGS with SCTT is analyzed based on Lyapunov's first method.Setting condition of downstream surge tank(SCDST)based on stability of HTGS with SCTT is derived based on the stability criterion.Finally,the characteristics and influence of SCDST based on stability of HTGS with SCTT are analyzed.The difference and relation between SCDST based on stability of HTGS with SCTT and SCDST based on stability of HTGS with pressurized tailrace tunnel(PTT)are revealed by using comparative analysis.The results indicate that the complete SCDST based on stability of HTGS with SCTT is composed of several inequalities.One of the inequalities is the dominant inequality and determines the stable domain of HTGS and the allowable value of flow inertia.The flow inertia of penstock corresponding to the endpoint of inequality interval is the allowable value of flow inertia that the downstream surge tank is not necessary to set.The section shape of SCTT almost has no effect on the SCDST.From the view of SCDST for hydropower station with SCTT,it is reasonable that the slope of SCTT takes small value.The allowable value of flow inertia of penstock for hydropower station with SCTT is greater than that for hydropower station with PTT.4 The study on the critical stable sectional area of downstream surge tank of hydropower station with sloping ceiling tailrace tunnelFirstly,two types of nonlinear mathematical model of hydropower plant with SCTT during transient process,i.e.model considering the assumption of steady power output of hydro-turbine and complete model,are established.Then,the criterion of operation stability of hydropower plant is obtained based on nonlinear stability theory.The algebraic stability criterion corresponding to the CSSA of downstream surge tank(DST)is determined.Formulae for the CSSAs of DST under two types of mathematical model are derived.Finally,the correctness of the formulae for CSSAs is verified.The similarities,differences and relationships of different CSSAs are clarified.The effect mechanisms of the assumption of steady power output of hydro-turbine and the SCTT on the CSSA of DST are revealed.The recommended use conditions of different CSSAs are explained.The results indicate that,under the assumption of steady power output of hydro-turbine,the formula for the CSSA of DST of hydropower plant with SCTT is analytical and has a simple expression.Under the complete model,the formula for the CSSA of DST of hydropower plant with SCTT is not analytical and has a complicated expression.The former formula is suggested to be given the priority of use because of good precision and concise expression.SCTT can improve the stability of hydropower plant and decrease the CSSA of DST.