Transient Process Control Of Turbine Governing System For Hydropower Station With Pressure Reduction Facilities

For the turbine governing system of hydropower station with pressure reduction facilities,including surge tank and sloping ceiling tailrace tunnel,there exist different coupling effects of disturbance,fluctuation and control with different properties and types during transient processes.The different coupling effects lead to extremely complicated transient characteristics and control for the turbine governing system.From the perspective of scientific research and engineering application guidance,the following three key problems should be concerned:coupled dynamic modeling of turbine governing system with pressure reduction facilities,transient characteristics of turbine governing system under the effect of pressure reduction facilities,and linear/nonlinear control of turbine governing system under the effect of pressure reduction facilities.Based on the above three key problems,four topics are studied:transient characteristics and control of the turbine governing system with surge tank based on reduced-order model,transient characteristics and control of the turbine governing system with surge tank based on sine wave,nonlinear control of turbine governing system with sloping ceiling tailrace tunnel,and transient characteristics and control of the turbine governing system under the combined effect of surge tank and sloping ceiling tailrace tunnel.The innovative achievements of the dissertation are as follows:(1)For the turbine governing system with surge tank,the order reduction for the high-order mathematical model is carried out.Two kinds of order reduction methods which have strict theoretical basis and generality are proposed.The low-order equivalent models for the turbine governing system with surge tank are constructed.Based on the low-order equivalent models,the transient characteristics of the turbine governing system are analyzed and the basis for the value of influence factors is put forward.The results indicate that the complete fifth order system always has a pair of dominant conjugate complex poles and three non-dominant poles.The primary fourth order equivalent system,which is obtained by primary order reduction,keeps the dominant poles almost unchanged,therefore it can represent and replace the complete fifth order system and it is obviously superior to other fourth order systems.The primary fourth order equivalent system is superimposed by two second-order subsystems,one of them is corresponding to two non-dominant real poles(i.e.head wave)and the other one is corresponding to a pair of dominant conjugate complex poles(i.e.tail wave),respectively.In the fluctuation process of frequency response,head wave decays very fast and works mainly in the beginning period while tail wave decays very slowly,fluctuates periodically and works throughout the period.The secondary order reduction of complete fifth order system can be conducted by using the second order system of tail wave,which is the main body of frequency response,to represent the fluctuation characteristics.The most important dynamic performance index that evaluates the regulation quality,i.e.settling time,is derived from the fluctuation equation of tail wave.The stability and regulation quality of system without surge tank is determined by time response of the frequency which only depends on water hammer wave in penstock,while for system with surge tank,the time response of the 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 effects the stability and time response of the frequency of system without surge tank as well as the stability and head wave of time response of the frequency with surge tank.Head loss of penstock mainly effects the stability and tail wave of time response of the frequency with surge tank.Based on the effect mechanism,the stability and regulation quality of the system can be improved and the low-order equivalent models for the system can be constructed.(2)For the turbine governing system with surge tank,a new idea for the study on the operation and control of hydropower station is proposed.Specifically,a given sine wave of the water level oscillation in surge tank is adopted to present the movement characteristics of unsteady flow in headrace tunnel and surge tank.The hydraulic parameters and dynamic characteristics of the headrace tunnel and surge tank are contained in the characteristic parameters of the sine wave of the water level oscillation in surge tank.The characteristic parameters of the sine wave are determined by a series of strict mathematical methods.By using the assumption of the sine wave of the water level oscillation in surge tank and its mathematical description,the dynamic response and transient control for primary frequency regulation of turbine governing system with surge tank are studied.The results indicate that for the primary frequency regulation under opening control mode and power control mode,the turbine governing system is absolutely stable and conditionally stable,respectively.The stable domain and the dynamic response process of power output of the system under power control mode have good robust performances.The critical stable sectional area of surge tank for primary frequency regulation makes the system reach the critical stable state,and is an important basis for the design of surge tank.The governor parameters and the critical stable sectional area of surge tank jointly determine the distributions of stability states of the system.The equation for the sine wave of the water level oscillation in surge tank can be used to replace the dynamic equation of headrace tunnel and continuity equation of surge tank.Under the assumption of the sine wave of the water level oscillation in surge tank,the obtained analytical solution for the dynamic response of unit power output under the step frequency disturbance is reasonable.The dynamic response of unit power output is superposed by four independent subwaves,i.e.constant term,governor term,penstock term and surge tank term.Based on the primary frequency regulation domain,the regulation quality for the turbine governing system with surge tank can be evaluated quantitatively.(3)For the turbine governing system with sloping ceiling tailrace tunnel,the mathematical model is nonlinear because of the existence of a nonlinear term for the dynamic equation of sloping ceiling tailrace tunnel.To improve the regulation quality of the turbine governing system with sloping ceiling tailrace tunnel,two kinds of nonlinear control strategies,i.e.nonlinear state feedback control strategy with polynomial functions and nonlinear disturbance decoupling control strategy,are designed.The functional mechanism and regulation performance of the proposed control strategies are analyzed.Based on the dynamic performance of turbine governing system and the index system of unit operation,the hydraulic design principle for sloping ceiling tailrace tunnel and the setting basis for governor parameters are proposed.The results indicate that the proposed nonlinear state feedback control strategy can make the frequency of turbine unit return to the initial value(i.e.rated frequency),and the regulation quality and the response speed are obviously better than those under PID strategy.The effect of the linear term of nonlinear state feedback control strategy is to modify the system's linear stability,to eliminate or delay an existing bifurcation.The effect of the nonlinear term of nonlinear state feedback control strategy can change the stability of bifurcation solutions,for example,converting a subcritical Hopf bifurcation to supercritical.The rigorous and complete construction method of the nominal output function is determined by the control objective of the original nonlinear system and the necessary and sufficient condition for the decoupling of the output with respect to the disturbance.Under the nonlinear disturbance decoupling control strategy,the turbine governing system is rapid and sensitive.The regulation quality and the response speed under the nonlinear disturbance decoupling control strategy are obviously better than those under the Proportional-Integral-Derivative strategy.The nonlinear disturbance decoupling control strategy has a favorable applicability on the sloping ceiling tailrace tunnel.The robustness of the turbine governing system using the nonlinear disturbance decoupling control strategy is excellent,and the system has a strong anti-interference ability.(4)Using the Hopf bifurcation theory,the transient characteristics and control of the turbine governing system with upstream/downstream surge tank and sloping ceiling tailrace tunnel are studied.From the perspective of combined effect and wave superposition,the effect mechanism of governor,the combined effect mechanism of upstream/downstream surge tank and sloping ceiling tailrace tunnel,and the wave superposition mechanism of mass wave,water hammer wave and gravity wave are revealed.The combined effects of upstream/downstream surge tank and sloping ceiling tailrace tunnel on the transient characteristics of the turbine governing system are investigated,and the methods to improve the system stability and regulation quality are proposed.The results indicate that the phase space trajectories of characteristic variables stabilize at the equilibrium points and stable limit cycles when the system state parameter point locates in the stable domain and unstable domain,respectively.The dynamic response processes of the characteristic variables of the turbine governing system under load disturbance show an obvious feature of wave superposition.To make the dynamic response process of the turbine governing system with upstream surge tank and sloping ceiling tailrace tunnel more stable and attenuate faster,the governor parameters should locate in the stable domain and keep away from the bifurcation point as much as possible.Under the combined effect of upstream surge tank and sloping ceiling tailrace tunnel,the dynamic performance of the turbine governing system shows an obvious difference on the two sides of the critical sectional area of surge chamber.There are two bifurcation lines when the sectional area is less than the Thoma sectional area,i.e.Bifurcation line 1 and Bifurcation line 2,which represent the stability characteristics of the flow oscillation of "penstock-sloping ceiling tailrace tunnel" and the water-level fluctuation in upstream surge chamber,respectively.The stable domain of the system is determined by Bifurcation line 2.The effect of upstream surge chamber mainly depends on its sectional area,while the effect of the sloping ceiling tailrace tunnel mainly depends on the sectional area of surge chamber,type of load disturbance and ceiling slope angle.For the turbine governing system with downstream surge tank and sloping ceiling tailrace tunnel,two types of bifurcation lines reflect the critical stability characteristics of the two subsystems and constitute the boundaries of the stable domain.The sloping ceiling tailrace tunnel cannot make an obvious change of the stability performances of the subsystem of penstock-turbine unit,but it has significant effect on the stability performances of the subsystem of downstream surge tank-sloping ceiling tailrace tunnel.