Research On The Stability Control Of Fractional-Order Hydro-Turbine Governing System

With the development of large capacity hydropower units and generators,and the construction of small hydropower stations,the demand for safe and stable operation of hydropower stations has been improved,which makes the requirements for the perfor?mance of hydro-turbine governing system(HTGS)more and more high.HTGS which is composed of the electric generator,penstock system,hydro-turbine and hydraulic servo system and so on is a nonlinear and non-minimum phase system.The traditional PID control strategy is a linear control strategy,which is difficult to meet the require-ments of stable operation of the highly complex nonlinear turbine-governing system.Therefore,it is significant to study the advanced nonlinear control method to control the safe and stable operation of HTGS.Moreover,because of the strong memory and historical dependence of HTGS,the fractional calculus is more suitable for describing its dynamic characteristics.Therefore,this paper mainly studies the dynamic behaviors and stability control of fractional-order hydro-turbine governing system(FOHTGS).The main research of this paper is as follows.(1)Based on the fractional calculus theory,the mathematical model of the FOH-TGS is established.The dynamic behaviors of the FOHTGS is analyzed under the con-dition without controller and PID control with different initial conditions.The FOH-TGS has been unable to operate steady in two cases without controller and PID control when the initial conditions are far from the equilibrium point.It reveals that the non-linear characteristics of the FOHTGS and the PID control as a linear control strategy which cannot be applied in the nonlinear FOHTGS when the initial conditions are far from the equilibrium point.Therefore,it is significant to research and apply the new nonlinear control methods.(2)Based on the sliding mode control theory and Lyapunov stability theory,the finite-time control method is proposed.The hydropower station will be able to restore stable operation as long as the HTGS can suppress the disturbances in a certain period of time.Therefore,the finite-time control method is proposed,which can make the FOHTGS reach the stable state in finite-time under different random disturbances and different initial conditions.Furthermore,the convergence time is given.Finally,simu-lation results confirm the correctness of the theoretical derivation and the robustness,feasibility and superiority of the controller(3)Based on sliding mode control theory,Lyapunov theory and fixed time control theory is proposed.The convergence time of the HTGS is related to the initial condi?tions by applying finite-time control.The convergence time cannot be obtained ahead of time when the initial condition is unknown.Therefore,in order to obtain the con-vergence time of the FOHTGS in advance,a fixed-time control method is proposed,which can control the stable operation of the nonlinear FOHTGS under different ran-dom disturbances and different initial conditions.Moreover,the bounded convergence time of the FOHTGS is calculated independent of the initial condition.Finally,simu-lation results confirm the correctness of the theoretical derivation and the robustness,feasibility and superiority of the controller.In conclusion,the finite-time control method and fixed-time control method which can effectively control the stability of the nonlinear FOHTGS under random disturb-ances are proposed.It is obvious that the convergence time is shorter,the amplitude is smaller,and the chattering phenomenon is significantly weakened.