Stability Analysis Of Steady State And Typical Transient Process Of The Pump-turbine Governing System

The pumped storage power station(PSPS)utilizes relatively cheap electricity from the grid during off-peak hours to move water from the lower reservoir to the upper one to store energy.During periods of high electricity demand(peak-hours),water is released from the upper reservoir to generate power at higher price.In addition,the PSPS has the function of FM phase modulation and emergency reserve,and can also improve the utilization efficiency of wind power,thermal power and nuclear power,which makes it play an increasingly important role in power system.The pump-turbine governing system(PTGS),which plays a key role in maintaining the safety,stability and economical operation of the PSPS,needs to be paid to special attentions.Previous studies of the pumped storage unit mainly focused on the pump-turbine.And these studies rarely brought the pump-turbine into the framework of the whole governing system and couldn't deeply reveal its dynamic evolution mechanism.In this paper,from the perspective of system engineering,we established differential mathematical models and conduct stability analysis for steady state and two kinds of typical transient process of the PTGS.Then,numerical simulation was presented by using bifurcation diagrams,time waveforms and phase orbits,which verified the correctness of the theoretical analysis results.The main contents and conclusions in this paper are as follows:(1)First of all,considering the elastic water-hammer model of the penstock with hydraulic friction,a nonlinear model of the PTGS was proposed.Then,utilizing the internal characteristics formulas,we obtained six analytical expressions of the transfer coefficients at pump mode.Based on a real case,we obtained the stable domains of the PID parameters by using the stability theorem,and verified the correctness of the theoretical analysis results from numerical experiments.Moreover,the effect of hydraulic friction on the stable domains was discussed and the result showed that hydraulic friction has an advantage in maintaining the stability of the system.Meanwhile,the change laws of stable domains of the PTGS as several parameters change were presented.Finally,the comparative analysis on stability of the PTGS at turbine mode and pump mode was made.(2)Combining the operation curve of an actual PSPS during transient process of outage of pump mode,we calculated values of the corresponding transfer coefficients from several point-in-time and obtained time-varying expressions of the transfer coefficients.Further,dynamic mathematical model of the PTGS during this transient process was acquired and the stability of the system at different point-in-time was analyzed by numerical simulation.It turned out that the closing speed of guide vane had a major impact on the stability of the governing system.Next,by observing and comparing three-dimensional and two-dimensional diagrams of stable domains with the change of time,we easily got that the stable domain decreased first and then gradually increased as time goes on.And the moment for the minimum range of stable domain was obtained,which can be called the worst time.(3)Aiming at the PTGS with the upstream surge,we established the differential mathematical model for the transient process of load rejection with refusing action of guide vane and deduced the stability criterion of runaway point.The results showed that the slope of the characteristic curve at the runaway point is an important factor to determine the stability of runaway point.Finally,based on the characteristic curve,we respectively obtained dynamic models of the PTGS at turbine mode,turbine braking mode and reverse pump mode and then explored the stability of S-shaped region of the pump-turbine by bifurcation diagrams.The results indicated that stable operation area of the system mainly concentrated on turbine mode and braking mode,and unstable area mainly concentrated on reverse pump mode.