ANALYSIS OF VARIABLE-FREQUENCY CURRENTS SUPERIMPOSED ON DC CURRENTS IN ASYNCHRONOUS HVDC LINKS IN STRESSING TURBINE-GENERATOR-EXCITER SHAFTS

The paper makes an indepth analysis of the excitation of shaft torsion al vibrations in steam turbine-generator-exciter shafts by variable-fr equency ripple currents superimposed on DC currents in asynchronous Li nks using finite element and reduced models of the machine shafts. Fre quencies at which sympathetic shaft torsional vibrations would be exci ted by modulation product harmonics in 50Hz/50Hz and 50Hz/60Hz asynchr onous Links as a function of deviation in system frequency are illustr ated. It is shown that amplitude of shaft torque due to steady resonan t torque excitation is a function of initial rate of increase of vibra tions at adjacent cells, the time constant for decay of the vibration, and stiffness between adjacent shaft cells. Time constants for decay of shaft torsional vibrations due to electrical and steam viscous damp ing at full-load and no-load for finite element and reduced shaft mode ls are then evaluated and compared. Modal torque correlation factors f or finite element and reduced shaft models which relate modal torque a t sections of shaft are also evaluated and compared. Amplitudes of mod al torques for finite element and reduced shaft models for given stead y state resonant torque excitations are illustrated The effect of gene rator load on shaft torque due to resonant excitation is also illustra ted. Typical shaft torques for generators connected directly to HVDC L ink rectifiers due to resonant excitation for the generator at full-lo ad and no-load are also compared. The paper then shows that shaft torq ues in multi-machine networks may be estimated by proportioning HVDC L ink disturbance current to each machine at risk using system network d ata, generator data, fault analysis data, and load flow data, consider ing frequency dependence of the system parameters. This scaling factor is calculated for different scenarios of system operation and load. E quivalent circuits for the synchronous generator are employed appropri ately to correlate HVDC Link disturbance current impressed on the gene rator stator with steady-state torque excitation from which magnitude of turbine-generator-exciter shaft torque is found. It is concluded th at onerous shaft torsional vibrations may be set up in large steam gen erator shafts by DC Link ripple currents and that torques evaluated us ing finite element and reduced shaft models can differ significantly. Finite element shaft models, therefore, should be used to evaluate mod al torque correlation factors, initial rate of increase of modal vibra tions due to application of steady resonant torque excitation, and tim e constants for decay of vibrations from which modal torque at shaft s ections due to steady resonant excitation is found. Detailed (2d,3q) r otor equivalent circuits should be used to evaluate steady-state torqu e excitation due to injected harmonic currents, and to proportion inje cted harmonic current to each machine of a multi-machine network which is at risk. Machines rated at 500 MW, 660 MW, 1000 MW and 1300 MW are considered in the analyses that are made.