Electromagnetic Torque From Event Report Data A Measure of Machine Performance Derrick Haas and Dale Finney Schweitzer Engineering Laboratories, Inc. 7 SEL Overview Electromagnetic torque calculation Modeling and validation Sources of error Real-world examples
Machine Equations p v R i qs S qs ds qs B B v p R i ds S ds qs ds B B i i e ds qs qs ds Integration to Calculate Flux From machine equations, integrate voltages v R i ds b ds s ds v R i qs b qs s qs Numerical integration methods, such as trapezoidal rule, are required i i h f i f i f i
Per Unit Dynamic Model + N a com Angle Breaker Control A B C System Fault A B C Bus com A B C Breaker a b c Parallel Load Feeder A B C.6, V, hp C B A Tm m Validation Comparison of Torque From Model and Calculation Per Unit Speed Torque (model) Torque (calculated)....
Stator Flux Phi qs (pu) Error Sources Incorrect Initialization... Model Calculated....... Expect no dc flux at steady state Begin integration whenever event report starts (arbitrary) Remove dc flux v R i DC ds b ds s qs d Torque Error Incorrect Initialization Model Calculated....... Torque oscillations occur during prefault or preswitching Results in overestimate of peak torque High oscillations occur after fault or switching event
Torque (pu) Torque (pu) Model Calculated Using 6 SPC Calculated Using 8 SPC Error Source Sampling Rate Model Calculated Using 6 SPC Calculated Using 8 SPC........8.9.. Error is.6% at 6 SPC and 8.% at 8 SPC Error Source Motor Stator Resistance Model Calculated Using R S = R Amb Calculated Using R S =....... R S unknown or varied R R S Amb No initial error T 9 % First peak.8% error Oscillations following switching event
Voltage (pu) Torque (pu) Torque (pu) Current (pu) Error Source CT Saturation Model Calculated Using a C CT Calculated Using a C CT Primary C Secondary C Secondary........... Error small for first peak, then increases as CT saturates......9.8.7.6. 6 7 Current (pu) Error Source Core Saturation Small impact.6% error for peak torque 6 Model Calculated....... 6
Simulations 8 test cases (8 terminal faults, 8 reclose events) Varied load, fault type, point-on-wave, and fault resistance for terminal faults Varied load and reclose angle for reclose events Largest error sources stator resistance and CT saturation Summary of Errors Stator Resistance Error (%) First Peak Torque Error (%) Terminal Faults Out-of-Phase Reclosing Avg Max Avg Max.76...8.86. 6.77.7 7
Example Start, hp Motor Relay M, hp 6 V FLA,79 rpm Torque With Errors 6 7 8 9 Oscillations in torque after motor is up to speed 8
Flux (pu) DC in Voltages. 6 7 8 9 A-Phase Linear decay in flux is indicator of dc in voltage Torque After DC Removal 6 7 8 9 Torque Torque (dc removed) 9
Example Motor Bus Transfer in Lab DC Supply hp V 7 FLA / 8 V Three-Phase AC Patch Panel to Supply Relay M Motor Coupled to DC Generator G Load Bank Torque for Transfer 8 6......6.7 Good initialization with some oscillations
Torque (pu) Torque With Stator Resistance Varied 7...8.8.9.9..... R S = R S =. R S =. R S =. Example Real-World Motor Bus Transfer 6.... Increasing oscillations after transfer
Flux (pu) DC in Voltages Once Again..... Phase AB Linear decay in flux is indicator of dc in voltage Torque After DC Removal....
Torque (pu) Torque vs. Stator Resistance 6.77.8.8.8 R S = R S =. R S =. R S =. Large variations in stator resistance impact torque calculation Refining estimate for RS helps Torque vs. Stator Resistance.77.8.8.8 R S =. R S =. R S =.6.87 Large variations in stator resistance impact torque calculation Refining estimate for RS helps R S =.7
Conclusions Torque calculation is based on validated measured electrical quantities Largest error sources are incorrect stator resistance and CT saturation Questions