# title
Han, Xu (2010-12). Analysis and Simulation of Mechanical Trains Driven by Variable Frequency Drive Systems. Master's Thesis.

# abstract
Induction motors and Variable Frequency Drives (VFDs) are widely used in industry to drive machinery trains. However, some mechanical trains driven by VFD-motor systems have encountered torsional vibration problems. This vibration can induce large stresses on shafts and couplings, and reduce the lifetime of these mechanical parts. Long before the designed lifetime, the mechanical train may encounter failure. This thesis focuses on VFDs with voltage source rectifiers for squirrel-cage induction motors of open-loop Volts/Hertz and closed-loop Field Oriented Control (FOC). First, the torsional vibration problems induced by VFDs are introduced. Then, the mathematical model for a squirrel-cage induction motor is given. Two common control methods used in VFD are discussed - open-loop Volts/Hertz and closed-loop FOC. SimPowerSystems and SimMechanics are used as the modeling software for electrical systems and mechanical systems respectively. Based on the models and software, two interface methods are provided for modeling the coupled system. A simple system is tested to verify the interface methods. The study of open-loop Volts/Hertz control method is performed. The closed-form of electromagnetic torque sideband frequency due to Pulse Width Modulation is given. A torsional resonance case is illustrated. The effects of non-ideal power switches are studied, which shows little in uence on the system response but which uses little energy consumption. A study of a non-ideal DC bus indicates that a DC bus voltage ripple can also induce a big torsional vibration. Next, the study of the closed-loop FOC control method is presented. Simulation for a complete VFD machinery train is performed. With the recti er and DC bus dynamic braking, the system shows a better performance than the ideal-DC bus case. Lastly, a parametric study of the FOC controller is performed. The effects of primary parameters are discussed. The results indicate that some control parameters (i.e. speed ramps, proportional gain in speed PI controller) are also responsible for the mechanical torsional vibration.

# websites[].label
Analysis and Simulation of Mechanical Trains Driven by Variable Frequency Drive Systems