VFD use to maintain constant flux

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Using a Variable Frequency Drive (VFD) allows for maintaining constant flux in an induction motor by reducing voltage in proportion to frequency. While torque is nearly constant across various speeds, it is not perfectly so, and each motor has a specific V/Hz relationship curve that details this behavior. As speed decreases, the mechanical output power also decreases since it is a product of output torque and angular velocity, which diminishes with frequency reduction. Understanding these dynamics is essential for optimizing motor performance with VFDs. Proper reference materials can provide further insights into these relationships.
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When using a VFD, am I right in thinking that for an induction motor, torque available at all speeds is constant as the voltage is reduced with frequency to maintain constant flux? Also, am I right in thinking that the mechanical output power of the motor will be less when speed is reduced, as it is the product of output torque and angular vel, which of course decreases with freq?
 
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The torque is not constant over all of the speeds but it is close - for each motor, if you dig enough there is a curve detailing the V/Hz relationship - a good reference is here : http://www.yaskawa.com/site/dmdrive.nsf/(DocID)/MNEN-5JFQNV/$File/AR.MOTOR.01.pdf
 
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