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The answer:
I am confused isn't peak power is at peak torque i.e. breakdown torque? Which is at just above 0 RPM?
Source:
NCEES
PE Electrical and Computer: Power Practice Exam, 2020
ISBN 978-1-947801-16-5
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\$\begingroup\$ From experience of looking at these curves, when the motor is turning over very slowly, the current will be at its highest. Power factor might be low at that speed honestly I am not sure. Nonetheless, I think the highest real power will occur at 1 RPM. But this is not really based on analysis. \$\endgroup\$– user57037Commented Aug 23, 2021 at 4:50
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2 Answers
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Maximum electrical power is at startup with max current.
But maximum mechanical power being the product of RPM and torque approaches max slip which is greater than rated power at 10 % slip.
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\$\begingroup\$ Can you please elaborate more? I didn't understand "approaches max slip which is greater than rated power at 10 % slip" \$\endgroup\$– OMARCommented Jul 22, 2021 at 7:13
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For an induction motor with a "normal" torque vs speed curve and a constant-torque load, that would be close to the peak of the motor's torque vs. speed curve. The phrase "the load acting upon the motor is at its design value" seems to mean that the load torque vs. speed is constant.
Since "the design slip is 5%" and "the breakdown torque occurs just after 0 RPM," this motor likely has a "high slip" torque vs speed curve with the torque essentially reducing steadily from zero RPM to synchronous RPM. The current also reduces steadily from zero RPM to synchronous RPM.
The mechanical power delivered to the load rises from zero at zero speed, so the power at zero speed is inrush current squared multiplied by (the stator resistance plus the parallel combination of magnetizing resistance and rotor resistance.) As speed increases, the current and the power lost in the resistive elements drops. At the full-load operating point, most of the real electrical power is converted to mechanical power in the load.
While the motor is accelerating, the mechanical power is applied to both accelerate the system inertia and to move the load in opposition to load friction. Any work done by the load can be considered to be friction. The peak power delivered to the load would tend to be at the point where the power applied to accelerating the inertia is equal to the power applied to overcoming friction. It is difficult to estimate the speed at which that point occurs except that it must be between standstill and the steady-state operating speed. With a torque curve that is practically flat at standstill and drops smoothly with speed increase, it seems more likely that the peak power would occur at 500 RPM than at 1 RPM.