Motor output doubles when the power supply voltage is doubled for either series or parallel-wired motors. Notice that a parallel-connected motor delivers performance identical to a series-connected motor running at twice the power supply voltage.
The drive is a current source in the constant torque region and adds no additional phase lag. In the constant power region however, the drive is a voltage source so it introduces an additional 90 degree phase lag. The total phase lag now is 180 degrees, which is a setup for a sustained and building motor oscillation. This oscillation is commonly called mid-band instability or mid-band resonance.
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