Not only you but the three professors from Indian Institute of Technology,Chennai (see post 174) had it wrong presumably:
Those three are wrong, I'm wrong, your posts #151 and #193 are wrong. But you are right? Is that what you mean because that's how it comes across, intentionally or otherwise.
You all assumed that motor operation is possible only in the conventional stable region of the motor characteristic.This is because the torque-speed of constant torque load ....
Neither my #170 nor your #193 related to constant torque loads. Your post #151also mentions a pump and the context suggests that it is probably centrifugal, not constant torque.
Figure 27 from your post #27 has a centrifugal load curve. Actually, as far as I can recall, NO constant torque application has been presented here.
is such that in the conventional unstable region of motor characteristic,it is either below or above the motor characteristic, as the voltage is reduced so that the motor accelerates to the operating point on the stable region of the motor characteristic or it stops altogether respectively.But in the case of fan type loads,the torque-speed characteristic of the load may be such that (i.e it satisfies the stability condition:its increase (decrease) in torque with speed is greater (less ) than that by motor) the operating point lies on the conventional unstable region of the motor characteristic i.e the conventional unstable region is actually stable operating region in this case.
Think you have this vice versa.
An operating point will be reached where load torque and motor torque are equal. This is normally in the low slip region. If there is increased load, the motor slows down a
little to a point where the motor torque matches the new load torque and all is fine and dandy and stable as it should be - and usually is.
There can also be anomalous situations where motor torque matches load torque on the "wrong" side of the speed torque curve and it just sits there at that speed. Bad things can happen and reduced voltage is not a viable control method to avoid this.
Look back the motor characteristics in my post #170.
First, note that the load is centrifugal, not constant torque.
All values in pu.
Look at the data for 0.6 speed. Typical fan and pump variable speed don't generally require a speed range wider than 0.6 to 1.0.
At 0.6 speed and rated voltage the motor torque is 0.84 and the load torque is about 0.25.
Under these operating conditions, motor current is about 6.24pu.
So, by reducing the motor voltage we could reduce the torque it develops by 0.25/0.84.
With me so far?
Motor torque is approximately proportional to the square of the voltage and current roughly proportional to it.
So, 0.55 pu voltage to provide the torque. And about 3.4pu current.
That is 3.4 times rated current.
Not a viable option.