1. Stability of Electric Drives
Dr. K. R. Rajagopal
Associate Professor
Electrical Engineering Department
Indian Institute of Technology, Delhi –
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2. Steady State Stability of an Electric Drive
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive
The drive is said to be in equilibrium if the torque developed by the motor is exactly equal to the load torque.
If the drive comes out of the state of equilibrium due to some disturbance, it comes back to steady state for stable equilibrium but for unstable equilibrium the speed of the drive increases uncontrollably or decreases to zero. When the drive coming out of the state of equilibrium preserves it steady state at different speed (lying in small range), it is said to be in neutral range.

3. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
The stability of the motor load combination is defined as the capacity of the system which enables it to develop forces of such a nature as to restore equilibrium after any small departure therefore.
Equilibrium state of the drive mainly disturbs because of the following two types of disturbances,
Changes from the state of equilibrium takes place slowly and the effect of either the inertia or the inductance is insignificant – Steady state stability.
Sudden and fast changes from the equilibrium state so effect of both inertia and inductance can not be neglected- Dynamic or transient stability.

4. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
Criteria for steady state stability:-
Let the equilibrium of the torques and speed is TM, TL and ω and the small deviations are ΔTm, ΔTL and Δω. After the displacement from the equilibrium state the torque equation becomes,

5. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
Considering the small deviation, changes can be expressed as a linear function of change in speed,
From the torque equation, where all quantities are expressed in terms of their deviations from the equilibrium,

6. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
Solution is,
Where, (Δω)0 is the initial value of the deviation in speed. For the stable system the exponent must be negative, so speed increment will disappear with time. The exponent will always be negative if,

7. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
Criteria for the steady state stability is for a decrease in the speed the motor torque must exceeds the load torque and for increase in speed the motor torque must be less than the load torque.
Load torque TL’ results in a stable equilibrium point, and the load torque TL’’ results in an unstable situation.

8. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
To check the stability at an operating point of the motor, if an increase in speed brings greater increase in load torque than the motor torque, the speed will tend to decrease and return to its original value, so operating point will be a stable point else operating point will be an unstable point.

9. Steady State Stability of an Electric Drive (Cont.)
Dr. K. R. Rajagopal
IIT Delhi
Steady State Stability of an Electric Drive (Cont.)
Cases (a), (b) and (c) represents stable operation of drive.
Cases (d), (e) and (f) represents unstable operation of drive.
Case (g) represents indeterminate condition.
Various Speed and Torque Curves of Motor and Load