### Steady State Stability of Electrical Drive

Equilibrium speed of the motor-load system can be obtained when motor torque equals the load torque. At this equilibrium speed, motor will operate in steady-state.

* This concept is readily evaluate the stability of an equilibrium point from the steady state speed-torque curves of the motor & load system.

* In electrical drives, During transient condition, electrical motor can be assumed to be in electrical equilibrium implying steady-state speed-torque curves applicable to the transient state operations also electrical time const is negligible compare to mechanical time const.

There are seven possible combination of speed and torque curves of motor and load :

(a) , (b) and (c) – Stable

(d) , (e) and (f) – Unstable

(g) – Interminate.

* Steady, state stability of equilibrium point ‘A’ termed as stable state when the operation will be restored it after a small depature from it due to disturbance in motor or load.

* Due to disturbance, a reduction at Δωm in speed. At new speed, electrical motor torque > load torque, then motor will accelerate and operation will be restored to point ‘A’. se in Δwm in speed, load torque > motor torque, resulting into deceleration and restoration of operation to a point A. Hence the electric drive is steady state stable at point ‘A’.

* Equilibrium point’B’ is obtained when the same motor drives another load. A se in speed causes the load torque > motor torque, electric drive decelerates and operating point moves away from point ‘B’. Similarly when working at point ‘B’ & se in speed will make motor torque > load torque, which will move the operating point away from point B. Thus, point ‘B’ is unstable point of equilibrium. Secondly stability point C & D.

* From above discussion, an equilibrium point will be stable when an se in speed cause load- torque to exceed the motor torque (w) when at equilibrium point following condition is satisfied

The system operating point will be stable when Δωm approaches to zero as t approaches infinity. For this happen the exponent term in equ (8) must be –ve. This yields the inequality of equ (7).

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