Steady State Stability of Electrical Drive

Steady state stability

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.

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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

1

2 3 

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).