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Question 3.AE.5: Figure E3.5.1 shows the torque–angular velocity relation (T ......

Figure E3.5.1 shows the torque–angular velocity relation (T – ω_m) of an induction motor supplying a mechanical load with nonlinear (parabolic) torque (T_L). Determine the stability of the operating pointQ_1.

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The stability conditions at the point where the two curves intersect is

\left.\begin{array}{rl} Q_1:\quad \frac{\Delta T_L}{\Delta \omega_m} & =\text { positive } \\ \frac{\Delta T}{\Delta \omega_m} & =\text { negative. } \end{array}\right\}>>>>>\text { stable. }

Therefore, an induction machine connected to a mechanical load with parabolic torquespeed characteristics as shown in Fig. E3.5.1 will not experience any steady-state stability problems.

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