Slip and Torque-Speed Characteristic

$s = \frac{N_s - N_r}{N_s} \qquad f_r = s f$

Typical full-load slip is 2–5 %. Torque:

$T = \frac{3}{\omega_s}\cdot\frac{V^2 R_2/s}{(R_1 + R_2/s)^2 + (X_1 + X_2)^2}$

Key points of the curve:

• Starting torque at $s = 1$;
• Maximum (breakdown) torque at $s_{max} \approx R_2/X_2$ — its value does not depend on rotor resistance;
• the stable operating region at low slip, where torque is roughly proportional to slip.

Torque is proportional to $V^2$, so a 10 % voltage dip cuts torque by about 19 %.