Define slip; linear portion of T-S curve

Slip

Slip is the fractional difference between synchronous speed and rotor speed, expressed as a fraction or percentage of synchronous speed:

$$s = \frac{N_s - N_r}{N_s}$$

Here $N_s = \frac{120f}{P}$ is the speed of the rotating magnetic field and $N_r$ is the rotor speed. At standstill $s = 1$; at synchronous speed $s = 0$. At rated load it is about 2 to 5 %. The rotor frequency is $f_r = sf$.

Why only the linear portion is used

The torque-slip curve is nearly a straight line for small slip (from $s=0$ to the slip at about full load) because $sX_2 \ll R_2$, so

$$T \approx \frac{3E_2^2}{\omega_s R_2}\,s \;\propto\; s$$

• This region lies on the stable side of the maximum torque ($s < s_m$). An increase in load slows the rotor a little, slip and torque increase, and the motor settles at a new steady speed.
• Beyond the maximum torque ($s > s_m$) the torque falls as slip increases, so any extra load makes the motor stall.
• In the linear region the rotor copper loss ($sP_g$) is small, so efficiency is high, and the speed is nearly constant.