1. Synchronous Speed & Slip: $N_s = \frac{120 f}{P} \text{ RPM}, \quad s = \frac{N_s - N_r}{N_s}$
2. Thevenin Equivalent Voltage & Impedance: $$V_{th} = \frac{V_{LL}}{\sqrt{3}} \frac{X_m}{\sqrt{R_1^2 + (X_1 + X_m)^2}}, \quad R_{th} \approx R_1 \left(\frac{X_m}{X_1 + X_m}\right)^2, \quad X_{th} \approx X_1$$
3. Electromagnetic Torque ($T_{em}$): $$T_{em} = \frac{3}{\omega_s} \frac{V_{th}^2 (R_2'/s)}{(R_{th} + R_2'/s)^2 + (X_{th} + X_2')^2}$$
4. Breakdown (Maximum) Torque & Slip: $$s_{max} = \frac{R_2'}{\sqrt{R_{th}^2 + (X_{th} + X_2')^2}}, \quad T_{max} = \frac{3 V_{th}^2}{2 \omega_s \left[R_{th} + \sqrt{R_{th}^2 + (X_{th} + X_2')^2}\right]}$$