Motor Torque: $T = \frac{3}{2} p [\Psi_m I_q + (L_d - L_q)I_d I_q]$

Voltage Equations: $V_d = R_s I_d - \omega_e L_q I_q$ | $V_q = R_s I_q + \omega_e L_d I_d + \omega_e \Psi_m$

Voltage Limit: $\sqrt{V_d^2 + V_q^2} \le V_{max}$, where $V_{max} = V_{dc}/\sqrt{3}$ (SVPWM) or $V_{dc}/2$ (SPWM).

Field Weakening: When back-EMF exceeds $V_{max}$, negative $I_d$ is injected to oppose the rotor flux ($\Psi_m$), keeping terminal voltage within the inverter limit while adhering to the current limit $I_d^2 + I_q^2 \le I_{max}^2$.