PMSM Limits

$K_e\ (\frac{V}{krpm})$ $L_{d}\ (uH)$ $L_{q}\ (uH)$
$R_s\ (m\Omega)$ Pole Pairs
Current Limits (A) DCLink Voltage (V)
Torque Curves (Nm)
Voltage Circles (RPM)

Equations Used:

Torque Curves

$$ T_e = \frac32 P (\lambda_m + (L_d - L_q)i_d)i_q $$

Maximum Torque Per Ampare (MTPA)

$$ i_d^2 - i_q^2 + \frac{\lambda_m}{L_d - L_q}i_d = 0 $$

Voltage Curves - Steady State

$$ V_{DC}^2 = v_d^2 + v_q^2 $$

$$ v_d = R_si_d + L_d\frac{di_d}{dt} - \omega_e L_q i_q $$

$$ v_q = R_si_q + L_q\frac{di_q}{dt} + \omega_e L_d i_d + \omega_e \lambda_m $$