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Permanent Magnet Synchronous Machine (PMSM)



Permanent Magnet Synchronous Machine (PMSM)

Model of a three-phase Permanent Magnet Synchronous Machine (PMSM) with sinusoidal back Electro-Motive Force (EMF). In motor operation torque and speed have the same sign. In this model, the flux linking each winding is assumed to depend linearly on all stator winding currents and it is assumed that the permanent magnet flux linkage is sinusoidal.

Electrical model and equations


\phi_d = L_d i_d + \phi_m
\phi_q = L_q i_q

where \phi_m = \frac{K_e}{N_{pp}} is the permanent magnet flux linkage, and \omega_r = N_{pp} \Omega is the electrical speed of the rotor field.

Electromechanical equations

Electro-magnetic torque:

T_e = 1.5 * N_{pp} * (i_q * \phi_d - id * \phi_q)

Mechanical rotational speed \Omega:

J \frac{d\Omega}{dt} = T_e - B \Omega


Electrical > Motors


Name Description
Pin_A Phase A (Electrical)
Pin_B Phase B (Electrical)
Pin_C Phase C (Electrical)
Pin_R Rotor (Rotational Mechanical)
Pin_Angle Rotor Angle in radians (Control)


Name Description
Rs Stator Winding Resistance [Ohm]
Ld Direct Axis Inductance [H]
Lq Quadratic Axis Inductance [H]
Ke Back-EMF Constant
J Rotor Inertia [kg.m²]
B Rotor Friction Coefficient [N.m/(rad/s)]
NPP Number of pole pairs