PMSM - dq model

5/17/20242 min read

Figure 1.: PMSM model in dq reference frame

PMSM model can be described in abc or alpha-beta or dq reference frame. PMSM is naturally described in abc reference frame since it is three-phase system. PMSM equations in abc reference frame are defined as follows:

Three-phase model is too complex, therefore it is beneficial to use Clark and Park transformations to transform 3-phase PMSM model into virtual dq reference frame rotating with electrical angular velocity. Differential equations for dq-current of PMSM in dq reference frame are defined as follows:

Electromagnetic torque of PMSM consists of synchronous torque (left term) and reluctance torque (right term) as follows:

Mechanical equation of PMSM describes acceleration of motor based on electromagnetic torque, load torque, motor inertia and friction as follows:

where B defines friction coefficient. Electrical speed and electrical position are defined by number of motor pole-pairs pp as follows:

Complete model of PMSM in dq reference frame according to equations above is located in fig. 1.

  1. P. Pillay, R. Krishnan, "Modeling, simulation, and analysis of permanent-magnet motor drives. I. The permanent-magnet synchronous motor drive,"

  2. H. Liu and S. Li, "Speed Control for PMSM Servo System Using Predictive Functional Control and Extended State Observer,"

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