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Synchronous machine excited by permanent magnets
Electrical / Machines
This three-phase permanent magnet synchronous machine has a sinusoidal back EMF.
The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. All electrical variables and parameters are viewed from the stator side. In the component icon, phase a is marked with a dot.
Stator flux linkages:
The machine model offers two different implementations of the electrical system: a traditional rotor reference frame and a voltage-behind-reactance formulation.
Rotor Reference Frame Using Park's transformation, the 3-phase circuit equations in physical variables are transformed to the dq rotor reference frame. This results in constant coefficients in the differential equations making the model numerically efficient. However, interfacing the dq model with the external 3-phase network may be difficult. Since the coordinate transformations are based on voltage-controlled current sources, inductors and naturally commutated devices such as diode rectifiers may not be directly connected to the stator terminals.
Voltage behind Reactance This formulation allows for direct interfacing of arbitrary external networks with the 3-phase stator terminals. The electrical system is described in circuit form. Due to the resulting time-varying inductance matrices, this implementation is numerically less efficient than the traditional rotor reference frame.
Electromagnetic torque:
Mechanical rotor speed :
The output vector “m” contains the following 3 signals:
If the stator inductance is independent of the rotor angle, i.e. , it is
computational more efficient to use the simplified Brushless DC Machine with
a sinusoidal back EMF. The parameters need to be converted as follows:
For back EMF shapes other than sinusoidal, and/or if the stator inductance has a complex angle dependency please use the sophisticated model of the Brushless DC Machine. The sophisticated BLDC machine can be configured as a PMSM with sinusoidal back EMF if the parameters are converted as follows: