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, positive terminal of phase a is marked with a dot.
The stator inductance parameters \(L_\mathrm{d}\),\(L_\mathrm{q}\), and \(L_\mathrm{ls}\) are related as follows:
\[L_\mathrm{d} = L_\mathrm{md} + L_\mathrm{ls}\]
\[L_\mathrm{q} = L_\mathrm{mq} + L_\mathrm{ls}\]
With \(L_\mathrm{md}\) and \(L_\mathrm{mq}\) representing the magnetizing inductances and \(L_\mathrm{ls}\) the stator leakage inductance.
The machine model offers two different implementations of the electrical system: a traditional rotor reference frame and a voltage behind reactance (VBR) formulation.
Using Park’s transformation, the 3-phase circuit equations in physical variables are transformed to the dq0 rotor reference frame. This results in constant coefficients in the differential equations making the model numerically efficient. However, interfacing the dq0 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.
Note
In the rotor reference frame implementation the voltage across each open ended stator winding is an input to the machine equations. The two electrical connections for each phase cannot be galvanically isolated, otherwise the phase voltage measurement is undefined. Therefore the rotor reference frame model does not support a floating star (y) connection.
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.
PLECS does not support code generation for models with time-varying inductance matrices. When generating code for the VBR model the machine equations are reformulated to interface electrically with a constant inductance and emulate the variable portion of the inductance with a voltage source.
Leakage inductance of stator windings in henries \((\mathrm{H})\). Stator leakage must be set to a non-zero value.
Initial stator currents
A three-element vector containing the initial stator currents \(i_\mathrm{a,0}\),\(i_\mathrm{b,0}\) and \(i_\mathrm{c,0}\) of phase a, b and c in amperes \((\mathrm{A})\).
Most probe signals for the Permanent Magnet Synchronous Machine are also available with this machine. Only the following probe signal is different:
Stator flux (dq0)
The stator flux linkages \(\varphi_\mathrm{d}\),\(\varphi_\mathrm{q}\) and \(\varphi_\mathrm{0}\) in the rotating reference frame in \((\mathrm{Vs})\).
q-axis
0-axis