Six Phase Permanent Magnet Synchronous Machine with Neutral Connection

A1, B1, C1, A2, B2, C2 are stator terminals and N is the neutral point terminal. Stator windings use the current source interface. Windings are grouped into A1 B1 C1 group and A2 B2 C2 group which can be displaced by 30 degrees or 60 degrees.

Electrical sub-system model

The electrical part of the machine is represented by the following system of equations which are derived by applying the decoupling VSD transformation to the initial machine model. VSD transformation transforms the space into three orthogonal subspaces representing the direct, inverse and zero order component. Only the direct order component takes part in electromechanical conversion.

If the linear model is chosen on the component's mask, the d-axis is aligned with the rotor magnets and q-axis permanent magnet flux is not considered ( ${\psi }_{\mathrm{PMq}}=\; 0$ ). Transformation matrix used to convert the model to a stationary αβ reference frame depends on the displacement angle chosen on the component mask. For 30 degree displacement transformation is given by:

$T_{30}=k\cdot \left[\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& \frac{1}{2}& \frac{1}{2}& -1\\ 1& -\frac{1}{2}& -\frac{1}{2}& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& \frac{1}{2}& \frac{1}{2}& -1\\ 1& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1\end{array}\right]$

For 60 degree displacement the transformation is given by:

$T_{60}=k\cdot \left[\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& \frac{1}{2}& -1& \frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0& -\frac{\sqrt{3}}{2}\\ 1& -\frac{1}{2}& -\frac{1}{2}& -\frac{1}{2}& 1& -\frac{1}{2}\\ 0& -\frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0& -\frac{\sqrt{3}}{2}\\ 1& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1\end{array}\right]$

Mechanical sub-system model

Motion equation:

Ports

• A1 (electrical)
  • Stator winding phase A1 port.

• B1 (electrical)
  • Stator winding phase B1 port.

• C1 (electrical)
  • Stator winding phase C1 port.

• A2 (electrical)
  • Stator winding phase A2 port.

• B2 (electrical)
  • Stator winding phase B2 port.

• C2 (electrical)
  • Stator winding phase C2 port.
• N (electrical)
  • Stator winding phase N port.

• in
  • Available if Model Load source is selected.

General (Tab)

• Rs
  • Stator phase resistance [Ω]
• Lls
  • Stator winding leakage inductance [H]
• Ld
  • Stator phase inductance in direct axis [H]
• Lq
  • Stator phase inductance in quadrature axis [H]
• Psi_pm
  • Flux amplitude established in stator phases by rotor permanent magnets [Wb]
• Displacement
  • Displacement between A1 B1 C1 and A2 B2 C2 winding groups [∘]

Mechanical (Tab)

• pms
  • Machine number of pole pairs
• Jm
  • Combined rotor and load moment of inertia [kgm2]
• Friction coefficient
  • Machine viscous friction coefficient [Nms]
• Unconstrained mechanical angle
  • Limiting mechanical angle between 0 and 2π

Load (Tab)

External load enables you to use an analog input signal from a HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) analog channel with the load_ai_pin address as an external torque/speed load, and to assign offset (V) and gain (Nm/V) to the input signal, according to the formula:

$T_l=load\_ai\_gain·\left(AI\right(load\_ai\_pin)+load\_ai\_offset)$

Feedback (Tab)

If an external resolver carrier source is selected, the source signal type can be set as either single ended or differential. The single ended external resolver carrier source type enables use of an analog input signal from the HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) analog channel with the res_ai_pin_1 address as the external carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal, according to the formula:

The differential external resolver carrier source type enables use of two analog input signals from the HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) analog channels with the res_ai_pin_1 and the res_ai_pin_2 addresses. Analog signals from these HIL/TyphoonSim (internal virtual IO bus in TyphoonSim) analog inputs are subtracted, and the resulting signal is used as the external differential carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal (similarly to the single ended case), according to the formula:

The following expression must hold in order to properly generate the encoder signals:

Table 3. Variables in the encoder limitation expression

symbol	description
enc_ppr	Encoder number of pulses per revolution
fm	Rotor mechanical frequency [Hz]
Ts	Simulation time step [s]

Snubber (Tab)

• Rsnb stator
  • Stator snubber resistance value [Ω]

All machines with current source based circuit interfaces have the Snubber tab in the properties window where the value of snubber resistance can be set. Snubbers are necessary in the cases when an inverter or a contactor is directly connected to the machine terminals. This value can be set to infinite (inf), but it is not recommended when a machine is directly connected to the inverter since there will be a current source directly connected to an open switch. In this case, one of each switch pairs S1 and S2, S3 and S4, and S5 and S6 will be forced closed by the circuit solver in order to avoid the topological conflicts. On the other hand, with finite snubber values, there's always a path for the currents Ia and Ib, so all inverter switches can be open in this case. Circuit representations of this circuit without and with snubber resistors are shown in Figure 5 and Figure 6 respectively. Snubbers are connected across the current sources.

Note: Snubbers exist only in the machine components that have the current source based circuit interface.

Note: Snubbers are dynamic, which means that the snubber is dynamically added to circuit modes where topological conflicts are detected.

Output (Tab)

Extras (Tab)

The Extras tab gives you the opportunity to set Signal Access Management for the component.