# Library

ARTEMiS/SSN Machines

## Blocks

### Description

The SSN Dual Stator Permanent Magnet Synchronous Machine (DSPMSM) implements a 3-phase double stator permanent synchronous machine modeled in the d-q rotor reference frame for use with the SSN solver. Stator windings are connected in wye to an internal neutral point. The 2nd stator is shifted physically by user set value of degrees from the 1^{st} one. The model is 4th order.

## Mask

# Parameters

Nominal power, voltage, frequency, field current [ Pn(VA) Vn(Vrms) fn(Hz)] | Nominal values for total power, line-line RMS voltage and frequency. Note that these values are not actually used internally in the model computation. |
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Stator parameters [ Rs(ohm), Ll, Lmd, Lmq(H)] | Stator resistance and leakage inductance, magnetization inductance for d-q axes. |

Magnet flux [Wb] | Magnet flux in Weber (or V.s) |

Pole pairs | Number of pair of poles |

Initial rotor angle (deg) | Initial rotor electrical angle in degree. A null angle makes the back-EMF voltage maximum on phase A of the 1^{st} stator and would make the machine generate a waveform on phase A on no-load conditions. |

Initial currents Iabc1 (A) (amplitude) Iabc1 (deg)(angle) Iabc2 (A) (amplitude) Iabc2 (deg)(angle) | Initial conditions for 1^{st} stator currents (amplitude and phase), 2^{nd} stator currents (amplitude and phase) |

Sample Time (s) | Sample time of the model in seconds. |

Backward Euler discretization | When checked, the SSN-SM equations are discretized with the Backward Euler method. This may help to obtain less oscillatory terminal voltages in some cases. |

Note: the model does not have the Delayed speed term option and therefore must be used only with the standard LU factorization of ARTEMiS-SSN. Without delays in the speed term, the model is more accurate but generates an asymmetrical admittance matrix that cannot be handled by the LDL^{T} factorization option of SSN. |

# Input and Output Signals

**Simulink Connection Points**

w_mec | Mechanical speed of the machine in rad/s. Typically, the speed will be computed from a separate mechanical model that will use this model electric torque (Te) as an input. A simple mechanical model is available in ARTEMiS/SSN/SSN rotating machines. | |
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meas | Measurements available: | |

flux phid1 phiq1 phid2 phiq2 (Wb) | Total flux states of the machine, that is the magnet flux and flux induced by coil currents. | |

Iabc1(A) | ABC terminal 1 currents in Amperes. | |

Iabc2(A) | ABC terminal 2 currents in Amperes. | |

Peo(W) | Total electric power generated by the machines in Watts. | |

Te (N.m) | Electric torque of the machine in N.m. | |

Angle(rad) | The electric angle of the rotor. The d-axis is aligned with phase A in this model. Therefore, at null load, the 0 angle corresponds to a null voltage of terminal A to ground, and with a negative slope. | |

Vdq1 Vdq2 (V) | Stator dq voltage in Volts for both stators | |

Idq1 dq2(A) | Stator dq current in Amperes for both stators. |

Note on Park referential and d-q values computed by the model: all SSN rotating machines internally use the following orthonormal Park transform, which is different from the classic North American one:

See the article **Park or DQ Transform variants** in the ARTEMiS application note section for more details. This power invariant transform has the particularity of NOT having the 3/2 factor on torque. It has the d-axis aligned with phase A when Θ = 0.

**Physical Modeling Connection Points**

A1,B1,C1 | Phase connection points of 1^{st} stator |
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A2,B2,C2 | Phase connection points of 2nd stator |

# Example

SSN_PMSMDualStator.slx is an example that uses the DSPMSM model.

# References

[1] C. Dufour, “Highly stable rotating machine models using the state-space-nodal real-time solver”, COMPENG-2018 conference, Oct. 10-12, 2018, Florence, Italia.

[2] Upcoming paper with DSSM and DSPMSM equations.