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ARTEMiS/SSN Machines



The SSN Double Stator Synchronous Machine (DSSM) implements a 3-phase double stator synchronous machine modelled 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 30° from the 1st one.  The model is 7th order, with one damper windings in each d-q axis. Steady-state saturation mode is supported using total flux in both d-q axis.



Nominal power, voltage, frequency, field current  [ Pn(VA) Vn(Vrms) fn(Hz) ifn(A) ] Nominal values for total power, line-line RMS voltage, frequency and field current
Stator parameters [ Rs(ohm), Ll, Lmd, Lmq(H), Lcanay(H), Ll12]

Stator resistance and leakage inductance, magnetization inductance for d-q axes. The Lcanay parameter is the Canay inductance correction that consider mutual flux couplings are not all equal on the d-axis. The parameter can be ignored or set to zero if unknown.

Ll12 is the coupling inductance between both stator windings. It is rarely specified and can be left to zero in most cases.

Field parameters [ Rf'(ohm)  Llfd'(H) ]Field resistance and leakage inductance (seen from the stator)
Dampers parameters [ Rkd',Llkd'  Rkq1',Llkq1'  ] (R=ohm,L=H)Dampers resistance and leakage inductance for each d-q axes (seen from the stator)
Pole pairsNumber 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 1st stator and would make the machine generate a  waveform on phase A on no-load conditions.
Initial currents  Ifd Iabc1 (A) (amplitude)  Iabc1 (deg)(angle ) Iabc2 (A) (amplitude)  Iabc2 (deg)(angle )Initial conditions for Field current, 1st stator currents (amplitude and phase), 2nd stator currents (amplitude and phase)
SaturationSaturation is used if selected. Only global saturation (or steady-state) saturation is supported

The next figure shows the difference between global inductance and differential saturations when the machine is operated at its nominal saturation point.

Open stator saturation curve: field current (pu)The pu base is the nominal field current.
Open stator saturation curve: phase-phase RMS voltage (pu) The pu base is the nominal terminal voltage specified in the first parameter above.
Plot saturation curvesPlot saturation curves
Sample Time (s)Sample time of the model in seconds.
Computed stator-to-field coil winding turn ratio

(Ns_to_Nf) is found using the following formula:


where Lmd (d-axis mutual inductance), Ifn (nominal field current), fn (nominal electric frequency) and Vn(machine line-line RMS voltage). This turn ratio is sometimes useful when trying to convert commonly available stator referenced values to actual field referenced values.

Backward Euler discretization: (model with External Neutral Terminal only)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 handle by the LDLT factorization option of SSN.

Input and Output signals

Simulink Connection Points

w_mecMechanical 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.
measMeasurements available:

  • flux: phid1  phiq1 phid2 phiq2 phif phikd phikq (Wb): flux states of the machine.
  • Iabc1(A): ABC terminal 1 currents in Amperes.
  • Iabc2(A): ABC terminal 2 currents in Amperes.
  • Ifield(A): Filed terminal current 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): 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.
  • phim_dq (Wb): This is the air gap flux in Wb.
  • saturation factor: this is the per-unit value global inductance. By definition, it has a value of 1 at the nominal operating point.
  • Vdq1 Vdq2 (V): stator dq voltage in Volts for both stators
  • Idq1Idq2A): stator dq current in Amperes for both stators.

Saturation factor: Display the Lmd/Ldm_nominal ratio. In unsaturated mode, this value should be 1 (or greater of the nominal point is slightly saturated). During saturation, the magnetizing inductance decreases and this value will drop below 1.

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:

Read 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  

Physical Modeling Connection Points

Field: positive field winding terminal. The negative field terminal is implicitly connected to ground.

A1,B1,C1: phase connection points of 1st stator

A2,B2,C2: phase connection points of 2nd stator

Standard Per Unit Synchronous machine parameters

The  ARTEMiS routine ssn_SynchronousMachine_STD2SI_conversion.m can be used to obtain SI parameters from a PU-Std model.


SSN_SynchronousMachineDualStator.slx is an example that uses the DSSM model. In the model, the machine is connected to two thyristor controlled rectifier (TCR). The field current is provided by a brushless rotating exciter, as found in aircraft and utility generators.


[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] A. Moeini, I. Kamwa, P. Brunelle and G. Sybille, "Synchronous Machine Stability Model, an Update to IEEE Std 1110-2002 Data Translation Technique," 2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, 2018, pp. 1-5. doi: 10.1109/PESGM.2018.8586169

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