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This model implements a 3-phase synchronous machine modelled according the VBR** formulation in d-q rotor reference frame. Stator windings are connected in wye to an internal neutral point. All the parameters must be introduced  as Fundamental parameters referred to the stator.  The model can be of  5th or 6th order with one damper winding in the d-axis and one or two damper windings in the q-axis (Round Rotor -RR or Salient Pole -SP machines). Saturation mode is supported using total flux in both d-q axis.

**VBR stands for Voltage Behind Reactance. In the VBR modelisation, the internal model is similar to a voltage source in series with a reactance. This provides typically better stability properties than SPS machines models that are internally modelled with a current source injection.



Power(Va), Voltage (Vrms LL), Frequency (Hz),Field Current (A), pair of poles (pp)

Nominal values of the synchronous machine: Power (Pn), Voltage (Vn), frequency (fn) and field current (If). The field current corresponds to the point of the saturation curve where the nominal voltage is reached at terminal of the machine at no-load condition. For no saturated machine does not be considered for the calculations. However, field current define the transformation ratio stator to field.

Rs (ohms), Ll (H), Lmd (H), Lmq(H) 

Stator resistance and leakage inductance, magnetization inductance for d-q axes. 
Rf (ohms), Llfd(H)Field resistance and leakage inductance (referred to the machine's stator)

Rkd(ohms), Llkd(H), Rkq (ohms), Llkq(H),


Dampers resistance and leakage inductance for each d-q axes (referred to the machine's stator). 

Field current (A), mechanical rotor angle (deg), Peak values Ia, Ib, Ic(A), current angles(deg)

Initial conditions for field current, rotor mechanical angle and stator phase currents (peak values and angles).

Saturation curve Vector of values for field current (A) and terminal voltages (Vrms LL). These values are visibles and only considered when the checkbox saturation is selected. However these vectors cannot be empty or null.
Time Step (Ts)Sample time of the model in seconds
number of Ts, factor KrCompensation factors for rotor angle and stator resistance. They are normally disabled (Kr =1, compensation mechanical angle = 0). The first factor compensates the losses in the stator resistance for very high Ts. The second one adds or subtracts a mechanical angle to the rotor. These values are visibles only when checkbox compensation is selected.  

Input and Output Signals

VfField voltage referred to the machine's stator in Volts (input). 
wmMechanical speed of the machine in rad/s (input). 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.

Measurements available as outputs:

Vabc : stator abc line-neutral voltages in Volts

Iabcstator abc currents coming out from the machine in Amperes

Vqd : stator qd voltages in Volts 

Iqd : stator qd currents in Amperes 

If : field current in Amperes

Te : electric torque of the machine in N.m

Pe : total electrical power generated by the machine in Watts

phimqd : magnetizing flux linkages in Wb

Calculation of initial conditions

For the following machine parameters and operation point:

Vn = 24 kV ; Lmd = 4.5696 mH ; Lmq = 4.432 mH ; Llf = 0.4545 mH

Ifo =1281 A ;  Ia = 8216.8 A  (peak value) , φa = -0.067º ;  Ib = 8216.8 A  (peak value) , φb = -120.067º ; Ic = 8216.8 A  (peak value) , φc = 119.933º ; Rotor initial mechanical angle, φr = -68.9004º ;  Ifn =1300 A ;  fn = 60 Hz

current DQ calculations 

Iq = -2/3•(Ia•sin(φa)•cos(φr)+ Ib•sin(φb)•cos(φr-120º)+ Ic•sin(φc)•cos(φr+120º)) = -7662.44 A

Id = -2/3•(Ia•sin(φa)•sin(φr)+ Ib•sin(φb)•sin(φr-120º)+ Ic•sin(φc)•sin(φr+120º)) = -2966.93 A

Field current (referenced to stator)

If' = 2/3•Ifo•Nf/Ns ; Ns/Nf = 0.8165•Lmd•Ifn•(2•π•fn)/Vn = 0.0762 ; If' = 2/3•Ifo•1/0.0762 = 11208.82 A

Intial Flux linkages calculations

λkq = Lmq•Iq = -33.959 Wb

λkd = Lmd•(Id+If')= 37.662 Wb

λf = λkd + Llf•If'= 42.756 Wb

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