: Public Class
Created: 15/03/2012 00:49:53
Modified: 22/02/2013 14:38:13
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The electrical equations for all variations of the synchronous models are based on the SynchronousEquivalentCircuit diagram for the direct and quadrature axes.<br/><br/><b>Equations for conversion between Equivalent Circuit and Time Constant Reactance forms:</b><br/><b>Xd</b> = <b>Xad</b> + <b>Xl</b><br/><b>X’d</b> = <b>Xl</b> + <b>Xad</b> * <b>Xfd</b> / (<b>Xad</b> + <b>Xfd</b>)<br/><b>X”d</b> = <b>Xl</b> + <b>Xad</b> * <b>Xfd </b>* <b>X1d</b> / (<b>Xad</b> * <b>Xfd</b> + <b>Xad</b> * <b>X1d</b> + <b>Xfd</b> * <b>X1d</b>)<br/><b>Xq</b> = <b>Xaq</b> + <b>Xl</b><br/><b>X’q</b> = <b>Xl</b> + <b>Xaq</b> * <b>X1q</b> / (<b>Xaq</b>+ <b>X1q</b>)<br/><b>X”q</b> = <b>Xl</b> + <b>Xaq</b> *<b> X1q</b>* <b>X2q</b> / (<b>Xaq</b> * <b>X1q</b> + <b>Xaq</b> * <b>X2q</b> + <b>X1q</b> * <b>X2q</b>)<br/><b>T’do</b> = (<b>Xad</b> + <b>Xfd</b>) / (<b>omega</b><b><sub>0</sub></b> * <b>Rfd</b>)<br/><b>T”do</b> = (<b>Xad</b> * <b>Xfd</b> + <b>Xad</b> * <b>X1d</b> + <b>Xfd</b> * <b>X1d</b>) / (<b>omega</b><b><sub>0</sub></b> * <b>R1d</b> * (<b>Xad</b> + <b>Xfd</b>)<br/><b>T’qo</b> = (<b>Xaq</b> + <b>X1q</b>) / (<b>omega</b><b><sub>0</sub></b> * <b>R1q</b>)<br/><b>T”qo</b> = (<b>Xaq</b> * <b>X1q</b> + <b>Xaq</b> * <b>X2q</b> + <b>X1q</b> * <b>X2q</b>)/ (<b>omega</b><b><sub>0</sub></b> * <b>R2q</b> * (<b>Xaq</b> + <b>X1q</b>)<br/><b><br/></b>Same equations using CIM attributes from SynchronousMachineTimeConstantReactance class on left of = sign and SynchronousMachineEquivalentCircuit class on right (except as noted):<br/>xDirectSync = xad + RotatingMachineDynamics.statorLeakageReactance<br/>xDirectTrans = RotatingMachineDynamics.statorLeakageReactance + xad * xfd / (xad + xfd)<br/>xDirectSubtrans = RotatingMachineDynamics.statorLeakageReactance + xad * xfd * x1d / (xad * xfd + xad * x1d + xfd * x1d)<br/>xQuadSync = xaq + RotatingMachineDynamics.statorLeakageReactance<br/>xQuadTrans = RotatingMachineDynamics.statorLeakageReactance + xaq * x1q / (xaq+ x1q)<br/>xQuadSubtrans = RotatingMachineDynamics.statorLeakageReactance + xaq * x1q* x2q / (xaq * x1q + xaq * x2q + x1q * x2q) <br/>tpdo = (xad + xfd) / (2*pi*nominal frequency * rfd)<br/>tppdo = (xad * xfd + xad * x1d + xfd * x1d) / (2*pi*nominal frequency * r1d * (xad + xfd)<br/>tpqo = (xaq + x1q) / (2*pi*nominal frequency * r1q)<br/>tppqo = (xaq * x1q + xaq * x2q + x1q * x2q)/ (2*pi*nominal frequency * r2q * (xaq + x1q).<br/><br/>Are only valid for a simplified model where "Canay" reactance is zero.<br/>
Attribute
Public PU
  r1d
Details:
Notes: D-axis damper 1 winding resistance.<br/>
Public PU
  r1q
Details:
Notes: Q-axis damper 1 winding resistance.<br/>
Public PU
  r2q
Details:
Notes: Q-axis damper 2 winding resistance.<br/>
Public PU
  rfd
Details:
Notes: Field winding resistance.<br/>
Public PU
  x1d
Details:
Notes: D-axis damper 1 winding leakage reactance.<br/>
Public PU
  x1q
Details:
Notes: Q-axis damper 1 winding leakage reactance.<br/>
Public PU
  x2q
Details:
Notes: Q-axis damper 2 winding leakage reactance.<br/>
Public PU
  xad
Details:
Notes: D-axis mutual reactance.<br/>
Public PU
  xaq
Details:
Notes: Q-axis mutual reactance.<br/>
Public PU
  xf1d
Details:
Notes: Differential mutual (“Canay”) reactance.<br/>
Public PU
  xfd
Details:
Notes: Field winding leakage reactance.<br/>
Object Type Connection Direction Notes
SynchronousMachineDetailed Class Generalization To