SynchronousMachineEquivalentCircuit
Class Description
The electrical equations for all variations of the synchronous models are based on the SynchronousEquivalentCircuit diagram for the direct- and quadrature- axes. Equations for conversion between equivalent circuit and time constant reactance forms: <i>Xd</i> = <i>Xad </i>+<i> Xl</i> <i>X’d</i> = <i>Xl</i> + <i>Xad</i> x <i>Xfd</i> / (<i>Xad</i> + <i>Xfd</i>) <i>X”d</i> = <i>Xl</i> + <i>Xad</i> x <i>Xfd</i> x <i>X1d</i> / (<i>Xad</i> x <i>Xfd</i> + <i>Xad</i> x <i>X1d</i> + <i>Xfd</i> x <i>X1d</i>) <i>Xq</i> = <i>Xaq</i> + <i>Xl</i> <i>X’q</i> = <i>Xl</i> + <i>Xaq</i> x <i>X1q</i> / (<i>Xaq</i> + <i>X1q</i>) <i>X”q</i> = <i>Xl</i> + <i>Xaq</i> x <i>X1q</i> x <i>X2q</i> / (<i>Xaq</i> x <i>X1q</i> + <i>Xaq</i> x <i>X2q</i> + <i>X1q</i> x <i>X2q</i>) <i>T’do</i> = (<i>Xad</i> + <i>Xfd</i>) / (<i>omega</i><i><sub>0</sub></i> x <i>Rfd</i>) <i>T”do</i> = (<i>Xad</i> x <i>Xfd</i> + <i>Xad</i> x <i>X1d</i> + <i>Xfd</i> x <i>X1d</i>) / (<i>omega</i><i><sub>0</sub></i> x <i>R1d</i> x (<i>Xad</i> + <i>Xfd</i>) <i>T’qo</i> = (<i>Xaq</i> + <i>X1q</i>) / (<i>omega</i><i><sub>0</sub></i> x <i>R1q</i>) <i>T”qo</i> = (<i>Xaq</i> x <i>X1q</i> + <i>Xaq</i> x <i>X2q</i> + <i>X1q</i> x <i>X2q</i>) / (<i>omega</i><i><sub>0</sub></i> x <i>R2q</i> x (<i>Xaq</i> + <i>X1q</i>) Same equations using CIM attributes from SynchronousMachineTimeConstantReactance class on left of "=" and SynchronousMachineEquivalentCircuit class on right (except as noted): xDirectSync = xad + RotatingMachineDynamics.statorLeakageReactance xDirectTrans = RotatingMachineDynamics.statorLeakageReactance + xad x xfd / (xad + xfd) xDirectSubtrans = RotatingMachineDynamics.statorLeakageReactance + xad x xfd x x1d / (xad x xfd + xad x x1d + xfd x x1d) xQuadSync = xaq + RotatingMachineDynamics.statorLeakageReactance xQuadTrans = RotatingMachineDynamics.statorLeakageReactance + xaq x x1q / (xaq+ x1q) xQuadSubtrans = RotatingMachineDynamics.statorLeakageReactance + xaq x x1q x x2q / (xaq x x1q + xaq x x2q + x1q x x2q) tpdo = (xad + xfd) / (2 x pi x nominal frequency x rfd) tppdo = (xad x xfd + xad x x1d + xfd x x1d) / (2 x pi x nominal frequency x r1d x (xad + xfd) tpqo = (xaq + x1q) / (2 x pi x nominal frequency x r1q) tppqo = (xaq x x1q + xaq x x2q + x1q x x2q) / (2 x pi x nominal frequency x r2q x (xaq + x1q) These are only valid for a simplified model where "Canay" reactance is zero.
Attributes
| Name | Type | Description |
|---|---|---|
| r1d | PU | Direct-axis damper 1 winding resistance. |
| r1q | PU | Quadrature-axis damper 1 winding resistance. |
| r2q | PU | Quadrature-axis damper 2 winding resistance. |
| rfd | PU | Field winding resistance. |
| x1d | PU | Direct-axis damper 1 winding leakage reactance. |
| x1q | PU | Quadrature-axis damper 1 winding leakage reactance. |
| x2q | PU | Quadrature-axis damper 2 winding leakage reactance. |
| xad | PU | Direct-axis mutual reactance. |
| xaq | PU | Quadrature-axis mutual reactance. |
| xf1d | PU | Differential mutual (“Canay”) reactance. |
| xfd | PU | Field winding leakage reactance. |
Relationships
Ancestors
Descendents
No descendent classes
Associations
None