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:
Xd = Xad + Xl
X’d = Xl + Xad x Xfd / (Xad + Xfd)
X”d = Xl + Xad x Xfd x X1d / (Xad x Xfd + Xad x X1d + Xfd x X1d)
Xq = Xaq + Xl
X’q = Xl + Xaq x X1q / (Xaq + X1q)
X”q = Xl + Xaq x X1q x X2q / (Xaq x X1q + Xaq x X2q + X1q x X2q)
T’do = (Xad + Xfd) / (omega0 x Rfd)
T”do = (Xad x Xfd + Xad x X1d + Xfd x X1d) / (omega0 x R1d x (Xad + Xfd)
T’qo = (Xaq + X1q) / (omega0 x R1q)
T”qo = (Xaq x X1q + Xaq x X2q + X1q x X2q) / (omega0 x R2q x (Xaq + X1q)
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

Inherits from

Descendant classes

  • No descendant classes

Leaf/Root class

IsLeaf IsRoot
False False

Associations

None