SynchronousMachineEquivalentCircuit

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.

URI: cim:SynchronousMachineEquivalentCircuit
Type: Class

 classDiagram
    class SynchronousMachineEquivalentCircuit
    click SynchronousMachineEquivalentCircuit href "../SynchronousMachineEquivalentCircuit"
      SynchronousMachineDetailed <|-- SynchronousMachineEquivalentCircuit
        click SynchronousMachineDetailed href "../SynchronousMachineDetailed"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.CrossCompoundTurbineGovernorDyanmics

          SynchronousMachineEquivalentCircuit --> CrossCompoundTurbineGovernorDynamics : SynchronousMachineDynamics.CrossCompoundTurbineGovernorDyanmics
          click CrossCompoundTurbineGovernorDynamics href "../CrossCompoundTurbineGovernorDynamics"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.CrossCompoundTurbineGovernorDynamics

          SynchronousMachineEquivalentCircuit --> CrossCompoundTurbineGovernorDynamics : SynchronousMachineDynamics.CrossCompoundTurbineGovernorDynamics
          click CrossCompoundTurbineGovernorDynamics href "../CrossCompoundTurbineGovernorDynamics"

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.damping

      SynchronousMachineEquivalentCircuit : IdentifiedObject.description

      SynchronousMachineEquivalentCircuit : SynchronousMachineDetailed.efdBaseRatio

      SynchronousMachineEquivalentCircuit : DynamicsFunctionBlock.enabled

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.ExcitationSystemDynamics

          SynchronousMachineEquivalentCircuit --> ExcitationSystemDynamics : SynchronousMachineDynamics.ExcitationSystemDynamics
          click ExcitationSystemDynamics href "../ExcitationSystemDynamics"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.GenICompensationForGenJ

          SynchronousMachineEquivalentCircuit --> GenICompensationForGenJ : SynchronousMachineDynamics.GenICompensationForGenJ
          click GenICompensationForGenJ href "../GenICompensationForGenJ"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDetailed.ifdBaseType

          SynchronousMachineEquivalentCircuit --> IfdBaseKind : SynchronousMachineDetailed.ifdBaseType
          click IfdBaseKind href "../IfdBaseKind"

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.inertia

          SynchronousMachineEquivalentCircuit --> Seconds : RotatingMachineDynamics.inertia
          click Seconds href "../Seconds"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.MechanicalLoadDynamics

          SynchronousMachineEquivalentCircuit --> MechanicalLoadDynamics : SynchronousMachineDynamics.MechanicalLoadDynamics
          click MechanicalLoadDynamics href "../MechanicalLoadDynamics"

      SynchronousMachineEquivalentCircuit : IdentifiedObject.mRID

      SynchronousMachineEquivalentCircuit : IdentifiedObject.name

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.r1d

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.r1d
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.r1q

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.r1q
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.r2q

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.r2q
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.rfd

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.rfd
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.saturationFactor

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.saturationFactor120

      SynchronousMachineEquivalentCircuit : SynchronousMachineDetailed.saturationFactor120QAxis

      SynchronousMachineEquivalentCircuit : SynchronousMachineDetailed.saturationFactorQAxis

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.statorLeakageReactance

          SynchronousMachineEquivalentCircuit --> PU : RotatingMachineDynamics.statorLeakageReactance
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : RotatingMachineDynamics.statorResistance

          SynchronousMachineEquivalentCircuit --> PU : RotatingMachineDynamics.statorResistance
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.SynchronousMachine

          SynchronousMachineEquivalentCircuit --> SynchronousMachine : SynchronousMachineDynamics.SynchronousMachine
          click SynchronousMachine href "../SynchronousMachine"

      SynchronousMachineEquivalentCircuit : SynchronousMachineDynamics.TurbineGovernorDynamics

          SynchronousMachineEquivalentCircuit --> TurbineGovernorDynamics : SynchronousMachineDynamics.TurbineGovernorDynamics
          click TurbineGovernorDynamics href "../TurbineGovernorDynamics"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.x1d

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.x1d
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.x1q

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.x1q
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.x2q

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.x2q
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.xad

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.xad
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.xaq

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.xaq
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.xf1d

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.xf1d
          click PU href "../PU"

      SynchronousMachineEquivalentCircuit : SynchronousMachineEquivalentCircuit.xfd

          SynchronousMachineEquivalentCircuit --> PU : SynchronousMachineEquivalentCircuit.xfd
          click PU href "../PU"

Inheritance

• IdentifiedObject
  • DynamicsFunctionBlock
    • RotatingMachineDynamics
      • SynchronousMachineDynamics
        • SynchronousMachineDetailed
          • SynchronousMachineEquivalentCircuit

Attributes

Name	URI	Cardinality and Range	Description	Inheritance
xad	cim:SynchronousMachineEquivalentCircuit.xad	1 PU	Direct-axis mutual reactance	direct
rfd	cim:SynchronousMachineEquivalentCircuit.rfd	1 PU	Field winding resistance	direct
xfd	cim:SynchronousMachineEquivalentCircuit.xfd	1 PU	Field winding leakage reactance	direct
r1d	cim:SynchronousMachineEquivalentCircuit.r1d	1 PU	Direct-axis damper 1 winding resistance	direct
x1d	cim:SynchronousMachineEquivalentCircuit.x1d	1 PU	Direct-axis damper 1 winding leakage reactance	direct
xf1d	cim:SynchronousMachineEquivalentCircuit.xf1d	1 PU	Differential mutual (“Canay”) reactance	direct
xaq	cim:SynchronousMachineEquivalentCircuit.xaq	1 PU	Quadrature-axis mutual reactance	direct
r1q	cim:SynchronousMachineEquivalentCircuit.r1q	1 PU	Quadrature-axis damper 1 winding resistance	direct
x1q	cim:SynchronousMachineEquivalentCircuit.x1q	1 PU	Quadrature-axis damper 1 winding leakage reactance	direct
r2q	cim:SynchronousMachineEquivalentCircuit.r2q	1 PU	Quadrature-axis damper 2 winding resistance	direct
x2q	cim:SynchronousMachineEquivalentCircuit.x2q	1 PU	Quadrature-axis damper 2 winding leakage reactance	direct
saturationFactorQAxis	cim:SynchronousMachineDetailed.saturationFactorQAxis	0..1 float	Quadrature-axis saturation factor at rated terminal voltage (S1q) (&gt...	SynchronousMachineDetailed
saturationFactor120QAxis	cim:SynchronousMachineDetailed.saturationFactor120QAxis	0..1 float	Quadrature-axis saturation factor at 120% of rated terminal voltage (S12q<...	SynchronousMachineDetailed
efdBaseRatio	cim:SynchronousMachineDetailed.efdBaseRatio	1 float	Ratio (exciter voltage/generator voltage) of Efd bases of exciter and ...	SynchronousMachineDetailed
ifdBaseType	cim:SynchronousMachineDetailed.ifdBaseType	1 IfdBaseKind	Excitation base system mode	SynchronousMachineDetailed
SynchronousMachine	cim:SynchronousMachineDynamics.SynchronousMachine	1 SynchronousMachine	Synchronous machine to which synchronous machine dynamics model applies	SynchronousMachineDynamics
CrossCompoundTurbineGovernorDyanmics	cim:SynchronousMachineDynamics.CrossCompoundTurbineGovernorDyanmics	0..1 CrossCompoundTurbineGovernorDynamics	The cross-compound turbine governor with which this high-pressure synchronous...	SynchronousMachineDynamics
CrossCompoundTurbineGovernorDynamics	cim:SynchronousMachineDynamics.CrossCompoundTurbineGovernorDynamics	0..1 CrossCompoundTurbineGovernorDynamics	The cross-compound turbine governor with which this low-pressure synchronous ...	SynchronousMachineDynamics
MechanicalLoadDynamics	cim:SynchronousMachineDynamics.MechanicalLoadDynamics	0..1 MechanicalLoadDynamics	Mechanical load model associated with this synchronous machine model	SynchronousMachineDynamics
ExcitationSystemDynamics	cim:SynchronousMachineDynamics.ExcitationSystemDynamics	0..1 ExcitationSystemDynamics	Excitation system model associated with this synchronous machine model	SynchronousMachineDynamics
TurbineGovernorDynamics	cim:SynchronousMachineDynamics.TurbineGovernorDynamics	* TurbineGovernorDynamics	Turbine-governor model associated with this synchronous machine model	SynchronousMachineDynamics
GenICompensationForGenJ	cim:SynchronousMachineDynamics.GenICompensationForGenJ	* GenICompensationForGenJ	Compensation of voltage compensator's generator for current flow out of this ...	SynchronousMachineDynamics
damping	cim:RotatingMachineDynamics.damping	1 float	Damping torque coefficient (D) (>= 0)	RotatingMachineDynamics
inertia	cim:RotatingMachineDynamics.inertia	1 Seconds	Inertia constant of generator or motor and mechanical load (H) (> 0...	RotatingMachineDynamics
saturationFactor	cim:RotatingMachineDynamics.saturationFactor	0..1 float	Saturation factor at rated terminal voltage (S1) (>= 0)	RotatingMachineDynamics
saturationFactor120	cim:RotatingMachineDynamics.saturationFactor120	0..1 float	Saturation factor at 120% of rated terminal voltage (S12) (>= Rotat...	RotatingMachineDynamics
statorLeakageReactance	cim:RotatingMachineDynamics.statorLeakageReactance	1 PU	Stator leakage reactance (Xl) (>= 0)	RotatingMachineDynamics
statorResistance	cim:RotatingMachineDynamics.statorResistance	1 PU	Stator (armature) resistance (Rs) (>= 0)	RotatingMachineDynamics
enabled	cim:DynamicsFunctionBlock.enabled	1 boolean	Function block used indicator	DynamicsFunctionBlock
description	cim:IdentifiedObject.description	0..1 string	The description is a free human readable text describing or naming the object	IdentifiedObject
mRID	cim:IdentifiedObject.mRID	1 string	Master resource identifier issued by a model authority	IdentifiedObject
name	cim:IdentifiedObject.name	0..1 string	The name is any free human readable and possibly non unique text naming the o...	IdentifiedObject

Identifier and Mapping Information

Schema Source

• from schema: http://iec.ch/TC57/ns/CIM/Dynamics-EU#Package_DynamicsProfile

Mappings

Mapping Type	Mapped Value
self	cim:SynchronousMachineEquivalentCircuit
native	this:SynchronousMachineEquivalentCircuit