modelSynchronousMachine4WindingsInternalParameters

Synchronous machine with 4 windings - internal parameters

Diagram of SynchronousMachine4WindingsInternalParameters

Extends from BaseClasses.OnePortACdqPU (Base class for one-port AC components with p.u. Park's transformation), Icons.Machine.

Information

Model of a sychronous machine with four windings. The transformer voltage terms are neglected if neglectTransformerTerms=true. The model parameters refer directly to internal physical parameters such as inductances and resistances.

The model is taken from the theory manual of the Eurostag software. For consistency with the base class OnePortACdq, however, the currents ifPu, idPu and iqPu are all assumed to be positive entering, while the Eurostag manual assumes them to be all positive leaving. Therefore, all the current and fluxes have an opposite sign in the Park equations.

This model is in fact equivalent to the model described in Kundur, Power Systems Stability and Control, Chapter 3, except for the current sign conventions, which in that case are assumed to be positive entering for the rotor winding and positive leaving for the direct and quadrature stator axes. The correspondance of the parameter symbols is given in the table, all parameters are in p.u. referred to the machine rated values.

PowerGrids	Kundur	Meaning
raPu	Ra	Armature resistance
rDPu	R1d	Resistance of the direct axis damper
rfPu	Rfd	Resistance of the excitation windings
rQ1	R1q	Resistance of the quadrature axis 1st damper
rQ2	R2q	Resistance of the quadrature axis 2nd damper
MdPu	Lad	Direct axis mutual inductance
MqPu	Laq	Quadrature axis mutual inductance
LdPu	Ll	Direct axis stator leakage
LqPu	Ll	Quadrature axis stator leakage
LDPu	L1d	Direct axis damper leakage
LQ1Pu	L1q	Quadrature axis 1st damper leakage
LQ2Pu	L2q	Quadrature axis 2nd damper leakage
LfPu	Lfd	Excitation winding leakage
mrcPu	Lfld-Lad	Canay's mutual inductance

Two different choices of base excitation voltage are available

Types.ExcitationPuType.nominalStatorVoltageNoLoad: 1 p.u. of excitation voltage gives 1 p.u. of air-gap stator voltage at no-load conditions
Types.ExcitationPuType.Kundur: base voltage as in Kundur, Power Systems Stability and Control, Chapter 3. Note that in this case, typical p.u. values are less than 0.001

Parameters

Type	Name	Default	Description
Types.Voltage	UNom (from OnePortAC)		Nominal/rated line-to-line voltage
Types.ApparentPower	SNom (from OnePortAC)		Nominal/rated apparent power
Boolean	portVariablesPhases (from OnePortAC)	false	Compute voltage and current phases for monitoring purposes only
Boolean	portVariablesPu (from OnePortAC)	true	Add per-unit variables to model
Boolean	generatorConvention (from OnePortAC)	false	Add currents with generator convention (i > 0 when exiting the device) to model
LocalInitializationOption	localInit (from OnePortAC)	LocalInitializationOption.none	Initialize the component locally in steady state from port start values
SI.Angle	thetaStart (from OnePortACdqPU)	UPhaseStart	Start value of rotation between machine rotor frame and port phasor frame
Types.PerUnit	udPuStart (from OnePortACdqPU)		Start value of udPu
Types.PerUnit	uqPuStart (from OnePortACdqPU)		Start value of uqPu
Types.PerUnit	idPuStart (from OnePortACdqPU)		Start value of idPu
Types.PerUnit	iqPuStart (from OnePortACdqPU)		Start value of iqPu
Types.ActivePower	PNom	SNom	Nominal active (turbine) power
Types.PerUnit	raPu		Armature resistance in p.u.
Types.PerUnit	LdPu		Direct axis stator leakage in p.u.
Types.PerUnit	MdPu		Direct axis mutual inductance in p.u.
Types.PerUnit	mrcPu		Canay's mutual inductance in p.u.
Types.PerUnit	LDPu		Direct axis damper leakage in p.u.
Types.PerUnit	rDPu		Resistance of the direct axis damper in p.u.
Types.PerUnit	LfPu		Excitation winding leakage in p.u.
Types.PerUnit	rfPu		Resistance of the excitation windings in p.u.
Types.PerUnit	LqPu		Quadrature axis stator leakage in p.u.
Types.PerUnit	MqPu		Quadrature axis mutual inductance in p.u.
Types.PerUnit	LQ1Pu		Quadrature axis 1st damper leakage in p.u.
Types.PerUnit	rQ1Pu		Quadrature axis 2nd damper leakage in p.u.
Types.PerUnit	LQ2Pu		Leakage of quadrature axis 2nd damper in p.u.
Types.PerUnit	rQ2Pu		Resistance of quadrature axis 2nd damper in p.u.
Types.PerUnit	DPu	0	Damping coefficient of the swing equation in p.u.
Modelica.SIunits.Time	H		Kinetic constant = kinetic energy / rated power
Types.Choices.ExcitationPuType	excitationPuType	PowerGrids.Types.Choices.ExcitationPuType.nominalStatorVoltageNoLoad	Choice of excitation base voltage
Boolean	neglectTransformerTerms	true	Neglect the transformer terms in the Park equations
Boolean	referenceGenerator	false	True if reference generator in an isolated synchronous system
Types.Choices.InitializationOption	initOpt	systemPowerGrids.initOpt	Initialization option
SI.AngularVelocity	omegaBase	systemPowerGrids.omegaNom	Base angular frequency value
Types.PerUnit	kuf		Scaling factor for excitation p.u. voltage
Types.PerUnit	omegaNomPu	1	Nominal frequency in p.u.
Types.PerUnit	lambdadPuStart		Start value of lambdadPu
Types.PerUnit	lambdaqPuStart		Start value of lambdaqPu
Types.PerUnit	ufPuStart		Start value of exciter voltage in p.u. (Kundur base)
Types.PerUnit	ufPuInStart		Start value of input exciter voltage in p.u. (user-selcted base
Types.PerUnit	ifPuStart		Start value of ifPu
Initialization
Types.Voltage	UStart (from OnePortAC)	UNom	Start value of phase-to-phase voltage phasor, absolute value
Types.Angle	UPhaseStart (from OnePortAC)	0	Start value of phase-to-phase voltage phasor, phase angle
Types.ActivePower	PStart (from OnePortAC)	SNom	Start value of active power flowing into the port
Types.ReactivePower	QStart (from OnePortAC)	0	Start value of reactive power flowing into the port

Connectors

Type	Name	Description
PowerGrids.Interfaces.TerminalAC	terminal (from OnePortAC)
Modelica.Blocks.Interfaces.RealInput	PmPu	Input mechanical power in p.u. (base PNom)
Modelica.Blocks.Interfaces.RealInput	ufPuIn	Input voltage of exciter winding in p.u. (user-selected base voltage)
Modelica.Blocks.Interfaces.RealOutput	omega	Angular frequency in rad/s for system object
Modelica.Blocks.Interfaces.RealOutput	omegaPu	Angular frequency in p.u.
Modelica.Blocks.Interfaces.RealOutput	VPu	Port voltage magnitude [pu]
Modelica.Blocks.Interfaces.RealOutput	PPu	Active Power Production [pu base PNom]

Components

Type	Name	Default	Description
PortAC	port (from OnePortAC)		AC port of node
Electrical.System	systemPowerGrids (from OnePortAC)		Reference to system object
Types.PerUnit	udPu (from OnePortACdqPU)		Voltage of direct axis in p.u.
Types.PerUnit	uqPu (from OnePortACdqPU)		Voltage of quadrature axis in p.u.
Types.PerUnit	idPu (from OnePortACdqPU)		Current of direct axis in p.u.
Types.PerUnit	iqPu (from OnePortACdqPU)		Current of quadrature axis in p.u.
Types.Angle	theta (from OnePortACdqPU)		Rotation between machine rotor frame and port phasor frame
Types.PerUnit	iDPu		Current of direct axis damper in p.u
Types.PerUnit	ifPu		Current of excitation winding in p.u.
Types.PerUnit	iQ1Pu		Current of quadrature axis 1st damper in p.u.
Types.PerUnit	iQ2Pu		Current of quadrature axis 2nd damper in p.u.
Types.PerUnit	ufPu		Voltage of exciter winding in p.u. (base voltage as per Kundur)
Types.PerUnit	lambdadPu		Flux of direct axis in p.u.
Types.PerUnit	lambdaqPu		Flux of quadrature axis in p.u.
Types.PerUnit	lambdaDPu		Flux of direct axis damper in p.u
Types.PerUnit	lambdafPu		Flux of excitation winding in p.u.
Types.PerUnit	lambdaQ1Pu		Flux of quadrature axis 1st damper in p.u.
Types.PerUnit	lambdaQ2Pu		Flux of quadrature axis 1st damper in p.u.
Types.PerUnit	omegaRefPu	systemPowerGrids.omegaRef/systemPowerGrids.omegaNom	Reference frequency in p.u.
Types.PerUnit	CmPu		Mechanical torque in p.u. (base PNom/omegaBase)
Types.PerUnit	CePu		Electrical torque in p.u. (base SNom/omegaBase)
Types.PerUnit	PePu		Electrical power in p.u. (base SNom)
Types.PerUnit	PePuPNom	PePu*SNom/PNom	Electrical active power in p.u. (base PNom)
Types.Frequency	f	systemPowerGrids.fNom*omegaPu	Frequency of rotation of d-q axes