modelSM_3ph

Simple three-phase synchronous machine

Extends from ComplexLib.Machines.Interfaces.PartialBasicElectricMachine3ph_wBalance (Basic model for three-phase electric machines (using current phasor balance, but no power calculation)).

Information

This approximation of a three-phase synchronous machine using phasor domain for the electrical subsystem is based on the behaviour of the steady-state equivalent circuit of such a machine. This behaviour is defined by appropriate equations. The machine is an extension of the partial Interface package model PartialBasicElectricMachine3ph_wBalance of an electric three-phase machine including the current balances.
The model has two electrical connectors of type ComplexPlug (which correspond to six connectors of type ComplexPin) and one mechanical rotational flange. The stator is assumed to be fixed in the housing.

The electrical submodel has three phases if the default value of the 'number of phases'-parameter m is used. In order to model a system with different number of phases, the 'number of phases'-parameter has to be changed in all appearing multi-phase components and connectors.
Each phase consists of a constant inductance (stator's self-inductance) and an electromagnetic force (emf) realising the effect of the rotor current on the stator via the mutual inductance. All inductances are assumed to be ideal (electrically linear, no saturation).
The mechanical submodel contains a shaft which is fixed to the rotor.

Using this model, one can carry out steady-state or quasi-stationary investigations of the electrical subsystem. The mechanical subsystem may show transient behaviour which must be sufficiently slow.

Attention!!!
To ensure that the phasor domain-based model works in a quasi-stationary mode, the torque angle δ (also called rotor displacement angle) may alter only very slowly in comparison with both the nominal frequency f=ω/(2π) and the dominant time constant of the electrical subsystem.

Main Author:
Olaf Enge-Rosenblatt
Fraunhofer IIS/EAS, Dresden
email: olaf.enge@eas.iis.fraunhofer.de

Parameters

TypeNameDefaultDescription
Modelica.SIunits.InertiaJ_Rotor (from PartialBasicMachine)1Rotor's moment of inertia
Integerm (from PartialBasicElectricMachine3ph_wBalance)3Number of phases
Integerp1Number of poles
SI.InductanceLs0.01Stator inductance per phase
SI.InductanceLm0.009Mutual inductance per phase
SI.VoltageVr1Dc voltage at rotor
SI.ResistanceRr1Rotor resistance
Realeps1e-12To avoid division by zero
Integerk1Phase index

Connectors

TypeNameDefaultDescription
Modelica.Mechanics.Rotational.Interfaces.Flange_ashaft (from PartialBasicMachine)Flange at shaft
ComplexLib.MultiPhase.Interfaces.PosComplexPlugplug_p (from PartialBasicElectricMachine3ph_wBalance)Positive complex plug
ComplexLib.MultiPhase.Interfaces.NegComplexPlugplug_n (from PartialBasicElectricMachine3ph_wBalance)Negative complex plug
Modelica.Blocks.Interfaces.RealOutputTrq_electricalElectrically produced torque

Components

TypeNameDefaultDescription
Modelica.Mechanics.Rotational.Components.InertiainertiaRotor (from PartialBasicMachine)
Modelica.Mechanics.Rotational.Components.FixedfixedHousing (from PartialBasicMachine)
SI.Voltage[m]v (from PartialBasicElectricMachine3ph_wBalance)Voltages between the two plugs
SI.Voltage[m]vRe (from PartialBasicElectricMachine3ph_wBalance)Active parts of voltage phasors
SI.Voltage[m]vIm (from PartialBasicElectricMachine3ph_wBalance)Reactive parts of voltage phasors
SI.Current[m]i (from PartialBasicElectricMachine3ph_wBalance)Currents flowing into positive plug
SI.Current[m]iRe (from PartialBasicElectricMachine3ph_wBalance)Active parts of current phasors
SI.Current[m]iIm (from PartialBasicElectricMachine3ph_wBalance)Reactive parts of current phasors
SI.CurrentIrRotor current
SI.VoltageEfMutual voltage source, depending on rotor current and angular difference between shaft and field
SI.AngularFrequencyomegaNAngular frequency of net voltage
SI.AngularFrequencyomegaFieldAngular frequency of field
SI.AngularFrequencyomegaMechAngular velocity of rotor
RealvSumSum of rms values of voltages of all phases
SI.TorqueTpPull-out (maximum) torque
SI.AnglegammaAngular difference between shaft and field
SI.AngledeltaTorque angle
SI.TorqueTrqTorque produced electrically
SI.PowerP_mechMechanical power
SI.ResistanceXsStator (or synchronous) reactance
SI.ResistanceXmMain reactance
SI.Anglephase_VsPhase of first stator voltage
SI.Anglephase_IsPhase of first stator current
SI.Anglephase_EfPhase of back-emf voltage
SI.AnglephasePhase of stator voltage with respect to stator current
SI.AnglephiNAngle of net voltage
SI.AnglephiFieldAngle of rotating field
SI.AnglephiMechAngle of shaft
ComplexLib.Machines.Interfaces.AirGapairgap