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Flux-Based PMSM

Flux-based permanent magnet synchronous motor

  • Library:
  • Powertrain Blockset / Propulsion / Electric Motors

Description

The Flux-Based PMSM block implements a flux-based three-phase permanent magnet synchronous motor (PMSM) with a tabular-based electromotive force. The block uses the three-phase input voltages to regulate the individual phase currents, allowing control of the motor torque or speed.

Flux-based motor models take into account magnetic saturation and iron losses. To calculate the magnetic saturation and iron loss, the Flux-Based PMSM block uses the inverse of the flux linkages. To obtain the block parameters, you can use finite-element analysis (FEA) or measure phase voltages using a dynamometer.

Three-Phase Sinusoidal Model Electrical System

The block implements equations that are expressed in a stationary rotor reference (dq) frame. The d-axis aligns with the a-axis. All quantities in the rotor reference frame are referred to the stator.

The block uses these equations.

CalculationEquation
q- and d-axis voltagevd=dψddt+Rsidωeψqvq=dψqdt+Rsiq+ωeψd
q- and d-axis currentid=f(ψd,ψq)iq=g(ψd,ψq)
Electromechanical torqueTe=1.5P[ψdiqψqid]

The equations use these variables.

ωm

Rotor mechanical speed

ωe

Rotor electrical speed

Θda

dq stator electrical angle with respect to the rotor a-axis

Rs, Rr

Resistance of the stator and rotor windings, respectively

iq, id

q- and d-axis current, respectively

vq, vd

q- and d-axis voltage, respectively

Ψq, Ψd

q- and d-axis magnet flux, respectively

P

Number of pole pairs

Te

Electromagnetic torque

Transforms

To calculate the voltages and currents in balanced three-phase (a, b) quantities, quadrature two-phase (α, β) quantities, and rotating (d, q) reference frames, the block uses the Clarke and Park Transforms.

In the transform equations.

ωe=Pωmdθedt= ωe

TransformDescriptionEquations

Clarke

Converts balanced three-phase quantities (a, b) into balanced two-phase quadrature quantities (α, β).

xα= 23xa 13xb 13xcxβ= 32xb 32xc

Park

Converts balanced two-phase orthogonal stationary quantities (α, β) into an orthogonal rotating reference frame (d, q).

xd= xαcosθe+ xβsinθexq= xαsinθe+ xβcosθe

Inverse Clarke

Converts balanced two-phase quadrature quantities (α, β) into balanced three-phase quantities (a, b).

xa= xaxb= 12xα+ 32xβxc= 12xα 32xβ

Inverse Park

Converts an orthogonal rotating reference frame (d, q) into balanced two-phase orthogonal stationary quantities (α, β).

xα= xdcosθe xqsinθexβ= xdsinθe+ xqcosθe

The transforms use these variables.

ωm

Rotor mechanical speed

P

Motor pole pairs

ωe

Rotor electrical speed

Θe

Rotor electrical angle

x

Phase current or voltage

Mechanical System

The rotor angular velocity is given by:

ddtωm=1J(TeTfFωmTm)dθmdt=ωm

The equations use these variables.

J

Combined inertia of rotor and load

F

Combined viscous friction of rotor and load

θm

Rotor mechanical angular position

Tm

Rotor shaft torque

Te

Electromagnetic torque

Tf

Combined rotor and load friction torque

ωm

Rotor mechanical speed

Ports

Input

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Rotor shaft input torque, Tm, in N·m.

Dependencies

To create this port, select Torque for the Port Configuration parameter.

Angular velocity of the rotor, ωm, in rad/s.

Dependencies

To create this port, select Speed for the Port Configuration parameter.

Stator terminal voltages, Va, Vb, and Vc, in V.

Dependencies

To create this port, select Speed or Torque for the Port Configuration parameter.

Output

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The bus signal contains these block calculations.

Signal DescriptionVariableUnits

IaStator

Stator phase current A

ia

A

IbStator

Stator phase current B

ib

A

IcStator

Stator phase current C

ic

A

IdSync

d-axis current

id

A

IqSync

qaxis current

iq

A

VdSync

d-axis voltage

vd

V

VqSync

q-axis axis voltage

vq

V

MtrSpd

Angular mechanical velocity of the rotor

ωm

rad/s

MtrPos

Rotor mechanical angular position

θm

rad

MtrTrq

Electromagnetic torque

Te

N·m

Parameters

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This table summarizes the port configurations.

Port ConfigurationCreates Ports

Torque

LdTrq

PhaseVolt

Info

Speed

Spd

PhaseVolt

Info

Stator phase resistance, Rs, in ohm.

d-axis flux, Ψd, in Wb.

q-axis flux, Ψq, in Wb.

d-axis current, id, in A.

q-axis current, iq, in A.

Motor pole pairs, P.

Initial d- and q-axis flux, Ψq0 and Ψd0, in Wb.

Initial rotor angular position, θm0, in rad.

Initial angular velocity of the rotor, ωm0, in rad/s.

Dependencies

To enable this parameter, select the Torque configuration parameter.

Mechanical properties of the rotor:

  • Inertia, J, in kgm^2

  • Viscous damping, F, in N·m/(rad/s)

  • Static friction, Tf, in N·m

Dependencies

To enable this parameter, select the Torque configuration parameter.

References

[1] Hu, Dakai, Yazan Alsmadi, and Longya Xu. “High fidelity nonlinear IPM modeling based on measured stator winding flux linkage.” IEEE® Transactions on Industry Applications, Vol. 51, No. 4, July/August 2015.

[2] Chen, Xiao, Jiabin Wang, Bhaskar Sen, Panagiotis Lasari, Tianfu Sun. “A High-Fidelity and Computationally Efficient Model for Interior Permanent-Magnet Machines Considering the Magnetic Saturation, Spatial Harmonics, and Iron Loss Effect.” IEEE Transactions on Industrial Electronics, Vol. 62, No. 7, July 2015.

Introduced in R2017b