PMSM

Permanent magnet synchronous motor (SDPM) with sinusoidal anti-EMF design.

blockType: AcausalElectricPowerSystems.Electromechanical.PMSM.ThreePhase

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/Physical Modeling/Electrical/Electromechanical/Permanent Magnet/PMSM

Description

Block PMSM simulates a synchronous motor with permanent magnets on a rotor and a three-phase stator with a winding connection according to the scheme «star» or «triangle» with a sinusoidal anti-EMF shape. The figure shows an equivalent electrical circuit for the stator windings.:

permanent magnet 1

You can also simulate the SDPM in the configuration «triangle» or «star» by setting the parameter Winding type in the value Delta-wound or Wye-wound accordingly.

Engine design

The permanent magnets of the rotor create a magnetic field that varies according to a sinusoidal law.

permanent magnet 2

If set for the parameter Rotor angle definition meaning Angle between the a-phase magnetic axis and the d-axis, then at zero mechanical angle of the rotor the flows of phase A and permanent magnets are aligned. When setting the parameter Rotor angle definition in the value Angle between the a-phase magnetic axis and the q-axis The mechanical angle of the rotor is equal to the angle between the magnetic axis of phase A and the q axis of the rotor.

The equations

Voltage across the stator windings:

where

, , — voltage of the stator windings;
— the equivalent resistance of each stator winding;
, , — currents in the winding;
, , — flow coupling differentials of the stator windings.

The flow coupling in the stator is created by two sources: the flow from the permanent magnets of the rotor and the currents in the inductance of the stator. Thus:

where

— flow coupling of the stator windings;
, , — intrinsic inductors of the stator phases;
, , etc. — mutual inductors between the phases of the stator;
, , — flow coupling of the permanent magnet with the corresponding phases of the stator.

The inductors of the stator windings are functions of the electric angle of the rotor and are determined as follows:

where

— mechanical angle of the rotor;
— electric angle of the rotor;
— equal to 0 if the electric angle of the rotor is set relative to the axis , or −π/2 if the electric angle of the rotor is set relative to the axis ;
— the intrinsic inductance of the stator winding. This value is the average value of the inductance of each of the stator windings.;
— oscillation of the stator inductance. Fluctuations of intrinsic inductors ( , , ) stator windings and mutual inductance fluctuations ( , , The difference between each two stator windings depends on the change in the angle of the rotor and always has the same value, i.e. ;
— mutual inductance of the stator windings. The value is the average value of the mutual inductance between the stator windings ( , , ).

Flow coupling of the permanent magnet of the phase winding maximum when and is equal to zero when . Thus, the flow coupling of the engine is determined by:

where — flow coupling of a permanent magnet.

Simplified electrical equations

Applying the Park–Gorev transformation to a block of electrical equations allows us to obtain an expression for a torque that does not depend on the angle of rotation of the rotor.

The Park–Gorev transformation is defined as follows:

where

— the electric angle, defined as ;
— the number of pairs of poles.

Applying the Park—Gorev transformation to the voltages and currents of the stator windings leads them to a coordinate system , which does not depend on the angle of rotation of the rotor:

Applying the Park—Gorev transformation to the first two electrical equations allows us to move on to other equations that determine the behavior of the block.:

where

— axis inductance the stator;
— axis inductance the stator;
— inductance of the zero sequence of the stator;
— mechanical speed of rotation of the rotor;
— the number of pairs of rotor poles;
— the torque of the rotor. The torque is transmitted from the motor housing (block port ) to the motor rotor (block port ).

In the block PMSM The original, non–orthogonal implementation of the Park-Gorev transformation is used.

Alternative parameterization of flow coupling

In addition to the direct method of setting the flux coupling value of a permanent magnet, there are other parameterization options.

You can adjust the engine parameters using the anti-EMF or torque, which are most often specified in the technical data sheets of engines using the parameter Permanent magnet flux linkage.

The EMF coefficient is the peak voltage generated by a permanent magnet per unit rotation speed of each of the phases. The relationship between the peak flux coupling of a permanent magnet and the counter-EMF has the form:

Anti-EMF for one phase it is:

The torque constant is the peak torque induced by the unit current of each phase. It is numerically identical to the EMF coefficient if both values are expressed in SI units.:

When if the currents in all three phases are balanced, then the total torque of the rotor is equal to:

where — peak current in any of the three windings.

Ratio it follows from the fact that in steady state it is the sum of the moments from all phases. Therefore, the torque constant It can also be:

where — measured total torque during balanced three-phase current tests with peak line voltage . The RMS value of the linear current is:

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# R — engine rotor
rotational mechanics

Details

A mechanical rotation port connected to the motor rotor.

Program usage name

rod_flange

# C — engine housing
rotational mechanics

Details

A mechanical rotation port connected to the motor housing.

Program usage name

case_flange

# ~ — three-phase port
electricity

Details

Expandable three-phase port.

Program usage name

port

# n — neutral
electricity

Details

The electrical port connected to the neutral.

Dependencies

To use this port, install Winding type in the value Wye-wound and Zero sequence (null sequence) in the value Include.

Program usage name

n

Parameters

Main

# Winding type — configuration of windings
Wye-wound | Delta-wound

Details

Select the winding configuration:

Wye-wound — star connection.
Delta-wound — triangle connection. Phase connects between ports A and B, phase — between ports b and c, phase — between ports c and a.

Values	`Wye-wound` \| `Delta-wound`
Default value	`Wye-wound`
Program usage name	`winding_type`
Evaluatable	No

# Modeling fidelity — the method of setting machine parameters
Constant Ld, Lq and PM

Details

Choose a method for setting machine parameters:

Constant Ld, Lq and PM — values , and they are constant and are determined by the appropriate parameters.

Values	`Constant Ld, Lq and PM`
Default value	`Constant Ld, Lq and PM`
Program usage name	`machine_parameterization`
Evaluatable	No

# Number of pole pairs — number of pairs of poles

Details

The number of pairs of rotor poles.

Default value	`6`
Program usage name	`N_pole_pairs`
Evaluatable	Yes

# Permanent magnet flux linkage parameterization — parameterization of the flux coupling of permanent magnets
Specify flux linkage | Specify torque constant | Specify back EMF constant

Details

Choose Specify flux linkage, Specify torque constant or Specify back EMF constant.

Values	`Specify flux linkage` \| `Specify torque constant` \| `Specify back EMF constant`
Default value	`Specify flux linkage`
Program usage name	`flux_parameterization`
Evaluatable	No

# Permanent magnet flux linkage — flow coupling with permanent magnets
Wb | mN*m/A | N*m/A | kN*m/A | kgf*m/A

Details

The peak value of the flux coupling of a permanent magnet with any of the stator windings.

Dependencies

To use this parameter, set for the parameter Permanent magnet flux linkage parameterization meaning Specify flux linkage and for the parameter Modeling fidelity meaning Constant Ld, Lq and PM.

Units	`Wb` \| `mNm/A` \| `Nm/A` \| `kNm/A` \| `kgfm/A`
Default value	`0.03 Wb`
Program usage name	`pm_flux_linkage`
Evaluatable	Yes

# Torque constant — the torque constant
Wb | mN*m/A | N*m/A | kN*m/A | kgf*m/A

Details

The torque constant for any of the stator windings.

Dependencies

To use this parameter, set for the parameter Permanent magnet flux linkage parameterization meaning Specify torque constant and for the parameter Modeling fidelity meaning Constant Ld, Lq and PM.

Units	`Wb` \| `mNm/A` \| `Nm/A` \| `kNm/A` \| `kgfm/A`
Default value	`0.18 N*m/A`
Program usage name	`torque_constant`
Evaluatable	Yes

# Back EMF constant — the anti-EMF ratio
V/rpm | V/(rad/s)

Details

The EMF coefficient for any of the stator windings.

The EMF coefficient is the peak voltage of each of the phases generated by a permanent magnet per unit rotation speed.

Dependencies

To use this parameter, set for the parameter Permanent magnet flux linkage parameterization meaning Specify back EMF constant and for the parameter Modeling fidelity meaning Constant Ld, Lq and PM.

Units	`V/rpm` \| `V/(rad/s)`
Default value	`0.18 V/(rad/s)`
Program usage name	`back_emf_constant`
Evaluatable	Yes

# Stator parameterization — parameterization of the stator
Specify Ld, Lq, and L0 | Specify Ls, Lm, and Ms

Details

The method of parameterization of the stator.

Choose Specify Ld, Lq, and L0 or Specify Ls, Lm, and Ms.

Values	`Specify Ld, Lq, and L0` \| `Specify Ls, Lm, and Ms`
Default value	`Specify Ld, Lq, and L0`
Program usage name	`stator_parameterization`
Evaluatable	No

# Stator d-axis inductance Ld — inductance along the d axis of the stator
H | nH | uH | mH

Details

The inductance along the d axis.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ld, Lq, and L0 and for the parameter Modeling fidelity meaning Constant Ld, Lq and PM.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.00019 H`
Program usage name	`L_d`
Evaluatable	Yes

# Stator q-axis inductance, Lq — inductance along the q axis of the stator
H | nH | uH | mH

Details

The inductance along the q axis.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ld, Lq, and L0 and for the parameter Modeling fidelity meaning Constant Ld, Lq and PM.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.00025 H`
Program usage name	`L_q`
Evaluatable	Yes

# Stator zero-sequence inductance, L0 — inductance of the zero sequence of the stator
H | nH | uH | mH

Details

The inductance of the zero sequence.

Dependencies

To use this parameter, set:

for the parameter Winding type meaning Wye-wound, for the parameter Zero sequence meaning Include, and for the parameter Stator parameterization meaning Specify Ld, Lq, and L0.
for the parameter Winding type meaning Delta-wound, and for the parameter Stator parameterization meaning Specify Ld, Lq, and L0.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.00016 H`
Program usage name	`L_0`
Evaluatable	Yes

# Stator self-inductance per phase, Ls — intrinsic phase inductance of the stator
H | nH | uH | mH

Details

The intrinsic phase inductance of the stator.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ls, Lm, and Ms.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.0002 H`
Program usage name	`L_s`
Evaluatable	Yes

# Stator inductance fluctuation, Lm — fluctuations in stator inductance
H | nH | uH | mH

Details

It is taken into account that the self-induction and mutual induction of the stator windings change with a change in the angle of rotation of the rotor.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ls, Lm, and Ms.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`-2e-05 H`
Program usage name	`L_m`
Evaluatable	Yes

# Stator mutual inductance, Ms — mutual inductance of the stator
H | nH | uH | mH

Details

The average mutual inductance between the stator windings.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ls, Lm, and Ms.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`2e-05 H`
Program usage name	`M_s`
Evaluatable	Yes

# Stator resistance per phase, Rs — stator phase resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Stator phase resistance.

Dependencies

To use this parameter, set for the parameter Stator parameterization meaning Specify Ls, Lm, and Ms.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.013 Ohm`
Program usage name	`R_s`
Evaluatable	Yes

# Zero sequence — zero sequence option
Exclude | Include

Details

The option to enable or exclude a null sequence.

Include — enables parameters with a zero sequence. Use this default setting to prioritize model accuracy.
Exclude — eliminates the conditions of the zero sequence. To increase the simulation speed for desktop simulation or real-time deployment, select this option.

Dependencies

This parameter is used if for the parameter Winding type the value is set Wye-wound.

Values	`Exclude` \| `Include`
Default value	`Include`
Program usage name	`zero_sequence`
Evaluatable	No

# Rotor angle definition — a reference point for measuring the rotation angle of the rotor
Angle between the a-phase magnetic axis and the d-axis | Angle between the a-phase magnetic axis and the q-axis

Details

A reference point for measuring the rotation angle of the rotor.

When selecting a value Angle between the a-phase magnetic axis and the d-axis The rotor fluxes and phases coincide when the rotation angle of the rotor is zero.

When selecting a value Angle between the a-phase magnetic axis and the q-axis The phase current A creates the maximum torque when the rotation angle of the rotor is zero.

Values	`Angle between the a-phase magnetic axis and the d-axis` \| `Angle between the a-phase magnetic axis and the q-axis`
Default value	`Angle between the a-phase magnetic axis and the d-axis`
Program usage name	`axes_parameterization`
Evaluatable	No

Mechanical

Details

Inertia of the rotor connected to the mechanical port R. The value can be zero.

Units	`kgm^2` \| `gm^2` \| `kgcm^2` \| `gcm^2` \| `lbmin^2` \| `lbmft^2` \| `slugin^2` \| `slugft^2`
Default value	`0.01 kg*m^2`
Program usage name	`J`
Evaluatable	Yes

# Rotor damping — rotor damping
N*m*s/rad | mN*m*s/rad | kN*m*s/rad | kgf*m*s/rad | lbf*ft*s/rad

Details

Damping during rotation.

Units	`Nms/rad` \| `mNms/rad` \| `kNms/rad` \| `kgfms/rad` \| `lbffts/rad`
Default value	`0.0 Nms/rad`
Program usage name	`D`
Evaluatable	Yes

PMSM

Description

Engine design

The equations

Simplified electrical equations

Alternative parameterization of flow coupling

Variables

Ports

Conserving

Parameters

Main

Mechanical

Examples