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PMSM

Permanent magnet synchronous motor with sinusoidal flux distribution

Libraries:
Simscape / Electrical / Electromechanical / Permanent Magnet

Description

The PMSM block models a permanent magnet synchronous motor with a three-phase wye-wound stator. The figure shows the equivalent electrical circuit for the stator windings.

You can choose different built-in parameterizations for this block. For more information, see the Predefined Parameterization section.

Motor Construction

This figure shows the motor construction with a single pole-pair on the rotor.

Permanent magnets generate a rotor magnetic field that creates a sinusoidal rate of change of flux based on the rotor angle.

For the axes convention, when you set the Rotor angle definition parameter to Angle between the a-phase magnetic axis and the d-axis, the a-phase and permanent magnet fluxes align when the rotor mechanical angle, θ_r, is zero. When you set the Rotor angle definition parameter to Angle between the a-phase magnetic axis and the q-axis, the rotor mechanical angle is the angle between the a-phase magnetic axis and the rotor q-axis.

Equations

Voltages across the stator windings are

$[\begin{matrix} v_{a} \\ v_{b} \\ v_{c} \end{matrix}] = [\begin{matrix} R_{s} & 0 & 0 \\ 0 & R_{s} & 0 \\ 0 & 0 & R_{s} \end{matrix}] [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}] + [\begin{matrix} \frac{d ψ_{a}}{d t} \\ \frac{d ψ_{b}}{d t} \\ \frac{d ψ_{c}}{d t} \end{matrix}],$

where:

v_a, v_b, and v_c are the individual phase voltages across the stator windings.
R_s is the equivalent resistance of each stator winding.
i_a, i_b, and i_c are the currents flowing in the stator windings.
$\frac{d ψ_{a}}{d t},$ $\frac{d ψ_{b}}{d t},$ and $\frac{d ψ_{c}}{d t}$ are the rates of change for the magnetic flux in each stator winding.

The permanent magnet and the three windings contribute to the total flux linking each winding. The total flux is

$[\begin{matrix} ψ_{a} \\ ψ_{b} \\ ψ_{c} \end{matrix}] = [\begin{matrix} L_{a a} & L_{a b} & L_{a c} \\ L_{b a} & L_{b b} & L_{b c} \\ L_{c a} & L_{c b} & L_{c c} \end{matrix}] [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}] + [\begin{matrix} ψ_{a m} \\ ψ_{b m} \\ ψ_{c m} \end{matrix}],$

where:

ψ_a, ψ_b, and ψ_c are the total fluxes linking each stator winding.
L_aa, L_bb, and L_cc are the self-inductances of the stator windings.
L_ab, L_ac, L_ba, and so on, are the mutual inductances of the stator windings.
ψ_am, ψ_bm, and ψ_cm are the permanent magnet fluxes linking the stator windings.

The inductances in the stator windings are functions of the rotor electrical angle and defined by

$θ_{e} = N θ_{r} + r o t o r o f f s e t$

$L_{a a} = L_{s} + L_{m} cos (2 θ_{e})$

$L_{b b} = L_{s} + L_{m} cos (2 (θ_{e} - 2 π / 3))$

$L_{c c} = L_{s} + L_{m} cos (2 (θ_{e} + 2 π / 3))$

$L_{a b} = L_{b a} = - M_{s} - L_{m} \cos (2 (θ_{e} + π / 6))$

$L_{b c} = L_{c b} = - M_{s} - L_{m} \cos (2 (θ_{e} + π / 6 - 2 π / 3))$

$L_{c a} = L_{a c} = - M_{s} - L_{m} \cos (2 (θ_{e} + π / 6 + 2 π / 3))$

where:

θ_r is the rotor mechanical angle.
θ_e is the rotor electrical angle.
rotor offset is 0 if you define the rotor electrical angle with respect to the d-axis, or -pi/2 if you define the rotor electrical angle with respect to the q-axis.
L_s is the stator self-inductance per phase. This value is the average self-inductance of each of the stator windings.
L_m is the stator inductance fluctuation. This value is the amount the self-inductance and mutual inductance fluctuate with the changing of the rotor angle.
M_s is the stator mutual inductance. This value is the average mutual inductance between the stator windings.

The permanent magnet flux linking winding a is a maximum when θ_e = 0° and zero when θ_e = 90°. Therefore, the linked motor flux is defined by:

$[\begin{matrix} ψ_{a m} \\ ψ_{b m} \\ ψ_{c m} \end{matrix}] = [\begin{matrix} ψ_{m} \cos θ_{e} \\ ψ_{m} \cos (θ_{e} - 2 π / 3) \\ ψ_{m} \cos (θ_{e} + 2 π / 3) \end{matrix}]$

where ψ_m is the permanent magnet flux linkage.

Simplified Electrical Equations

Applying Park’s transformation to the block electrical equations produces an expression for torque that is independent of the rotor angle.

Park’s transformation is defined by:

$P = 2 / 3 [\begin{matrix} \cos θ_{e} & \cos (θ_{e} - 2 π / 3) & \cos (θ_{e} + 2 π / 3) \\ - \sin θ_{e} & - \sin (θ_{e} - 2 π / 3) & - \sin (θ_{e} + 2 π / 3) \\ 0.5 & 0.5 & 0.5 \end{matrix}]$

where θ_e is the electrical angle defined as Nθ_r. N is the number of pole pairs.

Using Park's transformation on the stator winding voltages and currents transforms them to the dq0 frame, which is independent of the rotor angle:

$[\begin{matrix} v_{d} \\ v_{q} \\ v_{0} \end{matrix}] = P [\begin{matrix} v_{a} \\ v_{b} \\ v_{c} \end{matrix}]$

$[\begin{matrix} i_{d} \\ i_{q} \\ i_{0} \end{matrix}] = P [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}]$

Applying Park’s transformation to the first two electrical equations produces these equations that define the block behavior:

$v_{d} = R_{s} i_{d} + L_{d} \frac{d i_{d}}{d t} - N ω i_{q} L_{q}$

$v_{q} = R_{s} i_{q} + L_{q} \frac{d i_{q}}{d t} + N ω (i_{d} L_{d} + ψ_{m})$

$v_{0} = R_{s} i_{0} + L_{0} \frac{d i_{0}}{d t}$

$T = \frac{3}{2} N (i_{q} (i_{d} L_{d} + ψ_{m}) - i_{d} i_{q} L_{q})$

where:

L_d = L_s + M_s + 3/2 L_m. L_d is the stator d-axis inductance.
L_q = L_s + M_s − 3/2 L_m. L_q is the stator q-axis inductance.
L₀ = L_s – 2M_s. L₀ is the stator zero-sequence inductance.
ω is the rotor mechanical rotational speed.
N is the number of rotor permanent magnet pole pairs.
T is the rotor torque. Torque flows from the motor case (block physical port C) to the motor rotor (block physical port R).

The PMSM block uses the original, non-orthogonal implementation of the Park transform. If you try to apply the alternative implementation, you get different results for the dq0 voltage and currents.

Alternative Flux Linkage Parameterization

You can parameterize the motor using the back EMF or torque constants which are more commonly given on motor datasheets by using the Permanent magnet flux linkage parameter.

The back EMF constant is the peak voltage induced by the permanent magnet in the per-unit rotational speed of each of the phases. The relationship between the peak permanent magnet flux linkage and the back EMF is:

$k_{e} = N ψ_{m} .$

The back EMF, e_ph, for one phase is:

$e_{p h} = k_{e} ω .$

The torque constant is the peak torque induced by the per-unit current of each of the phases. It is numerically identical in value to the back EMF constant when both are expressed in SI units:

$k_{t} = N ψ_{m} .$

When L_d=L_q and the currents in all three phases are balanced, the combined torque T is:

$T = \frac{3}{2} k_{t} i_{q} = \frac{3}{2} k_{t} I_{p k},$

where I_pk is the peak current in any of the three windings.

The factor 3/2 follows from this being the steady-state sum of the torques from all phases. Therefore, the torque constant k_t can also be:

$k_{t} = \frac{2}{3} (\frac{T}{I_{p k}}),$

where T is the measured total torque when testing with a balanced three-phase current with peak line voltage I_pk. The RMS line current is:

$k_{t} = \frac{\sqrt{2}}{3} \frac{T}{i_{l i n e, r m s}} .$

Calculating Iron Losses

Iron losses are divided into two terms, one representing the main magnetizing path, and the other representing the cross-tooth tip path that becomes active during field weakened operation. The iron losses model, which is based on the work of Mellor [3].

The term representing the main magnetizing path depends on the induced RMS line-to-neutral stator voltage, $V_{m_{r m s}}^{}$ :

$P_{O C} (V_{m_{r m s}}^{}) = \frac{a_{h}}{k} V_{m_{r m s}}^{} + \frac{a_{j}}{k^{2}} V_{m_{r m s}}^{2} + \frac{a_{e x}}{k^{1.5}} V_{m_{r m s}}^{1.5}$

This is the dominant term during no-load operation. k is the back emf constant relating RMS volts per Hz. It is defined as $k = V_{m_{r m s}}^{} / f$ , where f is the electrical frequency. The first term on the right-hand side is the magnetic hysteresis loss, the second is the eddy current loss and the third is the excess loss. The three coefficients appearing on the numerators are derived from the values that you provide for the open-circuit hysteresis, eddy, and excess losses.

The term representing the cross-tooth tip path becomes important when a demagnetizing field is set up and can be determined from a finite element analysis short-circuit test. It depends on the RMS emf associated with the cross-tooth tip flux, $V_{d_{r m s}}^{*}$ :

$P_{S C} (V_{d_{r m s}}^{*}) = \frac{b_{h}}{k} V_{d_{r m s}}^{*} + \frac{b_{j}}{k^{2}} V_{d_{r m s}}^{* 2} + \frac{b_{e x}}{k^{1.5}} V_{d_{r m s}}^{* 1.5}$

The three numerator terms are derived from the values you provide for the short-circuit hysteresis, eddy, and excess losses.

Predefined Parameterization

There are multiple available built-in parameterizations for the PMSM block.

This pre-parameterization data allows you to set up the block to represent components by specific suppliers. The parameterizations of these permanent magnet synchronous motors match the manufacturer data sheets. To load a predefined parameterization, double-click the PMSM block, click the <click to select> hyperlink of the Selected part parameter and, in the Block Parameterization Manager window, select the part you want to use from the list of available components.

Note

The predefined parameterizations of Simscape™ components use available data sources for the parameter values. Engineering judgement and simplifying assumptions are used to fill in for missing data. As a result, expect deviations between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine component models as necessary.

For more information about pre-parameterization and for a list of the available components, see List of Pre-Parameterized Components.

Model Thermal Effects

You can expose thermal ports to model the effects of losses that convert power to heat. To expose the thermal ports, set the Modeling option parameter to either:

No thermal port — The block contains expanded electrical conserving ports associated with the stator windings, but does not contain thermal ports.
Show thermal port — The block contains expanded electrical conserving ports associated with the stator windings and thermal conserving ports for each of the windings and for the rotor.

For more information about using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. You can specify nominal values using different sources, including the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Electric Power Assisted Steering

Use a Permanent Magnet Synchronous Motor (PMSM) to amplify driver-applied force in a power-assisted automobile steering system.

Open Model

Faulted PMSM

Model a faulted permanent magnet synchronous motor (PMSM) using Simscape™ Electrical™. Normally when modeling a PMSM, you can represent each winding as a single entity with associated inductance, induced back electromotive force (EMF), and mutual inductive coupling to adjacent windings. However, when a winding fault occurs, the single entity assumption breaks down. To correctly capture the resulting dynamics, you have to model the motor at a winding slot level. This requires modeling in the magnetic domain.

Open Model

Three-Phase PMSM Drive

A Permanent Magnet Synchronous Machine (PMSM) in wye-wound and delta-wound configuration and an inverter sized for use in a typical hybrid vehicle. The inverter is connected directly to the vehicle battery, but you can also implement a DC-DC converter stage in between. You can use this model to design the PMSM controller, by selecting the architecture and gains to achieve the desired performance. To check the timing of IGBT turn-on and turn-off, you can replace the IGBT devices with the more detailed N-Channel IGBT block. For complete vehicle modeling, you can use the Motor & Drive (System Level) block to abstract the PMSM, inverter, and controller with an energy-based model. The Gmin resistor provides a very small conductance to ground that improves the numerical properties of the model when using a variable-step solver.

Open Model

Parameterize a Permanent Magnet Synchronous Motor

Estimate the back EMF and torque constants of a blackbox permanent magnet synchronous motor (PMSM) with an unknown flux linkage. You can use either the back EMF or torque constant to describe the flux linkage and parameterize a Simscape™ Electrical™ PMSM block. This parameterization allows you to accurately replicate the blackbox motor's behavior in simulation.

Open Model

Three-Phase PMSM Drive with Thermal Model

A Permanent Magnet Synchronous Machine (PMSM) and an inverter sized for use in a typical hybrid vehicle. The PMSM includes a thermal model and empirical iron losses. The inverter is connected directly to the vehicle battery, but you can also implement a DC-DC converter stage in between. You can use this model to design the PMSM controller, by selecting the architecture and the gains to achieve the desired performance. The initial temperature of the stator windings and rotor is set to 25 degrees Celsius. Ambient temperature is 27 degrees Celsius. The Scopes subsystem contains scopes that allow you to see the simulation results.

Open Model

Ports

Conserving

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~ — Three-phase port
electrical

Expandable three-phase port.

Dependencies

To enable this port, set Electrical connection to Composite three-phase ports.

a — a-phase
electrical

Electrical conserving port associated with a-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

b — b-phase
electrical

Electrical conserving port associated with b-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

c — c-phase
electrical

Electrical conserving port associated with c-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

n — Neutral phase
electrical

Electrical conserving port associated with the neutral phase.

Dependencies

To enable this port, set Winding Type to Wye-wound and Zero sequence to Include.

R — Motor rotor
mechanical

Mechanical rotational conserving port associated with the motor rotor.

C — Motor case
mechanical

Mechanical rotational conserving port associated with the motor case.

HA — Winding A thermal port
thermal

Thermal conserving port associated with winding A.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HB — Winding B thermal port
thermal

Thermal conserving port associated with winding B.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HC — Winding C thermal port
thermal

Thermal conserving port associated with winding C.

Dependencies

To enable this port, set Modeling option to Show thermal port.

HR — Rotor thermal port
thermal

Thermal conserving port associated with the rotor.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

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Selected part — Predefined parameterization option
`<click to select>` (default)

Option to parameterize the block to represent components by specific suppliers. Click the <click to select> hyperlink to open the Block Parameterization Manager window. For more information about the Block Parameterization Manager, see Load Predefined Parameterizations.

Modeling option — Whether to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Whether to enable the thermal ports of the block and model the effects of losses that convert power to heat.

Main

Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Whether to have composite or expanded three-phase ports.

Winding type — Windings configuration
`Wye-wound` (default) | `Delta-wound`

Select the configuration for the windings:

Wye-wound — The windings are wye-wound.
Delta-wound — The windings are delta-wound. The a-phase is connected between ports a and b, the b-phase between ports b and c and the c-phase between ports c and a.

Modeling fidelity — Modeling fidelity
`Constant Ld, Lq and PM` (default) | `Tabulated Ld, Lq and PM`

Select the modeling fidelity:

Constant Ld, Lq and PM — Ld, Lq and PM values are constant and defined by their respective parameters.
Tabulated Ld, Lq and PM — Ld, Lq and PM values are computed online from DQ currents look-up tables as follows:

$L_{d} = f_{1} (i_{d}, i_{q})$

$L_{d} = f_{2} (i_{d}, i_{q})$

$λ_{P M} = f_{2} (i_{d}, i_{q})$

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0.

Number of pole pairs — Number of pole pairs
`6` (default)

Number of permanent magnet pole pairs on the rotor.

Permanent magnet flux linkage parameterization — Permanent magnet flux linkage parameterization
`Specify flux linkage` (default) | `Specify torque constant` | `Specify back EMF constant`

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

Permanent magnet flux linkage — Permanent magnet flux linkage
`0.03` `Wb` (default)

Peak permanent magnet flux linkage with any of the stator windings.

Dependencies

To enable this parameter, set Permanent magnet flux linkage parameterization to Specify flux linkage and Modeling fidelity to Constant Ld, Lq and PM.

Torque constant — Torque constant
`0.18` `N*m/A` (default)

Torque constant with any of the stator windings.

Dependencies

To enable this parameter, set Permanent magnet flux linkage parameterization to Specify torque constant and Modeling fidelity to Constant Ld, Lq and PM.

Back EMF constant — Back EMF constant
`0.18` `V*s/rad` (default)

Back EMF constant with any of the stator windings.

Note

The back EMF constant is the peak voltage induced by the permanent magnet in the per-unit rotational speed of each of the phases.

Dependencies

To enable this parameter, set Permanent magnet flux linkage parameterization to Specify back EMF constant and Modeling fidelity to Constant Ld, Lq and PM.

Stator parameterization — Stator parameterization
`Specify Ld, Lq, and L0` (default) | `Specify Ls, Lm, and Ms`

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

Stator d-axis inductance, Ld — Stator d-axis inductance
`0.00022` `H` (default)

D-axis inductance.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Constant Ld, Lq and PM.

Stator q-axis inductance, Lq — Stator q-axis inductance
`0.00022` `H` (default)

Q-axis inductance.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Constant Ld, Lq and PM.

Direct-axis current vector, iD — Direct-axis current vector
`[-200, 0, 200]` `A` (default)

Direct-axis current vector, iD.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Tabulated Ld, Lq and PM.

Quadrature-axis current vector, iQ — Quadrature-axis current vector
`[-200, 0, 200]` `A` (default)

Quadrature-axis current vector, iQ.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Tabulated Ld, Lq and PM.

Ld matrix, Ld(id,iq) — Ld matrix
`0.0002 * ones(3, 3)` `H` (default)

Ld matrix.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Tabulated Ld, Lq and PM.

Lq matrix, Lq(id,iq) — Lq matrix
`0.0002 * ones(3, 3)` `H` (default)

Lq matrix.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ld, Lq, and L0 and Modeling fidelity to Tabulated Ld, Lq and PM.

Permanent magnet flux linkage, PM(id,iq) — Permanent magnet flux linkage
`0.1 * ones(3, 3)` `Wb` (default)

Permanent magnet flux linkage.

Dependencies

To enable this parameter, set:

Stator parameterization to Specify Ld, Lq, and L0
Modeling fidelity to Tabulated Ld, Lq and PM
Permanent magnet flux linkage parameterization to Specify flux linkage

Torque constant matrix, kt(id,iq) — Force constant matrix
`0.18 * ones(3, 3)` `N*m/A` (default)

Torque constant matrix.

Dependencies

To enable this parameter, set:

Stator parameterization to Specify Ld, Lq, and L0
Modeling fidelity to Tabulated Ld, Lq and PM
Permanent magnet flux linkage parameterization to Specify torque constant

Back EMF constant matrix, ke(id,iq) — Permanent magnet flux linkage
`0.18 * ones(3, 3)` `V/(rad/s)` (default)

Back EMF constant matrix.

Dependencies

To enable this parameter, set:

Stator parameterization to Specify Ld, Lq, and L0
Modeling fidelity to Tabulated Ld, Lq and PM
Permanent magnet flux linkage parameterization to Specify back EMF constant

Stator zero-sequence inductance, L0 — Stator zero-sequence inductance
`0.00016` `H` (default)

Zero-sequence inductance.

Dependencies

To enable this parameter either:

Set Winding Type to Wye-wound, Zero sequence to Include, and Stator parameterization to Specify Ld, Lq, and L0.
Set Winding Type to Delta-wound and Stator parameterization to Specify Ld, Lq, and L0.

Stator self-inductance per phase, Ls — Stator self-inductance per phase
`0.0002` `H` (default)

Average self-inductance of each of the three stator windings.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ls, Lm, and Ms.

Stator inductance fluctuation, Lm — Stator inductance fluctuation
`-0.0002` `H` (default)

Amount that the self-inductance and mutual inductance of the stator windings fluctuate with the rotor angle.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ls, Lm, and Ms.

Stator mutual inductance, Ms — Stator mutual inductance
`0.00002` `H` (default)

Average mutual inductance between the stator windings.

Dependencies

To enable this parameter, set Stator parameterization to Specify Ls, Lm, and Ms.

Stator resistance per phase, Rs — Stator resistance per phase
`0.013` `Ohm` (default)

Resistance of each of the stator windings.

Zero sequence — Zero sequence option
`Include` (default) | `Exclude`

Option to include or exclude zero-sequence terms.

Include — Include zero-sequence terms. To prioritize model fidelity, use this default setting. Using this option:
- Results in an error for simulations that use the Partitioning solver. For more information, see Increase Simulation Speed Using the Partitioning Solver.
- Exposes a zero-sequence parameter in the Impedances settings.
Exclude — Exclude zero-sequence terms. To prioritize simulation speed for desktop simulation or real-time deployment, select this option.

Dependencies

This parameter is visible only when you set the Winding Type parameter to Wye-wound.

Rotor angle definition — Reference point for the rotor angle measurement
`Angle between the a-phase magnetic axis and the d-axis` (default) | `Angle between the a-phase magnetic axis and the q-axis`

Reference point for the rotor angle measurement. Motor Construction figure shows the default value, Angle between the a-phase magnetic axis and the d-axis. When you select this value, the rotor and a-phase fluxes align when the rotor angle is zero.

When you select Angle between the a-phase magnetic axis and the q-axis, the a-phase current generates maximum torque when the rotor angle is zero.

Iron Losses

Model — Enable Iron losses computation
`None` (default) | `Empirical`

Specify the iron losses computational model.

Open-circuit iron losses, [P_hysteresis P_eddy P_excess] — Open-circuit iron losses
`[0, 0, 0]` `W` (default)

Row vector, of length 3, of the open-circuit iron losses due to hysteresis, Eddy, and excess losses, respectively, at the frequency specified by Electrical frequency at which losses determined.

Dependencies

To enable this parameter, set Model to Empirical.

Short-circuit iron losses, [P_hysteresis P_eddy P_excess] — Short-circuit iron losses
`[0, 0, 0]` `W` (default)

Row vector, of length 3, of the short-circuit iron losses due to hysteresis, Eddy, and excess losses, respectively, at the frequency specified by Electrical frequency at which losses determined.

Dependencies

To enable this parameter, set Model to Empirical.

Electrical frequency at which losses determined — Electrical frequency at which losses determined
`60` `Hz` (default)

Electrical frequency at which the open-circuit and short-circuit iron losses were measured.

Dependencies

To enable this parameter, set Model to Empirical.

Short-circuit RMS current for short-circuit iron losses — Short-circuit RMS current for short-circuit iron losses
`95` `A` (default)

The resulting short-circuit RMS phase current when measuring the short-circuit losses.

Dependencies

To enable this parameter, set Model to Empirical.

Mechanical

Rotor inertia — Rotor inertia
`0.01` `kg*m^2` (default) | nonnegative scalar

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

Rotor damping — Rotor damping
`0` `N*m/(rad/s)` (default) | nonnegative scalar

Rotary damping.

Temperature Dependence

To enable these parameters, set Modeling option to Show thermal port.

Measurement temperature — Measurement temperature
`298.15` `K` (default)

The temperature for which motor parameters are quoted.

Resistance temperature coefficient — Resistance temperature coefficient
`3.93e-3` `1/K` (default)

Coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The default value is for copper.

Permanent magnet flux temperature coefficient — Permanent magnet flux temperature coefficient
`-0.001` `1/K` (default) | scalar

Fractional rate at which the permanent magnet flux density changes with temperature. Use this parameter to linearly reduce the torque and the induced back EMF as temperature rises.

Thermal Port

To enable these parameters, set Modeling option to Show thermal port.

Thermal mass for each stator winding — Thermal mass for each stator winding
`100` `J/K` (default)

The thermal mass value for the A, B, and C windings. The thermal mass is the energy required to raise the temperature by one degree.

Rotor thermal mass — Rotor thermal mass
`200` `J/K` (default)

The thermal mass of the rotor, that is, the energy required to raise the temperature of the rotor by one degree.

Percentage of main flux path iron losses associated with the rotor — Percentage of main flux path iron losses associated with the rotor
`90` (default)

The percentage of the main flux path iron losses associated with the magnetic path through the rotor. It determines how much of the iron loss heating is attributed to the rotor thermal port HR, and how much is attributed to the three winding thermal ports HA, HB, and HC.

Dependencies

To enable this parameter, set Model to Empirical.

Percentage of cross-tooth flux path iron losses associated with the rotor — Percentage of cross-tooth flux path iron losses associated with the rotor
`30` (default)

The percentage of the cross-tooth flux path iron losses associated with the magnetic path through the rotor. It determines how much of the iron loss heating is attributed to the rotor thermal port HR, and how much is attributed to the three winding thermal ports HA, HB, and HC.

Dependencies

To enable this parameter, set Model to Empirical.

References

[1] Kundur, P. Power System Stability and Control. New York, NY: McGraw Hill, 1993.

[2] Anderson, P. M. Analysis of Faulted Power Systems. Hoboken, NJ: Wiley-IEEE Press, 1995.

[3] Mellor, P.H., R. Wrobel, and D. Holliday. “A computationally efficient iron loss model for brushless AC machines that caters for rated flux and field weakened operation.” IEEE Electric Machines and Drives Conference. May 2009.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2013b

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R2021b: Electrical connection ports update

From R2021b forward, to switch between composite and expanded ports, set the Electrical connection parameter to either Composite three-phase ports or Expanded three-phase ports.

As a result of these changes, inside a model saved in an earlier release, review the Electrical connection parameter of this block.

PMSM

Description

Motor Construction

Equations

Simplified Electrical Equations

Alternative Flux Linkage Parameterization

Calculating Iron Losses

Predefined Parameterization

Model Thermal Effects

Variables

Examples

Electric Power Assisted Steering

Faulted PMSM

Three-Phase PMSM Drive

Parameterize a Permanent Magnet Synchronous Motor

Three-Phase PMSM Drive with Thermal Model

Ports

Conserving

~ — Three-phase port electrical

Dependencies

a — a-phase electrical

Dependencies

b — b-phase electrical

Dependencies

c — c-phase electrical

Dependencies

n — Neutral phase electrical

Dependencies

R — Motor rotor mechanical

C — Motor case mechanical

HA — Winding A thermal port thermal

Dependencies

HB — Winding B thermal port thermal

Dependencies

HC — Winding C thermal port thermal

Dependencies

HR — Rotor thermal port thermal

Dependencies

Parameters

Selected part — Predefined parameterization option <click to select> (default)

Modeling option — Whether to enable thermal ports No thermal port (default) | Show thermal port

Main

Electrical connection — Electrical connection Composite three-phase ports (default) | Expanded three-phase ports

Winding type — Windings configuration Wye-wound (default) | Delta-wound

Modeling fidelity — Modeling fidelity Constant Ld, Lq and PM (default) | Tabulated Ld, Lq and PM

Dependencies

Number of pole pairs — Number of pole pairs 6 (default)

Permanent magnet flux linkage parameterization — Permanent magnet flux linkage parameterization Specify flux linkage (default) | Specify torque constant | Specify back EMF constant

Permanent magnet flux linkage — Permanent magnet flux linkage 0.03 Wb (default)

Dependencies

Torque constant — Torque constant 0.18 N*m/A (default)

Dependencies

Back EMF constant — Back EMF constant 0.18 V*s/rad (default)

Dependencies

Stator parameterization — Stator parameterization Specify Ld, Lq, and L0 (default) | Specify Ls, Lm, and Ms

Stator d-axis inductance, Ld — Stator d-axis inductance 0.00022 H (default)

Dependencies

Stator q-axis inductance, Lq — Stator q-axis inductance 0.00022 H (default)

Dependencies

Direct-axis current vector, iD — Direct-axis current vector [-200, 0, 200] A (default)

Dependencies

Quadrature-axis current vector, iQ — Quadrature-axis current vector [-200, 0, 200] A (default)

Dependencies

Ld matrix, Ld(id,iq) — Ld matrix 0.0002 * ones(3, 3) H (default)

Dependencies

Lq matrix, Lq(id,iq) — Lq matrix 0.0002 * ones(3, 3) H (default)

Dependencies

Permanent magnet flux linkage, PM(id,iq) — Permanent magnet flux linkage 0.1 * ones(3, 3) Wb (default)

Dependencies

Torque constant matrix, kt(id,iq) — Force constant matrix 0.18 * ones(3, 3) N*m/A (default)

Dependencies

Back EMF constant matrix, ke(id,iq) — Permanent magnet flux linkage 0.18 * ones(3, 3) V/(rad/s) (default)

Dependencies

Stator zero-sequence inductance, L0 — Stator zero-sequence inductance 0.00016 H (default)

Dependencies

Stator self-inductance per phase, Ls — Stator self-inductance per phase 0.0002 H (default)

Dependencies

Stator inductance fluctuation, Lm — Stator inductance fluctuation -0.0002 H (default)

Dependencies

Stator mutual inductance, Ms — Stator mutual inductance 0.00002 H (default)

~ — Three-phase port
electrical

a — a-phase
electrical

b — b-phase
electrical

c — c-phase
electrical

n — Neutral phase
electrical

R — Motor rotor
mechanical

C — Motor case
mechanical

HA — Winding A thermal port
thermal

HB — Winding B thermal port
thermal

HC — Winding C thermal port
thermal

HR — Rotor thermal port
thermal

Selected part — Predefined parameterization option
`<click to select>` (default)

Modeling option — Whether to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Electrical connection — Electrical connection
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Winding type — Windings configuration
`Wye-wound` (default) | `Delta-wound`

Modeling fidelity — Modeling fidelity
`Constant Ld, Lq and PM` (default) | `Tabulated Ld, Lq and PM`

Number of pole pairs — Number of pole pairs
`6` (default)

Permanent magnet flux linkage parameterization — Permanent magnet flux linkage parameterization
`Specify flux linkage` (default) | `Specify torque constant` | `Specify back EMF constant`

Permanent magnet flux linkage — Permanent magnet flux linkage
`0.03` `Wb` (default)

Torque constant — Torque constant
`0.18` `N*m/A` (default)

Back EMF constant — Back EMF constant
`0.18` `V*s/rad` (default)

Stator parameterization — Stator parameterization
`Specify Ld, Lq, and L0` (default) | `Specify Ls, Lm, and Ms`

Stator d-axis inductance, Ld — Stator d-axis inductance
`0.00022` `H` (default)

Stator q-axis inductance, Lq — Stator q-axis inductance
`0.00022` `H` (default)

Direct-axis current vector, iD — Direct-axis current vector
`[-200, 0, 200]` `A` (default)

Quadrature-axis current vector, iQ — Quadrature-axis current vector
`[-200, 0, 200]` `A` (default)

Ld matrix, Ld(id,iq) — Ld matrix
`0.0002 * ones(3, 3)` `H` (default)

Lq matrix, Lq(id,iq) — Lq matrix
`0.0002 * ones(3, 3)` `H` (default)

Permanent magnet flux linkage, PM(id,iq) — Permanent magnet flux linkage
`0.1 * ones(3, 3)` `Wb` (default)

Torque constant matrix, kt(id,iq) — Force constant matrix
`0.18 * ones(3, 3)` `N*m/A` (default)

Back EMF constant matrix, ke(id,iq) — Permanent magnet flux linkage
`0.18 * ones(3, 3)` `V/(rad/s)` (default)

Stator zero-sequence inductance, L0 — Stator zero-sequence inductance
`0.00016` `H` (default)

Stator self-inductance per phase, Ls — Stator self-inductance per phase
`0.0002` `H` (default)

Stator inductance fluctuation, Lm — Stator inductance fluctuation
`-0.0002` `H` (default)

Stator mutual inductance, Ms — Stator mutual inductance
`0.00002` `H` (default)

Stator resistance per phase, Rs — Stator resistance per phase
`0.013` `Ohm` (default)

Zero sequence — Zero sequence option
`Include` (default) | `Exclude`

Rotor angle definition — Reference point for the rotor angle measurement
`Angle between the a-phase magnetic axis and the d-axis` (default) | `Angle between the a-phase magnetic axis and the q-axis`

Model — Enable Iron losses computation
`None` (default) | `Empirical`

Open-circuit iron losses, [P_hysteresis P_eddy P_excess] — Open-circuit iron losses
`[0, 0, 0]` `W` (default)

Short-circuit iron losses, [P_hysteresis P_eddy P_excess] — Short-circuit iron losses
`[0, 0, 0]` `W` (default)

Electrical frequency at which losses determined — Electrical frequency at which losses determined
`60` `Hz` (default)

Short-circuit RMS current for short-circuit iron losses — Short-circuit RMS current for short-circuit iron losses
`95` `A` (default)

Rotor inertia — Rotor inertia
`0.01` `kg*m^2` (default) | nonnegative scalar

Rotor damping — Rotor damping
`0` `N*m/(rad/s)` (default) | nonnegative scalar

Measurement temperature — Measurement temperature
`298.15` `K` (default)

Resistance temperature coefficient — Resistance temperature coefficient
`3.93e-3` `1/K` (default)

Permanent magnet flux temperature coefficient — Permanent magnet flux temperature coefficient
`-0.001` `1/K` (default) | scalar

Thermal mass for each stator winding — Thermal mass for each stator winding
`100` `J/K` (default)

Rotor thermal mass — Rotor thermal mass
`200` `J/K` (default)

Percentage of main flux path iron losses associated with the rotor — Percentage of main flux path iron losses associated with the rotor
`90` (default)

Percentage of cross-tooth flux path iron losses associated with the rotor — Percentage of cross-tooth flux path iron losses associated with the rotor
`30` (default)

C/C++ Code Generation
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