Hybrid Excitation PMSM (DQ0)

R2026b

Direct-quadrature-zero representation of hybrid-excitation synchronous machine with three-phase wye-wound stator

Since R2026b

Libraries:
Simscape / Electrical / DQ0 Components / Machines

Description

The Hybrid Excitation PMSM (DQ0) block models the direct-quadrature-zero (dq0) frame representation of a hybrid-excitation synchronous machine with a three-phase wye-wound stator. Permanent magnets and excitation windings provide the machine excitation. Use this block to model hybrid-excitation permanent magnet synchronous motors (PMSMs), doubly-excited PMSMs, and synchronous motors.

If you set the Permanent magnet flux linkage parameter to 0, the Hybrid Excitation PMSM (DQ0) block operates as a magnet-free synchronous machine.

Note

Simscape™ Electrical™ includes several blocks that can model the same type of motor or actuator. Choose a block that has sufficient modeling detail for the engineering design questions that you need to answer. Do not use a block that has more modeling detail than you need, because higher-fidelity models slow down simulation and are more complex to parameterize.

Blocks like the Hybrid Excitation PMSM (DQ0) block model motors with fixed or parameter-dependent coefficients with a simple equivalent circuit. These models have an intermediate level of fidelity. Use this block to design controls or systems in actuation applications, such as robotics and mechatronics, and for efficiency predictions when saturation and harmonics only weakly impact losses. For more information about choosing the right block to model your motor at the right level of fidelity, see Choose Blocks to Model Motors or Actuators.

Equations

The block applies the Park transformation to its electrical defining equations, producing an expression for torque that is independent of rotor angle.

This equation defines the Park’s transformation:

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

where θ_e is the electrical angle and is equal to Nθ_r. N is the number of pole pairs.

By applying the Park transformation to the first two electrical defining equations, the block produces equations that define its behavior:

$\begin{array}{l} v_{d} = R_{s} i_{d} + L_{d} \frac{d i_{d}}{d t} + L_{m f} \frac{d i_{f}}{d t} - N ω i_{q} L_{q} \\ v_{q} = R_{s} i_{q} + L_{q} \frac{d i_{q}}{d t} + N ω (i_{d} L_{d} + ψ_{m} + i_{f} L_{m f}) \\ v_{0} = R_{s} i_{0} + L_{0} \frac{d i_{0}}{d t} \\ v_{f} = R_{f} i_{f} + L_{f} \frac{d i_{f}}{d t} + \frac{3}{2} L_{m f} \frac{d i_{d}}{d t} \\ T = \frac{3}{2} N [i_{q} (i_{d} L_{d} + ψ_{m} + i_{f} L_{m f}) - i_{d} i_{q} L_{q}] \\ J \frac{d ω}{d t} = T = T_{L} - B_{m} ω \end{array}$

where:

v_d, v_q, and v₀ are the d-axis, q-axis, and zero-sequence voltages:

$[\begin{matrix} v_{d} \\ v_{q} \\ v_{0} \end{matrix}] = P [\begin{matrix} v_{a} \\ v_{b} \\ v_{c} \end{matrix}] .$
i_d, i_q, and i₀ are the d-axis, q-axis, and zero-sequence currents:

$[\begin{matrix} i_{d} \\ i_{q} \\ i_{0} \end{matrix}] = P [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}] .$
$L_{d} = L_{s} + M_{s} + \frac{3}{2} L_{m}$ is the stator d-axis inductance.
ω is the mechanical rotational speed.
$L_{q} = L_{s} + M_{s} - \frac{3}{2} L_{m}$ is the stator q-axis inductance.
$L_{0} = L_{s} - 2 M_{s}$ is the stator zero-sequence inductance.
T is the rotor torque. In the Hybrid Excitation PMSM (DQ0) block, the torque flows from port C, which represents the machine case, to port R, which represents the machine rotor.
J is the rotor inertia.
T_L is the load torque.
B_m is the rotor damping.

Model Thermal Effects

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

No thermal port — The block contains the electrical conserving ports associated with the stator dq0 quantities but does not contain thermal ports.
Show thermal port — The block contains the electrical conserving ports associated with the stator dq0 quantities and the thermal conserving ports for the stator 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.

Ports

Conserving

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Note

The d, q, and 0 ports are electrical conserving ports that represent three‑phase quantities expressed in the rotating reference (dq0) frame. Connecting these ports to components outside the dq0 domain requires appropriate transformations to avoid modeling inconsistencies.

d — d-axis component
electrical

Electrical conserving port associated with the d-axis component.

q — q-axis component
electrical

Electrical conserving port associated with the q-axis component.

0 — Zero-sequence component
electrical

Electrical conserving port associated with the zero-sequence component.

Dependencies

To enable this port, set Zero sequence to Include.

R — Machine rotor
mechanical rotational

Mechanical rotational conserving port associated with the machine rotor.

C — Machine case
mechanical rotational

Mechanical rotational conserving port associated with the machine case.

fd+ — Field winding positive terminal
electrical

Electrical conserving port associated with the positive terminal of the field winding.

fd- — Field winding negative terminal
electrical

Electrical conserving port associated with the negative terminal of the field winding.

HR — Rotor thermal port
thermal

Thermal conserving port associated with the rotor.

Dependencies

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

HS — Stator windings thermal port
thermal

Thermal conserving port associated with the stator windings.

Dependencies

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

Parameters

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

Option to enable the thermal ports of the block and model the effects of generated heat and motor temperature.

Main

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

Select the modeling fidelity:

Constant Ld, Lq, Lmf, Lf, and PM — The Ld, Lq, Lmf, Lf, and PM values are constant. You define these values by specifying their respective parameters.
Tabulated Ld, Lq, Lmf, Lf, and PM — The block computes the Ld, Lq, Lmf, Lf, and PM values at each time step during the simulation from DQ and field currents lookup tables:

$\begin{array}{l} L_{d} = f_{1} (i_{d}, i_{q}, i_{f}) \\ L_{q} = f_{2} (i_{d}, i_{q}, i_{f}) \\ L_{m f} = f_{3} (i_{d}, i_{q}, i_{f}) \\ λ_{P M} = f_{4} (i_{d}, i_{q}, i_{f}) \\ L_{f} = f_{5} (i_{f}) \end{array}$

Dependencies

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

Number of pole pairs — Number of permanent magnet pole pairs on rotor
`6` (default) | positive scalar

Number of permanent magnet pole pairs on the rotor.

Permanent magnet flux linkage — Peak permanent magnet flux linkage
`0.09` `Wb` (default) | nonnegative scalar

Peak permanent magnet flux linkage for each of the stator windings.

If you set this parameter to 0, this block operates as a magnet-free synchronous machine.

Dependencies

To enable this parameter, set Modeling fidelity to Constant Ld, Lq, Lmf, Lf, and PM.

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

Parameterization option for the stator.

Stator d-axis inductance, Ld — Direct-axis inductance of machine stator
`0.0031` `H` (default)

Direct-axis inductance of the machine stator.

Dependencies

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

Stator q-axis inductance, Lq — Quadrature-axis inductance of machine stator
`0.0045` `H` (default)

Quadrature-axis inductance of the machine stator.

Dependencies

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