Induction Motor HDL

Three-phase induction motor

Since R2022b

• 

Libraries:
Motor Control Blockset HDL Support / Electrical Systems / Motors

Description

The Induction Motor HDL block implements a three-phase induction motor. The block uses three-phase input voltages to regulate the individual phase currents, thereby controlling the motor torque or speed.

The block generates code for fixed-step double- and single-precision targets using the Sample Time (s) parameter. It supports code generation for FPGA deployment and generates HDL-compatible code.

You can specify the induction motor parameters and operating mode using the Config input port. You can also use the Induction Motor Configuration block to generate the required configuration signal to specify at the Config input port.

Three-Phase Sinusoidal Model Electrical System

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

The block uses these equations to calculate the electrical speed (ω_em) and slip speed (ω_slip).

$\begin{array}{l}{\omega }_{em}=P{\omega }_m\\ {\omega }_{slip}= {\omega }_{syn}-{\omega }_{em}\end{array}$

To calculate the dq rotor electrical speed with respect to the rotor A-axis (dA), the block uses the difference between the stator a-axis (da) speed and the slip speed:

${\omega }_{dA}= {\omega }_{da}- {\omega }_{em}$

To simplify the equations for the flux, voltage, and current transformations, the block uses a stationary reference frame:

$\begin{array}{l}{\omega }_{da}=0\\ {\omega }_{dA}=-{\omega }_{em}\end{array}$

Calculation	Equation
Flux	$\begin{array}{l}\frac{d}{dt}\left[\begin{array}{c}{\lambda }_{sd}\\ {\lambda }_{sq}\end{array}\right]= \left[\begin{array}{c}{v}_{sd}\\ v_{sq}\end{array}\right]- R_s\left[\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\right]- {\omega }_{da}\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\left[\begin{array}{c}{\lambda }_{sd}\\ {\lambda }_{sq}\end{array}\right]\\ \frac{d}{dt}\left[\begin{array}{c}{\lambda }_{rd}\\ {\lambda }_{rq}\end{array}\right]= \left[\begin{array}{c}{v}_{rd}\\ v_{rq}\end{array}\right]- R_r\left[\begin{array}{c}{i}_{rd}\\ i_{rq}\end{array}\right]- {\omega }_{dA}\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\left[\begin{array}{c}{\lambda }_{rd}\\ {\lambda }_{rq}\end{array}\right]\end{array}$ $\left[\begin{array}{c}\begin{array}{c}{\lambda }_{sd}\\ {\lambda }_{sq}\end{array}\\ \begin{array}{c}{\lambda }_{rd}\\ {\lambda }_{rq}\end{array}\end{array}\right]= \left[\begin{array}{cc}\begin{array}{cc}{L}_s& 0\\ 0& L_s\end{array}& \begin{array}{cc}{L}_m& 0\\ 0& L_m\end{array}\\ \begin{array}{cc}{L}_m& 0\\ 0& L_m\end{array}& \begin{array}{cc}{L}_r& 0\\ 0& L_r\end{array}\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\\ \begin{array}{c}{i}_{rd}\\ i_{rq}\end{array}\end{array}\right]$
Current	$\left[\begin{array}{c}\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\\ \begin{array}{c}{i}_{rd}\\ i_{rq}\end{array}\end{array}\right]= \left(\frac{1}{L_m^2- L_r{L}_s}\right)\left[\begin{array}{cc}\begin{array}{cc}-L_r& 0\\ 0& -L_r\end{array}& \begin{array}{cc}{L}_m& 0\\ 0& L_m\end{array}\\ \begin{array}{cc}{L}_m& 0\\ 0& L_m\end{array}& \begin{array}{cc}-L_s& 0\\ 0& -L_s\end{array}\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{\lambda }_{sd}\\ {\lambda }_{sq}\end{array}\\ \begin{array}{c}{\lambda }_{rd}\\ {\lambda }_{rq}\end{array}\end{array}\right]$
Inductance	$\begin{array}{l}{L}_s= L_{ls}+L_m\\ L_r= L_{lr}+L_m\end{array}$
Electromagnetic torque	$T_e=P{L}_m(i_{sq}{i}_{rd}- i_{sd}{i}_{rq})$
Power invariant dq transformation to ensure that the dq and the three phase powers are equal	$\left[\begin{array}{c}{v}_{sd}\\ v_{sq}\end{array}\right]= \sqrt{\frac{2}{3}} \left[\begin{array}{ccc}\text{cos}({\Theta }_{da})& \text{cos}({\Theta }_{da}-\frac{2\pi }{3})& \text{cos}({\Theta }_{da}+\frac{2\pi }{3})\\ -\text{sin}({\Theta }_{da})& -\text{sin}({\Theta }_{da}-\frac{2\pi }{3})& -\text{sin}({\Theta }_{da}+\frac{2\pi }{3})\end{array}\right]\left[\begin{array}{c}{v}_a\\ v_b\\ v_c\end{array}\right]$ $\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]= \sqrt{\frac{2}{3}} \left[\begin{array}{cc}\text{cos}({\Theta }_{da})& -\text{sin}({\Theta }_{da})\\ \begin{array}{c}\text{cos}({\Theta }_{da}-\frac{2\pi }{3})\\ \text{cos}({\Theta }_{da}+\frac{2\pi }{3})\end{array}& \begin{array}{c}-\text{sin}({\Theta }_{da}-\frac{2\pi }{3})\\ -\text{sin}({\Theta }_{da}+\frac{2\pi }{3})\end{array}\end{array}\right]\left[\begin{array}{c}{i}_{sd}\\ i_{sq}\end{array}\right]$

The equations use these variables.

ωm	Angular velocity of the rotor (rad/s)
ωem	Electrical rotor speed (rad/s)
ωslip	Electrical rotor slip speed (rad/s)
ωsyn	Synchronous rotor speed (rad/s)
ωda	dq stator electrical speed with respect to the rotor a-axis (rad/s)
ωdA	dq stator electrical speed with respect to the rotor A-axis (rad/s)
Θda	dq stator electrical angle with respect to the rotor a-axis (rad)
ΘdA	dq stator electrical angle with respect to the rotor A-axis (rad)
Lq, Ld	q- and d-axis inductances (H)
Ls	Stator inductance (H)
Lr	Rotor inductance (H)
Lm	Magnetizing inductance (H)
Lls	Stator leakage inductance (H)
Llr	Rotor leakage inductance (H)
vsq, vsd	Stator q- and d-axis voltages (V)
isq, isd	Stator q- and d-axis currents (A)
λsq, λsd	Stator q- and d-axis flux (Wb)
irq, ird	Rotor q- and d-axis currents (A)
λrq, λrd	Rotor q- and d-axis flux (Wb)
va, vb, vc	Stator voltage phases a, b, c (V)
ia, ib, ic	Stator currents phases a, b, c (A)
Rs	Resistance of the stator windings (Ohm)
Rr	Resistance of the rotor windings (Ohm)
P	Number of pole pairs
Te	Electromagnetic torque (Nm)

Mechanical System

The motor angular velocity is given by:

$$\begin{array}{c}\frac{d}{dt}{\omega }_m=\frac{1}{J}\left(T_e-T_f-F{\omega }_m-T_m\right)\\ \frac{d{\theta }_m}{dt}={\omega }_m\end{array}$$

The equations use these variables.

J	Combined inertia of motor and load (kgm^2)
F	Combined viscous friction of motor and load (N·m/(rad/s))
θm	Motor mechanical angular position (rad)
Tm	Motor shaft torque (Nm)
Te	Electromagnetic torque (Nm)
Tf	Motor shaft static friction torque (Nm)
ωm	Angular mechanical velocity of the motor (rad/s)

Power Accounting

For motor power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
PwrInfo		PwrMtr	Mechanical power	Pmot	$P_{mot}= -{\omega }_m{T}_e$
		PwrBus	Electrical power	Pbus	$P_{bus}= v_{an}{i}_a+ v_{bn}{i}_b+v_{cn}{i}_c$
		PwrElecLoss	Resistive power loss	Pelec	$P_{elec}= -(R_s{i}_{sd}^2+R_s{i}_{sq}^2+-R_r{i}_{rd}^2+R_r{i}_{rq}^2)$
		PwrMechLoss	Mechanical power loss	Pmech	When Port Configuration is set to Torque: $P_{mech}= -\left({\omega }_m^{2}F+ \left|{\omega }_m\right|T_f\right)$ When Port Configuration is set to Speed: $P_{mech}= 0$
		PwrMtrStored	Stored motor power	Pstr	$P_{str}= P_{bus}+ P_{mot}+ P_{elec} + P_{mech}$

The equations use these variables.

Rs	Stator resistance (Ohm)
Rr	Rotor resistance (Ohm)
ia, ib, ic	Stator phase a, b, and c current (A)
isq, isd	Stator q- and d-axis currents (A)
van, vbn, vcn	Stator phase a, b, and c voltage (V)
ωm	Angular mechanical velocity of the rotor (rad/s)
F	Combined viscous damping of motor and load (N·m/(rad/s))
Te	Electromagnetic torque (Nm)
Tf	Combined friction torque of motor and load (Nm)

Examples

Field-Oriented Control (FOC) of PMSM Using Hardware-In-The-Loop (HIL) Simulation

Uses hardware-in-the-loop (HIL) simulation to implement the field-oriented control (FOC) algorithm to control the speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a quadrature encoder sensor. For more information on FOC, see Field-Oriented Control (FOC).

• Open Example

Ports

Input

Config — Block configuration signal

vector

Configuration signal for the Induction Motor HDL block containing the block configuration parameters.

Data Types: single

PhaseVolt — Stator terminal voltages

1-by-3 array

Stator terminal voltages, V_a, V_b, and V_c, in V.

Data Types: single

LdTrq/Spd — Load torque on motor or speed of motor shaft

scalar

The port supports one of these inputs:

• T_m — Load torque on the motor shaft, in N·m.

• ω_m — Angular velocity of the motor, in rad/s.

Data Types: single

Reset — Reset bus signal

scalar

Reset bus signal that the block uses to reset the internal integrators.

Data Types: Boolean

Output

Info — Bus signal

bus

The bus signal contains these block calculations.

Signal			Description	Variable	Units
IaStator			Stator phase current A	ia	A
IbStator			Stator phase current B	ib	A
IcStator			Stator phase current C	ic	A
IdSync			Direct axis current	id	A
IqSync			Quadrature axis current	iq	A
VdSync			Direct axis voltage	vd	V
VqSync			Quadrature axis voltage	vq	V
MtrSpd			Angular mechanical velocity of the rotor	ωm	rad/s
MtrMechPos			Rotor mechanical angular position	θm	rad
MtrPos			Rotor electrical angular position	θe	rad
MtrTrq			Electromagnetic torque	Te	N·m
PwrInfo	PwrTrnsfrd	PwrMtr	Mechanical power	Pmot	W
		PwrBus	Electrical power	Pbus	W
	PwrNotTrnsfrd	PwrElecLoss	Resistive power loss	Pelec	W
		PwrMechLoss	Mechanical power loss	Pmech	W
	PwrStored	PwrMtrStored	Stored motor power	Pstr	W

PhaseCurr — Current for phase a, b, and c

1-by-3 array

Current for phase a, b, and c, i_a, i_b, and i_c, respectively, in A.

Torque — Motor torque

scalar

Motor torque, T_mtr, in N·m.

Speed — Motor speed

scalar

Angular speed of the motor, ω_mtr, in rad/s.

MtrElecAngle — Motor electrical angle

scalar

Electrical position of the motor, θ_dq, in rad.

Data Types: single

Parameters

Sample time (s) — Sample time after which block executes again

1e-6 (default) | scalar

The fixed time interval (in seconds) between consecutive instances of block execution.

Extended Capabilities

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

Version History

Introduced in R2022b