ACIM Control Reference

Compute reference currents for field-oriented control of induction motor

Since R2020b

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Libraries:
Motor Control Blockset / Controls / Control Reference
Motor Control Blockset HDL Support / Controls / Control Reference

Description

The ACIM Control Reference block computes the d-axis and q-axis reference currents for the field-oriented control (and field-weakening) operation.

The block accepts the reference torque and feedback mechanical speed and outputs the corresponding d- and q-axes reference currents.

The block computes the reference current values by solving mathematical relationships. The calculations use the SI unit system. When working with the Per-Unit (PU) system (with the Input units parameter set to Per-Unit (PU)), the block converts PU input signals to SI units to perform the computations and converts them back to PU values at the output.

These equations describe how the block computes the reference d-axis and q-axis current values.

Mathematical Model of Induction Motor

These model equations describe the dynamics of induction motor in the rotor flux reference frame:

The machine inductances are represented as,

$L_s= L_{ls}+ L_m$

$L_r= L_{lr}+ L_m$

$\sigma =1-\left(\frac{L_m^2}{L_s\cdot L_r}\right)$

Stator voltages are represented as,

$v_{sd}= R_s{i}_{sd}+\sigma L_s\frac{d{i}_{sd}}{dt}+\frac{L_m}{L_r}\frac{d{\lambda }_{rd}}{dt}-{\omega }_e\sigma L_s{i}_{sq}$

$v_{sq}= R_s{i}_{sq}+\sigma L_s\frac{d{i}_{sq}}{dt}+\frac{L_m}{L_r}{\omega }_e{\lambda }_{rd}+{\omega }_e\sigma L_s{i}_{sd}$

In the preceding equations, the flux linkages can be represented as,

${\lambda }_{sd}= \frac{L_m}{L_r}{\lambda }_{rd}+\sigma L_s{i}_{sd}$

${\lambda }_{sq}= \sigma L_s{i}_{sq}$

$${\tau }_r\frac{d{\lambda }_{rd}}{dt}+ {\lambda }_{rd}=L_m{i}_{sd}$$

If we keep the rotor flux as constant and the d-axis is aligned to the rotor flux reference frame, then we can imply:

${\lambda }_{\text{rd}}=L_m{i}_{sd}$

${\lambda }_{\text{rq}}=0$

These equations describe the mechanical dynamics,

$T_e=\frac{3}{2}p\left(\frac{L_m}{L_r}\right){\lambda }_{rd}{i}_{sq}$

$T_e- T_L=J\frac{d{\omega }_m}{dt} +B{\omega }_m$

These equations describe the slip speed,

${\tau }_{\text{r}}= \left(\frac{L_{\text{r}}}{R_r}\right)$

${\omega }_{\text{e\_slip}}= \left(\frac{L_{\text{m}}\cdot i_{\text{sq}}^{ref}}{{\tau }_{\text{r}}\cdot {\lambda }_{\text{rd}}}\right)$

${\omega }_e= {\omega }_r+{\omega }_{e\text{\_}slip}$

$${\theta }_e= {\displaystyle \int {\omega }_e\cdot dt}={\displaystyle \int ({\omega }_r+{\omega }_{e\text{\_}slip})}\cdot dt={\theta }_r+{\theta }_{slip}$$

Reference Current Computation

These equations show computation of the reference currents,

$$i_{sd\_0}=\frac{{\lambda }_{\text{rd}}}{{\text{L}}_{\text{m}}}$$

$$i_{sq\_req}= \frac{T^{ref}}{\frac{3}{2}p\left(\frac{L_m}{L_r}\right){\lambda }_{rd}}$$

The reference currents are computed differently for operation below base speed and field weakening region,

If ${\omega }_m\le {\omega }_{rated}$:

$$i_{sd\_sat}=\min (i_{sd\_0},i_{\max })$$

If ${\omega }_m> {\omega }_{rated}$:

$i_{sd\_fw}=i_{sd\_0}\left(\frac{{\omega }_{rated}}{{\omega }_m}\right)$

$$i_{sd\_sat}=\min (i_{sd\_fw},i_{\max })$$

These equations indicate the q-axis current computation,

$i_{sq\_lim}= \sqrt{i_{max}^2- i_{sd\_sat}^2}$

$$i_{sq\_sat}=sat(i_{sq\_lim},i_{sq\_req})$$

The block outputs the following values,

$$i_{sd}^{ref}=i_{sd\_sat}$$

$$i_{sq}^{ref}=i_{sq\_sat}$$

where:

• $$p$$ is the number of pole pairs of the motor.

• $R_s$ is the stator phase winding resistance (Ohms).

• $$R_r$$ is the rotor resistance referred to stator (Ohms).

• $L_{ls}$ is the stator leakage inductance (Henry).

• $L_{lr}$ is the rotor leakage inductance (Henry).

• $L_s$ is the stator inductance (Henry).

• $L_m$ is the magnetizing inductance (Henry).

• $L_r$ is the rotor inductance referred to stator (Henry).

• $\sigma$ is the total leakage factor of the induction motor.

• ${\tau }_{\text{r}}$ is the rotor time constant (sec).

• $$v_{sd}$$ and $$v_{sq}$$ are the stator d- and q-axis voltages (Volts).

• $i_{sd}$ and $i_{sq}$ are the stator d- and q-axis currents (Amperes).

• $i_{sd\_0}$ is the rated d-axis current of the stator also known as magnetizing current (Amperes).

• $i_{max}$ is the maximum phase current (peak) of the motor (Amperes).

• ${\lambda }_{sd}$ is the d-axis flux linkage of the stator (Weber).

• ${\lambda }_{sq}$ is the q-axis flux linkage of the stator (Weber).

• ${\lambda }_{rd}$ is the d-axis flux linkage of the rotor (Weber).

• ${\lambda }_{rq}$ is the q-axis flux linkage of the rotor (Weber).

• ${\omega }_{\text{e\_slip}}$ is the electrical slip speed of the rotor (Radians/ sec).

• ${\omega }_{\text{slip}}$ is the mechanical slip speed of the rotor (Radians/ sec).

• ${\omega }_e$ is the electrical speed corresponding to frequency of stator voltages (Radians/ sec).

• $${\omega }_m$$ is the rotor mechanical speed (Radians/ sec).

• ${\omega }_r$ is the rotor electrical speed (Radians/ sec).

• ${\omega }_{rated}$ is the rated mechanical speed of the motor (Radians/ sec).

• $T_e$ is the electromechanical torque produced by the motor (Nm).

Examples

Field-Oriented Control of Induction Motor Using Speed Sensor

Implements the field-oriented control (FOC) technique to control the speed of a three-phase AC induction motor (ACIM). The FOC algorithm requires rotor speed feedback, which is obtained in this example by using a quadrature encoder sensor. For details about FOC, see Field-Oriented Control (FOC).

• Open Model

Ports

Input

T^ref — Reference torque value

scalar

Reference torque input value for which the block computes the reference current.

Data Types: single | double | fixed point

⍵_m — Mechanical speed

scalar

Reference mechanical speed value for which the block computes the reference current.

Data Types: single | double | fixed point

Output

I_sd^ref — Reference d-axis stator current

scalar

Reference d-axis stator current value.

Data Types: single | double | fixed point

I_sq^ref — Reference q-axis stator current

scalar

Reference q-axis stator current value.

Data Types: single | double | fixed point

Parameters

Number of pole pairs — Number of pole pairs available in motor

2 (default) | scalar

Number of pole pairs available in the induction motor.

Rotor leakage inductance (H) — Leakage inductance of rotor winding

6.81e-3 (default) | scalar

Inductance due to leakage flux linked to the rotor winding (in Henry).

Magnetizing Inductance (H) — Magnetizing inductance of induction motor

30e-3 (default) | scalar

Inductance due to the magnetizing flux (in Henry).

Rated Flux (Wb) — Rated flux of motor

38.2e-3 (default) | scalar

Rated flux of the induction motor (in Weber).

Rated Speed (rpm) — Rated speed of motor

1150 (default) | scalar

Rated speed of the induction motor according to motor data sheet (in rpm).

Synchronous Speed (rpm) — Synchronous speed of motor

1500 (default) | scalar

Synchronous speed of the induction motor (in rpm).

Max current (A) — Maximum phase current limit for motor (amperes)

3 (default) | scalar

Maximum phase current limit for the induction motor (amperes).

Input units — Unit of input values

Per-Unit (PU) (default) | SI Units

Unit of the input values.

Base Current (A) — Base current for per-unit system

5.3611 (default) | scalar

Base current (in Amperes) for per-unit system.

Dependencies

To enable this parameter, set Input units to Per-Unit (PU).

Base torque (Nm) — Base torque for per-unit system

0.50072 (default) | scalar

Base torque (in Nm) for per-unit system. See Per-Unit System page for more details.

This parameter is not configurable and uses a value that is internally computed using other parameters.

Dependencies

To display this parameter, set Input units to Per-Unit (PU).

References

[1] B. Bose, Modern Power Electronics and AC Drives. Prentice Hall, 2001. ISBN-0-13-016743-6.

[2] Lorenz, Robert D., Thomas Lipo, and Donald W. Novotny. "Motion control with induction motors." Proceedings of the IEEE, Vol. 82, Issue 8, August 1994, pp. 1215-1240.

[3] W. Leonhard, Control of Electrical Drives, 3rd ed. Secaucus, NJ, USA:Springer-Verlag New York, Inc., 2001.

[4] Briz, Fernando, Michael W. Degner, and Robert D. Lorenz. "Analysis and design of current regulators using complex vectors." IEEE Transactions on Industry Applications, Vol. 36, Issue 3, May/June 2000, pp. 817-825.

[5] Briz, Fernando, et al. "Current and flux regulation in field-weakening operation [of induction motors]." IEEE Transactions on Industry Applications, Vol. 37, Issue 1, Jan/Feb 2001, pp. 42-50.

[6] R. M. Prasad and M. A. Mulla, “A novel position-sensorless algorithm for field oriented control of DFIG with reduced current sensors,” IEEE Trans. Sustain. Energy, vol. 10, no. 3, pp. 1098–1108, July 2019.

Extended Capabilities

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

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).
FlattenHierarchy	Remove ACIM Control Reference block hierarchy from generated HDL code. The default is inherit. See also FlattenHierarchy (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).
SharingFactor	Number of functionally equivalent resources to map to a single shared resource. The default is 0. See also Resource Sharing (HDL Coder).

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2020b