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ACIM Control Reference

Compute reference currents for field oriented control of induction motor

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The ACIM Control Reference block computes the d-axis and q-axis reference currents for field-oriented control including 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 SI unit system. When working with the Per-Unit (PU) system (with Input units parameter set to Per-Unit (PU)), the block converts PU input signals to SI units to perform computations, and converts them back to PU values at the output.

These equations describe the computation of reference d-axis and q-axis current values by the block:

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,

Ls= Lls+ Lm

Lr= Llr+ Lm


Stator voltages are represented as,

vsd= Rsisd+σLsdisddt+LmLrdλrddtωeσLsisq

vsq= Rsisq+σLsdisqdt+LmLrωeλrd+ωeσLsisd

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

λsd= LmLrλrd+σLsisd

λsq= σLsisq

τrdλrddt+ λrd=Lmisd

In steady-state, the rotor flux is kept constant and the d-axis is aligned to the rotor flux reference frame. Therefore,



These equations describe the mechanical dynamics,


Te TL=Jdωmdt +Bωm

These equations describe the slip speed,

τr= (LrRr)

ωe_slip= (Lmisqrefτrλrd)

ωe= ωr+ωe_slip

θe= ωe dt=(ωr+ωe_slip)dt=θr+θslip

Reference Current Computation

These equations show computation of the reference currents,


isq_req= Tref32p(LmLr)λrd

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

If ωm ωbase:


If ωm> ωbase:



These equations indicate the q-axis current computation,

isq_lim= imax2 isd_sat2


The block outputs the following values,




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

  • Rs is the stator phase winding resistance (Ohms).

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

  • Lls is the stator leakage inductance (Henry).

  • Llr is the rotor leakage inductance (Henry).

  • Ls is the stator inductance (Henry).

  • Lm is the magnetizing inductance (Henry).

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

  • σ is the total leakage factor of the induction motor.

  • τr is the rotor time constant (sec).

  • vsd and vsq are the stator d- and q-axis voltages (Volts).

  • isd and isq are the stator d- and q-axis currents (Amperes).

  • isd_0 is the d-axis rated current.

  • imax is the maximum phase current (peak) of the motor (Amperes).

  • λsd is the d-axis flux linkage of the stator (Weber).

  • λsq is the q-axis flux linkage of the stator (Weber).

  • λrd is the d-axis flux linkage of the rotor (Weber).

  • λrq is the q-axis flux linkage of the rotor (Weber).

  • ωe_slip is the electrical slip speed of the rotor (Radians/ sec).

  • ωslip is the mechanical slip speed of the rotor (Radians/ sec).

  • ωe is the electrical speed corresponding to frequency of stator voltages (Radians/ sec).

  • ωm is the rotor mechanical speed (Radians/ sec).

  • ωr is the rotor electrical speed (Radians/ sec).

  • ωbase is the mechanical base speed of the motor (Radians/ sec).

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



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

Data Types: single | double | fixed point

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

Data Types: single | double | fixed point


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Reference d-axis stator current value.

Data Types: single | double | fixed point

Reference q-axis stator current value.

Data Types: single | double | fixed point


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Number of pole pairs available in the induction motor.

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

Inductance due to the magnetizing flux (in Henry).

Rated flux of the induction motor (in Weber).

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

Synchronous speed of the induction motor (in rpm).

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

Unit of the input values.

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


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


[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™.

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

Introduced in R2020b