Compute reference currents for field-oriented control of induction motor
Motor Control Blockset / Controls / Control Reference
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
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.
These model equations describe the dynamics of induction motor in the rotor flux reference frame:
The machine inductances are represented as,
Stator voltages are represented as,
In the preceding equations, the flux linkages can be represented as,
If we keep the rotor flux as constant and the d-axis is aligned to the rotor flux reference frame, then we can imply:
These equations describe the mechanical dynamics,
These equations describe the slip speed,
These equations show computation of the reference currents,
The reference currents are computed differently for operation below base speed and field weakening region,
These equations indicate the q-axis current computation,
The block outputs the following values,
is the number of pole pairs of the motor.
is the stator phase winding resistance (Ohms).
is the rotor resistance referred to stator (Ohms).
is the stator leakage inductance (Henry).
is the rotor leakage inductance (Henry).
is the stator inductance (Henry).
is the magnetizing inductance (Henry).
is the rotor inductance referred to stator (Henry).
is the total leakage factor of the induction motor.
is the rotor time constant (sec).
and are the stator d- and q-axis voltages (Volts).
and are the stator d- and q-axis currents (Amperes).
is the rated d-axis current of the stator also known as magnetizing current (Amperes).
is the maximum phase current (peak) of the motor (Amperes).
is the d-axis flux linkage of the stator (Weber).
is the q-axis flux linkage of the stator (Weber).
is the d-axis flux linkage of the rotor (Weber).
is the q-axis flux linkage of the rotor (Weber).
is the electrical slip speed of the rotor (Radians/ sec).
is the mechanical slip speed of the rotor (Radians/ sec).
is the electrical speed corresponding to frequency of stator voltages (Radians/ sec).
is the rotor mechanical speed (Radians/ sec).
is the rotor electrical speed (Radians/ sec).
is the mechanical base speed of the motor (Radians/ sec).
is the electromechanical torque produced by the motor (Nm).
Tref— Reference torque value
Reference torque input value for which the block computes the reference current.
⍵m— Mechanical speed
Reference mechanical speed value for which the block computes the reference current.
Isdref— Reference d-axis stator current
Reference d-axis stator current value.
Isqref— Reference q-axis stator current
Reference q-axis stator current value.
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) |
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.
To enable this parameter, set Input units to
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.
To display this parameter, set Input units to
 B. Bose, Modern Power Electronics and AC Drives. Prentice Hall, 2001. ISBN-0-13-016743-6.
 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.
 W. Leonhard, Control of Electrical Drives, 3rd ed. Secaucus, NJ, USA:Springer-Verlag New York, Inc., 2001.
 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.
 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.
 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.