ACIM Control Reference

Compute reference currents for field oriented control of induction motor

Library:
Motor Control Blockset / Controls / Control Reference

Description

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,

$L_{s} = L_{l s} + L_{m}$

$L_{r} = L_{l r} + L_{m}$

$σ = 1 - (\frac{L_{m}^{2}}{L_{s} \cdot L_{r}})$

Stator voltages are represented as,

$v_{s d} = R_{s} i_{s d} + σ L_{s} \frac{d i_{s d}}{d t} + \frac{L_{m}}{L_{r}} \frac{d λ_{r d}}{d t} - ω_{e} σ L_{s} i_{s q}$

$v_{s q} = R_{s} i_{s q} + σ L_{s} \frac{d i_{s q}}{d t} + \frac{L_{m}}{L_{r}} ω_{e} λ_{r d} + ω_{e} σ L_{s} i_{s d}$

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

$λ_{s d} = \frac{L_{m}}{L_{r}} λ_{r d} + σ L_{s} i_{s d}$

$λ_{s q} = σ L_{s} i_{s q}$

$τ_{r} \frac{d λ_{r d}}{d t} + λ_{r d} = L_{m} i_{s d}$

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

$λ_{rd} \approx L_{m} i_{s d}$

$λ_{rq} = 0$

These equations describe the mechanical dynamics,

$T_{e} = \frac{3}{2} p (\frac{L_{m}}{L_{r}}) λ_{r d} i_{s q}$

$T_{e} - T_{L} = J \frac{d ω_{m}}{d t} + B ω_{m}$

These equations describe the slip speed,

$τ_{r} = (\frac{L_{r}}{R_{r}})$

$ω_{e_slip} = (\frac{L_{m} \cdot i_{sq}^{r e f}}{τ_{r} \cdot λ_{rd}})$

$ω_{e} = ω_{r} + ω_{e_s l i p}$

$θ_{e} = \int ω_{e} \cdot d t = \int (ω_{r} + ω_{e_s l i p}) \cdot d t = θ_{r} + θ_{s l i p}$

Reference Current Computation

These equations show computation of the reference currents,

$i_{s d_0} = \frac{λ_{rd}}{L_{m}}$

$i_{s q_r e q} = \frac{T^{r e f}}{\frac{3}{2} p (\frac{L_{m}}{L_{r}}) λ_{r d}}$

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

If $ω_{m} \leq ω_{b a s e}$ :

$i_{s d_s a t} = \min (i_{s d_0}, i_{\max})$

If $ω_{m} > ω_{b a s e}$ :

$i_{s d_f w} = (\frac{i_{s d_0}}{| ω_{e} |})$

$i_{s d_s a t} = \min (i_{s d_f w}, i_{\max})$

These equations indicate the q-axis current computation,

$i_{s q_l i m} = \sqrt{i_{m a x}^{2} - i_{s d_s a t}^{2}}$

$i_{s q_s a t} = s a t (i_{s q_l i m}, i_{s q_r e q})$

The block outputs the following values,

$i_{s d}^{r e f} = i_{s d_s a t}$

$i_{s q}^{r e f} = i_{s q_s a t}$

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).
$L_{l s}$ is the stator leakage inductance (Henry).
$L_{l r}$ 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).
$σ$ is the total leakage factor of the induction motor.
$τ_{r}$ is the rotor time constant (sec).
$v_{s d}$ and $v_{s q}$ are the stator d- and q-axis voltages (Volts).
$i_{s d}$ and $i_{s q}$ are the stator d- and q-axis currents (Amperes).
$i_{s d_0}$ is the d-axis rated current.
$i_{m a x}$ is the maximum phase current (peak) of the motor (Amperes).
$λ_{s d}$ is the d-axis flux linkage of the stator (Weber).
$λ_{s q}$ is the q-axis flux linkage of the stator (Weber).
$λ_{r d}$ is the d-axis flux linkage of the rotor (Weber).
$λ_{r q}$ is the q-axis flux linkage of the rotor (Weber).
$ω_{e_slip}$ is the electrical slip speed of the rotor (Radians/ sec).
$ω_{slip}$ is the mechanical slip speed of the rotor (Radians/ sec).
$ω_{e}$ is the electrical speed corresponding to frequency of stator voltages (Radians/ sec).
$ω_{m}$ is the rotor mechanical speed (Radians/ sec).
$ω_{r}$ is the rotor electrical speed (Radians/ sec).
$ω_{b a s e}$ is the mechanical base speed of the motor (Radians/ sec).
$T_{e}$ is the electromechanical torque produced by the motor (Nm).

Ports

Input

expand all

`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

expand all

`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

expand all

`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).

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.

Documentation

ACIM Control Reference

Description

Mathematical Model of Induction Motor

Reference Current Computation

Ports

Input

`T^ref` — Reference torque value
scalar

`⍵_m` — Mechanical speed
scalar

Output

`I_sd^ref` — Reference d-axis stator current
scalar

`I_sq^ref` — Reference q-axis stator current
scalar

Parameters

`Number of pole pairs` — Number of pole pairs available in motor
`2` (default) | scalar

`Rotor leakage inductance (H)` — Leakage inductance of rotor winding
`6.81e-3` (default) | scalar

`Magnetizing Inductance (H)` — Magnetizing inductance of induction motor
`30e-3` (default) | scalar

`Rated Flux (Wb)` — Rated flux of motor
`38.2e-3` (default) | scalar

`Rated Speed (rpm)` — Rated speed of motor
`1150` (default) | scalar

`Synchronous Speed (rpm)` — Synchronous speed of motor
`1500` (default) | scalar

`Max current (A)` — Maximum phase current limit for motor (amperes)
3 (default) | scalar

`Input units` — Unit of input values
`Per-Unit (PU)` (default) | `SI Units`

`Base Current (A)` — Base current for per-unit system
`5.3611` (default) | scalar

Dependencies

References

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™.

See Also

Topics

Motor Control Blockset Documentation

Support

Documentation

ACIM Control Reference

Description

Mathematical Model of Induction Motor

Reference Current Computation

Ports

Input

Tref — Reference torque value scalar

⍵m — Mechanical speed scalar

Output

Isdref — Reference d-axis stator current scalar

Isqref — Reference q-axis stator current scalar

Parameters

Number of pole pairs — Number of pole pairs available in motor 2 (default) | scalar

Rotor leakage inductance (H) — Leakage inductance of rotor winding 6.81e-3 (default) | scalar

Magnetizing Inductance (H) — Magnetizing inductance of induction motor 30e-3 (default) | scalar

Rated Flux (Wb) — Rated flux of motor 38.2e-3 (default) | scalar

Rated Speed (rpm) — Rated speed of motor 1150 (default) | scalar

Synchronous Speed (rpm) — Synchronous speed of motor 1500 (default) | scalar

Max current (A) — Maximum phase current limit for motor (amperes) 3 (default) | scalar

Input units — Unit of input values Per-Unit (PU) (default) | SI Units

Base Current (A) — Base current for per-unit system 5.3611 (default) | scalar

Dependencies

References

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™.

See Also

Topics

Motor Control Blockset Documentation

Support

`T^ref` — Reference torque value
scalar

`⍵_m` — Mechanical speed
scalar

`I_sd^ref` — Reference d-axis stator current
scalar

`I_sq^ref` — Reference q-axis stator current
scalar

`Number of pole pairs` — Number of pole pairs available in motor
`2` (default) | scalar

`Rotor leakage inductance (H)` — Leakage inductance of rotor winding
`6.81e-3` (default) | scalar

`Magnetizing Inductance (H)` — Magnetizing inductance of induction motor
`30e-3` (default) | scalar

`Rated Flux (Wb)` — Rated flux of motor
`38.2e-3` (default) | scalar

`Rated Speed (rpm)` — Rated speed of motor
`1150` (default) | scalar

`Synchronous Speed (rpm)` — Synchronous speed of motor
`1500` (default) | scalar

`Max current (A)` — Maximum phase current limit for motor (amperes)
3 (default) | scalar

`Input units` — Unit of input values
`Per-Unit (PU)` (default) | `SI Units`

`Base Current (A)` — Base current for per-unit system
`5.3611` (default) | scalar

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™.