Induction Machine Field-Oriented Control (Single-Phase)

Per-unit discrete-time single-phase induction machine field-oriented control

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Libraries:
Simscape / Electrical / Control / Induction Machine Control

Description

The Induction Machine Field-Oriented Control (Single-Phase) block implements a single-phase induction machine field-oriented control structure.

Equations

The field-oriented control architecture for a single-phase induction machine is:

You can provide the torque reference as an input, or, in the case of speed control, generate the reference internally using a PI speed controller. The torque reference as derived from a PI speed controller is:

$$T*=(K_{p\_\omega }+K_{i\_\omega }\frac{T_{s}z}{z-1})({\omega }_{ref}-{\omega }_r)$$

where ω_r is the rotor angular mechanical speed in rad/s.

The block generates the flux reference as

$$\psi *=\frac{2\pi f_n{\psi }_n}{p\min (|{\omega }_r|,\frac{2\pi f_n}{p})}$$

where:

• p is the number of pole pairs.

• f_n is the rated frequency.

• ψ_n is the rated flux.

Current references are obtained from machine parameters:

$$i_q*=\frac{(L_{ms}+L_{lar})T*}{pa{L}_{ms}\psi *}$$

$$i_d*=\frac{\psi *}{a^2{L}_{ms}}$$

where:

• L_ms is the main winding mutual inductance.

• L_lar is the main winding rotor leakage inductance.

• a is the auxiliary-to-main windings turn ratio.

The angle is calculated by solving:

$$\frac{d\theta }{dt}=p{\omega }_r+\frac{a^3{L}_{ms}{R}_{ar}}{{\psi }^{*}(L_{ms}+L_{lar})}$$

The transformation to the stationary reference frame is done by using:

$$\left(\begin{array}{c}{i}_a\\ i_b\end{array}\right)=\left(\begin{array}{cc}{a}^2\sin (\theta )& a^2\cos (\theta )\\ \cos (\theta )& -\sin (\theta )\end{array}\right)\left(\begin{array}{c}{i}_d\\ i_q\end{array}\right)$$

Limitations

• The control structure is implemented in a single sample rate.

Ports

Input

Reference — Torque or angular velocity reference

scalar

Specify the angular velocity reference, in rad/s, or the torque reference, in Nm.

Data Types: single | double

iab — Stator currents

scalar

Stator currents for main and auxiliary windings.

Data Types: single | double

wr — Rotor angular speed

scalar

Measured rotor angular speed, in rad/s.

Data Types: single | double

Output

G — Inverter gate pulses

0 | 1

Inverter gate pulses, specified as a Boolean. The dead-time is not considered.

Data Types: single | double

Visualization — Internal signals for visualization

Reference | Rotor velocity | θ | iab | iabRef | TqRef | FluxRef

Bus containing internal signals for visualization. The signals are:

• Reference torque or speed

• Rotor velocity, in rad/s

• θ, in radians

• Stator currents (iab), in A

• Stator current reference (iabRef), in A

• Torque Reference (TqRef), in Nm

• Flux Reference (FluxRef), in Wb

Data Types: single | double | bus

Parameters

General

Control mode — Specify control mode

Speed control (default) | Torque control

Specify the control mode. The reference input is taken as angular speed, in rad/s, for Speed control and torque, in Nm for Torque control.

Rated electrical frequency (Hz) — Specify rated electrical frequency

60 (default) | positive scalar

Rated electrical frequency, in Hz.

Number of pole pairs — Specify pole pairs

2 (default) | positive scalar

Number of pole pairs.

Main winding rotor resistance, Rar' (Ohm) — Specify main winding rotor resistance

3.7080 (default) | positive scalar

Main winding rotor resistance, in Ohms.

Main winding rotor leakage inductance, Llar' (H) — Specify main winding rotor leakage inductance

0.0050 (default) | positive scalar

Main winding rotor leakage inductance, in H.

Main winding mutual inductance, Lms (H) — Specify main winding mutual inductance

0.1595 (default) | positive scalar

Main winding mutual inductance, in H.

Auxiliary/main windings turn ratio — Specify the auxiliary-to-main windings turn ratio

1.1 (default) | positive scalar

Auxiliary-to-main windings turns ratio.

Fundamental sample time (s) — Specify the block sample time

5e-6 (default) | positive scalar

Sample time for the block, in s.

Control sample time (s) — Specify the control sample time

5e-5 (default) | positive scalar

Control sample time, in s.

Outer Loop

This table shows how the visibility of some parameters in the Outer Loop tab depend on the option that you choose for the Control mode parameter in the General tab.

Control mode	Available Parameters
Speed control	Speed controller proportional gain
	Speed controller integral gain
	Speed controller integral anti-windup gain
	Maximum torque (Nm)
	Minimum torque (Nm)
	Rated flux (Wb)
Torque control	Rated flux (Wb)

Speed controller proportional gain — Specify the speed controller proportional gain

1 (default) | positive scalar

Proportional gain for the PI speed controller.

Speed controller integral gain — Specify the speed controller integral gain

10 (default) | positive scalar

Integral gain for the PI speed controller.

Speed controller integral anti-windup gain — Specify the speed controller integral anti-windup gain

1000 (default) | positive scalar

Integral anti-windup gain.

Maximum torque (Nm) — Specify the maximum torque

5 (default) | positive scalar

Maximum torque used in speed controller saturation, in Nm.

Minimum torque (Nm) — Specify the minimum torque

-5 (default) | scalar

Minimum torque used in speed controller saturation, in Nm.

Rated flux (Wb) — Specify the rated flux

0.5 (default) | positive scalar

Rated flux, in Wb. The rated flux is used to compute the flux reference.

Inner Loop

This table shows how the visibility of some parameters in the Inner Loop tab depend on the option that you choose for the Control type parameter.

Control type	Available Parameters
Hysteresis control	Current hysteresis band (A)
PI control	A-phase current proportional gain
	A-phase current integral gain
	A-phase current anti-windup gain
	B-phase current proportional gain
	B-phase current integral gain
	B-phase current anti-windup gain

Control type — Specify the control type

Hysteresis control (default) | PI control

Control type for current control loop.

Current hysteresis band (A) — Specify the current hysteresis band

0.5 (default) | positive scalar

Current hysteresis band for the controller, in A.

A-phase current proportional gain — Main winding current proportional gain

1 (default) | positive scalar

Proportional gain for the A-phase (main winding) controller current.

A-phase current integral gain — Main winding current integral gain

500 (default)

Integral gain for the A-phase (main winding) controller current.

A-phase current anti-windup gain — Main winding current anti-windup gain

1000 (default)

Anti-windup gain for the A-phase (main winding) controller current.

B-phase current proportional gain — Auxiliary winding current proportional gain

1 (default)

Proportional gain for the B-phase (auxiliary winding) controller current.

B-phase current integral gain — Auxiliary winding current integral gain

500 (default)

Integral gain for the B-phase (auxiliary winding) controller current.

B-phase current anti-windup gain — Auxiliary winding current anti-windup gain

1000 (default)

Anti-windup gain for the B-phase (auxiliary winding) controller current.

References

[1] Correa, M. B. R., Jacobina, C. B., Lima, A. M. N., Da Silva, E. R. C. "Field Oriented Control of a Single-Phase Induction Motor Drive." PESC 98 Record. 29th Annual IEEE Power Electronics Specialists Conference. Vol. 2, 1998, pp. 990 - 996.

Extended Capabilities

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

Version History

Introduced in R2018b