Induction Machine Direct Torque Control (Single-Phase)

Single-phase induction machine direct torque control

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Libraries:
Simscape / Electrical / Control / Induction Machine Control

Description

The Induction Machine Direct Torque Control (Single-Phase) block implements a single-phase induction machine direct torque control structure.

Equations

This diagram shows the direct torque control architecture for single-phase machines

The torque and flux estimation is based on machine voltage equations. The discrete-time voltage equations using the backward Euler discretization method, are:

$${\psi }_a=(v_a-i_a{R}_{as})\frac{T_{s}z}{z-1}$$

$${\psi }_b=(v_b-i_b{R}_{bs})\frac{T_{s}z}{z-1}$$

where:

• R_as and R_bs are the main winding resistance and the auxiliary winding resistance, respectively.

• i_a and i_b are the main winding current and the auxiliary winding current, respectively.

• v_a and v_b are the main and auxiliary winding voltage, respectively.

• ψ_a and ψ_b are the main and auxiliary winding flux, respectively.

The torque and flux are obtained from:

$$T=-p(a{\psi }_a{i}_b-\frac{1}{a}{\psi }_b{i}_a)$$

$${\psi }_s=\sqrt{{\psi }_a{}^2+{\psi }_b{}^2}$$

where:

• p is the number of pole pairs.

• a is the auxiliary to main windings turn ratio.

Employing simple hysteresis comparators detects the status of flux and torque errors. The following figures illustrate the hysteresis comparators and the switching sectors.

The table shows the optimum switching table (inverter high side).

cψ, cT, S(θ)		S0	S1	S2	S3
cψ = 1	cT = 1	1, 0	1, 1	0, 1	0, 0
	cT = 0	1, 1	0, 1	0, 0	1, 0
cψ = 0	cT = 1	0, 0	1, 0	1, 1	0, 1
	cT = 0	0, 1	0, 0	1, 0	1, 1

The torque reference can be provided as an input, or, in the case of speed control, be generated internally using a PI speed controller.

The flux reference is generated internally using:

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

where,

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

• f_n is the rated frequency.

• ψ_n is the rated flux.

Limitations

• The power inverter dead-times are not considered in this block. For hardware implementation, add the dead-time externally.

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

vab — Stator voltages

scalar

Stator voltages for main and auxiliary windings.

Data Types: single | double

wr — Rotor angular speed

scalar

Measure 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 | TqRef | FluxRef | Torque | Flux

Bus containing internal signals for visualization. The signals are:

• Reference torque or speed

• Rotor velocity, in rad/s

• Torque Reference, in Nm

• Flux Reference, in Wb

• Torque, in Nm

• Flux, 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 stator resistance, Ras (Ohm) — Specify main winding stator resistance

1.8180 (default) | positive scalar

Resistance of the main winding stator, in Ohms.

Auxiliary winding stator resistance, Rbs (Ohm) — Specify auxiliary winding stator resistance

6.4260 (default) | positive scalar

Resistance of the auxiliary winding stator, in Ohms.

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

1.1 (default) | positive scalar

Auxiliary-to-main windings turns ratio.

Sample time (-1 for inherited) — Block sample time

-1 (default) | positive scalar

Time, in s, between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

If this block is inside a triggered subsystem, inherit the sample time by setting this parameter to -1. If this block is in a continuous variable-step model, specify the sample time explicitly using a positive scalar.

Outer Loop

This table shows how the visibility of some parameters in the Outer Loop tab depends 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

Flux hysteresis band (Wb) — Specify the flux hysteresis band

0.02 (default) | positive scalar

Flux hysteresis band for the controller, in Wb.

Torque hysteresis band (Nm) — Specify the torque hysteresis band

0.1 (default) | positive scalar

Torque hysteresis band for the controller, in Nm.

References

[1] Takahashi, I., and T. Noguchi. "A New Quick-Response and High-Efficiency Control Strategy of an Induction Motor." IEEE Transactions on Industry Applications. Vol. IA-22, Number 5, 1986, pp. 820 - 827.

Extended Capabilities

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

Version History

Introduced in R2018b