Induction Machine Direct Torque Control

Induction machine DTC

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Description

The Induction Machine Direct Torque Control block implements an induction machine direct torque control (DTC) structure. The figure shows the equivalent circuit for the block.

Equations

To estimate the torque and flux, the Induction Machine Direct Torque Control block discretizes the machine voltage equations in the stationary ɑβ reference frame using the backward Euler method. The discrete-time equations for stator fluxes in the ɑβ frame are:

ψα=(vαiαRs)Tszz1

and

ψβ=(vβiβRs)Tszz1

where:

  • vɑ is ɑ-axis voltage.

  • iɑ is ɑ-axis current.

  • Rs is the stator resistance.

  • Ψɑ is the ɑ-axis stator flux.

  • vβ is β-axis voltage.

  • iβ is β-axis current.

  • Ψβ is the β-axis stator flux.

The block calculates the torque and flux as:

T=3p2(ψαiβψβiα)

and

ψs=ψα2+ψβ2

where:

  • p is the number of pole pairs.

  • Ψs is the stator flux.

To detect flux and torque estimation errors, the block uses hysteresis comparators. The figure shows hysteresis comparators and the associated switching sectors.

The table shows the optimum switching for an inverter high-side system.

cΨ, cTS(θ)S0S1S2S3S4S5
cΨ = 1cT = 11, 1, 00, 1, 00, 1, 10, 0, 11, 0, 11, 0, 0
cT = 01, 1, 10, 0, 01, 1, 10, 0, 01, 1, 10, 0, 0
cT = -11, 0, 11, 0, 01, 1, 00, 1, 00, 1, 10, 0, 1
cΨ = 0cT = 10, 1, 00, 1, 10, 0, 11, 0, 11, 0, 01, 1, 0
cT = 00, 0, 01, 1, 10, 0, 01, 1, 10, 0, 01, 1, 1
cT = -10, 0, 11, 0, 11, 0, 01, 1, 00, 1, 00, 1, 1

Assumptions and Limitations

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

Ports

Input

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Reference stator flux.

Data Types: single | double

Reference torque.

Data Types: single | double

Stator phase voltages.

Data Types: single | double

Stator phase currents.

Data Types: single | double

Output

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Inverter gate pulses. The block does not consider any dead time.

Data Types: single | double

Parameters

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Resistance of the machine stator.

Number of machine pole pairs.

Total bandwidth distributed symmetrically around the flux set point.

Total bandwidth distributed symmetrically around the set point.

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? (Simulink) and Specify Sample Time (Simulink).

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.

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™.

Introduced in R2017b