Induction Machine Direct Torque Control

Induction machine DTC

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Libraries:
Simscape / Electrical / Control / Induction Machine Control

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:

$ψ_{α} = (v_{α} - i_{α} R_{s}) \frac{T_{s} z}{z - 1}$

and

$ψ_{β} = (v_{β} - i_{β} R_{s}) \frac{T_{s} z}{z - 1}$

where:

v_ɑ is ɑ-axis voltage.
i_ɑ is ɑ-axis current.
R_s is the stator resistance.
Ψ_ɑ is the ɑ-axis stator flux.
v_β is β-axis voltage.
i_β is β-axis current.
Ψ_β is the β-axis stator flux.

The block calculates the torque and flux as:

$T = \frac{3 p}{2} (ψ_{α} i_{β} - ψ_{β} i_{α})$

and

$ψ_{s} = \sqrt{ψ_{α}^{2} + ψ_{β}^{2}}$

where:

p is the number of pole pairs.
Ψ_s 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.

c_Ψ, c_TS(θ)		S₀	S₁	S₂	S₃	S₄	S₅
c_Ψ = 1	c_T = 1	`1, 1, 0`	`0, 1, 0`	`0, 1, 1`	`0, 0, 1`	`1, 0, 1`	`1, 0, 0`
	c_T = 0	`1, 1, 1`	`0, 0, 0`	`1, 1, 1`	`0, 0, 0`	`1, 1, 1`	`0, 0, 0`
	c_T = -1	`1, 0, 1`	`1, 0, 0`	`1, 1, 0`	`0, 1, 0`	`0, 1, 1`	`0, 0, 1`
c_Ψ = 0	c_T = 1	`0, 1, 0`	`0, 1, 1`	`0, 0, 1`	`1, 0, 1`	`1, 0, 0`	`1, 1, 0`
	c_T = 0	`0, 0, 0`	`1, 1, 1`	`0, 0, 0`	`1, 1, 1`	`0, 0, 0`	`1, 1, 1`
	c_T = -1	`0, 0, 1`	`1, 0, 1`	`1, 0, 0`	`1, 1, 0`	`0, 1, 0`	`0, 1, 1`

Assumptions and Limitations

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

Examples

Asynchronous Machine Direct Torque
Control

Asynchronous Machine Direct Torque Control

Control an asynchronous machine (ASM) using the direct-torque control method. A PI-based speed controller supplies the torque reference. The direct-torque controller generates the inverter pulses.

Open Model

Ports

Input

FluxRef — Flux
scalar

Reference stator flux.

Data Types: single | double

TqRef — Torque
scalar

Reference torque.

Data Types: single | double

vabc — Voltage
vector

Stator phase voltages.

Data Types: single | double

iabc — Current
vector

Stator phase currents.

Data Types: single | double

Output

G — Gate pulses
vector | `0` or `1`

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

Data Types: single | double

Parameters

Stator resistance (Ohm) — Resistance
`0.25` (default) | positive scalar

Resistance of the machine stator.

Number of pole pairs — Pole number
`1` (default) | positive integer

Number of machine pole pairs.

Flux hysteresis bandwidth (Wb) — Flux
`0.02` (default) | positive scalar

Total bandwidth distributed symmetrically around the flux set point.

**Torque hysteresis bandwidth (N*m)** — Torque
`10` (default) | positive scalar

Total bandwidth distributed symmetrically around the set point.

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.

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 R2017b

See Also

Blocks

Induction Machine Current Controller | Induction Machine Direct Torque Control (Single-Phase) | Induction Machine Direct Torque Control with Space Vector Modulator | Induction Machine Field-Oriented Control | Induction Machine Field-Oriented Control (Single-Phase) | Induction Machine Flux Observer | Induction Machine Scalar Control