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Induction machine DTC

**Library:**Simscape / Electrical / Control / Induction Machine Control

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.

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:

${\psi}_{\alpha}=\left({v}_{\alpha}-{i}_{\alpha}{R}_{s}\right)\frac{{T}_{s}z}{z-1}$

and

${\psi}_{\beta}=\left({v}_{\beta}-{i}_{\beta}{R}_{s}\right)\frac{{T}_{s}z}{z-1}$

where:

*v*is_{ɑ}*ɑ*-axis voltage.*i*is_{ɑ}*ɑ*-axis current.*R*is the stator resistance._{s}*Ψ*is the_{ɑ}*ɑ*-axis stator flux.*v*is_{β}*β*-axis voltage.*i*is_{β}*β*-axis current.*Ψ*is the_{β}*β*-axis stator flux.

The block calculates the torque and flux as:

$T=\frac{3p}{2}\left({\psi}_{\alpha}{i}_{\beta}-{\psi}_{\beta}{i}_{\alpha}\right)$

and

${\psi}_{s}=\sqrt{{\psi}_{\alpha}^{2}+{\psi}_{\beta}^{2}}$

where:

*p*is the number of pole pairs.*Ψ*is the stator flux._{s}

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_{T}S(θ) | S_{0} | S_{1} | S_{2} | S_{3} | S_{4} | S_{5} | |
---|---|---|---|---|---|---|---|

c_{Ψ} = 1 | c = 1_{T}
| `1, 1, 0` | `0, 1, 0` | `0, 1, 1` | `0, 0, 1` | `1, 0, 1` | `1, 0, 0` |

c = 0_{T}
| `1, 1, 1` | `0, 0, 0` | `1, 1, 1` | `0, 0, 0` | `1, 1, 1` | `0, 0, 0` | |

c = -1_{T}
| `1, 0, 1` | `1, 0, 0` | `1, 1, 0` | `0, 1, 0` | `0, 1, 1` | `0, 0, 1` | |

c_{Ψ} = 0 | c = 1_{T}
| `0, 1, 0` | `0, 1, 1` | `0, 0, 1` | `1, 0, 1` | `1, 0, 0` | `1, 1, 0` |

c = 0_{T}
| `0, 0, 0` | `1, 1, 1` | `0, 0, 0` | `1, 1, 1` | `0, 0, 0` | `1, 1, 1` | |

c = -1_{T}
| `0, 0, 1` | `1, 0, 1` | `1, 0, 0` | `1, 1, 0` | `0, 1, 0` | `0, 1, 1` |

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

[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.

- 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