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Induction machine DTC structure with SVM

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

The Induction Machine Direct Torque Control with Space Vector Modulator implements an induction machine direct torque control structure (DTC) with space vector modulator (SVM). Use this block to generate the gate pulses for an inverter controlling an induction machine. This diagram shows the architecture of the block.

In the diagram:

You provide the reference torque,

*T**, and flux,*ψ**.The Flux and Torque Estimator estimates the actual torque,

*T*, and flux,*ψ*from the measured phase currents,*i*, and voltages,_{abc}*v*._{abc}Two PI controllers determine the reference

*d*and*q*voltages,*v*and_{d}*v*, from the flux and torque errors, respectively._{q}The SVM generates the gates pulses,

*G*, required to control an inverter driving the induction machine. Subscript_{ij}*i*corresponds to the phase (*a*,*b*, or*c*). Subscript*j*corresponds to the high,*H*, or low,*L*, signal.

To estimate the torque and flux, the 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:

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

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

Where:

*v*and_{ɑ}*v*are the_{β}*ɑ*- and*β*-axis voltages, respectively.*i*and_{ɑ}*i*are the_{β}*ɑ*- and*β*-axis currents, respectively.*Ψ*and_{ɑ}*Ψ*are the_{β}*ɑ*- and*β*-axis stator fluxes, respectively.*R*is the stator resistance._{s}

The block calculates the torque and total stator flux as:

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

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

Where:

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

The SVM converts the desired voltages into gate pulses, which you use to control an inverter. This figure shows possible switching states of a three-phase inverter.

The hexagon represents the space vector diagram. Each of the six
vertices represents a possible switching state
*(G _{AH},G_{BH},G_{CH})*
of the three-phase inverter. Each low gate takes the opposite state as its
corresponding high gate. The inverter diagram illustrates the current state.

The rotating vector in the space vector diagram corresponds to the complex
reference voltage vector, which rotates at the desired electrical frequency of the
machine. In reality, the switching frequency is much faster than this electrical
frequency. As a result, the inverter switches continually between the two states
enclosing its current region *Ri*, and the zero state corresponding
to *(0,0,0)*, to generate the desired voltages.

To learn about the implementation of this method, see the PWM Generator (Three-phase, Two-level) block.

[1] Buja, G. S., and M. P Kazmierkowski. "Direct Torque Control of PWM Inverter-Fed AC
Motors—A Survey." *IEEE Transactions on Industrial Electronics* 51,
no. 4, (2004): 744 - 757.

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