# Induction Machine Field-Oriented Control (Single-Phase)

Per-unit discrete-time single-phase induction machine field-oriented control

**Libraries:**

Simscape /
Electrical /
Control /
Induction Machine Control

## Description

The Induction Machine Field-Oriented Control (Single-Phase) block implements a single-phase induction machine field-oriented control structure.

### Equations

The field-oriented control architecture for a single-phase induction machine is:

You can provide the torque reference as an input, or, in the case of speed control, generate the reference internally using a PI speed controller. The torque reference as derived from a PI speed controller is:

$$T*=({K}_{p\_\omega}+{K}_{i\_\omega}\frac{{T}_{s}z}{z-1})({\omega}_{ref}-{\omega}_{r})$$

where *ω _{r}* is the rotor
angular mechanical speed in rad/s.

The block generates the flux reference as

$$\psi *=\frac{2\pi {f}_{n}{\psi}_{n}}{p\mathrm{min}(|{\omega}_{r}|,\frac{2\pi {f}_{n}}{p})}$$

where:

*p*is the number of pole pairs.*f*is the rated frequency._{n}*ψ*is the rated flux._{n}

Current references are obtained from machine parameters:

$${i}_{q}*=\frac{({L}_{ms}+{L}_{lar})T*}{pa{L}_{ms}\psi *}$$

$${i}_{d}*=\frac{\psi *}{{a}^{2}{L}_{ms}}$$

where:

*L*is the main winding mutual inductance._{ms}*L*is the main winding rotor leakage inductance._{lar}*a*is the auxiliary-to-main windings turn ratio.

The angle is calculated by solving:

$$\frac{d\theta}{dt}=p{\omega}_{r}+\frac{{a}^{3}{L}_{ms}{R}_{ar}}{{\psi}^{*}({L}_{ms}+{L}_{lar})}$$

The transformation to the stationary reference frame is done by using:

$$\left(\begin{array}{c}{i}_{a}\\ {i}_{b}\end{array}\right)=\left(\begin{array}{cc}{a}^{2}\mathrm{sin}(\theta )& {a}^{2}\mathrm{cos}(\theta )\\ \mathrm{cos}(\theta )& -\mathrm{sin}(\theta )\end{array}\right)\left(\begin{array}{c}{i}_{d}\\ {i}_{q}\end{array}\right)$$

### Limitations

The control structure is implemented in a single sample rate.

## Ports

### Input

### Output

## Parameters

## References

[1] Correa, M. B. R., Jacobina, C.
B., Lima, A. M. N., Da Silva, E. R. C. "Field Oriented Control of a Single-Phase
Induction Motor Drive." *PESC 98 Record. 29th Annual IEEE Power Electronics
Specialists Conference*. Vol. 2, 1998, pp. 990 - 996.

## Extended Capabilities

## Version History

**Introduced in R2018b**

## See Also

### Blocks

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