# ASM Flux Observer

Asynchronous machine flux observer

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• Simscape / Power Systems / Simscape Components / Control / Observers

## Description

The ASM Flux Observer block obtains the synchronous speed, ωe, and electrical angle, θe, that are required for performing rotor field-oriented control (FOC). The figure shows the equivalent circuit for the observer.

### Equations

To determine the synchronous speed and electrical angle, the ASM Flux Observer block uses these relationships:

`${\lambda }_{dr}^{\text{'}e}={L}_{r}^{\text{'}}{i}_{dr}^{\text{'}e}+{L}_{M}{i}_{ds}^{e}\triangleq {L}_{M}{i}_{mr},$`
`$0={R}_{r}^{\text{'}}{i}_{dr}^{\text{'}e}-\left({\omega }_{e}-{\omega }_{r}\right){\lambda }_{qr}^{\text{'}e}+\frac{d{\lambda }_{dr}^{\text{'}e}}{dt},$`
and
`${i}_{qr}^{\text{'}e}=-\frac{{L}_{M}}{{L}_{r}^{\text{'}}}{i}_{qs}^{e},$`

in these combined forms:

`${i}_{dr}^{\text{'}e}=\frac{{L}_{M}}{{L}_{r}^{\text{'}}}\left({i}_{mr}-{i}_{ds}^{e}\right)$`
`$\frac{d{i}_{mr}}{dt}=\frac{{R}_{r}^{\text{'}}}{{L}_{r}^{\text{'}}}\left({i}_{ds}^{e}-{i}_{mr}\right)$`
and
`${\omega }_{e}={\omega }_{r}+\frac{{R}_{r}^{\text{'}}}{{L}_{r}^{\text{'}}}\frac{{i}_{qs}^{e}}{{i}_{mr}}$`

where:

• ${\lambda }_{dr}^{\text{'}e}$ is the d-axis rotor flux.

• ${i}_{mr}$ is the magnetizing current.

• ${i}_{ds}^{e}$ and ${i}_{qs}^{e}$ are the d-axis and q-axis stator currents.

• ${i}_{dr}^{\text{'}e}$ and ${i}_{qr}^{\text{'}e}$ are the d-axis and q-axis rotor currents.

• ${\omega }_{e}$ is the synchronous speed.

• ${\omega }_{r}$ is the mechanical rotational speed.

• ${R}_{r}^{\text{'}}$ is the rotor resistance, referred to the stator side.

• ${L}_{r}^{\text{'}}$ is the rotor leakage inductance, referred to the stator side.

• ${L}_{M}$ the magnetizing inductance.

## Ports

### Input

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Measured stator currents in the per-unit system.

Data Types: `single` | `double`

Measured rotational speed.

Data Types: `single` | `double`

### Output

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Filtered d-axis and q-axis stator currents in the synchronous reference frame.

Data Types: `single` | `double`

Magnetizing rotor current.

Data Types: `single` | `double`

Rotor electrical angle.

Data Types: `single` | `double`

Rotor synchronous speed.

Data Types: `single` | `double`

## Parameters

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Machine rated electrical frequency.

Rotor resistance, referred to the stator side, in the per-unit system.

Rotor leakage inductance, referred to the stator side, in the per-unit system.

Magnetizing inductance in the per-unit system.

Time constant used to low-pass filter the d-q currents.

Time interval between samples. If the 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. For more information, see What Is Sample Time? (Simulink) and Specify Sample Time (Simulink).

## References

[1] Vas, P. Electrical Machines and Drives: A Space-vector Theory Approach. New York: Oxford University Press, 1992.