Induction Machine Flux Observer

Induction machine flux observer for field-oriented control

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Simscape / Electrical / Control / Observers

Description

The Induction Machine Flux Observer block obtains the synchronous speed, ω_e, and electrical angle, θ_e, 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 Induction Machine Flux Observer block uses these relationships:

$λ_{d r}^{' e} = L_{r}^{'} i_{d r}^{' e} + L_{M} i_{d s}^{e} ≜ L_{M} i_{m r},$

$0 = R_{r}^{'} i_{d r}^{' e} - (ω_{e} - ω_{r}) λ_{q r}^{' e} + \frac{d λ_{d r}^{' e}}{d t},$

and

$i_{q r}^{' e} = - \frac{L_{M}}{L_{r}^{'}} i_{q s}^{e},$

in these combined forms:

$i_{d r}^{' e} = \frac{L_{M}}{L_{r}^{'}} (i_{m r} - i_{d s}^{e})$

$\frac{d i_{m r}}{d t} = \frac{R_{r}^{'}}{L_{r}^{'}} (i_{d s}^{e} - i_{m r})$

and

$ω_{e} = ω_{r} + \frac{R_{r}^{'}}{L_{r}^{'}} \frac{i_{q s}^{e}}{i_{m r}}$

where:

$λ_{d r}^{' e}$ is the d-axis rotor flux.
$i_{m r}$ is the magnetizing current.
$i_{d s}^{e}$ and $i_{q s}^{e}$ are the d-axis and q-axis stator currents.
$i_{d r}^{' e}$ and $i_{q r}^{' e}$ are the d-axis and q-axis rotor currents.
$ω_{e}$ is the synchronous speed.
$ω_{r}$ is the mechanical rotational speed.
$R_{r}^{'}$ is the rotor resistance, referred to the stator side.
$L_{r}^{'}$ is the rotor leakage inductance, referred to the stator side.
$L_{M}$ the magnetizing inductance.

Examples

Three-Phase
Asynchronous Drive with Sensor Control

Three-Phase Asynchronous Drive with Sensor Control

Control and analyze the operation of an Asynchronous Machine (ASM) using sensored rotor field-oriented control. The model shows the main electrical circuit, with three additional subsystems containing the controls, measurements, and scopes. The Controls subsystem contains two controllers: one for the Grid-Side Converter (AC/DC) and one for the Machine-Side Converter (DC/AC). The Scopes subsystem contains two time scopes: one for the Grid-Side Converter and one for the ASM. When the model is executed, a Spectrum Analyzer opens and displays frequency data for the A-Phase Supply Current.

Open Model

Ports

Input

iabc — Current
vector

Measured stator currents in the per-unit system.

Data Types: single | double

wr — Speed
scalar

Measured rotational speed.

Data Types: single | double

Output

idqseF — Current
vector

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

Data Types: single | double

imr — Current
scalar

Magnetizing rotor current.

Data Types: single | double

theta — Electrical angle
scalar

Rotor electrical angle.

Data Types: single | double

we — Synchronous speed
scalar

Rotor synchronous speed.

Data Types: single | double

Parameters

Rated electrical frequency (Hz) — Frequency
`60` (default) | positive

Machine rated electrical frequency.

Rotor resistance, referred to the stator side (pu) — Resistance
`0.01` (default) | positive

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

Rotor leakage inductance, referred to the stator side (pu) — Inductance
`0.06` (default) | positive

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

Magnetizing inductance (pu) — Inductance
`2.7` (default) | positive

Magnetizing inductance in the per-unit system.

Time constant for dq currents filters (s) — Time constant
`1e-4` (default) | `0` or positive

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

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

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 | 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 Scalar Control