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Doubly-Fed Induction Machine

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Doubly-Fed Induction Machine

This block implements a doubly-fed induction machine (DFIM)

The DFIM block implements a three-phase induction machine (asynchronous machine) with an accessible wound rotor model with resolvers and encoders. The machine can operate in both motoring mode, when the mechanical torque is positive, and generating mode when the mechanical torque is negative.

Model Formulation

Q-d Transformation

The 3-phase to q-d transformation and the inverse used for the model are (amplitude-invariant sine-based Park transformation):

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The induction machine model uses the rotor as a reference, thus the angle of

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.

The saturated SCIM and DFIM use a different transform: the amplitude-invariant cosine-based Clarke transformation, which means that the rotating frame is aligned with phase A axis at

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. For the linear induction machines the rotating frame aligns
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behind phase A axis at
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.

Induction Machine Electrical Model

Induction machine models in state-space framework are based on magnetic fluxes. The state variables and winding currents (as the outputs) can be represented as follows:

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where the coefficient matrices are as follows:

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and

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The Induction Machine is modeled in rotor reference frame so ω=ωr.

In the model, all the rotor parameters and variables are seen from the stator distinguished by a prime sign. The stator to rotor turn ratio (Nsr) is applied as follows to transfer input three-phase rotor voltage to the stator side, and transfer back the output three-phase rotor current measurements to the rotor side:  

The electrical torque is calculated as follows:

Parameters and Measurements

The DFIM's parameters and measurements are separated in 4 different tabs, Electrical, Mechanical, Resolver and Encoder.

Electrical Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

Rs

Stator resistance

Stator winding resistance of phase a, b, and c

Ω

Edit-input

Lls

Stator leakage inductance

Stator winding leakage inductance of phase a, b, and c

H

Edit-input

Rr'

Rotor resistance

Equivalent rotor winding resistance referred to the stator of phase a, b, and c

Ω

Edit-input

Llr'

Rotor leakage inductance 

Equivalent rotor winding leakage inductance referred to the stator of phase a, b, and c

H

Edit-input

Lm

Mutual inductance

Stator-rotor mutual (magnetizing) inductance of phase a, b, and c

H

Edit-input

pp

Number of pole pairs

Number of pole pairs

N/A

Edit-input

is

Stator phase currents

Stator currents measured at phases a, b and c

A

Measurement

isdq

Stator dq currents

Stator currents in dq frame

A

Measurement

Φsdq

Stator dq fluxes

Stator fluxes in dq frame

Wb

Measurement

Vsdq

Stator dq voltages

Stator voltages in dq frame

V

Measurement

ir'

Rotor phase currents

Rotor equivalent phase a, b, and c currents, referred to the stator

A

Measurement

irdq

Rotor dq currents

Rotor currents in dq frame, referred to the stator

A

Measurement

Φrdq'

Rotor dq fluxes

Rotor fluxes in dq frame, referred to the stator

Wb

Measurement

Vrdq

Rotor dq voltages

Rotor voltages in dq frame, referred to the stator

V

Measurement

Rsn

Snubber resistance

Resistances of the snubber on phase A, B and C

Ω

Input

Csn

Snubber capacitance

Capacitance of the snubber on phase A, B and C

F

Input

Mechanical Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

J

Rotor inertia

Moment of inertia of the rotor

kg*m2

Input

Fv

Viscous friction coefficient

Viscous friction

N*m*s/rad

Input

Fs

Static friction torque

Static friction

N*m

Input

ctrl

Mechanical control mode

Control mode of the mechanical model. Has two possible values: speed or torque. In speed mode, the mechanical model is bypassed and the speed command is sent directly. In torque mode, the torque command is used to measure the speed using the mechanical parameters of the machine.



Input

T

Torque command

Torque command sent to the mechanical model

N*m

Input

ωrc

Rotor speed command

Speed command sent to the mechanical model

rpm

Input

ωr

Rotor speed

Speed of the rotor

rpm

Measurement

Te

Electromagnetic torque

Torque measured at the rotor

N*m

Measurement

θ0

Initial rotor angle

Rotor position at time t = 0

°

Input

θ

Rotor angle

Rotor position from 0 to 360 degrees

°

Measurement

OPAL-RT TECHNOLOGIES, Inc. | 1751, rue Richardson, bureau 1060 | Montréal, Québec Canada H3K 1G6 | opal-rt.com | +1 514-935-2323
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