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abc to dq0, dq0 to abc

Perform transformation from three-phase (abc) signal to dq0 rotating reference frame or the inverse

Library

Simscape / Electrical / Specialized Power Systems / Control & Measurements / Transformations

Description

The abc to dq0 block performs a Park transformation in a rotating reference frame.

The dq0 to abc block performs an inverse Park transformation.

The block supports the two conventions used in the literature for Park transformation:

  • Rotating frame aligned with A axis at t = 0, that is, at t = 0, the d-axis is aligned with the a-axis. This type of Park transformation is also known as the cosine-based Park transformation.

  • Rotating frame aligned 90 degrees behind A axis, that is, at t = 0, the q-axis is aligned with the a-axis. This type of Park transformation is also known as the sine-based Park transformation. Use it in Simscape™ Electrical™ Specialized Power Systems models of three-phase synchronous and asynchronous machines.

Deduce the dq0 components from abc signals by performing an abc to αβ0 Clarke transformation in a fixed reference frame. Then perform an αβ0 to dq0 transformation in a rotating reference frame, that is, −(ω.t) rotation on the space vector Us = uα + j· uβ.

The abc-to-dq0 transformation depends on the dq frame alignment at t = 0. The position of the rotating frame is given by ω.t (where ω represents the dq frame rotation speed).

When the rotating frame is aligned with A axis, the following relations are obtained:

Us=ud+juq=(ua+juβ)ejωt=23(ua+ubej2π3+ucej2π3)ejωtu0=13(ua+ub+uc)[uduqu0]=23[cos(ωt)cos(ωt2π3)cos(ωt+2π3)sin(ωt)sin(ωt2π3)sin(ωt+2π3)121212][uaubuc]

Inverse transformation is given by

[uaubuc]=[cos(ωt)sin(ωt)1cos(ωt2π3)sin(ωt2π3)1cos(ωt+2π3)sin(ωt+2π3)1][uduqu0]

When the rotating frame is aligned 90 degrees behind A axis, the following relations are obtained:

Us=ud+juq=(uα+juβ)ej(ωtπ2)[uduqu0]=23[sin(ωt)sin(ωt2π3)sin(ωt+2π3)cos(ωt)cos(ωt2π3)cos(ωt+2π3)121212][uaubuc]

Inverse transformation is given by

[uaubuc]=[sin(ωt)cos(ωt)1sin(ωt2π3)cos(ωt2π3)1sin(ωt+2π3)cos(ωt+2π3)1][uduqu0]

Parameters

Rotating frame alignment (at wt=0)

Select the alignment of rotating frame a t = 0 of the d-q-0 components of a three-phase balanced signal:

ua=sin(ωt); ub=sin(ωt2π3); uc=sin(ωt+2π3)

(positive-sequence magnitude = 1.0 pu; phase angle = 0 degree)

When you select Aligned with phase A axis, the d-q-0 components are d = 0, q = −1, and zero = 0.

When you select 90 degrees behind phase A axis, the default option, the d-q-0 components are d = 1, q = 0, and zero = 0.

Inputs and Outputs

abc

The vectorized abc signal.

dq0

The vectorized dq0 signal.

wt

The angular position of the dq rotating frame, in radians.

Examples

The power_Transformations example shows various uses of blocks performing Clarke and Park transformations.

Introduced in R2013a