dq0_to_abc Transformation - Perform Park transformation from dq0 reference frame to abc reference frame

Library

Extras/Measurements

A discrete version of this block is available in the Extras/Discrete Measurements library.

Description

The dq0_to_abc Transformation block performs the reverse of the so-called Park transformation, which is commonly used in three-phase electric machine models. It transforms three quantities (direct axis, quadratic axis, and zero-sequence components) expressed in a two-axis reference frame back to phase quantities. The following transformation is used:

where

The transformation is the same for the case of a three-phase current; you simply replace the V_a, V_b, V_c, V_d, V_q, and V₀ variables with the I_a, I_b, I_c, I_d, I_q, and I₀ variables.

The dq0_to_abc Transformation block is used in the model of the Synchronous Machine block where the stator quantities are referred to the rotor. The Park transformation then eliminates time-varying inductances by referring the stator and rotor quantities to a fixed or rotating reference frame. The I_d and I_q currents represent the two DC currents flowing in the two equivalent rotor windings (d winding on the same axis as the field winding, and q winding in quadratic) producing the same flux as the stator I_a, I_b, and I_c currents.

Dialog Box and Parameters

Inputs and Outputs

dq0: Connect to the first input a vectorized signal containing the sequence components [d q 0] to be converted.
sin_cos: Connect to the second input a vectorized signal containing the [sin(ωt) cos(ωt)] values, where ω is the rotation speed of the reference frame.
abc: The output is a vectorized signal containing the three-phase sinusoidal quantities [phase A phase B phase C].

Example

See the demo of the abc_to_dq0 Transformation block for an example using the dq0_to_abc Transformation block.