dq0_to_abc Transformation

Perform Park transformation from dq0 reference frame to abc reference frame

Library

powerlib_extras/Measurements, powerlib_extras/Discrete Measurements

Note

The Transformations section of the Control and Measurements library contains the dq0 to abc to block. This is an improved version of the dq0_to_abc Transformation block. The new block features a mechanism that eliminates duplicate continuous and discrete versions of the same block by basing the block configuration on the simulation mode. If your legacy models contain the dq0_to_abc Transformation block, they continue to work. However, for best performance, use the dq0 to abc block in your new models.

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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:

$$\begin{array}{c}{V}_a=V_d\sin (\omega t)+V_q\cos (\omega t)+V_0\\ V_b=V_d\sin (\omega t-2\pi /3)+V_q\cos (\omega t-2\pi /3)+V_0\\ V_c=V_d\sin (\omega t+2\pi /3)+V_q\cos (\omega t+2\pi /3)+V_0,\end{array}$$

where ω = rotation speed (rad/s) of the rotating frame.

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.

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], in the same units as the dq0 input signal.

Examples

See the example of the abc_to_dq0 Transformation block for an example using the dq0 to abc block (the improved version of the dq0_to_abc Transformation block).

References

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994, p.135.

Version History

Introduced before R2006a