Perform Park transformation from dq0 reference frame to abc reference frame
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 will continue to work. However, for best performance, use the dq0 to abc block in your new models. |
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:
$$\begin{array}{c}{V}_{a}={V}_{d}\mathrm{sin}(\omega t)+{V}_{q}\mathrm{cos}(\omega t)+{V}_{0}\\ {V}_{b}={V}_{d}\mathrm{sin}(\omega t-2\pi /3)+{V}_{q}\mathrm{cos}(\omega t-2\pi /3)+{V}_{0}\\ {V}_{c}={V}_{d}\mathrm{sin}(\omega t+2\pi /3)+{V}_{q}\mathrm{cos}(\omega t+2\pi /3)+{V}_{0},\end{array}$$
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 V_{0} variables with the I_{a}, I_{b}, I_{c}, I_{d}, I_{q}, and I_{0} 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.
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.
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).
[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994, p.135.