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Perform Park transformation from three-phase (abc) reference frame to dq0 reference frame

Extras/Measurements

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

The abc_to_dq0 Transformation block computes the direct axis, quadratic axis, and zero sequence quantities in a two-axis rotating reference frame for a three-phase sinusoidal signal. The following transformation is used:

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}*,

This transformation is commonly used in three-phase electric
machine models, where it is known as a Park transformation [1]. It allows you to
eliminate time-varying inductances by referring the stator and rotor
quantities to a fixed or rotating reference frame. In the case of
a synchronous machine, the stator quantities are referred to the rotor.
I_{d} and I_{q} represent
the two DC currents flowing in the two equivalent rotor windings (d
winding directly on the same axis as the field winding, and q winding
on the quadratic axis), producing the same flux as the stator I_{a},
I_{b}, and I_{c} currents.

You can use this block in a control system to measure the positive-sequence
component *V*_{1} of a set of
three-phase voltages or currents. The *V _{d}* and

You can use the Math Function block and the Trigonometric Function
block to obtain the modulus and angle of *V*_{1}:

This measurement system does not introduce any delay, but, unlike the Fourier analysis done in the Sequence Analyzer block, it is sensitive to harmonics and imbalances.

`abc`Connect to the first input the vectorized sinusoidal phase signal to be converted [phase A phase B phase C].

`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.

`dq0`The output is a vectorized signal containing the three sequence components [d q o], in the same units as the

`abc`input signal.

The `power_3phsignaldq``power_3phsignaldq` example
uses a Discrete Three-Phase Programmable Source block to generate
a 1 pu, 15 degrees positive sequence voltage. At 0.05 second the positive
sequence voltage is increased to 1.5 pu and at 0.1 second an imbalance
is introduced by the addition of a 0.3 pu negative sequence component
with a phase of −30 degrees. The magnitude and phase of the
positive-sequence component are evaluated in two different ways:

Sequence calculation of phasors using Fourier analysis

abc-to-dq0 transformation

Start the simulation and observe the instantaneous signals Vabc (Scope1), the signals returned by the Sequence Analyzer (Scope2), and the abc-to-dq0 transformation (Scope3).

Note that the Sequence Analyzer, which uses Fourier analysis, is immune to harmonics and imbalance. However, its response to a step is a one-cycle ramp. The abc-to-dqo transformation is instantaneous. However, an imbalance produces a ripple at the V1 and Phi1 outputs.

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