abc_to_dq0 Transformation (SimPowerSystems)

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

Library

Extras/Measurements

Description

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

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.

This transformation is commonly used in three-phase electric machine models, where it is known as a Park transformation. 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 V₁ of a set of three-phase voltages or currents. The V_d and V_q (or I_d and I_q) then represent the rectangular coordinates of the positive-sequence component.

You can use the Math Function block and the Trigonometric Function block to obtain the modulus and angle of V₁:

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 unbalances.

Dialog Box

Inputs and Outputs

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(t) cos(t)] values, where is the rotation speed of the reference frame.
dq0: The output is a vectorized signal containing the three sequence components [d q o].

Example

The psb3phsignaldq.mdl demo uses a Discrete 3-Phase Programmable Source block to generate a 1 p.u., 15 degrees positive sequence voltage. At 0.05 second the positive sequence voltage is increased to 1.5 p.u. and at 0.1 second an imbalance is introduced by the addition of a 0.3 p.u. 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.

See Also
dq0_to_abc Transformation

Blocks - Alphabetical List AC Current Source