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Sequence and abc_to_dq0 Transformations

This example shows the use of the Three-Phase Programmable Source, abc_dq0, and Sequence Analyzer blocks.

G. Sybille (Hydro-Quebec)


A Discrete 3-Phase ProgrammableSource block is used to generate a 1 pu, 15 degrees positive sequence voltage. At t = 0.05 s the positive sequence voltage is increased to 1.5 pu. At t = 0.1 s an unbalance is introduced by adding a 0.3 pu negative sequence component with a phase of -30 degrees.

The magnitude and phase of the positive-sequence component is evaluated in two different ways: 1) Sequence calculation of phasors using Fourier analysis; and 2) abc to dq0 transformation.

Math Function and Trigonometric Function blocks are used to evaluate the magnitude and phase of the positive sequence from the d and q components:

V1 = sqrt(Vd^2 + Vq^2) , Phi1 = atan(Vq/Vd))


Choose Simulation/Start and observe the instantaneous signals Vabc on Scope, the signal magnitude (V1) and phase (Phi1) returned by the Sequence Analyzer (Scope2) and the d, q and 0 components displayed on Scope3.

Note that the Sequence Analyzer using Fourier analysis is immune to harmonics and unbalance (yellow traces of Scope2). However, its response to a step is a one-cycle ramp.

The abc_dqo transformation is instantaneous. However, the imbalance starting at 0.1 s produces a ripple at the V1 and Phi1 outputs (magenta traces of Scope2).