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Three-Phase Sequence Analyzer

Measure positive-, negative-, and zero-sequence components of three-phase signal





The Three-Phase Sequence Analyzer block outputs the magnitude and phase of the positive- (denoted by the index 1), negative- (index 2), and zero-sequence (index 0) components of a set of three balanced or unbalanced signals. The signals can contain harmonics or not. The three sequence components of a three-phase signal (voltages V1 V2 V0 or currents I1 I2 I0) are computed as follows:

V1 = (Va + aVb+ a2Vc)/3
V2 = (Va + a2Vb + aVc)/3
V0 = (Va + Vb + Vc)/3


Va, Vb, Vc = three voltage phasors at specified frequency
a = ej2π/3 = 1∠120° complex operator.

A Fourier analysis over a sliding window of one cycle of the specified frequency is first applied to the three input signals. It evaluates the phasor values Va, Vb, and Vc at the specified fundamental or harmonic frequency. Then the transformation is applied to obtain the positive sequence, negative sequence, and zero sequence.

The Three-Phase Sequence Analyzer block is not sensitive to harmonics or imbalances. However, as this block uses a running average window to perform the Fourier analysis, one cycle of simulation has to be completed before the outputs give the correct magnitude and angle. For example, its response to a step change of V1 is a one-cycle ramp.

The discrete version of this block allows you to specify the initial magnitude and phase of the output signal. For the first cycle of simulation the outputs are held to the values specified by the initial input parameter.

You can modify any parameter during the simulation in order to obtain the different sequence and harmonic components of the input signals.

Dialog Box and Parameters

Fundamental frequency f1

The fundamental frequency, in hertz, of the three-phase input signal.

Harmonic n

Specify the harmonic component from which you want to evaluate the sequences. For DC, enter 0. For fundamental, enter 1.


Specify which sequence component the block outputs. Select Positive to calculate the positive sequence, select Negative to calculate the negative sequence, select 0 to compute the zero sequence of the fundamental or specified harmonic of the three-phase input signal. Select Positive Negative Zero to get all the sequences.

Inputs and Outputs


Connect to the input the vectorized signal of the three [a b c] sinusoidal signals.


The first output gives the magnitude (peak value) of the specified sequence component, in the same units as the abc input signals.


The second output gives the phase in degrees of the specified component(s).


The power_3phsignalseqpower_3phsignalseq example illustrates the use of the Discrete Sequence Analyzer block to measure the fundamental and harmonic components of a three-phase voltage. A 25kV, 100 MVA short-circuit level, equivalent network feeds a 5 MW, 2 Mvar capacitive load. The internal voltage of the source is controlled by the Discrete 3-phase Programmable Voltage Source block.

A positive sequence of 1.0 pu, 0 degrees is specified for the fundamental signal. At t = 0.05 s a step of 0.5 pu is applied on the positive-sequence voltage magnitude, then at t = 0.1 s, 0.08 pu of fifth harmonic in negative sequence is added to the 1.5 pu voltage.

Two Discrete Three-Phase Sequence Analyzer blocks are used to measure the positive-sequence fundamental component and the negative-sequence fifth harmonic of the three-phase voltage.

As the Three-Phase Sequence Analyzer blocks use Fourier analysis, their response time is delayed by one cycle of the fundamental frequency.

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