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

Control and Measurements/Measurements

The Sequence Analyzer block outputs the magnitude and phase
of the positive-, negative-, and zero-sequence components of a set
of three balanced or unbalanced signals. Index 1 denotes the positive
sequence, index 2 denotes the negative sequence, and index 0 denotes
the zero sequence. The signals can optionally contain harmonics. The
three sequence components of a three-phase signal (voltages V_{1} V_{2} V_{0} or
currents I_{1} I_{2} I_{0})
are computed as follows:

$$\begin{array}{l}{V}_{1}=\frac{1}{3}\left({V}_{a}+a\cdot {V}_{b}+{a}^{2}\cdot Vc\right)\\ {V}_{2}=\frac{1}{3}\left({V}_{a}+{a}^{2}\cdot {V}_{b}+a\cdot Vc\right)\\ {V}_{0}=\frac{1}{3}\left({V}_{a}+{V}_{b}+Vc\right)\\ {V}_{a},{V}_{b},{V}_{c}=\text{threevoltagephasorsatthespecifiedfrequency}\\ a={e}^{j2\pi /3}=1\angle {120}^{\circ}\text{complexoperator}\end{array}$$

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.

As the block uses a running average window to perform the Fourier analysis, one cycle of simulation must complete before the outputs give the correct magnitude and angle. For example, the block response to a step change of V1 is a one-cycle ramp. For the first cycle of simulation, the output is held constant using the values specified by the initial input parameters.

**Fundamental frequency (Hz)**Specify the fundamental frequency, in hertz, of the three-phase input signal.

**Harmonic n (1=fundamental)**Specify the harmonic component to evaluate the sequences. Set to 1 to compute the sequences at the fundamental frequency or to the number corresponding to the desired harmonic.

**Sequence**Specify the sequence component the block outputs. The options include

`Positive`

,`Negative`

,`Zero`

, and`Positive Negative Zero`

. Select`Positive Negative Zero`

to calculate all the sequences.**Initial input [ Mag, Phase (degrees) ]**Specify the initial magnitude and phase, in degrees, of the positive-sequence component of the input signal.

**Sample time**Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block.

`abc`

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

`Iabc`

The three-phase current signal.

`|u| Magnitude`

Outputs the magnitude (peak value) of the specified sequence component(s), in the same units as the abc input signals.

- $$\angle $$
`u Phase`

Outputs the phase, in degrees, of the specified components.

Sample Time | Specified in the Sample Time parameterContinuous if Sample Time = 0 |

Scalar Expansion | No |

Dimensionalized | No |

The `power_SequenceAnalyzer`

`power_SequenceAnalyzer`

model
shows the use of the Sequence Analyzer block to compute the three
sequence components of a three-phase sinusoidal voltage. The model
sample time

The model sample time is parameterized by the Ts variable set to a default value of 50e-6 s. Set Ts to 0 in the command window to simulate the model in continuous mode.

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