Symmetric components

Block appearance in REPEAT VISION

 The Symmetric components block calculates the parameters of symmetric components (direct, reverse, zero sequences) or parameters of a three-phase asymmetric system depending on the value of the property Transform type.

• It is necessary to supply three phase values sinusoidal signals to the block input when selecting the Direct value for the property Transform type. The result of the calculation will be the amplitudes and phases of components of the direct, reverse and zero sequences for phase A. In this case, one can select the parameters of which sequence one wants to calculate in the block in the property Calculatable sequence.

Note

Since this type of transformation performs Fourier analysis of input signals, it is necessary to additionally set the base frequency and harmonic number. The initial amplitude and phase values set in the block will be used to calculate symmetric components during the first base frequency period.

• It is necessary to supply the amplitudes and phases of the direct, reverse and zero sequences of phase A when selecting the Reverse value for the property Transform type. The calculation results will be the amplitudes and phases of the original three-phase system. In this case one can select which phase parameters should be calculated in the block in the property Calculatable phase.

 Calculation of symmetric components is implemented in accordance with the formula (1) [1], calculation of phase quantities - with the formula (2) [1].

(1)\[\begin{split}\begin{pmatrix}A_1 \\ A_2 \\ A_0 \\ \end {pmatrix}=\frac{1}{3}\cdot \begin{pmatrix} 1 & a & a^2\\ 1 & a^2 & a \\ 1 & 1 & 1 \\ \end{pmatrix}\cdot \begin{pmatrix}A \\ B\\ C \\ \end{pmatrix} \end{split}\]

(2)\[\begin{split}\begin{pmatrix}A \\ B\\ C \\ \end {pmatrix}= \begin{pmatrix} 1 & 1 & 1\\ a^2 & a & 1 \\ a & a^2 & 1 \\ \end{pmatrix}\cdot \begin{pmatrix}A_1 \\ A_2\\ A_0 \\ \end{pmatrix} \end{split}\]

where:

 \(a=e^{j\cdot \frac{2\cdot \pi}{3}}=-0.5+j\cdot \frac{\sqrt{3}}{2}\) – three-phase system operator [1];

 А, В, С – initial asymmetric system of three currents / voltages of the same frequency;

 A\(_1\), A\(_2\), A\(_0\) – vectors of the direct, reverse and zero sequences of phase A.

 If necessary, it is possible to calculate similar parameters for phases B (3) and С (4) using \(a\) three-phase system operator from the parameters of symmetric components of phase A obtained by the formula (1):

(3)\[\begin{split}\begin{cases}B_1=a^2 \cdot A_1 \\B_2=a \cdot A_2\\B_0=A_0 \end{cases}\end{split}\]

(4)\[\begin{split}\begin{cases}C_1=a \cdot A_1 \\C_2=a^2 \cdot A_2\\C_0=A_0 \end{cases}\end{split}\]

A graphic representation of the symmetric component method for the case of a two-phase ground fault is shown in Fig. 1:

Fig. 1 Current decomposition by the method of symmetric components at two-phase SC to ground: a) phase current vectors; b) direct sequence; c) reverse sequence; d) zero sequence

1.  Properties

Property	Default Value	Description	Units of measurement
Transform type: Direct; Inverse	Direct	-	-
Fundamental frequency, available when selecting Transform type - Direct	50	-	Hz
Harmonic number, available when selecting Transform type - Direct	1	-	-
Initial signal amplitude value, available when selecting Transform type - Direct	0	This value will be the same for three phases during the first base frequency period	-
Initial signal phase value, available when selecting Transform type - Direct	0	Value is set for phase A. During the first base frequency period, the three-phase value system is assumed to be symmetric	degr
Calculatable sequence: Positive; Negative; Zero; All, available when selecting Transform type - Direct	Direct	-	-
Calculatable phase: Phase A; Phase B; Phase C; All, available when selecting Transform type - Inverse	Phase A	-	-
Sampling type: Fundamental project frequency decimation; Sample time; Sampling frequency	Decimation factor of project fundamental discretization frequency	-	-
Sample time, available when selecting Sampling type - Sample time	0.05	-	s
Decimation factor of project fundamental discretization frequency, available when selecting Sampling type - Decimation factor of project fundamental discretization frequency	1	-	-
Sampling frequency, available when selecting Sampling type - Sampling frequency	20	-	Hz

2.  Inputs and outputs

Note

The block has a variable number of input and output ports depending on the value of the Transform type and Calculatable sequence / Calculatable phase properties:

Parameters	Input/Output	Description	Units of measurement	Port type
A	Input	Available when selecting Transform type - Direct	-	Automation
B	Input	Available when selecting Transform type - Direct	-	Automation
C	Input	Available when selecting Transform type - Direct	-	Automation
Amplitude \(A_1\)	Input	Available when selecting Transform type - Inverse	-	Automation
Phase \(A_1\)	Input	Available when selecting Transform type - Inverse	degr	Automation
Amplitude \(A_2\)	Input	Available when selecting Transform type - Inverse	-	Automation
Phase \(A_2\)	Input	Available when selecting Transform type - Inverse	degr	Automation
Amplitude \(A_0\)	Input	Available when selecting Transform type - Inverse	-	Automation
Phase \(A_0\)	Input	Available when selecting Transform type - Inverse	degr	Automation
Amplitude	Output	Available when selecting Calculatable sequence - Positive, Negative, Zero or Calculatable phase - Phase A, Phase B, Phase C	-	Automation
Phase	Output	Available when selecting Calculatable sequence - Positive, Negative, Zero or Calculatable phase - Phase A, Phase B, Phase C	degr	Automation
Output signal 1 (amplitude)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	-	Automation
Output signal 1 (phase)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	degr	Automation
Output signal 2 (amplitude)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	-	Automation
Output signal 2 (phase)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	degr	Automation
Output signal 3 (amplitude)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	-	Automation
Output signal 3 (phase)	Output	Available when selecting Calculatable sequence - All or Calculatable phase - All	degr	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports

3.  Sources

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[1] (1,2,3)

L.A. Bessonov. Theoretical foundations of electrical engineering. Electric circuits. - 9th ed., revised. and suppl. - M.: “Vysshaya shkola”, 1996. - 638 p.