# Calculation of symmetrical components

Symmetric components are very important quantities used in the implementation of relay protection and automation algorithms. Symmetrical components allow for more sensitive defenses.

The site has already provided a model of the filter of symmetrical components in Simulink.

Recall that the positive, negative and zero sequence components are calculated by the following expressions :

$$\underline{V}_1 = \frac{1}{3} \lparen \underline{V}_A + \underline{a} \cdot \underline{V}_B + \underline{a}^2 \cdot \underline{V}_C \rparen,$$

$$\underline{V}_2 = \frac{1}{3} \lparen \underline{V}_A + \underline{a}^2 \cdot \underline{V}_B + \underline{a} \cdot \underline{V}_C \rparen,$$

$$\underline{V}_0 = \frac{1}{3} \lparen \underline{V}_A + \underline{V}_B + \underline{V}_C \rparen,$$

where VA, VB, VC – phase currents or voltages; $\underline{a} = \exp \lparen j2 \pi /3 \rparen$ – rotation operator; V1, V2, V0 – symmetric components of the positive, negative and zero sequences, respectively.

Of the symmetrical components, the phase quantities are calculated by the following expressions:

$$\underline{V}_A = \frac{1}{3} \lparen \underline{V}_1 + \underline{V}_2 + \underline{V}_0 \rparen,$$

$$\underline{V}_B = \frac{1}{3} \lparen \underline{a}^2 \cdot \underline{V}_1 + \underline{a} \cdot \underline{V}_2 + \underline{V}_0 \rparen,$$

$$\underline{V}_C = \frac{1}{3} \lparen \underline{a} \cdot \underline{V}_1 + \underline{a}^2 \cdot \underline{V}_2 + \underline{V}_0 \rparen.$$

Use the calculator to calculate the symmetrical components online.

##### References
1. Zeveke G.V., Ionkin P.A., Netushil A.V., Strakhov S.V. Fundamentals of circuit theory. Textbook for high schools. Ed. 4th, revised. M., “Energy”, 1975.

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