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Introduction to symmetrical components

The method of symmetrical components is used to simplify fault analysis by converting a three-phase unbalanced system into two sets of balanced phasors and a set of single-phase phasors, or symmetrical components. These sets of phasors are called the positive-, negative-, and zero-sequence components.

Symmetrical Components - Theoretical and real-world examples for relay engineers
Symmetrical Components – Theoretical and real-world examples for relay engineers (on photo: Black Sea Transmission Network Project – synchronous interconnection between the 500 kV network of Georgia and the 400 kV network of Turkey; credit: JSC Georgian State Electrosystem)

These components allow for the simple analysis of power systems under faulted or other unbalanced conditions. Once the system is solved in the symmetrical component domain, the results can be transformed back to the phase domain.

The topic of symmetrical components is very broad and can take considerable time to cover in depth.

A summary of important points is included in this introduction, although it is highly recommended that other references be studied for a more thorough explanation of the mathematics involved.


Transformer Representations in the Sequence Networks

For information on the formation of the sequence networks as well as the representation of power system components in the sequence networks.

Transformers are simply represented as their positive- and negative-sequence impedances in the positive- and negative-sequence networks, respectively. However, the transformer representation in the zero-sequence network can be more complex and is dependent on the type of transformer connection.

Figure 1 shows some common transformer connections and the equivalent zero-sequence representations. For a complete list of transformer connections.

Zero-sequence circuits for various transformer types
Figure 1 – Zero-sequence circuits for various transformer types

Connecting the Sequence Networks

Once the sequence networks for the system are defined, the way they are connected is dependent on the type of fault. Sequence net work connections for common shunt fault types are shown in the remainder of this subsection.

Title:Tutorial on Symmetrical Components. Part 1: Examples; Part 2: Answer Key – Ariana Amberg and Alex Rangel, Schweitzer Engineering Laboratories, Inc.
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Symmetrical Components - Theoretical and real-world examples for relay engineers
Symmetrical Components – Theoretical and real-world examples for relay engineers

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4 Comments


  1. Rafael FLORES
    Sep 09, 2021

    MY EXPERIENCE IS SUBSTASIONS 115, 230, 400 KV


  2. Martin H. Hamanyanga
    Sep 08, 2021

    Your articles are meaningful and educative


  3. Martin H. Hamanyanga
    Sep 08, 2021

    I like your articles. They are very meaningful and educative


  4. Vinko Jarmanovic
    Nov 01, 2018

    I am works this substation from beginning to end by Siemens.

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