Premium Membership ♕

CYBER WEEK OFFER 💥 Save 20% on PRO Membership Plan and Video Courses with the coupon CYM23 and learn from experienced engineers.

Home / Download Center / Electrical Engineering Books and Technical Guides / Relay control and protection guides / Symmetrical components theoretical and real-world examples for relay engineers

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.
Size:742 KB
Download:Right here | Video Courses | Membership | Download Updates
Symmetrical Components - Theoretical and real-world examples for relay engineers
Symmetrical Components – Theoretical and real-world examples for relay engineers

Premium Membership

Get access to premium HV/MV/LV technical articles, advanced electrical engineering guides, papers, and much more! It will help you to shape up your technical skills in your everyday life as an electrical engineer.
50% Discount 💥 - Save 50% on all 90+ video courses with Enterprise Membership plan.

More Information


  1. Rafael FLORES
    Sep 09, 2021


  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.

Leave a Comment

Tell us what you're thinking. We care about your opinion! Please keep in mind that comments are moderated and rel="nofollow" is in use. So, please do not use a spammy keyword or a domain as your name, or it will be deleted. Let's have a professional and meaningful conversation instead. Thanks for dropping by!

  ×  eight  =  thirty two

Learn How to Design Power Systems

Learn to design LV/MV/HV power systems through professional video courses. Lifetime access. Enjoy learning!

Subscribe to Weekly Newsletter

Subscribe to our Weekly Digest newsletter and receive free updates on new technical articles, video courses and guides (PDF).
EEP Academy Courses - A hand crafted cutting-edge electrical engineering knowledge