# Symmetrical Components Made Easy – Part 1

Before computer software applications, the task of calculating fault currents for a three-phase electrical system was a challenging task. A mathematical theorem using Symmetrical Components and Sequence Networks was the most practical method to conduct fault studies. Although we now have computers systems to calculate and perform in-depth fault and coordination studies, there continues a need to have a good understanding of these theoretical components. Modern protective relays calculate Symmetrical Components and use these values for protection settings and logic.

There are three Symmetrical Components: positive, negative and zero sequence. The general equations to determine these sequence quantities from a three-phase system, is as follows:

## Positive Sequence Components in a Non-Faulted, three-phase power system

Below is a phasor diagram of a balanced, non-faulted three-phase power system. The phases are equal in amplitude and phase angle. The following set of drawings pictorially calculates the amount of positive sequence component in a balance system. The vector addition of 120^{o} and 240^{o} corresponds to the “a” and “a^{2}” constants in the Positive Sequence formula above.

Thus, the positive sequence component in a non-faulted, balanced system is equal to one of the phases.

## Negative Sequence Components in a Non-Faulted, three-phase power system

Performing the same phasor calculation, we can determine the amount of negative sequence component in a non-faulted, balanced three-phase power system. The negative sequence formula is proven.

Adding “a” and “a^{2}” to the appropriate phasors, as per the negative sequence formula, then adding the phasor by placing the arrow tip to arrow tail results in a return to zero position. Thus, there is no negative sequence component in a non-faulted, three-phase system.

## Zero Sequence Components in a Non-Faulted, three-phase power system

Lastly, we calculate the amount of Zero Sequence Component in the same three-phase system. The formula for zero sequence is straight forward, in that there is no angle addition (i.e. no “a” or “a^{2}“) and is simply phasor addition by placing the phasors “tip to tail”.

Thus, there is no zero-sequence component in a non-faulted, balanced three-phase system.

## Conclusion:

- Strong knowledge and understand of Symmetrical Components is key to testing and troubleshooting power system protection.
- Symmetrical Components are calculated and formulas proven by phasor diagrams.
- There is only positive sequence in a balanced three-phase system – no negative sequence or zero sequence.

In the next post we will examine the sequence components of a phase to ground fault.