# Symmetrical Components – Demystified

Learning symmetrical components can be overwhelming if you consider its mathematical aspect only. It is time to step back and understand this concept from a macro view.

### What is symmetrical component?

In simple terms, symmetrical component is a mathematical tool that simplifies the analysis of power system during unbalanced system conditions. It does so by decoupling the one 3-phase system into three 1-phase systems. It is easy and less confusing to calculate currents in a 1-phase network than in a 3-phase network.

Keep in mind that, once decoupled, each 1-phase network has no relationship to phase ‘a’, phase ‘b’ or phase ‘c’ of a 3-phase network. The networks obtained are purely abstract in concept. For example, when phase ‘a’ of the transmission line is de-energized due to single pole circuit breaker operation, the current in that phase drops to zero. However, in the symmetrical world, you will have non-zero current flowing through the open circuit.

### How are symmetrical components represented?

The three elements that make up the symmetrical components are

1. Positive sequence
2. Negative sequence
3. Zero sequence

Each one is a vector quantity. What is special about these elements is how they describe an event. For example, see the table below.

 Type of Fault Positive Sequence Negative Sequence Zero Sequence Balanced 3-phase X Unbalanced Line to Ground X X X Line to Line X X Double Line to Ground X X X One Open Conductor (due to single pole CB or fuse operation) X X X Two Open Conductor X X X
Table 1: Summary of symmetrical components for different fault scenarios

The following points can be inferred from the above table.

1. Balanced system operation or balanced 3-phase faults have positive sequence elements only.
2. Any fault involving ground must have zero sequence elements.
3. Negative sequence elements show up in unbalanced systems only.

If you commit these points to your memory then symmetrical components will help make sense of events in a power system. You can analyze data from the power system software or directly from relays and identify if there is a ground fault, phase-to-phase fault, etc. just by checking for symmetrical quantities.

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### 3 thoughts on “Symmetrical Components – Demystified”

1. Nice overview.

You are, however, forgetting the grounding systems that a single fault is “looking into”.

If you are operating an ungrounded system (ignoring line capacitances to ground), no fault to ground will cause any fault current. So if you don’t see ground somewhere in the system that is feeding the fault (looking into the lines from the fault and into the feeding system) the is no zero system and so no fault current.

But I have a question as well: Suppose we have a symmetrical system with 3 symmetrical line impedance and a zero resistance neutral line. Now we load that system with a real load between two of the phases.

The unloaded phase will obviously go on staying at its unloaded value as seen from the neutral line.

It is obviously as well that there will be a symmetrical and an inverse system. But will the phase-neutral RMS-voltage of the two loaded phases be the same (sometimes / always)?

This is no trick question and I might as well model the whole thing in EMTDC/PSCAD to find an answer. But maybe someone knows?

Kind regards

Morten

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