Principles of Symmetrical Components
Part 1.
This is the first part of the series on the introduction to the principles and theories of
symmetrical components used in Power Systems.
Now understanding symmetrical components is not difficult.
It's actually quite easy to learn but its sometimes presented in the most confusing and impractical manner.
Our goal is to get an intuitive understanding of symmetrical components.
In this introductory series, we'll go step by step and explain what symmetrical components are,
the value of symmetrical components,
how we use symmetrical components in setting breakers and relays,
and we'll look at some examples of symmetrical components as well.
Remember, our principle goal is get an intuitive understanding.
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In this part , let's try to answer our first fundamental question:
what are symmetrical components?
The short answer to that question is:
Symmetrical components simply transform an unbalanced set of phasors
into a balanced set of symmetrical components which are called
1) positive sequence component
2) Negative sequence component and
3) Zero sequence component
Now, if this is the first time that you've been exposed to symmetrical components,
this explanation means nothing to you.
And that's just the nature of learning something new.
So let's get a better picture of this by definition by asking another question:
why are symmetrical components so valuable?
Now the best way to understand the value of symmetrical components which is the language of some power systems engineers,
is to give an example without symmetrical components available to us.
In early 1900's before the discovery of symmetrical components,
we still have generators, transformers, transmission lines, and most importantly, faults and short circuits.
So let's start this example by drawing a simple 3 line diagram.
We'll start by drawing a 3 phase generator. The generator is connected a short transmission lines,
then we have step down power transformer connected Wye-grounded Wye-grounded.
We have an AC 3-phase circuit breaker on the secondary side of the transformer,
some distribution lines, and a 3 phase load.
As a power systems engineer, we are asked to set this circuit breaker so it trips for all types of faults on this distribution line feeding our load.
We are given all the system parameters like line impedance for example.
Now what does "all types" of fault mean?
In the power system, there can exist 1 line-to-ground fault,
2-line-to-ground faults,
line-to-line faults,
and lastly, a 3 phase faults.
We'll explain in in more details later.
So we arrogantly tell ourselves, yep this can be done. We can easily calculate the magnitude of all types of fault current - no problem.
Remember, this is early 1900's before symmetrical components were discovered
To determine the fault current, we begin by drawing an equivalent single phase diagram,
and like a simple circuits problem, calculated the short circuit current.
So we draw our voltage source which represents our generator, impedance of the transmission line, impedance of transformer,
impedance of the distribution line, and impedance of our load.
Now if we had a fault at the terminals of our load, which means we have short circuit here.
We should expect a huge surge of short circuit current that comes from our generator and feeds our fault.
To calculate this current, we take the voltage at the terminal of the our load
and divide by the equivalent impedance seen at the point of the fault?
This is ohm's law plain and simple -- Current equals voltage over impedance and it makes total sense.
And suppose we get 5,000A of 3 phase fault current. Wow, that was easy.
My friends, we have simply calculated a perfectly balanced 3 phase fault.
Now, how do we calculate unbalanced faults such as a LG, 2LG, and LL faults with the same methodology?
And that is the point. And that is the defining point.
Without symmetrical components, we can only calculate balanced 3 phase fault types.
Without symmetrical components, it would be extremely difficult for us to even attempt
to calculate unbalanced faults like 1LG, 2LG, and LL faults.
So in this example, what is the value of symmetrical components?
With it, we can easily calculate both balanced and unbalanced faults.
And we are able to properly set the breaker for all expected fault types on our distribution lines.
And that my friends, is extremely critical for the reliability, security, and integrity of the power systems.
But that's just one brief and conceptual introduction to symmetrical components.
In this series, we'll go step by step and explain how it all works in the most intuitive manner possible.
In the next part - in part 1b,
we'll take a step back and describe the balanced set of phasors and review basic phasor operations.
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