Fault Calculation - Symmetrical Components 

By on

Symbol - Definition
image23 - system voltage

image24, image25, image26 - unbalanced voltages
image27, image28, image29 - symmetrical voltages
image21 - circuit impedance

image25 - earth fault impedance

image16 - positive sequence impedance
image17 - negative sequence impedance
image18 - zero sequence impedance

For unbalanced conditions, the calculation of fault currents is more complex. One method of dealing with this is symmetrical components. Using symmetrical components, the unbalanced system is broken down into three separate symmetrical systems:

  • Positive sequence – where the three fields rotate clockwise
  • Negative sequence – where the three fields rotate anti-clockwise
  • Zero sequence – a single field which does not rotate

The positive sequence network rotates clockwise, with a phase of 120° between phases as per any standard a.c. system. 

The negative sequence network rotates anti-clockwise, and the zero sequence network with each phase together (0° apart).

 

Image(29)

Basic Symmetrical Component Theory

Mathematically, the relationship between the symmetrical networks and the actual electrical systems, make use of a rotational operator, denoted by a and given formally by:

Image(27)

Perhaps more simply, the a operator can be looked at as a 120° shift operator. It can also be shown that the following conditions hold true:

Image(28)

By using the a operator, any unbalanced any unbalance three-phase system Va, Vb, Vc can be broken down into three balanced (positive, negative and zero sequence) networks V1, V2, V0.

Unbalanced Network Symmetrical Network
image36   image39
image37  
image38

image41

The operator a, is the unit 120° vector: a = 1|120°. Note: a3=1 and a-1 = a2

Fault Solutions

Once the sequence networks are known, the determination of the magnitude of the fault is relatively straightforward.

The a.c. system is broken down into it's symmetrical components as shown above.  Each symmetrical system is then individually solved and the final solution obtained by superposition of these (as shown above).

For the more common fault conditions,  once the sequence networks are known, we can jump directly to the fault current.  During a fault and letting Un, be the nominal voltage across the branch, the use of symmetrical components gives the following solutions (excluding fault impedance):

Type of Fault Initial Fault Current Comments
three phase image34  
phase to phase image35  
phase to phase image36  
phase to phase to earth image37

image39

image38

Note: the example given assumes a phase to phase fault between L2 and L3 (then shorted to earth)

 

Sequence Impedance Data

Positive, negative and zero sequence impedance data is often available from manufacturers. 

A common assumption is that for non-rotating equipment the negative sequence values are taken to be the same as the positive. 

Zero sequence impedance values are closely tied to the type of earthing arrangements and do vary with equipment type.  While it is always better to use actual data, if it is not available (or at preliminary stages), the following approximations can be used:

Element Z(0)
Transformer  
No neutral connection ∞ (infinity)
Yyn or Zyn 10 to 15 x X(1)
Dyn or YNyn X(1)
Dzn or Yzn 0.1 to 0.2 x X(1)
Rotating Machine
Synchronous 0.5 x Z(1)
Asynchronous zero
Transmission Line 3 x Z(1)

Approximate Zero Sequence Data (source: Schneider)

Related Notes



Steven McFadyen's avatar Steven McFadyen

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

myElectrical Engineering

comments powered by Disqus



Bows and Arrows

It starts with me reading one of the Horrible History books with my son (Groovy Greeks). Arrows were mentioned which lead to the discussion of the bodkin...

Back to basics - the Watt (or kW)

When thinking about watts (W) or kilowatt (kW = 1000 W) it can be useful too keep in mind the fundamental ideas behind the unit. Watt is not a pure electrical...

GE's Shingijutsu Factory

GE's latest thinking on product manufacturing is he Shingijutsu philosophy or Lean production system. They have started applying this at the Louisville...

What does N+1 mean?

The term 'N+1' relates to redundancy and simply means that if you required 'N' items of equipment for something to work, you would have one additional...

Post Authorship

In 2011, with the introduction of it’s Panda search ranking algorithms, Google introduced tools for determining the original author of posts.  The intention...

Autonomous Vehicle Challenge

Two driverless and solar power vans have departed from Italy on their way to China via the silk road. During the 13,000 kM trip the vans will drive themselves...

Medium Voltage Switchgear Room Design Guide

Many medium voltage (MV) indoor switchgear rooms  exist worldwide. The complexity of these rooms varies considerably depending on location, function and...

Welcome back Bottle

‘Kept looking at a card, y’see? Kept looking at it. Welcome back Bottle. Gods below welcome home. The Crippled God A Tale of the Malazan Book of the...

Robotics - Home Innovations

We have a sister note to this (Robots - Interesting Video), in which I have posted some videos of interesting robots developed by commercial corporations...

What are you reading!

Reading is a bit of a hobby of mine and I"ve done a few off-topic posts in the past on this. Rather than continue doing the occasional post I thought ...

Have some knowledge to share

If you have some expert knowledge or experience, why not consider sharing this with our community.  

By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.

To get started and understand our policy, you can read our How to Write an Electrical Note