Fault Calculation - Per Unit System 

By on March 27th, 2013

Symbol   Definition
Image(11)_thumb[1] - per unit method current base
Image(25)_thumb[1] - per unit method power base
Image(26)_thumb[1] - per unit method voltage base
Image(17)_thumb[1] - per unit method admittance base
Image(14)_thumb[1] - per unit method impedance base

image37 - percentage impedance

image34 - per unit impedance
image35 - actual impedance
image36 - per unit base impedance

Per unit fault calculations is a method whereby system impedances and quantities are normalised across different voltage levels to a common base.  By removing the impact of varying voltages, the necessary calculations are simplified.  

To use the per unit method, we normalise all the system impedances (and admittances) within the network under consideration to a common base.  These normalised impedances are know as per unit impedances.  Any per unit impedance will have the same value on both the primary and secondary of a transformer and is independent of voltage level.

A network of per unit impedances can then be solved using standard network analysis (see the example).  From this fault level can be readily determined. 

In applying the per unit method, the first step is to select an arbitrary voltage (Vbase) and power (Pbase) base. 

Tip: while the base power and voltage be any value, typically it would make sense to select values related to the system under construction (for example 11 kV and 20 MVA may be appropriate for a distribution type system)

Per Unit Method

Having selected a base power and voltage, the base per unit values of impedance, admittance and current can be calculated from:

Per Unit Single Phase Three Phase











Dividing a system element by it’s per-unit base value gives the per-unit value of the element, for example


Some times per-unit values are available for a given base kV, but the problem being solved is using a different base.  In this instance it is possible to convert the unit:

{Z_{pu(new)}} = {Z_{pu(old)}}{\left( {\frac{{baseK{V_{old}}}}{{baseK{V_{new}}}}} \right)^2} \times \left( {\frac{{baseKV{A_{new}}}}{{basekV{A_{old}}}}} \right)

Fault calculation problems typically deal wit power sources, generators, transformers and system impedances.  Per-unit values for these elements can be quickly derived from:


Element Per-Unit Value
Source impedance image55
Generators image57
Transformers image58
Impedances image56, where V is in kV


Example - calculating per unit values

Consider a system of source impedance 4.48 Ω connected to a 20 MVA transformer (11/0.4 kV) at 6% impedance.  We want to find the fault level at the transformer secondary.

Selecting Pbase as 20 MVA and Vbase as 11 kV and using the above equations:

{I_{base}} = \frac{{{P_{base}}}}{{{V_{base}}\sqrt 3 }} = \frac{{20}}{{11 \times \sqrt 3 }} = 1.049\quad kA










  the Line-Neutral voltage on the secondary of the transformer is 0.4/√3 = 0.230 kV, giving:


Three Phase Fault Example

Three Phase Fault Example

Per unit analysis can be used to calculate system three phase fault levels and the current distributions.  To gain a better understanding, it is worth running through the typical steps required to solve a fault calculation problem.  

Given the system single line diagram, construct and simplify the per unit impedance diagram.

The fault level at the point under consideration is given by:


Where Zpu, is the total impedance between the source and the fault.


Fault flow through parallel branches is given by the ratio of impedances. As illustrated this can enable fault flows to be found through each branch.


Having calculated the fault flow in each branch, it is then relatively simple to find the current distribution using:




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

comments powered by Disqus

  1. FELIX JR.'s avatar FELIX JR. says:
    5/21/2013 7:52 AM

    greetings !, hello !

    this article which you have shared is a good explanation for short circuit current calculations using the P.U. Method based on a given kVA base, as this is the old school way (i.e. during my college days and my early prof. work with my employer).

    But how do you find and comment on the IEC-60909 way of using the ohmic method and also that of the MVA method, alternative ? So, which of the three (3) are more easy to use and accurate ?

    felix jr.

  2. gilly1's avatar gilly1 says:
    5/29/2013 6:41 PM

    Just wondering which method do you think the most accurate for calculating single phase-earth faults, the Ohmic Method or Symmetrical Component Method.
    The Symm. Comp. method is quite complex and while a lot of people use it to solve complex types of unbalanced faults it is not real in the sense that there aren't really 3 currents flowing at once : Pos, Neg and Zero sequence currents, whereas the Ohmic Method is based in reality with real impedances???

  3. Steven's avatar Steven says:
    5/30/2013 3:03 AM

    My opinion is that symmetrical components would be more accurate (especially for any unbalanced faults like phase to earth).

    If your looking for more practical guidance on using symmetrical components, then I would reefer to IEC 60909. This standard is also implemented in many software programs.

Comments are closed for this post:
  • have a question or need help, please use our Questions Section
  • spotted an error or have additional info that you think should be in this post, feel free to Contact Us

Latest Questions:

  1. Electrcial Distribution Cabinets B15
  2. Breakers
  3. Cable AC Resistance calculation
  4. Induction Machine Types
  5. Zone Delimiters in distribution network
  6. Voltage level
  7. Lightning Protection calculation Free Software
  8. How many motors, or of what kind, do I need to get the output to be 5 Volts under load?

most popular notesMost Popular Notes:

newsletter logo

Our Newsletter

Receive updates on new posts by email
down arrow

Electric Power Distribution Engineering, Third Edition
Electric Power Distribution Engineering, ...
Turan Gonen
Hardcover - 1061 pages
Solar Electricity Handbook - 2015 Edition: A simple, practical guide to solar energy - designing and installing solar PV systems.
Solar Electricity Handbook - 2015 Edition: ...
Michael Boxwell
Paperback - 204 pages
Photovoltaic Design and Installation For Dummies
Photovoltaic Design and Installation For ...
Ryan Mayfield
Paperback - 384 pages
How to Solar Power Your Home: Everything You Need to Know Explained Simply (Back to Basics Conserving)
How to Solar Power Your Home: Everything ...
Martha Maeda
Paperback - 336 pages
Independent Energy Guide: Electrical Power for Home, Boat, & RV
Independent Energy Guide: Electrical Power ...
Kevin Jeffrey
Paperback - 280 pages
Power System Relaying
Power System Relaying
Stanley H. Horowitz, ...
Hardcover - 398 pages
Energy Systems Engineering: Evaluation and Implementation, Second Edition
Energy Systems Engineering: Evaluation and ...
Francis Vanek, Louis ...
Hardcover - 672 pages
Smart Power Grids 2011 (Power Systems)
Smart Power Grids 2011 (Power Systems)
Hardcover - 696 pages
Submarine Power Cables: Design, Installation, Repair, Environmental Aspects (Power Systems)
Submarine Power Cables: Design, ...
Thomas Worzyk
Hardcover - 296 pages
Electric Power Substations Engineering, Third Edition (Electrical Engineering Handbook)
Electric Power Substations Engineering, ...
Hardcover - 536 pages
Renewable and Efficient Electric Power Systems
Renewable and Efficient Electric Power ...
Gilbert M. Masters
Hardcover - 712 pages
Electrical Power System Essentials
Electrical Power System Essentials
Pieter Schavemaker, ...
Hardcover - 340 pages
Do It Yourself 12 Volt Solar Power, 2nd Edition (Simple Living)
Do It Yourself 12 Volt Solar Power, 2nd ...
Michael Daniek
Paperback - 128 pages
Daniel Johnson
Kindle Edition - 36 pages
Power Electronics and Renewable Energy Systems: Proceedings of ICPERES 2014 (Lecture Notes in Electrical Engineering)
Power Electronics and Renewable Energy ...
Hardcover - 1607 pages
Grid Converters for Photovoltaic and Wind Power Systems
Grid Converters for Photovoltaic and Wind ...
Remus Teodorescu, ...
Hardcover - 416 pages
Solar Photovoltaic Basics: A Study Guide for the NABCEP Entry Level Exam
Solar Photovoltaic Basics: A Study Guide ...
Sean White
Paperback - 168 pages
Build Your Own Small Solar Power System
Build Your Own Small Solar Power System
Gavin Webber
Kindle Edition - 59 pages
Renewable Fuel Standard:: Potential Economic and Environmental Effects of U.S. Biofuel Policy
Renewable Fuel Standard:: Potential ...
Committee on Economic ...
Paperback - 250 pages
Photovoltaic Systems Engineering, Third Edition
Photovoltaic Systems Engineering, Third ...
Roger A. Messenger, ...
Hardcover - 528 pages
Photovoltaics: Design and Installation Manual
Photovoltaics: Design and Installation ...
Solar Energy ...
Paperback - 336 pages
Power Electronics for Modern Wind Turbines (Synthesis Lectures on Power Electronics)
Power Electronics for Modern Wind Turbines ...
Frede Blaabjerg, Zhe ...
Paperback - 120 pages
Power System Monitoring and Control
Power System Monitoring and Control
Hassan Bevrani, ...
Hardcover - 288 pages
Wind Energy Engineering
Wind Energy Engineering
Pramod Jain
Hardcover - 352 pages
Convex Optimization of Power Systems
Convex Optimization of Power Systems
Joshua Adam Taylor
Hardcover - 209 pages
Power Quality: Problems and Mitigation Techniques
Power Quality: Problems and Mitigation ...
Bhim Singh, Ambrish ...
Hardcover - 596 pages
Multi-Stage Flash Desalination: Modeling, Simulation, and Adaptive Control (Engineering Systems and Sustainability)
Multi-Stage Flash Desalination: Modeling, ...
Abraha Woldai
Paperback - 352 pages
Large-Scale Solar Power Systems: Construction and Economics (Sustainability Science and Engineering)
Large-Scale Solar Power Systems: ...
Dr Peter Gevorkian
Hardcover - 395 pages
Power from Pellets: Technology and Applications
Power from Pellets: Technology and ...
Stefan Döring
Hardcover - 223 pages

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