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Basics of Protective Relaying in Power System

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What is Power Factor?

Simply stated, the Power Factor is the percentage of Apparent Power that does real work.
To understand power factor in an electrical system, first of all we should have the knowledge of some basic terms which are used in an electrical system given below.

  • kW - Working Power (also called Actual Power or Active Power or Real Power) :- It is the power that actually powers the equipment and performs useful work.
  • kVAR - Reactive Power :- It is the power that magnetic equipment (transformer, motor and relay)needs to produce the magnetizing flux.
  • kVA - Apparent Power :- It is the “vectorial summation” of KVAR and KW.

Are you confused with these terms. It is better understand these term with some simple analogy.

Beer Mug Analogy

Let’s say you are at the park and it is a really hot day. You order up a mug of beer. 
  • The thirst quenching portion of your beer is represented by KW. This is the usable power.
  • Along with your beer comes a little bit of foam. (And that foam just doesn’t quench your thirst.) This foam is represented by KVAR. This part is the wasted power.
  • The total contents of your mug, KVA, is this summation of KW (the beer) and KVAR (the foam).

Understanding Power Factor

So, we understood some basic terms from the beer mug analogy. Now we are ready to learn about power factor:

Power Factor (Cos Φ) is the ratio of Working Power (True Power) to Apparent Power.


Looking at our beer mug analogy above, power factor would be the ratio of beer (KW) to beer plus foam (KVA).

PF = KW / (KW + KVAR)
Cos Φ = Beer / (Beer +Foam)

Thus, for a given KVA:
  1. The more foam you have (the higher the percentage of KVAR), the lower your ratio of KW (beer) to KVA (beer plus foam). Thus, the lower your power factor. 
  2. The less foam you have (the lower the percentage of KVAR), the higher your ratio of KW (beer) to KVA (beer plus foam). In fact, as your foam (or KVAR) approaches zero, your power factor approaches 1.0.

Power Triangle

The “Power Triangle” illustrates this relationship between KW, KVA, KVAR, and Power Factor:

PF = KW/KVAR = Cos Φ

Note that…in an ideal world…looking at the beer mug analogy:
  • KVAR would be very small (foam would be approaching zero)
  • KW and KVA would be almost equal (more beer; less foam)
So, In order to have an “efficient” system 
we want power factor to be as close to 1.0 as possible. A power factor of one or "unity power factor" is the goal of any electric utility company since if the power factor is less than one, they have to supply more current to the user for a given amount of power use. In so doing, they incur more line losses.