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Definition & importance

 Definition & importance

Change of base values

Advantages of per unit system

Inclusion of transformers













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  1. The synchronous reactance of a modern large size turbogenerator in pu is nearest to

  1. 1
  2. 2
  3. 3

Ans: (b)

  1. The base value of a power system is chosen based upon

  1. the rating of one machine in the system
  2. the largest machine in the system
  3. some average (rounded) values such that the pu machine ratings are not too large or too small.

Ans: (c)

  1. A bank of three single-phase transformers is star-star connected and has a % reactance of 10%. The same bank is then converted to satisfy rated star-delta connections. The per cent reactance of the transformer will now be

  1. 10/ Ö 3 %
  2. 10Ö 3 %
  3. 10 %

Ans: (c)

  1. A transmission line has a pu reactance of 30 %. If the working voltage is now increased to 110% of its original voltage ( the MVA rating of the line remaining the same), the pu reactance of the line will now be

  1. 33%
  2. 36.3%
  3. 24.8%

Ans: (c)

  1. The percentage reactance can be converted into ohmic value with the following formula

  1. X(ohms)=X(%)*100*kV2 /kVA
  2. X(ohms)=X(%)*1000*kV2 /kVA
  3. X(ohms)=X(%)*kV2 /(1000*kVA)

Ans. None of the above


 Definition & importance

Per unit (pu) system is equivalent to normalizing the quantities use and has special importance in the area of power system and machines, which involve the use of transformers. The per unit system values can also be expressed as per cent values.


Pu value = actual value in any unit/ base or reference value in the same unit

How to choose base or reference values?

For a single machine or apparatus, the base value chosen is often the rated values of the machine and therefore in pu system their values become 1pu each. However, when several machine or transmission lines are involved the common value chosen should be such that the calculated pu values should not be too large or too small compared to unity. This helps in improving numerical accuracy in many involved computations.

How many independent base quantities could there be in a power system?

They could be two. Usually, base VA (or MVAb), and base voltage (or kVb).

Others are derived quantities, such as,

Ib, Zb, Rb, Xb, Pb etc.


Base quantities in three- phase circuits

The numerical values of base voltage or base current may differ depending upon whether it refers to phase quantities or line quantities, but pu quantities remain unchanged whether expressed on line to line basis or phase basis.

For three -phase circuit s, one may define

Ib = VAb/(Ö 3 Vb)

Where VAb is three-phase value, Vb is line value and Ib is line current.

But base impedance is always defined on a per phase basis:

Zb + Vb (L-L) /(Ö 3 Ib) =- Vph/Iph

= Vb2/ VAb = (base line voltage) 2/ base VA

= (Base line voltage in kV) 2 /base MVA


Change of base values

Often the impedances of the transformers are calculated on their own ratings i.e. they have a pu value based on their own ratings and then may be required to be changed to another base value. In such cases,

Zpu (new) = Zpu (old) Vb(old) 2 VAb (new)/[Vb (new) 2VAb (old)]

Prove the above expression.

Advantages of per unit system

Inclusion of transformers in transmission circuit

  1. Actual transformer circuit with primary and secondary circuit leakage. Review of its equivalent circuit connected through ideal transformer.
  2. Nominal turns ratio & tappings
  3. Base voltages & base currents through ideal transformers. Base voltage in transmission line vis-à-vis other parts should be stressed.
  4. Effect of phase shift in transformers for voltage & current. For positive, negative, and zero sequences.
  5. It may be stressed that a transformer need not work at its rated value and the single- line diagram of a power system consisting of a generator, load, transmission line, and the sending end and receiving end transformers could be converted first to a pu impedance diagram and then the calculations made.