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# Change of Base

It is observed from equation that the pu value of impedance is proportional directly to the base MVA and inversely to the square of the base KV.

CHANGE OF BASE.

It is observed from equation (3) that the pu value of impedance is proportional directly to the base MVA and inversely to the square of the base KV. If Zpunew is the pu impedance required to be calculated on a new set of base values: MVAbnew & KVbnew from the already given per unit impedance Zpuold, specified on the old set of base values, MVAbold & KVbold , then we have

Zpunew = Zpu old (MVAb new/MVAb old) (KVb old/KVb new)2

On the other hand, the change of base can also be done by first converting the given pu impedance to its ohmic value and then calculating its pu value on the new set of base values.

## Merits and Demerits of pu System

Following are the advantages and disadvantages of adopting the pu system of computations in electric power systems:

### Merits:

Ø  The pu value is the same for both 1-phase and & 3-phase systems

Ø  The pu value once expressed on a proper base, will be the same when refereed to either side of the transformer. Thus the presence of transformer is totally eliminated

Ø  The variation of values is in a smaller range 9nearby unity). Hence the errors involved in pu computations are very less.

Ø  Usually the nameplate ratings will be marked in pu on the base of the name plate ratings, etc.

### Demerits:

Ø  If proper bases are not chosen, then the resulting pu values may be highly absurd (such as 5.8 pu, -18.9 pu, etc.). This may cause confusion to the user. However, this problem can be avoided by selecting the base MVA near the high-rated equipment and a convenient base KV in any section of the system.

## PU Impedance / Reactance Diagram

For a given power system with all its data with regard to the generators, transformers, transmission lines, loads, etc., it is possible to obtain the corresponding impedance or reactance diagram as explained above. If the parametric values are shown in pu on the properly selected base values of the system, then the diagram is referred as the per unit impedance or reactance diagram. In forming a pu diagram, the following are the procedural steps involved:

1.         Obtain the one line diagram based on the given data

2.         Choose a common base MVA for the system

3.         Choose a base KV in any one section (Sections formed by transformers)

4.         Find the base KV of all the sections present

5.         Find pu values of all the parameters: R,X, Z, E, etc.

6.         Draw the pu impedance/ reactance diagram.

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Power System Analysis : Introduction : Change of Base |