Per Unit Value – What Is It?
Per Unit Value of a quantity is
defined as the ratio of the actual value of that quantity to an arbitrarily
selected value of that quantity. This arbitrarily selected value is known as
the base value. The per-unit value is dimensionless because the actual value
and base value both are expressed in the same units.
Per Unit Impedance Calculation at a New Base Value - Formula
The per unit impedance is defined
as the ratio of the actual impedance to the base impedance.
In 3 phase-systems the base values are usually selected based on 3-phase kVA and line to line kV. Then,
Put the value of base current into the above equation we get,
For a circuit containing transformers, it is convenient to select the base kVA for both sides of transformers. However, the ratio of base voltages on the two sides is kept the same as the transformation ratio. Such a selection gives the same per unit impedance on either side of the transformer.
It is usually necessary to transform the
per unit impedance from one set of base values to a new set of base values.
This can be done by using the following equation.
Let’s see examples of how to calculate per unit impedance at a new base value by using the above equation.
Example: The per-unit impedance of an alternator corresponding to base value 13.3 kV and 20 MVA is 0.2 p.u. calculate p.u. value of the impedance for base values of 13.9 kV and 40 MVA in p.u?
Solution:
Given
Data:
Base kV(old) = 13.3 kV
Base kV(new) = 13.9 kV
Base MVA (old) = 20 MVA
Base MVA (new) = 40 MVA
Now,
the formula to calculate impedance at a new base value is given by,
Advantages of a Per Unit System
Some
of the advantages of a per-unit system are listed below.
Manufactures generally specify the
impedance values of equipment’s in a per unit of the equipment’s rating. If any
information is not available then it is easy to figure its per unit value than
its numerical value.
The power system contains a large
number of transformers. The ohmic value of an impedance is referred to the secondary
is different from the value as referred to the primary. Although, if the base
values are selected properly, the per-unit impedance is the same on both the
sides of the transformer.
The transformer connections in
3-phase circuits do not affect the per-unit value of impedance although the
base voltage on two sides depends on the connections.
When parameters expressed in a per
unit value then it is tending to fall in relatively narrow numerical ranges.
Hence, any erroneous data can be easily identified.
Per unit value represents yields
important information about relative magnitudes.
Manufactures generally specify the impedance values of equipment’s in a per unit of the equipment’s rating. If any information is not available then it is easy to figure its per unit value than its numerical value.
The power system contains a large number of transformers. The ohmic value of an impedance is referred to the secondary is different from the value as referred to the primary. Although, if the base values are selected properly, the per-unit impedance is the same on both the sides of the transformer.
The transformer connections in 3-phase circuits do not affect the per-unit value of impedance although the base voltage on two sides depends on the connections.
When parameters expressed in a per unit value then it is tending to fall in relatively narrow numerical ranges. Hence, any erroneous data can be easily identified.
Per unit value represents yields important information about relative magnitudes.
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