Page 91 - Power Electronic Control in Electrical Systems

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80 Power systems engineering ± fundamental concepts

Combining equations (2.74) and (2.75), we get
V 2
Z b ˆ b
(2:76)
S b
If V b is expressed in kV and S b in MVA, we can express equation (2.76) in the form
that is widely used by power engineers
(kV base ) 2
Z b ˆ
(2:77)
MVA base
2.13.2 Changing base

Sometimes the parameters for two elements in the same circuit are quoted in per-unit
on different bases. For example, we might have a cable whose series impedance is
quoted as 0:1 ‡ j0:3p:u: on a base of 100 MVA and 33 kV. Suppose this cable is
connected to a load whose impedance is given as 1:0 ‡ j0:2p:u: on a base of 150 MVA
and 22 kV. What is the combined series impedance? To proceed we must choose a
single set of base quantities and convert all per-unit impedances to that set. Let us
choose the cable's base values as the common base values: 100 MVA and 33 kV. We
can convert the load impedance to this base set by ratioing, using equation (2.77)
(kV b old ) 2 MVA b new
Z new ˆ Z old (2:78)
(kV b new ) 2 MVA b old
The per-unit load impedance on the new (cable) base is therefore
22 2 100
(1:0 ‡ j0:2) ˆ 0:2963 ‡ j0:0593 p:u: (2:79)
33 2 150
With both impedances on the same base, we can now add them together to get
0:3963 ‡ j0:3593 p:u: (on a base of 100 MVA and 33 kV).
It is clear that `p.u.' is not an absolute unit, since the same impedance can have different
values, depending on the base. A per-unit value is incomplete unless the base is stated.
Per-unit quantities are used widely in power engineering. They are useful for
expressing characteristics that are common to different devices. For example, in
power stations the series impedance of most large `unit transformers' (the ones that
step up the generator voltage to 400 kV) is almost always about 0.10±0.15 p.u. The
ohmic values differ widely according to the ratings and the actual voltages. Similarly,
the magnetizing current of small induction motors is typically in the range 0.2±0.5 p.u.
The ampere values vary over a wide range, depending on the ratings and the voltages,
and therefore they obscure the essential uniformity of this design characteristic.
Often a per-unit calculation can give insight that is not apparent when working in
ordinary units.

2.13.3 Transformers in per-unit systems

One of the most useful simplifications of working in per-unit is in dealing with
transformers. The ratio of base voltages between the primary and secondary can
logically be taken to be the turns ratio, n. Then the ratio of base currents must be the