SME
Power Systems · Problem type
Changing the per-unit base
Use this for “A generator is 0.1 pu on its 50 MVA rating. What is that on the 100 MVA system base at the same kV?”
Chart
This is an example. Type your own values to start a new problem.
Znew (pu)
=
Zold (pu)
×
(
Vold (kV)
÷
Vnew (kV)
)
2
×
(
Snew (MVA)
÷
Sold (MVA)
)
Formulas
Znew
=
Zold
×
(
Vold
Vnew
)
2
×
(
Snew
Sold
)
0.2
=
0.1
×
(
13.8
13.8
)
2
×
(
100
50
)
Assumptions
•
The ohms stay the same; only the base they are divided by changes.
•
Zbase = Vbase² ÷ Sbase, so a per-unit impedance grows with Sbase and falls with Vbase².
•
A nameplate gives Z on the machine’s own rating; a system study moves every Z to one common base.
Step-by-step
WE KNOW
Zold = 0.1 pu, Vold = 13.8 kV, Sold = 50 MVA, Vnew = 13.8 kV, Snew = 100 MVA
FIND
new per-unit impedance (Znew)
Step 1 · Find new per-unit impedance (Znew)
Use Znew = Zold × (Vold ÷ Vnew)² × (Snew ÷ Sold)
The ohms are fixed, so scale by the old base impedance over the new one.
Znew
=
0.1
×
(
13.8
13.8
)
2
×
(
100
50
)
Znew = 0.1 × 1 × 2
Znew = 0.2 pu
Check
Put the numbers back in. Both sides should match.
0.2
=
0.1
×
(
13.8
13.8
)
2
×
(
100
50
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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