SME
Power Systems · Problem type
Thévenin reactance from the short-circuit MVA
Use this for “A bus has 500 MVA of short-circuit power available. Find Xₜₕ on a 100 MVA base.”
Diagram
Xₜₕ = 0.2 pu: the source’s own reactance is all there is between it and the fault.
If
=
Vf
Xₜₕ
=
1
0.2
=
5
pu.
This is an example. Type your own values to start a new problem.
Xₜₕ (pu)
=
Sbase (MVA)
÷
Ssc (MVA)
If (pu)
=
1
÷
Xₜₕ (pu)
Formulas
Xₜₕ
=
Sbase
Ssc
0.2
=
100
500
If
=
1
Xₜₕ
5
=
1
0.2
Assumptions
•
The utility gives the source by its three-phase short-circuit power Ssc at the bus.
•
Reactances only, and the prefault voltage is 1 pu, so Ssc in pu is 1 ÷ Xₜₕ.
•
Ssc and Sbase are both three-phase powers in MVA.
Step-by-step
WE KNOW
Ssc = 500 MVA, Sbase = 100 MVA
FIND
Thévenin reactance (Xₜₕ), fault current (If)
Step 1 · Find Thévenin reactance (Xₜₕ)
Use Xₜₕ = Sbase ÷ Ssc
In
pu
the
fault
power
is
1
Xₜₕ
,
and
Ssc
Sbase
is
that
same
number.
Xₜₕ
=
100
500
Xₜₕ = 0.2 pu
Step 2 · Find fault current (If)
Use If = 1 ÷ Xₜₕ
A
1
pu
prefault
voltage
drives
1
Xₜₕ
through
the
source.
If
=
1
0.2
If = 5 pu
Check
Put the numbers back in. Both sides should match.
0.2
=
100
500
✓
5
=
1
0.2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Fault analysis
Main lesson
Single line-to-ground fault
Use this for “X₁ = X₂ = 0.2 pu and X₀ = 0.1 pu. Find the line-to-ground fault current on a 100 MVA, 13.8 kV base.”
Symmetrical components
Use this for “Iₐ = 10∠10° A, Ib = 8∠−100° A and Ic = 6∠140° A. Find the zero-, positive- and negative-sequence currents.”