SME
Power Systems
Fault analysis
Use this for “Find the fault current for a bolted three-phase fault with Xₜₕ = 0.2 pu on a 100 MVA, 13.8 kV base.”
Diagram
If
=
Vf
Xₜₕ
=
1
0.2
=
5
pu.
Ibase
=
Sbase
√
3
Vbase
=
100
√
3
× 13.8
=
4,180
A,
so
If
=
5
×
4,180
A
=
20.9
kA.
The fault MVA is If × Sbase = 5 × 100 = 500 MVA.
This is an example. Type your own values to start a new problem.
If (pu)
=
Vf (pu)
÷
Xₜₕ (pu)
Ibase (A)
=
Sbase (MVA)
÷
(
3
×
Vbase (kV)
)
IkA (kA)
=
If (pu)
×
Ibase (A)
Sf
Fault power
worked out (not typed) · MVA
Formulas
If
=
Vf
Xₜₕ
5
=
1
0.2
Ibase
=
Sbase
√
3
× Vbase
4.1837
=
100
√
3
× 13.8
IkA = If × Ibase
20.9185 = 5 × 4.1837
Sf = Vf × If × Sbase
500 = 1 × 5 × 100
Formulas are worked in kA. The step-by-step shows the conversions.
Assumptions
•
A bolted three-phase fault (no fault impedance); loads are ignored, so no current flows before it.
•
Reactances only: Xₜₕ is the whole network seen from the faulted bus, in pu on the common base.
•
Per-unit values are on the three-phase base power Sbase and the line-to-line base voltage Vbase.
Step-by-step
WE KNOW
Vf = 1 pu, Xₜₕ = 0.2 pu, Sbase = 100 MVA, Vbase = 13.8 kV
FIND
fault current (If), base current (Ibase), fault current in kA (IkA), fault power (Sf)
Step 1 · Find fault current (If)
Use If = Vf ÷ Xₜₕ
The prefault voltage drives the fault current through Xₜₕ alone.
If
=
1
0.2
If = 5 pu
Step 2 · Find base current (Ibase)
Use Ibase = Sbase ÷ (√3 × Vbase)
Three-phase
power
is
√
3
×
line
voltage
×
current,
and
MVA
kV
gives
kA.
Ibase
=
100
√
3
× 13.8
Ibase
=
100
1.732 × 13.8
Ibase
=
100
23.9016
Ibase = 4.1837 kA
Step 3 · Find fault current in kA (IkA)
Use IkA = If × Ibase
A per-unit current times the base current is the current itself.
IkA = 5 × 4.1837
IkA = 20.9185 kA
Step 4 · Find fault power (Sf)
Use Sf = Vf × If × Sbase
The per-unit power Vf × If, times the base power, is the fault power in MVA.
Sf = 1 × 5 × 100
Sf = 500 MVA
Step 5 · Convert the answers
Change each answer back to the unit you chose.
Ibase = 4.1837 kA = 4,183.698 A (1 kA = 1000 A)
Check
Put the numbers back in. Both sides should match.
5
=
1
0.2
✓
4.1837
=
100
√
3
× 13.8
✓
20.9185 = 5 × 4.1837 ✓
500 = 1 × 5 × 100 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
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.”
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.”
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.”