Engineering Tools

Short Circuit Impedance Calculator

Convert between available short-circuit current, short-circuit MVA, X/R ratio, Thevenin impedance, and per-unit impedance for three-phase and line-to-ground faults.

Short Circuit Impedance Calculator

Select whatever inputs are available and enter their values. The calculator automatically determines which additional parameters can be calculated.

Fault Type

Uses positive-sequence impedance.

1. Select Known Parameters

Select each input that's known.

2. Enter Known Values

Enter the known inputs here to calculate the values to the right.

Example: 500 MVA, X/R 10, 13.8 kV, 100 MVA base

Equations and calculation basis

Common equations

  • Apply to both fault types.
  • VLL is the nominal line-to-line voltage in volts and is also the per-unit voltage base. Current is in amperes.
  • S and Sbase are in MVA. Sbase is always a three-phase base.
  • Short-circuit MVA strength uses nominal VLL, not k × VLL.
Short-circuit MVA strength
S = √3 × VLL × I / 106
I = S × 106 / (√3 × VLL)
S (MVA) = S (kVA) / 1,000
Impedance base and per-unit conversion
ZbaseΩ = VLL2 / (Sbase × 106)
Zpu = ZΩ / ZbaseΩ
ZΩ = Zpu × ZbaseΩ
Sbase (MVA) = Sbase (kVA) / 1,000
Magnitude and X/R
Z = R + jX
|Z| = √(R2 + X2)
X/R = X ÷ R (infinite when R = 0, X > 0)
Resistance and reactance from magnitude
R = |Z| / √(1 + (X/R)2)
X = √(|Z|2 − R2)
For infinite X/R: R = 0 and X = |Z|

Three-phase faults

Selected

Use the per-phase positive-sequence impedance Z1. In the common equations, ZΩ is Z1Ω.

Three-phase fault current
I3φ = k × VLL / (√3 × |Z1Ω|)
|Z1Ω| = k × VLL / (√3 × I3φ)
Impedance from three-phase MVA strength
|Z1Ω| = k × VLL2 / (S3φ × 106)
|Z1pu| = k × Sbase / S3φ

Line-to-ground faults

Selected

Enter individual sequences and/or their combined sum in pu on the same base. Z2 is assumed equal to Z1 when its checkbox is unchecked. In the common equations, substitute ZLG,eqΩ for ZΩ and ILG for I.

Combined sequence impedance
ZΣ = Z1 + Z2 + Z0
ZΣ = 2Z1 + Z0 when Z2 = Z1
X/R = (X1 + X2 + X0) / (R1 + R2 + R0)
Equivalent line-to-ground Thevenin impedance
ZLG,eqΩ = ZΣΩ / 3
ZLG,eqpu = ZΣpu / 3
Line-to-ground fault current
ILG = √3 × k × VLL / |ZΣΩ|
ILG = k × VLL / (√3 × |ZLG,eqΩ|)
Impedance from line-to-ground MVA strength
SLG = √3 × VLL × ILG / 106
|ZLG,eqpu| = k × Sbase / SLG
|ZΣpu| = 3 × k × Sbase / SLG

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