Short Circuit Impedance Calculator

How the calculator works

Choose three-phase or line-to-ground mode, select the values you know in box 1, then enter them in box 2.

Equations and calculation basis

Short-circuit MVA strength

S = √3 × V_LL × Isc / 10⁶
Isc = S × 10⁶ / (√3 × V_LL)
S (MVA) = S (kVA) / 1,000

Thevenin impedance magnitude

|Z_Ω| = V_LL / (√3 × Isc)
|Z_Ω| = V_LL² / (S × 10⁶)

Resistance and reactance

R = |Z_Ω| / √(1 + (X/R)²)
X = X/R × R
Z_Ω = R + jX

Magnitude and X/R from complex impedance

|Z_Ω| = √(R² + X²)
X/R = X ÷ R (infinite when R = 0, X > 0)

Three-phase impedance base

Zbase_Ω = V_LL² / (Sbase × 10⁶)
Sbase (MVA) = Sbase (kVA) / 1,000

Per-unit conversion

Zpu = (R + jX) / Zbase_Ω
Z_Ω = Zpu × Zbase_Ω
|Zpu| = Sbase / S

Line-to-ground effective impedance

Z_LGΩ = (Z_1Ω + Z_2Ω + Z_0Ω) / 3
I_LG = √3 × V_LL / |Z_1Ω + Z_2Ω + Z_0Ω|
I_LG = V_LL / (√3 × |Z_LGΩ|)

Line-to-ground MVA strength convention

S = √3 × V_LL × I_LG / 10⁶
|Z_LGpu| = Sbase / S
Z_LGpu = Z_LGΩ / Zbase_Ω

In these equations, V_LL is in volts, current is in amperes, and S and Sbase are in MVA. Sbase always uses a three-phase base. The entered V_LL is also used as the per-unit voltage base. In three-phase mode, Z_Ω is the per-phase positive-sequence impedance Z_1Ω. In line-to-ground mode, substitute the effective impedance Z_LGΩ and current I_LG in the conversion equations.

Both the three-phase and line-to-ground modes assume balanced prefault voltage at 1 pu, zero fault impedance, and non-negative resistance and inductive reactance. Current is RMS symmetrical. DC offset, peak/asymmetrical duty, and voltage correction factors are not included. Base MVA is a chosen reference, not equipment fault capacity.