advanced Power Systems

Short-Circuit Fault Analysis

Calculate fault currents for the four main fault types — 3-phase, line-to-ground, line-to-line, and double line-to-ground — using the Z-bus / symmetrical-component method. Vary the fault impedance and Z₀/Z₁ ratio and watch the fault duty change.

Press "Run Power Flow" to solve.

BusTypeZf (pu)Z₀/Z₁

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Run the simulator with the default 3-phase fault at Bus 3. The Z-bus method works in three steps: (1) build Y-bus, (2) Z-bus = Y⁻¹, (3) the diagonal Z_kk is the Thevenin (positive-sequence) impedance at bus k. Fault current is V₀ / Z_kk.

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The Z_kk diagonal element represents the Thevenin equivalent impedance at bus k — what a fault 'sees' looking back into the network.
Switch the Type dropdown to 'Line-to-Ground (L-G)'. Compare the fault current to the 3-phase value. With Z₀/Z₁ ≈ 3 (typical), the L-G fault is often the highest-current fault on a transmission system. This sets the maximum interrupting duty for breakers.

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I_a = 3V₀ / (Z₁ + Z₂ + Z₀ + 3Z_f). Raising the Z₀/Z₁ ratio reduces L-G fault current (a high-impedance neutral grounding does the same in practice).
Switch to 'Line-to-Line (L-L)'. The L-L fault current is √3·V₀ / (Z₁ + Z₂) ≈ 0.87 of the 3-phase magnitude (since Z₂ ≈ Z₁). L-L faults are typically the lowest-magnitude phase fault but still need to be detectable by protection.

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Phase A carries no fault current; the current circulates between phases B and C with magnitude √3·|I_a1|.
Increase Zf (arc resistance) to 0.05 pu. All four fault types reduce in magnitude. In real life, low-current arcing faults are harder to detect — this is why distance protection has 'reach' settings and why fault-passage indicators matter on rural networks.

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Field studies show typical arc resistance of 1–10 Ω. On 132 kV with 100 MVA base, 1 Ω ≈ 0.0058 pu.
Switch to Bus 2 and re-run. Bus 2 (closer to generation) has lower Thevenin impedance and therefore higher fault current. Use the 'Bus CSV' button to download the result for your study log. This is the same workflow you'd use to populate a fault-level table in IEC 60909.

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Low Thevenin Z₁ = 'strong bus' = high fault current. Substations near major power stations have the highest fault duty and need the most robust circuit-breakers.