IEC 60909-09 min read

Minimum Earth Fault Current and the c-Factor: Will the Breaker Trip Instantaneously?

Part 5 of the short-circuit series. Maximum currents size equipment; minimum currents prove the protection works. At a DB 150 m away the minimum earth fault is 2.85 kA — too low for a 250 A breaker set at 10 × In.

Scenario

Network250 MVA, 11 kV grid (R/X = 0.1) → 1.6 MVA, 11/0.4 kV Dyn transformer, uk = 6 %, Pk = 15 kW
Feeder4-core 95 mm² Cu, 150 m; r = 0.193, x = 0.0779 Ω/km; r0 = 0.772, x0 = 0.234 Ω/km
Protection250 A MCCB at the LV board, instantaneous setting 10 × In, tolerance ±20 %

Step-by-step calculation

Step 1: Maximum fault currents at the DB

Step 2: Earth fault formula

Ik1 = √3 × c × Un / |2Z1 + Z0|
Z1 = 0.0299 + j0.0181 Ω; Z0 = 0.1167 + j0.0408 Ω (transformer + cable); |2Z1 + Z0| = 0.1926 Ω; Ik1 = √3 × 1.05 × 400 / 0.1926
Ik1 max = 3.78 kA

Step 3: Minimum case

IEC 60909 uses cmin = 0.95 at LV, leaves motors out and takes cable resistance at the end of the fault (×1.24 for copper at 80 °C).

Step 4: Check the instantaneous trip

Ii,max = setting × In × (1 + tolerance)
10 × 250 × 1.2 = 3,000 A > 2,845 A
Instantaneous operation is not guaranteed

The fault would then be cleared by the slower long-time element, which may exceed the disconnection time required by IEC 60364-4-41.

Step 5: Fix

Result summary

CheckRequirementActualStatus
Ik1 min vs 10 × In upper limitIk1 min > 3,000 A2,845 A✗ FAIL
Ik1 min vs 8 × In upper limitIk1 min > 2,400 A2,845 A✓ PASS
The minimum earth fault at the DB is 2.85 kA. A 250 A breaker at 10 × In might not trip instantaneously (upper limit 3.0 kA); reducing the setting to 8 × In (upper limit 2.4 kA) restores reliable fast clearing.

Key insight: Always calculate two values at every bus: the maximum current for equipment ratings and the minimum current for protection sensitivity. Long cables affect the minimum far more than the maximum.

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Frequently asked questions

Why is the earth fault so much lower than the three-phase fault here?

The cable's zero-sequence impedance (including the return path) is about four times its positive-sequence impedance, and the cable dominates the loop at 150 m.

What else can fix a low minimum fault current?

A larger cable or a separate protective conductor, an RCD or earth-fault relay, or a breaker with an electronic trip unit and earth-fault (G) protection.

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