Overview
The Earth Fault Loop Impedance Calculator determines whether a protective device (circuit breaker) will disconnect within the required time during an earth fault, as mandated by IEC 60364 and BS 7671.
It computes the total impedance of the earth fault loop — from the supply transformer, through the active (phase) conductor, through the fault, and back via the earth conductor — then compares this against the maximum impedance that still allows enough fault current to trip the breaker. The fault loop comprises:
- Supply transformer impedance (optional)
- Active (phase) conductor impedance — resistance and reactance over cable length
- Earth conductor impedance — including optional supplementary earth path in parallel
If the calculated loop impedance \( Z_s \) is less than or equal to the maximum allowed impedance \( Z_{max} \), the circuit is compliant and the breaker will trip within the required disconnection time.
Input Parameters
Transformer (conditional on use_transformer)
| Parameter | Type | Default | Range | Description |
|---|---|---|---|---|
use_transformer |
Boolean | False | — | Whether to include transformer impedance in the loop calculation |
transformer_mva |
Number | 1.0 | min 0.01 | Transformer rating in MVA |
transformer_z_percent |
Number | 6.0% | 0.1 – 20% | Transformer impedance percentage |
Cable
| Parameter | Type | Default | Range | Description |
|---|---|---|---|---|
insulation_type |
Enum | pvc | pvc / xlpe | Cable insulation type — affects resistance and reactance lookup values |
active_csa |
Enum | 4 mm² | 1 – 500 mm² | Active (phase) conductor cross-sectional area |
earth_csa |
Enum | 4 mm² | 1 – 500 mm² | Earth conductor cross-sectional area |
cable_length |
Number | 50 m | min 0.1 | Cable run length in metres |
Supplementary Earthing (conditional on use_supplementary)
| Parameter | Type | Default | Range | Description |
|---|---|---|---|---|
use_supplementary |
Boolean | False | — | Add a parallel supplementary earth conductor |
supplementary_csa |
Enum | 4 mm² | 1 – 500 mm² | Supplementary earth conductor cross-sectional area |
Electrical
| Parameter | Type | Default | Range | Description |
|---|---|---|---|---|
nominal_voltage |
Number | 230 V | 100 – 1000 V | Phase-to-neutral supply voltage (\( U_o \)) |
breaker_rating |
Number | 32 A | 1 – 1000 A | Protective device nominal current (\( I_n \)) |
trip_curve |
Enum | 7.5 | 4 / 7.5 / 12.5 | Trip multiplier — Type B = 4, Type C = 7.5, Type D = 12.5 |
Output Results
| Output | Unit | Description |
|---|---|---|
zs |
Ω | Total earth fault loop impedance |
zmax |
Ω | Maximum allowed impedance for disconnection |
is_compliant |
Boolean | Whether \( Z_s \leq Z_{max} \) |
trip_current |
A | Minimum fault current to trip the breaker (\( I_n \times K_t \)) |
transformer_impedance |
{r, x, Z} Ω | Transformer R + jX and magnitude |
active_impedance |
{r, x, Z} Ω | Active conductor impedance |
earth_main_impedance |
{r, x, Z} Ω | Main earth conductor impedance |
earth_equiv_impedance |
{r, x, Z} Ω | Equivalent earth impedance (with parallel supplementary if used) |
cable_loop_impedance |
{r, x, Z} Ω | Combined cable loop impedance (active + earth) |
total_loop_impedance |
{r, x, Z} Ω | Total loop impedance = transformer + cable loop |
table_8_2_check |
dict | Compliance against Table 8.2 maximum impedance limits |
table_b1_check |
dict | Compliance against Table B1 maximum cable length limits |
Formulas
Transformer Impedance
When a transformer is included, its impedance referred to the secondary (LV) side:
\[ V_{base} = U_o \times \sqrt{3} \] \[ |Z_t| = \frac{Z\%}{100} \times \frac{V_{base}^2}{S_{base}} \]An X/R ratio of 10 is assumed for typical distribution transformers, giving the R and X components:
\[ R_t = \frac{|Z_t|}{\sqrt{1 + (X\!/\!R)^2}}, \qquad X_t = R_t \times (X\!/\!R) \]where \( U_o \) is the nominal phase-to-neutral voltage, \( V_{base} \) is the line voltage, \( Z\% \) is the transformer impedance percentage, and \( S_{base} = S_{MVA} \times 10^6 \).
Cable Impedance per Length
Resistance and reactance are looked up from tables (per insulation type and CSA) and scaled by cable length:
\[ R_{cable} = R_{per\_km} \times \frac{L}{1000} \] \[ X_{cable} = X_{per\_km} \times \frac{L}{1000} \]where \( L \) is the cable length in metres.
Active Conductor Impedance
\[
Z_a = R_a + jX_a
\]
Earth Conductor Impedance
\[
Z_e = R_e + jX_e
\]
Parallel Earth (with supplementary earthing)
When a supplementary earth conductor is used, the two earth paths combine in parallel:
\[ Z_{e,equiv} = \frac{Z_e \times Z_{supp}}{Z_e + Z_{supp}} \]Cable Loop Impedance
\[
Z_c = Z_a + Z_{e,equiv}
\]
Total Loop Impedance
\[
Z_s = Z_t + Z_c
\]
\[
|Z_s| = \sqrt{R_{total}^2 + X_{total}^2}
\]
Trip Current
\[
I_a = I_n \times K_t
\]
where \( K_t \) is the trip multiplier: Type B = 4, Type C = 7.5, Type D = 12.5.
Maximum Impedance
\[
Z_{max} = \frac{U_o}{I_a} = \frac{U_o}{I_n \times K_t}
\]
Compliance Check
The circuit is compliant when:
\[ Z_s \leq Z_{max} \]Data Tables
Resistance Data (Ω/km @ 50 Hz)
| CSA (mm²) | PVC R (Ω/km) | XLPE R (Ω/km) |
|---|---|---|
| 1 | 25.8 | 27 |
| 1.5 | 16.5 | 17.3 |
| 2.5 | 9.01 | 9.45 |
| 4 | 5.61 | 5.88 |
| 6 | 3.75 | 3.93 |
| 10 | 2.23 | 2.33 |
| 16 | 1.4 | 1.47 |
| 25 | 0.884 | 0.927 |
| 35 | 0.638 | 0.668 |
| 50 | 0.471 | 0.494 |
| 70 | 0.327 | 0.342 |
| 95 | 0.236 | 0.247 |
| 120 | 0.188 | 0.197 |
| 150 | 0.153 | 0.16 |
| 185 | 0.123 | 0.129 |
| 240 | 0.0948 | 0.0991 |
| 300 | 0.077 | 0.0803 |
| 400 | 0.062 | 0.0646 |
| 500 | 0.0506 | 0.0525 |
Reactance Data (Ω/km @ 50 Hz)
| CSA (mm²) | PVC X (Ω/km) | XLPE X (Ω/km) |
|---|---|---|
| 1 | 0.119 | 0.114 |
| 1.5 | 0.111 | 0.107 |
| 2.5 | 0.102 | 0.0988 |
| 4 | 0.102 | 0.093 |
| 6 | 0.0967 | 0.0887 |
| 10 | 0.0906 | 0.084 |
| 16 | 0.0861 | 0.0805 |
| 25 | 0.0853 | 0.0808 |
| 35 | 0.0826 | 0.0786 |
| 50 | 0.0797 | 0.0751 |
| 70 | 0.077 | 0.0741 |
| 95 | 0.0766 | 0.0725 |
| 120 | 0.0743 | 0.0713 |
| 150 | 0.0745 | 0.0718 |
| 185 | 0.0744 | 0.072 |
| 240 | 0.0735 | 0.0709 |
| 300 | 0.0732 | 0.0704 |
| 400 | 0.0728 | 0.0702 |
| 500 | 0.0723 | 0.0707 |
Table 8.2 — Maximum Cable Resistance for Protection Devices (Ω)
| Active CSA (mm²) | CB Rating (A) | Type B (×4) | Type C (×7.5) | Type D (×12.5) |
|---|---|---|---|---|
| 2.5 | 16 | 2.32 | 1.24 | 0.74 |
| 2.5 | 20 | 1.86 | 1.00 | 0.60 |
| 4 | 25 | 1.50 | 0.80 | 0.48 |
| 4 | 32 | 1.17 | 0.62 | 0.37 |
| 6 | 40 | 0.93 | 0.50 | 0.30 |
| 10 | 50 | 0.76 | 0.40 | 0.24 |
| 16 | 63 | 0.60 | 0.32 | 0.19 |
Table B1 — Maximum Cable Length for Protection Devices (m)
| Active CSA (mm²) | CB Rating (A) | Type B (×4) | Type C (×7.5) | Type D (×12.5) |
|---|---|---|---|---|
| 1 | 6 | 170 | 91 | 55 |
| 1 | 10 | 102 | 55 | 33 |
| 1.5 | 10 | 153 | 82 | 49 |
| 1.5 | 16 | 96 | 51 | 31 |
| 2.5 | 16 | 160 | 85 | 51 |
| 2.5 | 20 | 128 | 68 | 41 |
| 4 | 20 | 126 | 67 | 40 |
| 4 | 32 | 98 | 52 | 31 |
| 6 | 40 | 90 | 48 | 29 |
| 10 | 50 | 117 | 62 | 37 |
| 16 | 63 | 142 | 76 | 45 |
| 16 | 80 | 112 | 59 | 36 |
| 25 | 80 | 124 | 66 | 40 |
| 25 | 100 | 99 | 53 | 32 |
| 35 | 100 | 159 | 85 | 51 |
| 35 | 125 | 127 | 68 | 41 |
| 50 | 125 | 198 | 106 | 63 |
| 50 | 160 | 155 | 83 | 51 |
| 70 | 160 | 235 | 126 | 75 |
| 70 | 200 | 188 | 100 | 60 |
Worked Examples
The 10 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_efli; worked examples for every calculation).
| # | Case | Zs (Ω) | Zmax (Ω) | If (A) | Lmax (m) | Governing | Result |
|---|---|---|---|---|---|---|---|
| 1 | 10 mm² with 4 mm² earth, 60 m, 50 A type C — fails Table 8.2 | 0.4705 | 0.6133 | 488.8 | 51 | table 8 2 loop resistance | FAIL |
| 2 | Same circuit rescued by a 10 mm² supplementary earth | 0.2297 | 0.6133 | 1,001.3 | 62 | table b1 route length | PASS |
| 3 | 120 mm² XLPE feeder, 200 m, 250 A type B at Uo = 400 V | 0.1116 | 0.4000 | 3,584.2 | 716 | earth fault loop impedance | PASS |
| 4 | 2.5 mm² PVC, 40 m, 16 A type D (c0003) | 0.7208 | 1.1500 | 319.1 | 41 | table 8 2 loop resistance | PASS |
| 5 | 4 mm² with 2.5 mm² earth, 50 m, 32 A type C (c0003) | 0.7310 | 0.9583 | 314.6 | 42 | table 8 2 loop resistance | FAIL |
| 6 | 4 mm² PVC, 25 m, 32 A type C (help-page example 1) | 0.2805 | 0.9583 | 820.0 | 52 | table b1 route length | PASS |
| 7 | 25 m circuit with a 1 MVA 6 % source transformer (help-page example 2, c0003) | 0.2818 | 0.9583 | 816.2 | 52 | table b1 route length | PASS |
| 8 | 4 mm² PVC, 30 m, 25 A type D (c0003) | 0.3366 | 0.7360 | 683.3 | 42 | table 8 2 loop resistance | PASS |
| 9 | 6 mm² PVC, 150 m, 63 A type C — too long | 1.1250 | 0.4867 | 204.4 | 64 | earth fault loop impedance | FAIL |
| 10 | 6 mm² XLPE, 60 m, 40 A type B (c0003) | 0.4717 | 1.4370 | 487.6 | 90 | table b1 route length | PASS |
Example 1 — 10 mm² with 4 mm² earth, 60 m, 50 A type C — fails Table 8.2
An undersized 4 mm² earth pushes the loop resistance past the Table 8.2 row while Zs itself still clears Zmax.
Given: 10 mm² PVC active with 4 mm² earth, route length 60 m, Uo = 230 V, 50 A type C MCB (trip multiple 7.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 10 mm² table: 2.23 + j0.0906 Ω/km → Z1 = (2.23 + j0.0906) × 60/1000 = 0.1338 + j0.0054 Ω |
| Earth conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z2 = (5.61 + j0.102) × 60/1000 = 0.3366 + j0.0061 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.1338 + j0.0054) + (0.3366 + j0.0061) = 0.4704 + j0.0116 Ω; loop resistance R = 0.4704 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.4704 + j0.0116| = √(0.4704² + 0.0116²) = 0.4705 Ω; rounded down to 4 s.f. → 0.4705 Ω |
| Trip current | Ia = In × k = 50 × 7.5 = 375 A; Zmax = Uo / Ia = 230 / 375 = 0.6133 Ω; rounded down to 4 s.f. → Zmax 0.6133 Ω, Ia 375 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 76.7 % of Zmax → 0.4705 vs limit 0.6133 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.4705 = 488.8 A ≥ Ia → 488.8 vs limit 375.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (10 mm², 50 A, type C) maximum loop resistance 0.40 Ω vs R = 0.4704 Ω → 0.4704 vs limit 0.4000 Ω FAIL |
| Table B1 | AS/NZS 3000 Table B1 row (10 mm², 50 A, type C) maximum length 62 m vs route 60 m → 60 vs limit 62 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.00784 + j0.00019)| = 0.6133 Ω → L = 78 m (≈ 0.6133 / 0.00784 Ω/m); Table 8.2: 0.40 / 0.00784 Ω/m = 51.0 → 51 m; Table B1: 62 m. Governing: 51 m (AS/NZS 3000 Table 8.2 resistance) |
| Result | 3/4 checks pass → FAIL; Zs 0.4705 Ω vs Zmax 0.6133 Ω; max route 51 m (AS/NZS 3000 Table 8.2 resistance); governing: table 8 2 loop resistance. Fails: table_8_2_loop_resistance. Options: shorten the route below 51 m, increase the active/earth size, use a lower-multiple curve, or provide additional protection such as an RCD (not assessed by this engine). |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 10 mm² 2.23 + j0.0906 Ω/km → Z1 = 0.13380 + j0.00544 Ω; earth 4 mm² 5.61 + j0.102 Ω/km → Z2 = 0.33660 + j0.00612 Ω; Zloop = 0.47040 + j0.01156 Ω; Zs = |0.47040 + j0.01156| = 0.47054 Ω; Ia = 50 × 7.5 = 375 A, Zmax = 230/375 = 0.61333 Ω; c0003 rounds down to 4 s.f.: Zs 0.4705 Ω, Zmax 0.6133 Ω, Ia 375 A; If = 230/0.4705 = 488.8 A; Zs = Zmax at 78.2 m → 78 m; Table 8.2 (10 mm², 50 A, C) 0.40 Ω: Rloop 0.4704 Ω > limit; 0.40/0.00784 = 51.0 → 51 m; Table B1 (10 mm², 50 A, C) 62 m: L 60 m ≤ limit (validation case c0003-10-4mm2-pvc-60m-50a-c-fail) |
Example 2 — Same circuit rescued by a 10 mm² supplementary earth
Paralleling a 10 mm² supplementary earth with the 4 mm² earth brings the loop resistance back under the Table 8.2 limit.
Given: 10 mm² PVC active with 4 mm² earth plus a 10 mm² supplementary earth in parallel over the same route, route length 60 m, Uo = 230 V, 50 A type C MCB (trip multiple 7.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 10 mm² table: 2.23 + j0.0906 Ω/km → Z1 = (2.23 + j0.0906) × 60/1000 = 0.1338 + j0.0054 Ω |
| Earth conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z2 = (5.61 + j0.102) × 60/1000 = 0.3366 + j0.0061 Ω |
| Supplementary earth | PVC 10 mm² table: 2.23 + j0.0906 Ω/km → Z3 = 0.1338 + j0.0054 Ω; in parallel: Ze = Z2·Z3 / (Z2 + Z3) = (0.3366 + j0.0061)(0.1338 + j0.0054) / (0.4704 + j0.0116) = 0.0958 + j0.0033 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.1338 + j0.0054) + (0.0958 + j0.0033) = 0.2296 + j0.0087 Ω; loop resistance R = 0.2296 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.2296 + j0.0087| = √(0.2296² + 0.0087²) = 0.2297 Ω; rounded down to 4 s.f. → 0.2297 Ω |
| Trip current | Ia = In × k = 50 × 7.5 = 375 A; Zmax = Uo / Ia = 230 / 375 = 0.6133 Ω; rounded down to 4 s.f. → Zmax 0.6133 Ω, Ia 375 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 37.5 % of Zmax → 0.2297 vs limit 0.6133 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.2297 = 1,001.3 A ≥ Ia → 1,001.3 vs limit 375.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (10 mm², 50 A, type C) maximum loop resistance 0.40 Ω vs R = 0.2296 Ω → 0.2296 vs limit 0.4000 Ω PASS |
| Table B1 | AS/NZS 3000 Table B1 row (10 mm², 50 A, type C) maximum length 62 m vs route 60 m → 60 vs limit 62 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.00383 + j0.00015)| = 0.6133 Ω → L = 160 m (≈ 0.6133 / 0.00383 Ω/m); Table 8.2: 0.40 / 0.00383 Ω/m = 104.6 → 104 m; Table B1: 62 m. Governing: 62 m (AS/NZS 3000 Table B1 length) |
| Result | 4/4 checks pass → PASS; Zs 0.2297 Ω vs Zmax 0.6133 Ω; max route 62 m (AS/NZS 3000 Table B1 length); governing: table b1 route length |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 10 mm² 2.23 + j0.0906 Ω/km → Z1 = 0.13380 + j0.00544 Ω; earth 4 mm² 5.61 + j0.102 Ω/km → Z2 = 0.33660 + j0.00612 Ω; supplementary 10 mm² Z3 = 0.13380 + j0.00544 Ω; Ze = Z2·Z3/(Z2+Z3) = 0.09575 + j0.00328 Ω; Zloop = 0.22955 + j0.00871 Ω; Zs = |0.22955 + j0.00871| = 0.22972 Ω; Ia = 50 × 7.5 = 375 A, Zmax = 230/375 = 0.61333 Ω; c0003 rounds down to 4 s.f.: Zs 0.2297 Ω, Zmax 0.6133 Ω, Ia 375 A; If = 230/0.2297 = 1001.3 A; Zs = Zmax at 160.2 m → 160 m; Table 8.2 (10 mm², 50 A, C) 0.40 Ω: Rloop 0.2296 Ω ≤ limit; 0.40/0.00383 = 104.6 → 104 m; Table B1 (10 mm², 50 A, C) 62 m: L 60 m ≤ limit (validation case c0003-10-4mm2-pvc-60m-50a-c-supp-10) |
Example 3 — 120 mm² XLPE feeder, 200 m, 250 A type B at Uo = 400 V
A large feeder outside both tables: only the Zs and trip-current checks run, and the maximum route is where Zs reaches Zmax.
Given: 120 mm² XLPE active with 70 mm² earth, route length 200 m, Uo = 400 V, 250 A type B MCB (trip multiple 4); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | XLPE 120 mm² table: 0.197 + j0.0713 Ω/km → Z1 = (0.197 + j0.0713) × 200/1000 = 0.0394 + j0.0143 Ω |
| Earth conductor | XLPE 70 mm² table: 0.342 + j0.0741 Ω/km → Z2 = (0.342 + j0.0741) × 200/1000 = 0.0684 + j0.0148 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.0394 + j0.0143) + (0.0684 + j0.0148) = 0.1078 + j0.0291 Ω; loop resistance R = 0.1078 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.1078 + j0.0291| = √(0.1078² + 0.0291²) = 0.1117 Ω; rounded down to 4 s.f. → 0.1116 Ω |
| Trip current | Ia = In × k = 250 × 4 = 1,000 A; Zmax = Uo / Ia = 400 / 1,000 = 0.4000 Ω; rounded down to 4 s.f. → Zmax 0.4 Ω, Ia 1,000 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 27.9 % of Zmax → 0.1116 vs limit 0.4000 Ω PASS |
| Fault current | If = Uo / Zs = 400 / 0.1116 = 3,584.2 A ≥ Ia → 3,584.2 vs limit 1,000.0 A PASS |
| Table 8.2 | No AS/NZS 3000 Table 8.2 row for 120 mm², 250 A, type B — resistance table not checked |
| Table B1 | No AS/NZS 3000 Table B1 row for 120 mm², 250 A, type B — length table not checked |
| Max route length | Zs = Zmax when |Zt + L × (0.00054 + j0.00015)| = 0.4000 Ω → L = 716 m (≈ 0.4000 / 0.00056 Ω/m). Governing: 716 m (Zs = Zmax) |
| Result | 2/2 checks pass → PASS; Zs 0.1116 Ω vs Zmax 0.4000 Ω; max route 716 m (Zs = Zmax); governing: earth fault loop impedance |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); XLPE 120 mm² 0.197 + j0.0713 Ω/km → Z1 = 0.03940 + j0.01426 Ω; earth 70 mm² 0.342 + j0.0741 Ω/km → Z2 = 0.06840 + j0.01482 Ω; Zloop = 0.10780 + j0.02908 Ω; Zs = |0.10780 + j0.02908| = 0.11165 Ω; Ia = 250 × 4 = 1000 A, Zmax = 400/1000 = 0.40000 Ω; c0003 rounds down to 4 s.f.: Zs 0.1116 Ω, Zmax 0.4 Ω, Ia 1000 A; If = 400/0.1116 = 3584.2 A; Zs = Zmax at 716.5 m → 716 m; Table 8.2 has no row for 120 mm² / 250 A; Table B1 has no row for 120 mm² / 250 A (validation case c0003-120-70mm2-xlpe-200m-250a-b-400v) |
Example 4 — 2.5 mm² PVC, 40 m, 16 A type D (c0003)
Type D on 2.5 mm²: the loop resistance sits at 97 % of the Table 8.2 limit, which becomes the governing check although all pass.
Given: 2.5 mm² PVC active with 2.5 mm² earth, route length 40 m, Uo = 230 V, 16 A type D MCB (trip multiple 12.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 2.5 mm² table: 9.01 + j0.102 Ω/km → Z1 = (9.01 + j0.102) × 40/1000 = 0.3604 + j0.0041 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.3604 + j0.0041 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.3604 + j0.0041) + (0.3604 + j0.0041) = 0.7208 + j0.0082 Ω; loop resistance R = 0.7208 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.7208 + j0.0082| = √(0.7208² + 0.0082²) = 0.7208 Ω; rounded down to 4 s.f. → 0.7208 Ω |
| Trip current | Ia = In × k = 16 × 12.5 = 200 A; Zmax = Uo / Ia = 230 / 200 = 1.1500 Ω; rounded down to 4 s.f. → Zmax 1.15 Ω, Ia 200 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 62.7 % of Zmax → 0.7208 vs limit 1.1500 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.7208 = 319.1 A ≥ Ia → 319.1 vs limit 200.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (2.5 mm², 16 A, type D) maximum loop resistance 0.74 Ω vs R = 0.7208 Ω → 0.7208 vs limit 0.7400 Ω PASS |
| Table B1 | AS/NZS 3000 Table B1 row (2.5 mm², 16 A, type D) maximum length 51 m vs route 40 m → 40 vs limit 51 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.01802 + j0.00020)| = 1.1500 Ω → L = 63 m (≈ 1.1500 / 0.01802 Ω/m); Table 8.2: 0.74 / 0.01802 Ω/m = 41.1 → 41 m; Table B1: 51 m. Governing: 41 m (AS/NZS 3000 Table 8.2 resistance) |
| Result | 4/4 checks pass → PASS; Zs 0.7208 Ω vs Zmax 1.1500 Ω; max route 41 m (AS/NZS 3000 Table 8.2 resistance); governing: table 8 2 loop resistance |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 2.5 mm² 9.01 + j0.102 Ω/km → Z1 = 0.36040 + j0.00408 Ω; earth 2.5 mm² same → Z2 = Z1; Zloop = 0.72080 + j0.00816 Ω; Zs = |0.72080 + j0.00816| = 0.72085 Ω; Ia = 16 × 12.5 = 200 A, Zmax = 230/200 = 1.15000 Ω; c0003 rounds down to 4 s.f.: Zs 0.7208 Ω, Zmax 1.15 Ω, Ia 200 A; If = 230/0.7208 = 319.1 A; Zs = Zmax at 63.8 m → 63 m; Table 8.2 (2.5 mm², 16 A, D) 0.74 Ω: Rloop 0.7208 Ω ≤ limit; 0.74/0.01802 = 41.1 → 41 m; Table B1 (2.5 mm², 16 A, D) 51 m: L 40 m ≤ limit (validation case c0003-2mm5-pvc-40m-16a-d) |
Example 5 — 4 mm² with 2.5 mm² earth, 50 m, 32 A type C (c0003)
The same reduced-earth circuit run through the c0003 engine, which rounds Zs and Zmax down to four significant figures; it fails Table 8.2 the same way.
Given: 4 mm² PVC active with 2.5 mm² earth, route length 50 m, Uo = 230 V, 32 A type C MCB (trip multiple 7.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z1 = (5.61 + j0.102) × 50/1000 = 0.2805 + j0.0051 Ω |
| Earth conductor | PVC 2.5 mm² table: 9.01 + j0.102 Ω/km → Z2 = (9.01 + j0.102) × 50/1000 = 0.4505 + j0.0051 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.2805 + j0.0051) + (0.4505 + j0.0051) = 0.7310 + j0.0102 Ω; loop resistance R = 0.7310 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.7310 + j0.0102| = √(0.7310² + 0.0102²) = 0.7311 Ω; rounded down to 4 s.f. → 0.731 Ω |
| Trip current | Ia = In × k = 32 × 7.5 = 240 A; Zmax = Uo / Ia = 230 / 240 = 0.9583 Ω; rounded down to 4 s.f. → Zmax 0.9583 Ω, Ia 240 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 76.3 % of Zmax → 0.7310 vs limit 0.9583 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.7310 = 314.6 A ≥ Ia → 314.6 vs limit 240.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (4 mm², 32 A, type C) maximum loop resistance 0.62 Ω vs R = 0.7310 Ω → 0.7310 vs limit 0.6200 Ω FAIL |
| Table B1 | AS/NZS 3000 Table B1 row (4 mm², 32 A, type C) maximum length 52 m vs route 50 m → 50 vs limit 52 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.01462 + j0.00020)| = 0.9583 Ω → L = 65 m (≈ 0.9583 / 0.01462 Ω/m); Table 8.2: 0.62 / 0.01462 Ω/m = 42.4 → 42 m; Table B1: 52 m. Governing: 42 m (AS/NZS 3000 Table 8.2 resistance) |
| Result | 3/4 checks pass → FAIL; Zs 0.7310 Ω vs Zmax 0.9583 Ω; max route 42 m (AS/NZS 3000 Table 8.2 resistance); governing: table 8 2 loop resistance. Fails: table_8_2_loop_resistance. Options: shorten the route below 42 m, increase the active/earth size, use a lower-multiple curve, or provide additional protection such as an RCD (not assessed by this engine). |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 4 mm² 5.61 + j0.102 Ω/km → Z1 = 0.28050 + j0.00510 Ω; earth 2.5 mm² 9.01 + j0.102 Ω/km → Z2 = 0.45050 + j0.00510 Ω; Zloop = 0.73100 + j0.01020 Ω; Zs = |0.73100 + j0.01020| = 0.73107 Ω; Ia = 32 × 7.5 = 240 A, Zmax = 230/240 = 0.95833 Ω; c0003 rounds down to 4 s.f.: Zs 0.731 Ω, Zmax 0.9583 Ω, Ia 240 A; If = 230/0.7310 = 314.6 A; Zs = Zmax at 65.5 m → 65 m; Table 8.2 (4 mm², 32 A, C) 0.62 Ω: Rloop 0.7310 Ω > limit; 0.62/0.01462 = 42.4 → 42 m; Table B1 (4 mm², 32 A, C) 52 m: L 50 m ≤ limit (validation case c0003-4-2mm5-pvc-50m-32a-c) |
Example 6 — 4 mm² PVC, 25 m, 32 A type C (help-page example 1)
A short domestic power circuit: both tables apply and every check passes with wide margin.
Given: 4 mm² PVC active with 4 mm² earth, route length 25 m, Uo = 230 V, 32 A type C MCB (trip multiple 7.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z1 = (5.61 + j0.102) × 25/1000 = 0.1403 + j0.0026 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.1403 + j0.0026 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.1403 + j0.0026) + (0.1403 + j0.0026) = 0.2805 + j0.0051 Ω; loop resistance R = 0.2805 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.2805 + j0.0051| = √(0.2805² + 0.0051²) = 0.2805 Ω; rounded down to 4 s.f. → 0.2805 Ω |
| Trip current | Ia = In × k = 32 × 7.5 = 240 A; Zmax = Uo / Ia = 230 / 240 = 0.9583 Ω; rounded down to 4 s.f. → Zmax 0.9583 Ω, Ia 240 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 29.3 % of Zmax → 0.2805 vs limit 0.9583 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.2805 = 820.0 A ≥ Ia → 820.0 vs limit 240.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (4 mm², 32 A, type C) maximum loop resistance 0.62 Ω vs R = 0.2805 Ω → 0.2805 vs limit 0.6200 Ω PASS |
| Table B1 | AS/NZS 3000 Table B1 row (4 mm², 32 A, type C) maximum length 52 m vs route 25 m → 25 vs limit 52 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.01122 + j0.00020)| = 0.9583 Ω → L = 85 m (≈ 0.9583 / 0.01122 Ω/m); Table 8.2: 0.62 / 0.01122 Ω/m = 55.3 → 55 m; Table B1: 52 m. Governing: 52 m (AS/NZS 3000 Table B1 length) |
| Result | 4/4 checks pass → PASS; Zs 0.2805 Ω vs Zmax 0.9583 Ω; max route 52 m (AS/NZS 3000 Table B1 length); governing: table b1 route length |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 4 mm² 5.61 + j0.102 Ω/km → Z1 = 0.14025 + j0.00255 Ω; earth 4 mm² same → Z2 = Z1; Zloop = 0.28050 + j0.00510 Ω; Zs = |0.28050 + j0.00510| = 0.28055 Ω; Ia = 32 × 7.5 = 240 A, Zmax = 230/240 = 0.95833 Ω; c0003 rounds down to 4 s.f.: Zs 0.2805 Ω, Zmax 0.9583 Ω, Ia 240 A; If = 230/0.2805 = 820.0 A; Zs = Zmax at 85.4 m → 85 m; Table 8.2 (4 mm², 32 A, C) 0.62 Ω: Rloop 0.2805 Ω ≤ limit; 0.62/0.01122 = 55.3 → 55 m; Table B1 (4 mm², 32 A, C) 52 m: L 25 m ≤ limit (validation case c0003-4mm2-pvc-25m-32a-c) |
Example 7 — 25 m circuit with a 1 MVA 6 % source transformer (help-page example 2, c0003)
Adding the transformer impedance raises Zs from 0.2805 Ω to 0.2818 Ω; the table checks are unaffected because they use the cable loop only.
Given: 4 mm² PVC active with 4 mm² earth, route length 25 m, Uo = 230 V, 32 A type C MCB (trip multiple 7.5); 1 MVA, 6 % source transformer (X/R 10). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | Vbase = 230 × √3 = 398.4 V; |Zt| = 6/100 × 398.4² / (1 × 10⁶) = 0.00952 Ω; with X/R = 10: Rt = 0.00952 / √(1 + 10²) = 0.00095 Ω, Xt = 10 × Rt = 0.00947 Ω |
|---|---|
| Active conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z1 = (5.61 + j0.102) × 25/1000 = 0.1403 + j0.0026 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.1403 + j0.0026 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.1403 + j0.0026) + (0.1403 + j0.0026) = 0.2805 + j0.0051 Ω; loop resistance R = 0.2805 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.2814 + j0.0146| = √(0.2814² + 0.0146²) = 0.2818 Ω; rounded down to 4 s.f. → 0.2818 Ω |
| Trip current | Ia = In × k = 32 × 7.5 = 240 A; Zmax = Uo / Ia = 230 / 240 = 0.9583 Ω; rounded down to 4 s.f. → Zmax 0.9583 Ω, Ia 240 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 29.4 % of Zmax → 0.2818 vs limit 0.9583 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.2818 = 816.2 A ≥ Ia → 816.2 vs limit 240.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (4 mm², 32 A, type C) maximum loop resistance 0.62 Ω vs R = 0.2805 Ω → 0.2805 vs limit 0.6200 Ω PASS |
| Table B1 | AS/NZS 3000 Table B1 row (4 mm², 32 A, type C) maximum length 52 m vs route 25 m → 25 vs limit 52 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.01122 + j0.00020)| = 0.9583 Ω → L = 85 m; Table 8.2: 0.62 / 0.01122 Ω/m = 55.3 → 55 m; Table B1: 52 m. Governing: 52 m (AS/NZS 3000 Table B1 length) |
| Result | 4/4 checks pass → PASS; Zs 0.2818 Ω vs Zmax 0.9583 Ω; max route 52 m (AS/NZS 3000 Table B1 length); governing: table b1 route length |
| Reference | Hand calculation (help-page formulas and tables): Vbase = 230 × √3 = 398.4 V, |Zt| = 6/100 × 398.4² / 1,000,000 = 0.00952 Ω, Rt = 0.00952/√101 = 0.00095 Ω, Xt = 0.00947 Ω; PVC 4 mm² 5.61 + j0.102 Ω/km → Z1 = 0.14025 + j0.00255 Ω; earth 4 mm² same → Z2 = Z1; Zloop = 0.28050 + j0.00510 Ω; Zs = |0.28145 + j0.01457| = 0.28182 Ω; Ia = 32 × 7.5 = 240 A, Zmax = 230/240 = 0.95833 Ω; c0003 rounds down to 4 s.f.: Zs 0.2818 Ω, Zmax 0.9583 Ω, Ia 240 A; If = 230/0.2818 = 816.2 A; Zs = Zmax at 85.3 m → 85 m; Table 8.2 (4 mm², 32 A, C) 0.62 Ω: Rloop 0.2805 Ω ≤ limit; 0.62/0.01122 = 55.3 → 55 m; Table B1 (4 mm², 32 A, C) 52 m: L 25 m ≤ limit (validation case c0003-4mm2-pvc-25m-32a-c-1mva) |
Example 8 — 4 mm² PVC, 30 m, 25 A type D (c0003)
Type D on 4 mm² at 25 A: Table 8.2 has a row but Table B1 does not, so the resistance table is the only table check appended and it governs the maximum route.
Given: 4 mm² PVC active with 4 mm² earth, route length 30 m, Uo = 230 V, 25 A type D MCB (trip multiple 12.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 4 mm² table: 5.61 + j0.102 Ω/km → Z1 = (5.61 + j0.102) × 30/1000 = 0.1683 + j0.0031 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.1683 + j0.0031 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.1683 + j0.0031) + (0.1683 + j0.0031) = 0.3366 + j0.0061 Ω; loop resistance R = 0.3366 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.3366 + j0.0061| = √(0.3366² + 0.0061²) = 0.3367 Ω; rounded down to 4 s.f. → 0.3366 Ω |
| Trip current | Ia = In × k = 25 × 12.5 = 312.5 A; Zmax = Uo / Ia = 230 / 312.5 = 0.7360 Ω; rounded down to 4 s.f. → Zmax 0.736 Ω, Ia 312.5 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 45.7 % of Zmax → 0.3366 vs limit 0.7360 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.3366 = 683.3 A ≥ Ia → 683.3 vs limit 312.5 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (4 mm², 25 A, type D) maximum loop resistance 0.48 Ω vs R = 0.3366 Ω → 0.3366 vs limit 0.4800 Ω PASS |
| Table B1 | No AS/NZS 3000 Table B1 row for 4 mm², 25 A, type D — length table not checked |
| Max route length | Zs = Zmax when |Zt + L × (0.01122 + j0.00020)| = 0.7360 Ω → L = 65 m (≈ 0.7360 / 0.01122 Ω/m); Table 8.2: 0.48 / 0.01122 Ω/m = 42.8 → 42 m. Governing: 42 m (AS/NZS 3000 Table 8.2 resistance) |
| Result | 3/3 checks pass → PASS; Zs 0.3366 Ω vs Zmax 0.7360 Ω; max route 42 m (AS/NZS 3000 Table 8.2 resistance); governing: table 8 2 loop resistance |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 4 mm² 5.61 + j0.102 Ω/km → Z1 = 0.16830 + j0.00306 Ω; earth 4 mm² same → Z2 = Z1; Zloop = 0.33660 + j0.00612 Ω; Zs = |0.33660 + j0.00612| = 0.33666 Ω; Ia = 25 × 12.5 = 312.5 A, Zmax = 230/312.5 = 0.73600 Ω; c0003 rounds down to 4 s.f.: Zs 0.3366 Ω, Zmax 0.736 Ω, Ia 312.5 A; If = 230/0.3366 = 683.3 A; Zs = Zmax at 65.6 m → 65 m; Table 8.2 (4 mm², 25 A, D) 0.48 Ω: Rloop 0.3366 Ω ≤ limit; 0.48/0.01122 = 42.8 → 42 m; Table B1 has no row for 4 mm² / 25 A (validation case c0003-4mm2-pvc-30m-25a-d) |
Example 9 — 6 mm² PVC, 150 m, 63 A type C — too long
A long 6 mm² run on a 63 A breaker: Zs is more than double Zmax and the fault current cannot reach the instantaneous trip level.
Given: 6 mm² PVC active with 6 mm² earth, route length 150 m, Uo = 230 V, 63 A type C MCB (trip multiple 7.5); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | PVC 6 mm² table: 3.75 + j0.0967 Ω/km → Z1 = (3.75 + j0.0967) × 150/1000 = 0.5625 + j0.0145 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.5625 + j0.0145 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.5625 + j0.0145) + (0.5625 + j0.0145) = 1.1250 + j0.0290 Ω; loop resistance R = 1.1250 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |1.1250 + j0.0290| = √(1.1250² + 0.0290²) = 1.1254 Ω; rounded down to 4 s.f. → 1.125 Ω |
| Trip current | Ia = In × k = 63 × 7.5 = 472.5 A; Zmax = Uo / Ia = 230 / 472.5 = 0.4868 Ω; rounded down to 4 s.f. → Zmax 0.4867 Ω, Ia 472.5 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 231.1 % of Zmax → 1.1250 vs limit 0.4867 Ω FAIL |
| Fault current | If = Uo / Zs = 230 / 1.1250 = 204.4 A ≥ Ia → 204.4 vs limit 472.5 A FAIL |
| Table 8.2 | No AS/NZS 3000 Table 8.2 row for 6 mm², 63 A, type C — resistance table not checked |
| Table B1 | No AS/NZS 3000 Table B1 row for 6 mm², 63 A, type C — length table not checked |
| Max route length | Zs = Zmax when |Zt + L × (0.00750 + j0.00019)| = 0.4867 Ω → L = 64 m (≈ 0.4867 / 0.00750 Ω/m). Governing: 64 m (Zs = Zmax) |
| Result | 0/2 checks pass → FAIL; Zs 1.1250 Ω vs Zmax 0.4867 Ω; max route 64 m (Zs = Zmax); governing: earth fault loop impedance. Fails: earth_fault_loop_impedance, disconnection_instantaneous_trip. Options: shorten the route below 64 m, increase the active/earth size, use a lower-multiple curve, or provide additional protection such as an RCD (not assessed by this engine). |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); PVC 6 mm² 3.75 + j0.0967 Ω/km → Z1 = 0.56250 + j0.01450 Ω; earth 6 mm² same → Z2 = Z1; Zloop = 1.12500 + j0.02901 Ω; Zs = |1.12500 + j0.02901| = 1.12537 Ω; Ia = 63 × 7.5 = 472.5 A, Zmax = 230/472.5 = 0.48677 Ω; c0003 rounds down to 4 s.f.: Zs 1.125 Ω, Zmax 0.4867 Ω, Ia 472.5 A; If = 230/1.1250 = 204.4 A; Zs = Zmax at 64.9 m → 64 m; Table 8.2 has no row for 6 mm² / 63 A; Table B1 has no row for 6 mm² / 63 A (validation case c0003-6mm2-pvc-150m-63a-c-fail) |
Example 10 — 6 mm² XLPE, 60 m, 40 A type B (c0003)
Type B on XLPE: Zs is a third of Zmax, so the Table B1 length (90 m) rather than Zs sets the maximum route.
Given: 6 mm² XLPE active with 6 mm² earth, route length 60 m, Uo = 230 V, 40 A type B MCB (trip multiple 4); no source impedance (circuit cable only). Engine c0003 (Zs, Zmax and Ia rounded down to 4 s.f.).
| Source impedance | No source transformer given: Zt = 0 — Zs is the circuit cable's own contribution only |
|---|---|
| Active conductor | XLPE 6 mm² table: 3.93 + j0.0887 Ω/km → Z1 = (3.93 + j0.0887) × 60/1000 = 0.2358 + j0.0053 Ω |
| Earth conductor | Same size as the active: Z2 = Z1 = 0.2358 + j0.0053 Ω |
| Cable loop | Zcable = Z1 + Ze = (0.2358 + j0.0053) + (0.2358 + j0.0053) = 0.4716 + j0.0106 Ω; loop resistance R = 0.4716 Ω |
| Loop impedance | Zs = |Zt + Zcable| = |0.4716 + j0.0106| = √(0.4716² + 0.0106²) = 0.4717 Ω; rounded down to 4 s.f. → 0.4717 Ω |
| Trip current | Ia = In × k = 40 × 4 = 160 A; Zmax = Uo / Ia = 230 / 160 = 1.4375 Ω; rounded down to 4 s.f. → Zmax 1.437 Ω, Ia 160 A |
| Zs ≤ Zmax | AS/NZS 3000 Clause 8.3.9 basis, Zs at 32.8 % of Zmax → 0.4717 vs limit 1.4370 Ω PASS |
| Fault current | If = Uo / Zs = 230 / 0.4717 = 487.6 A ≥ Ia → 487.6 vs limit 160.0 A PASS |
| Table 8.2 | AS/NZS 3000 Table 8.2 row (6 mm², 40 A, type B) maximum loop resistance 0.93 Ω vs R = 0.4716 Ω → 0.4716 vs limit 0.9300 Ω PASS |
| Table B1 | AS/NZS 3000 Table B1 row (6 mm², 40 A, type B) maximum length 90 m vs route 60 m → 60 vs limit 90 m PASS |
| Max route length | Zs = Zmax when |Zt + L × (0.00786 + j0.00018)| = 1.4370 Ω → L = 182 m (≈ 1.4370 / 0.00786 Ω/m); Table 8.2: 0.93 / 0.00786 Ω/m = 118.3 → 118 m; Table B1: 90 m. Governing: 90 m (AS/NZS 3000 Table B1 length) |
| Result | 4/4 checks pass → PASS; Zs 0.4717 Ω vs Zmax 1.4370 Ω; max route 90 m (AS/NZS 3000 Table B1 length); governing: table b1 route length |
| Reference | Hand calculation (help-page formulas and tables): no source impedance (Zt = 0); XLPE 6 mm² 3.93 + j0.0887 Ω/km → Z1 = 0.23580 + j0.00532 Ω; earth 6 mm² same → Z2 = Z1; Zloop = 0.47160 + j0.01064 Ω; Zs = |0.47160 + j0.01064| = 0.47172 Ω; Ia = 40 × 4 = 160 A, Zmax = 230/160 = 1.43750 Ω; c0003 rounds down to 4 s.f.: Zs 0.4717 Ω, Zmax 1.437 Ω, Ia 160 A; If = 230/0.4717 = 487.6 A; Zs = Zmax at 182.8 m → 182 m; Table 8.2 (6 mm², 40 A, B) 0.93 Ω: Rloop 0.4716 Ω ≤ limit; 0.93/0.00786 = 118.3 → 118 m; Table B1 (6 mm², 40 A, B) 90 m: L 60 m ≤ limit (validation case c0003-6mm2-xlpe-60m-40a-b) |
Standards
| Standard | Title | Relevant Clauses |
|---|---|---|
| IEC 60364 | Low-voltage electrical installations | Part 4-41: Protection against electric shock |
| BS 7671 | Requirements for Electrical Installations (IET Wiring Regulations) | Clause 411.4.4 — Automatic disconnection in TN systems; Chapter 41 |
| AS/NZS 3000 | Wiring Rules | Table 8.2 (maximum loop impedance); Table B1 (maximum cable lengths) |
Tips & Limitations
Tips
- Always ensure the earth CSA is adequate — undersized earth conductors increase \( Z_s \) and can cause non-compliance.
- Supplementary earthing significantly reduces \( Z_s \) by providing a parallel return path.
- Type B breakers require the lowest fault current (easiest to comply with); Type D breakers need the highest (watch for compliance on long cable runs).
- Cable temperature affects resistance — the lookup values in the tables are at rated conductor operating temperature.
Limitations
- This calculator does not account for external earth fault loop impedance (\( Z_e \)) from the supply authority. The calculated \( Z_s \) represents only the installation-side impedance.
- For TT systems, RCD protection calculations should be used instead of earth fault loop impedance verification.
- The data tables assume copper conductors at 50 Hz. Aluminium conductors or other frequencies require different lookup values.
Architecture
File Layout
components/c0003_earth_fault_loop/component.py |
Calculator class, parameter schema, registration, equation builder |
components/c0003_earth_fault_loop/calculations.py |
Advanced calculation logic with complex impedance math |
components/c0003_earth_fault_loop/equations.py |
Equation builder for formatted calculation reports |
core/electrical_utils.py |
ComplexNumber class used for R+jX arithmetic |
Calculator Class
EarthFaultLoopCalculator extends ElectricalCalculator (which extends BaseCalculator).
It auto-registers with the component registry on app startup via register_component().
Two Calculation Implementations
component.py contains a simplified resistance-only model suitable for quick checks.
calculations.py provides the full complex impedance model with R+jX using the ComplexNumber class.
The advanced version is more accurate for detailed engineering analysis.
Data Tables
Four Python dicts are defined at module level in calculations.py:
RESISTANCE_DATA, REACTANCE_DATA, TABLE_8_2_DATA, and TABLE_B1_DATA.
These drive all lookups and compliance checks.
Code Paths
Key Functions in calculations.py
| Function | Purpose |
|---|---|
calculate_conductor_impedance(csa, length, insulation_type) |
Lookup R and X from tables, scale by cable length, return ComplexNumber |
calculate_earth_fault_loop_impedance(data) |
Main orchestrator — computes all impedances, trip current, and compliance |
check_table_8_2(active_csa, breaker_rating, trip_multiplier, cable_resistance) |
Verify cable resistance against Table 8.2 maximum limits |
check_table_b1(active_csa, breaker_rating, trip_multiplier, cable_length) |
Verify cable length against Table B1 maximum length limits |
Key Functions in electrical_utils.py
| Function | Purpose |
|---|---|
calculate_transformer_impedance(mva, z_percent, voltage) |
Compute transformer impedance \( Z_t \) with X/R=10 assumption, return ComplexNumber |
calculate_parallel_impedance(z1, z2) |
Parallel combination of two complex impedances |
Extending the Calculator
- New insulation types: Add entries to
RESISTANCE_DATAandREACTANCE_DATAincalculations.py, and extend theinsulation_typeenum in the parameter schema. - New breaker types: Extend the
trip_curveenum in the schema and add corresponding entries toTABLE_8_2_DATAandTABLE_B1_DATA.
Testing
Running Tests
pytest calcs/test_c0003_earth_fault_loop.py -v
The worked examples on this page are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_efli/, engine c0003) by
python manage.py generate_help_examples --tool fe_calc_efli; calcs/test_help_examples.py fails when the committed fragment is stale.
Test Coverage
Tests should cover the full calculation path: transformer impedance, cable impedance lookups, parallel earth combination, total loop impedance, trip current, and compliance checks against both Table 8.2 and Table B1.
Adding Tests
Follow the existing test patterns in the calcs/ test suite. Key scenarios to cover
when extending:
- With and without transformer
- With and without supplementary earthing
- PVC vs XLPE insulation types
- All three breaker trip curves (B, C, D)
- Boundary cases where \( Z_s \approx Z_{max} \)
- Compliance pass and fail scenarios