Cable Size Range — help

Same engine as Load Cable Sizing. This calculator runs the seven checks of the Load Cable Sizing (3-phase) calculator for every standard conductor size and reports the range that conforms, instead of verifying one size you have chosen. It uses the AS/NZS 3008.1.1:2017 tables, the only supported edition. The earth conductor for each size is the AS/NZS 3000 Table 5.1 minimum.

Overview

You specify the load (power or current, voltage, power factor, design factor), the installation (method, arrangement, grouping, ambient or soil conditions) and the cable construction (conductor material, insulation, fixed or flexible, multicore or single-core). The calculator then evaluates all 20 standard sizes from 1 mm² to 630 mm² against:

Check 1 — Current Carrying Capacity: derated capacity \(I_Z\) must cover the design current.
Check 2 — Voltage Drop: within the allowable percentage over the run, evaluated at the design current \(I_B = I_{load} \times k_{design}\).
Check 3 — Short Circuit Withstand: adiabatic withstand of the prospective fault for the clearing time (AS/NZS 3008 Table 52).
Check 4 — Earth Fault Loop Impedance: enough fault current to trip the device instantaneously from the far end. The loop is \(Z_{source} + L\sqrt{R_c^2 + X_c^2} + L\sqrt{R_e^2 + X_e^2}\): the earth conductor's reactance \(X_e\) (Table 30 at the earth size) is included with its resistance.
Check 5 — Overload Coordination: \(I_B \le I_N \le I_Z\) with the entered device rating (AS/NZS 3000 Clause 2.5.3.1).
Check 6 — Earth Conductor Size: the earth is at least the AS/NZS 3000 Table 5.1 minimum. Every candidate uses that minimum, so this check always passes here.
Check 7 — Earth Conductor Withstand: the Table 5.1 earth must carry the largest earth-fault current, \(I_{ef} = V_{ph} / Z_{source}\) for a fault at the cable origin, for the earth-fault clearing time: \(S_e \geq I_{ef}\sqrt{t_{ef}}/k\) with the phase conductor's Table 52 \(k\) (the earth is an integral core of the same cable).

A size conforms when all seven checks pass. The report lists every candidate with its check results, states the smallest and largest conforming sizes, names the check that rules out the next smaller size, and then works the seven checks in full for the smallest conforming size exactly as the Load Cable Sizing report does.

Input Parameters

The inputs are those of Load Cable Sizing without the conductor size, earth conductor and sizing mode:

Group	Parameters
Standard	AS/NZS 3008 edition; power factor direction (lagging or leading)
Load	Specify by power (kW, W or HP with power factor) or by current; supply voltage; load type label; design factor; cable length and unit; maximum voltage drop
Cable construction	Cable type (fixed, flexible, MIMS); formation (multicore or single-core) and arrangement; insulation (XLPE, PVC, EPR); conductor material (Cu, Al)
Installation	Installation method and its sub-options (unenclosed type, air arrangement, tiers, grouping, enclosure, conduit or buried spacing, thermal insulation); air ambient or burial depth, soil temperature and soil resistivity
Circuit breaker	Prospective fault current; clearing time; earth-fault clearing time \(t_{ef}\) (default 0.04 s); protective device rating \(I_N\); instantaneous trip multiplier; source impedance

The protective device rating matters: Check 5 rejects any size whose derated capacity is below \(I_N\), so a device chosen generously for the load pushes the minimum size up. So do the source impedance and the earth-fault clearing time: a strong source cleared slowly needs a larger Table 5.1 earth (Check 7), which only comes with a larger phase size.

The earth-fault clearing time \(t_{ef}\) is separate from the protection time used for the short-circuit check. The earth withstand is checked for a fault at the cable origin, whose current is far above the device's instantaneous threshold, so it clears in the instantaneous operating time (default 0.04 s). Enter the upstream device's backup time instead if clearance relies on it.

Output Results

Candidate table: one row per standard size with its Table 5.1 earth conductor, the seven check marks (CCC, VD, SC, EFL, OVL, ESZ, EWT), \(I_Z\) and loading, voltage drop, withstand time, earth fault and required currents, the device rating against \(I_Z\), and the Table 5.1 and adiabatic minimum earth sizes (earth_min_mm2, earth_withstand_min_mm2). Sizes the selected edition does not tabulate for the construction are shown as n/a.
Conforming range: the list of conforming sizes, the smallest and largest, whether the range is contiguous, and the check(s) that fail for the next smaller size (what sets the minimum).
Verification: the full equation chain for the smallest conforming size (or for the largest tabulated size when nothing conforms), with the governing criterion.
Summary cards: load current, smallest conforming size, conforming range, minimum set by, loading and voltage drop of the smallest conforming size, overall result.

Method

For each size \(S\) in the standard series the earth conductor is read from AS/NZS 3000 Table 5.1, the AS/NZS 3008 tables are looked up for that size (base rating, derating factors, \(R_c\), \(X_c\), the earth conductor's \(R_e\) and its Table 30 \(X_e\), Table 52 \(k\)), and the same seven check functions used by Load Cable Sizing are run with the design current

\[ I_{design} = I_{load} \times k_{design}, \qquad I_{load} = \frac{P}{\sqrt{3}\,V\,PF} \]

Because capacity, voltage drop, withstand and earth fault current all improve with size, the conforming set is normally every size from the first that passes up to the largest the standard tabulates. The calculator does not assume this: it flags a gap when a larger size fails after a smaller one passes (for example where a size band changes the burial-depth factor).

Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C), for the voltage drop and the earth fault loop alike.

Combinations the installed edition does not tabulate are reported per size rather than approximated (for example multicore above 500 mm² or aluminium below 16 mm²). When no size at all is tabulated for the construction and installation, the calculation returns a “not supported by the selected standard” error, as Load Cable Sizing does. Single-core cables with the conductors spaced, or one conductor per conduit (Dedicated), are rejected outright: AS/NZS 3008 Table 30 tabulates single-core reactance only for trefoil and flat touching, and using those values for spaced conductors would understate the voltage drop and loop impedance.

Worked Examples

The 20 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_cable_size_range; worked examples for every calculation).

#	Case	I_design (A)	Smallest (mm²)	Largest (mm²)	Contiguous	Governing	Result
1	90 kW distribution board feeder on a perforated tray	152.8	70	500	yes	overload coordination	PASS
2	5 kW final sub-circuit in conduit on a 16 A breaker	8.0	16	500	yes	short-circuit withstand	PASS
3	15 kW lighting board at the end of a 180 m run	22.0	35	500	yes	overload coordination	PASS
4	30 kW pump feeder, 300 m, 2 % voltage-drop allowance	50.9	95	500	yes	voltage drop	PASS
5	37 kW on a 250 m run with a type-D breaker	62.8	150	500	yes	earth-fault loop	PASS
6	100 kW at a 36 kA fault level cleared in 0.3 s	169.8	150	500	yes	overload coordination	PASS
7	20 kW at 230 V three-phase with a 1.25 design factor	69.7	16	500	yes	overload coordination	PASS
8	250 kVA sub-main specified in kVA	347.8	185	500	yes	overload coordination	PASS
9	320 A measured load on a ladder rack	320.0	185	500	yes	overload coordination	PASS
10	400 A capacitor-bank feeder at 0.5 leading power factor, 1 % limit	400.0	185	300	no (400, 500)	overload coordination	PASS
11	200 kW on aluminium multicore cable	320.8	240	500	yes	overload coordination	PASS
12	60 kW PVC cable in a wiring enclosure with two other circuits	101.9	95	240	yes	overload coordination	PASS
13	100 kW on an elastomeric (EPR) cable	169.8	50	500	yes	earth-fault loop	PASS
14	500 kW at 690 V on single-core cables in trefoil	464.9	240	630	yes	overload coordination	PASS
15	45 kW cable among six touching on a tray	76.4	50	500	yes	overload coordination	PASS
16	75 kW feeder in a 55 °C switchroom	127.4	70	500	yes	overload coordination	PASS
17	22 kW cable completely surrounded by thermal insulation	37.4	35	35	yes	overload coordination	PASS
18	110 kW feeder direct buried at 1.0 m	186.8	95	500	yes	earth-fault loop	PASS
19	90 kW in a buried conduit beside a second circuit	152.8	95	500	yes	earth-fault loop	PASS
20	400 kW over 350 m on an 800 A device: no size passes	641.5	none	none	–	earth-fault loop	FAIL

Example 1 — 90 kW distribution board feeder on a perforated tray

Baseline case: 50 mm² carries the 152.8 A load but its 182 A capacity is below the 200 A device, so the minimum is 70 mm²; its 16 mm² earth would cover the 10.8 mm² the 7.7 kA near-end earth fault needs in 0.04 s. 9 of the 19 tabulated sizes conform.

Given: 90 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 80 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 200 A device with 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 90 kW × 1000 / (√3 × 400 × 0.85) = 152.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 152.8 A, 200 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	121.82	0.000	53	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	78.15	0.000	83	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	42.80	0.001	150	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	26.72	0.003	184	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	17.93	0.007	210	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	10.72	0.020	336	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	6.84	0.052	500	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	116.0	4.40	0.128	551	10.77	FAIL CCC, EFL, OVL, EWT
35 (10)	144.0	3.23	0.251	854	10.77	FAIL CCC, EFL, OVL, EWT
50 (16)	182.0	2.43	0.511	1,230	10.77	FAIL OVL
70 (25)	230.0	1.75	1.002	1,743	10.77	PASS
95 (25)	275.0	1.32	1.846	1,846	10.77	PASS
120 (35)	327.0	1.09	2.945	2,295	10.77	PASS
150 (50)	375.0	0.92	4.601	2,749	10.77	PASS
185 (70)	428.0	0.78	6.999	3,304	10.77	PASS
240 (95)	511.0	0.65	11.779	3,819	10.77	PASS
300 (120)	584.0	0.56	18.404	4,172	10.77	PASS
400 (120)	692.0	0.49	32.718	4,242	10.77	PASS
500 (120)	794.0	0.44	51.123	4,288	10.77	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 70 to 500 mm² (9 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination (50 mm² is the largest size that fails).

Check 1 — capacity (70 mm²) Base rating Table 14, column 2, row 70: 230 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 230 × 1.00 = 230.0 A vs I_design 152.8 A (loading 66.4 %) PASS

Check 2 — voltage drop R_c = 0.343 Ω/km (Table 35), X_c = 0.0741 Ω/km (Table 30). At the design current: ΔV = √3 × 152.8 × 0.080 × (0.343 × 0.85 + 0.0741 × 0.527) = 7.00 V (drop) = 1.75 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 70)² / 10,000² = 1.002 s vs 0.1 s; S_min = 10,000 × √0.1 / 143 = 22.1 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.927 Ω/km and X_e = 0.0808 Ω/km (Table 30 at 25 mm²): Z_loop = 0.03 + 0.0281 (phase) + 0.0744 (earth) = 0.1325 Ω. I_fault = 400/√3 / 0.1325 = 1,743 A vs 200 × 5 = 1,000 A; L_max = 157 m vs 80 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 152.8 A ≤ 200 A ≤ 230.0 A (device at 87.0 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 70 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.03 = 7,698 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 7,698 × √0.04 / 143 = 10.77 mm² vs 25 mm² (t_max = (143 × 25 / 7,698)² = 0.2157 s) PASS

Result 8/8 checks pass → PASS; conforming 70–500 mm² (9 of 19); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 90 kW × 1000 / (√3 × 400 × 0.85) = 152.83 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.03 Ω = 7698 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 50 mm² (earth 16 mm²): I_Z = 182 × 1.000 = 182.00 A, VD = 2.432 %, t = (k·S/I)² = (143 × 50 / 10000)² = 0.5112 s, I_ef = 400/√3 / 0.1878 Ω = 1230.0 A vs 1000 A required, earth S_min = 7698 × √0.04 / 143 = 10.77 mm² vs 16 mm² — fails OVL, which sets the minimum. 70 mm² (earth 25 mm²): base 230 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 230 × 1.00 × 1.00 = 230.00 A vs 152.83 A; ΔV = √3 × 152.83 × 0.080 × (0.343 × 0.85 + 0.0741 × 0.527) = 7.00 V = 1.750 % (limit 5 %); t = (143 × 70 / 10000)² = 1.0020 s vs 0.1 s; Z_loop = 0.03 + 0.08·√(0.343² + 0.0741²) + 0.08·√(0.927² + 0.0808²) = 0.03 + 0.0281 + 0.0744 = 0.1325 Ω, I_ef = 230.9 / 0.1325 = 1742.8 A vs 200 × 5 = 1000 A (L_max = 156.8 m); I_B 152.83 ≤ I_N 200 ≤ I_Z 230.00 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 7698 × √0.04 / 143 = 10.77 mm² ≤ 25 mm². Conforming sizes 70 to 500 mm² (9 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-90kw-400v-80m-tray-200a)

Example 2 — 5 kW final sub-circuit in conduit on a 16 A breaker

A small load where the adiabatic withstand of a 6 kA fault, not the load current, rules out the smallest sizes: 10 mm² survives it for only 0.057 s of the 0.1 s clearing time, so 16 mm² is the minimum and short-circuit withstand governs it (69 %).

Given: 5 kW at PF 0.9 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 25 m; in conduit in air, 1 circuit(s), air ambient 40 °C. Protection: prospective fault 6 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 16 A device with 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 5 kW × 1000 / (√3 × 400 × 0.9) = 8.0 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 8.0 A, 16 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	2.11	0.001	159	3.23	FAIL SC, EWT
1.5 (1.5)	20.0	1.36	0.001	239	3.23	FAIL SC, EWT
2.5 (2.5)	29.0	0.74	0.004	403	3.23	FAIL SC, EWT
4 (2.5)	37.0	0.46	0.009	478	3.23	FAIL SC, EWT
6 (2.5)	46.0	0.31	0.020	531	3.23	FAIL SC, EWT
10 (4)	63.0	0.19	0.057	756	3.23	FAIL SC
16 (6)	81.0	0.12	0.145	982	3.23	PASS
25 (6)	107.0	0.08	0.355	1,042	3.23	PASS
35 (10)	130.0	0.06	0.696	1,319	3.23	PASS
50 (16)	155.0	0.04	1.420	1,547	3.23	PASS
70 (25)	193.0	0.03	2.783	1,749	3.23	PASS
95 (25)	233.0	0.02	5.126	1,780	3.23	PASS
120 (35)	270.0	0.02	8.180	1,892	3.23	PASS
150 (50)	304.0	0.02	12.781	1,976	3.23	PASS
185 (70)	348.0	0.01	19.441	2,053	3.23	PASS
240 (95)	411.0	0.01	32.718	2,109	3.23	PASS
300 (120)	463.0	0.01	51.123	2,140	3.23	PASS
400 (120)	524.0	0.01	90.884	2,145	3.23	PASS
500 (120)	601.0	0.01	142.007	2,149	3.23	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 16 to 500 mm² (13 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by short-circuit withstand (10 mm² is the largest size that fails).

Check 1 — capacity (16 mm²) Base rating Table 14, column 25, row 16: 81 A. Derating Table 22, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 81 × 1.00 = 81.0 A vs I_design 8.0 A (loading 9.9 %) PASS

Check 2 — voltage drop R_c = 1.47 Ω/km (Table 35), X_c = 0.0805 Ω/km (Table 30). At the design current: ΔV = √3 × 8.0 × 0.025 × (1.47 × 0.9 + 0.0805 × 0.436) = 0.47 V (drop) = 0.12 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 16)² / 6,000² = 0.145 s vs 0.1 s; S_min = 6,000 × √0.1 / 143 = 13.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 3.93 Ω/km and X_e = 0.0887 Ω/km (Table 30 at 6 mm²): Z_loop = 0.1 + 0.0368 (phase) + 0.0983 (earth) = 0.2351 Ω. I_fault = 400/√3 / 0.2351 = 982 A vs 16 × 5 = 80 A; L_max = 516 m vs 25 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 8.0 A ≤ 16 A ≤ 81.0 A (device at 19.8 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 16 mm² phase conductor: 6 mm²; earth 6 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.1 = 2,309 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 6 mm² (t_max = (143 × 6 / 2,309)² = 0.1380 s) PASS

Result 8/8 checks pass → PASS; conforming 16–500 mm² (13 of 19); governing: short circuit withstand

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 5 kW × 1000 / (√3 × 400 × 0.9) = 8.02 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.1 Ω = 2309 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 10 mm² (earth 4 mm²): I_Z = 63 × 1.000 = 63.00 A, VD = 0.185 %, t = (k·S/I)² = (143 × 10 / 6000)² = 0.0568 s, I_ef = 400/√3 / 0.3053 Ω = 756.4 A vs 80 A required, earth S_min = 2309 × √0.04 / 143 = 3.23 mm² vs 4 mm² — fails SC, which sets the minimum. 16 mm² (earth 6 mm²): base 81 A (Table 14), derating Table 22 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 81 × 1.00 × 1.00 = 81.00 A vs 8.02 A; ΔV = √3 × 8.02 × 0.025 × (1.47 × 0.9 + 0.0805 × 0.436) = 0.47 V = 0.118 % (limit 5 %); t = (143 × 16 / 6000)² = 0.1454 s vs 0.1 s; Z_loop = 0.1 + 0.025·√(1.47² + 0.0805²) + 0.025·√(3.93² + 0.0887²) = 0.1 + 0.0368 + 0.0983 = 0.2351 Ω, I_ef = 230.9 / 0.2351 = 982.4 A vs 16 × 5 = 80 A (L_max = 515.8 m); I_B 8.02 ≤ I_N 16 ≤ I_Z 81.00 holds; earth 6 mm² ≥ Table 5.1 minimum 6 mm², S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 6 mm². Conforming sizes 16 to 500 mm² (13 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-5kw-400v-25m-conduit-16a)

Example 3 — 15 kW lighting board at the end of a 180 m run

Voltage drop rules out 6 mm² over 180 m, but the earth sets the minimum: the 0.05 Ω upstream loop drives 4.8 kA into a fault at the origin, needing a 6.7 mm² earth even when cleared instantaneously in 0.04 s, so every size up to 25 mm² (6 mm² earth) fails earth withstand and the range starts at 35 mm² (10 mm² earth).

Given: 15 kW at PF 0.95 lagging, 415 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 180 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 2 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 25 A device with 3× instantaneous trip, upstream loop impedance 0.05 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 15 kW × 1000 / (√3 × 415 × 0.95) = 22.0 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 22.0 A, 25 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	42.39	0.005	25	6.70	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	27.18	0.012	38	6.70	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	14.87	0.032	69	6.70	FAIL VD, SC, EFL, EWT
4 (2.5)	36.0	9.27	0.082	85	6.70	FAIL VD, SC, EWT
6 (2.5)	46.0	6.21	0.184	97	6.70	FAIL VD, EWT
10 (4)	66.0	3.70	0.511	157	6.70	FAIL EWT
16 (6)	87.0	2.35	1.309	234	6.70	FAIL EWT
25 (6)	116.0	1.49	3.195	259	6.70	FAIL EWT
35 (10)	144.0	1.09	6.263	405	6.70	PASS
50 (16)	182.0	0.81	12.781	592	6.70	PASS
70 (25)	230.0	0.58	25.050	854	6.70	PASS
95 (25)	275.0	0.43	46.138	908	6.70	PASS
120 (35)	327.0	0.35	73.616	1,147	6.70	PASS
150 (50)	375.0	0.29	115.026	1,397	6.70	PASS
185 (70)	428.0	0.24	174.967	1,714	6.70	PASS
240 (95)	511.0	0.19	294.466	2,021	6.70	PASS
300 (120)	584.0	0.16	460.103	2,238	6.70	PASS
400 (120)	692.0	0.14	817.960	2,282	6.70	PASS
500 (120)	794.0	0.12	1,278.062	2,311	6.70	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 35 to 500 mm² (11 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by earth conductor withstand (25 mm² is the largest size that fails).

Check 1 — capacity (35 mm²) Base rating Table 14, column 2, row 35: 144 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 144 × 1.00 = 144.0 A vs I_design 22.0 A (loading 15.3 %) PASS

Check 2 — voltage drop R_c = 0.669 Ω/km (Table 35), X_c = 0.0786 Ω/km (Table 30). At the design current: ΔV = √3 × 22.0 × 0.180 × (0.669 × 0.95 + 0.0786 × 0.312) = 4.52 V (drop) = 1.09 % of 415 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 35)² / 2,000² = 6.263 s vs 0.1 s; S_min = 2,000 × √0.1 / 143 = 4.4 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 2.33 Ω/km and X_e = 0.0840 Ω/km (Table 30 at 10 mm²): Z_loop = 0.05 + 0.1212 (phase) + 0.4197 (earth) = 0.5909 Ω. I_fault = 415/√3 / 0.5909 = 405 A vs 25 × 3 = 75 A; L_max = 1,046 m vs 180 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 22.0 A ≤ 25 A ≤ 144.0 A (device at 17.4 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 35 mm² phase conductor: 10 mm²; earth 10 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 415/√3 / 0.05 = 4,792 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 4,792 × √0.04 / 143 = 6.70 mm² vs 10 mm² (t_max = (143 × 10 / 4,792)² = 0.0891 s) PASS

Result 8/8 checks pass → PASS; conforming 35–500 mm² (11 of 19); governing: ocpd coordination. The upstream earth-loop impedance (0.05 Ω) gives 4792 A of earth-fault current at the cable origin, more than the 2 kA prospective fault: the two inputs are inconsistent Check the upstream loop impedance against the prospective fault level; the earth withstand check uses the loop impedance

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 15 kW × 1000 / (√3 × 415 × 0.95) = 21.97 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (415/√3)/0.05 Ω = 4792 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 25 mm² (earth 6 mm²): I_Z = 116 × 1.000 = 116.00 A, VD = 1.495 %, t = (k·S/I)² = (143 × 25 / 2000)² = 3.1952 s, I_ef = 415/√3 / 0.9251 Ω = 259.0 A vs 75 A required, earth S_min = 4792 × √0.04 / 143 = 6.70 mm² vs 6 mm² — fails earth withstand, which sets the minimum. 35 mm² (earth 10 mm²): base 144 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 144 × 1.00 × 1.00 = 144.00 A vs 21.97 A; ΔV = √3 × 21.97 × 0.180 × (0.669 × 0.95 + 0.0786 × 0.312) = 4.52 V = 1.089 % (limit 5 %); t = (143 × 35 / 2000)² = 6.2625 s vs 0.1 s; Z_loop = 0.05 + 0.18·√(0.669² + 0.0786²) + 0.18·√(2.33² + 0.084²) = 0.05 + 0.1212 + 0.4197 = 0.5909 Ω, I_ef = 239.6 / 0.5909 = 405.5 A vs 25 × 3 = 75 A (L_max = 1046.4 m); I_B 21.97 ≤ I_N 25 ≤ I_Z 144.00 holds; earth 10 mm² ≥ Table 5.1 minimum 10 mm², S_min = 4792 × √0.04 / 143 = 6.70 mm² ≤ 10 mm². Conforming sizes 35 to 500 mm² (11 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-15kw-415v-180m-tray-25a-vd)

Example 4 — 30 kW pump feeder, 300 m, 2 % voltage-drop allowance

A tight voltage-drop budget on a long run pushes the minimum far above the capacity-limited size.

Given: 30 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 300 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 8 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 63 A device with 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 2 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 30 kW × 1000 / (√3 × 400 × 0.85) = 50.9 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 50.9 A, 63 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	152.27	0.000	14	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	97.69	0.001	22	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	53.50	0.002	40	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	33.40	0.005	49	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	22.42	0.012	56	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	13.40	0.032	90	3.23	FAIL VD, SC, EFL
16 (6)	87.0	8.55	0.082	134	3.23	FAIL VD, SC, EFL
25 (6)	116.0	5.50	0.200	148	3.23	FAIL VD, EFL
35 (10)	144.0	4.04	0.391	231	3.23	FAIL VD, EFL
50 (16)	182.0	3.04	0.799	334	3.23	FAIL VD
70 (25)	230.0	2.19	1.566	477	3.23	FAIL VD
95 (25)	275.0	1.65	2.884	506	3.23	PASS
120 (35)	327.0	1.36	4.601	633	3.23	PASS
150 (50)	375.0	1.15	7.189	763	3.23	PASS
185 (70)	428.0	0.98	10.935	925	3.23	PASS
240 (95)	511.0	0.81	18.404	1,078	3.23	PASS
300 (120)	584.0	0.70	28.756	1,184	3.23	PASS
400 (120)	692.0	0.61	51.123	1,205	3.23	PASS
500 (120)	794.0	0.55	79.879	1,219	3.23	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 95 to 500 mm² (8 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by voltage drop (70 mm² is the largest size that fails).

Check 1 — capacity (95 mm²) Base rating Table 14, column 2, row 95: 275 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 275 × 1.00 = 275.0 A vs I_design 50.9 A (loading 18.5 %) PASS

Check 2 — voltage drop R_c = 0.248 Ω/km (Table 35), X_c = 0.0725 Ω/km (Table 30). At the design current: ΔV = √3 × 50.9 × 0.300 × (0.248 × 0.85 + 0.0725 × 0.527) = 6.59 V (drop) = 1.65 % of 400 V, limit 2 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 95)² / 8,000² = 2.884 s vs 0.1 s; S_min = 8,000 × √0.1 / 143 = 17.7 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.927 Ω/km and X_e = 0.0808 Ω/km (Table 30 at 25 mm²): Z_loop = 0.1 + 0.0775 (phase) + 0.2792 (earth) = 0.4567 Ω. I_fault = 400/√3 / 0.4567 = 506 A vs 63 × 5 = 315 A; L_max = 533 m vs 300 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 50.9 A ≤ 63 A ≤ 275.0 A (device at 22.9 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 95 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.1 = 2,309 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 25 mm² (t_max = (143 × 25 / 2,309)² = 2.3964 s) PASS

Result 8/8 checks pass → PASS; conforming 95–500 mm² (8 of 19); governing: voltage drop. Voltage drop margin is very tight (0.35%)

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 30 kW × 1000 / (√3 × 400 × 0.85) = 50.94 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.1 Ω = 2309 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 70 mm² (earth 25 mm²): I_Z = 230 × 1.000 = 230.00 A, VD = 2.188 %, t = (k·S/I)² = (143 × 70 / 8000)² = 1.5656 s, I_ef = 400/√3 / 0.4844 Ω = 476.7 A vs 315 A required, earth S_min = 2309 × √0.04 / 143 = 3.23 mm² vs 25 mm² — fails VD, which sets the minimum. 95 mm² (earth 25 mm²): base 275 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 275 × 1.00 × 1.00 = 275.00 A vs 50.94 A; ΔV = √3 × 50.94 × 0.300 × (0.248 × 0.85 + 0.0725 × 0.527) = 6.59 V = 1.648 % (limit 2 %); t = (143 × 95 / 8000)² = 2.8836 s vs 0.1 s; Z_loop = 0.1 + 0.3·√(0.248² + 0.0725²) + 0.3·√(0.927² + 0.0808²) = 0.1 + 0.0775 + 0.2792 = 0.4567 Ω, I_ef = 230.9 / 0.4567 = 505.7 A vs 63 × 5 = 315 A (L_max = 532.5 m); I_B 50.94 ≤ I_N 63 ≤ I_Z 275.00 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 25 mm². Conforming sizes 95 to 500 mm² (8 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-30kw-400v-300m-tray-63a-vd-2pct)

Example 5 — 37 kW on a 250 m run with a type-D breaker

Earth-fault loop impedance sets the minimum: a 10 × In magnetic trip needs 800 A from the far end of a 250 m loop with the Table 5.1 earth.

Given: 37 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 250 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 80 A device with 10× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 37 kW × 1000 / (√3 × 400 × 0.85) = 62.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 62.8 A, 80 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	156.50	0.000	17	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	100.40	0.000	26	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	54.99	0.001	48	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	34.33	0.003	59	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	23.04	0.007	67	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	13.77	0.020	107	3.23	FAIL VD, SC, EFL, OVL
16 (6)	87.0	8.79	0.052	159	3.23	FAIL VD, SC, EFL
25 (6)	116.0	5.65	0.128	176	3.23	FAIL VD, EFL
35 (10)	144.0	4.15	0.251	271	3.23	FAIL EFL
50 (16)	182.0	3.13	0.511	389	3.23	FAIL EFL
70 (25)	230.0	2.25	1.002	549	3.23	FAIL EFL
95 (25)	275.0	1.69	1.846	581	3.23	FAIL EFL
120 (35)	327.0	1.39	2.945	720	3.23	FAIL EFL
150 (50)	375.0	1.18	4.601	859	3.23	PASS
185 (70)	428.0	1.00	6.999	1,028	3.23	PASS
240 (95)	511.0	0.83	11.779	1,183	3.23	PASS
300 (120)	584.0	0.72	18.404	1,288	3.23	PASS
400 (120)	692.0	0.63	32.718	1,309	3.23	PASS
500 (120)	794.0	0.57	51.123	1,323	3.23	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 150 to 500 mm² (6 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by earth-fault loop (120 mm² is the largest size that fails).

Check 1 — capacity (150 mm²) Base rating Table 14, column 2, row 150: 375 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 375 × 1.00 = 375.0 A vs I_design 62.8 A (loading 16.8 %) PASS

Check 2 — voltage drop R_c = 0.160 Ω/km (Table 35), X_c = 0.0718 Ω/km (Table 30). At the design current: ΔV = √3 × 62.8 × 0.250 × (0.160 × 0.85 + 0.0718 × 0.527) = 4.73 V (drop) = 1.18 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 150)² / 10,000² = 4.601 s vs 0.1 s; S_min = 10,000 × √0.1 / 143 = 22.1 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.494 Ω/km and X_e = 0.0751 Ω/km (Table 30 at 50 mm²): Z_loop = 0.1 + 0.0438 (phase) + 0.1249 (earth) = 0.2688 Ω. I_fault = 400/√3 / 0.2688 = 859 A vs 80 × 10 = 800 A; L_max = 279 m vs 250 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 62.8 A ≤ 80 A ≤ 375.0 A (device at 21.3 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 150 mm² phase conductor: 50 mm²; earth 50 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.1 = 2,309 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 50 mm² (t_max = (143 × 50 / 2,309)² = 9.5855 s) PASS

Result 8/8 checks pass → PASS; conforming 150–500 mm² (6 of 19); governing: earth fault loop impedance. Earth fault trip margin is very low (1.07x) Review protection settings - fault current barely exceeds trip threshold

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 37 kW × 1000 / (√3 × 400 × 0.85) = 62.83 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.1 Ω = 2309 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 120 mm² (earth 35 mm²): I_Z = 327 × 1.000 = 327.00 A, VD = 1.394 %, t = (k·S/I)² = (143 × 120 / 10000)² = 2.9447 s, I_ef = 400/√3 / 0.3208 Ω = 719.9 A vs 800 A required, earth S_min = 2309 × √0.04 / 143 = 3.23 mm² vs 35 mm² — fails EFL, which sets the minimum. 150 mm² (earth 50 mm²): base 375 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 375 × 1.00 × 1.00 = 375.00 A vs 62.83 A; ΔV = √3 × 62.83 × 0.250 × (0.16 × 0.85 + 0.0718 × 0.527) = 4.73 V = 1.182 % (limit 5 %); t = (143 × 150 / 10000)² = 4.6010 s vs 0.1 s; Z_loop = 0.1 + 0.25·√(0.16² + 0.0718²) + 0.25·√(0.494² + 0.0751²) = 0.1 + 0.0438 + 0.1249 = 0.2688 Ω, I_ef = 230.9 / 0.2688 = 859.3 A vs 80 × 10 = 800 A (L_max = 279.5 m); I_B 62.83 ≤ I_N 80 ≤ I_Z 375.00 holds; earth 50 mm² ≥ Table 5.1 minimum 50 mm², S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 50 mm². Conforming sizes 150 to 500 mm² (6 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-37kw-400v-250m-type-d-breaker-efl)

Example 6 — 100 kW at a 36 kA fault level cleared in 0.3 s

Short-circuit withstand sets the minimum: S ≥ I·√t / k = 36 000·√0.3 / 143 = 138 mm², so 120 mm² fails and 150 mm² is the smallest conforming size. Its 50 mm² earth needs only 16.2 mm² for the 11.5 kA near-end earth fault cleared instantaneously (0.04 s), and overload coordination (I_B/I_N = 84.9 %) narrowly out-ranks the 84.5 % short-circuit utilisation as the governing check.

Given: 100 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 50 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 36 kA cleared in 0.3 s, earth-fault clearing time 0.04 s (default), 200 A device with 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 100 kW × 1000 / (√3 × 400 × 0.85) = 169.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 169.8 A, 200 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	84.60	0.000	85	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	54.27	0.000	132	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	29.72	0.000	239	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	18.56	0.000	294	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	12.45	0.001	335	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	7.44	0.002	536	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	4.75	0.004	796	16.15	FAIL CCC, SC, EFL, OVL, EWT
25 (6)	116.0	3.05	0.010	878	16.15	FAIL CCC, SC, EFL, OVL, EWT
35 (10)	144.0	2.24	0.019	1,356	16.15	FAIL CCC, SC, OVL, EWT
50 (16)	182.0	1.69	0.039	1,947	16.15	FAIL SC, OVL, EWT
70 (25)	230.0	1.22	0.077	2,747	16.15	FAIL SC
95 (25)	275.0	0.92	0.142	2,907	16.15	FAIL SC
120 (35)	327.0	0.75	0.227	3,600	16.15	FAIL SC
150 (50)	375.0	0.64	0.355	4,296	16.15	PASS
185 (70)	428.0	0.54	0.540	5,140	16.15	PASS
240 (95)	511.0	0.45	0.909	5,915	16.15	PASS
300 (120)	584.0	0.39	1.420	6,442	16.15	PASS
400 (120)	692.0	0.34	2.525	6,546	16.15	PASS
500 (120)	794.0	0.31	3.945	6,616	16.15	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 150 to 500 mm² (6 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by short-circuit withstand (120 mm² is the largest size that fails).

Check 2 — voltage drop R_c = 0.160 Ω/km (Table 35), X_c = 0.0718 Ω/km (Table 30). At the design current: ΔV = √3 × 169.8 × 0.050 × (0.160 × 0.85 + 0.0718 × 0.527) = 2.56 V (drop) = 0.64 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 150)² / 36,000² = 0.355 s vs 0.3 s; S_min = 36,000 × √0.3 / 143 = 137.9 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.494 Ω/km and X_e = 0.0751 Ω/km (Table 30 at 50 mm²): Z_loop = 0.02 + 0.0088 (phase) + 0.0250 (earth) = 0.0538 Ω. I_fault = 400/√3 / 0.0538 = 4,296 A vs 200 × 5 = 1,000 A; L_max = 312 m vs 50 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 169.8 A ≤ 200 A ≤ 375.0 A (device at 53.3 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 150 mm² phase conductor: 50 mm²; earth 50 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.02 = 11,547 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 11,547 × √0.04 / 143 = 16.15 mm² vs 50 mm² (t_max = (143 × 50 / 11,547)² = 0.3834 s) PASS

Result 8/8 checks pass → PASS; conforming 150–500 mm² (6 of 19); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 100 kW × 1000 / (√3 × 400 × 0.85) = 169.81 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.02 Ω = 11547 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 120 mm² (earth 35 mm²): I_Z = 327 × 1.000 = 327.00 A, VD = 0.754 %, t = (k·S/I)² = (143 × 120 / 36000)² = 0.2272 s, I_ef = 400/√3 / 0.0642 Ω = 3599.7 A vs 1000 A required, earth S_min = 11547 × √0.04 / 143 = 16.15 mm² vs 35 mm² — fails SC, which sets the minimum. 150 mm² (earth 50 mm²): base 375 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 375 × 1.00 × 1.00 = 375.00 A vs 169.81 A; ΔV = √3 × 169.81 × 0.050 × (0.16 × 0.85 + 0.0718 × 0.527) = 2.56 V = 0.639 % (limit 5 %); t = (143 × 150 / 36000)² = 0.3550 s vs 0.3 s; Z_loop = 0.02 + 0.05·√(0.16² + 0.0718²) + 0.05·√(0.494² + 0.0751²) = 0.02 + 0.0088 + 0.0250 = 0.0538 Ω, I_ef = 230.9 / 0.0538 = 4296.4 A vs 200 × 5 = 1000 A (L_max = 312.5 m); I_B 169.81 ≤ I_N 200 ≤ I_Z 375.00 holds; earth 50 mm² ≥ Table 5.1 minimum 50 mm², S_min = 11547 × √0.04 / 143 = 16.15 mm² ≤ 50 mm². Conforming sizes 150 to 500 mm² (6 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-100kw-400v-50m-36ka-0p3s-sc)

Example 7 — 20 kW at 230 V three-phase with a 1.25 design factor

The design factor applies to every load-dependent check, voltage drop included: I_design = 1.25 × 55.8 A = 69.7 A is more than 10 mm² carries and drops 5.6 % across it, so the minimum is 16 mm² (3.57 % at the design current).

Given: 20 kW at PF 0.9 lagging, 230 V three-phase, design factor 1.25. Copper XLPE (90 °C) fixed multicore cable, 50 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 6 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 80 A device with 3× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 20 kW × 1000 / (√3 × 230 × 0.9) = 55.8 A; I_design = 55.8 × 1.25 = 69.7 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 69.7 A, 80 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	63.93	0.001	47	1.86	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	41.00	0.001	73	1.86	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	22.44	0.004	127	1.86	FAIL CCC, VD, SC, EFL, OVL
4 (2.5)	36.0	14.00	0.009	153	1.86	FAIL CCC, VD, SC, EFL, OVL
6 (2.5)	46.0	9.39	0.020	173	1.86	FAIL CCC, VD, SC, EFL, OVL
10 (4)	66.0	5.60	0.057	260	1.86	FAIL CCC, VD, SC, OVL
16 (6)	87.0	3.57	0.145	359	1.86	PASS
25 (6)	116.0	2.28	0.355	387	1.86	PASS
35 (10)	144.0	1.67	0.696	531	1.86	PASS
50 (16)	182.0	1.25	1.420	669	1.86	PASS
70 (25)	230.0	0.90	2.783	809	1.86	PASS
95 (25)	275.0	0.67	5.126	833	1.86	PASS
120 (35)	327.0	0.55	8.180	921	1.86	PASS
150 (50)	375.0	0.46	12.781	993	1.86	PASS
185 (70)	428.0	0.39	19.441	1,063	1.86	PASS
240 (95)	511.0	0.32	32.718	1,116	1.86	PASS
300 (120)	584.0	0.27	51.123	1,146	1.86	PASS
400 (120)	692.0	0.24	90.884	1,152	1.86	PASS
500 (120)	794.0	0.21	142.007	1,156	1.86	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 16 to 500 mm² (13 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by current-carrying capacity, voltage drop, short-circuit withstand, overload coordination (10 mm² is the largest size that fails).

Check 1 — capacity (16 mm²) Base rating Table 14, column 2, row 16: 87 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 87 × 1.00 = 87.0 A vs I_design 69.7 A (loading 80.1 %) PASS

Check 2 — voltage drop R_c = 1.47 Ω/km (Table 35), X_c = 0.0805 Ω/km (Table 30). At the design current: ΔV = √3 × 69.7 × 0.050 × (1.47 × 0.9 + 0.0805 × 0.436) = 8.20 V (drop) = 3.57 % of 230 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 16)² / 6,000² = 0.145 s vs 0.1 s; S_min = 6,000 × √0.1 / 143 = 13.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 3.93 Ω/km and X_e = 0.0887 Ω/km (Table 30 at 6 mm²): Z_loop = 0.1 + 0.0736 (phase) + 0.1966 (earth) = 0.3702 Ω. I_fault = 230/√3 / 0.3702 = 359 A vs 80 × 3 = 240 A; L_max = 84 m vs 50 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 69.7 A ≤ 80 A ≤ 87.0 A (device at 92.0 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 16 mm² phase conductor: 6 mm²; earth 6 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 230/√3 / 0.1 = 1,328 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 1,328 × √0.04 / 143 = 1.86 mm² vs 6 mm² (t_max = (143 × 6 / 1,328)² = 0.4175 s) PASS

Result 8/8 checks pass → PASS; conforming 16–500 mm² (13 of 19); governing: ocpd coordination. Cable utilization is elevated (80.1%) - monitor for load changes Power loss (3.43%) is significant Consider larger conductor to reduce energy losses

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 20 kW × 1000 / (√3 × 230 × 0.9) = 55.78 A, I_design = 55.78 × 1.25 = 69.73 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (230/√3)/0.1 Ω = 1328 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 10 mm² (earth 4 mm²): I_Z = 66 × 1.000 = 66.00 A, VD = 5.602 %, t = (k·S/I)² = (143 × 10 / 6000)² = 0.0568 s, I_ef = 230/√3 / 0.5106 Ω = 260.1 A vs 240 A required, earth S_min = 1328 × √0.04 / 143 = 1.86 mm² vs 4 mm² — fails CCC, VD, SC, OVL, which sets the minimum. 16 mm² (earth 6 mm²): base 87 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 87 × 1.00 × 1.00 = 87.00 A vs 69.73 A; ΔV = √3 × 69.73 × 0.050 × (1.47 × 0.9 + 0.0805 × 0.436) = 8.20 V = 3.566 % (limit 5 %); t = (143 × 16 / 6000)² = 0.1454 s vs 0.1 s; Z_loop = 0.1 + 0.05·√(1.47² + 0.0805²) + 0.05·√(3.93² + 0.0887²) = 0.1 + 0.0736 + 0.1966 = 0.3702 Ω, I_ef = 132.8 / 0.3702 = 358.7 A vs 80 × 3 = 240 A (L_max = 83.9 m); I_B 69.73 ≤ I_N 80 ≤ I_Z 87.00 holds; earth 6 mm² ≥ Table 5.1 minimum 6 mm², S_min = 1328 × √0.04 / 143 = 1.86 mm² ≤ 6 mm². Conforming sizes 16 to 500 mm² (13 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-20kw-230v-50m-design-factor-1p25-80a)

Example 8 — 250 kVA sub-main specified in kVA

Load given as apparent power: I = S / (√3·V) with no power-factor term, then the 400 A device sets the minimum.

Given: 250 kVA (PF 0.85 lagging for voltage drop), 415 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 60 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 20 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 400 A device with 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 250 kVA × 1000 / (√3 × 415) = 347.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 347.8 A, 400 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	200.41	0.000	73	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	128.56	0.000	114	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	70.41	0.000	208	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	43.96	0.001	255	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	29.50	0.002	291	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	17.63	0.005	467	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	11.25	0.013	696	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	116.0	7.23	0.032	769	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	144.0	5.31	0.063	1,196	16.76	FAIL CCC, VD, SC, EFL, OVL, EWT
50 (16)	182.0	4.00	0.128	1,732	16.76	FAIL CCC, EFL, OVL, EWT
70 (25)	230.0	2.88	0.251	2,473	16.76	FAIL CCC, OVL
95 (25)	275.0	2.17	0.461	2,623	16.76	FAIL CCC, OVL
120 (35)	327.0	1.79	0.736	3,283	16.76	FAIL CCC, OVL
150 (50)	375.0	1.51	1.150	3,960	16.76	FAIL OVL
185 (70)	428.0	1.29	1.750	4,800	16.76	PASS
240 (95)	511.0	1.06	2.945	5,592	16.76	PASS
300 (120)	584.0	0.92	4.601	6,141	16.76	PASS
400 (120)	692.0	0.81	8.180	6,250	16.76	PASS
500 (120)	794.0	0.72	12.781	6,324	16.76	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 185 to 500 mm² (5 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination (150 mm² is the largest size that fails).

Check 1 — capacity (185 mm²) Base rating Table 14, column 2, row 185: 428 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 428 × 1.00 = 428.0 A vs I_design 347.8 A (loading 81.3 %) PASS

Check 2 — voltage drop R_c = 0.129 Ω/km (Table 35), X_c = 0.0720 Ω/km (Table 30). At the design current: ΔV = √3 × 347.8 × 0.060 × (0.129 × 0.85 + 0.0720 × 0.527) = 5.33 V (drop) = 1.29 % of 415 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 185)² / 20,000² = 1.750 s vs 0.1 s; S_min = 20,000 × √0.1 / 143 = 44.2 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.343 Ω/km and X_e = 0.0741 Ω/km (Table 30 at 70 mm²): Z_loop = 0.02 + 0.0089 (phase) + 0.0211 (earth) = 0.0499 Ω. I_fault = 415/√3 / 0.0499 = 4,800 A vs 400 × 5 = 2,000 A; L_max = 200 m vs 60 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 347.8 A ≤ 400 A ≤ 428.0 A (device at 93.5 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 185 mm² phase conductor: 70 mm²; earth 70 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 415/√3 / 0.02 = 11,980 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 11,980 × √0.04 / 143 = 16.76 mm² vs 70 mm² (t_max = (143 × 70 / 11,980)² = 0.6982 s) PASS

Result 8/8 checks pass → PASS; conforming 185–500 mm² (5 of 19); governing: ocpd coordination. Cable utilization is elevated (81.3%) - monitor for load changes

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 250 kVA × 1000 / (√3 × 415) = 347.80 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (415/√3)/0.02 Ω = 11980 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 150 mm² (earth 50 mm²): I_Z = 375 × 1.000 = 375.00 A, VD = 1.514 %, t = (k·S/I)² = (143 × 150 / 20000)² = 1.1503 s, I_ef = 415/√3 / 0.0605 Ω = 3960.1 A vs 2000 A required, earth S_min = 11980 × √0.04 / 143 = 16.76 mm² vs 50 mm² — fails OVL, which sets the minimum. 185 mm² (earth 70 mm²): base 428 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 428 × 1.00 × 1.00 = 428.00 A vs 347.80 A; ΔV = √3 × 347.80 × 0.060 × (0.129 × 0.85 + 0.072 × 0.527) = 5.33 V = 1.285 % (limit 5 %); t = (143 × 185 / 20000)² = 1.7497 s vs 0.1 s; Z_loop = 0.02 + 0.06·√(0.129² + 0.072²) + 0.06·√(0.343² + 0.0741²) = 0.02 + 0.0089 + 0.0211 = 0.0499 Ω, I_ef = 239.6 / 0.0499 = 4799.8 A vs 400 × 5 = 2000 A (L_max = 200.1 m); I_B 347.80 ≤ I_N 400 ≤ I_Z 428.00 holds; earth 70 mm² ≥ Table 5.1 minimum 70 mm², S_min = 11980 × √0.04 / 143 = 16.76 mm² ≤ 70 mm². Conforming sizes 185 to 500 mm² (5 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-250kva-415v-60m-tray-400a)

Example 9 — 320 A measured load on a ladder rack

Load specified as a current on ladder/rack support (Table 24 column); a 400 A device needs more cable than the load does.

Given: 320 A at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 100 m; unenclosed, spaced from the surface on ladder, racks or cleats, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 25 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 400 A device with 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 320.0 A (specified)

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 320.0 A, 400 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	318.84	0.000	43	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	204.54	0.000	66	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	112.02	0.000	120	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	69.93	0.001	148	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	46.93	0.001	169	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	28.06	0.003	271	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	17.90	0.008	405	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	116.0	11.51	0.020	447	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	144.0	8.45	0.040	699	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
50 (16)	182.0	6.37	0.082	1,017	10.77	FAIL CCC, VD, SC, EFL, OVL
70 (25)	230.0	4.58	0.160	1,460	10.77	FAIL CCC, EFL, OVL
95 (25)	275.0	3.45	0.295	1,551	10.77	FAIL CCC, EFL, OVL
120 (35)	327.0	2.84	0.471	1,952	10.77	FAIL EFL, OVL
150 (50)	375.0	2.41	0.736	2,369	10.77	FAIL OVL
185 (70)	428.0	2.04	1.120	2,892	10.77	PASS
240 (95)	511.0	1.69	1.885	3,392	10.77	PASS
300 (120)	584.0	1.47	2.945	3,743	10.77	PASS
400 (120)	692.0	1.29	5.235	3,813	10.77	PASS
500 (120)	794.0	1.15	8.180	3,861	10.77	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 185 to 500 mm² (5 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination (150 mm² is the largest size that fails).

Check 2 — voltage drop R_c = 0.129 Ω/km (Table 35), X_c = 0.0720 Ω/km (Table 30). At the design current: ΔV = √3 × 320.0 × 0.100 × (0.129 × 0.85 + 0.0720 × 0.527) = 8.18 V (drop) = 2.04 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 185)² / 25,000² = 1.120 s vs 0.1 s; S_min = 25,000 × √0.1 / 143 = 55.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.343 Ω/km and X_e = 0.0741 Ω/km (Table 30 at 70 mm²): Z_loop = 0.03 + 0.0148 (phase) + 0.0351 (earth) = 0.0799 Ω. I_fault = 400/√3 / 0.0799 = 2,892 A vs 400 × 5 = 2,000 A; L_max = 171 m vs 100 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 320.0 A ≤ 400 A ≤ 428.0 A (device at 93.5 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 185 mm² phase conductor: 70 mm²; earth 70 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.03 = 7,698 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 7,698 × √0.04 / 143 = 10.77 mm² vs 70 mm² (t_max = (143 × 70 / 7,698)² = 1.6909 s) PASS

Result 8/8 checks pass → PASS; conforming 185–500 mm² (5 of 19); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 320 A (specified); every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.03 Ω = 7698 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 150 mm² (earth 50 mm²): I_Z = 375 × 1.000 = 375.00 A, VD = 2.409 %, t = (k·S/I)² = (143 × 150 / 25000)² = 0.7362 s, I_ef = 400/√3 / 0.0975 Ω = 2368.5 A vs 2000 A required, earth S_min = 7698 × √0.04 / 143 = 10.77 mm² vs 50 mm² — fails OVL, which sets the minimum. 185 mm² (earth 70 mm²): base 428 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 428 × 1.00 × 1.00 = 428.00 A vs 320.00 A; ΔV = √3 × 320.00 × 0.100 × (0.129 × 0.85 + 0.072 × 0.527) = 8.18 V = 2.045 % (limit 5 %); t = (143 × 185 / 25000)² = 1.1198 s vs 0.1 s; Z_loop = 0.03 + 0.1·√(0.129² + 0.072²) + 0.1·√(0.343² + 0.0741²) = 0.03 + 0.0148 + 0.0351 = 0.0799 Ω, I_ef = 230.9 / 0.0799 = 2891.6 A vs 400 × 5 = 2000 A (L_max = 171.4 m); I_B 320.00 ≤ I_N 400 ≤ I_Z 428.00 holds; earth 70 mm² ≥ Table 5.1 minimum 70 mm², S_min = 7698 × √0.04 / 143 = 10.77 mm² ≤ 70 mm². Conforming sizes 185 to 500 mm² (5 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-320a-400v-100m-ladder-400a)

Example 10 — 400 A capacitor-bank feeder at 0.5 leading power factor, 1 % limit

Leading power factor: ΔV = √3·I·L·(R·pf − X·sinφ) passes through zero near 185 mm² and becomes a rise that grows with size, so 400 and 500 mm² fail voltage drop and the conforming range (185–300 mm²) is not contiguous.

Given: 400 A at PF 0.5 leading, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 250 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 25 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 400 A device with 3× instantaneous trip, upstream loop impedance 0.01 Ω, voltage-drop limit 1 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 400.0 A (specified)

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 400.0 A, 400 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	580.29	0.000	17	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	370.54	0.000	27	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	200.89	0.000	49	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	123.82	0.001	60	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	81.76	0.001	69	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	47.30	0.003	112	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	28.81	0.008	170	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	116.0	17.04	0.020	188	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	144.0	11.54	0.040	303	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
50 (16)	182.0	7.88	0.082	459	32.30	FAIL CCC, VD, SC, EFL, OVL, EWT
70 (25)	230.0	4.65	0.160	699	32.30	FAIL CCC, VD, EFL, OVL, EWT
95 (25)	275.0	2.65	0.295	752	32.30	FAIL CCC, VD, EFL, OVL, EWT
120 (35)	327.0	1.59	0.471	1,001	32.30	FAIL CCC, VD, EFL, OVL
150 (50)	375.0	0.77	0.736	1,292	32.30	FAIL CCC, OVL
185 (70)	428.0	0.09	1.120	1,715	32.30	PASS
240 (95)	511.0	0.50	1.885	2,195	32.30	PASS
300 (120)	584.0	0.88	2.945	2,588	32.30	PASS
400 (120)	692.0	1.21	5.235	2,673	32.30	FAIL VD
500 (120)	794.0	1.45	8.180	2,732	32.30	FAIL VD
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 185 to 300 mm² (3 of 19 tabulated sizes; 1 not tabulated). Range not contiguous: 400, 500 mm² fail above a passing size. Minimum set by current-carrying capacity, overload coordination (150 mm² is the largest size that fails).

Check 2 — voltage drop R_c = 0.129 Ω/km (Table 35), X_c = 0.0720 Ω/km (Table 30). At the design current: ΔV = √3 × 400.0 × 0.250 × (0.129 × 0.5 − 0.0720 × 0.866) = 0.37 V (drop) = 0.09 % of 400 V, limit 1 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 185)² / 25,000² = 1.120 s vs 0.1 s; S_min = 25,000 × √0.1 / 143 = 55.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.343 Ω/km and X_e = 0.0741 Ω/km (Table 30 at 70 mm²): Z_loop = 0.01 + 0.0369 (phase) + 0.0877 (earth) = 0.1347 Ω. I_fault = 400/√3 / 0.1347 = 1,715 A vs 400 × 3 = 1,200 A; L_max = 366 m vs 250 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 400.0 A ≤ 400 A ≤ 428.0 A (device at 93.5 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 185 mm² phase conductor: 70 mm²; earth 70 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.01 = 23,094 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 23,094 × √0.04 / 143 = 32.30 mm² vs 70 mm² (t_max = (143 × 70 / 23,094)² = 0.1879 s) PASS

Result 8/8 checks pass → PASS; conforming 185–300 mm² (3 of 19); governing: ocpd coordination. The conforming range is not contiguous: 400 mm², 500 mm² fail although a smaller size passes Cable utilization is very high (93.5%) - limited margin for load growth Voltage drop margin is very tight (0.91%) Power loss (11.17%) is significant Consider larger conductor to reduce energy losses

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 400 A (specified); every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.01 Ω = 23094 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 150 mm² (earth 50 mm²): I_Z = 375 × 1.000 = 375.00 A, VD = 0.772 %, t = (k·S/I)² = (143 × 150 / 25000)² = 0.7362 s, I_ef = 400/√3 / 0.1788 Ω = 1291.9 A vs 1200 A required, earth S_min = 23094 × √0.04 / 143 = 32.30 mm² vs 50 mm² — fails CCC, OVL, which sets the minimum. 185 mm² (earth 70 mm²): base 428 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 428 × 1.00 × 1.00 = 428.00 A vs 400.00 A; ΔV = √3 × 400.00 × 0.250 × (0.129 × 0.5 − 0.072 × 0.866) = 0.37 V = 0.093 % (limit 1 %); t = (143 × 185 / 25000)² = 1.1198 s vs 0.1 s; Z_loop = 0.01 + 0.25·√(0.129² + 0.072²) + 0.25·√(0.343² + 0.0741²) = 0.01 + 0.0369 + 0.0877 = 0.1347 Ω, I_ef = 230.9 / 0.1347 = 1715.0 A vs 400 × 3 = 1200 A (L_max = 365.9 m); I_B 400.00 ≤ I_N 400 ≤ I_Z 428.00 holds; earth 70 mm² ≥ Table 5.1 minimum 70 mm², S_min = 23094 × √0.04 / 143 = 32.30 mm² ≤ 70 mm². Conforming sizes 185 to 300 mm² (3 of 19 tabulated), gaps at 400, 500 mm². Not tabulated for this construction: 630 mm². (validation case c0042-400a-400v-250m-leading-pf-0p5-range-gap)

Example 11 — 200 kW on aluminium multicore cable

Aluminium: fewer sizes are tabulated (none below 16 mm²), the ratings are lower and k = 94.

Given: 200 kW at PF 0.9 lagging, 400 V three-phase, design factor 1. Aluminium XLPE (90 °C) fixed multicore cable, 120 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 15 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 400 A device with 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 200 kW × 1000 / (√3 × 400 × 0.9) = 320.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 320.8 A, 400 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	not tabulated for this construction					INFO
1.5 (1.5)	not tabulated for this construction					INFO
2.5 (2.5)	not tabulated for this construction					INFO
4 (2.5)	not tabulated for this construction					INFO
6 (2.5)	not tabulated for this construction					INFO
10 (4)	not tabulated for this construction					INFO
16 (6)	not tabulated for this construction					INFO
25 (6)	not tabulated for this construction					INFO
35 (10)	not tabulated for this construction					INFO
50 (16)	140.0	12.88	0.099	546	16.29	FAIL CCC, VD, SC, EFL, OVL, EWT
70 (25)	178.0	9.07	0.194	813	16.29	FAIL CCC, VD, EFL, OVL
95 (25)	220.0	6.69	0.358	871	16.29	FAIL CCC, VD, EFL, OVL
120 (35)	256.0	5.39	0.572	1,135	16.29	FAIL CCC, VD, EFL, OVL
150 (50)	293.0	4.50	0.893	1,426	16.29	FAIL CCC, EFL, OVL
185 (70)	340.0	3.70	1.358	1,837	16.29	FAIL EFL, OVL
240 (95)	405.0	2.95	2.286	2,280	16.29	PASS
300 (120)	467.0	2.48	3.572	2,631	16.29	PASS
400 (120)	546.0	2.05	6.350	2,721	16.29	PASS
500 (120)	629.0	1.76	9.922	2,782	16.29	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 240 to 500 mm² (4 of 10 tabulated sizes; 10 not tabulated). Range contiguous. Minimum set by earth-fault loop, overload coordination (185 mm² is the largest size that fails).

Check 1 — capacity (240 mm²) Base rating Table 14, column 4, row 240: 405 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 405 × 1.00 = 405.0 A vs I_design 320.8 A (loading 79.2 %) PASS

Check 2 — voltage drop R_c = 0.162 Ω/km (Table 35), X_c = 0.0709 Ω/km (Table 30). At the design current: ΔV = √3 × 320.8 × 0.120 × (0.162 × 0.9 + 0.0709 × 0.436) = 11.78 V (drop) = 2.95 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 94 (Table 52). t_max = (94 × 240)² / 15,000² = 2.286 s vs 0.1 s; S_min = 15,000 × √0.1 / 94 = 50.2 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.411 Ω/km and X_e = 0.0725 Ω/km (Table 30 at 95 mm²): Z_loop = 0.03 + 0.0212 (phase) + 0.0501 (earth) = 0.1013 Ω. I_fault = 400/√3 / 0.1013 = 2,280 A vs 400 × 5 = 2,000 A; L_max = 144 m vs 120 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 320.8 A ≤ 400 A ≤ 405.0 A (device at 98.8 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 240 mm² phase conductor: 95 mm²; earth 95 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.03 = 7,698 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 94.5 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 7,698 × √0.04 / 94.5 = 16.29 mm² vs 95 mm² (t_max = (94.5 × 95 / 7,698)² = 1.3600 s) PASS

Result 8/8 checks pass → PASS; conforming 240–500 mm² (4 of 10); governing: ocpd coordination. Earth fault trip margin is limited (1.14x) Confirm the device's pickup tolerance and operating time at this fault current

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 200 kW × 1000 / (√3 × 400 × 0.9) = 320.75 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.03 Ω = 7698 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 185 mm² (earth 70 mm²): I_Z = 340 × 1.000 = 340.00 A, VD = 3.703 %, t = (k·S/I)² = (94.5 × 185 / 15000)² = 1.3584 s, I_ef = 400/√3 / 0.1257 Ω = 1836.9 A vs 2000 A required, earth S_min = 7698 × √0.04 / 94.5 = 16.29 mm² vs 70 mm² — fails EFL, OVL, which sets the minimum. 240 mm² (earth 95 mm²): base 405 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 405 × 1.00 × 1.00 = 405.00 A vs 320.75 A; ΔV = √3 × 320.75 × 0.120 × (0.162 × 0.9 + 0.0709 × 0.436) = 11.78 V = 2.945 % (limit 5 %); t = (94.5 × 240 / 15000)² = 2.2861 s vs 0.1 s; Z_loop = 0.03 + 0.12·√(0.162² + 0.0709²) + 0.12·√(0.411² + 0.0725²) = 0.03 + 0.0212 + 0.0501 = 0.1013 Ω, I_ef = 230.9 / 0.1013 = 2279.7 A vs 400 × 5 = 2000 A (L_max = 143.8 m); I_B 320.75 ≤ I_N 400 ≤ I_Z 405.00 holds; earth 95 mm² ≥ Table 5.1 minimum 95 mm², S_min = 7698 × √0.04 / 94.5 = 16.29 mm² ≤ 95 mm². Conforming sizes 240 to 500 mm² (4 of 10 tabulated), contiguous. (validation case c0042-200kw-400v-120m-al-tray-400a)

Example 12 — 60 kW PVC cable in a wiring enclosure with two other circuits

PVC (75 °C) ratings with the Table 22 three-circuit grouping factor and the lower Table 52 k.

Given: 60 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper PVC (75 °C) fixed multicore cable, 70 m; in a wiring enclosure in air with 3 circuit(s), air ambient 40 °C. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 125 A device with 5× instantaneous trip, upstream loop impedance 0.05 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 60 kW × 1000 / (√3 × 400 × 0.85) = 101.9 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 101.9 A, 125 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	8.2	67.92	0.000	63	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	10.5	43.49	0.000	98	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	15.0	23.82	0.001	176	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	18.8	14.89	0.002	215	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	24.8	10.00	0.004	245	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	33.0	6.00	0.012	386	8.32	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	43.5	3.82	0.032	562	8.32	FAIL CCC, SC, EFL, OVL, EWT
25 (6)	57.0	2.46	0.077	616	8.32	FAIL CCC, SC, EFL, OVL, EWT
35 (10)	70.5	1.81	0.151	919	8.32	FAIL CCC, OVL
50 (16)	84.0	1.37	0.308	1,272	8.32	FAIL CCC, OVL
70 (25)	106.5	0.98	0.604	1,702	8.32	FAIL OVL
95 (25)	132.8	0.74	1.112	1,783	8.32	PASS
120 (35)	151.5	0.61	1.774	2,115	8.32	PASS
150 (50)	171.0	0.52	2.772	2,422	8.32	PASS
185 (70)	197.2	0.44	4.217	2,763	8.32	PASS
240 (95)	237.0	0.37	7.097	3,047	8.32	PASS
300 (120)	not tabulated for this construction					INFO
400 (120)	not tabulated for this construction					INFO
500 (120)	not tabulated for this construction					INFO
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 95 to 240 mm² (5 of 16 tabulated sizes; 4 not tabulated). Range contiguous. Minimum set by overload coordination (70 mm² is the largest size that fails).

Check 1 — capacity (95 mm²) Base rating Table 13, column 11, row 95: 177 A. Derating Table 22, row 3: 0.750; Table 27(1), 75 °C conductor column, row 40: 1.00 → F = 0.750. I_Z = 177 × 0.750 = 132.8 A vs I_design 101.9 A (loading 76.7 %) PASS

Check 2 — voltage drop R_c = 0.236 Ω/km (Table 35), X_c = 0.0766 Ω/km (Table 30). At the design current: ΔV = √3 × 101.9 × 0.070 × (0.236 × 0.85 + 0.0766 × 0.527) = 2.98 V (drop) = 0.74 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 111 (Table 52). t_max = (111 × 95)² / 10,000² = 1.112 s vs 0.1 s; S_min = 10,000 × √0.1 / 111 = 28.5 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.884 Ω/km and X_e = 0.0853 Ω/km (Table 30 at 25 mm²): Z_loop = 0.05 + 0.0174 (phase) + 0.0622 (earth) = 0.1295 Ω. I_fault = 400/√3 / 0.1295 = 1,783 A vs 125 × 5 = 625 A; L_max = 281 m vs 70 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 101.9 A ≤ 125 A ≤ 132.8 A (device at 94.2 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 95 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.05 = 4,619 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 111 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 4,619 × √0.04 / 111 = 8.32 mm² vs 25 mm² (t_max = (111 × 25 / 4,619)² = 0.3610 s) PASS

Result 8/8 checks pass → PASS; conforming 95–240 mm² (5 of 16); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 60 kW × 1000 / (√3 × 400 × 0.85) = 101.89 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.05 Ω = 4619 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 70 mm² (earth 25 mm²): I_Z = 142 × 0.750 = 106.50 A, VD = 0.984 %, t = (k·S/I)² = (111 × 70 / 10000)² = 0.6037 s, I_ef = 400/√3 / 0.1357 Ω = 1702.1 A vs 625 A required, earth S_min = 4619 × √0.04 / 111 = 8.32 mm² vs 25 mm² — fails OVL, which sets the minimum. 95 mm² (earth 25 mm²): base 177 A (Table 13), derating Table 22 row 3 = 0.75; Table 27(1) row 40 = 1.00 → I_Z = 177 × 0.75 × 1.00 = 132.75 A vs 101.89 A; ΔV = √3 × 101.89 × 0.070 × (0.236 × 0.85 + 0.0766 × 0.527) = 2.98 V = 0.744 % (limit 5 %); t = (111 × 95 / 10000)² = 1.1120 s vs 0.1 s; Z_loop = 0.05 + 0.07·√(0.236² + 0.0766²) + 0.07·√(0.884² + 0.0853²) = 0.05 + 0.0174 + 0.0622 = 0.1295 Ω, I_ef = 230.9 / 0.1295 = 1782.8 A vs 125 × 5 = 625 A (L_max = 281.2 m); I_B 101.89 ≤ I_N 125 ≤ I_Z 132.75 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 4619 × √0.04 / 111 = 8.32 mm² ≤ 25 mm². Conforming sizes 95 to 240 mm² (5 of 16 tabulated), contiguous. Not tabulated for this construction: 300, 400, 500, 630 mm². (validation case c0042-60kw-400v-70m-pvc-enclosed-3-circuits-125a)

Example 13 — 100 kW on an elastomeric (EPR) cable

EPR uses the 110 °C rating column, 110 °C resistance and the Table 52 k for a 110 °C initial temperature.

Given: 100 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper EPR (110 °C) fixed multicore cable, 90 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 15 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 200 A device with 5× instantaneous trip, upstream loop impedance 0.04 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 100 kW × 1000 / (√3 × 400 × 0.85) = 169.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 169.8 A, 200 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	20.0	161.92	0.000	44	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	25.0	103.95	0.000	69	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	35.0	56.66	0.000	126	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	47.0	35.48	0.001	154	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	59.0	23.82	0.003	176	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	81.0	14.29	0.008	280	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	107.0	9.09	0.020	415	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	144.0	5.85	0.048	458	8.75	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	177.0	4.29	0.095	705	8.75	FAIL SC, EFL, OVL
50 (16)	216.0	3.24	0.194	1,011	8.75	PASS
70 (25)	272.0	2.33	0.379	1,421	8.75	PASS
95 (25)	337.0	1.75	0.699	1,504	8.75	PASS
120 (35)	391.0	1.44	1.115	1,856	8.75	PASS
150 (50)	447.0	1.22	1.742	2,209	8.75	PASS
185 (70)	515.0	1.03	2.650	2,637	8.75	PASS
240 (95)	611.0	0.85	4.461	3,029	8.75	PASS
300 (120)	701.0	0.74	6.970	3,289	8.75	PASS
400 (120)	810.0	0.64	12.390	3,342	8.75	PASS
500 (120)	921.0	0.57	19.360	3,378	8.75	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 50 to 500 mm² (10 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by short-circuit withstand, earth-fault loop, overload coordination (35 mm² is the largest size that fails).

Check 1 — capacity (50 mm²) Base rating Table 15, column 2, row 50: 216 A. Derating Table 24, row 1: 1.00; Table 27(1), 110 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 216 × 1.00 = 216.0 A vs I_design 169.8 A (loading 78.6 %) PASS

Check 2 — voltage drop R_c = 0.524 Ω/km (Table 35), X_c = 0.0829 Ω/km (Table 30). At the design current: ΔV = √3 × 169.8 × 0.090 × (0.524 × 0.85 + 0.0829 × 0.527) = 12.95 V (drop) = 3.24 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 132 (Table 52). t_max = (132 × 50)² / 15,000² = 0.194 s vs 0.1 s; S_min = 15,000 × √0.1 / 132 = 35.9 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 1.56 Ω/km and X_e = 0.0913 Ω/km (Table 30 at 16 mm²): Z_loop = 0.04 + 0.0477 (phase) + 0.1406 (earth) = 0.2284 Ω. I_fault = 400/√3 / 0.2284 = 1,011 A vs 200 × 5 = 1,000 A; L_max = 91 m vs 90 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 169.8 A ≤ 200 A ≤ 216.0 A (device at 92.6 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 50 mm² phase conductor: 16 mm²; earth 16 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.04 = 5,774 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 132 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 5,774 × √0.04 / 132 = 8.75 mm² vs 16 mm² (t_max = (132 × 16 / 5,774)² = 0.1338 s) PASS

Result 8/8 checks pass → PASS; conforming 50–500 mm² (10 of 19); governing: earth fault loop impedance. Power loss (4.08%) is significant Earth fault trip margin is very low (1.01x) Consider larger conductor to reduce energy losses Review protection settings - fault current barely exceeds trip threshold

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 100 kW × 1000 / (√3 × 400 × 0.85) = 169.81 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.04 Ω = 5774 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 35 mm² (earth 10 mm²): I_Z = 177 × 1.000 = 177.00 A, VD = 4.295 %, t = (k·S/I)² = (132 × 35 / 15000)² = 0.0949 s, I_ef = 400/√3 / 0.3277 Ω = 704.6 A vs 1000 A required, earth S_min = 5774 × √0.04 / 132 = 8.75 mm² vs 10 mm² — fails SC, EFL, OVL, which sets the minimum. 50 mm² (earth 16 mm²): base 216 A (Table 15), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 216 × 1.00 × 1.00 = 216.00 A vs 169.81 A; ΔV = √3 × 169.81 × 0.090 × (0.524 × 0.85 + 0.0829 × 0.527) = 12.95 V = 3.236 % (limit 5 %); t = (132 × 50 / 15000)² = 0.1936 s vs 0.1 s; Z_loop = 0.04 + 0.09·√(0.524² + 0.0829²) + 0.09·√(1.56² + 0.0913²) = 0.04 + 0.0477 + 0.1406 = 0.2284 Ω, I_ef = 230.9 / 0.2284 = 1011.2 A vs 200 × 5 = 1000 A (L_max = 91.2 m); I_B 169.81 ≤ I_N 200 ≤ I_Z 216.00 holds; earth 16 mm² ≥ Table 5.1 minimum 16 mm², S_min = 5774 × √0.04 / 132 = 8.75 mm² ≤ 16 mm². Conforming sizes 50 to 500 mm² (10 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-100kw-400v-90m-epr-200a)

Example 14 — 500 kW at 690 V on single-core cables in trefoil

Single-core trefoil on a ladder: every size up to 630 mm² is tabulated and the range runs to the largest size in the table.

Given: 500 kW at PF 0.9 lagging, 690 V three-phase, design factor 1. Copper XLPE (90 °C) fixed single-core cable (trefoil), 110 m; unenclosed, spaced from the surface on ladder, racks or cleats, 1 circuit(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 30 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 630 A device with 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 500 kW × 1000 / (√3 × 690 × 0.9) = 464.9 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 464.9 A, 630 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	19.0	312.84	0.000	67	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	25.0	200.72	0.000	104	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	35.0	109.96	0.000	189	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	46.0	68.66	0.000	232	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	59.0	46.09	0.001	265	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	81.0	27.55	0.002	427	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	108.0	17.57	0.006	638	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	146.0	11.28	0.014	705	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	180.0	8.27	0.028	1,104	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
50 (16)	221.0	6.22	0.057	1,610	18.57	FAIL CCC, VD, SC, EFL, OVL, EWT
70 (25)	282.0	4.45	0.111	2,323	18.57	FAIL CCC, EFL, OVL
95 (25)	350.0	3.34	0.205	2,468	18.57	FAIL CCC, EFL, OVL
120 (35)	410.0	2.75	0.327	3,116	18.57	FAIL CCC, EFL, OVL
150 (50)	472.0	2.32	0.511	3,787	18.57	FAIL OVL
185 (70)	550.0	1.96	0.778	4,644	18.57	FAIL OVL
240 (95)	660.0	1.60	1.309	5,462	18.57	PASS
300 (120)	766.0	1.38	2.045	6,026	18.57	PASS
400 (120)	899.0	1.19	3.635	6,138	18.57	PASS
500 (120)	1,051.0	1.05	5.680	6,218	18.57	PASS
630 (120)	1,230.0	0.94	9.018	6,278	18.57	PASS

Conforming range Conforming sizes 240 to 630 mm² (5 of 20 tabulated sizes; 0 not tabulated). Range contiguous. Minimum set by overload coordination (185 mm² is the largest size that fails).

Check 1 — capacity (240 mm²) Base rating Table 8, column 2, row 240: 660 A. Derating Table 23, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 660 × 1.00 = 660.0 A vs I_design 464.9 A (loading 70.4 %) PASS

Check 2 — voltage drop R_c = 0.0991 Ω/km (Table 34), X_c = 0.0818 Ω/km (Table 30). At the design current: ΔV = √3 × 464.9 × 0.110 × (0.0991 × 0.9 + 0.0818 × 0.436) = 11.06 V (drop) = 1.60 % of 690 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 240)² / 30,000² = 1.309 s vs 0.1 s; S_min = 30,000 × √0.1 / 143 = 66.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.247 Ω/km and X_e = 0.0868 Ω/km (Table 30 at 95 mm²): Z_loop = 0.03 + 0.0141 (phase) + 0.0288 (earth) = 0.0729 Ω. I_fault = 690/√3 / 0.0729 = 5,462 A vs 630 × 5 = 3,150 A; L_max = 247 m vs 110 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 464.9 A ≤ 630 A ≤ 660.0 A (device at 95.5 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 240 mm² phase conductor: 95 mm²; earth 95 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 690/√3 / 0.03 = 13,279 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (separate earth cable, taken at the phase conductor's Table 52 k as if it started at the insulation's operating temperature: conservative). S_min = I_ef × √t_ef / k = 13,279 × √0.04 / 143 = 18.57 mm² vs 95 mm² (t_max = (143 × 95 / 13,279)² = 1.0466 s) PASS

Result 8/8 checks pass → PASS; conforming 240–630 mm² (5 of 20); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 500 kW × 1000 / (√3 × 690 × 0.9) = 464.86 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (690/√3)/0.03 Ω = 13279 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 185 mm² (earth 70 mm²): I_Z = 550 × 1.000 = 550.00 A, VD = 1.957 %, t = (k·S/I)² = (143 × 185 / 30000)² = 0.7776 s, I_ef = 690/√3 / 0.0858 Ω = 4643.9 A vs 3150 A required, earth S_min = 13279 × √0.04 / 143 = 18.57 mm² vs 70 mm² — fails OVL, which sets the minimum. 240 mm² (earth 95 mm²): base 660 A (Table 8), derating Table 23 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 660 × 1.00 × 1.00 = 660.00 A vs 464.86 A; ΔV = √3 × 464.86 × 0.110 × (0.0991 × 0.9 + 0.0818 × 0.436) = 11.06 V = 1.602 % (limit 5 %); t = (143 × 240 / 30000)² = 1.3087 s vs 0.1 s; Z_loop = 0.03 + 0.11·√(0.0991² + 0.0818²) + 0.11·√(0.247² + 0.0868²) = 0.03 + 0.0141 + 0.0288 = 0.0729 Ω, I_ef = 398.4 / 0.0729 = 5462.1 A vs 630 × 5 = 3150 A (L_max = 247.2 m); I_B 464.86 ≤ I_N 630 ≤ I_Z 660.00 holds; earth 95 mm² ≥ Table 5.1 minimum 95 mm², S_min = 13279 × √0.04 / 143 = 18.57 mm² ≤ 95 mm². Conforming sizes 240 to 630 mm² (5 of 20 tabulated), contiguous. (validation case c0042-500kw-690v-110m-sc-trefoil-630a)

Example 15 — 45 kW cable among six touching on a tray

Table 24 grouping (0.76 for six touching multicore cables) takes 35 mm² from 144 A to 109 A, below the 125 A device, so overload coordination rules it out (its 10 mm² earth also falls just short of the 10.8 mm² the 7.7 kA near-end earth fault needs in 0.04 s); 50 mm² at 138 A with a 16 mm² earth is the minimum.

Given: 45 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 60 m; unenclosed, spaced from the surface on horizontal perforated tray, 6 cable(s) per tier touching, 1 tier(s), air ambient 40 °C. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 125 A device with 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 45 kW × 1000 / (√3 × 400 × 0.85) = 76.4 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 76.4 A, 125 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	12.2	45.68	0.000	71	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	15.2	29.31	0.000	110	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	20.5	16.05	0.001	198	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	27.4	10.02	0.003	243	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	35.0	6.72	0.007	277	10.77	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	50.2	4.02	0.020	442	10.77	FAIL CCC, SC, EFL, OVL, EWT
16 (6)	66.1	2.56	0.052	652	10.77	FAIL CCC, SC, OVL, EWT
25 (6)	88.2	1.65	0.128	718	10.77	FAIL OVL, EWT
35 (10)	109.4	1.21	0.251	1,098	10.77	FAIL OVL, EWT
50 (16)	138.3	0.91	0.511	1,557	10.77	PASS
70 (25)	174.8	0.66	1.002	2,161	10.77	PASS
95 (25)	209.0	0.49	1.846	2,279	10.77	PASS
120 (35)	248.5	0.41	2.945	2,783	10.77	PASS
150 (50)	285.0	0.35	4.601	3,276	10.77	PASS
185 (70)	325.3	0.29	6.999	3,854	10.77	PASS
240 (95)	388.4	0.24	11.779	4,370	10.77	PASS
300 (120)	443.8	0.21	18.404	4,711	10.77	PASS
400 (120)	525.9	0.18	32.718	4,778	10.77	PASS
500 (120)	603.4	0.17	51.123	4,822	10.77	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 50 to 500 mm² (10 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination, earth conductor withstand (35 mm² is the largest size that fails).

Check 1 — capacity (50 mm²) Base rating Table 14, column 2, row 50: 182 A. Derating Table 24, row 6: 0.760; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 0.760. I_Z = 182 × 0.760 = 138.3 A vs I_design 76.4 A (loading 55.2 %) PASS

Check 2 — voltage drop R_c = 0.494 Ω/km (Table 35), X_c = 0.0751 Ω/km (Table 30). At the design current: ΔV = √3 × 76.4 × 0.060 × (0.494 × 0.85 + 0.0751 × 0.527) = 3.65 V (drop) = 0.91 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 50)² / 10,000² = 0.511 s vs 0.1 s; S_min = 10,000 × √0.1 / 143 = 22.1 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 1.47 Ω/km and X_e = 0.0805 Ω/km (Table 30 at 16 mm²): Z_loop = 0.03 + 0.0300 (phase) + 0.0883 (earth) = 0.1483 Ω. I_fault = 400/√3 / 0.1483 = 1,557 A vs 125 × 5 = 625 A; L_max = 172 m vs 60 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 76.4 A ≤ 125 A ≤ 138.3 A (device at 90.4 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 50 mm² phase conductor: 16 mm²; earth 16 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.03 = 7,698 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 7,698 × √0.04 / 143 = 10.77 mm² vs 16 mm² (t_max = (143 × 16 / 7,698)² = 0.0883 s) PASS

Result 8/8 checks pass → PASS; conforming 50–500 mm² (10 of 19); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 45 kW × 1000 / (√3 × 400 × 0.85) = 76.41 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.03 Ω = 7698 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 35 mm² (earth 10 mm²): I_Z = 144 × 0.760 = 109.44 A, VD = 1.211 %, t = (k·S/I)² = (143 × 35 / 10000)² = 0.2505 s, I_ef = 400/√3 / 0.2103 Ω = 1098.1 A vs 625 A required, earth S_min = 7698 × √0.04 / 143 = 10.77 mm² vs 10 mm² — fails OVL, earth withstand, which sets the minimum. 50 mm² (earth 16 mm²): base 182 A (Table 14), derating Table 24 row 6 = 0.76; Table 27(1) row 40 = 1.00 → I_Z = 182 × 0.76 × 1.00 = 138.32 A vs 76.41 A; ΔV = √3 × 76.41 × 0.060 × (0.494 × 0.85 + 0.0751 × 0.527) = 3.65 V = 0.912 % (limit 5 %); t = (143 × 50 / 10000)² = 0.5112 s vs 0.1 s; Z_loop = 0.03 + 0.06·√(0.494² + 0.0751²) + 0.06·√(1.47² + 0.0805²) = 0.03 + 0.0300 + 0.0883 = 0.1483 Ω, I_ef = 230.9 / 0.1483 = 1557.1 A vs 125 × 5 = 625 A (L_max = 172.2 m); I_B 76.41 ≤ I_N 125 ≤ I_Z 138.32 holds; earth 16 mm² ≥ Table 5.1 minimum 16 mm², S_min = 7698 × √0.04 / 143 = 10.77 mm² ≤ 16 mm². Conforming sizes 50 to 500 mm² (10 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-45kw-400v-60m-six-cables-touching-tray-125a)

Example 16 — 75 kW feeder in a 55 °C switchroom

Table 27(1) at 55 °C removes about a fifth of the 90 °C rating, moving the minimum up a size.

Given: 75 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 60 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 55 °C. Protection: prospective fault 15 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 160 A device with 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 75 kW × 1000 / (√3 × 400 × 0.85) = 127.4 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 127.4 A, 160 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	13.0	76.14	0.000	69	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	16.2	48.84	0.000	106	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	21.9	26.75	0.001	187	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	29.2	16.70	0.001	226	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	37.3	11.21	0.003	256	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	53.5	6.70	0.009	390	3.23	FAIL CCC, VD, SC, EFL, OVL
16 (6)	70.5	4.27	0.023	544	3.23	FAIL CCC, SC, EFL, OVL
25 (6)	94.0	2.75	0.057	590	3.23	FAIL CCC, SC, EFL, OVL
35 (10)	116.6	2.02	0.111	824	3.23	FAIL CCC, OVL
50 (16)	147.4	1.52	0.227	1,058	3.23	FAIL OVL
70 (25)	186.3	1.09	0.445	1,306	3.23	PASS
95 (25)	222.8	0.82	0.820	1,348	3.23	PASS
120 (35)	264.9	0.68	1.309	1,510	3.23	PASS
150 (50)	303.8	0.58	2.045	1,644	3.23	PASS
185 (70)	346.7	0.49	3.111	1,778	3.23	PASS
240 (95)	413.9	0.40	5.235	1,880	3.23	PASS
300 (120)	473.0	0.35	8.180	1,940	3.23	PASS
400 (120)	560.5	0.31	14.542	1,952	3.23	PASS
500 (120)	643.1	0.28	22.721	1,959	3.23	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 70 to 500 mm² (9 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination (50 mm² is the largest size that fails).

Check 1 — capacity (70 mm²) Base rating Table 14, column 2, row 70: 230 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 55: 0.810 → F = 0.810. I_Z = 230 × 0.810 = 186.3 A vs I_design 127.4 A (loading 68.4 %) PASS

Check 2 — voltage drop R_c = 0.343 Ω/km (Table 35), X_c = 0.0741 Ω/km (Table 30). At the design current: ΔV = √3 × 127.4 × 0.060 × (0.343 × 0.85 + 0.0741 × 0.527) = 4.38 V (drop) = 1.09 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 70)² / 15,000² = 0.445 s vs 0.1 s; S_min = 15,000 × √0.1 / 143 = 33.2 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.927 Ω/km and X_e = 0.0808 Ω/km (Table 30 at 25 mm²): Z_loop = 0.1 + 0.0211 (phase) + 0.0558 (earth) = 0.1769 Ω. I_fault = 400/√3 / 0.1769 = 1,306 A vs 160 × 5 = 800 A; L_max = 147 m vs 60 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 127.4 A ≤ 160 A ≤ 186.3 A (device at 85.9 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 70 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.1 = 2,309 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 25 mm² (t_max = (143 × 25 / 2,309)² = 2.3964 s) PASS

Result 8/8 checks pass → PASS; conforming 70–500 mm² (9 of 19); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 75 kW × 1000 / (√3 × 400 × 0.85) = 127.36 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.1 Ω = 2309 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 50 mm² (earth 16 mm²): I_Z = 182 × 0.810 = 147.42 A, VD = 1.520 %, t = (k·S/I)² = (143 × 50 / 15000)² = 0.2272 s, I_ef = 400/√3 / 0.2183 Ω = 1057.8 A vs 800 A required, earth S_min = 2309 × √0.04 / 143 = 3.23 mm² vs 16 mm² — fails OVL, which sets the minimum. 70 mm² (earth 25 mm²): base 230 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 55 = 0.81 → I_Z = 230 × 1.00 × 0.81 = 186.30 A vs 127.36 A; ΔV = √3 × 127.36 × 0.060 × (0.343 × 0.85 + 0.0741 × 0.527) = 4.38 V = 1.094 % (limit 5 %); t = (143 × 70 / 15000)² = 0.4453 s vs 0.1 s; Z_loop = 0.1 + 0.06·√(0.343² + 0.0741²) + 0.06·√(0.927² + 0.0808²) = 0.1 + 0.0211 + 0.0558 = 0.1769 Ω, I_ef = 230.9 / 0.1769 = 1305.6 A vs 160 × 5 = 800 A (L_max = 147.2 m); I_B 127.36 ≤ I_N 160 ≤ I_Z 186.30 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 25 mm². Conforming sizes 70 to 500 mm² (9 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-75kw-400v-60m-55c-ambient-160a)

Example 17 — 22 kW cable completely surrounded by thermal insulation

The most onerous rating column: only nine sizes are tabulated in thermal insulation and only the largest of them, 35 mm², covers the 50 A device, so the range is a single size.

Given: 22 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 40 m; completely surrounded by thermal insulation, enclosed, air ambient 40 °C. Protection: prospective fault 6 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 50 A device with 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 22 kW × 1000 / (√3 × 400 × 0.85) = 37.4 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 37.4 A, 50 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	6.0	14.89	0.001	102	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	8.0	9.55	0.001	156	3.23	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	12.0	5.23	0.004	270	3.23	FAIL CCC, VD, SC, OVL, EWT
4 (2.5)	15.0	3.27	0.009	324	3.23	FAIL CCC, SC, OVL, EWT
6 (2.5)	19.0	2.19	0.020	364	3.23	FAIL CCC, SC, OVL, EWT
10 (4)	26.0	1.31	0.057	539	3.23	FAIL CCC, SC, OVL
16 (6)	34.0	0.84	0.145	731	3.23	FAIL CCC, OVL
25 (6)	46.0	0.54	0.355	784	3.23	FAIL OVL
35 (10)	57.0	0.39	0.696	1,049	3.23	PASS
50 (16)	not tabulated for this construction					INFO
70 (25)	not tabulated for this construction					INFO
95 (25)	not tabulated for this construction					INFO
120 (35)	not tabulated for this construction					INFO
150 (50)	not tabulated for this construction					INFO
185 (70)	not tabulated for this construction					INFO
240 (95)	not tabulated for this construction					INFO
300 (120)	not tabulated for this construction					INFO
400 (120)	not tabulated for this construction					INFO
500 (120)	not tabulated for this construction					INFO
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 35 to 35 mm² (1 of 9 tabulated sizes; 11 not tabulated). Range contiguous. Minimum set by overload coordination (25 mm² is the largest size that fails).

Check 1 — capacity (35 mm²) Base rating Table 14, column 21, row 35: 57 A. Derating Table 22, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 57 × 1.00 = 57.0 A vs I_design 37.4 A (loading 65.5 %) PASS

Check 2 — voltage drop R_c = 0.669 Ω/km (Table 35), X_c = 0.0786 Ω/km (Table 30). At the design current: ΔV = √3 × 37.4 × 0.040 × (0.669 × 0.85 + 0.0786 × 0.527) = 1.58 V (drop) = 0.39 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 35)² / 6,000² = 0.696 s vs 0.1 s; S_min = 6,000 × √0.1 / 143 = 13.3 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 2.33 Ω/km and X_e = 0.0840 Ω/km (Table 30 at 10 mm²): Z_loop = 0.1 + 0.0269 (phase) + 0.0933 (earth) = 0.2202 Ω. I_fault = 400/√3 / 0.2202 = 1,049 A vs 50 × 5 = 250 A; L_max = 274 m vs 40 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 37.4 A ≤ 50 A ≤ 57.0 A (device at 87.7 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 35 mm² phase conductor: 10 mm²; earth 10 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.1 = 2,309 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 10 mm² (t_max = (143 × 10 / 2,309)² = 0.3834 s) PASS

Result 8/8 checks pass → PASS; conforming 35–35 mm² (1 of 9); governing: ocpd coordination

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 22 kW × 1000 / (√3 × 400 × 0.85) = 37.36 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.1 Ω = 2309 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 25 mm² (earth 6 mm²): I_Z = 46 × 1.000 = 46.00 A, VD = 0.537 %, t = (k·S/I)² = (143 × 25 / 6000)² = 0.3550 s, I_ef = 400/√3 / 0.2945 Ω = 784.3 A vs 250 A required, earth S_min = 2309 × √0.04 / 143 = 3.23 mm² vs 6 mm² — fails OVL, which sets the minimum. 35 mm² (earth 10 mm²): base 57 A (Table 14), derating Table 22 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 57 × 1.00 × 1.00 = 57.00 A vs 37.36 A; ΔV = √3 × 37.36 × 0.040 × (0.669 × 0.85 + 0.0786 × 0.527) = 1.58 V = 0.395 % (limit 5 %); t = (143 × 35 / 6000)² = 0.6958 s vs 0.1 s; Z_loop = 0.1 + 0.04·√(0.669² + 0.0786²) + 0.04·√(2.33² + 0.084²) = 0.1 + 0.0269 + 0.0933 = 0.2202 Ω, I_ef = 230.9 / 0.2202 = 1048.8 A vs 50 × 5 = 250 A (L_max = 274.1 m); I_B 37.36 ≤ I_N 50 ≤ I_Z 57.00 holds; earth 10 mm² ≥ Table 5.1 minimum 10 mm², S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 10 mm². Conforming sizes 35 to 35 mm² (1 of 9 tabulated), contiguous. Not tabulated for this construction: 50, 70, 95, 120, 150, 185, 240, 300, 400, 500, 630 mm². (validation case c0042-22kw-400v-40m-thermal-insulation-50a)

Example 18 — 110 kW feeder direct buried at 1.0 m

A single buried circuit takes no grouping factor; the depth factor (Table 28(1)) is banded by size and the soil-resistivity factor (Table 29) derates every size.

Given: 110 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 100 m; direct buried, 1 circuit(s), depth 1 m, soil 1.2 K·m/W at 25 °C. Protection: prospective fault 15 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 250 A device with 5× instantaneous trip, upstream loop impedance 0.05 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 110 kW × 1000 / (√3 × 400 × 0.85) = 186.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 186.8 A, 250 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	15.2	186.11	0.000	42	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	19.0	119.39	0.000	66	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.5	65.39	0.001	119	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	35.1	40.82	0.001	146	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	43.7	27.40	0.003	166	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	59.8	16.38	0.009	265	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	104.5	10.45	0.023	391	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	135.8	6.72	0.057	431	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	163.4	4.93	0.111	659	6.46	FAIL CCC, EFL, OVL
50 (16)	191.8	3.72	0.227	934	6.46	FAIL EFL, OVL
70 (25)	235.9	2.67	0.445	1,296	6.46	FAIL OVL
95 (25)	283.9	2.01	0.820	1,367	6.46	PASS
120 (35)	323.4	1.66	1.309	1,670	6.46	PASS
150 (50)	361.9	1.41	2.045	1,965	6.46	PASS
185 (70)	408.9	1.19	3.111	2,313	6.46	PASS
240 (95)	473.8	0.99	5.235	2,622	6.46	PASS
300 (120)	533.0	0.86	8.180	2,827	6.46	PASS
400 (120)	588.8	0.75	14.542	2,867	6.46	PASS
500 (120)	656.9	0.67	22.721	2,893	6.46	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 95 to 500 mm² (8 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by overload coordination (70 mm² is the largest size that fails).

Check 1 — capacity (95 mm²) Base rating Table 14, column 23, row 95: 302 A. Derating Table 27(2), 90 °C conductor column, row 25: 1.00; Table 28(1), row 1: 0.940; Table 29, row 1.2: 1.00 → F = 0.940. I_Z = 302 × 0.940 = 283.9 A vs I_design 186.8 A (loading 65.8 %) PASS

Check 2 — voltage drop R_c = 0.248 Ω/km (Table 35), X_c = 0.0725 Ω/km (Table 30). At the design current: ΔV = √3 × 186.8 × 0.100 × (0.248 × 0.85 + 0.0725 × 0.527) = 8.06 V (drop) = 2.01 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 95)² / 15,000² = 0.820 s vs 0.1 s; S_min = 15,000 × √0.1 / 143 = 33.2 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.927 Ω/km and X_e = 0.0808 Ω/km (Table 30 at 25 mm²): Z_loop = 0.05 + 0.0258 (phase) + 0.0931 (earth) = 0.1689 Ω. I_fault = 400/√3 / 0.1689 = 1,367 A vs 250 × 5 = 1,250 A; L_max = 113 m vs 100 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 186.8 A ≤ 250 A ≤ 283.9 A (device at 88.1 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 95 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.05 = 4,619 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 4,619 × √0.04 / 143 = 6.46 mm² vs 25 mm² (t_max = (143 × 25 / 4,619)² = 0.5991 s) PASS

Result 8/8 checks pass → PASS; conforming 95–500 mm² (8 of 19); governing: earth fault loop impedance. Earth fault trip margin is very low (1.09x) Review protection settings - fault current barely exceeds trip threshold

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 110 kW × 1000 / (√3 × 400 × 0.85) = 186.79 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.05 Ω = 4619 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 70 mm² (earth 25 mm²): I_Z = 251 × 0.940 = 235.94 A, VD = 2.674 %, t = (k·S/I)² = (143 × 70 / 15000)² = 0.4453 s, I_ef = 400/√3 / 0.1781 Ω = 1296.4 A vs 1250 A required, earth S_min = 4619 × √0.04 / 143 = 6.46 mm² vs 25 mm² — fails OVL, which sets the minimum. 95 mm² (earth 25 mm²): base 302 A (Table 14), derating Table 27(2) row 25 = 1.00; Table 28(1) row 1 = 0.94; Table 29 row 1.2 = 1.00 → I_Z = 302 × 1.00 × 0.94 × 1.00 = 283.88 A vs 186.79 A; ΔV = √3 × 186.79 × 0.100 × (0.248 × 0.85 + 0.0725 × 0.527) = 8.06 V = 2.014 % (limit 5 %); t = (143 × 95 / 15000)² = 0.8202 s vs 0.1 s; Z_loop = 0.05 + 0.1·√(0.248² + 0.0725²) + 0.1·√(0.927² + 0.0808²) = 0.05 + 0.0258 + 0.0931 = 0.1689 Ω, I_ef = 230.9 / 0.1689 = 1367.4 A vs 250 × 5 = 1250 A (L_max = 113.3 m); I_B 186.79 ≤ I_N 250 ≤ I_Z 283.88 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 4619 × √0.04 / 143 = 6.46 mm² ≤ 25 mm². Conforming sizes 95 to 500 mm² (8 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-110kw-400v-100m-direct-buried-250a)

Example 19 — 90 kW in a buried conduit beside a second circuit

Buried conduit: Table 26 grouping for two conduits 0.3 m apart, 30 °C soil, 0.6 m depth and 1.2 K·m/W resistivity all stack.

Given: 90 kW at PF 0.85 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 150 m; in buried conduit, 2 conduit(s) 0.3 m apart, depth 0.6 m, soil 1.2 K·m/W at 30 °C. Protection: prospective fault 15 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 200 A device with 5× instantaneous trip, upstream loop impedance 0.05 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 90 kW × 1000 / (√3 × 400 × 0.85) = 152.8 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 152.8 A, 200 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	14.6	228.41	0.000	28	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	18.2	146.53	0.000	44	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	26.5	80.25	0.001	80	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	33.8	50.10	0.001	98	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	42.0	33.62	0.003	112	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	57.5	20.10	0.009	180	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	73.9	12.82	0.023	268	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	97.6	8.24	0.057	296	6.46	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	118.6	6.06	0.111	461	6.46	FAIL CCC, VD, EFL, OVL
50 (16)	141.4	4.56	0.227	668	6.46	FAIL CCC, EFL, OVL
70 (25)	176.1	3.28	0.445	953	6.46	FAIL EFL, OVL
95 (25)	212.6	2.47	0.820	1,011	6.46	PASS
120 (35)	246.3	2.04	1.309	1,266	6.46	PASS
150 (50)	277.3	1.73	2.045	1,527	6.46	PASS
185 (70)	317.5	1.46	3.111	1,851	6.46	PASS
240 (95)	374.9	1.21	5.235	2,156	6.46	PASS
300 (120)	422.4	1.05	8.180	2,367	6.46	PASS
400 (120)	478.0	0.92	14.542	2,410	6.46	PASS
500 (120)	548.3	0.83	22.721	2,438	6.46	PASS
630 (120)	not tabulated for this construction					INFO

Conforming range Conforming sizes 95 to 500 mm² (8 of 19 tabulated sizes; 1 not tabulated). Range contiguous. Minimum set by earth-fault loop, overload coordination (70 mm² is the largest size that fails).

Check 1 — capacity (95 mm²) Base rating Table 14, column 25, row 95: 233 A. Derating Table 26(2), row 2: 0.950; Table 27(2), 90 °C conductor column, row 30: 0.970; Table 28(2), row 0.6: 0.990; Table 29, row 1.2: 1.00 → F = 0.912. I_Z = 233 × 0.912 = 212.6 A vs I_design 152.8 A (loading 71.9 %) PASS

Check 2 — voltage drop R_c = 0.248 Ω/km (Table 35), X_c = 0.0725 Ω/km (Table 30). At the design current: ΔV = √3 × 152.8 × 0.150 × (0.248 × 0.85 + 0.0725 × 0.527) = 9.89 V (drop) = 2.47 % of 400 V, limit 5 % PASS

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 95)² / 15,000² = 0.820 s vs 0.1 s; S_min = 15,000 × √0.1 / 143 = 33.2 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.927 Ω/km and X_e = 0.0808 Ω/km (Table 30 at 25 mm²): Z_loop = 0.05 + 0.0388 (phase) + 0.1396 (earth) = 0.2283 Ω. I_fault = 400/√3 / 0.2283 = 1,011 A vs 200 × 5 = 1,000 A; L_max = 152 m vs 150 m PASS

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 152.8 A ≤ 200 A ≤ 212.6 A (device at 94.1 % of cable capacity) PASS

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 95 mm² phase conductor: 25 mm²; earth 25 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.05 = 4,619 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 4,619 × √0.04 / 143 = 6.46 mm² vs 25 mm² (t_max = (143 × 25 / 4,619)² = 0.5991 s) PASS

Result 8/8 checks pass → PASS; conforming 95–500 mm² (8 of 19); governing: earth fault loop impedance. Earth fault trip margin is very low (1.01x) Review protection settings - fault current barely exceeds trip threshold

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 90 kW × 1000 / (√3 × 400 × 0.85) = 152.83 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.05 Ω = 4619 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 70 mm² (earth 25 mm²): I_Z = 193 × 0.912 = 176.07 A, VD = 3.282 %, t = (k·S/I)² = (143 × 70 / 15000)² = 0.4453 s, I_ef = 400/√3 / 0.2422 Ω = 953.5 A vs 1000 A required, earth S_min = 4619 × √0.04 / 143 = 6.46 mm² vs 25 mm² — fails EFL, OVL, which sets the minimum. 95 mm² (earth 25 mm²): base 233 A (Table 14), derating Table 26(2) row 2 = 0.95; Table 27(2) row 30 = 0.97; Table 28(2) row 0.6 = 0.99; Table 29 row 1.2 = 1.00 → I_Z = 233 × 0.95 × 0.97 × 0.99 × 1.00 = 212.56 A vs 152.83 A; ΔV = √3 × 152.83 × 0.150 × (0.248 × 0.85 + 0.0725 × 0.527) = 9.89 V = 2.472 % (limit 5 %); t = (143 × 95 / 15000)² = 0.8202 s vs 0.1 s; Z_loop = 0.05 + 0.15·√(0.248² + 0.0725²) + 0.15·√(0.927² + 0.0808²) = 0.05 + 0.0388 + 0.1396 = 0.2283 Ω, I_ef = 230.9 / 0.2283 = 1011.4 A vs 200 × 5 = 1000 A (L_max = 152.2 m); I_B 152.83 ≤ I_N 200 ≤ I_Z 212.56 holds; earth 25 mm² ≥ Table 5.1 minimum 25 mm², S_min = 4619 × √0.04 / 143 = 6.46 mm² ≤ 25 mm². Conforming sizes 95 to 500 mm² (8 of 19 tabulated), contiguous. Not tabulated for this construction: 630 mm². (validation case c0042-90kw-400v-150m-buried-conduit-2-circuits-200a)

Example 20 — 400 kW over 350 m on an 800 A device: no size passes

When no size up to the largest tabulated passes every check the status is fail and the largest tabulated size is reported with its failures.

Given: 400 kW at PF 0.9 lagging, 400 V three-phase, design factor 1. Copper XLPE (90 °C) fixed multicore cable, 350 m; unenclosed, spaced from the surface on horizontal perforated tray, 1 cable(s) per tier spaced, 1 tier(s), air ambient 40 °C. Protection: prospective fault 36 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 800 A device with 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. AS/NZS 3008.1.1:2017 tables; earth conductor per AS/NZS 3000 Table 5.1 for every size.

Load current I_load = 400 kW × 1000 / (√3 × 400 × 0.9) = 641.5 A

Candidate sizes

Each standard size with its Table 5.1 earth is run through the seven checks at I_design 641.5 A, 800 A device:

Size (earth) mm²	I_Z (A)	V_d (%)	t_max (s)	I_fault (A)	Earth S_min (mm²)	Result
1 (1)	16.0	2,367.33	0.000	12	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
1.5 (1.5)	20.0	1,518.28	0.000	19	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
2.5 (2.5)	27.0	831.06	0.000	35	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
4 (2.5)	36.0	518.44	0.000	43	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
6 (2.5)	46.0	347.63	0.001	49	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
10 (4)	66.0	207.43	0.002	80	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
16 (6)	87.0	132.04	0.004	121	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
25 (6)	116.0	84.54	0.010	134	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
35 (10)	144.0	61.87	0.019	215	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
50 (16)	182.0	46.41	0.039	325	16.15	FAIL CCC, VD, SC, EFL, OVL, EWT
70 (25)	230.0	33.15	0.077	493	16.15	FAIL CCC, VD, SC, EFL, OVL
95 (25)	275.0	24.77	0.142	530	16.15	FAIL CCC, VD, EFL, OVL
120 (35)	327.0	20.26	0.227	702	16.15	FAIL CCC, VD, EFL, OVL
150 (50)	375.0	17.04	0.355	901	16.15	FAIL CCC, VD, EFL, OVL
185 (70)	428.0	14.34	0.540	1,187	16.15	FAIL CCC, VD, EFL, OVL
240 (95)	511.0	11.74	0.909	1,507	16.15	FAIL CCC, VD, EFL, OVL
300 (120)	584.0	10.09	1.420	1,764	16.15	FAIL CCC, VD, EFL, OVL
400 (120)	692.0	8.71	2.525	1,819	16.15	FAIL VD, EFL, OVL
500 (120)	794.0	7.73	3.945	1,857	16.15	FAIL VD, EFL, OVL
630 (120)	not tabulated for this construction					INFO

Conforming range No size up to 500 mm² passes every check (19 tabulated sizes evaluated); the largest tabulated size is worked below.

Check 1 — capacity (500 mm²) Base rating Table 14, column 2, row 500: 794 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_Z = 794 × 1.00 = 794.0 A vs I_design 641.5 A (loading 80.8 %) PASS

Check 2 — voltage drop R_c = 0.0544 Ω/km (Table 35), X_c = 0.0700 Ω/km (Table 30). At the design current: ΔV = √3 × 641.5 × 0.350 × (0.0544 × 0.9 + 0.0700 × 0.436) = 30.91 V (drop) = 7.73 % of 400 V, limit 5 % FAIL

Check 3 — short circuit k = 143 (Table 52). t_max = (143 × 500)² / 36,000² = 3.945 s vs 0.1 s; S_min = 36,000 × √0.1 / 143 = 79.6 mm² PASS

Check 4 — earth fault loop Z_loop = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 0.197 Ω/km and X_e = 0.0713 Ω/km (Table 30 at 120 mm²): Z_loop = 0.02 + 0.0310 (phase) + 0.0733 (earth) = 0.1244 Ω. I_fault = 400/√3 / 0.1244 = 1,857 A vs 800 × 5 = 4,000 A; L_max = 127 m vs 350 m FAIL

Check 5 — overload coordination I_B ≤ I_N ≤ I_Z: 641.5 A ≤ 800 A ≤ 794.0 A (device at 100.8 % of cable capacity) FAIL

Check 6 — earth size AS/NZS 3000 Table 5.1 minimum for a 500 mm² phase conductor: 120 mm²; earth 120 mm² PASS

Check 7 — earth withstand Largest earth-fault current, a fault at the cable origin: I_ef = 400/√3 / 0.02 = 11,547 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 11,547 × √0.04 / 143 = 16.15 mm² vs 120 mm² (t_max = (143 × 120 / 11,547)² = 2.2085 s) PASS

Result 4/8 checks pass → FAIL; no conforming size; 500 mm² shown; governing: earth fault loop impedance. No standard size up to 500 mm² passes all seven checks for this load Cable utilization is elevated (80.8%) - monitor for load changes Power loss (5.88%) is significant Consider larger conductor to reduce energy losses Consider parallel cables for currents above 500A

Reference Hand calculation with AS/NZS 3008.1.1:2017 table values: I = 400 kW × 1000 / (√3 × 400 × 0.9) = 641.50 A; every size is paired with its AS/NZS 3000 Table 5.1 earth, and the near-end earth fault I_ef,0 = (400/√3)/0.02 Ω = 11547 A, far above any instantaneous trip, clears in t_ef = 0.04 s (the default) and needs an earth of S_min = I_ef,0·√t_ef/k; the earth-fault loop adds the earth conductor's Table 30 reactance at its own size, Z_loop = Z_ext + L·√(R² + X²) + L·√(R_e² + X_e²). 500 mm² (earth 120 mm²): base 794 A (Table 14), derating Table 24 row 1 = 1.00; Table 27(1) row 40 = 1.00 → I_Z = 794 × 1.00 × 1.00 = 794.00 A vs 641.50 A; ΔV = √3 × 641.50 × 0.350 × (0.0544 × 0.9 + 0.07 × 0.436) = 30.91 V = 7.726 % (limit 5 %); t = (143 × 500 / 36000)² = 3.9446 s vs 0.1 s; Z_loop = 0.02 + 0.35·√(0.0544² + 0.07²) + 0.35·√(0.197² + 0.0713²) = 0.02 + 0.0310 + 0.0733 = 0.1244 Ω, I_ef = 230.9 / 0.1244 = 1857.1 A vs 800 × 5 = 4000 A (L_max = 126.6 m); I_B 641.50 ≤ I_N 800 ≤ I_Z 794.00 fails; earth 120 mm² ≥ Table 5.1 minimum 120 mm², S_min = 11547 × √0.04 / 143 = 16.15 mm² ≤ 120 mm². No size up to 500 mm² passes; 500 mm² fails VD, EFL, OVL. Not tabulated for this construction: 630 mm². (validation case c0042-400kw-400v-350m-800a-no-size-passes)

Tips & Limitations

Use the Cable Permissible Load calculator for the reverse question: what load a given cable may carry.
The device rating is an input, not a result. If the minimum is set by overload coordination, reconsider the device rating before choosing a larger cable.
If the minimum is set by earth conductor withstand, a smaller cable with a larger-than-minimum earth, or a shorter earth-fault clearing time, may be acceptable: check it in Load Cable Sizing with the earth entered explicitly.
A warning that the inputs are inconsistent means \(V_{ph} / Z_{source}\) exceeds the prospective fault current; an earth fault at the origin cannot exceed the three-phase fault, so correct the source impedance or the fault level before relying on Check 7.
The range is for a single cable per phase; parallel cables are not evaluated.
Single-core and multicore constructions are tabulated over different size ranges; the candidate table shows which sizes exist for your selection.
Voltage drop is checked at the design current (load current times the design factor), as in Load Cable Sizing; the design factor applies to capacity, voltage drop and overload coordination alike.

Developer Guide

Component: calcs/components/c0042_cable_size_range/ (calc type cable_size_range). calculations.py loops over STANDARD_SIZES, maps parameters with c0030's map_calcs_to_webcalcs_params_load, calls the AS/NZS 3008 gateway once per size and runs the shared check functions from calcs/core/cable_utils.py. build_single_size_result builds a c0030-shaped result for the smallest conforming size so equations.py can reuse c0030's input tables and check sections (renumbered and with prefixed article ids).

Tests:

pytest calcs/test_c0042_cable_size_range.py -v

The mocked tests work every expectation by hand from a synthetic table.

Worked examples: the examples above are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_cable_size_range/, renderer calcs/core/help_examples/cable_size_range.py) with python manage.py generate_help_examples --tool fe_calc_cable_size_range, which needs the AS/NZS 3008.1.1:2017 rows installed; calcs/test_help_examples.py checks the committed fragment is current.