Load Cable Sizing worked backwards. This calculator takes the seven checks of the
Load Cable Sizing (3-phase) calculator and
solves each for the load it permits on a cable you have already chosen. The load-type label used when
sizing (control panel, distribution board, VSD supply, …) does not change the permissible load;
only the load current, power factor and design factor do. It uses the AS/NZS 3008.1.1:2017
tables, the only supported edition.
Overview
You specify the cable (size, earth conductor, material, insulation, construction, length), its installation and the protection data (fault level, clearing time, instantaneous trip multiplier, source impedance) together with the supply voltage, the power factor and design factor of the loads to be supplied, and the motor efficiency used for the kW load table. The calculator reports:
- the largest load current the cable may carry and the equivalent kW and kVA,
- which of the three load limits governs (capacity, voltage drop or protection),
- the largest preferred protective device rating the cable may be protected by, and
- a table of preferred load ratings (kW series or device ratings) showing which conform.
Input Parameters
| Group | Parameters |
|---|---|
| Standard | AS/NZS 3008 edition; power factor direction |
| Supply & load basis | Permissible load table (preferred kW ratings or preferred device ratings); supply voltage; power factor; motor efficiency (kW table only, default 95 %); design factor; cable length and unit; maximum voltage drop |
| Cable | Cable type; formation and arrangement; conductor size; insulation; conductor material; earth conductor size |
| Installation | As for Load Cable Sizing: method and sub-options, ambient or soil conditions |
| Circuit breaker | Prospective fault current; clearing time; earth-fault clearing time \(t_{ef}\) (default 0.04 s); instantaneous trip multiplier; source impedance (the device rating is a result) |
Output Results
- Limit 1, capacity: derating factors, \(I_Z\), and \(I_{L,CCC} = I_Z / k_{design}\).
- Limit 2, voltage drop: effective impedance, volts per ampere over the run, and \(I_{L,VD}\), the load current whose design current \(I_{L,VD} \times k_{design}\) brings the drop to the limit.
- Short circuit withstand: independent of the load; the cable must withstand the prospective fault for the clearing time or there is no permissible load.
- Earth conductor: independent of the load. The earth must be at least the AS/NZS 3000 Table 5.1 minimum for the phase size, and it must withstand the largest earth-fault current for the earth-fault clearing time \(t_{ef}\). If either check fails there is no permissible load.
- Limit 3, protection: earth fault current of the loop, the largest device for instantaneous earth fault tripping \(I_{N,EFL} = I_{fault}/k_{mag}\), the largest device within the cable capacity, the largest preferred rating below both, and \(I_{L,prot}\).
- Envelope: \(I_{L,max}\), \(P_{max}\) (electrical input), the motor output \(P_{max}\,\eta\), \(S_{max}\), governing limit, and the seven checks verified at that point.
- Permissible loads table: each preferred load is protected by the smallest preferred device rating at or above its design current and run through all seven checks.
Method
With the cable fixed, each check is linear or monotonic in the load current, so it can be solved directly:
\[ I_{L,CCC} = \frac{I_Z}{k_{design}}, \qquad I_{L,VD} = \frac{V_{d,max}}{\sqrt{3}\,L_{km}\,(R_c\cos\varphi \pm X_c\sin\varphi) \times k_{design}} \]
Voltage drop is evaluated at the design current \(I_B = I_L \times k_{design}\), the same current the capacity and protection limits use, so \(I_{L,VD} = V_{d,max} / ((V_d/I) \times k_{design})\).
\[ I_{N,max} = \min\!\left(I_Z,\; \frac{I_{fault}}{k_{mag}}\right) \;\rightarrow\; I_{N,std} \;\text{(largest preferred rating)}, \qquad I_{L,prot} = \frac{I_{N,std}}{k_{design}} \]
\[ I_{L,max} = \min(I_{L,CCC},\; I_{L,VD},\; I_{L,prot}), \qquad P_{max} = \sqrt{3}\,V\,I_{L,max}\cos\varphi \]
The protection limit combines Check 4 (the device must trip instantaneously on an earth fault at the far end, \(I_{fault} \ge k_{mag} I_N\)) with Check 5 (\(I_B \le I_N \le I_Z\), AS/NZS 3000 Clause 2.5.3.1). Preferred device ratings follow AS/NZS 60898, AS/NZS 60947.2 and AS 60269 (6, 10, 13, 16, 20, 25, 32, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500 A). The kW series follows the IEC 60072 ratings from 1.5 kW to 1000 kW. These are motor shaft output ratings, so each is converted to line current at the motor efficiency input \(\eta\) (default 95 %): \(I = P / (\sqrt{3}\,V\cos\varphi\,\eta)\). The table also shows the electrical input \(P/\eta\). The envelope \(P_{max}\) is electrical input; the largest motor it supplies is \(P_{max}\,\eta\). The efficiency does not affect the device-ratings table.
Earth conductor checks. Both are independent of the load. The size check compares the earth conductor with the AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor. The withstand check uses the largest earth-fault current, which flows for a fault at the supply end of the cable where only the source impedance limits it:
\[ I_{ef} = \frac{V}{\sqrt{3}\,Z_{source}}, \qquad S_{min} = \frac{I_{ef}\sqrt{t_{ef}}}{k}, \qquad t_{max} = \left(\frac{k\,S_{earth}}{I_{ef}}\right)^2 \]
Here \(t_{ef}\) is the earth-fault clearing time input (default 0.04 s), not the protection time of the short-circuit check: the near-end fault is far above the device's instantaneous threshold, so it clears in the instantaneous operating time. Enter the upstream device's backup time instead if clearance relies on it. \(k\) is the phase conductor's AS/NZS 3008 Table 52 value. For a multicore cable the earth is an integral core, so it starts at the insulation's operating temperature and ends at the same final temperature. For single-core sets the earth is a separate cable that runs cooler; the same \(k\) is used, which is conservative. The check passes when \(S_{earth} \ge S_{min}\).
Loop impedance method. \(Z_{loop}\) adds the source impedance and the impedance magnitudes of the phase conductor, \(L\sqrt{R_c^2 + X_c^2}\), and of the earth conductor, \(L\sqrt{R_e^2 + X_e^2}\), where \(X_e\) is the AS/NZS 3008 Table 30 reactance at the earth conductor's size for the phase cable's arrangement. Adding magnitudes gives an upper bound on the phasor sum. Resistances are read from Tables 34/35 at the insulation's operating temperature (PVC 75 °C, XLPE 90 °C, elastomeric 110 °C; aluminium at most 90 °C), and the same resistance gives the 3 I²R losses. The resulting trip margin is nominal: it ignores the device's pickup tolerance and operating time. AS/NZS 3000 Appendix B applies \(0.8\,U_o\) to allow for the impedance upstream of the circuit; this calculator models that impedance explicitly as \(Z_{ext}\), so the full \(U_o\) is used.
Governing limit and the loads table. The governing limit names the sub-limit that binds: capacity, voltage drop, the earth-fault loop (when \(I_{fault}/k_{mag}\) sets the device), or the preferred device step below \(I_Z\). When the short-circuit or an earth-conductor check fails, or no preferred device fits, there is no permissible load: the envelope is zero and the capacity, voltage-drop and overload checks are reported as not evaluated. The three limits are still shown. The loads table runs up to and including the first rating above the capacity limit. When no overcurrent device can trip instantaneously on the earth-fault loop, the calculator recommends an RCD; a very high upstream loop impedance against a large prospective fault is flagged as a TT or high-impedance earthing arrangement, and an upstream loop impedance that gives more earth-fault current than the prospective fault is flagged as inconsistent (an earth fault at the origin cannot exceed the three-phase fault, so one of the two inputs is wrong).
Single-core spacing. AS/NZS 3008 Table 30 tabulates single-core reactance only for trefoil and flat touching arrangements, so single-core cables with the conductors spaced, or one conductor per conduit (Dedicated), are rejected with an explanatory error rather than given the touching reactance, which would understate the voltage drop and loop impedance.
Worked Examples
The 22 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_permissible_load; worked examples for every calculation).
| # | Case | Cable | IZ (A) | Device (A) | Max load (A) | Governing | Result |
|---|---|---|---|---|---|---|---|
| 1 | 95 mm² XLPE feeder on a perforated tray | 95 Cu XLPE | 275.0 | 250 | 250.0 | ocpd coordination | PASS |
| 2 | 2.5 mm² PVC sub-circuit in conduit, device series | 2.5 Cu PVC | 25.0 | 25 | 25.0 | current carrying capacity | PASS |
| 3 | 4 mm² enclosed in thermal insulation | 4 Cu XLPE | 15.0 | 13 | 13.0 | ocpd coordination | PASS |
| 4 | 6 mm² on a weak source with a C-curve breaker | 6 Cu XLPE | 46.0 | 10 | 10.0 | earth fault loop impedance | PASS |
| 5 | 10 mm² behind a 10 Ω loop: no device fits | 10 Cu XLPE | 66.0 | none | 0.0 | earth fault loop impedance | FAIL |
| 6 | 16 mm² in a wiring enclosure, four circuits at 50 °C | 16 Cu XLPE | 43.1 | 40 | 40.0 | ocpd coordination | PASS |
| 7 | 25 mm² bunched on a catenary, three circuits at 25 °C | 25 Cu XLPE | 100.0 | 100 | 100.0 | ocpd coordination | PASS |
| 8 | 35 mm² PVC, six cables touching on a ladder | 35 Cu PVC | 101.4 | 100 | 100.0 | ocpd coordination | PASS |
| 9 | 35 mm² single-core, three cores in one buried conduit, two circuits | 35 Cu XLPE 1C | 125.9 | 125 | 125.0 | ocpd coordination | PASS |
| 10 | 50 mm² over 250 m with a 3 % drop limit | 50 Cu XLPE | 182.0 | 63 | 60.3 | voltage drop | PASS |
| 11 | 50 mm² with a 1.25 design factor, three cables on tray | 50 Cu XLPE | 178.4 | 160 | 128.0 | ocpd coordination | PASS |
| 12 | 50 mm² aluminium direct buried in 1.2 K·m/W soil | 50 Al XLPE | 152.6 | 80 | 80.0 | earth fault loop impedance | PASS |
| 13 | 70 mm² single-core trefoil, two circuits on tray at 415 V | 70 Cu XLPE 1C | 273.5 | 250 | 250.0 | ocpd coordination | PASS |
| 14 | 95 mm² elastomeric (EPR) on a ladder | 95 Cu EPR | 337.0 | 200 | 200.0 | earth fault loop impedance | PASS |
| 15 | 120 mm² aluminium in buried conduits, three circuits 0.3 m apart | 120 Al XLPE | 183.3 | 125 | 125.0 | earth fault loop impedance | PASS |
| 16 | 150 mm² single-core flat touching on a ladder, 25 kA | 150 Cu XLPE 1C | 472.0 | 400 | 400.0 | ocpd coordination | PASS |
| 17 | 185 mm² PVC with a leading power factor over 200 m | 185 Cu PVC | 348.0 | 200 | 200.0 | earth fault loop impedance | PASS |
| 18 | 240 mm² aluminium flat touching at 690 V over 300 m | 240 Al XLPE 1C | 487.3 | 400 | 351.7 | voltage drop | PASS |
| 19 | 300 mm² at 50 kA cleared in 1 s: withstand fails | 300 Cu XLPE | 584.0 | 500 | 0.0 | short circuit withstand | FAIL |
| 20 | 400 mm² on perforated tray at 45 °C, 36 kA | 400 Cu XLPE | 650.5 | 630 | 630.0 | ocpd coordination | PASS |
| 21 | 25 mm² on a perforated tray, motor efficiency 0.90 | 25 Cu XLPE | 116.0 | 100 | 100.0 | ocpd coordination | PASS |
| 22 | 50 mm² behind a 0.02 Ω loop, 0.4 s backup clearing: earth withstand fails | 50 Cu XLPE | 182.0 | 160 | 0.0 | earth conductor withstand | FAIL |
Example 1 — 95 mm² XLPE feeder on a perforated tray
The baseline case: the 250 A preferred device rating, not the 275 A cable capacity, limits the load.
Given: 95 mm² copper XLPE (X-90) fixed multicore cable with a 25 mm² earth (given), 80 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.03 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 95: 275 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 275 × 1.00 = 275.00 A; IL,CCC = 275.00 / 1 = 275.00 A. At the envelope Idesign = 250.00 A vs IZ 275.00 A PASS |
|---|---|
| Limit 2 — voltage drop | Rc = 0.248 Ω/km (Table 35, column 5, row 95), Xc = 0.0725 Ω/km (Table 30, column 10, row 95). Zeff = 0.248 × 0.85 + 0.0725 × 0.527 = 0.2490 Ω/km; Vd/I = √3 × 0.080 × 0.2490 = 0.03450 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.03450 × 1) = 579.69 A. At the envelope Vd = 2.16 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 95)² / 10,000² = 1.8455 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 1.8455 s 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: Ief = 400/√3 / 0.03 = 7,698 A, cleared in tef = 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). Smin = Ief × √tef / k = 7,698 × √0.04 / 143 = 10.77 mm² vs 25 mm² (tmax = (143 × 25 / 7,698)² = 0.2157 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.03 + 0.080 × √(0.248² + 0.0725²) + 0.080 × √(0.927² + 0.0808²) (earth 25 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.03 + 0.0207 + 0.0744 = 0.1251 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.1251 = 1,845.9 A; IN,EFL = 1,845.9 / 5 = 369.17 A (Zs,max for a 250 A device = 400/√3 / (250 × 5)). The 1.48× margin over the 250 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1251 vs limit 0.1848 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 275.00, IN,EFL 369.17) = 275.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 250 A; IL,prot = 250 / 1 = 250.00 A. IB ≤ IN ≤ IZ: 250.00 ≤ 250 ≤ 275.00 A PASS |
| Envelope | IL,max = min(275.00, 579.69, 250.00) = 250.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 250.00 × 0.85 / 1000 = 147.22 kW (electrical input); motor output Pmax × η = 147.22 × 0.95 = 139.86 kW; Smax = √3 × 400 × 250.00 / 1000 = 173.21 kVA; losses 3 I²R at 90 °C = 3,720 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 18 of 19 preferred loads conform; largest 132 kW (235.9 A on a 250 A device, 85.8 % of IZ, Vd 2.04 %). First to fail: 160 kW (286.0 A, 315 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 250.00 A = 147.22 kW on a 250 A device; governing: ocpd coordination. Cable utilization is very high (90.9%) - limited margin for load growth |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 95 mm² Cu XLPE with a 25 mm² earth (user) over 80 m at 400 V, PF 0.85, design factor 1: base rating 275 A (Table 14 column 2 row 95), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 275 × 1 × 1 = 275.00 A, I_L,CCC = 275.00 A; Rc = 0.248 Ω/km (Table 35, Column 5), Xc = 0.0725 Ω/km (Table 30, Column 10): Z_eff = 0.248·0.85 + 0.0725·0.5268 = 0.24899 Ω/km, V_d/I = √3·0.08·0.24899 = 0.03450 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.03450 × 1) = 579.69 A; k = 143 (Table 52 row 90), t = (143·95/10000)² = 1.8455 s vs 0.1 s (holds); Z_loop = 0.03 + 0.08·√(0.248² + 0.0725²) + 0.08·√(0.927² + 0.0808²) (earth: R from Table 35, X from Table 30 at 25 mm²) = 0.03 + 0.0207 + 0.0744 = 0.1251 Ω, I_fault = 400/√3/0.1251 = 1845.9 A, /5 = 369.17 A; I_N,max = min(275.00, 369.17) = 275.00 A → largest preferred rating 250 A, I_L,prot = 250.00 A; I_L,max = min(275.00, 579.69, 250.00) = 250.00 A = √3·400·250.00·0.85/1000 = 147.22 kW input (139.86 kW motor output at η 0.95; 173.21 kVA); earth: 25 mm² vs Table 5.1 minimum 25 mm² (holds), near-end I_ef = (400/√3)/0.03 = 7698 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 7698·√0.04/143 = 10.77 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 160 kW (285.99 A, the first above I_Z/k_design), largest conforming 132 kW. (validation case c0043-95mm2-400v-80m-tray) |
Example 2 — 2.5 mm² PVC sub-circuit in conduit, device series
Smallest tabulated size at a 2 kA sub-board, with the current-limiting breaker clearing faults in 0.01 s (also given as the earth-fault clearing time): I_Z lands exactly on the 25 A preferred rating, so capacity and protection tie and capacity is reported as governing; the loads table is the device-rating series.
Given: 2.5 mm² copper PVC (V-75) fixed multicore cable with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum), 30 m, in conduit in air, 1 circuit bunched in air; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 2 kA cleared in 0.01 s, earth-fault clearing time 0.01 s, 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: preferred device ratings (A).
| Limit 1 — capacity | Base rating Table 13, column 25, row 2.5: 25 A. Derating Table 22, column 2, row 1: 1.00; Table 27(1), 75 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 25 × 1.00 = 25.00 A; IL,CCC = 25.00 / 1 = 25.00 A. At the envelope Idesign = 25.00 A vs IZ 25.00 A PASS |
|---|---|
| Limit 2 — voltage drop | Rc = 9.01 Ω/km (Table 35, column 4, row 2.5), Xc = 0.102 Ω/km (Table 30, column 9, row 2.5). Zeff = 9.01 × 0.85 + 0.102 × 0.527 = 7.712 Ω/km; Vd/I = √3 × 0.030 × 7.712 = 0.4007 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.4007 × 1) = 49.91 A. At the envelope Vd = 2.50 % vs 5 % PASS |
| Short circuit | k = 111 (Table 52, row 75). tmax = (111 × 2.5)² / 2,000² = 0.0193 s; Smin = 2,000 × √0.01 / 111 = 1.8 mm² → 0.0100 vs limit 0.0193 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 2.5 mm² phase conductor: 2.5 mm²; earth 2.5 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 0.01 s (given: the upstream backup clearing time the design relies on). k = 111 (integral earth core: the phase conductor's Table 52 k). Smin = Ief × √tef / k = 2,309 × √0.01 / 111 = 2.08 mm² vs 2.5 mm² (tmax = (111 × 2.5 / 2,309)² = 0.0144 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.030 × √(9.01² + 0.102²) + 0.030 × √(9.01² + 0.102²) (earth 2.5 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.2703 + 0.2703 = 0.6406 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 75 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.6406 = 360.5 A; IN,EFL = 360.5 / 5 = 72.10 A (Zs,max for a 25 A device = 400/√3 / (25 × 5)). The 2.88× margin over the 25 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.6406 vs limit 1.8475 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 25.00, IN,EFL 72.10) = 25.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 25 A; IL,prot = 25 / 1 = 25.00 A. IB ≤ IN ≤ IZ: 25.00 ≤ 25 ≤ 25.00 A PASS |
| Envelope | IL,max = min(25.00, 49.91, 25.00) = 25.00 A (Current Carrying Capacity); Pmax = √3 × 400 × 25.00 × 0.85 / 1000 = 14.72 kW (electrical input); motor output Pmax × η = 14.72 × 0.95 = 13.99 kW; Smax = √3 × 400 × 25.00 / 1000 = 17.32 kVA; losses 3 I²R at 75 °C = 507 W |
| Preferred loads | 6 of 7 preferred loads conform; largest 25 A (25.0 A on a 25 A device, 100.0 % of IZ, Vd 2.50 %). First to fail: 32 A (32.0 A, 32 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 25.00 A = 14.72 kW on a 25 A device; governing: current carrying capacity. Cable utilization is very high (100.0%) - limited margin for load growth Power loss (3.44%) is significant The upstream earth-loop impedance (0.1 Ω) gives 2309 A of earth-fault current at the cable origin, more than the 2 kA prospective fault: the two inputs are inconsistent Consider larger conductor to reduce energy losses 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 tables for 2.5 mm² Cu PVC with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 30 m at 400 V, PF 0.85, design factor 1: base rating 25 A (Table 13 column 25 row 2.5), derating Table 22 column 2 row 1 = 1; Table 27(1) 75 °C conductor column row 40 = 1 → I_Z = 25 × 1 × 1 = 25.00 A, I_L,CCC = 25.00 A; Rc = 9.01 Ω/km (Table 35, Column 4), Xc = 0.102 Ω/km (Table 30, Column 9): Z_eff = 9.01·0.85 + 0.102·0.5268 = 7.71223 Ω/km, V_d/I = √3·0.03·7.71223 = 0.40074 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.40074 × 1) = 49.91 A; k = 111 (Table 52 row 75), t = (111·2.5/2000)² = 0.0193 s vs 0.01 s (holds); Z_loop = 0.1 + 0.03·√(9.01² + 0.102²) + 0.03·√(9.01² + 0.102²) (earth: R from Table 35, X from Table 30 at 2.5 mm²) = 0.1 + 0.2703 + 0.2703 = 0.6406 Ω, I_fault = 400/√3/0.6406 = 360.5 A, /5 = 72.10 A; I_N,max = min(25.00, 72.10) = 25.00 A → largest preferred rating 25 A, I_L,prot = 25.00 A; I_L,max = min(25.00, 49.91, 25.00) = 25.00 A = √3·400·25.00·0.85/1000 = 14.72 kW input (13.99 kW motor output at η 0.95; 17.32 kVA); earth: 2.5 mm² vs Table 5.1 minimum 2.5 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.01 s (given), S_min = 2309·√0.01/111 = 2.08 mm² (holds); governing current_carrying_capacity; loads table (device-rating series) runs to 32 A (32.00 A, the first above I_Z/k_design), largest conforming 25 A. (validation case c0043-2p5mm2-pvc-conduit-device-series) |
Example 3 — 4 mm² enclosed in thermal insulation
Complete thermal-insulation derating pulls a 4 mm² cable down to 15 A, so the largest preferred device is 13 A (faults, including the near-end earth fault, cleared by the breaker in 0.01 s).
Given: 4 mm² copper XLPE (X-90) fixed multicore cable with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum), 20 m, completely surrounded by thermal insulation, enclosed; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 3 kA cleared in 0.01 s, earth-fault clearing time 0.01 s, 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: preferred device ratings (A).
| Limit 1 — capacity | Base rating Table 14, column 21, row 4: 15 A. Derating Table 22, column 2, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 15 × 1.00 = 15.00 A; IL,CCC = 15.00 / 1 = 15.00 A. At the envelope Idesign = 13.00 A vs IZ 15.00 A PASS |
|---|---|
| Limit 2 — voltage drop | Rc = 5.88 Ω/km (Table 35, column 5, row 4), Xc = 0.0930 Ω/km (Table 30, column 10, row 4). Zeff = 5.88 × 0.85 + 0.0930 × 0.527 = 5.047 Ω/km; Vd/I = √3 × 0.020 × 5.047 = 0.1748 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.1748 × 1) = 114.39 A. At the envelope Vd = 0.57 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 4)² / 3,000² = 0.0364 s; Smin = 3,000 × √0.01 / 143 = 2.1 mm² → 0.0100 vs limit 0.0364 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 4 mm² phase conductor: 2.5 mm²; earth 2.5 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 0.01 s (given: the upstream backup clearing time the design relies on). k = 143 (integral earth core: the phase conductor's Table 52 k). Smin = Ief × √tef / k = 2,309 × √0.01 / 143 = 1.61 mm² vs 2.5 mm² (tmax = (143 × 2.5 / 2,309)² = 0.0240 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.020 × √(5.88² + 0.0930²) + 0.020 × √(9.45² + 0.0988²) (earth 2.5 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.1176 + 0.1890 = 0.4066 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.4066 = 567.9 A; IN,EFL = 567.9 / 5 = 113.59 A (Zs,max for a 13 A device = 400/√3 / (13 × 5)). The 8.74× margin over the 13 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.4066 vs limit 3.5529 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 15.00, IN,EFL 113.59) = 15.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 13 A; IL,prot = 13 / 1 = 13.00 A. IB ≤ IN ≤ IZ: 13.00 ≤ 13 ≤ 15.00 A PASS |
| Envelope | IL,max = min(15.00, 114.39, 13.00) = 13.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 13.00 × 0.85 / 1000 = 7.66 kW (electrical input); motor output Pmax × η = 7.66 × 0.95 = 7.27 kW; Smax = √3 × 400 × 13.00 / 1000 = 9.01 kVA; losses 3 I²R at 90 °C = 60 W |
| Preferred loads | 3 of 4 preferred loads conform; largest 13 A (13.0 A on a 13 A device, 86.7 % of IZ, Vd 0.57 %). First to fail: 16 A (16.0 A, 16 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 13.00 A = 7.66 kW on a 13 A device; governing: ocpd coordination. Cable utilization is elevated (86.7%) - monitor for load changes |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 4 mm² Cu XLPE with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 20 m at 400 V, PF 0.85, design factor 1: base rating 15 A (Table 14 column 21 row 4), derating Table 22 column 2 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 15 × 1 × 1 = 15.00 A, I_L,CCC = 15.00 A; Rc = 5.88 Ω/km (Table 35, Column 5), Xc = 0.093 Ω/km (Table 30, Column 10): Z_eff = 5.88·0.85 + 0.093·0.5268 = 5.04699 Ω/km, V_d/I = √3·0.02·5.04699 = 0.17483 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.17483 × 1) = 114.39 A; k = 143 (Table 52 row 90), t = (143·4/3000)² = 0.0364 s vs 0.01 s (holds); Z_loop = 0.1 + 0.02·√(5.88² + 0.093²) + 0.02·√(9.45² + 0.0988²) (earth: R from Table 35, X from Table 30 at 2.5 mm²) = 0.1 + 0.1176 + 0.1890 = 0.4066 Ω, I_fault = 400/√3/0.4066 = 567.9 A, /5 = 113.59 A; I_N,max = min(15.00, 113.59) = 15.00 A → largest preferred rating 13 A, I_L,prot = 13.00 A; I_L,max = min(15.00, 114.39, 13.00) = 13.00 A = √3·400·13.00·0.85/1000 = 7.66 kW input (7.27 kW motor output at η 0.95; 9.01 kVA); earth: 2.5 mm² vs Table 5.1 minimum 2.5 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.01 s (given), S_min = 2309·√0.01/143 = 1.61 mm² (holds); governing ocpd_coordination; loads table (device-rating series) runs to 16 A (16.00 A, the first above I_Z/k_design), largest conforming 13 A. (validation case c0043-4mm2-thermal-insulation-enclosed) |
Example 4 — 6 mm² on a weak source with a C-curve breaker
A 1.5 Ω upstream loop and a 10× magnetic trip make the earth-fault loop, not the cable, set the device at 10 A.
Given: 6 mm² copper XLPE (X-90) fixed multicore cable with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum), 60 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 2 kA cleared in 0.02 s, earth-fault clearing time 0.04 s (default), 10× instantaneous trip, upstream loop impedance 1.5 Ω, voltage-drop limit 5 %. Loads table: preferred device ratings (A).
| Limit 1 — capacity | Base rating Table 14, column 2, row 6: 46 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 46 × 1.00 = 46.00 A; IL,CCC = 46.00 / 1 = 46.00 A. At the envelope Idesign = 10.00 A vs IZ 46.00 A PASS |
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| Limit 2 — voltage drop | Rc = 3.93 Ω/km (Table 35, column 5, row 6), Xc = 0.0887 Ω/km (Table 30, column 10, row 6). Zeff = 3.93 × 0.85 + 0.0887 × 0.527 = 3.387 Ω/km; Vd/I = √3 × 0.060 × 3.387 = 0.3520 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.3520 × 1) = 56.82 A. At the envelope Vd = 0.88 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 6)² / 2,000² = 0.1840 s; Smin = 2,000 × √0.02 / 143 = 2.0 mm² → 0.0200 vs limit 0.1840 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 6 mm² phase conductor: 2.5 mm²; earth 2.5 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 1.5 = 154 A, cleared in tef = 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). Smin = Ief × √tef / k = 154 × √0.04 / 143 = 0.22 mm² vs 2.5 mm² (tmax = (143 × 2.5 / 154)² = 5.3918 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 1.5 + 0.060 × √(3.93² + 0.0887²) + 0.060 × √(9.45² + 0.0988²) (earth 2.5 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 1.5 + 0.2359 + 0.5670 = 2.3029 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 2.3029 = 100.3 A; IN,EFL = 100.3 / 10 = 10.03 A (Zs,max for a 10 A device = 400/√3 / (10 × 10)). The 1.00× margin over the 10 A trip threshold is nominal (pickup tolerance and operating time are not included) → 2.3029 vs limit 2.3094 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 46.00, IN,EFL 10.03) = 10.03 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 10 A; IL,prot = 10 / 1 = 10.00 A. IB ≤ IN ≤ IZ: 10.00 ≤ 10 ≤ 46.00 A PASS |
| Envelope | IL,max = min(46.00, 56.82, 10.00) = 10.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 10.00 × 0.85 / 1000 = 5.89 kW (electrical input); motor output Pmax × η = 5.89 × 0.95 = 5.59 kW; Smax = √3 × 400 × 10.00 / 1000 = 6.93 kVA; losses 3 I²R at 90 °C = 71 W |
| Preferred loads | 2 of 9 preferred loads conform; largest 10 A (10.0 A on a 10 A device, 21.7 % of IZ, Vd 0.88 %). First to fail: 13 A (13.0 A, 13 A device) on earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 10.00 A = 5.89 kW on a 10 A device; governing: earth fault loop impedance. The upstream earth-loop impedance (1.5 Ω) allows at most 154 A of earth-fault current, far below the 2 kA prospective fault Earth fault trip margin is very low (1.00x) The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load These inputs fit a TT or high-impedance earthing arrangement, where an RCD provides automatic disconnection; otherwise check the upstream loop impedance and the prospective fault level Review protection settings - fault current barely exceeds trip threshold |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 6 mm² Cu XLPE with a 2.5 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 60 m at 400 V, PF 0.85, design factor 1: base rating 46 A (Table 14 column 2 row 6), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 46 × 1 × 1 = 46.00 A, I_L,CCC = 46.00 A; Rc = 3.93 Ω/km (Table 35, Column 5), Xc = 0.0887 Ω/km (Table 30, Column 10): Z_eff = 3.93·0.85 + 0.0887·0.5268 = 3.38723 Ω/km, V_d/I = √3·0.06·3.38723 = 0.35201 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.35201 × 1) = 56.82 A; k = 143 (Table 52 row 90), t = (143·6/2000)² = 0.1840 s vs 0.02 s (holds); Z_loop = 1.5 + 0.06·√(3.93² + 0.0887²) + 0.06·√(9.45² + 0.0988²) (earth: R from Table 35, X from Table 30 at 2.5 mm²) = 1.5 + 0.2359 + 0.5670 = 2.3029 Ω, I_fault = 400/√3/2.3029 = 100.3 A, /10 = 10.03 A; I_N,max = min(46.00, 10.03) = 10.03 A → largest preferred rating 10 A, I_L,prot = 10.00 A; I_L,max = min(46.00, 56.82, 10.00) = 10.00 A = √3·400·10.00·0.85/1000 = 5.89 kW input (5.59 kW motor output at η 0.95; 6.93 kVA); earth: 2.5 mm² vs Table 5.1 minimum 2.5 mm² (holds), near-end I_ef = (400/√3)/1.5 = 154 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 154·√0.04/143 = 0.22 mm² (holds); governing earth_fault_loop_impedance; loads table (device-rating series) runs to 50 A (50.00 A, the first above I_Z/k_design), largest conforming 10 A. (validation case c0043-6mm2-weak-source-c-curve-efl-limits) |
Example 5 — 10 mm² behind a 10 Ω loop: no device fits
With a 15× trip and a 10 Ω upstream loop even a 6 A device cannot trip instantaneously, so the tool reports no permissible load.
Given: 10 mm² copper XLPE (X-90) fixed multicore cable with a 4 mm² earth (AS/NZS 3000 Table 5.1 minimum), 50 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 6 kA cleared in 0.01 s, earth-fault clearing time 0.04 s (default), 15× instantaneous trip, upstream loop impedance 10 Ω, voltage-drop limit 5 %. Loads table: preferred device ratings (A).
| Limit 1 — capacity | Base rating Table 14, column 2, row 10: 66 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 66 × 1.00 = 66.00 A; IL,CCC = 66.00 / 1 = 66.00 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
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| Limit 2 — voltage drop | Rc = 2.33 Ω/km (Table 35, column 5, row 10), Xc = 0.0840 Ω/km (Table 30, column 10, row 10). Zeff = 2.33 × 0.85 + 0.0840 × 0.527 = 2.025 Ω/km; Vd/I = √3 × 0.050 × 2.025 = 0.1753 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.1753 × 1) = 114.06 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 10)² / 6,000² = 0.0568 s; Smin = 6,000 × √0.01 / 143 = 4.2 mm² → 0.0100 vs limit 0.0568 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 10 mm² phase conductor: 4 mm²; earth 4 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 10 = 23 A, cleared in tef = 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). Smin = Ief × √tef / k = 23 × √0.04 / 143 = 0.03 mm² vs 4 mm² (tmax = (143 × 4 / 23)² = 613.4700 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 10 + 0.050 × √(2.33² + 0.0840²) + 0.050 × √(5.88² + 0.0930²) (earth 4 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 10 + 0.1166 + 0.2940 = 10.4106 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 10.4106 = 22.2 A; IN,EFL = 22.2 / 15 = 1.48 A FAIL |
| Limit 3 — device | IN,max = min(IZ 66.00, IN,EFL 1.48) = 1.48 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → no preferred rating (6 A is the smallest) fits, so IL,prot = 0 A INFO |
| Envelope | IL,max = min(66.00, 114.06, 0.00) = 0.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 0.00 × 0.85 / 1000 = 0.00 kW (electrical input); motor output Pmax × η = 0.00 × 0.95 = 0.00 kW; Smax = √3 × 400 × 0.00 / 1000 = 0.00 kVA; losses 3 I²R at 90 °C = 0 W |
| Preferred loads | 0 of 11 preferred loads conform. First to fail: 6 A (6.0 A, 6 A device) on earth fault loop impedance. |
| Result | 3/4 checks pass → FAIL; no permissible load; governing: earth fault loop impedance. No preferred device rating is at or below 1.5 A, the limit set by the earth fault loop (I_N ≤ I_fault / k_mag) The permissible load current is zero The upstream earth-loop impedance (10 Ω) allows at most 23 A of earth-fault current, far below the 6 kA prospective fault No overcurrent device can trip instantaneously on this earth-fault loop: provide automatic disconnection with an RCD, or check the upstream loop impedance These inputs fit a TT or high-impedance earthing arrangement, where an RCD provides automatic disconnection; otherwise check the upstream loop impedance and the prospective fault level |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 10 mm² Cu XLPE with a 4 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 50 m at 400 V, PF 0.85, design factor 1: base rating 66 A (Table 14 column 2 row 10), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 66 × 1 × 1 = 66.00 A, I_L,CCC = 66.00 A; Rc = 2.33 Ω/km (Table 35, Column 5), Xc = 0.084 Ω/km (Table 30, Column 10): Z_eff = 2.33·0.85 + 0.084·0.5268 = 2.02475 Ω/km, V_d/I = √3·0.05·2.02475 = 0.17535 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.17535 × 1) = 114.06 A; k = 143 (Table 52 row 90), t = (143·10/6000)² = 0.0568 s vs 0.01 s (holds); Z_loop = 10 + 0.05·√(2.33² + 0.084²) + 0.05·√(5.88² + 0.093²) (earth: R from Table 35, X from Table 30 at 4 mm²) = 10 + 0.1166 + 0.2940 = 10.4106 Ω, I_fault = 400/√3/10.4106 = 22.2 A, /15 = 1.48 A; I_N,max = min(66.00, 1.48) = 1.48 A → largest preferred rating none (6 A is the smallest), I_L,prot = 0.00 A; I_L,max = min(66.00, 114.06, 0.00) = 0.00 A = √3·400·0.00·0.85/1000 = 0.00 kW input (0.00 kW motor output at η 0.95; 0.00 kVA); earth: 4 mm² vs Table 5.1 minimum 4 mm² (holds), near-end I_ef = (400/√3)/10 = 23 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 23·√0.04/143 = 0.03 mm² (holds); governing earth_fault_loop_impedance — no permissible load; loads table (device-rating series) runs to 80 A (80.00 A, the first above I_Z/k_design), none conforms. (validation case c0043-10mm2-10ohm-source-no-device-fits) |
Example 6 — 16 mm² in a wiring enclosure, four circuits at 50 °C
Bunched-circuit grouping and a 50 °C ambient compound to derate the cable to 43 A; a 40 A device governs.
Given: 16 mm² copper XLPE (X-90) fixed multicore cable with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum), 45 m, enclosed in a wiring enclosure in air, 4 circuits; air ambient 50 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 6 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 11, row 16: 68 A. Derating Table 22, column 2, row 4: 0.720; Table 27(1), 90 °C conductor column, row 50: 0.880 → F = 0.634. IZ = 68 × 0.634 = 43.08 A; IL,CCC = 43.08 / 1 = 43.08 A. At the envelope Idesign = 40.00 A vs IZ 43.08 A PASS |
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| Limit 2 — voltage drop | Rc = 1.47 Ω/km (Table 35, column 5, row 16), Xc = 0.0805 Ω/km (Table 30, column 10, row 16). Zeff = 1.47 × 0.85 + 0.0805 × 0.527 = 1.292 Ω/km; Vd/I = √3 × 0.045 × 1.292 = 0.1007 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.1007 × 1) = 198.62 A. At the envelope Vd = 1.01 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 16)² / 6,000² = 0.1454 s; Smin = 6,000 × √0.1 / 143 = 13.3 mm² → 0.1000 vs limit 0.1454 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 6 mm² (tmax = (143 × 6 / 2,309)² = 0.1380 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.045 × √(1.47² + 0.0805²) + 0.045 × √(3.93² + 0.0887²) (earth 6 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0662 + 0.1769 = 0.3431 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.3431 = 673.0 A; IN,EFL = 673.0 / 5 = 134.60 A (Zs,max for a 40 A device = 400/√3 / (40 × 5)). The 3.37× margin over the 40 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.3431 vs limit 1.1547 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 43.08, IN,EFL 134.60) = 43.08 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 40 A; IL,prot = 40 / 1 = 40.00 A. IB ≤ IN ≤ IZ: 40.00 ≤ 40 ≤ 43.08 A PASS |
| Envelope | IL,max = min(43.08, 198.62, 40.00) = 40.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 40.00 × 0.85 / 1000 = 23.56 kW (electrical input); motor output Pmax × η = 23.56 × 0.95 = 22.38 kW; Smax = √3 × 400 × 40.00 / 1000 = 27.71 kVA; losses 3 I²R at 90 °C = 318 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 10 of 11 preferred loads conform; largest 22 kW (39.3 A on a 40 A device, 91.3 % of IZ, Vd 0.99 %). First to fail: 30 kW (53.6 A, 63 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 40.00 A = 23.56 kW on a 40 A device; governing: ocpd coordination. Cable utilization is very high (92.8%) - limited margin for load growth |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 16 mm² Cu XLPE with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 45 m at 400 V, PF 0.85, design factor 1: base rating 68 A (Table 14 column 11 row 16), derating Table 22 column 2 row 4 = 0.72; Table 27(1) 90 °C conductor column row 50 = 0.88 → I_Z = 68 × 0.72 × 0.88 = 43.08 A, I_L,CCC = 43.08 A; Rc = 1.47 Ω/km (Table 35, Column 5), Xc = 0.0805 Ω/km (Table 30, Column 10): Z_eff = 1.47·0.85 + 0.0805·0.5268 = 1.29191 Ω/km, V_d/I = √3·0.045·1.29191 = 0.10069 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.10069 × 1) = 198.62 A; k = 143 (Table 52 row 90), t = (143·16/6000)² = 0.1454 s vs 0.1 s (holds); Z_loop = 0.1 + 0.045·√(1.47² + 0.0805²) + 0.045·√(3.93² + 0.0887²) (earth: R from Table 35, X from Table 30 at 6 mm²) = 0.1 + 0.0662 + 0.1769 = 0.3431 Ω, I_fault = 400/√3/0.3431 = 673.0 A, /5 = 134.60 A; I_N,max = min(43.08, 134.60) = 43.08 A → largest preferred rating 40 A, I_L,prot = 40.00 A; I_L,max = min(43.08, 198.62, 40.00) = 40.00 A = √3·400·40.00·0.85/1000 = 23.56 kW input (22.38 kW motor output at η 0.95; 27.71 kVA); earth: 6 mm² vs Table 5.1 minimum 6 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/143 = 3.23 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 30 kW (53.62 A, the first above I_Z/k_design), largest conforming 22 kW. (validation case c0043-16mm2-enclosed-4-circuits-50c) |
Example 7 — 25 mm² bunched on a catenary, three circuits at 25 °C
Catenary cables take the bunched-circuit grouping table; a 25 °C ambient uprates the cable above its 40 °C rating.
Given: 25 mm² copper XLPE (X-90) fixed multicore cable with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum), 50 m, unenclosed, bunched on a catenary wire, 3 circuits; air ambient 25 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 25: 116 A. Derating Table 22, column 2, row 3: 0.750; Table 27(1), 90 °C conductor column, row 25: 1.15 → F = 0.862. IZ = 116 × 0.862 = 100.05 A; IL,CCC = 100.05 / 1 = 100.05 A. At the envelope Idesign = 100.00 A vs IZ 100.05 A PASS |
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| Limit 2 — voltage drop | Rc = 0.927 Ω/km (Table 35, column 5, row 25), Xc = 0.0808 Ω/km (Table 30, column 10, row 25). Zeff = 0.927 × 0.85 + 0.0808 × 0.527 = 0.8305 Ω/km; Vd/I = √3 × 0.050 × 0.8305 = 0.07192 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.07192 × 1) = 278.07 A. At the envelope Vd = 1.80 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 25)² / 10,000² = 0.1278 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 0.1278 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 25 mm² phase conductor: 6 mm²; earth 6 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 6 mm² (tmax = (143 × 6 / 2,309)² = 0.1380 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.050 × √(0.927² + 0.0808²) + 0.050 × √(3.93² + 0.0887²) (earth 6 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0465 + 0.1966 = 0.3431 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.3431 = 673.1 A; IN,EFL = 673.1 / 5 = 134.63 A (Zs,max for a 100 A device = 400/√3 / (100 × 5)). The 1.35× margin over the 100 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.3431 vs limit 0.4619 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 100.05, IN,EFL 134.63) = 100.05 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 100 A; IL,prot = 100 / 1 = 100.00 A. IB ≤ IN ≤ IZ: 100.00 ≤ 100 ≤ 100.05 A PASS |
| Envelope | IL,max = min(100.05, 278.07, 100.00) = 100.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 100.00 × 0.85 / 1000 = 58.89 kW (electrical input); motor output Pmax × η = 58.89 × 0.95 = 55.95 kW; Smax = √3 × 400 × 100.00 / 1000 = 69.28 kVA; losses 3 I²R at 90 °C = 1,390 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 14 of 15 preferred loads conform; largest 55 kW (98.3 A on a 100 A device, 98.3 % of IZ, Vd 1.77 %). First to fail: 75 kW (134.1 A, 160 A device) on current carrying capacity, earth fault loop impedance, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 100.00 A = 58.89 kW on a 100 A device; governing: ocpd coordination. Cable utilization is very high (100.0%) - limited margin for load growth |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 25 mm² Cu XLPE with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 50 m at 400 V, PF 0.85, design factor 1: base rating 116 A (Table 14 column 2 row 25), derating Table 22 column 2 row 3 = 0.75; Table 27(1) 90 °C conductor column row 25 = 1.15 → I_Z = 116 × 0.75 × 1.15 = 100.05 A, I_L,CCC = 100.05 A; Rc = 0.927 Ω/km (Table 35, Column 5), Xc = 0.0808 Ω/km (Table 30, Column 10): Z_eff = 0.927·0.85 + 0.0808·0.5268 = 0.83051 Ω/km, V_d/I = √3·0.05·0.83051 = 0.07192 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.07192 × 1) = 278.07 A; k = 143 (Table 52 row 90), t = (143·25/10000)² = 0.1278 s vs 0.1 s (holds); Z_loop = 0.1 + 0.05·√(0.927² + 0.0808²) + 0.05·√(3.93² + 0.0887²) (earth: R from Table 35, X from Table 30 at 6 mm²) = 0.1 + 0.0465 + 0.1966 = 0.3431 Ω, I_fault = 400/√3/0.3431 = 673.1 A, /5 = 134.63 A; I_N,max = min(100.05, 134.63) = 100.05 A → largest preferred rating 100 A, I_L,prot = 100.00 A; I_L,max = min(100.05, 278.07, 100.00) = 100.00 A = √3·400·100.00·0.85/1000 = 58.89 kW input (55.95 kW motor output at η 0.95; 69.28 kVA); earth: 6 mm² vs Table 5.1 minimum 6 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/143 = 3.23 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 75 kW (134.06 A, the first above I_Z/k_design), largest conforming 55 kW. (validation case c0043-25mm2-catenary-3-circuits-25c) |
Example 8 — 35 mm² PVC, six cables touching on a ladder
Six touching multicore cables on one ladder tier at 35 °C; PVC resistance at 75 °C sets the voltage drop.
Given: 35 mm² copper PVC (V-75) fixed multicore cable with a 10 mm² earth (AS/NZS 3000 Table 5.1 minimum), 40 m, unenclosed on ladder, racks or cleats, touching, 1 tier, 6 cables per tier; air ambient 35 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 13, column 2, row 35: 120 A. Derating Table 24, column 13, row 6: 0.790; Table 27(1), 75 °C conductor column, row 35: 1.07 → F = 0.845. IZ = 120 × 0.845 = 101.44 A; IL,CCC = 101.44 / 1 = 101.44 A. At the envelope Idesign = 100.00 A vs IZ 101.44 A PASS |
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| Limit 2 — voltage drop | Rc = 0.638 Ω/km (Table 35, column 4, row 35), Xc = 0.0826 Ω/km (Table 30, column 9, row 35). Zeff = 0.638 × 0.85 + 0.0826 × 0.527 = 0.5858 Ω/km; Vd/I = √3 × 0.040 × 0.5858 = 0.04059 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.04059 × 1) = 492.78 A. At the envelope Vd = 1.01 % vs 5 % PASS |
| Short circuit | k = 111 (Table 52, row 75). tmax = (111 × 35)² / 10,000² = 0.1509 s; Smin = 10,000 × √0.1 / 111 = 28.5 mm² → 0.1000 vs limit 0.1509 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 111 = 4.16 mm² vs 10 mm² (tmax = (111 × 10 / 2,309)² = 0.2310 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.040 × √(0.638² + 0.0826²) + 0.040 × √(2.23² + 0.0906²) (earth 10 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0257 + 0.0893 = 0.2150 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 75 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.2150 = 1,074.1 A; IN,EFL = 1,074.1 / 5 = 214.82 A (Zs,max for a 100 A device = 400/√3 / (100 × 5)). The 2.15× margin over the 100 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.2150 vs limit 0.4619 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 101.44, IN,EFL 214.82) = 101.44 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 100 A; IL,prot = 100 / 1 = 100.00 A. IB ≤ IN ≤ IZ: 100.00 ≤ 100 ≤ 101.44 A PASS |
| Envelope | IL,max = min(101.44, 492.78, 100.00) = 100.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 100.00 × 0.85 / 1000 = 58.89 kW (electrical input); motor output Pmax × η = 58.89 × 0.95 = 55.95 kW; Smax = √3 × 400 × 100.00 / 1000 = 69.28 kVA; losses 3 I²R at 75 °C = 766 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 14 of 15 preferred loads conform; largest 55 kW (98.3 A on a 100 A device, 96.9 % of IZ, Vd 1.00 %). First to fail: 75 kW (134.1 A, 160 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 100.00 A = 58.89 kW on a 100 A device; governing: ocpd coordination. Cable utilization is very high (98.6%) - limited margin for load growth |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 35 mm² Cu PVC with a 10 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 40 m at 400 V, PF 0.85, design factor 1: base rating 120 A (Table 13 column 2 row 35), derating Table 24 column 13 row 6 = 0.79; Table 27(1) 75 °C conductor column row 35 = 1.07 → I_Z = 120 × 0.79 × 1.07 = 101.44 A, I_L,CCC = 101.44 A; Rc = 0.638 Ω/km (Table 35, Column 4), Xc = 0.0826 Ω/km (Table 30, Column 9): Z_eff = 0.638·0.85 + 0.0826·0.5268 = 0.58581 Ω/km, V_d/I = √3·0.04·0.58581 = 0.04059 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.04059 × 1) = 492.78 A; k = 111 (Table 52 row 75), t = (111·35/10000)² = 0.1509 s vs 0.1 s (holds); Z_loop = 0.1 + 0.04·√(0.638² + 0.0826²) + 0.04·√(2.23² + 0.0906²) (earth: R from Table 35, X from Table 30 at 10 mm²) = 0.1 + 0.0257 + 0.0893 = 0.2150 Ω, I_fault = 400/√3/0.2150 = 1074.1 A, /5 = 214.82 A; I_N,max = min(101.44, 214.82) = 101.44 A → largest preferred rating 100 A, I_L,prot = 100.00 A; I_L,max = min(101.44, 492.78, 100.00) = 100.00 A = √3·400·100.00·0.85/1000 = 58.89 kW input (55.95 kW motor output at η 0.95; 69.28 kVA); earth: 10 mm² vs Table 5.1 minimum 10 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/111 = 4.16 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 75 kW (134.06 A, the first above I_Z/k_design), largest conforming 55 kW. (validation case c0043-35mm2-pvc-ladder-6-touching-35c) |
Example 9 — 35 mm² single-core, three cores in one buried conduit, two circuits
Single cores sharing one buried conduit per circuit take the Table 26(2) conduit grouping (0.93 at 0.15 m); the derated 125.9 A capacity, just below the 135.6 A earth-fault-loop limit, sets the 125 A device.
Given: 35 mm² copper XLPE (X-90) fixed single-core (trefoil) cable with a 10 mm² earth (AS/NZS 3000 Table 5.1 minimum), 80 m, in shared buried conduit, 2 circuits spaced 0.15 m; soil 25 °C, depth 0.8 m, thermal resistivity 1 K·m/W. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 8, column 24, row 35: 137 A. Derating Table 26(2), column 2, row 2: 0.930; Table 27(2), 90 °C conductor column, row 25: 1.00; Table 28(2), column 2, row 0.8: 0.950; Table 29, column 6, row 1: 1.04 → F = 0.919. IZ = 137 × 0.919 = 125.88 A; IL,CCC = 125.88 / 1 = 125.88 A. At the envelope Idesign = 125.00 A vs IZ 125.88 A PASS |
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| Limit 2 — voltage drop | Rc = 0.668 Ω/km (Table 34, column 6, row 35), Xc = 0.0982 Ω/km (Table 30, column 4, row 35). Zeff = 0.668 × 0.85 + 0.0982 × 0.527 = 0.6195 Ω/km; Vd/I = √3 × 0.080 × 0.6195 = 0.08584 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.08584 × 1) = 232.98 A. At the envelope Vd = 2.68 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 35)² / 10,000² = 0.2505 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 0.2505 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 10 mm² (tmax = (143 × 10 / 2,309)² = 0.3834 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.080 × √(0.668² + 0.0982²) + 0.080 × √(2.33² + 0.114²) (earth 10 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0540 + 0.1866 = 0.3406 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.3406 = 678.0 A; IN,EFL = 678.0 / 5 = 135.59 A (Zs,max for a 125 A device = 400/√3 / (125 × 5)). The 1.08× margin over the 125 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.3406 vs limit 0.3695 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 125.88, IN,EFL 135.59) = 125.88 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 125 A; IL,prot = 125 / 1 = 125.00 A. IB ≤ IN ≤ IZ: 125.00 ≤ 125 ≤ 125.88 A PASS |
| Envelope | IL,max = min(125.88, 232.98, 125.00) = 125.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 125.00 × 0.85 / 1000 = 73.61 kW (electrical input); motor output Pmax × η = 73.61 × 0.95 = 69.93 kW; Smax = √3 × 400 × 125.00 / 1000 = 86.60 kVA; losses 3 I²R at 90 °C = 2,505 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 14 of 15 preferred loads conform; largest 55 kW (98.3 A on a 100 A device, 78.1 % of IZ, Vd 2.11 %). First to fail: 75 kW (134.1 A, 160 A device) on current carrying capacity, earth fault loop impedance, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 125.00 A = 73.61 kW on a 125 A device; governing: ocpd coordination. Cable utilization is very high (99.3%) - limited margin for load growth Power loss (3.40%) is significant Earth fault trip margin is very low (1.08x) 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 tables for 35 mm² Cu XLPE with a 10 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 80 m at 400 V, PF 0.85, design factor 1: base rating 137 A (Table 8 column 24 row 35), derating Table 26(2) column 2 row 2 = 0.93; Table 27(2) 90 °C conductor column row 25 = 1; Table 28(2) column 2 row 0.8 = 0.95; Table 29 column 6 row 1 = 1.04 → I_Z = 137 × 0.93 × 1 × 0.95 × 1.04 = 125.88 A, I_L,CCC = 125.88 A; Rc = 0.668 Ω/km (Table 34, Column 6), Xc = 0.0982 Ω/km (Table 30, Column 4): Z_eff = 0.668·0.85 + 0.0982·0.5268 = 0.61953 Ω/km, V_d/I = √3·0.08·0.61953 = 0.08584 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.08584 × 1) = 232.98 A; k = 143 (Table 52 row 90), t = (143·35/10000)² = 0.2505 s vs 0.1 s (holds); Z_loop = 0.1 + 0.08·√(0.668² + 0.0982²) + 0.08·√(2.33² + 0.114²) (earth: R from Table 34, X from Table 30 at 10 mm²) = 0.1 + 0.0540 + 0.1866 = 0.3406 Ω, I_fault = 400/√3/0.3406 = 678.0 A, /5 = 135.59 A; I_N,max = min(125.88, 135.59) = 125.88 A → largest preferred rating 125 A, I_L,prot = 125.00 A; I_L,max = min(125.88, 232.98, 125.00) = 125.00 A = √3·400·125.00·0.85/1000 = 73.61 kW input (69.93 kW motor output at η 0.95; 86.60 kVA); earth: 10 mm² vs Table 5.1 minimum 10 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/143 = 3.23 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 75 kW (134.06 A, the first above I_Z/k_design), largest conforming 55 kW. (validation case c0043-35mm2-single-core-shared-buried-conduit-2) |
Example 10 — 50 mm² over 250 m with a 3 % drop limit
A long route with a tight voltage-drop limit: the permissible load is set by voltage drop, below both the cable capacity and the device.
Given: 50 mm² copper XLPE (X-90) fixed multicore cable with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum), 250 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 3 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 50: 182 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 182 × 1.00 = 182.00 A; IL,CCC = 182.00 / 1 = 182.00 A. At the envelope Idesign = 60.32 A vs IZ 182.00 A PASS |
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| Limit 2 — voltage drop | Rc = 0.494 Ω/km (Table 35, column 5, row 50), Xc = 0.0751 Ω/km (Table 30, column 10, row 50). Zeff = 0.494 × 0.85 + 0.0751 × 0.527 = 0.4595 Ω/km; Vd/I = √3 × 0.250 × 0.4595 = 0.1990 V/A; Vd,max = 3 % × 400 = 12.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 12.00 / (0.1990 × 1) = 60.32 A. At the envelope Vd = 3.00 % vs 3 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 50)² / 10,000² = 0.5112 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 0.5112 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 16 mm² (tmax = (143 × 16 / 2,309)² = 0.9816 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.250 × √(0.494² + 0.0751²) + 0.250 × √(1.47² + 0.0805²) (earth 16 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.1249 + 0.3681 = 0.5930 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.5930 = 389.5 A; IN,EFL = 389.5 / 5 = 77.89 A (Zs,max for a 63 A device = 400/√3 / (63 × 5)). The 1.24× margin over the 63 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.5930 vs limit 0.7331 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 182.00, IN,EFL 77.89) = 77.89 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 63 A; IL,prot = 63 / 1 = 63.00 A. IB ≤ IN ≤ IZ: 60.32 ≤ 63 ≤ 182.00 A PASS |
| Envelope | IL,max = min(182.00, 60.32, 63.00) = 60.32 A (Voltage Drop); Pmax = √3 × 400 × 60.32 × 0.85 / 1000 = 35.52 kW (electrical input); motor output Pmax × η = 35.52 × 0.95 = 33.74 kW; Smax = √3 × 400 × 60.32 / 1000 = 41.79 kVA; losses 3 I²R at 90 °C = 1,348 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 11 of 17 preferred loads conform; largest 30 kW (53.6 A on a 63 A device, 29.5 % of IZ, Vd 2.67 %). First to fail: 37 kW (66.1 A, 80 A device) on voltage drop, earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 60.32 A = 35.52 kW on a 63 A device; governing: voltage drop. Power loss (3.79%) is significant Voltage drop governs: a shorter route or a larger conductor raises the permissible load Consider larger conductor to reduce energy losses |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 50 mm² Cu XLPE with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 250 m at 400 V, PF 0.85, design factor 1: base rating 182 A (Table 14 column 2 row 50), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 182 × 1 × 1 = 182.00 A, I_L,CCC = 182.00 A; Rc = 0.494 Ω/km (Table 35, Column 5), Xc = 0.0751 Ω/km (Table 30, Column 10): Z_eff = 0.494·0.85 + 0.0751·0.5268 = 0.45946 Ω/km, V_d/I = √3·0.25·0.45946 = 0.19895 V/A, 3 % of 400 V = 12.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 12.00 / (0.19895 × 1) = 60.32 A; k = 143 (Table 52 row 90), t = (143·50/10000)² = 0.5112 s vs 0.1 s (holds); Z_loop = 0.1 + 0.25·√(0.494² + 0.0751²) + 0.25·√(1.47² + 0.0805²) (earth: R from Table 35, X from Table 30 at 16 mm²) = 0.1 + 0.1249 + 0.3681 = 0.5930 Ω, I_fault = 400/√3/0.5930 = 389.5 A, /5 = 77.89 A; I_N,max = min(182.00, 77.89) = 77.89 A → largest preferred rating 63 A, I_L,prot = 63.00 A; I_L,max = min(182.00, 60.32, 63.00) = 60.32 A = √3·400·60.32·0.85/1000 = 35.52 kW input (33.74 kW motor output at η 0.95; 41.79 kVA); earth: 16 mm² vs Table 5.1 minimum 16 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/143 = 3.23 mm² (holds); governing voltage_drop; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 110 kW (196.62 A, the first above I_Z/k_design), largest conforming 30 kW. (validation case c0043-50mm2-250m-3pct-vd-governs) |
Example 11 — 50 mm² with a 1.25 design factor, three cables on tray
The design factor scales every limit: the load is reported before the factor and each preferred device is checked against 1.25 × the load.
Given: 50 mm² copper XLPE (X-90) fixed multicore cable with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum), 55 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 3 cables per tier; air ambient 40 °C. Supply 415 V three-phase; loads at PF 0.85 lagging, design factor 1.25. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: preferred device ratings (A).
| Limit 1 — capacity | Base rating Table 14, column 2, row 50: 182 A. Derating Table 24, column 10, row 3: 0.980; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 0.980. IZ = 182 × 0.980 = 178.36 A; IL,CCC = 178.36 / 1.25 = 142.69 A. At the envelope Idesign = 160.00 A vs IZ 178.36 A PASS |
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| Limit 2 — voltage drop | Rc = 0.494 Ω/km (Table 35, column 5, row 50), Xc = 0.0751 Ω/km (Table 30, column 10, row 50). Zeff = 0.494 × 0.85 + 0.0751 × 0.527 = 0.4595 Ω/km; Vd/I = √3 × 0.055 × 0.4595 = 0.04377 V/A; Vd,max = 5 % × 415 = 20.75 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.75 / (0.04377 × 1.25) = 379.26 A. At the envelope Vd = 1.69 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 50)² / 10,000² = 0.5112 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 0.5112 s 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: Ief = 415/√3 / 0.1 = 2,396 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,396 × √0.04 / 143 = 3.35 mm² vs 16 mm² (tmax = (143 × 16 / 2,396)² = 0.9119 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.055 × √(0.494² + 0.0751²) + 0.055 × √(1.47² + 0.0805²) (earth 16 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0275 + 0.0810 = 0.2085 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 415/√3 / 0.2085 = 1,149.4 A; IN,EFL = 1,149.4 / 5 = 229.88 A (Zs,max for a 160 A device = 415/√3 / (160 × 5)). The 1.44× margin over the 160 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.2085 vs limit 0.2995 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 178.36, IN,EFL 229.88) = 178.36 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 160 A; IL,prot = 160 / 1.25 = 128.00 A. IB ≤ IN ≤ IZ: 160.00 ≤ 160 ≤ 178.36 A PASS |
| Envelope | IL,max = min(142.69, 379.26, 128.00) = 128.00 A (Device rating (I_N ≤ I_Z, preferred step)); Idesign = 128.00 × 1.25 = 160.00 A; Pmax = √3 × 415 × 128.00 × 0.85 / 1000 = 78.21 kW (electrical input); motor output Pmax × η = 78.21 × 0.95 = 74.30 kW; Smax = √3 × 415 × 128.00 / 1000 = 92.01 kVA; losses 3 I²R at 90 °C = 1,336 W |
| Preferred loads | 13 of 14 preferred loads conform; largest 125 A (125.0 A on a 160 A device, 87.6 % of IZ, Vd 1.65 %). First to fail: 160 A (160.0 A, 200 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 128.00 A = 78.21 kW on a 160 A device; governing: ocpd coordination. Cable utilization is elevated (89.7%) - monitor for load changes |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 50 mm² Cu XLPE with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 55 m at 415 V, PF 0.85, design factor 1.25: base rating 182 A (Table 14 column 2 row 50), derating Table 24 column 10 row 3 = 0.98; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 182 × 0.98 × 1 = 178.36 A, I_L,CCC = 142.69 A; Rc = 0.494 Ω/km (Table 35, Column 5), Xc = 0.0751 Ω/km (Table 30, Column 10): Z_eff = 0.494·0.85 + 0.0751·0.5268 = 0.45946 Ω/km, V_d/I = √3·0.055·0.45946 = 0.04377 V/A, 5 % of 415 V = 20.75 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.75 / (0.04377 × 1.25) = 379.26 A; k = 143 (Table 52 row 90), t = (143·50/10000)² = 0.5112 s vs 0.1 s (holds); Z_loop = 0.1 + 0.055·√(0.494² + 0.0751²) + 0.055·√(1.47² + 0.0805²) (earth: R from Table 35, X from Table 30 at 16 mm²) = 0.1 + 0.0275 + 0.0810 = 0.2085 Ω, I_fault = 415/√3/0.2085 = 1149.4 A, /5 = 229.88 A; I_N,max = min(178.36, 229.88) = 178.36 A → largest preferred rating 160 A, I_L,prot = 128.00 A; I_L,max = min(142.69, 379.26, 128.00) = 128.00 A = √3·415·128.00·0.85/1000 = 78.21 kW input (74.30 kW motor output at η 0.95; 92.01 kVA); earth: 16 mm² vs Table 5.1 minimum 16 mm² (holds), near-end I_ef = (415/√3)/0.1 = 2396 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2396·√0.04/143 = 3.35 mm² (holds); governing ocpd_coordination; loads table (device-rating series) runs to 160 A (160.00 A, the first above I_Z/k_design), largest conforming 125 A. (validation case c0043-50mm2-design-factor-1p25-device-series) |
Example 12 — 50 mm² aluminium direct buried in 1.2 K·m/W soil
A single buried aluminium circuit takes no grouping factor but is derated for soil resistivity; the earth-fault loop sets the device.
Given: 50 mm² aluminium XLPE (X-90) fixed multicore cable with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum), 120 m, direct buried, 1 circuit; soil 25 °C, depth 0.8 m, thermal resistivity 1.2 K·m/W. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 24, row 50: 159 A. Derating Table 27(2), 90 °C conductor column, row 25: 1.00; Table 28(1), column 3, row 0.8: 0.960; Table 29, column 2, row 1.2: 1.00 → F = 0.960. IZ = 159 × 0.960 = 152.64 A; IL,CCC = 152.64 / 1 = 152.64 A. At the envelope Idesign = 80.00 A vs IZ 152.64 A PASS |
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| Limit 2 — voltage drop | Rc = 0.822 Ω/km (Table 35, column 10, row 50), Xc = 0.0751 Ω/km (Table 30, column 10, row 50). Zeff = 0.822 × 0.85 + 0.0751 × 0.527 = 0.7383 Ω/km; Vd/I = √3 × 0.120 × 0.7383 = 0.1534 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.1534 × 1) = 130.34 A. At the envelope Vd = 3.07 % vs 5 % PASS |
| Short circuit | k = 94.5 (Table 52, row 90). tmax = (94.5 × 50)² / 10,000² = 0.2233 s; Smin = 10,000 × √0.1 / 94.5 = 33.5 mm² → 0.1000 vs limit 0.2233 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 94.5 = 4.89 mm² vs 16 mm² (tmax = (94.5 × 16 / 2,309)² = 0.4287 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.120 × √(0.822² + 0.0751²) + 0.120 × √(2.45² + 0.0805²) (earth 16 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0991 + 0.2942 = 0.4932 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.4932 = 468.2 A; IN,EFL = 468.2 / 5 = 93.65 A (Zs,max for a 80 A device = 400/√3 / (80 × 5)). The 1.17× margin over the 80 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.4932 vs limit 0.5774 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 152.64, IN,EFL 93.65) = 93.65 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 80 A; IL,prot = 80 / 1 = 80.00 A. IB ≤ IN ≤ IZ: 80.00 ≤ 80 ≤ 152.64 A PASS |
| Envelope | IL,max = min(152.64, 130.34, 80.00) = 80.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 80.00 × 0.85 / 1000 = 47.11 kW (electrical input); motor output Pmax × η = 47.11 × 0.95 = 44.76 kW; Smax = √3 × 400 × 80.00 / 1000 = 55.43 kVA; losses 3 I²R at 90 °C = 1,894 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 12 of 16 preferred loads conform; largest 37 kW (66.1 A on a 80 A device, 43.3 % of IZ, Vd 2.54 %). First to fail: 45 kW (80.4 A, 100 A device) on earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 80.00 A = 47.11 kW on a 80 A device; governing: earth fault loop impedance. Power loss (4.02%) is significant Earth fault trip margin is limited (1.17x) The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load Consider larger conductor to reduce energy losses Confirm the device's pickup tolerance and operating time at this fault current |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 50 mm² Al XLPE with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 120 m at 400 V, PF 0.85, design factor 1: base rating 159 A (Table 14 column 24 row 50), derating Table 27(2) 90 °C conductor column row 25 = 1; Table 28(1) column 3 row 0.8 = 0.96; Table 29 column 2 row 1.2 = 1 → I_Z = 159 × 1 × 0.96 × 1 = 152.64 A, I_L,CCC = 152.64 A; Rc = 0.822 Ω/km (Table 35, Column 10), Xc = 0.0751 Ω/km (Table 30, Column 10): Z_eff = 0.822·0.85 + 0.0751·0.5268 = 0.73826 Ω/km, V_d/I = √3·0.12·0.73826 = 0.15344 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.15344 × 1) = 130.34 A; k = 94.5 (Table 52 row 90), t = (94.5·50/10000)² = 0.2233 s vs 0.1 s (holds); Z_loop = 0.1 + 0.12·√(0.822² + 0.0751²) + 0.12·√(2.45² + 0.0805²) (earth: R from Table 35, X from Table 30 at 16 mm²) = 0.1 + 0.0991 + 0.2942 = 0.4932 Ω, I_fault = 400/√3/0.4932 = 468.2 A, /5 = 93.65 A; I_N,max = min(152.64, 93.65) = 93.65 A → largest preferred rating 80 A, I_L,prot = 80.00 A; I_L,max = min(152.64, 130.34, 80.00) = 80.00 A = √3·400·80.00·0.85/1000 = 47.11 kW input (44.76 kW motor output at η 0.95; 55.43 kVA); earth: 16 mm² vs Table 5.1 minimum 16 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/94.5 = 4.89 mm² (holds); governing earth_fault_loop_impedance; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 90 kW (160.87 A, the first above I_Z/k_design), largest conforming 37 kW. (validation case c0043-50mm2-al-direct-buried-120m) |
Example 13 — 70 mm² single-core trefoil, two circuits on tray at 415 V
Single-core trefoil cables on a perforated tray use the single-core tray grouping table; a 35 mm² earth is supplied.
Given: 70 mm² copper XLPE (X-90) fixed single-core (trefoil) cable with a 35 mm² earth (given), 60 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 2 circuits per tier; air ambient 40 °C. Supply 415 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 8, column 2, row 70: 282 A. Derating Table 23, column 15, row 2: 0.970; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 0.970. IZ = 282 × 0.970 = 273.54 A; IL,CCC = 273.54 / 1 = 273.54 A. At the envelope Idesign = 250.00 A vs IZ 273.54 A PASS |
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| Limit 2 — voltage drop | Rc = 0.342 Ω/km (Table 34, column 6, row 70), Xc = 0.0893 Ω/km (Table 30, column 4, row 70). Zeff = 0.342 × 0.85 + 0.0893 × 0.527 = 0.3377 Ω/km; Vd/I = √3 × 0.060 × 0.3377 = 0.03510 V/A; Vd,max = 5 % × 415 = 20.75 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.75 / (0.03510 × 1) = 591.18 A. At the envelope Vd = 2.11 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 70)² / 10,000² = 1.0020 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 1.0020 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 70 mm² phase conductor: 25 mm²; earth 35 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 415/√3 / 0.1 = 2,396 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,396 × √0.04 / 143 = 3.35 mm² vs 35 mm² (tmax = (143 × 35 / 2,396)² = 4.3635 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.060 × √(0.342² + 0.0893²) + 0.060 × √(0.668² + 0.0982²) (earth 35 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0212 + 0.0405 = 0.1617 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 415/√3 / 0.1617 = 1,481.6 A; IN,EFL = 1,481.6 / 5 = 296.32 A (Zs,max for a 250 A device = 415/√3 / (250 × 5)). The 1.19× margin over the 250 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1617 vs limit 0.1917 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 273.54, IN,EFL 296.32) = 273.54 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 250 A; IL,prot = 250 / 1 = 250.00 A. IB ≤ IN ≤ IZ: 250.00 ≤ 250 ≤ 273.54 A PASS |
| Envelope | IL,max = min(273.54, 591.18, 250.00) = 250.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 415 × 250.00 × 0.85 / 1000 = 152.75 kW (electrical input); motor output Pmax × η = 152.75 × 0.95 = 145.11 kW; Smax = √3 × 415 × 250.00 / 1000 = 179.70 kVA; losses 3 I²R at 90 °C = 3,848 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 415 × 0.85 × 0.95). 18 of 19 preferred loads conform; largest 132 kW (227.4 A on a 250 A device, 83.1 % of IZ, Vd 1.92 %). First to fail: 160 kW (275.7 A, 315 A device) on current carrying capacity, earth fault loop impedance, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 250.00 A = 152.75 kW on a 250 A device; governing: ocpd coordination. Cable utilization is very high (91.4%) - limited margin for load growth Earth fault trip margin is limited (1.19x) Confirm the device's pickup tolerance and operating time at this fault current |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 70 mm² Cu XLPE with a 35 mm² earth (user) over 60 m at 415 V, PF 0.85, design factor 1: base rating 282 A (Table 8 column 2 row 70), derating Table 23 column 15 row 2 = 0.97; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 282 × 0.97 × 1 = 273.54 A, I_L,CCC = 273.54 A; Rc = 0.342 Ω/km (Table 34, Column 6), Xc = 0.0893 Ω/km (Table 30, Column 4): Z_eff = 0.342·0.85 + 0.0893·0.5268 = 0.33774 Ω/km, V_d/I = √3·0.06·0.33774 = 0.03510 V/A, 5 % of 415 V = 20.75 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.75 / (0.03510 × 1) = 591.18 A; k = 143 (Table 52 row 90), t = (143·70/10000)² = 1.0020 s vs 0.1 s (holds); Z_loop = 0.1 + 0.06·√(0.342² + 0.0893²) + 0.06·√(0.668² + 0.0982²) (earth: R from Table 34, X from Table 30 at 35 mm²) = 0.1 + 0.0212 + 0.0405 = 0.1617 Ω, I_fault = 415/√3/0.1617 = 1481.6 A, /5 = 296.32 A; I_N,max = min(273.54, 296.32) = 273.54 A → largest preferred rating 250 A, I_L,prot = 250.00 A; I_L,max = min(273.54, 591.18, 250.00) = 250.00 A = √3·415·250.00·0.85/1000 = 152.75 kW input (145.11 kW motor output at η 0.95; 179.70 kVA); earth: 35 mm² vs Table 5.1 minimum 25 mm² (holds), near-end I_ef = (415/√3)/0.1 = 2396 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2396·√0.04/143 = 3.35 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 160 kW (275.66 A, the first above I_Z/k_design), largest conforming 132 kW. (validation case c0043-70mm2-single-core-trefoil-tray-2-circuits) |
Example 14 — 95 mm² elastomeric (EPR) on a ladder
The 110 °C elastomer rating column and its k value; the earth-fault loop, not the cable capacity, sets the device.
Given: 95 mm² copper elastomeric (EPR, 110 °C) fixed multicore cable with a 25 mm² earth (given), 70 m, unenclosed on ladder, racks or cleats, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 15, column 2, row 95: 337 A. Derating Table 24, column 16, row 1: 1.00; Table 27(1), 110 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 337 × 1.00 = 337.00 A; IL,CCC = 337.00 / 1 = 337.00 A. At the envelope Idesign = 200.00 A vs IZ 337.00 A PASS |
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| Limit 2 — voltage drop | Rc = 0.262 Ω/km (Table 35, column 6, row 95), Xc = 0.0790 Ω/km (Table 30, column 8, row 95). Zeff = 0.262 × 0.85 + 0.0790 × 0.527 = 0.2643 Ω/km; Vd/I = √3 × 0.070 × 0.2643 = 0.03205 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.03205 × 1) = 624.09 A. At the envelope Vd = 1.60 % vs 5 % PASS |
| Short circuit | k = 132 (Table 52, row 110). tmax = (132 × 95)² / 10,000² = 1.5725 s; Smin = 10,000 × √0.1 / 132 = 24.0 mm² → 0.1000 vs limit 1.5725 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 132 = 3.50 mm² vs 25 mm² (tmax = (132 × 25 / 2,309)² = 2.0419 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.070 × √(0.262² + 0.0790²) + 0.070 × √(0.984² + 0.0895²) (earth 25 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0192 + 0.0692 = 0.1883 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 110 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.1883 = 1,226.3 A; IN,EFL = 1,226.3 / 5 = 245.26 A (Zs,max for a 200 A device = 400/√3 / (200 × 5)). The 1.23× margin over the 200 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1883 vs limit 0.2309 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 337.00, IN,EFL 245.26) = 245.26 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 200 A; IL,prot = 200 / 1 = 200.00 A. IB ≤ IN ≤ IZ: 200.00 ≤ 200 ≤ 337.00 A PASS |
| Envelope | IL,max = min(337.00, 624.09, 200.00) = 200.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 200.00 × 0.85 / 1000 = 117.78 kW (electrical input); motor output Pmax × η = 117.78 × 0.95 = 111.89 kW; Smax = √3 × 400 × 200.00 / 1000 = 138.56 kVA; losses 3 I²R at 110 °C = 2,201 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 17 of 20 preferred loads conform; largest 110 kW (196.6 A on a 200 A device, 58.3 % of IZ, Vd 1.57 %). First to fail: 132 kW (235.9 A, 250 A device) on earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 200.00 A = 117.78 kW on a 200 A device; governing: earth fault loop impedance. The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 95 mm² Cu EPR with a 25 mm² earth (user) over 70 m at 400 V, PF 0.85, design factor 1: base rating 337 A (Table 15 column 2 row 95), derating Table 24 column 16 row 1 = 1; Table 27(1) 110 °C conductor column row 40 = 1 → I_Z = 337 × 1 × 1 = 337.00 A, I_L,CCC = 337.00 A; Rc = 0.262 Ω/km (Table 35, Column 6), Xc = 0.079 Ω/km (Table 30, Column 8): Z_eff = 0.262·0.85 + 0.079·0.5268 = 0.26432 Ω/km, V_d/I = √3·0.07·0.26432 = 0.03205 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.03205 × 1) = 624.09 A; k = 132 (Table 52 row 110), t = (132·95/10000)² = 1.5725 s vs 0.1 s (holds); Z_loop = 0.1 + 0.07·√(0.262² + 0.079²) + 0.07·√(0.984² + 0.0895²) (earth: R from Table 35, X from Table 30 at 25 mm²) = 0.1 + 0.0192 + 0.0692 = 0.1883 Ω, I_fault = 400/√3/0.1883 = 1226.3 A, /5 = 245.26 A; I_N,max = min(337.00, 245.26) = 245.26 A → largest preferred rating 200 A, I_L,prot = 200.00 A; I_L,max = min(337.00, 624.09, 200.00) = 200.00 A = √3·400·200.00·0.85/1000 = 117.78 kW input (111.89 kW motor output at η 0.95; 138.56 kVA); earth: 25 mm² vs Table 5.1 minimum 25 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/132 = 3.50 mm² (holds); governing earth_fault_loop_impedance; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 200 kW (357.49 A, the first above I_Z/k_design), largest conforming 110 kW. (validation case c0043-95mm2-epr-ladder-spaced) |
Example 15 — 120 mm² aluminium in buried conduits, three circuits 0.3 m apart
Buried-conduit grouping at 0.3 m spacing, 30 °C soil and 1.0 m depth all derate an aluminium multicore cable.
Given: 120 mm² aluminium XLPE (X-90) fixed multicore cable with a 35 mm² earth (given), 150 m, in buried conduit, 3 circuits spaced 0.3 m; soil 30 °C, depth 1 m, thermal resistivity 1 K·m/W. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 27, row 120: 210 A. Derating Table 26(2), column 3, row 3: 0.910; Table 27(2), 90 °C conductor column, row 30: 0.970; Table 28(2), column 3, row 1: 0.960; Table 29, column 4, row 1: 1.03 → F = 0.873. IZ = 210 × 0.873 = 183.29 A; IL,CCC = 183.29 / 1 = 183.29 A. At the envelope Idesign = 125.00 A vs IZ 183.29 A PASS |
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| Limit 2 — voltage drop | Rc = 0.325 Ω/km (Table 35, column 10, row 120), Xc = 0.0713 Ω/km (Table 30, column 10, row 120). Zeff = 0.325 × 0.85 + 0.0713 × 0.527 = 0.3138 Ω/km; Vd/I = √3 × 0.150 × 0.3138 = 0.08153 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.08153 × 1) = 245.31 A. At the envelope Vd = 2.55 % vs 5 % PASS |
| Short circuit | k = 94.5 (Table 52, row 90). tmax = (94.5 × 120)² / 10,000² = 1.2860 s; Smin = 10,000 × √0.1 / 94.5 = 33.5 mm² → 0.1000 vs limit 1.2860 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 120 mm² phase conductor: 35 mm²; earth 35 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 94.5 = 4.89 mm² vs 35 mm² (tmax = (94.5 × 35 / 2,309)² = 2.0512 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.150 × √(0.325² + 0.0713²) + 0.150 × √(1.11² + 0.0786²) (earth 35 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0499 + 0.1669 = 0.3168 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.3168 = 728.9 A; IN,EFL = 728.9 / 5 = 145.78 A (Zs,max for a 125 A device = 400/√3 / (125 × 5)). The 1.17× margin over the 125 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.3168 vs limit 0.3695 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 183.29, IN,EFL 145.78) = 145.78 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 125 A; IL,prot = 125 / 1 = 125.00 A. IB ≤ IN ≤ IZ: 125.00 ≤ 125 ≤ 183.29 A PASS |
| Envelope | IL,max = min(183.29, 245.31, 125.00) = 125.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 125.00 × 0.85 / 1000 = 73.61 kW (electrical input); motor output Pmax × η = 73.61 × 0.95 = 69.93 kW; Smax = √3 × 400 × 125.00 / 1000 = 86.60 kVA; losses 3 I²R at 90 °C = 2,285 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 14 of 17 preferred loads conform; largest 55 kW (98.3 A on a 100 A device, 53.6 % of IZ, Vd 2.00 %). First to fail: 75 kW (134.1 A, 160 A device) on earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 125.00 A = 73.61 kW on a 125 A device; governing: earth fault loop impedance. Power loss (3.10%) is significant Earth fault trip margin is limited (1.17x) The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load Consider larger conductor to reduce energy losses Confirm the device's pickup tolerance and operating time at this fault current |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 120 mm² Al XLPE with a 35 mm² earth (user) over 150 m at 400 V, PF 0.85, design factor 1: base rating 210 A (Table 14 column 27 row 120), derating Table 26(2) column 3 row 3 = 0.91; Table 27(2) 90 °C conductor column row 30 = 0.97; Table 28(2) column 3 row 1 = 0.96; Table 29 column 4 row 1 = 1.03 → I_Z = 210 × 0.91 × 0.97 × 0.96 × 1.03 = 183.29 A, I_L,CCC = 183.29 A; Rc = 0.325 Ω/km (Table 35, Column 10), Xc = 0.0713 Ω/km (Table 30, Column 10): Z_eff = 0.325·0.85 + 0.0713·0.5268 = 0.31381 Ω/km, V_d/I = √3·0.15·0.31381 = 0.08153 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.08153 × 1) = 245.31 A; k = 94.5 (Table 52 row 90), t = (94.5·120/10000)² = 1.2860 s vs 0.1 s (holds); Z_loop = 0.1 + 0.15·√(0.325² + 0.0713²) + 0.15·√(1.11² + 0.0786²) (earth: R from Table 35, X from Table 30 at 35 mm²) = 0.1 + 0.0499 + 0.1669 = 0.3168 Ω, I_fault = 400/√3/0.3168 = 728.9 A, /5 = 145.78 A; I_N,max = min(183.29, 145.78) = 145.78 A → largest preferred rating 125 A, I_L,prot = 125.00 A; I_L,max = min(183.29, 245.31, 125.00) = 125.00 A = √3·400·125.00·0.85/1000 = 73.61 kW input (69.93 kW motor output at η 0.95; 86.60 kVA); earth: 35 mm² vs Table 5.1 minimum 35 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/94.5 = 4.89 mm² (holds); governing earth_fault_loop_impedance; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 110 kW (196.62 A, the first above I_Z/k_design), largest conforming 55 kW. (validation case c0043-120mm2-al-buried-conduit-3-spaced) |
Example 16 — 150 mm² single-core flat touching on a ladder, 25 kA
Single-core cables laid flat and touching on a ladder (Table 30 flat-touching reactance) with a 25 kA fault level cleared in 0.2 s and a stiff 0.02 Ω source.
Given: 150 mm² copper XLPE (X-90) fixed single-core (flat touching) cable with a 70 mm² earth (given), 100 m, unenclosed on ladder, racks or cleats, spaced, 1 tier, 1 circuit per tier; air ambient 40 °C. Supply 415 V three-phase; loads at PF 0.9 lagging, design factor 1. Protection: prospective fault 25 kA cleared in 0.2 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 8, column 2, row 150: 472 A. Derating Table 23, column 18, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 472 × 1.00 = 472.00 A; IL,CCC = 472.00 / 1 = 472.00 A. At the envelope Idesign = 400.00 A vs IZ 472.00 A PASS |
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| Limit 2 — voltage drop | Rc = 0.160 Ω/km (Table 34, column 6, row 150), Xc = 0.0996 Ω/km (Table 30, column 7, row 150). Zeff = 0.160 × 0.9 + 0.0996 × 0.436 = 0.1874 Ω/km; Vd/I = √3 × 0.100 × 0.1874 = 0.03246 V/A; Vd,max = 5 % × 415 = 20.75 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.75 / (0.03246 × 1) = 639.23 A. At the envelope Vd = 3.13 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 150)² / 25,000² = 0.7362 s; Smin = 25,000 × √0.2 / 143 = 78.2 mm² → 0.2000 vs limit 0.7362 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 150 mm² phase conductor: 50 mm²; earth 70 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 415/√3 / 0.02 = 11,980 A, cleared in tef = 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). Smin = Ief × √tef / k = 11,980 × √0.04 / 143 = 16.76 mm² vs 70 mm² (tmax = (143 × 70 / 11,980)² = 0.6982 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.02 + 0.100 × √(0.160² + 0.0996²) + 0.100 × √(0.342² + 0.104²) (earth 70 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.02 + 0.0188 + 0.0357 = 0.0746 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 415/√3 / 0.0746 = 3,212.1 A; IN,EFL = 3,212.1 / 5 = 642.42 A (Zs,max for a 400 A device = 415/√3 / (400 × 5)). The 1.61× margin over the 400 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.0746 vs limit 0.1198 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 472.00, IN,EFL 642.42) = 472.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 400 A; IL,prot = 400 / 1 = 400.00 A. IB ≤ IN ≤ IZ: 400.00 ≤ 400 ≤ 472.00 A PASS |
| Envelope | IL,max = min(472.00, 639.23, 400.00) = 400.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 415 × 400.00 × 0.9 / 1000 = 258.77 kW (electrical input); motor output Pmax × η = 258.77 × 0.95 = 245.83 kW; Smax = √3 × 415 × 400.00 / 1000 = 287.52 kVA; losses 3 I²R at 90 °C = 7,680 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 415 × 0.9 × 0.95). 20 of 22 preferred loads conform; largest 200 kW (325.4 A on a 400 A device, 68.9 % of IZ, Vd 2.54 %). First to fail: 250 kW (406.8 A, 500 A device) on ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 400.00 A = 258.77 kW on a 400 A device; governing: ocpd coordination. Cable utilization is elevated (84.7%) - monitor for load changes |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 150 mm² Cu XLPE with a 70 mm² earth (user) over 100 m at 415 V, PF 0.9, design factor 1: base rating 472 A (Table 8 column 2 row 150), derating Table 23 column 18 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 472 × 1 × 1 = 472.00 A, I_L,CCC = 472.00 A; Rc = 0.16 Ω/km (Table 34, Column 6), Xc = 0.0996 Ω/km (Table 30, Column 7): Z_eff = 0.16·0.9 + 0.0996·0.4359 = 0.18741 Ω/km, V_d/I = √3·0.1·0.18741 = 0.03246 V/A, 5 % of 415 V = 20.75 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.75 / (0.03246 × 1) = 639.23 A; k = 143 (Table 52 row 90), t = (143·150/25000)² = 0.7362 s vs 0.2 s (holds); Z_loop = 0.02 + 0.1·√(0.16² + 0.0996²) + 0.1·√(0.342² + 0.104²) (earth: R from Table 34, X from Table 30 at 70 mm²) = 0.02 + 0.0188 + 0.0357 = 0.0746 Ω, I_fault = 415/√3/0.0746 = 3212.1 A, /5 = 642.42 A; I_N,max = min(472.00, 642.42) = 472.00 A → largest preferred rating 400 A, I_L,prot = 400.00 A; I_L,max = min(472.00, 639.23, 400.00) = 400.00 A = √3·415·400.00·0.9/1000 = 258.77 kW input (245.83 kW motor output at η 0.95; 287.52 kVA); earth: 70 mm² vs Table 5.1 minimum 50 mm² (holds), near-end I_ef = (415/√3)/0.02 = 11980 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 11980·√0.04/143 = 16.76 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 315 kW (512.55 A, the first above I_Z/k_design), largest conforming 200 kW. (validation case c0043-150mm2-single-core-flat-touching-ladder) |
Example 17 — 185 mm² PVC with a leading power factor over 200 m
A leading power factor subtracts the reactive term, reducing the drop; at PF 0.95 on 185 mm² the voltage still drops (a rise needs X·sinφ > R·cosφ).
Given: 185 mm² copper PVC (V-75) fixed multicore cable with a 70 mm² earth (given), 200 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.95 leading, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 13, column 2, row 185: 348 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 75 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 348 × 1.00 = 348.00 A; IL,CCC = 348.00 / 1 = 348.00 A. At the envelope Idesign = 200.00 A vs IZ 348.00 A PASS |
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| Limit 2 — voltage drop | Rc = 0.123 Ω/km (Table 35, column 4, row 185), Xc = 0.0744 Ω/km (Table 30, column 9, row 185). Zeff = 0.123 × 0.95 − 0.0744 × 0.312 = 0.09362 Ω/km (leading: the reactive term subtracts, reducing the drop); Vd/I = √3 × 0.200 × 0.09362 = 0.03243 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.03243 × 1) = 616.70 A. At the envelope Vd = 1.62 % vs 5 % PASS |
| Short circuit | k = 111 (Table 52, row 75). tmax = (111 × 185)² / 10,000² = 4.2169 s; Smin = 10,000 × √0.1 / 111 = 28.5 mm² → 0.1000 vs limit 4.2169 s 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: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 111 = 4.16 mm² vs 70 mm² (tmax = (111 × 70 / 2,309)² = 11.3199 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.200 × √(0.123² + 0.0744²) + 0.200 × √(0.327² + 0.0770²) (earth 70 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0288 + 0.0672 = 0.1959 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 75 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.1959 = 1,178.6 A; IN,EFL = 1,178.6 / 5 = 235.73 A (Zs,max for a 200 A device = 400/√3 / (200 × 5)). The 1.18× margin over the 200 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1959 vs limit 0.2309 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 348.00, IN,EFL 235.73) = 235.73 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 200 A; IL,prot = 200 / 1 = 200.00 A. IB ≤ IN ≤ IZ: 200.00 ≤ 200 ≤ 348.00 A PASS |
| Envelope | IL,max = min(348.00, 616.70, 200.00) = 200.00 A (Earth Fault Loop (I_N ≤ I_fault / k_mag)); Pmax = √3 × 400 × 200.00 × 0.95 / 1000 = 131.64 kW (electrical input); motor output Pmax × η = 131.64 × 0.95 = 125.05 kW; Smax = √3 × 400 × 200.00 / 1000 = 138.56 kVA; losses 3 I²R at 75 °C = 2,952 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.95 × 0.95). 17 of 21 preferred loads conform; largest 110 kW (175.9 A on a 200 A device, 50.6 % of IZ, Vd 1.43 %). First to fail: 132 kW (211.1 A, 250 A device) on earth fault loop impedance. |
| Result | 7/7 checks pass → PASS; permissible load 200.00 A = 131.64 kW on a 200 A device; governing: earth fault loop impedance. Earth fault trip margin is limited (1.18x) The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load Confirm the device's pickup tolerance and operating time at this fault current |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 185 mm² Cu PVC with a 70 mm² earth (user) over 200 m at 400 V, PF 0.95 leading, design factor 1: base rating 348 A (Table 13 column 2 row 185), derating Table 24 column 10 row 1 = 1; Table 27(1) 75 °C conductor column row 40 = 1 → I_Z = 348 × 1 × 1 = 348.00 A, I_L,CCC = 348.00 A; Rc = 0.123 Ω/km (Table 35, Column 4), Xc = 0.0744 Ω/km (Table 30, Column 9): Z_eff = 0.123·0.95 − 0.0744·0.3122 = 0.09362 Ω/km, V_d/I = √3·0.2·0.09362 = 0.03243 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.03243 × 1) = 616.70 A; k = 111 (Table 52 row 75), t = (111·185/10000)² = 4.2169 s vs 0.1 s (holds); Z_loop = 0.1 + 0.2·√(0.123² + 0.0744²) + 0.2·√(0.327² + 0.077²) (earth: R from Table 35, X from Table 30 at 70 mm²) = 0.1 + 0.0288 + 0.0672 = 0.1959 Ω, I_fault = 400/√3/0.1959 = 1178.6 A, /5 = 235.73 A; I_N,max = min(348.00, 235.73) = 235.73 A → largest preferred rating 200 A, I_L,prot = 200.00 A; I_L,max = min(348.00, 616.70, 200.00) = 200.00 A = √3·400·200.00·0.95/1000 = 131.64 kW input (125.05 kW motor output at η 0.95; 138.56 kVA); earth: 70 mm² vs Table 5.1 minimum 70 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/111 = 4.16 mm² (holds); governing earth_fault_loop_impedance; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 250 kW (399.83 A, the first above I_Z/k_design), largest conforming 110 kW. (validation case c0043-185mm2-pvc-leading-pf-200m) |
Example 18 — 240 mm² aluminium flat touching at 690 V over 300 m
A 690 V feeder on unperforated tray where voltage drop governs ahead of the 400 A device.
Given: 240 mm² aluminium XLPE (X-90) fixed single-core (flat touching) cable with a 120 mm² earth (given), 300 m, unenclosed on unperforated tray, spaced, 1 tier, 1 circuit per tier; air ambient 40 °C. Supply 690 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 20 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 8, column 4, row 240: 513 A. Derating Table 23, column 12, row 1: 0.950; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 0.950. IZ = 513 × 0.950 = 487.35 A; IL,CCC = 487.35 / 1 = 487.35 A. At the envelope Idesign = 351.67 A vs IZ 487.35 A PASS |
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| Limit 2 — voltage drop | Rc = 0.162 Ω/km (Table 34, column 12, row 240), Xc = 0.0970 Ω/km (Table 30, column 7, row 240). Zeff = 0.162 × 0.85 + 0.0970 × 0.527 = 0.1888 Ω/km; Vd/I = √3 × 0.300 × 0.1888 = 0.09810 V/A; Vd,max = 5 % × 690 = 34.50 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 34.50 / (0.09810 × 1) = 351.67 A. At the envelope Vd = 5.00 % vs 5 % PASS |
| Short circuit | k = 94.5 (Table 52, row 90). tmax = (94.5 × 240)² / 20,000² = 1.2860 s; Smin = 20,000 × √0.1 / 94.5 = 66.9 mm² → 0.1000 vs limit 1.2860 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 240 mm² phase conductor: 95 mm²; earth 120 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 690/√3 / 0.02 = 19,919 A, cleared in tef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 94.5 (separate earth cable, taken at the phase conductor's Table 52 k as if it started at the insulation's operating temperature: conservative). Smin = Ief × √tef / k = 19,919 × √0.04 / 94.5 = 42.16 mm² vs 120 mm² (tmax = (94.5 × 120 / 19,919)² = 0.3241 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.02 + 0.300 × √(0.162² + 0.0970²) + 0.300 × √(0.325² + 0.0996²) (earth 120 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.02 + 0.0566 + 0.1020 = 0.1786 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 690/√3 / 0.1786 = 2,230.3 A; IN,EFL = 2,230.3 / 5 = 446.05 A (Zs,max for a 400 A device = 690/√3 / (400 × 5)). The 1.12× margin over the 400 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1786 vs limit 0.1992 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 487.35, IN,EFL 446.05) = 446.05 A, limited by the earth fault loop (I_N ≤ I_fault / k_mag) → largest preferred rating 400 A; IL,prot = 400 / 1 = 400.00 A. IB ≤ IN ≤ IZ: 351.67 ≤ 400 ≤ 487.35 A PASS |
| Envelope | IL,max = min(487.35, 351.67, 400.00) = 351.67 A (Voltage Drop); Pmax = √3 × 690 × 351.67 × 0.85 / 1000 = 357.25 kW (electrical input); motor output Pmax × η = 357.25 × 0.95 = 339.38 kW; Smax = √3 × 690 × 351.67 / 1000 = 420.29 kVA; losses 3 I²R at 90 °C = 18,032 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 690 × 0.85 × 0.95). 22 of 24 preferred loads conform; largest 315 kW (326.4 A on a 400 A device, 67.0 % of IZ, Vd 4.64 %). First to fail: 400 kW (414.5 A, 500 A device) on voltage drop, earth fault loop impedance, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 351.67 A = 357.25 kW on a 400 A device; governing: voltage drop. Power loss (5.05%) is significant Earth fault trip margin is limited (1.12x) Voltage drop governs: a shorter route or a larger conductor raises the permissible load Consider larger conductor to reduce energy losses Confirm the device's pickup tolerance and operating time at this fault current |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 240 mm² Al XLPE with a 120 mm² earth (user) over 300 m at 690 V, PF 0.85, design factor 1: base rating 513 A (Table 8 column 4 row 240), derating Table 23 column 12 row 1 = 0.95; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 513 × 0.95 × 1 = 487.35 A, I_L,CCC = 487.35 A; Rc = 0.162 Ω/km (Table 34, Column 12), Xc = 0.097 Ω/km (Table 30, Column 7): Z_eff = 0.162·0.85 + 0.097·0.5268 = 0.18880 Ω/km, V_d/I = √3·0.3·0.18880 = 0.09810 V/A, 5 % of 690 V = 34.50 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 34.50 / (0.09810 × 1) = 351.67 A; k = 94.5 (Table 52 row 90), t = (94.5·240/20000)² = 1.2860 s vs 0.1 s (holds); Z_loop = 0.02 + 0.3·√(0.162² + 0.097²) + 0.3·√(0.325² + 0.0996²) (earth: R from Table 34, X from Table 30 at 120 mm²) = 0.02 + 0.0566 + 0.1020 = 0.1786 Ω, I_fault = 690/√3/0.1786 = 2230.3 A, /5 = 446.05 A; I_N,max = min(487.35, 446.05) = 446.05 A → largest preferred rating 400 A, I_L,prot = 400.00 A; I_L,max = min(487.35, 351.67, 400.00) = 351.67 A = √3·690·351.67·0.85/1000 = 357.25 kW input (339.38 kW motor output at η 0.95; 420.29 kVA); earth: 120 mm² vs Table 5.1 minimum 95 mm² (holds), near-end I_ef = (690/√3)/0.02 = 19919 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 19919·√0.04/94.5 = 42.16 mm² (holds); governing voltage_drop; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 500 kW (518.10 A, the first above I_Z/k_design), largest conforming 315 kW. (validation case c0043-240mm2-al-single-core-flat-touching-690v) |
Example 19 — 300 mm² at 50 kA cleared in 1 s: withstand fails
The adiabatic withstand time is shorter than the clearing time, so there is no permissible load whatever the other limits say.
Given: 300 mm² copper XLPE (X-90) fixed multicore cable with a 150 mm² earth (given), 40 m, unenclosed on ladder, racks or cleats, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 50 kA cleared in 1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.01 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 300: 584 A. Derating Table 24, column 16, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 584 × 1.00 = 584.00 A; IL,CCC = 584.00 / 1 = 584.00 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
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| Limit 2 — voltage drop | Rc = 0.0812 Ω/km (Table 35, column 5, row 300), Xc = 0.0704 Ω/km (Table 30, column 10, row 300). Zeff = 0.0812 × 0.85 + 0.0704 × 0.527 = 0.1061 Ω/km; Vd/I = √3 × 0.040 × 0.1061 = 0.007351 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.007351 × 1) = 2,720.64 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 300)² / 50,000² = 0.7362 s; Smin = 50,000 × √1 / 143 = 349.7 mm² → 1.0000 vs limit 0.7362 s FAIL |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 300 mm² phase conductor: 120 mm²; earth 150 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.01 = 23,094 A, cleared in tef = 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). Smin = Ief × √tef / k = 23,094 × √0.04 / 143 = 32.30 mm² vs 150 mm² (tmax = (143 × 150 / 23,094)² = 0.8627 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.01 + 0.040 × √(0.0812² + 0.0704²) + 0.040 × √(0.160² + 0.0718²) (earth 150 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.01 + 0.0043 + 0.0070 = 0.0213 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.0213 = 10,835.3 A; IN,EFL = 10,835.3 / 5 = 2,167.06 A (Zs,max for a 500 A device = 400/√3 / (500 × 5)). The 4.33× margin over the 500 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.0213 vs limit 0.0924 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 584.00, IN,EFL 2,167.06) = 584.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 500 A; IL,prot = 500 / 1 = 500.00 A. IB ≤ IN ≤ IZ: 0.00 ≤ 500 ≤ 584.00 A INFO |
| Envelope | min(584.00, 2,720.64, 500.00) = 500.00 A would hold for the load-dependent checks, but the short-circuit withstand check does not depend on the load and fails, so there is no permissible load: IL,max = 0 A |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 0 of 23 preferred loads conform. First to fail: 1.5 kW (2.7 A, 6 A device) on short circuit withstand. |
| Result | 3/4 checks pass → FAIL; no permissible load; governing: short circuit withstand. Insufficient withstand: 0.736s < 1.0s |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 300 mm² Cu XLPE with a 150 mm² earth (user) over 40 m at 400 V, PF 0.85, design factor 1: base rating 584 A (Table 14 column 2 row 300), derating Table 24 column 16 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 584 × 1 × 1 = 584.00 A, I_L,CCC = 584.00 A; Rc = 0.0812 Ω/km (Table 35, Column 5), Xc = 0.0704 Ω/km (Table 30, Column 10): Z_eff = 0.0812·0.85 + 0.0704·0.5268 = 0.10611 Ω/km, V_d/I = √3·0.04·0.10611 = 0.00735 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.00735 × 1) = 2720.64 A; k = 143 (Table 52 row 90), t = (143·300/50000)² = 0.7362 s vs 1 s (FAILS); Z_loop = 0.01 + 0.04·√(0.0812² + 0.0704²) + 0.04·√(0.16² + 0.0718²) (earth: R from Table 35, X from Table 30 at 150 mm²) = 0.01 + 0.0043 + 0.0070 = 0.0213 Ω, I_fault = 400/√3/0.0213 = 10835.3 A, /5 = 2167.06 A; I_N,max = min(584.00, 2167.06) = 584.00 A → largest preferred rating 500 A, I_L,prot = 500.00 A; min(584.00, 2720.64, 500.00) = 500.00 A, but the short-circuit withstand fails independently of the load, so I_L,max = 0 A (0 kW, 0 kVA; capacity, voltage drop and overload coordination not evaluated); earth: 150 mm² vs Table 5.1 minimum 120 mm² (holds), near-end I_ef = (400/√3)/0.01 = 23094 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 23094·√0.04/143 = 32.30 mm² (holds); governing short_circuit_withstand — no permissible load; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 400 kW (714.98 A, the first above I_Z/k_design), none conforms. (validation case c0043-300mm2-50ka-1s-withstand-fails) |
Example 20 — 400 mm² on perforated tray at 45 °C, 36 kA
Largest tabulated multicore size: ambient derating at 45 °C and a 630 A device within the cable capacity.
Given: 400 mm² copper XLPE (X-90) fixed multicore cable with a 120 mm² earth (given), 40 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 45 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 36 kA cleared in 0.4 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.012 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 400: 692 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 45: 0.940 → F = 0.940. IZ = 692 × 0.940 = 650.48 A; IL,CCC = 650.48 / 1 = 650.48 A. At the envelope Idesign = 630.00 A vs IZ 650.48 A PASS |
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| Limit 2 — voltage drop | Rc = 0.0656 Ω/km (Table 35, column 5, row 400), Xc = 0.0702 Ω/km (Table 30, column 10, row 400). Zeff = 0.0656 × 0.85 + 0.0702 × 0.527 = 0.09274 Ω/km; Vd/I = √3 × 0.040 × 0.09274 = 0.006425 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.006425 × 1) = 3,112.73 A. At the envelope Vd = 1.01 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 400)² / 36,000² = 2.5246 s; Smin = 36,000 × √0.4 / 143 = 159.2 mm² → 0.4000 vs limit 2.5246 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 400 mm² phase conductor: 120 mm²; earth 120 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.012 = 19,245 A, cleared in tef = 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). Smin = Ief × √tef / k = 19,245 × √0.04 / 143 = 26.92 mm² vs 120 mm² (tmax = (143 × 120 / 19,245)² = 0.7951 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.012 + 0.040 × √(0.0656² + 0.0702²) + 0.040 × √(0.197² + 0.0713²) (earth 120 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.012 + 0.0038 + 0.0084 = 0.0242 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.0242 = 9,533.7 A; IN,EFL = 9,533.7 / 5 = 1,906.75 A (Zs,max for a 630 A device = 400/√3 / (630 × 5)). The 3.03× margin over the 630 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.0242 vs limit 0.0733 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 650.48, IN,EFL 1,906.75) = 650.48 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 630 A; IL,prot = 630 / 1 = 630.00 A. IB ≤ IN ≤ IZ: 630.00 ≤ 630 ≤ 650.48 A PASS |
| Envelope | IL,max = min(650.48, 3,112.73, 630.00) = 630.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 630.00 × 0.85 / 1000 = 371.01 kW (electrical input); motor output Pmax × η = 371.01 × 0.95 = 352.46 kW; Smax = √3 × 400 × 630.00 / 1000 = 436.48 kVA; losses 3 I²R at 90 °C = 3,124 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 22 of 23 preferred loads conform; largest 315 kW (563.0 A on a 630 A device, 86.6 % of IZ, Vd 0.90 %). First to fail: 400 kW (715.0 A, 800 A device) on current carrying capacity, ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 630.00 A = 371.01 kW on a 630 A device; governing: ocpd coordination. Cable utilization is very high (96.9%) - limited margin for load growth Consider parallel cables for currents above 500A |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 400 mm² Cu XLPE with a 120 mm² earth (user) over 40 m at 400 V, PF 0.85, design factor 1: base rating 692 A (Table 14 column 2 row 400), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 45 = 0.94 → I_Z = 692 × 1 × 0.94 = 650.48 A, I_L,CCC = 650.48 A; Rc = 0.0656 Ω/km (Table 35, Column 5), Xc = 0.0702 Ω/km (Table 30, Column 10): Z_eff = 0.0656·0.85 + 0.0702·0.5268 = 0.09274 Ω/km, V_d/I = √3·0.04·0.09274 = 0.00643 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.00643 × 1) = 3112.73 A; k = 143 (Table 52 row 90), t = (143·400/36000)² = 2.5246 s vs 0.4 s (holds); Z_loop = 0.012 + 0.04·√(0.0656² + 0.0702²) + 0.04·√(0.197² + 0.0713²) (earth: R from Table 35, X from Table 30 at 120 mm²) = 0.012 + 0.0038 + 0.0084 = 0.0242 Ω, I_fault = 400/√3/0.0242 = 9533.7 A, /5 = 1906.75 A; I_N,max = min(650.48, 1906.75) = 650.48 A → largest preferred rating 630 A, I_L,prot = 630.00 A; I_L,max = min(650.48, 3112.73, 630.00) = 630.00 A = √3·400·630.00·0.85/1000 = 371.01 kW input (352.46 kW motor output at η 0.95; 436.48 kVA); earth: 120 mm² vs Table 5.1 minimum 120 mm² (holds), near-end I_ef = (400/√3)/0.012 = 19245 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 19245·√0.04/143 = 26.92 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 400 kW (714.98 A, the first above I_Z/k_design), largest conforming 315 kW. (validation case c0043-400mm2-tray-45c-36ka) |
Example 21 — 25 mm² on a perforated tray, motor efficiency 0.90
The kW loads table is motor shaft output: at η = 0.90 a 55 kW motor draws 103.8 A, more than the 100 A device the cable allows, so the largest conforming rating drops to 45 kW (at the default 0.95 it is 55 kW, 98.3 A).
Given: 25 mm² copper XLPE (X-90) fixed multicore cable with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum), 50 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.1 s, earth-fault clearing time 0.04 s (default), 5× instantaneous trip, upstream loop impedance 0.1 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.9).
| Limit 1 — capacity | Base rating Table 14, column 2, row 25: 116 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 116 × 1.00 = 116.00 A; IL,CCC = 116.00 / 1 = 116.00 A. At the envelope Idesign = 100.00 A vs IZ 116.00 A PASS |
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| Limit 2 — voltage drop | Rc = 0.927 Ω/km (Table 35, column 5, row 25), Xc = 0.0808 Ω/km (Table 30, column 10, row 25). Zeff = 0.927 × 0.85 + 0.0808 × 0.527 = 0.8305 Ω/km; Vd/I = √3 × 0.050 × 0.8305 = 0.07192 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.07192 × 1) = 278.07 A. At the envelope Vd = 1.80 % vs 5 % PASS |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 25)² / 10,000² = 0.1278 s; Smin = 10,000 × √0.1 / 143 = 22.1 mm² → 0.1000 vs limit 0.1278 s PASS |
| Check 6 — earth size | AS/NZS 3000 Table 5.1 minimum for a 25 mm² phase conductor: 6 mm²; earth 6 mm² PASS |
| Check 7 — earth withstand | Largest earth-fault current, a fault at the cable origin: Ief = 400/√3 / 0.1 = 2,309 A, cleared in tef = 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). Smin = Ief × √tef / k = 2,309 × √0.04 / 143 = 3.23 mm² vs 6 mm² (tmax = (143 × 6 / 2,309)² = 0.1380 s) PASS |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.1 + 0.050 × √(0.927² + 0.0808²) + 0.050 × √(3.93² + 0.0887²) (earth 6 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.1 + 0.0465 + 0.1966 = 0.3431 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.3431 = 673.1 A; IN,EFL = 673.1 / 5 = 134.63 A (Zs,max for a 100 A device = 400/√3 / (100 × 5)). The 1.35× margin over the 100 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.3431 vs limit 0.4619 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 116.00, IN,EFL 134.63) = 116.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 100 A; IL,prot = 100 / 1 = 100.00 A. IB ≤ IN ≤ IZ: 100.00 ≤ 100 ≤ 116.00 A PASS |
| Envelope | IL,max = min(116.00, 278.07, 100.00) = 100.00 A (Device rating (I_N ≤ I_Z, preferred step)); Pmax = √3 × 400 × 100.00 × 0.85 / 1000 = 58.89 kW (electrical input); motor output Pmax × η = 58.89 × 0.9 = 53.00 kW; Smax = √3 × 400 × 100.00 / 1000 = 69.28 kVA; losses 3 I²R at 90 °C = 1,390 W |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.9). 13 of 15 preferred loads conform; largest 45 kW (84.9 A on a 100 A device, 73.2 % of IZ, Vd 1.53 %). First to fail: 55 kW (103.8 A, 125 A device) on ocpd coordination. |
| Result | 7/7 checks pass → PASS; permissible load 100.00 A = 58.89 kW on a 100 A device; governing: ocpd coordination. Cable utilization is elevated (86.2%) - monitor for load changes |
| Reference | Hand calculation with AS/NZS 3008.1.1:2017 tables for 25 mm² Cu XLPE with a 6 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 50 m at 400 V, PF 0.85, design factor 1: base rating 116 A (Table 14 column 2 row 25), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 116 × 1 × 1 = 116.00 A, I_L,CCC = 116.00 A; Rc = 0.927 Ω/km (Table 35, Column 5), Xc = 0.0808 Ω/km (Table 30, Column 10): Z_eff = 0.927·0.85 + 0.0808·0.5268 = 0.83051 Ω/km, V_d/I = √3·0.05·0.83051 = 0.07192 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.07192 × 1) = 278.07 A; k = 143 (Table 52 row 90), t = (143·25/10000)² = 0.1278 s vs 0.1 s (holds); Z_loop = 0.1 + 0.05·√(0.927² + 0.0808²) + 0.05·√(3.93² + 0.0887²) (earth: R from Table 35, X from Table 30 at 6 mm²) = 0.1 + 0.0465 + 0.1966 = 0.3431 Ω, I_fault = 400/√3/0.3431 = 673.1 A, /5 = 134.63 A; I_N,max = min(116.00, 134.63) = 116.00 A → largest preferred rating 100 A, I_L,prot = 100.00 A; I_L,max = min(116.00, 278.07, 100.00) = 100.00 A = √3·400·100.00·0.85/1000 = 58.89 kW input (53.00 kW motor output at η 0.9; 69.28 kVA); earth: 6 mm² vs Table 5.1 minimum 6 mm² (holds), near-end I_ef = (400/√3)/0.1 = 2309 A cleared in t_ef = 0.04 s (default: instantaneous clearing of a fault at the origin), S_min = 2309·√0.04/143 = 3.23 mm² (holds); governing ocpd_coordination; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.9) runs to 75 kW (141.51 A, the first above I_Z/k_design), largest conforming 45 kW. (validation case c0043-25mm2-tray-motor-efficiency-0p90) |
Example 22 — 50 mm² behind a 0.02 Ω loop, 0.4 s backup clearing: earth withstand fails
Every load-dependent limit is met, but the design relies on a 0.4 s upstream backup to clear the 11.5 kA near-end earth fault (earth_fault_clearing_time_s = 0.4), which needs 51 mm² of earth: the 16 mm² Table 5.1 earth fails, so the cable has no permissible load and no preferred rating conforms.
Given: 50 mm² copper XLPE (X-90) fixed multicore cable with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum), 60 m, unenclosed on horizontal perforated tray, spaced, 1 tier, 1 cable per tier; air ambient 40 °C. Supply 400 V three-phase; loads at PF 0.85 lagging, design factor 1. Protection: prospective fault 10 kA cleared in 0.4 s, earth-fault clearing time 0.4 s, 5× instantaneous trip, upstream loop impedance 0.02 Ω, voltage-drop limit 5 %. Loads table: IEC 60072 kW ratings (motor shaft output, efficiency 0.95).
| Limit 1 — capacity | Base rating Table 14, column 2, row 50: 182 A. Derating Table 24, column 10, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00 (ratings already based on 40 °C ambient air). IZ = 182 × 1.00 = 182.00 A; IL,CCC = 182.00 / 1 = 182.00 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
|---|---|
| Limit 2 — voltage drop | Rc = 0.494 Ω/km (Table 35, column 5, row 50), Xc = 0.0751 Ω/km (Table 30, column 10, row 50). Zeff = 0.494 × 0.85 + 0.0751 × 0.527 = 0.4595 Ω/km; Vd/I = √3 × 0.060 × 0.4595 = 0.04775 V/A; Vd,max = 5 % × 400 = 20.00 V. The drop is checked at the design current kdesign × IL, so IL,VD = Vd,max / (Vd/I × kdesign) = 20.00 / (0.04775 × 1) = 418.86 A. At the envelope: not evaluated: there is no permissible load to check it at INFO |
| Short circuit | k = 143 (Table 52, row 90). tmax = (143 × 50)² / 10,000² = 0.5112 s; Smin = 10,000 × √0.4 / 143 = 44.2 mm² → 0.4000 vs limit 0.5112 s 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: Ief = 400/√3 / 0.02 = 11,547 A, cleared in tef = 0.4 s (given: the upstream backup clearing time the design relies on). k = 143 (integral earth core: the phase conductor's Table 52 k). Smin = Ief × √tef / k = 11,547 × √0.4 / 143 = 51.07 mm² vs 16 mm² (tmax = (143 × 16 / 11,547)² = 0.0393 s) FAIL |
| Limit 3 — earth-fault loop | Zloop = Zext + L·|Zphase| + L·√(Re² + Xe²) = 0.02 + 0.060 × √(0.494² + 0.0751²) + 0.060 × √(1.47² + 0.0805²) (earth 16 mm²: R from the phase cable's resistance table, X from Table 30 at the earth size) = 0.02 + 0.0300 + 0.0883 = 0.1383 Ω (phase and earth impedance magnitudes added arithmetically; resistances at 90 °C; Zext is modelled explicitly, so the AS/NZS 3000 0.8·Uo allowance is not applied); Ifault = 400/√3 / 0.1383 = 1,669.7 A; IN,EFL = 1,669.7 / 5 = 333.94 A (Zs,max for a 160 A device = 400/√3 / (160 × 5)). The 2.09× margin over the 160 A trip threshold is nominal (pickup tolerance and operating time are not included) → 0.1383 vs limit 0.2887 Ω PASS |
| Limit 3 — device | IN,max = min(IZ 182.00, IN,EFL 333.94) = 182.00 A, limited by the cable capacity (I_N ≤ I_Z) → largest preferred rating 160 A; IL,prot = 160 / 1 = 160.00 A. IB ≤ IN ≤ IZ: 0.00 ≤ 160 ≤ 182.00 A INFO |
| Envelope | min(182.00, 418.86, 160.00) = 160.00 A would hold for the load-dependent checks, but the earth conductor withstand check does not depend on the load and fails, so there is no permissible load: IL,max = 0 A |
| Preferred loads | kW ratings are motor shaft output: I = P × 1000 / (√3 × 400 × 0.85 × 0.95). 0 of 17 preferred loads conform. First to fail: 1.5 kW (2.7 A, 6 A device) on earth conductor withstand. |
| Result | 3/4 checks pass → FAIL; no permissible load; governing: earth conductor withstand. Earth conductor 16 mm² < 51.1 mm² needed for 11547 A in 0.4 s The upstream earth-loop impedance (0.02 Ω) gives 11547 A of earth-fault current at the cable origin, more than the 10 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 tables for 50 mm² Cu XLPE with a 16 mm² earth (AS/NZS 3000 Table 5.1 minimum) over 60 m at 400 V, PF 0.85, design factor 1: base rating 182 A (Table 14 column 2 row 50), derating Table 24 column 10 row 1 = 1; Table 27(1) 90 °C conductor column row 40 = 1 → I_Z = 182 × 1 × 1 = 182.00 A, I_L,CCC = 182.00 A; Rc = 0.494 Ω/km (Table 35, Column 5), Xc = 0.0751 Ω/km (Table 30, Column 10): Z_eff = 0.494·0.85 + 0.0751·0.5268 = 0.45946 Ω/km, V_d/I = √3·0.06·0.45946 = 0.04775 V/A, 5 % of 400 V = 20.00 V → at the design current I_L,VD = V_d,max / (V_d/I × k_design) = 20.00 / (0.04775 × 1) = 418.86 A; k = 143 (Table 52 row 90), t = (143·50/10000)² = 0.5112 s vs 0.4 s (holds); Z_loop = 0.02 + 0.06·√(0.494² + 0.0751²) + 0.06·√(1.47² + 0.0805²) (earth: R from Table 35, X from Table 30 at 16 mm²) = 0.02 + 0.0300 + 0.0883 = 0.1383 Ω, I_fault = 400/√3/0.1383 = 1669.7 A, /5 = 333.94 A; I_N,max = min(182.00, 333.94) = 182.00 A → largest preferred rating 160 A, I_L,prot = 160.00 A; min(182.00, 418.86, 160.00) = 160.00 A, but the earth withstand fails independently of the load, so I_L,max = 0 A (0 kW, 0 kVA; capacity, voltage drop and overload coordination not evaluated); earth: 16 mm² vs Table 5.1 minimum 16 mm² (holds), near-end I_ef = (400/√3)/0.02 = 11547 A cleared in t_ef = 0.4 s (given), S_min = 11547·√0.4/143 = 51.07 mm² (FAILS); governing earth_conductor_withstand — no permissible load; loads table (kW ratings are shaft output, I = P/(√3·V·PF·η) with η = 0.95) runs to 110 kW (196.62 A, the first above I_Z/k_design), none conforms. (validation case c0043-50mm2-0p02ohm-0p4s-earth-withstand-fails) |
Tips & Limitations
- Use the Cable Size Range calculator for the forward question: which sizes suit a given load.
- If the envelope is governed by protection while \(I_Z\) is higher, an adjustable-trip device set between the two values recovers the difference; the calculator only uses preferred fixed ratings.
- If the earth fault loop limits the device, a larger earth conductor, a lower trip multiplier (type B rather than C or D) or a stiffer source raises the limit.
- The permissible load current is reported before the design factor; the design current at that load is shown alongside it.
- The voltage-drop limit uses the design current (load current times the design factor) and the entered power factor; a leading power factor subtracts the reactive term, reducing the drop; the voltage only rises when \(X_c\sin\varphi > R_c\cos\varphi\), which needs a large conductor and a low leading power factor.
- Single cable per phase only; parallel cables are not evaluated.
Developer Guide
Component: calcs/components/c0043_cable_permissible_load/ (calc type
cable_permissible_load). calculations.py calls the AS/NZS 3008 gateway once at a
1 A reference current, derives the three limits analytically, picks the preferred device with
largest_standard_device_rating from calcs/core/cable_utils.py, verifies the
envelope point with the shared check functions, and sweeps PREFERRED_LOAD_KW or
STANDARD_DEVICE_RATINGS through the same checks. Voltage drop from the strict gateway is
rescaled from the reference current because it is linear in current.
Tests:
pytest calcs/test_c0043_cable_permissible_load.py -vThe mocked tests work every limit by hand from a fixed 95 mm² envelope; the live tests skip unless the 2017 rows are installed.
Worked examples: the examples above are generated from the validation corpus
(mcp_public/validation/cases/fe_calc_cable_permissible_load/) by
python manage.py generate_help_examples --tool fe_calc_cable_permissible_load, which writes
_cable_permissible_load_examples.html; the renderer is
calcs/core/help_examples/cable_permissible_load.py. Regenerate after any table re-import or
engine change; calcs/test_help_examples.py fails when the committed fragment is stale.