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Motor Cable Sizing

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Edition and voltage-change convention: The calculation uses the AS/NZS 3008.1.1:2017 tables, the only supported edition; any other edition is rejected with a validation error. For lagging power factor the effective term is \(R PF + X\sqrt{1-PF^2}\); for leading power factor it is \(R PF - X\sqrt{1-PF^2}\). The signed result reports voltage drop or rise, while compliance uses its absolute magnitude.

Overview

Comprehensive motor cable sizing calculator performing six critical verification checks per AS/NZS 3008.1.1:2017 and AS/NZS 3000:2018. The calculator determines whether a selected cable is suitable for a given three-phase motor by verifying:

  1. Check 1 — Current Carrying Capacity (CCC): Base ampacity from AS/NZS 3008 Table 22 derated for ambient temperature, circuit grouping, burial depth, soil resistivity, and ground temperature.
  2. Check 2 — Voltage Drop (VD): Three-phase voltage drop must remain within the allowable percentage.
  3. Check 3 — Short Circuit Withstand (SC): Cable must withstand the prospective fault current for the protection device clearing time (adiabatic equation).
  4. Check 4 — Earth Fault Loop Impedance (EFL): Earth fault current must be sufficient to operate the protection device within the required disconnection time.
  5. Check 5 — Earth Conductor Size: The protective earth conductor must not be smaller than the AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor size.
  6. Check 6 — Earth Conductor Withstand: The earth conductor must withstand the largest earth-fault current (a fault at the cable origin, \(I_{ef} = (V_{LL} / \sqrt{3}) / Z_{source}\)) for the fault clearing time (adiabatic equation).

A cable passes overall only when all six checks pass. Use this calculator when sizing cables for three-phase induction motors on LV systems (up to 1 kV).

Input Parameters

Motor Parameters

Parameter Type Default Range Description
power Number 90 0.1 – 10000 Motor rated power (active power output)
powertype Enum: kW / watt / HP kW — Power unit
voltage Number 400 V 100 – 11000 V Three-phase line-to-line supply voltage
powerfactor Number 0.85 0.5 – 1.0 Motor power factor (cos φ)
efficiency Number 95% 50 – 100% Motor efficiency (η)
starting_method Enum: DOL / StarDelta / VSD / SoftStart DOL — Motor starting method (affects starting current multiplier)

Cable

Parameter Type Default Range Description
cable_type Enum: Fixed / Flexible / MIMS Fixed — Cable construction type
cable_formation Enum: Multicore / Singlecore Multicore — Conductor formation
conductor Enum 50 mm² 1 – 630 mm² Phase conductor cross-sectional area
multicore_arrangement Enum: Circular / Shaped Circular — Multicore cable arrangement (visible when cable_formation = Multicore)
singlecore_arrangement Enum: Trefoil / Flat Trefoil — Singlecore cable arrangement (visible when cable_formation = Singlecore)
cable_insulation Enum: XLPE / PVC / EPR XLPE — Insulation material type
metal Enum: Cu / Al Cu — Conductor material (hidden when cable_type = MIMS)
earth_conductor Enum 50 mm² 1 – 630 mm² Protective earth conductor size (defaults to phase size)

Cable Installation

Fields in this section are conditionally visible based on the selected installation method and cable formation.

Parameter Type Default Visible When Description
installation_method Enum Unenclosed Always Unenclosed, DirectBuried, Enclosed, Conduit, BuriedConduit, ThermalInsulation
unenclosed_type_mc Enum Spaced from Surface Unenclosed + Multicore Exposed To Sun, Spaced from Surface, Touching Surface
unenclosed_type_sc Enum Spaced from Surface & Trefoil or Flat Touching Unenclosed + Singlecore Singlecore unenclosed arrangement options. “Spaced from Surface & Conductors Spaced” is rejected: Table 30 gives single-core reactance only for trefoil and flat touching cores.
unenclosed_in_air Enum Perforated Trays Horizontal Unenclosed (not touching) Tray/ladder/catenary arrangement
unenclosed_catinerary Enum Bunched on Catinerary Wire Air = On Catinerary Wire Spaced or Bunched on catenary
cables_per_tier Enum: 1–9 1 Unenclosed + MC + not bunched Number of multicore cables per tier
circuits_per_tier Enum: 1–3 1 Unenclosed + SC + not bunched Number of singlecore circuits per tier
ladder_spacing Enum: Touching / Spaced / Bunched Spaced Unenclosed + not catenary Spacing on ladder/tray
ladder_tiers Enum: 1Tier / 2Tier / 3Tier 1Tier Ladder spacing ≠ Bunched Number of ladder tiers
bunched_circuits_cables Enum: 1–>18 1 Unenclosed + MC Number of bunched cables/circuits
bunched_unenclosed_type Enum Bunched In Air Unenclosed + MC Bunched arrangement type
thermal_ins_type1 Enum: Completely / Partial Completely ThermalInsulation Thermal insulation coverage
thermal_ins_type2 Enum: Unenclosed / Enclosed Enclosed ThermalInsulation Thermal insulation method
enclosed_install_type Enum Wiring Enclosure in Air Enclosed Wiring Enclosure in Air, Metalic Enclosure in Air
conduit_spacing Enum Touching Conduit Touching, Spaced 0.3m, 0.45m, 0.6m
sc_conduit_install_type Enum: Shared / Dedicated Shared Singlecore + Conduit SC conduit arrangement. Dedicated (one core per conduit) is rejected: Table 30 gives single-core reactance only for trefoil and flat touching cores.
direct_buried_spacing Enum Touching DirectBuried Touching, Spaced 0.15m, 0.3m, 0.45m, 0.6m
buried_circuits_cables Enum: 1–12 3 Conduit or DirectBuried Number of buried circuits/cables
ambient_temp Enum: 15–85 °C 40 °C Not DirectBuried, not Conduit Air ambient temperature for derating
burial_depth Enum: 0.5–3+ m 0.8 DirectBuried or Conduit Depth of burial for underground cables
soil_ambient Enum: 10–40 °C 25 °C DirectBuried or Conduit Soil ambient temperature
soil_resistivity Enum: 0.8–3 K·m/W 1 DirectBuried or Conduit Soil thermal resistivity
num_circuits Integer 1 Always Number of grouped circuits for derating (1–20)

Protection Parameters

Parameter Type Default Range Description
fault_current Number 10000 A 100 – 100000 A Prospective short circuit fault current at load
protection_time Number 0.1 s 0.01 – 5.0 s Protection device maximum clearing time, used for the phase short circuit withstand check (Check 3)
earth_fault_clearing_time Number 0.04 s 0.005 – 5.0 s Earth-fault clearing time \(t_{ef}\) for the earth conductor withstand check (Check 6). A fault at the cable origin draws far more than the device's instantaneous threshold, so this is the device's instantaneous operating time; enter the upstream backup time instead if that device is relied on to clear the fault.
trip_current Number 100 A 1 – 10000 A Protection device (CB or fuse) rating
trip_multiplier Number 5 3 – 15 Instantaneous magnetic trip multiplier (typically 5–10× In)
source_impedance Number 0.1 Ω 0.001 – 10.0 Ω Source impedance (transformer + upstream cables)

Calculation Settings

Parameter Type Default Range Description
voltagedropmax Number 5% 1 – 10% Maximum allowable voltage drop percentage

Output Results

Motor Currents

Output Unit Description
full_load_current A Motor full load current (FLC)
starting_current A Motor starting current (FLC × starting multiplier)

Check 1 — Current Carrying Capacity

Output Unit Description
base_current A Base ampacity from Table 22 (before derating)
derating_factor — Combined derating factor (product of all applicable factors)
derated_current A Derated current capacity \(I_{base} \times f_{derate}\)
design_current A Design current (1.25 × FLC for motors per AS/NZS 3000)
utilization_percent % Cable utilisation percentage
passes Boolean Whether derated capacity ≥ design current

Check 2 — Voltage Drop

Output Unit Description
rc Ω/km Cable resistance per km
xc Ω/km Cable reactance per km
impedance Ω/km Cable impedance \(Z_c = \sqrt{R_c^2 + X_c^2}\)
voltage_drop V Voltage drop in volts
voltage_drop_percent % Voltage drop as percentage of supply
passes Boolean Whether \(V_{d\%} \leq V_{d,max\%}\)

Check 3 — Short Circuit Withstand

Output Unit Description
k_factor — Material/insulation k-factor from Table 52
conductor_area mm² Conductor cross-sectional area
max_withstand_time s Maximum time cable can withstand the fault current
protection_time s Protection device clearing time (must be ≤ withstand time)
passes Boolean Whether \(t_{max} \geq t_{protection}\)

Check 4 — Earth Fault Loop Impedance

Output Unit Description
z_source Ω Source impedance (transformer + upstream cables)
z_phase Ω Phase conductor impedance for cable length
z_earth Ω Earth conductor impedance \(L_{km}\sqrt{R_e^2 + X_e^2}\)
rc_earth Ω/km Earth conductor AC resistance at the insulation's operating temperature
xc_earth Ω/km Earth conductor reactance: AS/NZS 3008 Table 30 at the earth size, phase-cable arrangement
z_loop Ω Total earth fault loop impedance
fault_current A Prospective earth fault current \(V_{ph} / Z_{loop}\)
required_fault_current A Minimum current to operate protection device
passes Boolean Whether \(I_{fault} \geq I_{trip} \times k_{mag}\)

Check 5 — Earth Conductor Size (check_earth_size)

Output Unit Description
earth_area mm² Earth conductor checked (as entered; the Table 5.1 minimum in auto-size mode)
minimum_earth_area mm² AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor size
utilization_percent % Minimum as a share of the earth conductor size
passes Boolean Whether \(S_e \geq S_{e,5.1}\)

Check 6 — Earth Conductor Withstand (check_earth_withstand)

Output Unit Description
fault_current A Largest earth-fault current, at the cable origin: \(I_{ef} = V_{ph} / Z_{source}\)
k_factor — The phase conductor's AS/NZS 3008 Table 52 k (the earth is an integral core)
min_csa mm² Adiabatic minimum earth size \(I_{ef} \sqrt{t_{ef}} / k\)
max_withstand_time s Longest time the earth conductor can carry \(I_{ef}\)
passes Boolean Whether \(S_e \geq S_{e,min}\)

Overall Result

Output Type Description
all_checks_pass Boolean True only when all six checks pass
status text "PASS" or "FAIL"
num_checks_passed Integer Count of passing checks (0–6)
num_checks Integer Number of checks run (6)
failure_reasons List Descriptions of any failing checks

Formulas

Motor Full Load Current

\[ I_{FLC} = \frac{P \times 1000}{\sqrt{3} \times V \times \cos\phi \times \eta} \]

Where \(P\) is motor power in kW, \(V\) is line-to-line voltage, \(\cos\phi\) is power factor, and \(\eta\) is efficiency as a decimal. For HP input, multiply by 0.7457 to convert to kW first.

Starting Current Multipliers

Starting Method Multiplier Starting Current
DOL (Direct On Line)6.0\(I_{start} = 6.0 \times I_{FLC}\)
Star-Delta2.0\(I_{start} = 2.0 \times I_{FLC}\)
Soft Starter3.0\(I_{start} = 3.0 \times I_{FLC}\)
VSD1.5\(I_{start} = 1.5 \times I_{FLC}\)

Check 1: Current Carrying Capacity

\[ I_{derated} = I_{base} \times f_{temp} \times f_{group} \times f_{depth} \times f_{soil} \times f_{ground} \]

Where \(I_{base}\) is the base ampacity from AS/NZS 3008 Table 22, and each \(f\) is the applicable derating factor from Tables 27–29. Only factors relevant to the installation are applied (underground factors are omitted for above-ground installations).

\[ I_{derated} \geq I_{design} \implies \text{PASS} \]

For motor circuits, \(I_{design} = 1.25 \times I_{FLC}\) per AS/NZS 3000 Clause 4.7.

Temperature Derating Factors (Table 27, base 75°C XLPE)

Ambient (°C) 2530354045 505560657075
Factor 1.201.141.071.000.93 0.850.760.670.570.450.00

Grouping Derating Factors (Table 28)

Circuits 12345 678910 1214161820
Factor 1.000.800.700.650.60 0.570.540.520.500.48 0.450.430.410.400.38

Burial Depth Derating Factors

Depth (m) 0.50.81.01.251.52.0
Factor 1.000.970.950.930.910.88

Soil Thermal Resistivity Derating Factors

Resistivity (K·m/W) 0.50.71.01.52.02.5
Factor 1.281.201.000.860.760.70

Ground Temperature Derating Factors

Ground Temp (°C) 101520253035
Factor 1.071.041.000.960.920.88

Check 2: Voltage Drop

\[ Z_c = \sqrt{R_c^2 + X_c^2} \quad (\Omega/\text{km}) \]

Where \(R_c\) and \(X_c\) are looked up from AS/NZS 3008 tables based on conductor material, size, insulation, and temperature.

\[ V_d = \sqrt{3} \, I_{FLC} \, L_{km} \left(R_c \cos\phi \pm X_c \sin\phi\right) \]

Where \(I_{FLC}\) is the motor full load current (A) and \(L_{km}\) is the cable length in km; the sign is + for a lagging and − for a leading power factor. Voltage drop is evaluated at the running current \(I_{FLC}\), not at the design current: the design factor (125 % motor rule) applies to cable capacity and protection only.

\[ V_{d\%} = \frac{V_d}{V_{supply}} \times 100 \] \[ V_{d\%} \leq V_{d,max\%} \implies \text{PASS} \]

Check 3: Short Circuit Withstand

\[ t_{max} = \frac{k^2 \times S^2}{I_f^2} \]

Adiabatic equation where \(k\) is the conductor/insulation factor (Table 52), \(S\) is conductor CSA in mm², and \(I_f\) is prospective fault current in amps.

\[ t_{max} \geq t_{protection} \implies \text{PASS} \]

k-Factors (Table 52)

Conductor Insulation Initial Temp (°C) Final Temp (°C) k
CopperPVC70160115
CopperXLPE90250143
CopperEPR90250143
AluminiumPVC7016076
AluminiumXLPE9025094
AluminiumEPR9025094

Check 4: Earth Fault Loop Impedance

\[ Z_{loop} = Z_{source} + Z_{phase} + Z_{earth} \] \[ L_{max} = \frac{V_{ph} / I_a - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \quad (\text{m}) \]

Where \(Z_{source}\) is the transformer/upstream impedance, \(Z_{phase} = Z_c \times L_{km}\) for the phase conductor, and \(Z_{earth} = L_{km}\sqrt{R_e^2 + X_e^2}\) for the earth conductor.

The earth conductor impedance includes its reactance: \(R_e\) is the earth conductor's AC resistance at the insulation's operating temperature and \(X_e\) is its AS/NZS 3008 Table 30 reactance at the earth conductor size, in the same arrangement as the phase cable. Leaving \(X_e\) out understates the loop impedance and overstates the fault current, most for large earth conductors where \(X_e\) approaches \(R_e\). The maximum length uses the same model: \(|z_{phase}|\) and \(|z_{earth}|\) are per-kilometre impedance magnitudes, and adding magnitudes gives a loop impedance no smaller than the phasor sum.

\[ I_{fault} = \frac{V_{ph}}{Z_{loop}} = \frac{V_{LL} / \sqrt{3}}{Z_{loop}} \] \[ I_{fault} \geq I_{trip} \times k_{mag} \implies \text{PASS} \]

The earth fault current must exceed the protection device magnetic trip threshold (\(I_{trip} \times k_{mag}\)) to ensure automatic disconnection within the required time.

Check 5: Earth Conductor Size

\[ S_e \geq S_{e,5.1} \implies \text{PASS} \]

\(S_{e,5.1}\) is the AS/NZS 3000:2018 Table 5.1 minimum protective earth conductor for the phase conductor size (for example 25 mm² for a 95 mm² phase). In auto-size mode the earth conductor is the Table 5.1 minimum for each candidate size, so this check always passes there; in manual mode an earth below the minimum fails the calculation.

Check 6: Earth Conductor Withstand

\[ I_{ef} = \frac{V_{LL} / \sqrt{3}}{Z_{source}} \] \[ S_{e,min} = \frac{I_{ef} \sqrt{t_{ef}}}{k} \qquad t_{e,max} = \left(\frac{k \, S_e}{I_{ef}}\right)^2 \] \[ S_e \geq S_{e,min} \implies \text{PASS} \]

The largest earth-fault current flows for a fault at the cable origin, where only the source impedance limits it (\(V_{ph} = V_{LL} / \sqrt{3}\)); a fault further along the cable adds cable impedance and draws less current. \(t_{ef}\) is the earth-fault clearing time (earth_fault_clearing_time, default 0.04 s), not the CB clearance time used for Check 3: a fault at the cable origin draws far more than the protective device's instantaneous threshold, so it clears in the instantaneous operating time. If an upstream device is relied on to clear that fault instead, enter its clearing time. A multicore cable's earth is an integral core, so it shares the phase conductor's AS/NZS 3008 Table 52 \(k\): it starts at the insulation's operating temperature and ends at the same final temperature. With single-core cables the earth is a separate cable; it is still given the phase conductor's \(k\), as if it started at the insulation's operating temperature, which is conservative.

\(I_{ef}\) comes from the upstream loop impedance, while Check 3 uses the prospective fault current input. If \(V_{ph} / Z_{source}\) exceeds the prospective fault current, the calculation warns that the two inputs are inconsistent: check the upstream loop impedance against the fault level.

Length Conversion Factors

From To Meters
1 Kilometer1000 m
1 Foot0.3048 m
1 Mile1609.34 m
1 Yard0.9144 m

Worked Examples

The 2 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_cable_size; worked examples for every calculation).

#CaseCableIdesign (A)Iderated (A)Vd (%)GoverningResult
155 kW motor, 80 m, auto-sized: earth-fault loop governs35 mm² Cu XLPE (auto)124.1144.02.12earth-fault loop impedancePASS
214.5 A motor on 4 mm², 120 m, 2 kA fault: phase and earth withstand fail4 mm² Cu XLPE18.136.03.67earth conductor thermal withstandFAIL

Example 1 — 55 kW motor, 80 m, auto-sized: earth-fault loop governs

Three-phase motor at 1.25 × FLC on a 125 A device: 25 mm² fails capacity and the loop-impedance check; 35 mm² with its AS/NZS 3000 Table 5.1 10 mm² earth meets the 625 A loop requirement at 92 % and is selected, the loop being the highest utilisation.

Given: 55 kW three-phase motor at 400 V, PF 0.86 lagging, efficiency 0.93, design factor 1.25 (default). Auto sizing of a copper XLPE (X-90) fixed multicore cable, route 80 m; unenclosed, spaced from surface, on perforated trays horizontal, 1 cable(s) per tier, 1 tier(s), spaced, air ambient 40 °C (default). Protection: prospective fault 10 kA (default) cleared in 0.1 s (default), earth-fault clearing time 0.04 s (default), 125 A device with 5× instantaneous trip (default), upstream loop impedance 0.1 Ω (default), voltage-drop limit 5 % (default). AS/NZS 3008.1.1:2017 tables.

Full-load currentIFLC = 55 kW × 1000 / (√3 × 400 × 0.86 × 0.93) = 99.26 A; Idesign = 99.26 × 1.25 = 124.07 A (DOL starting current ≈ 596 A, informative only)
Sizes tried1 (fails CCC, VD, SC, EFL, EWT), 1.5 (fails CCC, VD, SC, EFL, EWT), 2.5 (fails CCC, VD, SC, EFL, EWT), 4 (fails CCC, VD, SC, EFL, EWT), 6 (fails CCC, VD, SC, EFL, EWT), 10 (fails CCC, VD, SC, EFL), 16 (fails CCC, SC, EFL), 25 (fails CCC, EFL), 35 (passes). Selected 35 mm² with a 10 mm² earth.
Check 1 — capacityBase rating Table 14, column 2, row 35: 144 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. Iderated = 144 × 1.00 = 144.00 A vs Idesign 124.07 A (loading 86.2 %) PASS
Check 2 — voltage dropRc = 0.669 Ω/km (Ref: Table 35, Column 5, Row: 35mm²), Xc = 0.0786 Ω/km (Ref: Table 30, Column 10, Row: 35mm²). At the full-load current: ΔV = √3 × 99.26 × 0.080 × (0.669 × 0.86 + 0.0786 × 0.510) = 8.46 V (drop) = 2.12 % of 400 V, limit 5 % PASS
Check 3 — short circuitk = 143 (Table 52, Cu 90 → 250 °C). tmax = (143 × 35)² / 10,000² = 0.2505 s vs 0.1 s clearing; Smin = 10,000 × √0.1 / 143 = 22.11 mm² PASS
Check 4 — earth fault loopZs = Zext + L·√(Rc² + Xc²) + L·√(Re² + Xe²) with the earth's Re = 2.33 Ω/km and Xe = 0.0840 Ω/km (Table 30 at 10 mm²): Zs = 0.1 + 0.0539 (phase) + 0.1865 (earth) = 0.3404 Ω vs Zs,max = 400/√3 / (125 × 5) = 0.3695 Ω; Ifault = 230.9 / 0.3404 = 678 A vs 625 A PASS. Lmax = (0.3695 − 0.1) / 3.005 Ω/km = 89.7 m vs 80 m PASS
Check 5 — earth sizeAS/NZS 3000 Table 5.1 minimum for a 35 mm² phase conductor: 10 mm²; earth 10 mm² PASS
Check 6 — earth withstandLargest 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 10 mm² (tmax = (143 × 10 / 2,309)² = 0.3834 s) PASS
Result7/7 checks pass → PASS; 35 mm² Cu with 10 mm² earth; power loss 1,582 W (2.88 %); governing: earth fault loop impedance. Cable utilization is elevated (86.2%) - monitor for load changes Earth fault trip margin is very low (1.09x) Review protection settings - fault current barely exceeds trip threshold Motor starting voltage dip is not checked by this tool.
ReferenceHand calculation: FLC = 55 kW / (√3 × 400 × 0.86 × 0.93) = 99.26 A, design 1.25 × FLC = 124.07 A (calcs/test_c0006 motor current formula); the loop must drive 5 × 125 A = 625 A, so Zs,max = (400/√3)/625 = 0.3695 Ω. With AS/NZS 3008.1.1:2017 Table 14/35/30 values (the earth conductor's reactance taken from Table 30 at its own size): 25 mm² (116 A < 124.07 A) + 6 mm² earth gives Zs = 0.1 + 0.08·√(0.927² + 0.0808²) + 0.08·√(3.93² + 0.0887²) = 0.1 + 0.0744 + 0.3145 = 0.4889 Ω > 0.3695 Ω (fails capacity and the loop); 35 mm² (144 A) + 10 mm² earth (AS/NZS 3000 Table 5.1) gives Zs = 0.1 + 0.08·√(0.669² + 0.0786²) + 0.08·√(2.33² + 0.084²) = 0.1 + 0.0539 + 0.1865 = 0.3404 Ω ≤ 0.3695 Ω (92 %, the highest utilisation, so the loop governs), I_ef = 230.9/0.3404 = 678.4 A, Lmax = (0.3695 − 0.1)/(0.6736 + 2.3315 Ω/km) = 89.7 m; ΔV = √3 × 99.26 × 0.08 × (0.669 × 0.86 + 0.0786 × 0.510) = 8.46 V = 2.12 % (motor: drop at the full-load current); earth withstand: I_ef = (400/√3)/0.1 Ω = 2309 A at the origin, cleared instantaneously in the default t_ef = 0.04 s, S_min = 2309 × √0.04 / 143 = 3.23 mm² ≤ 10 mm². (validation case c0006-55kw-motor-400v-80m-auto)

Example 2 — 14.5 A motor on 4 mm², 120 m, 2 kA fault: phase and earth withstand fail

Check mode: 4 mm² survives 2 kA for only 0.08 s, short of the 0.1 s clearing time, and its 2.5 mm² earth is below the 3.35 mm² the 2.4 kA near-end earth fault needs even when cleared instantaneously in 0.04 s (134 %, governing), although capacity, voltage drop and the earth-fault loop all pass.

Given: three-phase motor of 14.5 A at 415 V, PF 0.85 (default) lagging (for voltage drop), design factor 1.25 (default). Check 4 mm² copper XLPE (X-90) fixed multicore cable with a 2.5 mm² earth, route 120 m; unenclosed, spaced from surface, on perforated trays horizontal, 1 cable(s) per tier, 1 tier(s), spaced, air ambient 40 °C (default). Protection: prospective fault 2 kA cleared in 0.1 s (default), earth-fault clearing time 0.04 s (default), 20 A device with 5× instantaneous trip (default), upstream loop impedance 0.1 Ω (default), voltage-drop limit 5 % (default). AS/NZS 3008.1.1:2017 tables.

Full-load currentIFLC = 14.50 A (given); Idesign = 14.50 × 1.25 = 18.12 A (DOL starting current ≈ 87 A, informative only)
Check 1 — capacityBase rating Table 14, column 2, row 4: 36 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. Iderated = 36 × 1.00 = 36.00 A vs Idesign 18.12 A (loading 50.3 %) PASS
Check 2 — voltage dropRc = 5.88 Ω/km (Ref: Table 35, Column 5, Row: 4mm²), Xc = 0.0930 Ω/km (Ref: Table 30, Column 10, Row: 4mm²). At the full-load current: ΔV = √3 × 14.50 × 0.120 × (5.88 × 0.85 + 0.0930 × 0.527) = 15.21 V (drop) = 3.67 % of 415 V, limit 5 % PASS
Check 3 — short circuitk = 143 (Table 52, Cu 90 → 250 °C). tmax = (143 × 4)² / 2,000² = 0.0818 s vs 0.1 s clearing; Smin = 2,000 × √0.1 / 143 = 4.42 mm² FAIL
Check 4 — earth fault loopZs = Zext + L·√(Rc² + Xc²) + L·√(Re² + Xe²) with the earth's Re = 9.45 Ω/km and Xe = 0.0988 Ω/km (Table 30 at 2.5 mm²): Zs = 0.1 + 0.7057 (phase) + 1.1341 (earth) = 1.9398 Ω vs Zs,max = 415/√3 / (20 × 5) = 2.3960 Ω; Ifault = 239.6 / 1.9398 = 124 A vs 100 A PASS. Lmax = (2.3960 − 0.1) / 15.331 Ω/km = 149.8 m vs 120 m PASS
Check 5 — earth sizeAS/NZS 3000 Table 5.1 minimum for a 4 mm² phase conductor: 2.5 mm²; earth 2.5 mm² PASS
Check 6 — earth withstandLargest 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 2.5 mm² (tmax = (143 × 2.5 / 2,396)² = 0.0223 s) FAIL
Result5/7 checks pass → FAIL; 4 mm² Cu with 2.5 mm² earth; power loss 445 W (5.02 %); governing: earth conductor withstand. Power loss (5.02%) is significant The upstream earth-loop impedance (0.1 Ω) gives 2396 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 Motor starting voltage dip is not checked by this tool.
ReferenceHand calculation: design current 1.25 × 14.5 = 18.13 A; withstand t = (k·S/I)² = (143 × 4 / 2000)² = 0.0818 s < 0.1 s clearing time, so the phase adiabatic check fails (122 %); the earth carries the near-end earth fault I_ef = (415/√3)/0.1 Ω = 2396 A, far above the instantaneous trip, for the default t_ef = 0.04 s, so S_min = 2396 × √0.04 / 143 = 3.35 mm² > 2.5 mm² (134 %, the governing criterion) although 2.5 mm² is the AS/NZS 3000 Table 5.1 minimum for 4 mm²; ΔV = √3·14.5·0.12·(5.88·0.85 + 0.093·0.527) with AS/NZS 3008.1.1:2017 Table 35/30 values for 4 mm² = 15.21 V = 3.67 % (motor: drop at the full-load current); Zs = 0.1 + 0.12·√(5.88² + 0.093²) + 0.12·√(9.45² + 0.0988²) (earth reactance from Table 30 at 2.5 mm²) = 0.1 + 0.7057 + 1.1341 = 1.9398 Ω ≤ (415/√3)/(5 × 20 A) = 2.396 Ω, Lmax = (2.396 − 0.1)/(5.8807 + 9.4505 Ω/km) = 149.8 m. (validation case c0006-check-4mm2-motor-415v-120m)

Standards & References

  • AS/NZS 3008.1.1:2017 — Electrical installations — Selection of cables — Cables for alternating voltages up to and including 0.6/1 kV
    • Table 4 — Installation methods
    • Table 22 — Current carrying capacity (base ratings)
    • Table 27 — Temperature derating factors
    • Table 28 — Grouping derating factors
    • Table 30 — Reactance at 50 Hz for multicore cables
    • Table 35 — AC resistance at 50 Hz
    • Table 52 — Short circuit k-factors (adiabatic equation, Checks 3 and 6)
  • AS/NZS 3000:2018 — Wiring Rules
    • Clause 4.7 — Motor circuit requirements (1.25× FLC)
    • Clause 2.5.6 — Maximum voltage drop limits
    • Clause 5.8 — Earth fault loop impedance and disconnection times
    • Table 5.1 — Minimum size of protective earthing conductors (Check 5)
  • IEC 60364 — Low-voltage electrical installations — general principles for earth fault loop impedance verification

Tips & Limitations

Tips
  • Start with the motor data (power, voltage, PF, efficiency) to determine full load current, then select a cable that passes all six checks.
  • If Check 6 (earth withstand) fails, the source is strong or the clearing time long for the earth size: increase the earth conductor, or shorten the fault clearing time.
  • VSD starting (multiplier 1.5×) produces the lowest starting current — use it when possible to reduce cable sizing demands.
  • Check 1 (CCC) typically drives the cable size up; Check 2 (VD) is more critical on long runs; Check 3 (SC) on high fault level installations; Check 4 (EFL) on long runs with high source impedance.
  • Underground cables accumulate multiple derating factors (grouping, burial depth, soil resistivity, ground temperature) — the combined effect can reduce capacity by 40% or more.
  • Aluminium cables have approximately 1.6× the resistance of copper — typically require one size larger for equivalent performance.
  • If Check 4 (EFL) fails, consider reducing the earth conductor impedance (increase earth conductor size) or reducing source impedance.
  • The 5% voltage drop default is common for sub-mains; motor feeders from the MCC to the motor may allow up to 2.5% in some standards.
Limitations
  • Three-phase only — this calculator is for three-phase motors. Use c0032 for single-phase motor cable sizing.
  • Simplified derating — derating uses the closest tabulated value; linear interpolation between table entries is not performed.
  • XLPE only for CCC table — base current ratings are currently from the Cu XLPE table. PVC and EPR tables are not yet implemented for Check 1.
  • Single-core reactance — AS/NZS 3008 Table 30 tabulates single-core reactance only for trefoil and flat touching cores. Single-core cables with spaced conductors (unenclosed_type_sc = Spaced from Surface & Conductors Spaced) or one core per conduit (sc_conduit_install_type = Dedicated) are rejected rather than given touching-core reactance, which would understate voltage drop and loop impedance.
  • Balanced system assumed — the calculator assumes balanced three-phase loading. Unbalanced phase loading is not modelled.
  • Earth conductor impedance — Check 4 includes the earth conductor reactance (AS/NZS 3008 Table 30 at the earth size, same arrangement as the phase cable). Resistances are taken at the insulation's operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium at most 90 °C).
  • Harmonic currents — not considered. For VSD-driven motors with significant harmonics, additional cable derating may be required.

Developer Guide

Architecture

File layout:

  • components/c0006_motor_cable_sizing/component.py — Component registration, parameter schema, equation builder, summary cards builder
  • components/c0006_motor_cable_sizing/calculations.py — Orchestration (calculate_motor_cable_sizing), motor current calculation, webcalcs parameter mapping
  • core/cable_utils.py — Shared cable utilities: all six check functions, lookup tables, derating factors, webcalcs API call (used by c0006, c0020, c0030, c0031, c0032)
  • core/earthing_utils.py — Earthing k-factor lookup (EARTHING_K_FACTORS)
  • components/c0006_motor_cable_sizing/equations.py — MathJax equation builder for PDF report generation
  • components/c0006_motor_cable_sizing/excel_generator.py — Excel export generation
  • components/c0006_motor_cable_sizing/templates/.../sidebar_form.html — Sidebar input form template

The calculator class is MotorCableSizingCalculator, registered as motor_cable_sizing via register_component(). It extends ElectricalCalculator (from calcs.core.base_calculator).

Lookup tables in core/cable_utils.py:

  • BASE_CURRENT_CU_XLPE_75C — Table 22 base ampacity by installation method
  • TEMP_DERATING_FACTORS — Table 27 temperature derating
  • GROUPING_DERATING_FACTORS — Table 28 grouping derating
  • BURIAL_DEPTH_DERATING_FACTORS — Burial depth derating
  • SOIL_RESISTIVITY_DERATING_FACTORS — Soil thermal resistivity derating
  • GROUND_TEMP_DERATING_FACTORS — Ground temperature derating
  • RC_CU_XLPE_MULTICORE_75C — Copper XLPE resistance (Ω/km)
  • RC_AL_XLPE_MULTICORE_75C — Aluminium XLPE resistance (Ω/km)
  • XC_MULTICORE_CIRCULAR — Multicore circular reactance (Ω/km)
  • STARTING_CURRENT_MULTIPLIERS — Motor starting method multipliers

Lookup tables in core/earthing_utils.py:

  • EARTHING_K_FACTORS — Table 52 short circuit k-factors

Webcalcs integration: Checks 1 and 2 use the webcalcs API (call_webcalcs_api) for AS/NZS 3008 standard table lookups. Checks 3 and 4 use local calculation functions. map_calcs_to_webcalcs_params() translates c0006 parameter names to the webcalcs format.

Code Paths

Key functions in calculations.py:

Function Purpose
calculate_motor_cable_sizing(data) Main entry point — orchestrates all six checks and returns combined results
calculate_motor_current(power, voltage, pf, eff, power_type) Motor full load current calculation
get_starting_current(flc, starting_method) Apply starting method multiplier to FLC
map_calcs_to_webcalcs_params(data) Translate c0006 parameters to webcalcs API format

Key functions in core/cable_utils.py:

Function Purpose
check_current_capacity_with_webcalcs(data, webcalcs_results) Check 1: CCC using webcalcs API results
check_voltage_drop_with_webcalcs(data, webcalcs_results) Check 2: Voltage drop using webcalcs API results
check_short_circuit(data) Check 3: Adiabatic short circuit withstand (local calc)
check_earth_fault_loop(data) Check 4: Earth fault loop impedance (local calc)
check_earth_conductor_size(data) Check 5: Earth conductor against the AS/NZS 3000 Table 5.1 minimum
check_earth_conductor_withstand(data, k_override, phases=3, table_reference) Check 6: Adiabatic earth withstand at Ief = (V / √3) / Zsource
call_webcalcs_api(calcVals) Internal call to webcalcs RunCalculation endpoint
lookup_base_current(conductor, metal, insulation, method) Fallback Table 22 lookup (used when webcalcs is unavailable)
calculate_derating_factor(...) Compute combined derating factor from all applicable tables
lookup_rc_xc(metal, conductor, insulation) Lookup resistance and reactance from local tables
get_k_factor(metal, insulation) Get k-factor for adiabatic equation from Table 52 (via core/earthing_utils.py)

Request flow:

  1. MotorCableSizingCalculator.validate_parameters() validates all inputs
  2. MotorCableSizingCalculator.calculate() assembles data dict and calls calculate_motor_cable_sizing(data)
  3. Motor current is computed locally via calculate_motor_current()
  4. Parameters are mapped to webcalcs format via map_calcs_to_webcalcs_params()
  5. Webcalcs API is called for CCC and VD table lookups
  6. All six checks run and results are aggregated into overall pass/fail
  7. equation_builder() converts results to unified article format for PDF output

Testing

Running tests:

pytest calcs/test_c0006_motor_cable_sizing.py -v

Worked examples: the examples above are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_cable_size/) by python manage.py generate_help_examples --tool fe_calc_cable_size, which writes help/_motor_cable_sizing_examples.html; calcs/test_help_examples.py fails if the committed fragment is stale.

How to extend:

  1. Add new cable material/insulation combinations by extending the lookup tables (BASE_CURRENT_*, RC_*) and updating the lookup_base_current() and lookup_rc_xc() functions.
  2. Add PVC/EPR base current tables for Check 1 CCC (currently only Cu XLPE is implemented).
  3. Add singlecore arrangement reactance tables for trefoil/flat configurations.
  4. Extend PARAMETER_SCHEMA enums in component.py to expose new options.
  5. Write tests covering new lookup values, edge cases (zero fault current, maximum length, boundary derating), and verify all six checks independently.