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Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name
Project: Project Name
Project No.: P001
Client: Client Name

Cable Size Range Calculation

Every standard conductor size is checked against AS/NZS 3008.1.1:2017 (current-carrying capacity, voltage drop, short-circuit withstand, earth fault loop impedance and the adiabatic withstand of the earth conductor) and AS/NZS 3000:2018 (Clause 2.5.3.1 overload coordination with the entered protective device, and the Table 5.1 earth conductor size). The earth conductor for each size is the AS/NZS 3000 Table 5.1 minimum. The result is the range of sizes that pass all seven checks; it is not a claim of compliance with a newer edition.

1.1 Load Parameters

Load electrical parameters and operating conditions:
Parameter Symbol Value Notes
AS/NZS 3008 Edition 2017 The only supported edition
Power Factor Direction lagging Controls the sign of the reactive voltage component
Specify By Power Rating Input mode
Load Power P 90 kW Rated load power
Power Unit kW Power measurement unit
Supply Voltage Vpp 400 V Phase-to-phase voltage
Power Factor PF 0.85 cos(φ)
Load Type General Load Type of load
Design Factor kdesign 1 Design margin multiplier
Cable Length L 100 Meter Cable run length
Length Unit Meter Length measurement unit
Max Voltage Drop Vd,max 5 % Maximum allowable

1.2 Cable Construction

Cable construction common to every candidate size:
Parameter Symbol Value Notes
Cable Type Fixed Cable construction
Cable Formation Multicore Multicore or Singlecore
MC Arrangement Circular Conductor arrangement
Cable Insulation XLPE Insulation type
Conductor Material Material Cu Cu or Al

1.3 Cable Installation

Installation method and environmental conditions:
Parameter Symbol Value Notes
Installation Method Unenclosed
Unenclosed Type (MC) Spaced from Surface
Air Arrangement Perforated Trays Horizontal
Cables Per Tier 1
Ladder Spacing Spaced
Ladder Tiers 1Tier
Air Ambient Temp 40
Cables per Tier 1

1.4 Circuit Breaker

Protection device parameters:
Parameter Symbol Value Notes
Prospective Fault Current If 10 kA Maximum fault current
CB Clearance Time tprot 100 ms Protection device time
Earth Fault Clearing Time tef 40 ms Near-end earth fault (earth withstand)
Protection Device Rating Itrip 100 A CB rating
Instantaneous Trip Multiplier kmag 5 Magnetic trip factor
Source Impedance Zsource 100 mΩ Upstream impedance

2. Load Current Calculations

Determine load current and design current for cable sizing criteria.

2.1 Load Current (I_load)

Three-phase load current from rated power: This is the continuous operating current for which the cable must be sized.

Formula: $$ \begin{aligned} I_{load} &= \frac{P}{\sqrt{3} \times V_{pp} \times PF} \times 1000 \\ &= \frac{90}{\sqrt{3} \times 400 \times 0.85} \times 1000 \\ &= 153 \; \text{A} \end{aligned} $$

2.2 Design Current (I_design)

Design current with factor k_design = 1.0: Design current accounts for load growth and safety margin.

Formula: $$ \begin{aligned} I_{design} &= I_{load} \times k_{design} \\ &= 153 \times 1 \\ &= 153 \; \text{A} \end{aligned} $$

3. Candidate Cable Sizes

All 20 standard sizes evaluated with the Table 5.1 earth conductor; 19 are tabulated for this construction and installation. CCC = current-carrying capacity, VD = voltage drop, SC = short-circuit withstand, EFL = earth fault loop, OVL = overload coordination, ESZ = earth conductor size (Table 5.1), EWT = earth conductor withstand; the Symbol column shows the seven marks in that order. S_e min is the Table 5.1 minimum / the adiabatic minimum earth size.
Parameter Symbol Value Notes
1 mm² (earth 1 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✗ FAIL I_Z 16.0 A (955 %), V_d 152.27 %, t 0.00 s, I_f 42/500 A, I_N 100 A, S_e min 1/3.2 mm²
1.5 mm² (earth 1.5 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✗ FAIL I_Z 20.0 A (764 %), V_d 97.69 %, t 0.00 s, I_f 65/500 A, I_N 100 A, S_e min 1.5/3.2 mm²
2.5 mm² (earth 2.5 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✗ FAIL I_Z 27.0 A (566 %), V_d 53.50 %, t 0.00 s, I_f 116/500 A, I_N 100 A, S_e min 2.5/3.2 mm²
4 mm² (earth 2.5 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✗ FAIL I_Z 36.0 A (425 %), V_d 33.40 %, t 0.00 s, I_f 141/500 A, I_N 100 A, S_e min 2.5/3.2 mm²
6 mm² (earth 2.5 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✗ FAIL I_Z 46.0 A (332 %), V_d 22.42 %, t 0.01 s, I_f 161/500 A, I_N 100 A, S_e min 2.5/3.2 mm²
Parameter Symbol Value Notes
10 mm² (earth 4 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✓ FAIL I_Z 66.0 A (232 %), V_d 13.40 %, t 0.02 s, I_f 251/500 A, I_N 100 A, S_e min 4/3.2 mm²
16 mm² (earth 6 mm²) ✗ ✗ ✗ ✗ ✗ ✓ ✓ FAIL I_Z 87.0 A (176 %), V_d 8.55 %, t 0.05 s, I_f 361/500 A, I_N 100 A, S_e min 6/3.2 mm²
25 mm² (earth 6 mm²) ✗ ✗ ✓ ✗ ✗ ✓ ✓ FAIL I_Z 116.0 A (132 %), V_d 5.50 %, t 0.13 s, I_f 394/500 A, I_N 100 A, S_e min 6/3.2 mm²
35 mm² (earth 10 mm²) ✗ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 144.0 A (106 %), V_d 4.04 %, t 0.25 s, I_f 577/500 A, I_N 100 A, S_e min 10/3.2 mm²
50 mm² (earth 16 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 182.0 A (84 %), V_d 3.04 %, t 0.51 s, I_f 777/500 A, I_N 100 A, S_e min 16/3.2 mm²
Parameter Symbol Value Notes
70 mm² (earth 25 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 230.0 A (66 %), V_d 2.19 %, t 1.00 s, I_f 1,012/500 A, I_N 100 A, S_e min 25/3.2 mm²
95 mm² (earth 25 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 275.0 A (56 %), V_d 1.65 %, t 1.85 s, I_f 1,055/500 A, I_N 100 A, S_e min 25/3.2 mm²
120 mm² (earth 35 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 327.0 A (47 %), V_d 1.36 %, t 2.94 s, I_f 1,226/500 A, I_N 100 A, S_e min 35/3.2 mm²
150 mm² (earth 50 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 375.0 A (41 %), V_d 1.15 %, t 4.60 s, I_f 1,379/500 A, I_N 100 A, S_e min 50/3.2 mm²
185 mm² (earth 70 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 428.0 A (36 %), V_d 0.98 %, t 7.00 s, I_f 1,541/500 A, I_N 100 A, S_e min 70/3.2 mm²
Parameter Symbol Value Notes
240 mm² (earth 95 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 511.0 A (30 %), V_d 0.81 %, t 11.78 s, I_f 1,673/500 A, I_N 100 A, S_e min 95/3.2 mm²
300 mm² (earth 120 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 584.0 A (26 %), V_d 0.70 %, t 18.40 s, I_f 1,754/500 A, I_N 100 A, S_e min 120/3.2 mm²
400 mm² (earth 120 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 692.0 A (22 %), V_d 0.61 %, t 32.72 s, I_f 1,769/500 A, I_N 100 A, S_e min 120/3.2 mm²
500 mm² (earth 120 mm²) ✓ ✓ ✓ ✓ ✗ ✓ ✓ FAIL I_Z 794.0 A (19 %), V_d 0.55 %, t 51.12 s, I_f 1,779/500 A, I_N 100 A, S_e min 120/3.2 mm²
630 mm² (earth 120 mm²) n/a Not tabulated by the selected edition for this cable and installation

4. Conforming Range

No standard size up to 500 mm² passes all seven checks for this load and installation. Failure reasons for the largest tabulated size: - Device rating (100A) < Design current (152.8A) Consider parallel cables, a shorter route, a different installation method, a larger protective device rating within the cable capacity, or a lower load.

5. Verification of the largest tabulated size (500 mm²)

The seven checks are worked in full for this size, exactly as in the Load Cable Sizing calculation. Sections 6 to 13 follow the same order as that report.

6. CHECK 1: Current Carrying Capacity (CCC)

Verify cable can continuously carry load current with all derating factors applied (AS/NZS 3008 Tables 22-29).
Parameter Symbol Value Notes
Table 24 $$F_{ladder}$$ 1 Table 24 (Col: Row 10, Row: 1)
Table 27(1) $$F_{temp}$$ 1 Table 27(1) (Col: Row 90, Row: 40)

6.2 Combined Derating Factor

Combined derating factor from applicable AS/NZS 3008 tables:

Formula: $$ \begin{aligned} F_{derating} &= F_{ladder} \times F_{temp} \\ &= 1.0 \times 1.0 \\ &= 1.000 \end{aligned} $$

6.3 Derated Cable Capacity

Base current rating adjusted for installation conditions: Ref: Table 14, Column 2, Row: 500mm²

Formula: $$ I_{derated} = F_{derating} \times I_C = 1.000 \times 794.0 = 794.000 \; \text{A} $$

6.4 CCC Verification

Check if derated capacity meets or exceeds design current:

Formula: $$ \begin{aligned} \text{Check: } I_{rated} \geq I_{design} \\ \quad 794 \geq 153 \\ \quad \text{PASS ✓} \end{aligned} $$

6.5 Cable Loading

Cable utilization as a percentage of derated capacity:

Formula: $$ \begin{aligned} \text{Cable Loading} &= \frac{I_{design}}{I_{derated}} \times 100 \\ &= \frac{153}{794} \times 100 \\ &= 19.2 \; \% \end{aligned} $$

7. CHECK 2: Voltage Drop

Verify voltage drop does not exceed maximum allowable limit (AS/NZS 3000 typically 5%).

7.1 Cable Impedance

Calculate cable impedance from resistance and reactance: Rc Ref: Table 35, Column 5, Row: 500mm². Values from AS/NZS 3008 impedance tables.

Formula: $$ Z_{v} = R_c PF \, + \, X_c\sqrt{1-PF^2} $$

7.2 Voltage Drop Calculation

Three-phase voltage drop at the design current I_B = I_load × k_design (152.8 A), the same current the capacity and device checks use: Absolute voltage drop in volts. Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C).

Formula: $$ \begin{aligned} \Delta V &= \sqrt{3} I_B L_{km}\left(R_c PF \, + \, X_c\sqrt{1-PF^2}\right) \\ &= \sqrt{3} \times 153 \times 0.1 \times \left(0.0544 \times 0.85 \, + \, 0.07 \times 0.527\right) \\ &= 2.2 \; \text{V}\;\text{(drop)} \\ &= 2.2 \; \text{V} \end{aligned} $$

7.3 Voltage Drop Percentage

Express voltage drop as percentage of supply voltage: Compared against maximum allowable limit.

Formula: $$ \begin{aligned} V_{d\%} &= \frac{V_d}{V} \times 100 \\ &= \frac{2.2}{400} \times 100 \\ &= 0.55 \; \% \end{aligned} $$

7.4 Voltage Drop Verification

Check if voltage drop is within acceptable limits:

Formula: $$ \begin{aligned} \text{Check: } V_{d\%} \leq V_{d,max} \\ \quad 0.55 \leq 5 \\ \quad \text{PASS ✓} \end{aligned} $$

7A. Cable Power Loss

Cable I²R losses indicate energy cost of the cable selection.

7A.1 Power Loss

Three-phase cable resistive power loss:

Formula: $$ \begin{aligned} P_{loss} &= 3 \times I^2 \times R_c \times L_{km} \\ &= 3 \times (153)^2 \times 0.0544 \times 0.1 \\ &= 381 \; \text{W} \end{aligned} $$

7A.2 Power Loss Percentage

Power loss as percentage of transmitted power: Power loss: 381.2 W (0.42%)

Formula: $$ P_{loss\%} = \frac{P_{loss}}{P_{transmitted}} \times 100 = 0.424 \; \% $$

8. CHECK 3: Short Circuit Withstand

Verify cable can withstand fault current for protection device operating time (adiabatic equation per AS/NZS 3008 Table 52).

8.1 Adiabatic Equation

Maximum fault withstand time from k-factor and conductor area: k-factor = 143.0 for Cu XLPE

Formula: $$ \begin{aligned} t_{max} &= \frac{k^2 \times S^2}{I_f^2} \\ &= \frac{(143)^2 \times (500)^2}{(10000)^2} \\ &= 51.1 \; \text{s} \end{aligned} $$

8.2 Short Circuit Verification

Check if cable can withstand fault for protection operating time:

Formula: $$ \begin{aligned} \text{Check: } t_{max} \geq t_{prot} \\ \quad 51.1 \geq 0.1 \\ \quad \text{PASS ✓} \end{aligned} $$

8.3 Minimum Conductor Size

Minimum conductor cross-sectional area to withstand the fault:

Formula: $$ \begin{aligned} S_{min} &= \frac{I_f \times \sqrt{t}}{k} \\ &= \frac{10000 \times \sqrt{0.1}}{143} \\ &= 22.1 \; \text{mm²} \end{aligned} $$

8.4 Conductor Size Verification

Check if selected conductor meets minimum size requirement:

Formula: $$ \begin{aligned} \text{Check: } S \geq S_{min} \\ \quad 500 \geq 22.1 \\ \quad \text{PASS ✓} \end{aligned} $$

9. CHECK 4: Earth Fault Loop Impedance

Verify earth fault current is sufficient to operate protection device (AS/NZS 3000 and IEC 60364).

9.1 Phase Conductor Impedance

Active conductor impedance over the cable length: Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C).

Formula: $$ \begin{aligned} Z_{phase} &= L_{km}\sqrt{R_c^2 + X_c^2} \\ &= 0.1 \times \sqrt{0.0544^2 + 0.07^2} \\ &= 0.00887 \; \Omega \end{aligned} $$

9.2 Earth Conductor Impedance

Protective earth conductor impedance, resistance and reactance at the earth size: R_e from Tables 34/35 and X_e from AS/NZS 3008.1.1:2017 Table 30 at 120 mm² (multicore, circular), read with the phase cable's arrangement. Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C).

Formula: $$ \begin{aligned} Z_{earth} &= L_{km}\sqrt{R_e^2 + X_e^2} \\ &= 0.1 \times \sqrt{0.197^2 + 0.0713^2} \\ &= 0.021 \; \Omega \end{aligned} $$

9.3 Total Loop Impedance

Sum of source, phase cable, and earth cable impedances: The magnitudes are added arithmetically, an upper bound on the phasor sum. Total impedance determines fault current magnitude.

Formula: $$ \begin{aligned} Z_{loop} &= Z_{source} + Z_{phase} + Z_{earth} \\ &= 0.1 + 0.00887 + 0.021 \\ &= 0.13 \; \Omega \end{aligned} $$

9.4 Earth Fault Current

Fault current from phase-to-earth voltage and loop impedance: Must exceed magnetic trip threshold of protection device.

Formula: $$ \begin{aligned} I_{fault} &= \frac{V_{ph}}{Z_{loop}} \\ &= \frac{231}{0.13} \\ &= 1779 \; \text{A} \end{aligned} $$

9.5 Maximum Cable Length

Maximum cable length that still meets earth fault protection (same loop model, per-km impedances): z_phase and z_earth are the phase and earth impedances in Ω/km.

Formula: $$ \begin{aligned} L_{max} &= \frac{V_{ph} / I_{a} - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \\ &= \frac{231 / 500 - 0.1}{0.0887 + 0.21} \times 1000 \\ &= 1214 \; \text{m} \end{aligned} $$

9.6 Cable Length Verification

Check if actual cable length is within maximum:

Formula: $$ \begin{aligned} \text{Check: } L \leq L_{max} \\ \quad 100 \leq 1214 \\ \quad \text{PASS ✓} \end{aligned} $$

9.7 Earth Fault Current Verification

Check if fault current will reliably trip protection:

Formula: $$ \begin{aligned} \text{Check: } I_{fault} \geq I_{trip} \times k_{mag} \\ \quad 1779 \geq 500 \\ \quad \text{PASS ✓} \end{aligned} $$

10. CHECK 5: Overload Coordination

Verify the overload protective device coordinates with the conductor (AS/NZS 3000:2018 Clause 2.5.3.1): its rating must cover the design current and must not exceed the derated cable capacity. The companion condition I_2 ≤ 1.45 I_Z is met by devices to AS/NZS 60898, AS/NZS 60947.2 or AS 60269.

10.1 Coordination Verification

Design current, device rating and derated cable capacity in ascending order: Device rating (100A) < Design current (152.8A)

Formula: $$ \begin{aligned} \text{Check: } I_B \leq I_N \leq I_Z \\ \quad 153 \leq 100 \leq 794 \\ \quad \text{FAIL ✗} \end{aligned} $$

11. CHECK 6: Earth Conductor Size

Verify the protective earth conductor is not smaller than the minimum AS/NZS 3000:2018 Table 5.1 sets for a 500 mm² phase conductor (120 mm²). The earth conductor is as entered.

11.1 Earth Conductor Size Verification

Earth conductor against the AS/NZS 3000:2018 Table 5.1 minimum: The earth conductor meets the Table 5.1 minimum.

Formula: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,5.1} \\ \quad 120 \geq 120 \\ \quad \text{PASS ✓} \end{aligned} $$

12. CHECK 7: Earth Conductor Withstand

Verify the protective earth conductor withstands the largest earth-fault current for the earth-fault clearing time t_ef (adiabatic equation). The largest earth-fault current flows for a fault at the cable origin, where only the source impedance limits it. That current is far above the device's instantaneous threshold, so t_ef is the instantaneous clearing time, not the protection time used in Check 3; enter the upstream backup time instead if clearance relies on it. The earth is an integral core of the same cable, so it shares the phase conductor's k: it starts at the insulation's operating temperature and ends at the same final temperature.

12.1 Earth-Fault Current at the Cable Origin

Phase-to-earth voltage over the source impedance (near-end fault): A fault further along the cable adds cable impedance and draws less current.

Formula: $$ \begin{aligned} I_{ef} &= \frac{V_{ph}}{Z_{source}} \\ &= \frac{231}{0.1} \\ &= 2309 \; \text{A} \end{aligned} $$

12.2 Minimum Earth Conductor Size

Adiabatic minimum cross-sectional area for the earth-fault clearing time: k = 143 from AS/NZS 3008.1.1:2017 Table 52 (Cu, initial 90 °C, final 250 °C); t_ef = 0.04 s (input).

Formula: $$ \begin{aligned} S_{e,min} &= \frac{I_{ef} \times \sqrt{t_{ef}}}{k} \\ &= \frac{2309 \times \sqrt{0.04}}{143} \\ &= 3.23 \; \text{mm²} \end{aligned} $$

12.3 Earth Conductor Maximum Withstand Time

Longest time the earth conductor can carry the earth-fault current:

Formula: $$ \begin{aligned} t_{e,max} &= \left(\frac{k \times S_e}{I_{ef}}\right)^2 \\ &= \left(\frac{143 \times 120}{2309}\right)^2 \\ &= 55.2 \; \text{s} \end{aligned} $$

12.4 Earth Conductor Withstand Verification

Check the earth conductor against the adiabatic minimum: The earth conductor withstands the earth-fault current for the earth-fault clearing time.

Formula: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,min} \\ \quad 120 \geq 3.23 \\ \quad \text{PASS ✓} \end{aligned} $$

13. Governing Criterion

Governing check: **Overload** - Overload: 152.8% utilization <-- GOVERNING - CCC: 19.2% utilization - Voltage Drop: 11.0% utilization - Short Circuit: 0.2% utilization - Earth Fault: 28.1% utilization - Earth Withstand: 2.7% utilization

14. Summary of Results

Range result and the checks for the smallest conforming size:
Parameter Symbol Value Notes
Load Current Iload 152.8 A
Design Current Idesign 152.8 A, design factor 1.0
Sizes Evaluated 19 of 20 Tabulated by the selected edition
Conforming Sizes 0 None
Smallest Conforming Size Smin None
Largest Conforming Size Smax None largest tabulated 500 mm²
Minimum Set By - check(s) failed by the next smaller size
Derated Capacity (500 mm²) IZ 794.0 A, 19.2 % loaded
Voltage Drop (500 mm²) Vd% 0.55 %, limit 5 %
Withstand Time (500 mm²) tmax 51.123 s, protection time 0.1 s
Earth Fault Current (500 mm²) Ifault 1,779 A, required 500 A
Device Rating IN 100 A, must not exceed I_Z 794.0 A
Earth Conductor Se 120 mm² Table 5.1 minimum 120 mm²
Earth Withstand Minimum Se,min 3.23 mm², 2,309 A earth fault at the origin cleared in t_ef 0.04 s
Governing Check Overload for 500 mm²

15. Overall Assessment

OVERALL STATUS: ✗ FAIL - no standard size conforms

16. Warnings & Recommendations

Warnings: No standard size up to 500 mm² passes all seven checks for this load

17. Standards Compliance

Selected cable-table basis: AS/NZS 3008.1.1:2017. Other referenced design standards: AS/NZS 3000:2018 (Clause 2.5.3.1 and Table 5.1) and IEC 60364.

Approval:

This calculation has been reviewed and approved by:
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Checked
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Approved
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Client Approved
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