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

Load Cable Sizing Calculation

This calculation uses AS/NZS 3008.1.1:2017 for its cable checks, with AS/NZS 3000:2018 Clause 2.5.3.1 for overload coordination and Table 5.1 for the earth conductor size; 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 Data

Cable construction and conductor specifications:
Parameter Symbol Value Notes
Sizing Mode Manual Cable sizing approach
Cable Type Fixed Cable construction
Cable Formation Multicore Multicore or Singlecore
Conductor Size A 50 Phase conductor CSA
MC Arrangement Circular Conductor arrangement
Cable Insulation XLPE Insulation type
Conductor Material Material Cu Cu or Al
Earth Conductor 50 Earth conductor CSA

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. 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)

3.2 Combined Derating Factor

Combined derating factor from applicable AS/NZS 3008 tables:

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

3.3 Derated Cable Capacity

Base current rating adjusted for installation conditions: Ref: Table 14, Column 2, Row: 50mm²

Formula: $$ I_{derated} = F_{derating} \times I_C = 1.000 \times 182.0 = 182.000 \; \text{A} $$

3.4 CCC Verification

Check if derated capacity meets or exceeds design current:

Formula: $$ \begin{aligned} \text{Check: } I_{rated} \geq I_{design} \\ \quad 182 \geq 153 \\ \quad \text{PASS ✓} \end{aligned} $$

3.5 Cable Loading

Cable utilization as a percentage of derated capacity:

Formula: $$ \begin{aligned} \text{Cable Loading} &= \frac{I_{design}}{I_{derated}} \times 100 \\ &= \frac{153}{182} \times 100 \\ &= 84 \; \% \end{aligned} $$

4. CHECK 2: Voltage Drop

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

4.1 Cable Impedance

Calculate cable impedance from resistance and reactance: Rc Ref: Table 35, Column 5, Row: 50mm². Values from AS/NZS 3008 impedance tables.

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

4.2 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: $$ \begin{aligned} \Delta V &= \sqrt{3} I_B L_{km}\left(R_c PF \, + \, X_c\sqrt{1-PF^2}\right) \\ &= \sqrt{3} \times 153 \times 0.1 \times \left(0.494 \times 0.85 \, + \, 0.0751 \times 0.527\right) \\ &= 12.2 \; \text{V}\;\text{(drop)} \\ &= 12.2 \; \text{V} \end{aligned} $$

4.3 Voltage Drop Percentage

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

Formula: $$ \begin{aligned} V_{d\%} &= \frac{V_d}{V} \times 100 \\ &= \frac{12.2}{400} \times 100 \\ &= 3.04 \; \% \end{aligned} $$

4.4 Voltage Drop Verification

Check if voltage drop is within acceptable limits:

Formula: $$ \begin{aligned} \text{Check: } V_{d\%} \leq V_{d,max} \\ \quad 3.04 \leq 5 \\ \quad \text{PASS ✓} \end{aligned} $$

4A. Cable Power Loss

Cable I²R losses indicate energy cost of the cable selection.

4A.1 Power Loss

Three-phase cable resistive power loss:

Formula: $$ \begin{aligned} P_{loss} &= 3 \times I^2 \times R_c \times L_{km} \\ &= 3 \times (153)^2 \times 0.494 \times 0.1 \\ &= 3461 \; \text{W} \end{aligned} $$

4A.2 Power Loss Percentage

Power loss as percentage of transmitted power: Power loss: 3461.4 W (3.85%)

Formula: $$ P_{loss\%} = \frac{P_{loss}}{P_{transmitted}} \times 100 = 3.85 \; \% $$

5. CHECK 3: Short Circuit Withstand

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

5.1 Adiabatic Equation

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

Formula: $$ \begin{aligned} t_{max} &= \frac{k^2 \times S^2}{I_f^2} \\ &= \frac{(143)^2 \times (50)^2}{(10000)^2} \\ &= 0.511 \; \text{s} \end{aligned} $$

5.2 Short Circuit Verification

Check if cable can withstand fault for protection operating time:

Formula: $$ \begin{aligned} \text{Check: } t_{max} \geq t_{prot} \\ \quad 0.511 \geq 0.1 \\ \quad \text{PASS ✓} \end{aligned} $$

5.3 Minimum Conductor Size

Minimum conductor cross-sectional area to withstand the fault:

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

5.4 Conductor Size Verification

Check if selected conductor meets minimum size requirement:

Formula: $$ \begin{aligned} \text{Check: } S \geq S_{min} \\ \quad 50 \geq 22.1 \\ \quad \text{PASS ✓} \end{aligned} $$

6. CHECK 4: Earth Fault Loop Impedance

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

6.1 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: $$ \begin{aligned} Z_{phase} &= L_{km}\sqrt{R_c^2 + X_c^2} \\ &= 0.1 \times \sqrt{0.494^2 + 0.0751^2} \\ &= 0.05 \; \Omega \end{aligned} $$

6.2 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 50 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: $$ \begin{aligned} Z_{earth} &= L_{km}\sqrt{R_e^2 + X_e^2} \\ &= 0.1 \times \sqrt{0.494^2 + 0.0751^2} \\ &= 0.05 \; \Omega \end{aligned} $$

6.3 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: $$ \begin{aligned} Z_{loop} &= Z_{source} + Z_{phase} + Z_{earth} \\ &= 0.1 + 0.05 + 0.05 \\ &= 0.2 \; \Omega \end{aligned} $$

6.4 Earth Fault Current

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

Formula: $$ \begin{aligned} I_{fault} &= \frac{V_{ph}}{Z_{loop}} \\ &= \frac{231}{0.2} \\ &= 1155 \; \text{A} \end{aligned} $$

6.5 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: $$ \begin{aligned} L_{max} &= \frac{V_{ph} / I_{a} - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \\ &= \frac{231 / 500 - 0.1}{0.5 + 0.5} \times 1000 \\ &= 362 \; \text{m} \end{aligned} $$

6.6 Cable Length Verification

Check if actual cable length is within maximum:

Formula: $$ \begin{aligned} \text{Check: } L \leq L_{max} \\ \quad 100 \leq 362 \\ \quad \text{PASS ✓} \end{aligned} $$

6.7 Earth Fault Current Verification

Check if fault current will reliably trip protection:

Formula: $$ \begin{aligned} \text{Check: } I_{fault} \geq I_{trip} \times k_{mag} \\ \quad 1155 \geq 500 \\ \quad \text{PASS ✓} \end{aligned} $$

7. 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.

7.1 Coordination Verification

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

Formula: $$ \begin{aligned} \text{Check: } I_B \leq I_N \leq I_Z \\ \quad 153 \leq 100 \leq 182 \\ \quad \text{FAIL ✗} \end{aligned} $$

8. 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 50 mm² phase conductor (16 mm²). The earth conductor is as entered.

8.1 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: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,5.1} \\ \quad 50 \geq 16 \\ \quad \text{PASS ✓} \end{aligned} $$

9. 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.

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

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

9.3 Earth Conductor Maximum Withstand Time

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

Formula: $$ \begin{aligned} t_{e,max} &= \left(\frac{k \times S_e}{I_{ef}}\right)^2 \\ &= \left(\frac{143 \times 50}{2309}\right)^2 \\ &= 9.59 \; \text{s} \end{aligned} $$

9.4 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: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,min} \\ \quad 50 \geq 3.23 \\ \quad \text{PASS ✓} \end{aligned} $$

10. Governing Criterion

Governing check: **Overload** - Overload: 152.8% utilization <-- GOVERNING - CCC: 84.0% utilization - Voltage Drop: 60.8% utilization - Short Circuit: 19.6% utilization - Earth Fault: 43.3% utilization - Earth Withstand: 6.5% utilization

11. Summary of Results

Complete results from all seven cable verification checks:
Parameter Symbol Value Notes
Load Current Iload 153 A Full load current
Design Current Idesign 153 A I_load × 1.0
Base Current Rating Ibase 182 A Ref: Table 14, Column 2, Row: 50mm²
Derated Capacity Irated 182 A After derating factors
CCC Margin ΔICCC 29.2 A Available capacity margin
Cable Impedance Zc 500 mΩ/km Per kilometer
Voltage Drop Vd 12.2 V Absolute voltage drop
Voltage Drop % Vd% 3.04 % As percentage of supply
Max Withstand Time tmax 511 ms Cable withstand capability
Protection Time tprot 100 ms Device operating time
Loop Impedance Zloop 200 mΩ Total earth fault loop
Fault Current Ifault 1.16 kA Earth fault current
Device Rating IN 100 A Overload protective device (I_B ≤ I_N ≤ I_Z)
Max Device Rating IZ 182 A Derated cable capacity, the largest device the cable may have
Minimum Earth Conductor Se,5.1 16 mm² AS/NZS 3000:2018 Table 5.1 for a 50 mm² phase conductor
Earth-Fault Current at Origin Ief 2.31 kA Largest earth-fault current, V_ph / Z_source
Earth Withstand Minimum Se,min 3.23 mm² Adiabatic minimum earth size, I_ef√t_ef / k
Earth Max Withstand Time te,max 9.59 s Earth conductor withstand at I_ef

12. Overall Assessment

Cable: 50 mm² Cu XLPE Checks Passed: 6 / 7 - Check 1 (Current Capacity): PASS ✓ - Check 2 (Voltage Drop): PASS ✓ - Check 3 (Short Circuit): PASS ✓ - Check 4 (Earth Fault): PASS ✓ - Check 5 (Overload Coordination): FAIL ✗ - Check 6 (Earth Conductor Size): PASS ✓ - Check 7 (Earth Conductor Withstand): PASS ✓ OVERALL STATUS: ✗ FAIL - Cable is NOT SUITABLE Failure Reasons: - Device rating (100A) < Design current (152.8A)

13. Warnings & Recommendations

Warnings: Cable utilization is elevated (84.0%) - monitor for load changes Power loss (3.85%) is significant Recommendations: Consider larger conductor to reduce energy losses

14. Standards Compliance

Selected cable-table basis: AS/NZS 3008.1.1:2017. Other referenced design standards: AS/NZS 3000:2018 and IEC 60364.

Approval:

This calculation has been reviewed and approved by:
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