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

Single-Phase Load Cable Sizing Calculation

This calculation uses AS/NZS 3008.1.1:2017 for its six cable 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 5 kW Rated load power
Power Unit kW Power measurement unit
Supply Voltage V 230 V Single-phase supply 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 30 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
Conductor Size A 16 Phase conductor CSA
MC Arrangement Circular Conductor arrangement
Cable Insulation XLPE Insulation type
Conductor Material Material Cu Cu or Al
Earth Conductor 16 Earth conductor CSA

1.3 Cable Installation

Installation method and environmental conditions:
Parameter Symbol Value Notes
Installation Method Unenclosed
Unenclosed Type 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 Earth-conductor withstand: instantaneous operation, or upstream backup if relied on
Protection Device Rating Itrip 32 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)

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

Formula: $$ \begin{aligned} I_{load} &= \frac{P}{V \times PF} \times 1000 \\ &= \frac{5}{230 \times 0.85} \times 1000 \\ &= 25.6 \; \text{A} \end{aligned} $$

2.2 Design Current (I_design)

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

Formula: $$ \begin{aligned} I_{design} &= I_{load} \times k_{design} \\ &= 25.6 \times 1 \\ &= 25.6 \; \text{A} \end{aligned} $$

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 11, Column 2, Row: 16mm²

Formula: $$ I_{derated} = F_{derating} \times I_C = 1.000 \times 104.0 = 104.000 \; \text{A} $$

3.4 CCC Verification

Check if derated capacity meets or exceeds design current:

Formula: $$ \begin{aligned} \text{Check: } I_{rated} \geq I_{design} \\ \quad 104 \geq 25.6 \\ \quad \text{PASS ✓} \end{aligned} $$

3.5 Cable Loading

Cable utilization as a percentage of derated capacity:

Formula: $$ \begin{aligned} \text{Cable Loading} &= \frac{I_{design}}{I_{derated}} \times 100 \\ &= \frac{25.6}{104} \times 100 \\ &= 24.6 \; \% \end{aligned} $$

4. CHECK 2: Voltage Drop

Verify voltage drop does not exceed maximum allowable limit (AS/NZS 3000 typically 5%). Uses factor of 2 for single-phase go+return path. Voltage drop is evaluated at the design current I_B = I_L × k_design = 25.58 A, the current the cable and protective device are sized for.

4.1 Cable Impedance

Calculate cable impedance from resistance and reactance: Rc Ref: Table 35, Column 5, Row: 16mm². Values from AS/NZS 3008 impedance tables.

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

4.2 Voltage Drop Calculation

Single-phase voltage drop at the design current I_B = 25.58 A (factor of 2 for go+return): Absolute voltage drop in volts.

Formula: $$ \begin{aligned} \Delta V &= 2 I_B L_{km}\left(R_c PF \, + \, X_c\sqrt{1-PF^2}\right) \\ &= 1.98 \; \text{V}\;\text{(drop)} \\ &= 1.98 \; \text{V} \end{aligned} $$

4.3 Voltage Drop Percentage

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

Formula: $$ \begin{aligned} V_{d\%} &= \frac{V_d}{V} \times 100 \\ &= \frac{1.98}{230} \times 100 \\ &= 0.862 \; \% \end{aligned} $$

4.4 Voltage Drop Verification

Check if voltage drop is within acceptable limits:

Formula: $$ \begin{aligned} \text{Check: } V_{d\%} \leq V_{d,max} \\ \quad 0.862 \leq 5 \\ \quad \text{PASS ✓} \end{aligned} $$

4.5 Cable Power Loss

I²R power loss in cable at the load current I_L (2 conductors for single-phase go+return):

Formula: $$ \begin{aligned} P_{loss} &= 2 \times I_L^2 \times R_c \times L_{km} \\ &= 2 \times (25.6)^2 \times 1.47 \times 0.03 \\ &= 57.7 \; \text{W} \end{aligned} $$

4.6 Power Loss Percentage

Power loss as percentage of transmitted power:

Formula: $$ \begin{aligned} P_{loss\%} &= \frac{P_{loss}}{P_{transmitted}} \times 100 \\ &= 1.15 \; \% \end{aligned} $$

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: $$ \begin{aligned} t_{max} &= \frac{k^2 \times S^2}{I_f^2} \\ &= \frac{(143)^2 \times (16)^2}{(10000)^2} \\ &= 0.0523 \; \text{s} \end{aligned} $$

5.2 Short Circuit Verification

Check if cable can withstand fault for protection operating time: Insufficient withstand: 0.052s < 0.1s

Formula: $$ \begin{aligned} \text{Check: } t_{max} \geq t_{prot} \\ \quad 0.0523 \geq 0.1 \\ \quad \text{FAIL ✗} \end{aligned} $$

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: $$ \begin{aligned} \text{Check: } S \geq S_{min} \\ \quad 16 \geq 22.1 \\ \quad \text{FAIL ✗} \end{aligned} $$

6. CHECK 4: Earth Fault Loop Impedance

Verify earth fault current is sufficient to operate protection device (AS/NZS 3000 and IEC 60364). For single-phase, V_ph = V (supply is phase voltage). The earth conductor impedance includes its AS/NZS 3008 Table 30 reactance at the earth size.

6.1 Earth Conductor Impedance

Earth conductor impedance from its resistance and reactance at the earth size: R_e = 1.47 Ω/km: AC resistance at 90 °C, the operating temperature of Cu XLPE cable. X_e = 0.0805 Ω/km: AS/NZS 3008.1.1:2017 Table 30 reactance at the 16 mm² earth size, same cable arrangement as the phase conductor.

Formula: $$ \begin{aligned} Z_{earth} &= L_{km}\sqrt{R_e^2 + X_e^2} \\ &= 0.03 \times \sqrt{(1.47)^2 + (0.0805)^2} \\ &= 0.0442 \; \Omega \end{aligned} $$

6.2 Total Loop Impedance

Sum of source, phase cable, and earth cable impedances: Total impedance determines fault current magnitude.

Formula: $$ \begin{aligned} Z_{loop} &= Z_{source} + Z_{phase} + Z_{earth} \\ &= 0.1 + 0.0442 + 0.0442 \\ &= 0.188 \; \Omega \end{aligned} $$

6.3 Earth Fault Current

Fault current from phase voltage and loop impedance (V_ph = V for single-phase): Must exceed magnetic trip threshold of protection device.

Formula: $$ \begin{aligned} I_{fault} &= \frac{V_{ph}}{Z_{loop}} \\ &= \frac{230}{0.188} \\ &= 1221 \; \text{A} \end{aligned} $$

6.4 Maximum Cable Length

Maximum cable length that still meets earth fault protection: |z_phase| = |R_c + jX_c| and |z_earth| = |R_e + jX_e| per kilometre. Impedances are added as magnitudes, which gives a loop impedance no smaller than the phasor sum.

Formula: $$ \begin{aligned} L_{max} &= \frac{V_{ph} / I_{a} - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \\ &= \frac{230 / 160 - 0.1}{1.47 + 1.47} \times 1000 \\ &= 454 \; \text{m} \end{aligned} $$

6.5 Cable Length Verification

Check if actual cable length is within maximum:

Formula: $$ \begin{aligned} \text{Check: } L \leq L_{max} \\ \quad 30 \leq 454 \\ \quad \text{PASS ✓} \end{aligned} $$

6.6 Earth Fault Current Verification

Check if fault current will reliably trip protection:

Formula: $$ \begin{aligned} \text{Check: } I_{fault} \geq I_{trip} \times k_{mag} \\ \quad 1221 \geq 160 \\ \quad \text{PASS ✓} \end{aligned} $$

7. CHECK 5: Earth Conductor Size

Verify the protective earth conductor is not smaller than the AS/NZS 3000:2018 Table 5.1 minimum for a 16 mm² phase conductor.

7.1 Earth Conductor Size Verification

Table 5.1 minimum earth conductor S_e,min = 6.0 mm²; earth conductor given S_e = 16.0 mm²: Earth conductor meets the Table 5.1 minimum.

Formula: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,min} \\ \quad 16 \geq 6 \\ \quad \text{PASS ✓} \end{aligned} $$

8. CHECK 6: 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 (V_ph = V for single-phase). That current is far above the protective device's instantaneous threshold, so t_ef is the device's instantaneous operating time (t_ef = 0.04 s), not the clearance time used for Check 3; enter the upstream backup time instead if that device is relied on to clear the fault.

8.1 Earth-Fault Current at the Cable Origin

Near-end earth fault current from supply voltage and source impedance: Cable impedance is zero at the origin, so this is the largest earth-fault current the earth conductor can see.

Formula: $$ \begin{aligned} I_{ef} &= \frac{V}{Z_{source}} \\ &= \frac{230}{0.1} \\ &= 2300 \; \text{A} \end{aligned} $$

8.2 Minimum Earth Conductor Size

Adiabatic minimum for the earth-fault clearing time t_ef = 0.04 s, with k = 143 from AS/NZS 3008.1.1:2017 Table 52 (Cu, initial 90 °C, final 250 °C): The earth is an integral core of the same cable, so it starts at the insulation operating temperature and ends at the same final temperature as the phase conductor; it shares the phase conductor's Table 52 k.

Formula: $$ \begin{aligned} S_{e,min} &= \frac{I_{ef} \times \sqrt{t_{ef}}}{k} \\ &= \frac{2300 \times \sqrt{0.04}}{143} \\ &= 3.22 \; \text{mm²} \end{aligned} $$

8.3 Earth Conductor Maximum Withstand Time

Maximum time the earth conductor can carry the near-end earth fault current:

Formula: $$ \begin{aligned} t_{max,e} &= \left(\frac{k \times S_e}{I_{ef}}\right)^2 \\ &= \left(\frac{143 \times 16}{2300}\right)^2 \\ &= 0.99 \; \text{s} \end{aligned} $$

8.4 Earth Conductor Withstand Verification

Check if the earth conductor meets the adiabatic minimum: Earth conductor can withstand the earth fault for the clearing time.

Formula: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,min} \\ \quad 16 \geq 3.22 \\ \quad \text{PASS ✓} \end{aligned} $$

9. Summary of Results

Complete results from all six cable verification checks:
Parameter Symbol Value Notes
Load Current Iload 25.6 A Full load current
Design Current Idesign 25.6 A I_load × 1.0
Base Current Rating Ibase 104 A Ref: Table 11, Column 2, Row: 16mm²
Derated Capacity Irated 104 A After derating factors
CCC Margin ΔICCC 78.4 A Available capacity margin
Cable Impedance Zc 1.47 Ω/km Per kilometer
Voltage Drop Vd 1.98 V Absolute voltage drop
Voltage Drop % Vd% 0.862 % As percentage of supply
Max Withstand Time tmax 52.3 ms Cable withstand capability
Protection Time tprot 100 ms Device operating time
Loop Impedance Zloop 188 mΩ Total earth fault loop
Fault Current Ifault 1.22 kA Earth fault current
Min Earth Conductor Se,min 6 mm² AS/NZS 3000:2018 Table 5.1 minimum; earth used 16.0 mm²
Max Earth Fault Current Ief 2.3 kA Near-end earth fault, V / Z_source
Earth Withstand Min CSA Se,adb 3.22 mm² I_ef √t / k, k = 143.0
Power Loss Ploss 57.7 W 1.15% of transmitted power

10. Overall Assessment

Cable: 16 mm² Cu XLPE Checks Passed: 5 / 6 • Check 1 (Current Capacity): PASS ✓ • Check 2 (Voltage Drop): PASS ✓ • Check 3 (Short Circuit): FAIL ✗ • Check 4 (Earth Fault): PASS ✓ • Check 5 (Earth Conductor Size): PASS ✓ • Check 6 (Earth Conductor Withstand): PASS ✓ Governing Criterion: Short Circuit Power Loss: 57.7 W (1.15%) OVERALL STATUS: ✗ FAIL - Cable is NOT SUITABLE Failure Reasons: • Insufficient withstand: 0.052s < 0.1s

12. 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:
Created By
Engineer Name
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Checked
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Date: ..........................
Approved
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Client Approved
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