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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 Motor 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 Motor Parameters

Motor 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
Motor Power P 2.2 kW Rated motor power
Power Unit kW Power measurement unit
Supply Voltage V 230 V Single-phase supply voltage
Power Factor PF 0.85 cos(φ)
Motor Efficiency η 85 % Motor efficiency
Starting Method Start DOL Motor starting method
Design Factor kdesign 1.25 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 6 Phase conductor CSA
MC Arrangement Circular Conductor arrangement
Cable Insulation XLPE Insulation type
Conductor Material Material Cu Cu or Al
Earth Conductor 6 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 6 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 20 A CB rating
Instantaneous Trip Multiplier kmag 5 Magnetic trip factor
Source Impedance Zsource 100 mΩ Upstream impedance

2. Motor Current Calculations

Calculate full load and starting currents for cable sizing criteria.

2.1 Full Load Current (I_FL)

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

Formula: $$ \begin{aligned} I_{FL} &= \frac{P/\eta}{V \times PF} \times 1000 \\ &= \frac{2.2/0.85}{230 \times 0.85} \times 1000 \\ &= 13.2 \; \text{A} \end{aligned} $$

2.2 Starting Current (I_start) - DOL

Motor starting current depends on starting method (DOL): Starting current affects short-term thermal considerations but not continuous capacity.

Formula: $$ \begin{aligned} I_{start} &= I_{FL} \times k_{start} \\ &= 13.2 \times 6 \\ &= 79.4 \; \text{A} \end{aligned} $$

3. CHECK 1: Current Carrying Capacity (CCC)

Verify cable can continuously carry motor 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: 6mm²

Formula: $$ I_{derated} = F_{derating} \times I_C = 1.000 \times 57.0 = 57.000 \; \text{A} $$

3.4 Motor Design Current

Design current for motor circuits per AS/NZS 3000 (1.25× full load current):

Formula: $$ \begin{aligned} I_{design} &= 1.25 \times I_{FL} \\ &= 1.25 \times 13.2 \\ &= 16.5 \; \text{A} \end{aligned} $$

3.5 CCC Verification

Check if derated capacity meets or exceeds design current:

Formula: $$ \begin{aligned} \text{Check: } I_{rated} \geq I_{design} \\ \quad 57 \geq 16.5 \\ \quad \text{PASS ✓} \end{aligned} $$

3.6 Cable Loading

Cable utilization as a percentage of derated capacity:

Formula: $$ \begin{aligned} \text{Cable Loading} &= \frac{I_{design}}{I_{derated}} \times 100 \\ &= \frac{16.5}{57} \times 100 \\ &= 29 \; \% \end{aligned} $$

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 motor full-load current I_FL; the design factor k_design (125 % motor rule) applies to cable capacity and protection only.

4.1 Cable Impedance

Calculate cable impedance from resistance and reactance: Rc Ref: Table 35, Column 5, Row: 6mm². 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 motor full-load current I_FL = 13.24 A (factor of 2 for go+return): Absolute voltage drop in volts.

Formula: $$ \begin{aligned} \Delta V &= 2 I_{FL} L_{km}\left(R_c PF \, + \, X_c\sqrt{1-PF^2}\right) \\ &= 2.69 \; \text{V}\;\text{(drop)} \\ &= 2.69 \; \text{V} \end{aligned} $$

4.3 Voltage Drop Percentage

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

Formula: $$ \begin{aligned} V_{d\%} &= \frac{V_d}{V} \times 100 \\ &= \frac{2.69}{230} \times 100 \\ &= 1.17 \; \% \end{aligned} $$

4.4 Voltage Drop Verification

Check if voltage drop is within acceptable limits:

Formula: $$ \begin{aligned} \text{Check: } V_{d\%} \leq V_{d,max} \\ \quad 1.17 \leq 5 \\ \quad \text{PASS ✓} \end{aligned} $$

4.5 Cable Power Loss

I²R power loss in cable (2 conductors for single-phase go+return):

Formula: $$ \begin{aligned} P_{loss} &= 2 \times I_{FL}^2 \times R_c \times L_{km} \\ &= 2 \times (13.2)^2 \times 3.93 \times 0.03 \\ &= 41.3 \; \text{W} \end{aligned} $$

4.6 Power Loss Percentage

Power loss as percentage of transmitted power:

Formula: $$ \begin{aligned} P_{loss\%} &= \frac{P_{loss}}{P_{transmitted}} \times 100 \\ &= 1.88 \; \% \end{aligned} $$

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: $$ \begin{aligned} t_{max} &= \frac{k^2 \times S^2}{I_f^2} \\ &= \frac{(143)^2 \times (6)^2}{(6000)^2} \\ &= 0.0204 \; \text{s} \end{aligned} $$

5.2 Short Circuit Verification

Check if cable can withstand fault for protection operating time: Insufficient withstand: 0.020s < 0.1s

Formula: $$ \begin{aligned} \text{Check: } t_{max} \geq t_{prot} \\ \quad 0.0204 \geq 0.1 \\ \quad \text{FAIL ✗} \end{aligned} $$

5.3 Minimum Conductor Size

Minimum conductor cross-sectional area to withstand the fault:

Formula: $$ \begin{aligned} S_{min} &= \frac{I_f \times \sqrt{t}}{k} \\ &= \frac{6000 \times \sqrt{0.1}}{143} \\ &= 13.3 \; \text{mm²} \end{aligned} $$

5.4 Conductor Size Verification

Check if selected conductor meets minimum size requirement:

Formula: $$ \begin{aligned} \text{Check: } S \geq S_{min} \\ \quad 6 \geq 13.3 \\ \quad \text{FAIL ✗} \end{aligned} $$

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 = 3.93 Ω/km: AC resistance at 90 °C, the operating temperature of Cu XLPE cable. X_e = 0.0887 Ω/km: AS/NZS 3008.1.1:2017 Table 30 reactance at the 6 mm² earth size, same cable arrangement as the phase conductor.

Formula: $$ \begin{aligned} Z_{earth} &= L_{km}\sqrt{R_e^2 + X_e^2} \\ &= 0.03 \times \sqrt{(3.93)^2 + (0.0887)^2} \\ &= 0.118 \; \Omega \end{aligned} $$

6.2 Total Loop Impedance

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

Formula: $$ \begin{aligned} Z_{loop} &= Z_{source} + Z_{phase} + Z_{earth} \\ &= 0.1 + 0.118 + 0.118 \\ &= 0.336 \; \Omega \end{aligned} $$

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: $$ \begin{aligned} I_{fault} &= \frac{V_{ph}}{Z_{loop}} \\ &= \frac{230}{0.336} \\ &= 685 \; \text{A} \end{aligned} $$

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: $$ \begin{aligned} L_{max} &= \frac{V_{ph} / I_{a} - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \\ &= \frac{230 / 100 - 0.1}{3.93 + 3.93} \times 1000 \\ &= 280 \; \text{m} \end{aligned} $$

6.5 Cable Length Verification

Check if actual cable length is within maximum:

Formula: $$ \begin{aligned} \text{Check: } L \leq L_{max} \\ \quad 30 \leq 280 \\ \quad \text{PASS ✓} \end{aligned} $$

6.6 Earth Fault Current Verification

Check if fault current will reliably trip protection:

Formula: $$ \begin{aligned} \text{Check: } I_{fault} \geq I_{trip} \times k_{mag} \\ \quad 685 \geq 100 \\ \quad \text{PASS ✓} \end{aligned} $$

7. CHECK 5: Earth Conductor Size

Verify the protective earth conductor is not smaller than the minimum AS/NZS 3000:2018 Table 5.1 sets for a 6 mm² phase conductor (2.5 mm²). The earth conductor is as entered.

7.1 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: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,5.1} \\ \quad 6 \geq 2.5 \\ \quad \text{PASS ✓} \end{aligned} $$

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. 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.

8.1 Earth-Fault Current at the Cable Origin

Supply voltage (single-phase, V_ph = V) over the source impedance (near-end fault): A fault further along the cable adds cable impedance and draws less current.

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

8.2 Minimum Earth Conductor Size

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

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

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

Formula: $$ \begin{aligned} t_{e,max} &= \left(\frac{k \times S_e}{I_{ef}}\right)^2 \\ &= \left(\frac{143 \times 6}{2300}\right)^2 \\ &= 0.139 \; \text{s} \end{aligned} $$

8.4 Earth Conductor Withstand Verification

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

Formula: $$ \begin{aligned} \text{Check: } S_e \geq S_{e,min} \\ \quad 6 \geq 3.22 \\ \quad \text{PASS ✓} \end{aligned} $$

9. Summary of Results

Complete results from all six cable verification checks:
Parameter Symbol Value Notes
Full Load Current IFL 13.2 A Motor full load current
Starting Current Istart 79.4 A Motor starting current
Base Current Rating Ibase 57 A Ref: Table 11, Column 2, Row: 6mm²
Derated Capacity Irated 57 A After derating factors
CCC Margin ΔICCC 40.5 A Available capacity margin
Cable Impedance Zc 3.93 Ω/km Per kilometer
Voltage Drop Vd 2.69 V Absolute voltage drop
Voltage Drop % Vd% 1.17 % As percentage of supply
Max Withstand Time tmax 20.4 ms Cable withstand capability
Protection Time tprot 100 ms Device operating time
Loop Impedance Zloop 336 mΩ Total earth fault loop
Fault Current Ifault 685 A Earth fault current
Minimum Earth Conductor Se,5.1 2.5 mm² AS/NZS 3000:2018 Table 5.1 for a 6 mm² phase conductor
Earth-Fault Current at Origin Ief 2.3 kA Largest earth-fault current, V / Z_source
Earth Withstand Minimum Se,min 3.22 mm² Adiabatic minimum earth size, I_ef√t / k
Earth Max Withstand Time te,max 139 ms Earth conductor withstand at I_ef
Power Loss Ploss 41.3 W 1.88% of transmitted power

10. Overall Assessment

Cable: 6 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: 41.3 W (1.88%) OVERALL STATUS: ✗ FAIL - Cable is NOT SUITABLE Failure Reasons: • Insufficient withstand: 0.020s < 0.1s

12. Standards Compliance

Selected cable-table basis: AS/NZS 3008.1.1:2017. Other referenced design standards: AS/NZS 3000:2018, IEC 60364, and IEC 60034.

Approval:

This calculation has been reviewed and approved by:
Created By
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