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Cable Permissible Load

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AS/NZS 3008 edition

The calculation and its reports use the AS/NZS 3008.1.1:2017 tables.

Power factor direction

Permissible load table

Series of loads checked against the cable; the envelope is reported either way.

Supply voltage (V) *

Power factor

Motor efficiency

The kW table is motor shaft output (IEC 60072): I = P / (√3·V·PF·η).

Design factor

Cable length *

Length unit

Maximum voltage drop

Cable type

Cable formation

Conductor size (mm²) *

Multicore arrangement

Singlecore arrangement

Cable insulation

Conductor material

Earth conductor size (mm²)

Installation method

Unenclosed type (MC)

Unenclosed type (SC)

Air arrangement

Catinerary

Cables per tier

Circuits per tier

Ladder spacing

Ladder tiers

Bunched circuits/cables

Bunched arrangement

Thermal ins coverage

Thermal ins method

Enclosed type

Conduit spacing

SC conduit type

Direct buried spacing

Buried circuits/cables

Air ambient temperature (°C)

Burial depth (m)

Soil ambient temperature (°C)

Soil resistivity (K·m/W)

Prospective fault current

CB clearance time

Earth fault clearing time

Earth conductor withstand: a fault at the cable origin clears instantaneously; enter the upstream backup time if relied on.

Instantaneous trip multiplier

Source impedance

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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 Permissible Load Calculation

The seven checks of the load cable sizing method (AS/NZS 3008.1.1:2017 for current-carrying capacity, voltage drop, short-circuit withstand and earth fault loop impedance; AS/NZS 3000:2018 Clause 2.5.3.1 for overload coordination and Table 5.1 for the earth conductor size; the adiabatic equation for the earth conductor withstand) are worked backwards for the selected cable and installation to find the largest load the cable may supply and the largest protective device it may be protected by. The load-type label used for sizing (control panel, distribution board, VSD, ...) does not change the permissible load; only its current, power factor and design factor do.

1.1 Supply and Load Basis

Supply voltage, power factor and design factor of the loads to be supplied:

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
Supply Voltage	V_pp	400 V	Phase-to-phase voltage
Design Factor	k_design	1	Design margin multiplier
Cable Length	L	100 Meter	Cable run length
Length Unit		Meter	Length measurement unit
Max Voltage Drop	V_d,max	5 %	Maximum allowable
Motor Efficiency	η	95 %	kW load table only: IEC 60072 ratings are shaft output, I = P / (√3 V PF η)

1.2 Cable Data

Cable construction and conductor specifications:

Parameter	Symbol	Value	Notes
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		16	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 Protection

Fault level, clearing time, instantaneous trip multiplier and source impedance:

Parameter	Symbol	Value	Notes
Prospective Fault Current	I_f	10 kA	Maximum fault current
CB Clearance Time	t_prot	100 ms	Protection device time
Earth Fault Clearing Time	t_ef	40 ms	Near-end earth fault (earth withstand)
Instantaneous Trip Multiplier	k_mag	5	Magnetic trip factor
Source Impedance	Z_source	100 mΩ	Upstream impedance

2. Limit 1: Current Carrying Capacity

Derated capacity of the cable from AS/NZS 3008 Tables with all applicable derating factors.

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)

2.2 Combined Derating Factor

Combined derating factor from applicable AS/NZS 3008 tables:

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

2.3 Derated Cable Capacity

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

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

2.4 Capacity-Limited Load Current

The design current (load current times the design factor) may not exceed the derated capacity:

Formula: $$ \begin{aligned} I_{L,CCC} &= \frac{I_Z}{k_{design}} \\ &= \frac{182}{1} \\ &= 182 \; \text{A} \end{aligned} $$

3. Limit 2: Voltage Drop

The three-phase voltage drop over 100 m may not exceed 5.0 % of 400 V. It is evaluated at the design current I_B = I_L × k_design, the same current the capacity and device limits use. Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C).

3.1 Effective Impedance

Signed AS/NZS 3008 impedance for the load power factor (lagging adds the reactive term): Rc Ref: Table 35, Column 5, Row: 50mm². Xc Ref: Table 30, Column 10, Row: 50mm².

Formula: $$ \begin{aligned} Z_{eff} &= R_c \cos\varphi + X_c \sin\varphi \\ &= 0.49400 \times 0.85 + 0.07510 \times 0.5268 \\ &= 0.45946 \; \Omega/\text{km} \end{aligned} $$

3.2 Voltage Drop per Ampere

Formula: $$ \begin{aligned} \frac{V_d}{I} &= \sqrt{3} \times L_{km} \times Z_{eff} \\ &= \sqrt{3} \times 0.10000 \times 0.45946 \\ &= 0.07958 \; \text{V/A} \end{aligned} $$

3.3 Voltage-Drop-Limited Load Current

Largest load current whose design current keeps the drop within the limit:

Formula: $$ \begin{aligned} I_{L,VD} &= \frac{V_{d,max}}{(V_d / I) \times k_{design}} \\ &= \frac{5\% \times 400}{0.07958 \times 1} \\ &= \frac{20.0}{0.07958} \\ &= 251 \; \text{A} \end{aligned} $$

4. Short Circuit Withstand

Independent of the load: the cable must withstand the prospective fault current for the clearing time (adiabatic equation, AS/NZS 3008 Table 52). A cable that fails this check has no permissible load with the entered protection.

4.1 Adiabatic Equation

k-factor = 143.0 for Cu XLPE

Formula: $$ \begin{aligned} t_{max} &= \frac{k^2 S^2}{I_f^2} \\ &= \frac{(143)^2 \times (50)^2}{(10000)^2} \\ &= 0.5112 \; \text{s} \end{aligned} $$

4.2 Short Circuit Verification

Minimum conductor size for the fault: S_min = 22.1 mm².

Formula: $$ \text{Check: } t_{max} \geq t_{prot} \quad 0.5112 \geq 0.1 \quad \text{PASS ✓} $$

5. Earth Conductor

Independent of the load: the protective earth conductor must be at least the AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor size, and it must withstand the largest earth-fault current for the earth-fault clearing time t_ef (adiabatic equation). A near-end fault is far above the device's instantaneous threshold, so t_ef is the instantaneous clearing time, not the protection time of the short-circuit check; enter the upstream backup time if clearance relies on it. A cable that fails either check has no permissible load.

5.1 Earth Conductor Size (AS/NZS 3000 Table 5.1)

AS/NZS 3000:2018 Table 5.1 minimum for a 50 mm² phase conductor: 16 mm².

Formula: $$ \text{Check: } S_{earth} \geq S_{earth,min} \quad 16 \geq 16 \; \text{mm}^2 \quad \text{PASS ✓} $$

5.2 Largest Earth Fault Current

A fault at the supply end of the cable is limited only by the source impedance, so the near-end fault gives the largest earth-fault current:

Formula: $$ \begin{aligned} I_{ef} &= \frac{V}{\sqrt{3} \, Z_{source}} \\ &= \frac{400}{\sqrt{3} \times 0.10000} \\ &= 2309 \; \text{A} \end{aligned} $$

5.3 Minimum Earth Conductor Size for Withstand

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

Formula: $$ \begin{aligned} S_{min} &= \frac{I_{ef} \sqrt{t_{ef}}}{k} \\ &= \frac{2309 \times \sqrt{0.04}}{143} \\ &= 3.23 \; \text{mm}^2 \end{aligned} $$

5.4 Earth Conductor Withstand Verification

Withstand time of the earth conductor: t_max = (k S_earth / I_ef)² = 0.982 s against an earth-fault clearing time of 0.04 s.

Formula: $$ \text{Check: } S_{earth} \geq S_{min} \quad 16 \geq 3.23 \; \text{mm}^2 \quad \text{PASS ✓} $$

6. Limit 3a: Earth Fault Loop Impedance

The earth fault current of this loop fixes the largest instantaneous trip setting, and so the largest device rating, that still disconnects on an earth fault at the far end.

6.1 Phase Conductor Impedance

Resistances are read at the insulation operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium capped at 90 °C).

Formula: $$ \begin{aligned} Z_{phase} &= L_{km} \sqrt{R_c^2 + X_c^2} \\ &= 0.10000 \times \sqrt{0.49400^2 + 0.07510^2} \\ &= 0.04997 \; \Omega \end{aligned} $$

6.2 Earth Conductor Impedance

Earth conductor 16 mm²: R_e from Tables 34/35 and X_e from AS/NZS 3008.1.1:2017 Table 30 at 16 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: $$ \begin{aligned} Z_{earth} &= L_{km} \sqrt{R_e^2 + X_e^2} \\ &= 0.10000 \times \sqrt{1.470^2 + 0.08050^2} \\ &= 0.14722 \; \Omega \end{aligned} $$

6.3 Total Loop Impedance

The magnitudes are added arithmetically, an upper bound on the phasor sum.

Formula: $$ \begin{aligned} Z_{loop} &= Z_{source} + Z_{phase} + Z_{earth} \\ &= 0.10000 + 0.04997 + 0.14722 \\ &= 0.29719 \; \Omega \end{aligned} $$

6.4 Earth Fault Current

Formula: $$ \begin{aligned} I_{fault} &= \frac{V_{ph}}{Z_{loop}} \\ &= \frac{231}{0.29719} \\ &= 777 \; \text{A} \end{aligned} $$

6.5 Largest Device Rating for Earth Fault Protection

The device must see at least its instantaneous trip current, I_fault >= I_N x k_mag:

Formula: $$ \begin{aligned} I_{N,EFL} &= \frac{I_{fault}}{k_{mag}} \\ &= \frac{777}{5} \\ &= 155 \; \text{A} \end{aligned} $$

7. Limit 3b: Overload Coordination

AS/NZS 3000:2018 Clause 2.5.3.1 requires I_B <= I_N <= I_Z: the device rating may not exceed the derated cable capacity and must cover the design current. 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 Largest Permissible Device Rating

Limited by the earth fault loop (I_N ≤ I_fault / k_mag). Largest preferred rating (AS/NZS 60898 / 60947.2 / AS 60269) not exceeding this: 125 A.

Formula: $$ \begin{aligned} I_{N,max} &= \min(I_Z, I_{N,EFL}) \\ &= \min(182, 155) \\ &= 155 \; \text{A} \end{aligned} $$

7.2 Protection-Limited Load Current

With the largest preferred device, the design current may not exceed the device rating:

Formula: $$ \begin{aligned} I_{L,prot} &= \frac{I_{N,std}}{k_{design}} \\ &= \frac{125}{1} \\ &= 125 \; \text{A} \end{aligned} $$

8. Permissible Load Envelope

The permissible load current is the smallest of the three limits; the short-circuit check and both earth-conductor checks must also pass.

8.1 Permissible Load Current

Governing limit: Earth Fault Loop (I_N ≤ I_fault / k_mag). Design current at this load: 125.0 A.

Formula: $$ \begin{aligned} I_{L,max} &= \min(I_{L,CCC}, I_{L,VD}, I_{L,prot}) \\ &= \min(182, 251, 125) \\ &= 125 \; \text{A} \end{aligned} $$

8.2 Permissible Load Power

Apparent power S_max = 86.6 kVA. Power loss at this load: 2,316 W (3.15 %).

Formula: $$ \begin{aligned} P_{max} &= \sqrt{3} \times V \times I_{L,max} \times \cos\varphi / 1000 \\ &= \sqrt{3} \times 400 \times 125 \times 0.85 / 1000 \\ &= 73.6 \; \text{kW} \end{aligned} $$

8.3 Permissible Motor Output

P_max is electrical input; the largest motor (IEC 60072 shaft rating) it supplies is lower by the efficiency:

Formula: $$ \begin{aligned} P_{motor} &= P_{max} \times \eta \\ &= 73.6 \times 0.95 \\ &= 69.9 \; \text{kW} \end{aligned} $$

9. Permissible Loads

Series of preferred motor ratings (IEC 60072 kW shaft output, line current I = P / (√3 V PF η) at η = 95 %) checked with all seven checks; each load is protected by the smallest preferred device rating at or above its design current. CCC = current-carrying capacity, VD = voltage drop, SC = short-circuit withstand, EFL = earth fault loop, OVL = overload coordination, ESZ = earth conductor size, EWT = earth conductor withstand; the Symbol column shows the seven marks in that order.

Parameter	Symbol	Value	Notes
1.5 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	2.7 A (1.6 kW input, 2 kVA), I_N 6 A, 1 % loaded, V_d 0.05 %, I_f 777/30 A
2.2 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	3.9 A (2.3 kW input, 3 kVA), I_N 6 A, 2 % loaded, V_d 0.08 %, I_f 777/30 A
3 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	5.4 A (3.2 kW input, 4 kVA), I_N 6 A, 3 % loaded, V_d 0.11 %, I_f 777/30 A
4 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	7.1 A (4.2 kW input, 5 kVA), I_N 10 A, 4 % loaded, V_d 0.14 %, I_f 777/50 A
5.5 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	9.8 A (5.8 kW input, 7 kVA), I_N 10 A, 5 % loaded, V_d 0.20 %, I_f 777/50 A

Parameter	Symbol	Value	Notes
7.5 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	13.4 A (7.9 kW input, 9 kVA), I_N 16 A, 7 % loaded, V_d 0.27 %, I_f 777/80 A
11 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	19.7 A (11.6 kW input, 14 kVA), I_N 20 A, 11 % loaded, V_d 0.39 %, I_f 777/100 A
15 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	26.8 A (15.8 kW input, 19 kVA), I_N 32 A, 15 % loaded, V_d 0.53 %, I_f 777/160 A
18.5 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	33.1 A (19.5 kW input, 23 kVA), I_N 40 A, 18 % loaded, V_d 0.66 %, I_f 777/200 A
22 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	39.3 A (23.2 kW input, 27 kVA), I_N 40 A, 22 % loaded, V_d 0.78 %, I_f 777/200 A

Parameter	Symbol	Value	Notes
30 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	53.6 A (31.6 kW input, 37 kVA), I_N 63 A, 29 % loaded, V_d 1.07 %, I_f 777/315 A
37 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	66.1 A (38.9 kW input, 46 kVA), I_N 80 A, 36 % loaded, V_d 1.32 %, I_f 777/400 A
45 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	80.4 A (47.4 kW input, 56 kVA), I_N 100 A, 44 % loaded, V_d 1.60 %, I_f 777/500 A
55 kW	✓ ✓ ✓ ✓ ✓ ✓ ✓	PASS	98.3 A (57.9 kW input, 68 kVA), I_N 100 A, 54 % loaded, V_d 1.96 %, I_f 777/500 A
75 kW	✓ ✓ ✓ ✗ ✓ ✓ ✓	FAIL	134.1 A (78.9 kW input, 93 kVA), I_N 160 A, 74 % loaded, V_d 2.67 %, I_f 777/800 A

Parameter	Symbol	Value	Notes
90 kW	✓ ✓ ✓ ✗ ✗ ✓ ✓	FAIL	160.9 A (94.7 kW input, 111 kVA), I_N 200 A, 88 % loaded, V_d 3.20 %, I_f 777/1,000 A
110 kW	✗ ✓ ✓ ✗ ✗ ✓ ✓	FAIL	196.6 A (115.8 kW input, 136 kVA), I_N 200 A, 108 % loaded, V_d 3.91 %, I_f 777/1,000 A

10. Summary of Results

Permissible load envelope for the selected cable:

Parameter	Symbol	Value	Notes
Cable		50 mm² Cu XLPE	earth 16 mm², 100 m
Derated Capacity	I_Z	182.0	A
Capacity-Limited Load Current	I_L,CCC	182.0	A, design factor 1
Voltage-Drop-Limited Load Current	I_L,VD	251.3	A, 5.0 % limit
Earth Fault Current	I_fault	777	A
Largest Device Rating	I_N,max	125	A preferred rating; theoretical limit 155.4 A, earth fault loop (I_N ≤ I_fault / k_mag)
Protection-Limited Load Current	I_L,prot	125.0	A
Short Circuit Withstand	t_max	0.511	s vs 0.1 s protection time: PASS
Earth Conductor Size	S_earth	16	mm² vs Table 5.1 minimum 16 mm²: PASS
Earth Conductor Withstand	S_min	3.23	mm² for I<sub>ef</sub> 2,309 A in t<sub>ef</sub> 0.04 s (t<sub>max</sub> 0.982 s): PASS
Permissible Load Current	I_L,max	125.0	A, governed by Earth Fault Loop (I_N ≤ I_fault / k_mag)
Permissible Load Power	P_max	73.6	kW at PF 0.85
Permissible Motor Output	P_motor	69.9	kW shaft output at η 95 %
Permissible Apparent Power	S_max	86.6	kVA
Conforming Loads in Table		14 of 17	largest 55 kW

11. Overall Assessment

OVERALL STATUS: ✓ PASS - the cable may supply up to 125.0 A (73.6 kW at PF 0.85) protected by a device of up to 125 A

12. Warnings & Recommendations

Warnings:
  Power loss (3.15%) is significant

Recommendations:
  The earth fault loop limits the device rating: a larger earth conductor or a lower instantaneous trip multiplier raises the permissible load
  Consider larger conductor to reduce energy losses

13. 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, Table 5.1) and IEC 60364. Preferred device ratings per AS/NZS 60898, AS/NZS 60947.2 and AS 60269; preferred motor ratings per IEC 60072.

Approval:

This calculation has been reviewed and approved by:

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