AS/NZS 3008 Cable Sizing Calculations: Step-by-Step Guide

Learn How to Size Active, Neutral, and Earth Cables Using AS/NZS 3008.1

Overview of Cable Sizing Requirements

This comprehensive guide provides step-by-step instructions on how to size electrical cables according to Australian Standards, specifically AS/NZS 3008.1. Whether you’re an electrical engineer, contractor, or student, this resource will help you master the essential calculations for selecting the correct cable sizes in various applications. Key topics covered:

Current-carrying capacity calculations
Voltage drop requirements
Short-circuit performance
Neutral and earth cable sizing

We’ll walk through two detailed examples, demonstrating how to:

Calculate load currents
Select initial cable sizes
Determine cable operating temperatures
Check voltage drop compliance
Verify short-circuit performance
Choose appropriate active, neutral, and earth cable sizes

By following this guide, you’ll learn how to accurately size cables for different electrical installations while ensuring compliance with Australian Standards. Whether you’re working on residential, commercial, or industrial projects, these calculations are crucial for safe and efficient electrical systems.Use this article as your go-to reference for cable sizing calculations, and feel confident in your ability to design electrical systems that meet all necessary requirements and safety standards.

Example 1 - Three-Phase 400 V: Cable Sizing for High Current Load Over a Long Run

Three-phase 400 V system. Load current = 1200 A. Length of run = 260 m. The cable type is single core, copper, and XLPE 90 degrees. Buried in separate conduits. The voltage drop limit is 3.2 %. The fault level is 15 kA, and the clearing time is 1 second. Based on AS/NZS 3008.1, calculate the smallest active conductor, neutral, and earth cable sizes.

Step 1: Minimum size to meet current-carrying capacity

To determine the cable that could carry the 1200 A load, an initial cable size assumption would have to be made. A practical assumption would be to have 2 sets of 400 mm² cables, which equates to 1252 A. From this assumption, we would proceed to the succeeding steps to determine whether this could provide sufficient current-carrying capacity, adequate voltage drop, and short-circuit performance.

The correct current rating table must be selected from AS/NZS 3008.1 based on the cable type and phases to make a valid assumption. Once the correct reference table has been identified, the correct column based on the installation method and conductor type must be selected.

The appropriate table and column for this problem is Table 8, Column 27.

Step 2: Minimum size to meet voltage drop requirement

For the purposes of the voltage drop calculation we will use 3 sets of 630 mm2 cables.

The voltage drop for 3 sets of 630 mm²cables will be calculated with a 1200 A load current.

The rated current of the assumed cable is:

\(I_R = 2460\ A\) (the value from Table 8 Column 27 is multiplied by 3, which is the number of runs chosen)

Determine cable operating temperature

To determine the Voltage Drop for a cable selected, the operating temperature \((\theta_0)\) must first be calculated using the equation:

\(\left(\frac{I_0}{I_R}\right)^2 = \frac{\theta_0 – \theta_A}{\theta_R – \theta_A}\)

Where:

\(I_0\) = operating current, in Amperes

\(I_R\) = rated current given in Tables 4 to 21 (AS/NZS 3008.1), in amperes

\(\theta_R\) = operating temperature of the cable when carrying \(I_R\), in degrees Celsius

\(\theta_A\) = ambient air or soil temperature, in degrees Celsius

The values for these are as follows:

\(I_0 = 1200\,A\)

\(\theta_R = 90°C\) (temperature rating for the XLPE 90 degrees cable)

\(\theta_A = 25°C\) (standard ambient temperature for soil)

\(I_R = 2460\ A\)

From these, the calculated operating temperature is:

\(\theta_0 = 40.47°C\)

\(\theta_0\) is then raised to the nearest temperature of 45°C, 60°C, 75°C, 80°C, 90°C or 110°C. For the calculated operating temperature, the nearest would be 45°C.

Determine cable resistance based on cable operating temperature

This rounded-up operating temperature would be used to get the a.c. resistance \(R_c\) of the chosen cable.

\(R_c = 0.0389\ \Omega/km\) (from Table 34 Column 2 of AS/NZS 3008.1, single core cables)

Determine cable reactance

The cable reactance \(X_c\) can also be determined from the cable type (XLPE)

\(X_c = 0.0787\ \Omega/km\) (from Table 30 Column 4 of AS/NZS 3008.1, the appropriate table for this cable type)

The \(R_c\) and \(X_c\) values will be used to calculate the voltage drop on the cables, considering the load dictated by the problem. Take note that these would need to be converted to Ω/m.

Calculate voltage drop based on power factor and cable operating temperature

The following equation is used to calculate the voltage drop on the cables:

\(V_{d3\phi} = IL\left[\sqrt{3}(R_c \cos \theta + X_c \sin \theta)\right]\)

\(I = 1260\ A\) (Load Current)

\(L=260\, m\) (Length of the Cable)

A standard power factor of 0.9 can be used to calculate the power factor angle:

\(\theta = 25.84°C\)

From these values, the voltage drop on the cable can be calculated:

\(V_{d3\phi} = 12.49\ V\)

The %VD is as follows:

\(\%VD = (12.49\ V/400\ V)*100\%\)

\(\%VD = 3.12\%\)

The calculated voltage drop is within the 3.2% limit specified in the problem. Therefore, the chosen cable (3 runs of 630 mm2) is appropriate. The calculated percentage voltage drop is almost at the limit. Any cable smaller than this would result in a voltage drop exceeding the specified limit. It can be said that the voltage drop is the determining criterion for the smallest cable size.

Step 3: Minimum size to handle the prospective short-circuit current

The fault level dictated by the impedances must be calculated to evaluate the short-circuit performance.

Calculate the total impedance of the cable \(Z_t\) from the values of \(R_c\) and \(X_c\):

\(Z_t=\sqrt{R_c^2 + X_c^2}=0.0878\ \Omega/km\):

Multiply this by the length (260m) to get the cable impedance:

\(Z_c=0.0228\ \Omega\):

The impedance of the network \(Z_n\) can be calculated by Ohm’s law using the supply voltage and the fault level at the supply end of the cable:

\(Z_n=400\ V/15000\ A=0.027\ \Omega\):

The voltage at the end of the cable can also be calculated by subtracting the calculated voltage drop from the supply voltage.

\(V_{\text{end}}=400\ V-12.49\ V=387.51\ V\):

The fault level can be calculated using the equation:

\(I=\frac{V_{\text{end}}}{Z_{c} + Z_{n}}=\frac{387.51}{0.0228+0.027}\):

\(I=7829.78\ A\):

This is the fault level at the end of the cable, which must be considered in calculating the minimum cross-sectional area.

Now, the minimum cross-sectional area of the cable can be calculated:

\(I^2 t = K^2 S^2\):

Where:

\(I=7829.78\ A\):

\(t=1s\):

The initial and final temperatures are needed to determine the K constant. The 45°C operating temperature calculated earlier would be the initial temperature. The final temperature would depend on the insulating materials in contact with the conductors. As per Table 53 of AS/NZS 3008.1, for XLPE 90, the final temperature would be 250°C.

Using these temperatures, the value of K can be determined from Table 52 of AS/NZS 3008.1.

\(K=168\):

From the values of \(I\), \(t\), and \(K\), the minimum cross-sectional area of the conductor can be calculated.

\(S=46.61\ mm^2\)

The result suggests that the chosen cable (3 runs of 630 mm2) can also handle the specified fault level.

Active Cable Size = 3 runs of 630 mm2

Step 4: Select the neutral cable size

Neutral Cable Size = 3 runs of 630 mm2

As per Section 3.5.2 of AS/NZS 3000, the neutral cable will be the same size as the smallest active conductor and meet the load current requirements.

Step 5: Select the earthing cable size

As per Table 5.1 of AS/NZS 3000, for cables greater than 630 mm2, the nominal size of Copper earthing conductors shall be 25% of the active size.

The cumulative cross-sectional area of the active cables calculated above is 1890 mm2. 25% of this is 472.5 mm2, which can be rounded up to the standard cable size of 500 mm2.

However, the minimum earth cable size that can handle a phase-to-earth fault must also be checked. The equation for the minimum conductor cross-section used in Step 5 will also be used. The only difference is the phase-to-earth short circuit current will be used.

\(I_{\text{1ph}} = \frac{I_{\text{3ph}}}{\sqrt{3}} = \frac{7829.78\ A}{\sqrt{3}}\)

\(I_{\text{1ph}}=4520.53\ A\)

The same values of \(t\), and \(K\) in Step 3 will be used to calculate the minimum conductor cross-section \(S\).

\(S=26.91 mm^2\)

Therefore, the earth cable size selected from Table 5.1 is acceptable.

Earth Cable Size = 500 mm2

Example 2 - 690 V Fire-Rated Cable Selection for 75 kW Load

The load is 75 kW, 3 phase, with a power factor of 0.9 at 690 V. The cable is Fire-Rated, Cu, single-core length = 5 m, unenclosed touching. There are no derating factors. The maximum allowed voltage drop is 2.5 %, fault level = 15 kA, and fault time (fault clearing time) = 0.15 s.

Step 1. Minimum size to meet current-carrying capacity

The load current is:

\(I_0 = \frac{P}{\sqrt{3} V \cos(\theta)}\)

Where:

\(P=75000\ W\)

\(V=690\ V\)

\(\cos(\theta)=0.9\) (power factor)

\(I_0=69.73\ A\)

To determine the cable that could carry the 69.73 A load, an initial cable size assumption would have to be made. A practical assumption would be to have 10 mm2 cables, which equates to 81 A. From this assumption, we would proceed to the succeeding steps to determine whether this could provide sufficient current-carrying capacity, adequate voltage drop, and short-circuit performance.

The appropriate table and column for this problem is Table 9, Column 6.

Step 2: Minimum size to meet voltage drop requirement

For the purposes of the voltage drop calculation we will use 35 mm2 cables.

The voltage drop for 35 mm2 cables will be calculated with a 69.73 A load current.

Determine cable operating temperature

Calculate the operating temperature \((\theta_0)\)

\(\left(\frac{I_0}{I_R}\right)^2 = \frac{\theta_0 – \theta_A}{\theta_R – \theta_A}\)

Where:

\(\theta_R = 110°C\) (temperature rating for Fire-Rated Copper cables)

\(\theta_A = 40°C\) (standard ambient temperature for air)

\(I_0=69.73\ A\)

\(I_R=176\ A\) (The value is from Table 9 Column 6 of AS/NZS 3008.1, the appropriate table for single-core, fire-rated cables. The cable size assumption is 35 mm2)

From these, the calculated operating temperature is:

\(\theta_0 = 50.98°C\)

\(\theta_0\) is then raised to the nearest temperature of 45°C, 60°C, 75°C, 80°C, 90°C or 110°C. For the calculated operating temperature, the nearest would be 60°C.

Determine cable resistance based on cable operating temperature

This rounded-up operating temperature would be used to get the a.c. resistance \(R_c\) of the chosen cable.

\(R_c = 0.607\ \Omega/km\) (from Table 34 Column 3 of AS/NZS 3008.1, single core cables)

Determine cable reactance

\(X_c = 0.12\ \Omega/km\) (from Table 30 Column 5 of AS/NZS 3008.1, the appropriate table for this cable type)

The \(R_c\) and \(X_c\) values will be used to calculate the voltage drop on the cables, considering the load dictated by the problem. Take note that these would need to be converted to Ω/m.

Calculate voltage drop based on power factor and cable operating temperature

The following equation is used to calculate the voltage drop on the cables:

\(V_{d3\phi} = IL\left[\sqrt{3}(R_c \cos \theta + X_c \sin \theta)\right]\)

\(I = 69.73\ A\) (Load Current)

\(L=5\ m\) (Length of the Cable)

A standard power factor of 0.9 can be used to calculate the power factor angle:

\(\theta = 25.84°\)

From these values, the voltage drop on the cable can be calculated:

\(V_{d3\phi} = 0.36\ V\)

The %VD is as follows:

\(\%VD=(0.36\ V/690\ V)*100\%\)

\(\%VD = 0.05\%\)

The calculated voltage drop is within the 2.5% voltage drop limit specified in the problem. Therefore, the chosen cable (35 mm2) is appropriate.

Step 3: Minimum size to handle the prospective short-circuit current

The fault level dictated by the impedances must be calculated to evaluate the short-circuit performance.

Calculate the total impedance of the cable \(Z_t\) from the values of \(R_c\) and \(X_c\):

\(Z_t=\sqrt{R_c^2 + X_c^2}=0.618\ \Omega/km\)

Multiply this by the length (5m) to get the cable impedance:

\(Z_c=0.0031\ \Omega\)

The impedance of the network \(Z_n\) can be calculated by Ohm’s law using the supply voltage and the fault level at the supply end of the cable:

\(Z_n=690\ V/15000\ A=0.046\ \Omega\)

The voltage at the end of the cable can also be calculated by subtracting the calculated voltage drop from the supply voltage.

\(V_{\text{end}}=690\ V-0.36\ V=689.64\ V\)

The fault level can be calculated using the equation:

\(I=\frac{V_{\text{end}}}{Z_{c} + Z_{n}}=\frac{689.64}{0.0031+0.046}\)

\(I=14047.38\ A\)

This is the fault level at the end of the cable, which must be considered in calculating the minimum cross-sectional area.

Now, the minimum cross-sectional area of the cable can be calculated:

\(I^2 t = K^2 S^2\)

Where:

\(I=14047.38\ A\)

\(t=0.15s\)

\(K=165\) (from Table 52)

The final temperature is as per Table 53 for fire-rated cables (250°C).

The initial temperature used is 50°C as per the nearest available initial temperature to the calculated operating temperature.

Using these temperatures, the value of K can be determined from Table 52 of AS/NZS 3008.1.

From the values of \(I\), \(t\), and \(K\), the minimum cross-sectional area of the conductor can be calculated.

\(S=32.97 mm^2\)

The result suggests that the chosen cable (35 mm2) can also handle the specified fault level.

Active Cable Size = 35 mm2

Step 4: Select the neutral cable size

Neutral Cable Size = 35 mm2

As per Section 3.5.2 of AS/NZS 3000, the neutral cable will be the same size as the smallest active conductor and meet the load current requirements.

Step 5: Select the earthing cable size

Table 5.1 of AS/NZS 3000 shows that the earth cable size shall be 10 mm2 for 35 mm2 active cables.

\(I_{\text{1ph}} = \frac{I_{\text{3ph}}}{\sqrt{3}} = \frac{14047.38\ A}{\sqrt{3}}\)

\(I_{\text{1ph}} = 8110.52\ A\)

The same values of \(t\), and \(K\) in Step 3 will be used to calculate the minimum conductor cross-section \(S\).

\(S=19.04 mm^2\)

The next standard cable size that would meet the calculated minimum conductor cross-section is 25 mm2.

Earth Cable Size = 25 mm2

References:

[1] Electrical installations – Selection of cables – Cables for alternating voltages up to and including 0.6/1 kV – Typical Australian installation conditions (AS/NZS 3008.1.1:2017). Standards Australia and Standards New Zealand. (2017).

[2] Electrical installations (known as the Australian/New Zealand Wiring Rules) (AS/NZS 3000:2018). Standards Australia and Standards New Zealand. (2018).