Busbar Size Calculation Formula | Aluminium and Copper Examples

If the equations are not displayed correctly, please use the desktop view

Busbar size explanation will give us hard time sometimes but it is necessary for every electrical installation.

In every electrical installation, we need to take caution of everything that may cause faults and fires. It can be caused by an accident, natural incident, or incendiary.

If you have read about fire incidents happening in a house, factory, or big building, a natural incident is very rarely to happen. Natural incidents are caused by natural factors and of course buildings won’t be affected by nature easily.

The most important thing we need to prevent is accidents. This one can occur if we didn’t plan, design, analyze, or calculate carefully when doing and using electrical installation.

These faults and fires are caused by the most common element we know: HEAT.

When looking at the source of the HEAT from electrical perspective, we can list its causes:

• Short circuit.
• Overload.
• Poor quality of electrical designs and cablings.
• Poor quality of electrical devices and materials.
• Poor quality of electrical connections.
• Poor quality of earthing designs and materials.
• Lacks of ventilation in the panels.

Those points are quite hard to detect before happening. The best thing we can do is to prevent the faults by eliminating those causes above.

What is Busbar

Electrical wires are commonly used to deliver currents from one point to another point. Of course it doesn’t have to be a wire, it can be anything that can conduct electricity such as copper.

Electrical wires are very flexible because we can bend it, roll it, put insulation on it, move it around, string it to our liking and many more.

But electrical wires sometimes are not an efficient and wise choice when we are dealing with high currents. You will find it easier to use a conductor bar or solid conductor to carry high currents from place to place.

This solid conductor bar is known as a busbar. It is made from copper in the shape of a “bar”. Of course we can’t bend it, roll it, or string it like wires. This busbar is capable of carrying high currents where most electrical wires will burn out.

Even if you insist on using electrical wires, you need really big and thick electrical wires so it is not convenient for prices and installations.

Don’t worry about its designs and installations, we can use bolts to connect one bar to another bar to our liking. This bolt is installed on the insulator to attach any busbar altogether without causing any accident.

Over its advantages, busbar has its own disadvantages. We absolutely do not want to unplug a busbar or move it without proper procedure. You may come across “Busbar Down for Maintenance” warning signs somewhere.

This sign indicates that the power line has been shut down so we can do maintenance on them, unplug them, clean them, replace them, or anything.

Keep in mind that a busbar is literally a copper bar where it rarely has insulation on them. We have to keep it safe from animals, birds, or rodents touching it. It may cause short circuits between busbars and of course kill animals that touched it.

How to Calculate Busbar Size

On this occasion, we will talk about busbar size calculation to prevent any overheat occurring in your electrical systems. We will study how important it is to calculate busbar size to prevent overheat that further causes faults.

The busbar size calculation is not only focused on HT (High Tension or High Voltage) systems. You are wrong if you think a LT (Low Tension or Low Voltage) system is not worth calculating and analyzing.

Hence, we will study for both HT and LT systems.

There is a common rule used by most electricians, electrical engineers, and consultants called the “Thumb Rule” method.

Back in the day when calculating busbar size was done manually and of course they will spend quiet time on it, they grow impatient. This is where the Thumb Rule helped them. But don’t worry, nowadays there is a lot of software to do busbar size calculation. They are easy to use and of course save you a lot of time.

Thumb Rule for Busbar Amp Size

This Thumb Rule shows how much current a 1 square mm (Sq.mm) busbar can withstand.

There are two common materials for producing a busbar, they are aluminium and copper. Both aluminium and copper have their own ability to withstand currents.

A 1 Sq.mm of aluminium busbar can withstand 0.7 Amperes.

A 1 Sq.mm of copper busbar can withstand 1.2 Amperes.

Of course the examples above did not come from an international standard because we can’t find the tolerance values. Some people may still use an aluminium busbar to deliver 1 Amp. Some other people use a copper busbar to deliver 1.5 Amps.

Later on, because this primitive method became unreliable for high current in thousand amps, we needed to do proper calculation with a proper standard.

Electrical Busbar Size

Even further, electrical consultants and engineers have to analyze and calculate other supporting factors that are important to consider:

• Minimum clearance for phase-to-phase and phase-to-ground.
• Proper selection of busbar insulator deadlock.
• Safe and adequate bolt installation for multiple busbar connections.
• Thermal effects produced by busbar and insulator for both normal and extreme (faulty) conditions.
• Mechanical resonances and electrodynamic forces under normal and extreme (faulty)  conditions.

We should consider the two factors below:

• Maximum Allowable Temperature Rise for Bolt
• Busbar Minimum Clearances

Maximum allowable temperature for bolt connecting busbar to busbar or busbar to panel is needed to be planned properly.

Right now we will look at international standard, IEC 62271-1, where it is summarized in the table below:

The second is the busbar clearance where we will use IEC 62271-1 as an example. Observe the table below:

Standard Busbar Size in mm

The size of a busbar is determined by the current rating, type of material, shape, and cross-sectional area. Of course the maximum allowable temperature rise for each type of material is also important.

From the IEC 62271-1 we can also study about the  thermal rise effect, thermal limit, bar dimensions, and withstand current rating in the table below:

How to Size Busbar

Busbar size is not solely determined by the current alone. Its temperature rise has to be in allowable specification in national or international standard. The standards we are talking about are:

• British Standard, BS 159,
• American Standard, ANSI C37.20, and
• etc.

British Standard, BS 159 states that maximum temperature rises is 50^oC higher than ambient temperature in 24 hour. The ambient temperature is 35^oC to 40^oC at its peak.

American Standard, ANSI C37.20 states that maximum temperature rises is 65^oC higher than ambient temperature in 24 hour. The ambient temperature is 40^oC and silver-plated termination bolts are used. If there is no bolt installed, the allowable temperature rise is 30^oC.

The very basic idea on how to size a copper busbar is 2 Amps/1 Sq.mm (mm²) or 1250 Amps/1 Sq.in (in²), these can be different in some countries. Of course this is like a “first-aid” decision, but the final decision should count on more factors. You should check the catalog of the manufacturer.

Busbar Size Depends On

Check the list below to learn what we mentioned about “more factors” above. We should take the “application areas” into account when doing busbar size calculation.

1. Voltage drop
   Busbar has lower impedance thus the voltage drop is lower than electrical wires.
2. Main switchboard
   Only one output for each riser hence the cost and size for the main panel are reduced.
3. Shaft size
   The common size for a busbar with 1600 A current rating is 185 x 180 mm. Compared to the electrical wires to carry with the same current, a busbar is much cheaper to build a riser shaft size.
4. Number of circuits
   Only one circuit is needed for all floors.
5. Fire and safety
   Insulator materials used for busbar don’t produce toxic gasses and corrosive effects to cause a fire.
6. Fault withstand level
   A busbar has a much higher maximum current rating, normally a 1600 A riser can withstand 60 – 70 kA.
7. Installation time
   Busbar installation wastes less time.

Busbar Size vs Current

Observe the short circuit rating for a busbar below:

1. Current rating 0 – 400 A = 25 kA for 1 second.
2. Current rating 600 – 1000 A = 50 kA for 1 second.
3. Current rating 1000 – 2000 A = 65 – 100 kA for 1 second.
4. Current rating 2000 – 5000 A = 100 – 225 kA for 1 second.

After we listed the current rating along with its fault current rating, we can list them further along with its cross-section of 1 squared mm (Sq.mm / mm²).

Aluminium Busbar Size

Let us do a simple example of aluminium busbar size calculation.

Assume that we need a busbar to carry 2000 A current and have to withstand 35 kA current fault for 1 second. Looking back at the table above, the minimum cross-section area of the busbar we need is 443 Sq.mm.

To get this 443 Sq.mm aluminium busbar, we can use a 100 x 5 mm busbar. This is the minimum cross-section size.

Assuming that we have a current density of 1 A/Sq.mm, skin effect, and temperature rise, we might need a 4 x 100 x 5 mm busbar.

Copper Busbar Size

Similar to the calculation above, the copper busbar size calculation is quite straightforward.

Assume that we need a busbar to carry 2000 A and withstand a 35 kA fault current for 1 second. Scrolling a bit above to our table, we found that at least 285 Sq.mm is needed. We can use a 60 x 5 mm busbar as a minimum cross-section.

Assuming that we have a current density of 1.6 A/Sq.mm, skin effect, and temperature rise, we might need a 4 x 60 x 5 mm busbar.

How to Size Busbar

At long last, we will do some busbar size calculation with some known formulas.

Assume we have a busbar with current rating as stated below:

Rated Voltage = 415V,50Hz ,

Desire Maximum Current Rating of Bus bar =630Amp.

Fault Current (I_sc)= 50KA

Fault Duration (t) =1sec.

The operating temperature rises for the busbar is:

Operating Temperature of Bus bar (θ) = 85°C.

Final Temperature of Bus bar during Fault (θ₁) =185°C.

Temperature rise of Bus Bar Bar during Fault (θ_t=θ₁-θ) = 100°C.

Ambient Temperature (θ_n) =50°C.

Maximum Busbar Temperature Rise = 55°C.

Busbar is covered with an enclosure with specifications below:

Installation of Panel= Indoors (well Ventilated)

Altitude of Panel Installation on Site= 2000 Meter

Panel Length= 1200 mm ,Panel width= 600 mm, Panel Height= 2400 mm

Our busbar’s material details:

Bus bar Material= Copper

Bus bar Strip Arrangements = Vertical

Current Density of Bus Bar Material =1.6

Temperature Coefficient of Material Resistance at 20°C (α₂₀) = 0.00403

Material Constant(K) = 1.166

Busbar Material Permissible Strength = 1200 kg/cm²

Busbar Insulating Material = Bare

Busbar Position = Edge-mounted bars

Busbar Installation Medium = Non-ventilated ducting

Busbar Artificial Ventilation Scheme = without artificial ventilation

Our busbar size is:

Busbar Width (e) = 75 mm

Busbar Thickness (s) = 10 mm

Number of Bus Bar per Phase (n) = 2

Bus bar Length per Phase (a) = 500 mm

Distance between Two Bus Strip per Phase (e) = 75 mm

Busbar Phase Spacing (p) = 400 mm

Total No of Circuit = 3

Since busbar doesn’t have its own insulation, we provide it with insulator as written below:

Distance between insulators on Same Phase (l) = 500 mm

Insulator Height (H) = 100 mm

Distance from the head of the insulator to the bus bar center of gravity (h) = 5 mm

Permissible Strength of Insulator (F’)=1000 Kg/cm2

And now we will calculate busbar size with coefficient factors “K” below.

Derating Factor of Busbar

We will calculate eight derating factors of a busbar step by step.

1. Bus Strip Derating Factors (K1)

De rating factor per phase busbar:

Bus bar Width (e) is 75mm and Bus bar Length per Phase (a) is 500mm so

Number of busbar per phase is 2.
From following table value of de rating factor is 1.83

Number of Bus Bar Strip per Phase (K1)

2. Insulator Material Derating Factor (K2)

Busbar doesn’t have insulating material. So we say it is “bare”, thus the derating factor is 1 from the table below.

3. Position Derating Factor (K3)

The position of our busbar is an Edge-mounted bar, thus the derating factor is 1 from the table below.

4. Installation Medium Derating Factor (K4)

Our installation for the busbar is non-ventilated ducting, thus the derating factor is 0.8 from the table below.

5. Artificial Ventilation Derating Factor (K5)

We don’t use artificial ventilation, thus the derating factor is 0.9 from the table below.

6. Enclosure and Ventilation Derating Factor (K6)

Busbar cross-section area per phase (A)

Total busbar cross-section area for enclosure =

Here we used Size of Neutral Bus is equal to Size of Phase Bus

Total busbar Area for Enclosure

Total enclosure Area

Total busbar Area for Enclosure / Total Enclosure Area =9000000/1728000000

Total busbar Area for Enclosure / Total Enclosure Area=0.53%

Busbar artificial ventilation plan is without artificial ventilation so the derating factor is 0.95 from the table below.

7. Proxy Effect Derating Factor (K7)

Busbar Phase Spacing (p) is 400mm.

Busbar Width (e) is 75mm

Space between each bus of phase is 75mm

Hence, total bus length of phase with spacing (w) =75+75+75+75+75=225mm

Busbar phase spacing (p) / total bus length of phase with spacing (w) = 400 / 225 =2

From the table below, the derating factor is 0.82.

8. Altitude of Busbar Installation Derating Factor (K8)

We installed the busbar 2000 m above the ground so the derating factor is 0.88 based on the table below.

Total Derating Factor

After we get the eight derating factors, it is time to sum them all up.

Total derating factor

Busbar Size Calculation Formula

Desire Current Rating of Bus bar (I₂) =630 Amp

Current rating of busbar after derating factor (I₁)

Busbar Cross Section Area as per Current (A)

Busbar Cross Section Area as per Short Circuit (A_sc)

Select Higher Size for Busbar Cross section area between 436 Sq.mm and 626 Sq.mm

Final Calculated Busbar Cross Section Area =626 Sq.mm

Actual Selected busbar size is 75×10=750 Sq.mm

We have selected 2 number of Bus bar per Phase, hence:

Actual Busbar cross section Area per Phase (A_P)

Actual Busbar Size is Less than calculated Bus bar size.

Electromagnetic Forces Generated by Busbar when Short Circuit

Peak electromagnetic forces between phase conductors (F₁)

Total width of busbar per phase(w)=75+75+75=225mm =2.25cm

Busbar Phase to Phase Distance (d)=400+225=625mm=6.25cm

Actual Forces at the head of the supports or busbar (F)

Permissible strength of the insulator (F’) is 10 Kg/mm2.

Actual Forces at the head of the Supports or Bus Bar is less than Permissible Strength.

Forces on Insulation are within Limits.

Mechanical Strength of the Busbar

Mechanical strength of a busbar can be calculated using:

Since we have two bus strips per phase then our inertia modulus is 14.45.

The mechanical strength of our busbar is

The allowable strength of a busbar is 12 Kg/mm².

Our actual busbar’s strength is still within allowable value.

Temperature Rise of the Busbar

The maximum temperature rise (T₁) is 35^oC.

The calculated maximum temperature rise (T₂) is

Calculated busbar temperature rise is less than specified maximum temperature rise.

Final Result

Size of the busbar = 2 busbars 75x10mm each Phase.

Number of feeders = 3.

Total number of busbar = 6 busbars 75x10mm for phase and 1 busbar 75x10mm for neutral.

Electromagnetic forces at the tip of the supports of busbar (F) = 3 Kg/mm².

Mechanical strength of the busbar = 0.7 Kg/mm².

Maximum temperature rise = 30^oC.

Earthing Busbar Size Calculation

Earth conductor size PE measured in Sq.mm can be calculated from:

Where:
I_fault = fault current (A)
t(s) = operating time (s)
k = constant of the material

The constant of the material can be read from the list below:

Example:

Assume that we have to calculate an earthing busbar size for 20 kA fault current at 0.5s using GI material.

You could use a 50×3.5 mm or 25×8 mm busbar.

Calculate Busbar Size and Voltage Drop

Since we have done the busbar size calculation, we will skip to its voltage drop calculation.

And we need to remind you that we can’t calculate voltage without knowing the values of the current and resistance.

When you have those values, you can use the simple Ohm’s law. The voltage drop is equal to the I x R.

Where I is the current carried by the busbar and the R is the busbar’s resistance (aluminium or copper).

Frequently Asked Questions