Key takeaways
- Sizing is three checks: temperature rise at the continuous current, voltage drop over the run and short-circuit withstand.
- The heat balance uses the bar surface, the convection and radiation coefficients and the allowable rise.
- Resistance rises with temperature, so the calculation has to be iterated, not done once at 20 °C.
- A bar that passes the thermal check can still fail the fault check or the voltage drop limit.
What a sizing calculation has to prove
Sizing a busbar is not a single lookup. It is a set of checks that answer three different questions. Will the bar stay below its allowable temperature at the continuous current? Will the voltage at the far end stay within the limit at the rated load? Will the bar and its supports survive a short circuit for the time it takes the protection to clear?
A bar can pass one check and fail another. A short, thick bar may pass the thermal check easily and still fail the fault check because its supports are too far apart. A long bar may pass the thermal check and fail the voltage drop limit. The three checks use different inputs and different limits, and each one has to be recorded.
The inputs to collect first
Start with the load and the environment, not with a bar size. The continuous current should be the RMS value of the worst-case load, including any known overload that lasts long enough to heat the bar. The ambient should be the maximum air temperature inside the enclosure, because a sealed panel can run well above room temperature.
The allowable temperature depends on what is touching the bar. Bare copper in open air can run hotter than a bar with a cable lug or a plastic support against it. The touch temperature and the insulation class of nearby parts may set a lower limit than the copper itself. State the limit and where it comes from.
| Input | Symbol | Source |
|---|---|---|
| Continuous current | I | Load schedule, RMS value |
| Ambient temperature | Ta | Enclosure thermal survey |
| Allowable bar temperature | Tmax | Insulation, touch and material limits |
| Bar width and thickness | w, t | Selected section |
| Bar length | L | Layout |
| Fault current and duration | Icw, t | Protection study |
| Allowable voltage drop | ΔV | System or customer limit |
The heat balance
A bar in steady state dissipates the heat it generates. The heat generated per metre is the current squared times the resistance per metre. The heat dissipated is the surface area per metre times the combined convection and radiation coefficient times the temperature rise above ambient.
For a rectangular bar, the surface area per metre is approximately the perimeter, which is twice the sum of the width and the thickness. For a 50 x 10 mm bar, that is 0.12 m² per metre. The combined coefficient for natural convection and radiation in still air is often in the range of 10 to 14 W/m²K for the temperatures used in panel equipment. The exact value depends on orientation, surface finish and the surrounding surfaces.
Set the generated heat equal to the dissipated heat and solve for the temperature rise. Because the resistance depends on temperature, the result has to be checked with the resistance at the calculated temperature. One or two iterations are usually enough.
The surface matters as much as the size. A bright bare copper bar has a low emissivity, while a painted or oxidised surface radiates more heat at the same temperature. That is one reason a painted bar can run cooler than a bare bar of the same section, even though the paint adds a thin thermal layer. If the bar is sleeved or enclosed, the outer surface of the sleeve is what radiates, so the calculation has to use the right surface.
The coefficient is an estimate, not a constant
A bar in a sealed box with no air movement does not dissipate heat like a bar on a bench. Treat the heat balance as a first pass and confirm it with a test when the enclosure is tight.
A worked copper example
Take a 50 x 10 mm copper bar carrying 1,000 A in still air at 40 °C, with an allowable bar temperature of 90 °C. The cross-section is 500 mm². At 20 °C the resistance per metre is about 0.0344 mΩ. At 60 °C, using a temperature coefficient of 0.00393 per kelvin, it is about 0.0398 mΩ per metre, and the heat generated is about 39.8 W per metre.
The surface area is 0.12 m² per metre. With a combined coefficient of 12 W/m²K, the dissipated heat is 1.44 W per metre per kelvin of rise. The rise is therefore about 27.6 K, which puts the bar at about 67.6 °C in a 40 °C ambient. That is below the 90 °C limit, so the section passes the thermal check with margin.
A second iteration, using the resistance at about 68 °C, gives a rise of about 28 K and a bar temperature of about 68 °C, so the result has settled. The difference is small, but showing the iteration makes the method clear and keeps the answer honest.
The voltage drop at 1,000 A is about 39.8 mV per metre. Over a two metre run, with two joints, the bar drop is about 80 mV plus the joint drop. If the system allows 200 mV, the run passes. If it allows 100 mV, the joints and the return path decide whether it still passes.
| Quantity | Value | Basis |
|---|---|---|
| Cross-section | 500 mm² | 50 mm x 10 mm |
| Resistance at 20 °C | 0.0344 mΩ/m | Copper resistivity 1.72 x 10^-8 Ωm |
| Resistance at 60 °C | 0.0398 mΩ/m | Temperature coefficient 0.00393/K |
| Heat generated at 1,000 A | 39.8 W/m | I²R |
| Surface area | 0.12 m²/m | Perimeter of the section |
| Temperature rise | 27.6 K | Heat balance at 12 W/m²K |
| Bar temperature | 67.6 °C | 40 °C ambient |
| Voltage drop | 39.8 mV/m | At 1,000 A |
Illustrative only. The coefficients, ambient, allowable temperature and joint resistance must be confirmed for the actual installation.
The voltage drop check
Voltage drop is the current times the total resistance of the run, including the return path and the joints. For a busbar, the bar resistance is usually small and the joints can dominate. A joint with a contact resistance of 10 micro-ohms adds 10 mV at 1,000 A, which is a quarter of the drop of a one metre bar.
Calculate the bar resistance at the operating temperature, not at 20 °C. Add the joint resistance for each joint, using a measured value or a conservative estimate. Include the return path if the circuit is not balanced. Then compare the total with the allowable drop at the rated current.
If the drop is too high, the answer is not always a larger bar. A shorter route, fewer joints, a better joint preparation or a parallel path can be more effective and cheaper than adding copper.
The short-circuit check
The fault check has two parts. The thermal part asks whether the bar can absorb the fault energy for the clearing time without exceeding its allowable temperature. The mechanical part asks whether the force between conductors will bend the bar or pull it off its supports.
For the thermal part, an adiabatic estimate is often enough for a first pass. The temperature rise depends on the current density squared and the duration. A bar with a high current density for a long clearing time will heat quickly. For the mechanical part, the force per metre between two parallel conductors depends on the square of the peak current and inversely on the spacing. Closer bars see a larger force.
The result sets the support spacing and the strength of the fixings. It may also force a larger bar, even when the continuous current is well within the thermal limit.
Document the result
Record the inputs, the section, the assumed coefficients, the calculated temperatures, the voltage drop and the fault check. State which values are estimates and which are measured. If a test is used instead of a calculation, record the test conditions: ambient, current, mounting, thermocouple positions and the time to steady state.
A sizing sheet that shows the method is more useful than a single current number. It lets the next engineer see why the bar was chosen, and it makes a change in ambient, fault level or route easy to re-check. Keep the sheet with the drawing revision so the two never drift apart.
- 01
Collect the duty
Current, ambient, allowable temperature, fault level and duration, route length.
- 02
Choose a section
Start from a table for a similar mounting, then check it with the heat balance.
- 03
Iterate the rise
Use the resistance at the calculated temperature until the result settles.
- 04
Add the joints
Include contact resistance and the return path in the voltage drop.
- 05
Check the fault
Confirm thermal withstand and support spacing for the peak force.
- 06
Record the basis
Keep the inputs, assumptions and results with the drawing.
Frequently asked questions
What is the formula for busbar temperature rise?
Set the heat generated, I²R per metre, equal to the surface area per metre times the combined convection and radiation coefficient times the rise. Solve for the rise, then repeat with the resistance at the calculated temperature. The coefficients depend on the mounting and the enclosure.
How do I calculate busbar voltage drop?
Multiply the current by the total resistance of the run, including the bar, the return path and the joints, at the operating temperature. Compare the result with the allowable drop at the rated current.
Can I size a busbar from a current table?
A table is a starting point only. It is valid for the ambient, mounting, orientation and temperature rise behind the table. Check the actual installation with a heat balance or a test, then check voltage drop and fault withstand.
Why does my calculated temperature not match the test?
The convection and radiation coefficients, the enclosure, the nearby heat sources and the joint resistance are all estimates. A sealed enclosure, a vertical run or a bundle of cables can change the result. Use the test to correct the model for that installation.
Sources and further reading
- IEC 61439-1, Low-voltage switchgear and controlgear assemblies
- IEC 60943, Guidance concerning the permissible temperature rise for parts of electrical equipment
- Qumek busbar sizing and thermal review notes
Qumek Engineering Desk
Engineering team
The engineering team behind Qumek drawings, DFM notes, tolerances and inspection standards. Every guide is reviewed against the drawings and processes used on live programmes.
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