Busbar voltage drop: a worked example

Why voltage drop deserves its own check

A busbar that stays cool can still deliver too little voltage to the load. The thermal check asks whether the bar survives the current. The voltage drop check asks whether the load receives enough voltage to work, and whether the loss is acceptable for the system efficiency.

The limit is usually set by the system or the customer. A common rule is a few per cent of the nominal voltage, but the right value depends on the load. A 48 V DC system has much less room in absolute terms than a 400 V AC system, so the same millivolt drop can be negligible in one and significant in the other.

The drop is also a heat source. Every millivolt lost in the bar or the joint becomes heat in the enclosure. A joint with a high resistance is both a voltage drop and a hot spot.

The formula

The voltage drop is the current multiplied by the total resistance of the circuit path. For a busbar link, the path includes the outgoing bar, the return bar, the joints at each end and any terminal contact resistance. The bar resistance is the resistivity times the length divided by the cross-section.

Copper resistivity is about 1.72 x 10^-8 ohm metres at 20 °C. The resistance rises with temperature according to the temperature coefficient, about 0.00393 per kelvin for copper. A bar at 70 °C has a resistance about 20% higher than the same bar at 20 °C.

That correction is not optional. A bar sized at 20 °C will look better than it is. Use the maximum operating temperature from the thermal check, or the allowable temperature if the actual value is not known.

Step 1: the bar resistance

Take a 50 x 10 mm copper bar with a cross-section of 500 mm². At 20 °C the resistance per metre is 1.72 x 10^-8 divided by 500 x 10^-6, which is 0.0344 mΩ per metre. At 70 °C the correction factor is 1 + 0.00393 x 50, or 1.1965, which gives 0.0412 mΩ per metre.

If the run is two metres from the source to the load, the outgoing bar has a resistance of 0.0823 mΩ. If the return path is a second bar of the same section and length, it adds the same resistance. The two bars together are 0.1646 mΩ.

Step 2: the joints

A bolted joint is not a perfect connection. It has a contact resistance that depends on the contact area, the surface finish, the plating, the bolt torque and the number of interfaces. A clean, correctly torqued tin-plated joint can be in the range of a few micro-ohms to tens of micro-ohms. A poor joint can be much higher.

For the example, assume two joints at 15 micro-ohms each. That is 30 micro-ohms in total, or 0.030 mΩ. At 1,000 A, the joints add 30 mV. The two bars add 164.6 mV. The total is 196.6 mV.

The joint contribution is about 15% of the total in this example. Change the joint resistance to 30 micro-ohms each and the joints add 60 mV, which is a quarter of the total. That is why a voltage drop calculation without a joint assumption is incomplete.

If no measured joint resistance is available, build the estimate from the contact area and the surface condition, then add a margin. A clean, flat, tin-plated joint with the specified torque is a different component from a painted or oxidised face. For a critical link, measure the millivolt drop across a sample joint at the rated current and use that value in the model.

Record the assumed joint resistance on the calculation sheet. If the design later changes the bolt size, the washer or the plating, the assumption changes with it, and the voltage drop has to be recalculated rather than carried forward.

Step 3: AC effects

The calculation above uses DC resistance. At AC, the current distribution in a conductor is not uniform. Skin effect pushes current toward the surface, and proximity effect pushes it toward or away from a nearby conductor. Both raise the effective resistance above the DC value.

At 50 Hz, the skin depth in copper is about 9.4 mm. A 10 mm thick bar is therefore comparable to the skin depth, and the AC resistance can be a few per cent above DC. A thicker bar does not help as much as the DC calculation suggests. At higher frequencies, the difference grows and a thin, wide bar or a laminated stack becomes more attractive.

For most panel busbars at power frequency, the DC calculation plus a small allowance is enough. For a high-current bar, a thick section, a high-frequency converter link or a tightly spaced pair of bars, ask for the AC resistance from the supplier or calculate it with a method that includes skin and proximity.

Step 4: compare with the limit

The total drop of about 197 mV is 0.41% of a 48 V system and 0.05% of a 400 V system. For the 48 V system, that may be acceptable if the load tolerance allows it. For a 12 V system, it would be 1.6%, which could matter.

Compare the drop at the rated current with the limit at the same current. Do not compare a full-load drop with a no-load voltage limit. If the load is intermittent, check the drop at the peak current as well, because the instantaneous voltage at the load may dip below its minimum.

The same applies to a load that is fed from a battery or a rectifier with a falling output voltage. The busbar drop adds to the source sag, so the end-of-discharge case is often the one that decides the limit.

1. 01

   Fix the current

   Use the rated current and the peak current if the load is intermittent.

2. 02

   Set the temperature

   Use the maximum operating temperature from the thermal check.

3. 03

   Calculate the bars

   Include the outgoing and return paths at the operating temperature.

4. 04

   Add the joints

   Use a measured value or a conservative bound for each joint.

5. 05

   Allow for AC

   Add a skin and proximity allowance for thick or high-frequency bars.

6. 06

   Compare

   Check the total against the system limit at the same current.

How to reduce the drop

The cheapest fix is usually the joint. Clean the contact faces, use the correct plating and torque, and check the contact resistance. A joint that is 30 micro-ohms instead of 15 micro-ohms adds more drop than a 50% increase in bar length at the same section.

The next fix is the route. A shorter run, a more direct path or a parallel bar reduces resistance. A parallel bar also shares the current, but it needs its own joints and its own current sharing check. Two bars in parallel do not automatically share equally.

The last fix is the section. A larger bar reduces resistance, but it adds weight, cost and space, and the benefit is limited by skin effect at high frequency. Try the joint and the route first.

• Improve joint preparation and torque before adding copper.
• Shorten the route or remove unnecessary joints.
• Use a parallel path with a current sharing check.
• Increase the section only after the first three options.
• Re-check the thermal design after any change.