Worked Example: 630 A Switchboard Busbar, Start to Finish
One distribution busbar taken from a blank sheet to insulation distances, using six of the calculators in sequence. Every step links to the calculator with the values already entered, so you can change one number and watch it propagate. The design is a 630 A, 400 V three-phase riser: 12 m of 40 x 10 mm copper per phase inside a switchboard.
Starting point
| Duty | 630 A continuous, 400 V three-phase, 50 Hz |
| Conductor | One 40 x 10 mm bare copper bar per phase, on edge |
| Run | 12 m, one bolted lap joint per phase per section |
| Environment | 45 degC air inside the enclosure, still air, emissivity 0.4 |
| Limits | 90 degC bolted-copper limit; 4% voltage-drop budget |
Where these numbers come from. Everything computed below comes from the calculators on this site - nothing is quoted from a table. The design choices are ours: the bar size, the 45 degC internal ambient, the 20 kN joint force and the 0.12 mOhm/m reactance are engineering assumptions made to build a self-consistent example, not values from a real product. An enclosed assembly rated under IEC 61439 is ultimately verified by test, not by any calculation.
1 Temperature rise
Is 40 x 10 mm per phase enough for 630 A?
The sizing decision comes first, and it is thermal, not electrical: the bar carries whatever current keeps its temperature acceptable. At 630 A a vertical 40 x 10 mm copper bar dissipates 19.8 W per metre, sheds a third of that by radiation even at emissivity 0.4, and settles 21 K above the enclosure air. Against 45 degC internal air that is 66 degC - well inside the usual 90 degC limit for bolted copper, which leaves margin for the enclosure effects the model cannot see.
Conductor 66.0 degC at 45 degC ambient: rise 21.0 K, loss 19.8 W/m, h = 6.2 W/(m2.K), radiation share 34%.
2 AC resistance of the run
What does the 12 m run cost in copper loss?
At the 66 degC operating point, the 12 m of bar per phase is 0.595 mOhm DC. Skin depth in copper at 50 Hz and that temperature is 10.0 mm - almost exactly the bar thickness - so the AC penalty is a mere 0.55%. This is why 50 Hz busbars are sized on thermal and mechanical grounds, not skin effect; the picture changes with fatter sections, parallel bars or 400 Hz supplies.
Rdc 0.595 mOhm, Rac/Rdc 1.006, skin depth 10.0 mm, 237 W per phase in the run at 630 A.
3 Voltage drop
Does the riser eat into the voltage budget?
The hot bar is 0.0499 mOhm/m; a typical flat-bar phase spacing contributes about 0.12 mOhm/m of reactance. At 630 A and 0.85 power factor the 12 m run drops 1.38 V line to line - 0.35% of 400 V, a rounding error against the usual 4% budget. Notice the split: only 40% of that drop is resistive. At busbar cross-sections the reactance already dominates, so more copper would buy almost nothing here.
Drop 1.38 V = 0.35% of 400 V; resistive share 40%; 713 W lost in the run across all three phases.
4 The bolted joint
What does each joint add?
Each section joint is a lapped connection clamped by two M12 bolts at around 20 kN total. Clean and properly torqued, the constriction and cluster terms come to 1.36 microohm - half a watt at 630 A, invisible next to the 237 W in the bar. The same joint with a grown oxide film nearly doubles, with the film carrying half the total. That factor-of-two is the difference between a joint that lasts decades and one that thermographs bright in five years.
Clean joint 1.36 uOhm, 0.54 W and 0.86 mV at 630 A. Oxidised: 2.56 uOhm, film share 47%.
5 Cooling cross-check
Was the convection coefficient in step 1 honest?
Step 1 derived h = 6.2 W/(m2.K) internally. Check it independently: a vertical surface 40 mm tall at 21 K above 45 degC air gives exactly the same figure from the Churchill-Chu correlation, and over the 1.2 m2 of bar surface in the run it carries 156 W - matching the convective share of step 1 to within a watt. When two routes to the same number agree, the number is probably right; the remaining 81 W of the 237 W total leaves by radiation.
h = 6.19 W/(m2.K), convected heat 156 W over 1.2 m2 - agrees with step 1 both ways.
6 Insulation distances
How far apart do the phases and supports have to be?
The riser is fixed installation on a 230/400 V system - overvoltage category III, so each insulation sees a 4 kV rated impulse. For the phase-to-phase working voltage of 400 V on standard supports (pollution degree 2, material group IIIa), IEC 60664-1 asks for 3.0 mm of clearance and 4.0 mm of creepage for basic insulation. Real switchboards use far more for mechanical and arc-flash reasons - but these are the floors everything else must respect, and they are what the support ribs are buying.
Clearance 3.0 mm, creepage 4.0 mm at 400 V working, 4 kV impulse, basic insulation.
Where this stops being trustworthy
Every number above came from a closed-form model, and each carries the assumptions listed on its own page. Three of them are doing real work here and deserve suspicion:
- Free air on all faces. The ampacity model cools an isolated bar. In the real enclosure the three phases heat each other, the air is stratified, and barriers block both the buoyant flow and the radiation view to cold surfaces. The 45 degC ambient absorbs some of that, but an IEC 61439 assembly is verified by temperature-rise test precisely because no free-air formula survives contact with an enclosure.
- No proximity effect. The AC resistance model treats each bar alone. Phase bars at typical spacings distort each other's current distribution, and paralleled bars per phase would make the effect strong enough to change the answer.
- The reactance is an input, not a result. The 0.12 mOhm/m came from typical flat-bar spacing; the real value depends on the exact phase geometry and enclosure steel. Since the drop here is 60% reactive, that assumption owns the voltage-drop answer.
Take this design further
Trafolo solves the 3D electromagnetic and thermal fields for exactly this class of problem - proximity effect between phases, eddy losses in the enclosure steel, and the coupled convection problem inside a real switchboard that the models above have to assume away.