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What are the differences between 380VAC, 400VAC and 415VAC Mains Supplies and what voltage equipment should I use?

For many years, mainland Western Europe has used a mains, 3 phase, electricity supply rated at nominally 380VAC 50Hz. The UK used 415VAC 50Hz.
Currently, ALL Western European 3 phase supplies are classified 400VAC. In reality there is no 400VAC supply unless you create one locally. 400VAC was a “standard” created during European "harmonisation" to give a single voltage standard across Western Europe, including UK and Irish Republic.
Although the ideal would have been to have a single voltage there were too many political, financial and technical obstacles to reduce UK voltage to European levels or to increase European voltage to UK levels, so a new standard was created to cover both. This was achieved by changing the tolerances of previously existing supply standards. UK voltage  to 415VAC + 6% and - 10% and European to 380VAC +10% and -6%  (thereby creating a manageable overlap) and we would call these two combined 400VAC, despite the fact that nobody was intentionally generating at 400VAC!
Depending on the voltage sensitivity of the product and the variance from nominal of the actual supplied voltage, it may not be advisable to use a 380VAC specific device in the UK or a 415VAC specific device in Mainland Europe etc. For instance a 415VAC supply can rise to as high as 439.9VAC and still be within tolerance, but the maximum assured rated voltage for a 380VAC product is only 418VAC. A 380VAC supply can drop as low as 357.2VAC within tolerance but the minimum assured voltage for correct performance of a 415VAC product is 373.5VAC It may work perfectly well either way but it could be, technically, outside the specification of the equipment with obvious implications. A 400VAC product must be compatible with all voltages across this range
If a product is to be used in the UK a 415VAC rated device is ideal but either 415VAC or 400VAC products can be used with confidence.
If a product is to be used in mainland Europe or Irish Republic a 380VAC rated device is ideal but either 380VAC or 400VAC products can be used with confidence.
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