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The Netherlands uses the largest and most powerful dredging ship in the world, The Queen of the Netherlands. Each of the dredging pumps are 8,000 horsepower (6 MW) and there are two of them. Even the short-range ship-to-shore connections used by container ships are in the 2 MW range. Running "wires" would be ambitious.
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Those giant bucket wheel excavators are also electrically powered, by cables. And they use up to 16 MW, so I wouldn't call it completely unrealistic.

Of course running them over some dirt is easier than through possibly moving water, but still.

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cables can get pretty big, you could run maybe 75-90MW through a 66kV 1200mm2 Cu offshore wind array cable, maybe 500MW through a 275kV 2000mm2 cu export cable and 1.3GW through a 320kV hvdc bipole set of cables (2GW through 525kv HVDC!) - you would just have the minor inconvenience of convertors and or substations to deal with at either end ;)
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> Running "wires" would be ambitious.

It’s definitely possible, I don’t have an in depth knowledge of ships connected to shore power with cables, but if the distance isn’t too great, it seems possible.

Raising voltage lowers the ampacity to allow for smaller conductors.

6MW at 7200V is only ~500A, 6MW at 13.8kV is only 250A.

There are massive electric powered hydraulic mining machines that operate connected to power cables.

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We already have 25kV for rail electrification which move 6MW all over the place, surely at boat speeds making some strange double-pantograph system for shipping could be strung up alongside most of the canals, maybe electric tugs could be used as well as normal shipping?
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> surely at boat speeds making some strange double-pantograph system for shipping could be strung up alongside most of the canals, maybe electric tugs could be used as well as normal shipping?

I like it, very similar to how mules used to pull barges thru canals except with electrical cables and a rail pantograph running on distribution lines next to the canal instead of mules and ropes.

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For canals, I'd say yes. I mean related, before steam / fossil / etc we'd have a "trekschuit", which was a canal boat pulled by people and / or animals that walked on a path alongside the canals. Wired propulsion, if you will. I can see a system similar to trains/trams but for ships would work.
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