Please see the linkNo, an external SSD (whether it be placing an SSD in an external enclosure or something produced by a company like WD) should be able to be powered completely by USB. It would be no different compared to a portable 2.5" HDD.
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The Amazon listing may be in error, or there may be a little lithium battery inside.The technical details mentions " one lithium ion battery required'
Lithium Battery Energy Content 2 Kilowatt Hours Lithium Battery Packaging Batteries packed with equipment Lithium Battery Weight 2 Grams Number Of Lithium Ion Cells 5 Number of Lithium Metal Cells 5