Power line lasting for generations (7)

I believe the answer is:

dynasty

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'power line' is the definition.
(I've seen this before)

I don't understand the remainder of the clue.

(Other definitions for dynasty that I've seen before include "House" , "Family line of rulers" , "Succession of rulers from one family" , "Song, say" , "royal family" .)

I've seen this clue in The Globe and Mail.

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