Hail, Giantfriend! Long time no read.
It boots little, methinks, to consider the Rings of Power as engines dependent on either an inbuilt fuel cell or an external energy source; nor do I think that the way Sauron imbued the One with his will and power was categorically different from the way every maker imbues their creations with some of their own personalities, values, desires, and the greater the art the greater the maker's control over what and how much of them gets put into the product (see the little story
The Faithful Stone in UT for an illustration of the principle).
Now Sauron, he was all about power and domination, so the will and power to dominate was what he put into his creation. The smiths of Eregion desired other things - preservation of what they kept, restoration of (a semblance of) what they had lost, so it was these desires that guided them in the making of their rings.
As for the Three, it would seem that Nenya was an instrument of preservation, used by Galadriel to create and preserve in Lothlórien an echo of the Undying Lands she had been exiled from, and fiddling with time was just part of its modus operandi. About Narya we have Círdan's words when he gave it to Gandalf:
Quote:
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Originally Posted by Unfinished Tales, The Istari
'It was entrusted to me only to keep secret, and here upon the West-shores it is idle; but I deem that in days ere long to come it should be in nobler hands than mine, that may wield it for the kindling of all hearts to courage.'
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Judging from this, I'd guess that Narya's special purpose was to inspire and wake courage and dedication. About Vilya we have very little, but it may have had something to do with Elrond's renowned healing powers (restoration).
We don't know how the Three accomplished their functions, but I don't think they were powered by anything else than the enchantments wrought into them by the art of their makers, and to explain how these worked would mean to explain the nature of Elven 'magic' in general. We might as well ask what powered the cloaks of the Fellowship or Sam's
hithlain rope or the Lady's starglass. They work the way they do because they were made to, and that's it.
Or at least this is my take on the matter.