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A small computer UPS would work, but might be troublesome to transport during travel (due to the sealed lead-acid battery contained within). I've seen them as cheap as $40 US for a 350VA unit. As a plus you could connect your cellphone, tablet, camera charger etc. and ensure that they were at 100% when you awaken.
You could also consider a similar clock with backup battery built in, but the quality may not be as good as Philips. Some do exist.