Much depends on your definition of what constitutes a powerful float rod, skill level and venue. I do little else but trot floats these days and have a slightly OTT selection of rods to do it with. Unlike others, I will not resort to using Avon or barbel rods to fulfil the heavier end of the spectrum. I consider the vast bulk of such rods to be too heavy to comfortably trot with and too through actioned for good float control and fast pick up on the strike.
The heaviest genuine float rod I own is a 1lb 6oz test Freespirit. It can actually be too brutal, unless you are fishing for decent sized barbel (or carp) with 8-10lb lines.
The lighter end of the spectrum are the Drennan IM8 Crystalight, Drennan Acolyte Ultras and Drennan Matchpro Ultralight. I wouldn't deliberately target barbel with any of them. These I consider to be out and out bit bashing rods. Anything much over 4lb or so is far too interesting an experience!
A step up from those would include the Drennan Acolyte Plus, several Shimano Fast Action match rods and a Normark Titan. I'd be much less concerned about the prospect of tangling with barbel with this tier of rods, but I'd use them to deliberately target big chub rather than barbel. If you've got a bit of space and a fair level of skill, reasonable barbel shouldn't be too much bother.
The rods I consider to be barbel float rods are a step further up, but not to the level of the aforementioned Freespirits. They consist of a couple of Shimano Specimen Match rods, a Specialist Float Rod and a Normark Avenger. These have enough beef to allow the use of heavier lines in more tricky situations. They are not so heavy as to make catching smaller fish and bits that come along a totally pointless affair.