LED light strings/fairy lights question

[Moondog55]

Cecile loves Fairy lights. But the controllers don't last forever and I have 4 sets of lights here that I'd like to set-up using a toroidal transformer I have on my desk
The controllers are 31Volts AC and the toroid is 28-0-28 so if I combiner the two positive leads I'll have 28V and plenty of amperage.
But I'm a little unsure about finding out which of the two leads on each LED string is +Pos and which is -Neg; don't want twinkling; want them always on.
Anybody here got an idea or expertise in doing this