Unlike supergirl origin (Earth 1) Powergirl has similar origin (the supergirl TV series).
Kara Zor-L was born in Kandor (the first of three colonized moons of planet Krypton), Kandor was doomed with the explosion of Krypton in a matter of hours, the space rocket kal-L baby had already left Krypton toward land, Kara Zor-L was three years older than the baby Kal-L, in this story parallel, described as Zor-L older brother of Jor-L.
Alura In-Z engineer built hastily the space rocket to his daughter, the rocket was launched at the time of Krypton explosion destroyed the moon of Kandor, the rocket got stuck in Krypton fragments for 30 years, Kara was in animation state by a "wormhole" of phantom zone, who was near to Krypton, the fragments pushed the space rocket out of the wormhole following to the earth, Kal-L (superman) was 50 years old, finding Kara Zor-L 33 years age.
Five years later, the anti monitor caused a collapse of the multiverse, destroying the dimensions, INCLUDING earth 2, the young scientist Alexander Luthor managed to save Kara in dimensional portal to earth 1 that he built, she watching the death of his cousin Kal-L with Lois Lane.
The starting point of their arrival was Gotham City, Alexander Luthor was killed in a Joker ambush, avenging his friend, she defeated the Joker and handing the police, will go to Metropolis, Kara was alone in a different parallel universe, met superman asking for his help, was also presented to a parallel image Kara Zor-El (Supergirl) where the two have differences conflict.
She adopted the identity of Karen Starr (with tied hair and glasses) and founded a software company in "Brooklyn" New York, and join the Justice League International and Justice Society of America, which became the first woman leader of the team. She recently welcomed a young mutant called Earth, which became his great friend, and founded the JSA All-Stars, It has the same powers as Superman, and also the weakness of the deadly kryptonite.