Primarily Power Yoga is a more freely structured version of ashtanga initially developed by Beryl Bender Birch to cater to we Yanks. It's derivitives are often called "Vinyasa Flow."

I've found that unless I weighed under 100 lbs and been practicing ashtanga since my youth, adhereing only to ashtanga would be a frustrating experience. Now Power I can do.

I won't go into the philosophy behind ashtanga; no time or room on this venue but there are myriad souces and books and teachers out there.