Green Power Stars, or simply known just as Green Stars, are first found in Super Mario Galaxy. There are three, one in Battlerock Galaxy, Buoy Base Galaxy, and the Dusty Dune Galaxy. Once all three are found, the Trial Galaxies are unlocked. The Green Power Stars will turn into Green Lumas.
In Super Mario Galaxy 2, Green Power Stars can be found once the 120 star ending has been seen. Every single Green Power Star is summoned by Green Prankster Comets, which swarm all of the galaxies after the 120 Star ending (Get 120 Power Stars, and then defeat Bowser in World 6). These stars are hidden throughout each of the Galaxies, with one Green Power Star for every Star in a galaxy. For example, if there are three normal Power Stars in a galaxy, there will be three Green Stars, making a total of six. All 120 Green Stars are required to unlock the final galaxy of the game, Grandmaster Galaxy, which is the only galaxy that does not have Green Stars.
Green Stars are the replacement for Star Coins in Super Mario 3D World. There are 380 Green Stars in all for this installment.