From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
The Power Ball was used to mimic the presence of a full moon. By combining Ki with the planet's atmosphere, a sphere of condensed Blutz Waves was created. Using this, a Saiyan could achieve the Great Ape Transformation even when a full moon (or similar planetary body) was not present.
Dragon Ball Z
Dragon Ball Z: The Tree of Might
Tullece used this attack in Dragon Ball Z: The Tree of Might to make Son Gohan transform into a Great Ape and attack Goku. Haiya Dragon stopped Gohan in time and Gohan then seemed to get control over his Great Ape form and tried to attack Tullece instead. Tullece tried to attack Gohan, but Goku managed to cut off Gohan's tail in time and save him from Tullece's attack.
In the Budokai Tenkaichi video game series, Vegeta, Tullece, and King Vegeta can use the Power Ball to transform into a Great Ape at any time, while other Saiyans with tails must be on a stage with a full moon in order to transform (Raditz, Nappa, Bardock, Selypa, and Kid Goku).
Vegeta revealed that Goku's father (never referred to by name), as a scientist, invented the Power Ball technique in the Ocean Group dub of the anime. This is a continuity error because Bardock is shown to be a soldier, not a scientist, in Dragon Ball Z: Bardock: The Father of Goku.