Full Power Super Saiyan 3 is the mastered version of the Super Saiyan 3 transformation.
In this version, the Saiyan can gain a massive lightning aura. The hair also gains a golden shade, and like the normal Super Saiyan 3 form, the Saiyan grows long hair that goes down to the waist. The Saiyan gains a sense of confidence, and because they can control their Ki levels in this form, they can stay in this form as long as they want, which can prove to be useful when the user is fighting an opponent.
This form is available to Goku (and Vegeta, in alternate universe scenarios and in some DBAF Fanfics). This is because they were able to perfect their Super Saiyan 3 forms during the twenty years between the Kid Buu Saga and Dragon Ball GT.
This form doesn't change the multiplier of the Super Saiyan 3 form, which means that it still multipies a Super Saiyan 2's power level by 4. This form, however, looks and seems powerful because the user can control his or her Ki levels, making the transformation more stable. It also helps the Saiyan ascend into the False Super Saiyan 4 form.