Commonly occurs by accident as well and is highly embarrassing and mortifying.
(Starts to pee)
"Wow I'm splattering all over the place ! This is a power pee ! "
It is also when you have a limited time to "relieve yourself," and you do so as quickly as possible. Usually leads to a return trip to the restroom half an hour later.
Lisa was told by her teacher that she could visit the restroom, as long as she chopped down the mightiest tree in the forest with A HERRING, and took less than 5 minutes to complete that task, as well as going to the restroom and finding a nice shrubbery for the principal. Any longer, and she would be expelled. That warranted a major power pee.
nerd: Oh em gee nerdina, I just got nerdy to the power of pee! Yesss!