At the age of ten, everybody discovered that Willow Matthews wasn't actually, Willow Matthews but instead the Vanderbilt's and the Matthews had made a deal. The Matthews weren't capable of having children and the Vanderbilt had one more child than allowed so they made the deal that the Matthews would take the youngest of the Vanderbilt girls and never speak anything of it, that is until the night of Samantha Vanderbilts 18th birthday, she decided now that she was of the age of being floated if she did anything wrong, she would get on the councils good side, so she told them everything about Willow and the deal.
The Vanderbilt's and the Matthews were all floated for the crime of having a second child and for keeping it a secret, Willow was a smart girl and the Ark was already doing dying, they needed a solution so that brings us to today..
Willow Vanderbilt was sent, alone to the ground to test if it was survivable.
They were never told, she had no contact to the Ark, everybody thought she was dead.

At first Willow was treated like a God because she was different but they thought she must have been sent from the previous commanders and her blood wasn't red, it was black, Willow later learned that it meant she was what grounders considered royalty, then three years later, she ran.
She didn't want to rule the world.
She found this guy, Lincoln and the two became friends, basically siblings.