3 wires on a (bipolar) DC plug - what are they for?
There is two reasons. Remote voltage sense as tony suggests.

And because some of these chargers are actually both barrel and center pin, making them have 3 conductors. The third conductor is typically a 1 Wire type data connection, and is used to signal what type of charger is being used.



Dell and Lenovo use these extensively.



Based on a few searches for replacement XPS 15 jacks, you have the data pin. Based on your 4 conductor wire, it uses both reasons.