where I preformed research on elucidating the function of XX in XX
To me, the above in red is a subordinate clause in a complex sentence. It is not an independent clause.
You would be correct, therefore, in sticking with your sentence as written:
Most of my experience was gained while completing my Ph.D. at XXX University, where I preformed research on elucidating the function of XX in XX.
On the other hand, You have more education than I. Hope others can provide more authoritative help.
Student or Learner