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Everyone has a lot of real stories to tell. It's just about how you narrate the story and link it to the scenario at hand. Try writing down a few of your personal stories and then you would be able to figure out how it can relate to not one - but several competency sets!
I believe that this might only happen with new graduates. If you have any real work experience you should have something to tell, maybe you're not thinking it worth telling. Here is an article that may help you: Competency Based Questions.
Good luck!
