When I moved here was during a point when it was hard for a new immigrant to get an id unless vouched for. Banks could issue id then. My friends had a Swedbank account, so I was able to get set up with them.
What is the best bank in Sweden? I guess I should say, what is the best one with an office in Trollhättan?
Also, I live above the Swedbank. In the worst case scenario I can easily (with some wait time, because Swedbank) do my banking in person.