Are the different series with the same characters?

The only characters from the 1st are Lund, her boss, mother and son. It's a entirely new case

As far as I'm aware the 3rd series isn't out yet. In the 2nd Lund has a new partner (obviously), but still at the centre of things and still reporting to Brix. It's a completely unrelated case though, so the suspects etc. are different.