\When writing a series there are three important ingredients. The plot is necessary and so are the characters. But for each story in a series, the characters may change, or they could be the same in each story. Though the characters can stay the same, they need to change and grow. The plot for each story may change and should. Having the same problem solved in the same way with the same internal and external conflicts and the reader will lose interest.
Different characters or the same. A plot with internal and external conflicts that should change. Both of these could cause both the reader and the writer problems. What can hold them together?
Setting is the answer. When writing a series the setting needs to be consistent. Now not every place in the series needs to be the same but there has to be a unity. Take a period in history and build your series around this world. Medieval, Regency,the contemporary world or a world one has invented can be what holds the series together. Not every space in this world needs to be the same but with certain places or customs or some other feature of the world that makes the reader know this book is part of a series.
I'm working on a series in an alternate Egypt. The Nile is a constant in these stories. The desert is another constant. Another series is in a town in the US. Here I've chosen several features that are in every story. The lake the town is named for, a hamburger place that's unique to this town. They occur in every story in the series so far and they give the reader something concrete to put them and the characters into that world. Of course there are others because a series needs some consistency and that can be the world that's created. This could be a town, an agency and anything a writer can dream into being.
So when working on a series make sure the world you've build is consistent. Give the reader a place to stand.