How to conert the space advantage?

#1
Space is overrated. It is almost never possible to convert a space advantage into a win. You can convert an advantage in the center by attacking. If you control the center, then you can bring more pieces to attack than your opponent can bring pieces to defend. You should be able to convert an advantage of +1 or +2 to a win. If you post an example then we can tell you how to convert, but it is not possible to answer that in an abstract way.