City of Ember Series by Jeanne DuPrau........
http://www.jeanneduprau.com/index.shtml

Book 1 The City of Ember
Book 2 The People of Sparks
Book 3 The Prophet of Yonwood
Book 4 The Diamond of Darkhold

The City of Ember has also been made into a movie.

Terrible tradegy has befallen life on earth. The City of Ember is unaware of life outside of their city limits. However, as their city begins to deteriorate, Lina and Doon realize that they need to find a way out of the city to try and find help.