city center vs principal city

city center

noun
  • The central business and shopping area of a city. 

principal city

noun
  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see principal, city. 

How often have the words city center and principal city occurred in a corpus of books? (source: Google Ngram Viewer )