Principal components analysis with compositional data
I'm in the same situation as you.  PCA seems to have some difficulties for compositional data.  I've listed some papers below that have been helpful to me.  I'm still trying to understand everything, but these papers have a good overview I think.  Or googling "Compositional Data" or "Compositional Data Principal Component Analysis" returns a lot of other papers that are freely available and informative.

Principal component analysis of compositional data J. Aitchinson

A Concise Guide to Compositional Data Analysis J. Aitchinson

Principal components analysis for compositional data with outliers P. Filzmoser, et al.