I am about to submit a paper on power for a multi-group design (but not longitudinal). The core of our paper (Carlucci and I) is that few researchers care just about whether just the F statistic is significant (what is given by Cohen's tables and the typical power packages like G*Power), but are interested in, say a three group study, that group 1 differs from 2 and 2, or that all groups differ in the correct direction, or things like that.

Are you just interested in finding a single significant overall F (or whatever) statistic, or are you interested in a more "elaborate" (Fisher's word) set of hypotheses? I have a (still being evaluated) R function for the non-longitudinal case for power analysis for multiple-hypotheses designs, but someone could extend it to longitudinal designs. 

But if you are only interested in the significance of one overall statistic, then ignore this comment.  

Hello Luiz

The power calculation may depend of your data distribution and the test/hypothesis you use...

Please find more information on power calculation in the link below.

Regards

http://www.statmethods.net/stats/power.html

Thank you Cyril.

Hello Luiz,

Sample size calculation for study having more than one group, one easy way is to choose two groups having maximum diffence in their SD.

Thank you, Jagathnath.