It seems like it's possible to use variables in some configuration directives but not in others. This works:

root /usr/www/$sitename/httpdocs;

works, while these:

access_log /var/log/www/$sitename/access.log;
proxy_cache $sitename;

do not, instead generating errors when I try to restart nginx.

Is there any documentation that explains where I can and cannot use a variable? Or is there some syntax I should be using to indicate variable interpolation? It would be immensely helpful if they worked in all these contexts, because then we wouldn't have to repeat so much across different site configuration files, leading to the requirement for generating them with clunky scripts. As it is, the variables are of very limited utility.