Will this affect the site's ranking with Google and if so, how?
First of all, unless you planned on the site going down every day at the same time, you have a hosting problem and you should fix that ASAP. There just isn't any good reason for your current hosting provider to go offline that often, for that long, and that consistently. If it is a planned outage, please be sure to serve up a notice so there isn't a bare 404 error page (assuming the site can even respond properly during the outage).
To more directly answer the question, this could have a negative effect on your SEO in a couple of ways. If Google is trying to index the site during the outage window and it consistently can't get a response or gets a 404 error then you will probably incur some quality penalties and/or have pages dropped out of the index.
The other thing to look out for is negative user behavior due to the frequent outages. Going from a link in Google to a dead site or dead page will probably result in a quick bounce back to Google. If you have a high bounce rate, the implication is that there is poor content or a poor user experience on your site and Google will penalize you for quality reasons.
In short, it certainly will not HELP your ranking and it will very possibly hurt you.
Google, and all the other Search Engines, crawlers, bots, etc., crawl your site every day (if your site is big enough indeed). Google crawls the important pages for changes at a higher rate, like your homepage and your highest quality content pages, and randomly the rest of your pages to make sure that it's up to date.
Now, the pages that randomly Google will try to crawl during that 15 minutes will return a 404 or a 500 HTTP response, and will eventually be penalized, but will slowly recover as they get correctly indexed again.
Also penalized, but with less harm, will be the pages that link to those temporary 404 pages, and a little less SEO harm will get the pages that are being linked from those pages.
Personally I wouldn't bother that much if it's only 15 minutes, take into account that many pages do maintenance. Just try it to be 5 minutes or less to minimize the harm to your site.