I am a Droid Turbo user researching battery life problems after a software update and using Qi wireless charging. I would like to offer a suggestion that worked for some of our phones and I would be interested to see if it works on your platform as well.
What appeared at first to be a rapidly draining battery, or a slow charging battery, actually turned out to be that the phone's ability to properly determine the charge level of the battery was out of whack. Still not sure why, may have been the software update (not Lollipop but a smaller update) or may have been caused by Qi charging. At any rate this was the fix to recalibrate the phone's battery monitor.
First, perform the "Clear Cache Partition" which seemed to be a major benefit. Some users do this after every software upgrade or even just as a preventive measure every so often. The first time you do it, you may have to let it run quite a while... mine took over 15 minutes to complete.
Then, power off the phone and plug it into a wall charger while powered off and leave it for several hours, possibly overnight. Make sure it charges to 100% and then let it keep charging while powered off for an hour or more.
This recalibrates the phone's battery level indicator settings. So far, my phone seems cured, but I don't know if it will last or if I will have to do it again from time to time. But, I was ready to send my phone in for a new battery until I found this procedure and tired it.
Hope this helps. I would be interested in hearing if it has any effect.