i not sure if this feature was on previous samsung model but on some other phones it is possibile to auto switch ON power saving mode if battery gets lower than X %
Good news - yes you can, bad news - not easy to do, and not with Touchwiz. To get to that setting you will have to use a launcher like Nova and access the shortcut/activities/setting/power saving mode and the one with green icon (in my screen shot). I was able to set mine to 15% but there is also a 5% option.