jvloyola is correct. The Power Cover for the Surface Pro/Surface 2 does not work with the Surface 3 at all. It can snap into place and both the keyboard and trackpad will work but the Surface 3 won't see an additional battery because the unit itself lacks the power pins on the bottom (Microsoft took them away).
You can, however, buy a portable power bank. I have a 15000 mAh one I purchased from Amazon for $17. It outputs up to 3.1 amps (10 watts) when using one port or 2.1 A 5W and 1 A 5W when using both USB ports at the same time. It holds enough to completely recharge the Surface 3 once. I tried it out yesterday when my Surface 3 was at 15% battery left and it worked just fine. The battery bank is about the size of a Note 4 and charges via micro USB. Well worth the money and it's a much better, more portable option than carrying around a Power Cover.