The original power adapter for my MacBook Air 13" (mid 2012) died about 2 months ago.
I purchased a MagSafe1 power adapter knock off from Malaysia and a MagSafe1-to-MagSafe2 converter. The combination worked, but it my MacBook was super-slow to charge.
I gave in, went to the local Mac Store, spent $85 for a true MagSafe2 power adapter. It seems as if it does, in fact, charge my MacBook quickly sometimes, but other times it's glacial.
I attribute some of the slowness to Parallels, which is an energy hog. Last night, however, I powered down Parallels and the Mac, with the battery at 45%, left it plugged in, and woke up to find the battery at 88%. I can't blame the slowness to charge on Parallels.
Finally, take a look at the image below, this represents the battery charge as shown in the Activity Monitor. The steep part of the curve represents the battery when the MacBook was on. (Trust me, the curve is often close to flat when the MacBook is on but last night the battery was charging quickly.). The less-steep portion of the curve represents the Mac when was off. It's as if the Mac decided that it really didn't need to charge quickly.