Same here. Never had a frayed end, but have had the magnetic connector get really dirty, which causes it to either get REALLY hot when charging, or just stop charging completely.

One time I just bought a replacement connector/cable, disassembled the power supply, and soldered the new cable in place. That worked for a while.

The second time I just bought a new charger. (Well: two new chargers, actually. The first, which was listed on amazon as made by apple, never worked [I believe it was counterfeit, since some very small details differ from the official charger], so I bought a new one at best buy).