Navion pilot reported an ADS-B transponder issue and subsequent electrical failure in class B airspace.

Narrative

On Day 0 I departed ZZZ at XA34 MST after completing a preflight with no abnormal findings. Upon reaching pattern altitude and making my westbound turn; ZZZ Tower informed me they weren't receiving my ADS-B output and asked me to reset my transponder. I recycled my Garmin GTX-335 transponder successfully the first time; but Tower still did not receive my signal. I reset my transponder again and this time; the display indicated 'XPNDR FAIL.' I then looked at my generator AMP indication; which showed significant discharge. At that point I realized I had suffered an electrical supply system failure. I attempted to remove all unnecessary loads but was never able to get my generator to show a positive charge. I subsequently shutdown my electrical system and remained clear of the ZZZ1 Class B airspace and continued to my refueling stop; ZZZ2; then ultimately to my destination at ZZZ3 via ZZZ4-ZZZ5 In order to remain clear of the 30 NM ZZZ6 airspace since I had no functioning ADS-B. This report is filed in recognition that until I left the 30 NM radius from ZZZ1 I did not have a functioning ADS-B transmitter.