Pilot flying C-172 aircraft reported electrical failure on approach.

Narrative

Experienced electrical failure in flight; which caused a loss of communication just after ZZZ Approach instructed me to contact Tower.The flight was the 2nd flight after the plane came out of maintenance for an avionics upgrade and alternator replacement. The first flight was completed earlier the same morning; and a comprehensive check of all the aircraft systems was completed. Two small discrepancies were noted during the first flight; we returned to the shop at ZZZ1 to have them corrected. (The discrepancies were V-speed bugs on the new Garmin GI275 and gain rate for the autopilot.) They were corrected and I departed for a flight to verify functionality and return the plane to its home base at ZZZ.While flying level at 2000 ft and on the localizer for runway XX; I noted erratic fluctuations in the radio displays. Shortly after that; Approach instructed me to contact Tower. At that moment I lost the ability to transmit. I attempted to troubleshoot and switch radios; but the displays started failing; and I realized I was experiencing a total electrical failure. Without a landing clearance; I elected to break off the approach and orbited to the west of the extended center line. Though I did have a handheld backup radio in my flight bag; I forgot about it at that moment. I used my cell phone to call Tower's landline number; but that got me to 2 levels of menus; so I elected to call the Clearance Delivery number. The person who answered either transferred the call or coordinated my landing clearance. They also coordinated my ground clearance after touchdown and stayed on the call with me until I parked at the FBO.The crew at ZZZ tower was excellent and very helpful. We are currently investigating the reason for the electrical failure and have contacted the mechanic who performed the work.