Single Engine Pilot reported an electrical failure causing communication and navigation failures. The pilot and safety pilot used their EFB devices to navigate to the airport. Communication was reestablished on the ground by use of a handheld radio.

Narrative

Conditions were widespread IFR with 500 AGL ceilings and about 6000 MSL tops. The aircraft was an Aircraft X equipped with 1 PFD; 1 HSI slaved to a computer and magnetometer (no battery backup); and the remaining standard gauges. Each instrument had its own independent battery backup. The left seat pilot was the aircraft owner and a CFI. The right seat pilot was a CFI/CFI-IA/MEI. Both pilots were IFR current and proficient and had recently flown together in this aircraft under simulated and actual IFR without incident. The right seat pilot also had an EFB device with an ADSB (independent battery + accelerometer) as a backup navigation source (was turned on and accuracy verified prior to takeoff) and a handheld NAV/COM radio. The right seat pilot filed an IFR flight plan from A-B-C-A with airport D as an alternate. The departure and approaches to airports B and C were without incident. After executing the ATC assigned missed approach at airport C and reestablishing contact with ATC; ATC requested that we disable the transponder altitude reporting capability as it was sending faulty altitude information that was incorrect by several thousand feet. Several minutes later; all power to all the Nav/Com was lost. The right seat pilot assumed the controls as the pilot flying and continued to fly the aircraft using the functional PFD/AI and utilized his EFB device app for GPS position and course information. The left seat pilot was able to temporarily reboot the Nav/Com and reported to ATC that we were experiencing intermittent electrical failures. We again lost all Nav/Com power including the GPS and HSI. We were initially unsuccessful in restoring power to the Nav/Com. The left seat pilot disabled all unnecessary electronics and continued to troubleshoot; including reviewing the POH emergency procedures. He also noticed that the HSI circuit breaker had popped and reset it. He was able to restore power to the Nav/Com again for about 20-30 seconds; long enough to obtain an ATC clearance for the approach to Airport A. The HSI had lost all input from the computer and the magnetometer since neither had a battery backup. The only sources of navigation remaining were the EFB device slaved to the ADSB and the magnetic compass. The NAV/COM radio could potentially have been used to fly the localizer once we were close enough to the airport; however; we were unable to pick up ATC / Tower or localizer using the handheld at the time (no external antenna). Neither pilot was able to get a cell phone signal to call ATC/Tower. The ceilings that had previously been reported (and currently reported via the ADSB) for home airport A; the alternate and in the surrounding airport were all about 500 AGL; which is just above the MDA for the LNAV for the approach at airport A for which we were previously cleared by ATC. With no operable communication; the pilots continued to intercept the assigned final approach course and fly it using the EFB device providing position and course information along with a georeferenced approach plate. The approach was completed without incident; transitioning to VMC above the minimum descent altitude (MDA). Once on the ground; the pilots were able to communicate with Tower via the handheld radio that was reported as weak but readable. It was later discovered that the wire providing power to the electrical/avionics bus had somehow shifted and was severely burned by the exhaust manifold.