A PA34 IN DSCNT AT 4000 FT DECLARED AN EMER DUE TO THE L ALTERNATOR FAILED AND SHORTLY AFTER THE R ALTERNATOR FAILED. BATTERY WAS WEAK. DSNDED TO 2000 FT AND RECOGNIZED FREEWAY TO ARPT.

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MY STUDENT AND I WERE VFR ON TOP WHEN WE NOTICED AN ANNUNCIATOR INDICATING WE HAD AN ALTERNATOR FAILURE. WE RAN THE EMER CHKLIST AND THE ANNUNCIATOR LIGHT WENT OUT. WE PICKED UP AN IFR CLRNC FROM APCH; BEGAN A DSCNT TO OUR ASSIGNED ALT; AND TURNED TO A NE HDG TO BEGIN VECTORS FOR THE ILS RWY 23 INTO ZZZ. AT ABOUT 4500 FT MSL WE ENTERED THE CLOUD LAYER AND BEGAN TO PICK UP LIGHT RIME ICE. WE TURNED THE DEICING EQUIP ON AND THE ALTERNATOR ANNUNCIATOR ILLUMINATED AGAIN. WE RAN THE CHKLIST AGAIN BUT THE LIGHT DID NOT GO OUT THIS TIME. WE BEGAN TO LOAD-SHED AND GOT A CALL FROM APCH TO DSND FURTHER TO 2500 FT MSL. I WENT TO REPEAT BACK THE INSTRUCTION AND TO ALSO ADVISE APCH OF OUR ELECTRICAL PROB BUT THEY DID NOT HEAR ME. THEY REPEATED THEIR INSTRUCTION AND I TRIED AGAIN TO SAY IT BACK BUT STILL THEY DID NOT HEAR ME. WE SQUAWKED 7600 FOR LOST COMS AND SECONDS AFTER LOST ALL ELECTRICAL PWR. WE HAD A DUAL ALTERNATOR FAILURE AND A WEAK BATTERY. WE CONTINUED THE DSCNT TO 2500 FT MSL KNOWING THAT WE'D BE ABLE TO SEE THE GND AT THAT ALT. IN THE DSCNT WE INADVERTENTLY TURNED TO A S HDG. ONCE UNDERNEATH THE CLOUDS WE WERE DISORIENTED. OUR WINDSCREEN WAS COMPLETELY COVERED IN ICE MAKING IT IMPOSSIBLE TO SEE THROUGH IT; OUR PROP SPINNER HAD ICE COLLECTED ON IT; THE LEADING EDGES WERE COATED WITH MODERATE RIME; AND OUR AIRSPD INDICATOR DROPPED TO ZERO INDICATING OUR PITOT TUBE WAS FROZEN OVER. WE DSNDED FURTHER TO 2000 FT MSL HOPING TO GET BELOW THE FREEZING LEVEL AND MELT OFF WHAT WE COULD. EVENTUALLY WE FOUND THE FREEWAY AND RECOGNIZED ZZZ1 SO AT LEAST WE KNEW HOW TO GET HOME TO ZZZ. THE ICE MELTED OFF OF OUR WINDSCREEN; PROP SPINNER; AND PITOT TUBE. WE FOLLOWED THE FREEWAY SBOUND AND REALIZED OUR CELL PHONES WERE RECEIVING SVC. ONCE OVER THE FREEWAY INTERCHANGE; WE CALLED ZZZ TWR FOR OUR LNDG CLRNC. WE MANUALLY EXTENDED THE LNDG GEAR AND LANDED ON RWY 23. I REGRET NOT NOTIFYING APCH AT THE FIRST INDICATION OF AN ALTERNATOR PROB. I HAD ASSUMED SINCE WE GOT THE LIGHT TO GO OUT THAT THE PROB WAS SOLVED AND NO FURTHER ACTION WOULD BE NECESSARY. WE ARE GRATEFUL THE CEILING WAS AS HIGH AS IT WAS; IT WAS DAYLIGHT; AND WE WERE IN THE ZZZ LCL AREA. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ALTERNATOR ANNUNCIATOR LIGHT FIRST ILLUMINATED AND WHEN THE EMER CHKLIST WAS COMPLETED THE LIGHT WENT OUT. ABOUT 4000 FT WE HAD A TOTAL ELECTRICAL FAILURE INCLUDING A WEAK BATTERY. FORTUNATELY WE WERE FLYING LOCALLY AND AT 2000 FT THE FREEWAY WAS LOCATED AND LED TO THE HOME ARPT. THE CAUSE OF THE L ALTERNATOR FAILURE WAS THE ALTERNATOR DRIVE COUPLING FAILURE AND THE R ALTERNATOR JUST FAILED POSSIBLY FROM OVERLOAD. THE R ALTERNATOR WAS REPLACED AS WELL AS THE L DRIVE COUPLING.