SMA HAS ALTERNATOR FAILURE; LINES UP WITH WRONG ARPT RWY.

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ON APCH TO BOEING FIELD; SHOOTING THE LOC (BACK COURSE) RWY 31L. I WAS RADAR VECTORED ONTO THE LOC AND CLRED FOR THE APCH BY SEATTLE APCH. APCH CTL HANDED ME OFF TO BOEING TWR AT LACRE INTXN (7.6 DME FROM BFI). BFI TWR CLRED ME TO LAND ON RWY 31L. AT LACRE INTXN I DSNDED FROM 2600 FT TO 1600 FT. DURING THE DSCNT; IN IMC CONDITIONS; I EXPERIENCED AN ALTERNATOR FAILURE. I STARTED MY TROUBLESHOOT PROC IN AN ATTEMPT TO GET THE ALTERNATOR BACK ON LINE. WHILE DOING THIS I DRIFTED R (E) OF THE LOC. I GOT THE ALTERNATOR WORKING AND AT THE SAME TIME BROKE OUT OF THE CLOUDS. I SAW THE REIL LIGHTS FOR WHAT I THOUGHT WAS BOEING FIELD AND HEADED FOR THEM. IN REALITY; I WAS GOING TOWARDS RENTON ARPT. AT THAT TIME; BOEING TWR ADVISED I WAS ON A 2 MI FINAL FOR RENTON AND NEEDED TO TURN L TO INTERCEPT THE LOC. I TURNED L AND AT THAT TIME WENT INTO THE CLOUDS AGAIN (MY ALT WAS LEVEL AT 1600 FT). AT THIS TIME I WAS NOT COMFORTABLE WITH THE SIT AND EXECUTED A MISSED APCH PROC. I ADVISED BOEING TWR I WAS GOING MISSED AND REQUESTED INSTRUCTIONS. THEY ASSIGNED A HDG AND ALT AND HANDED ME BACK TO SEATTLE APCH. I REQUESTED RADAR VECTORS BACK TO BREMERTON ARPT (MY ORIGINAL DEP POINT). AT BREMERTON; I SHOT AN ILS AND WAS UNABLE TO BREAK OUT BECAUSE OF FOG (AWOS WAS RPTING 100 FT CEILING AND VISIBILITY 3/4 IN FOG). I WENT MISSED AND PROCEEDED TO TACOMA NARROWS ARPT AND SHOT THE ILS TO A FULL STOP LNDG. THE WX AT TACOMA WAS MUCH BETTER. THE PROB OCCURRED ON APCH AT BOEING FIELD. THE ELECTRICAL FAILURE CAUSED A DISTR AND THUS THE DEV R (E) OF COURSE. I FAILED TO TELL ATC OF MY SIT AND I MADE THE MISTAKE OF IGNORING MY CDI ONCE I SAW A RWY. THE FINAL TO RWY 31 AT BOEING AND FINAL TO RWY 33 AT RENTON DO INTERSECT AT ABOUT THE POINT OF MY BREAKING OUT OF THE CLOUDS. I SHOULD HAVE RECOGNIZED THAT I WAS SEEING RENTON AND NOT ABLE TO SEE BOEING YET BECAUSE OF THE LOW VISIBILITY. THE TWR'S RECOGNITION OF THE SIT PREVENTED ME FROM LNDG AT RENTON WITHOUT A CLRNC. MY MISTAKE WAS HDG FOR THE WRONG RWY; BUT I BELIEVE I MADE THE CORRECT DECISION BY EXECUTING A MISSED APCH AND RETURNING TO BREMERTON.