A D328 FLT CREW NOTICED A BURNING ELECTRICAL SMELL AFTER USING ELECTRICAL ANTI-ICE. THEY WERE DSNDING TO DEST. CREW DECLARED AN EMER AND LANDED.

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WE WERE DSNDING INTO ZZZ FROM YYY; REPOSITIONING AN ACFT FOR A PART 135 REVENUE FLT. OUT OF APPROX 17000 FT MSL; WE ENCOUNTERED IMC WITH TURB (MODERATE) AND RAIN (MODERATE). I ACTIVATED OUR D328 JET'S ANTI-ICE SYS; WHICH INCLUDES AC ELECTRIC ELEVATOR HORN (TIPS) HEAT; AND THE L SIDE FAILED. I CYCLED THE SWITCH APPROX 3 TIMES IN 1-2 MINS; HOWEVER; IT REMAINED FAILED. ABOUT THIS TIME MY FO AND I NOTICED A STRONG SMELL OF BURNING ELECTRICAL EQUIP. I LOOKED BACK TO THE FLT ATTENDANT SITTING IN THE LAST ROW NEAR THE LAVATORY; WHO INDICATED SHE TOO SMELLED SMOKE. WE WERE ALREADY DSNDING; AND I ADVISED ATC WE HAD SMOKE IN THE AFT AND NEEDED LOWER. THERE APPEARED TO BE A HAZE IN THE COCKPIT AS WELL. ATC GAVE IMMEDIATE VECTORS TO ZZZ AND STILL LOWER ALTS. AS THE FO AND I PREPARED TO DON OXYGEN MASKS AND GOGGLES; THE SMELL IMPROVED. WE RAN CHKLISTS; DECLARED AN EMER; SET UP FOR AN ILS AT ZZZ. UPON LNDG WITHOUT INCIDENT; CFR MET US AND CHKED ACFT WITH A HEAT CAMERA; FINDING NO HOT SPOTS. IT WAS DETERMINED BY MAINT TO BE AN ELECTRICAL RELAY BENEATH MY SEAT WHICH HAD FAILED/OVERHEATED WHEN I HAD CYCLED THE FAILED ELEVATOR HORN HEAT; CAUSING SMOKE AND BURNING SMELL.