Driving a 15V, 150W AC halogen
IF it is a 150W Tungsten filament operating at 15Vrms or dc, then the current at 4000'K is about 150W/15V=10A and the resistance is 15V/10A= 1.5 Ohms.

We know that that PTC characteristics for tungsten are 1:10 Ohms cold:hot thus the cold resistance should be 1.5Ohms/10= 150 milliohms which results in a surge current of 15V/0.15 Ohms = 100 A or 10x the hot current.  In order to minimize transformer losses the secondary winding DCR should be about the same order of cold filament resistance  or less , which help to reduce the surge current in half or less at the expense of 5% additional conduction losses.

side note

But if you need a regulated current limiter, these bulbs make great series current regulators with 10~20W power LEDs or 4x3W LEDS operating at 15 Vdc and work like PTC active Polyfuses when used with less than half of its voltage rating. So you can replace the 150W wasted halogen power with 20W 12V LEDs using 15Vdc ( if you had such a supply)