XPS 8700 Special Edition - restarts when playing games with a newly installed GTX 970

Hi,

I have an XPS 8700 SE (I7-4770, 32GB, 256 SSD, 3GB HDD, 450W original power supply).

I've replaced the R9 270 that the came with the machine with a Gigabyte GTX 970 Overclocked. The computer works fine until I start playing a game, and then it restarts after a minute or two of playing. The behavior is constant. I have the A10 BIOS which I understand is required to run the new Nvidia cards.

Is this problem related to the power supply? If so, are there any recommendations in terms of brand and size? 

Thanks.