PSU won't change a thing, if your system is stable the PSU is fine.
As I said, good emulation requires a good CPU, at the moment the recommended CPU is a high clocked i7, we've taken advantage of the modern CPUs the best we can.
For non-MAME emulators (Dolphin, DCEMUL etc.) you need a good graphics card too, none of this onboard or budget junk.
Emulation is costly, that is the thing to understand here. Bad emulation is cheap, but in the last 5ish years most people have moved away from bad emulation to try and get something better, which has increased the hardware demands significantly.
If you try to cut corners you will get burned. No matter how much we stress this some people try.
Once you have a good PC (high end Intel; AMDs are at least a generation, maybe 2 behind ) make sure you have a good GFX card and the DirectX 9 stuff properly installed, a recent OS (Windows 10 is fine, aside a current Xbox1 controller issue) and the proper drivers for your hardware. At that point you're ready to run the most recent emulators.
People will recommend less, but if you want hassle free that's the way to go. Note, I don't stand to benefit from latest hardware sales, or software sales, that's just the genuine advice from somebody who has worked doing emulation development for 15+ years.
You could consider emulation requirements on par, if not in excess of current game requirements, the higher level of accuracy we aim for the better spec required.