Thank you for the replies!
Tim, I have read the manual, and set the supply limit [to 2A] accordingly. Yup, I realise that this power supply is totally inadequate - it was one I had from ages ago, and figured it will do until I choose a proper one.
Your comment about the battery is noted. I have some more arriving this week, and can't wait to compare.
Dennis, thank you for your reply, and your links. That generator looks way cool[!], as do the server power supplies. I never realised how many choices there were in this field! I'm off to do some more reading.
Thanks again, guys - I appreciate you taking time out to help a noob...