Since you have a good amount of natural light the addition of HPS bulbs would promote flowers. That being said, unless your plumeria are young seedlings it would probably be a better idea to allow them to go dormant. What else do you have in your greenhouse?

I bought a couple 1000 watt MH lights for the plants that are inside the house. I'm not worried about flowers or fruit and just want to keep the darn things alive. lol I also want the extra heat that the HID lights provide. We do use high output fluorescent lights in the greenhouse for starting seeds early. We have propane heaters in there so we don't need the additional heat.

There are some systems that will run both HPS and MH bulbs at the same time but they are very pricey. If you don't want or need additional heat you would probably do well with the fluorescent bulbs. Here's a link that has some good info on different grow lights.
http://www.littlegreenhouse.com/guide3.shtml
Karyn

You can also get what they call 'light movers' to move the High-Intensity lamp back and forth slowly along a track. This will ultimately illuminate much bigger area. It might be something to think about for your space.

Here is a link that might be useful: Light Rail 3.5

Dave do you use those light movers? I saw them when I was looking at the lights but didn't want to spend the extra money. It's bad enough that I have all these lights in the house, I could just imagine them automatically moving across the ceiling! God knows what the neighbors would think if they saw that through the window. lol
Karyn

Karyn (LOL), it's not like they zoom back and forth! I think they actually move quite slowly. No, I don't use them. But, you'd probably have room for about four of these systems moving back and forth downstairs! Think of the potential! :-)

It's still a disaster in my house. I take a few plants up to the farm everyday and steal a little more greenhouse space. I just keep telling my husband that I've been rearranging them inside to give us more room. lol At least most of the brugs have lost their leaves and can be put away for a few months. The smell of the flowers became overwhelming so I cut off all the blooms. The plumies are slowly dropping their leaves. As soon as they are bare I'll put them in the unheated greenhouse. I've probably used up all the heated greenhouse space that I can grab at this point. I just keep envisioning those lights looking like some sort of laser show in the family room. lol
Karyn