Since there are 10 trays each for Ground and Space, I just fill EVERY spot. So Cryptic can't put whatever skill wherever, whenever they like since it's full.
Alas, they found a way to irritate me by randomly swapping my 'Intergral Remodulation' and my Omega 3-piece Stealth ability. But I'm used to checking the ground powers tray every time I enter a ground STF.
Also if you haven't already noticed, if you swap a device... the power in the tray doesn't (it used to prior to S7). So if you swap a Shield battery (on your ship) with an Engine battery (from inventory), it's anyone guess where the Engine battery icon will show up. What's for certain, is that the spot where the Shield battery used to be will stay stubbornly empty (right-click on it, it'll show some nonsensical veteran power or something equally moronic).
To fix this, BEFORE you swap a device/etc, right-click on the relevenat icon (in this case, Shield battery) and drag it off the tray to deliberately empty it (blank does NOT equal 'empty'). Now swap in your new device, if you have filled in ALL the other tray slots... Cryptic has to admit defeat and put in your new device power... where the old one was.
I had this problem, but may have found a fix. I'm not sure if all parts of this are necessary, but it worked for me:
1) Open up Available Skills panel (little button on top right of power tray) and make sure 'Lock Tray' is deselected.
2) Open up Character Status panel (U key, by default), go to 'Stations' screen and clear all your stations.
3) Hit OK on Available Skills panel and close Character Status panel.
4) Open up both panels again, then add back your bridge officers to their stations, one at a time, clearing the skills from the power tray as you add each one.
5) Reposition whatever you want on your power tray to the place where you want it, then select 'Lock Tray' in Available Skills panel, hit OK on there, then close the Character Status panel.
Since then, I've still had the annoyance of getting my space Bridge Officer skills added back onto the power tray if I either retrained or levelled them, but that seems to solve the problem of them popping back on there with every map change.