Sorry to be a downer, but this isn't a very good idea. You're not going to be in any health trouble or anything like that, but it definitely isn't as beneficial as a full night's sleep.
Some quotes because I don't really want to explain it:
Deep sleep allows the brain to go on a little vacation needed to restore the energy we expend during our waking hours. Blood flow decreases to the brain in this stage, and redirects itself towards the muscles, restoring physical energy. Research also shows that immune functions increase during deep sleep.
At about 70 to 90 minutes into your sleep cycle, you enter REM sleep. You usually have three to five REM episodes per night. This stage is associated with processing emotions, retaining memories and relieving stress.
You enter deep sleep about an hour into a normal night's sleep and REM sleep at about 80 minutes in, so since you're only sleeping for half hour intervals, you're not going to get much of the actual benefit of sleeping.