Every strip project I’ve done so far has been portable power:
Led Fur Gauntlet was 1 square lipo pack (Like this: http://www.adafruit.com/products/328) which is plugged directly into a flora with the JST-PH connector. From the flora I have power going out of the VIN/GND to a 5v boost regulator (http://www.pololu.com/catalog/product/2564). This powers 66 WS2811 Leds with at least 6 hours of life at 100% brightness (though I’d say half of the modes on there only have some pixels lit up each frame). I’ve never seen it run out of power, but the lowest the battery was when I had to recharge it was 3.4v.
Led Tie uses 6 AA alkalines (Here is a good set of benchmark tests of common Alkaline brands under high load: http://www.batteryshowdown.com/results-hi.html). I’m using a 6 battery holder behind the tie, wired into an Osepp Nano, with VIN and GND going into a 5v step down regulator (Also from Pololu). This powers 114 WS2811 LEDS for more then 6 hours (I’ve also not seen the power run out on this wearable yet).
Led Hat uses 2 26650 LI Ion batteries ( These http://www.amazon.com/gp/product/B008YAPRUQ/ref=cm_cr_ryp_prd_ttl_sol_0) wired in series, and regulated by a 5v step down regulator from pololu. This is running 120 LEDS forever basically… as an example I wore this almost non-stop at burning man when the sun went down, so at least 20+ hours and still going strong.
Led Vest is a bit more complicated of a power system. I rushed this to completion before Burning man and fried my Teensy with not enough time to get a replacement. I ended up dividing the vest into 2 halves with their own separate but shared power systems and Osepp Nanos that talked to each other. basically 2 units of 6 AA battery holders with an adjustable/higher current regulator (http://www.aliexpress.com/item/Ultra-small-LM2596-power-supply-module-DC-DC-BUCK-3A-adjustable-buck-module-regulator-ultra-LM2576/739489407.html). This was running 358 LEDS but I think I only got about 3 hours out of it… Though I think I blame the weird power system, and the possibly “not quite exactly in sync” voltage setting of the 2 regulators.
My LED Staff used 2 18650 Li Ion Rechargeables in series and a 5v Step down regulator for 120 LEDS for about 3 hours as well (full brightness)
Another LED vest I helped my girlfriend make was only a 4AA battery pack to a flora (With diode) to 144 LEDS though at 75% brightness which would last about 4 hours on Ikea batteries before starting to get dimmer.
Also an LED Tutu we made with WS2801 12mm LED strand (Only using 21 leds) was also a 4AA battery pack that ran about 6 hours so far… still no battery change out.
Overall I’ve found pololu’s tiny buck/boost regulators to be awesome up to about 2A when it gets too hot and starts causing issues with lights… so anything about 120 LEDS or less it is ideal for. But if running more then that on a single power source it might be good to go with the bulkier/higher current regulators (if regulating is key).
I’ve also used some of the “charging packs” in a pinch. I think I got 2 hours on my LED Tie at a festival with one of these plugged into the Nano Usb port: (http://compare.ebay.ca/like/251210390689?var=lv<yp=AllFixedPriceItemTypes&var=sbar&_lwgsi=y&cbt=y&lpid=33&item_id=251210390689).
My next project is to build an electric scooter which will already have a regulated 5v 3A power source pulling from the main 44v drive batteries(12s3p LIPO packs), so I will likely LED all over that thing easier then usual.