I've tried all sorts of power options with my BMPCC's, including the Anker 15000/20000 (I have 3 of them) and some solutions that used Sony and Canon batteries.
The first power option that has really worked for me is the Juicebox battery. I saw someone recommend it on here. It can be purchased at Amazon and it's about $100. I think it's rated at about 50,000 mAh.
I recommend it over the Anker because it does 9v at 2 amps, or 12v and 1.5 amps, adn that seemed to be *just* barely enough, which, I believe, led to power disconnects. For instance, I would see that the camera wasn't charging off the Anker, so I'd press the power button on the Anker and it'd start again. I've tried 4 or 5 different power cords, so I'm 99 percent sure it's not a cord issue. The Juicebox has always stayed connected and I think that's due to it's 12v 2 amp current. I was able to shoot 8-10 hour days with this battery in pretty tough conditions, so I can vouch for it on the BMPCC.
A v-lock battery would also work, as would some other options that cost $200 and up. But after trying to save money and failing, I went for the Juicebox and it's been great. I'll try to post a picture with it attached to my camera.
(I have no affiliation with this company, and honestly think they need to market this better.)