My back-of-the-envelope assumption was that you get 4 effective hours of daylight per 24 hours. Which means that for every 1W of power generation at peak, you get 1/6W of average power consumption, which translates to 3.33Wh of storage to keep things running overnight. (For a land-based installation you would probably want a multiple-day power reserve to handle cloudy days, but I'm assuming that's not an issue for a stratospheric balloon.)