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Can energy be stored long enough in batteries so that the cold winter days can go without any shortage in power supply, or should the energy be converted to hydrogen which will be used as a fuel later on?

Alternatively, is there some other way around to cope up with winter days when there is little sunshine?

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Yes, energy can be stored long enough in batteries to provide enough power for the winter, though it would be very expensive, use a lot of space and require inverters for AC power. Take a look at lead crystal batteries.

"Or should the energy be converted to hydrogen to be used as a fuel"

Well... if you don't mind using an explosive gas as a fuel, think about possible gas leaks... hydrogen in automotive vehicles are usually compressed to about 300 bar as well, so you would need to use energy to produce and compress it. Also transporting highly compressed gas is always dangerous, especially in vehicles.

Please elaborate on your question by adding the amount of power needed in the winter and for what purpose? I.e heating, cooking, lighting, transport or general use electricity. How much you can produce and how it would be produced also plays a factor.

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    What you forget is that it isn't the storage of compressed gas that is dangerous, but the storage of large amounts of energy. Give me the same energy in batteries and I can make the same huge ass 'splosion
    – Aron
    Aug 12, 2015 at 14:21
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    @Aron with hydrogen there are two things though, the highly compressed gas is dangerous by itself even it it's inert; hydrogen is explosive and flammable so it's dangerous again. Also, recovering the energy used to compress the hydrogen is hard, but not doing so adds another inefficiency to the system. It's usually easier to store methane or methanol for longer periods, because they're bigger molecules which are easier to handle and don't leak as readily.
    – Móż
    Aug 20, 2015 at 11:27
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    Burning lithium in LiPO batteries in itself is pretty dangerous. As is a the H2SO4 in lead acid batteries. What is your point?
    – Aron
    Aug 20, 2015 at 11:37
  • And no. It is not hard to extract the potential energy in the compressed gas. It is ludicrously simple. There just isn't enough of it to justify the extra engine.
    – Aron
    Aug 20, 2015 at 11:43
  • Compressing any gas is a terribly inefficient process in itself. compressed air is probably the most expensive widely used way of transferring energy. that's the inefficiency I believe Moz is referring to, and regarding dangerous H2SO4, lead crystal batteries do not use a liquid electrolyte, making it safer than both hydrogen lead acid batteries as a means to store energy.
    – TheDoop
    Aug 24, 2015 at 12:13

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