It seems like a paradox, but solar refrigerators only need the sun to come out before they will chill your drinks.
Solar fridge/freezer systems work with power from a solar panel (must be in a sunny spot outside). During the day power is generated and stored, and at night (when it is usually colder) the stored power is used up. The fridge itself is a box that can be placed wherever is convenient.
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Intelligent Power System‘s Sunfrost fridge is just like a normal fridge, ideal for an off-grid house. It doesn’t come with the solar panels. Around $2000.
Creative Energy Technology‘s solar fridges are a favourite. Elegant, small and practical and they come with solar panels and a 25 years warranty. Prices to match between $1897 and $3897.
Solar fridges are also available from alphasolar. They are cheaper, around $900.
Small power systems will work on the design of your solar fridge with you.