I am trying to figure out a way to have it automatically come on at night and stay on until morning or at least several hours.
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You could use one of the small battery maintainer cells at an auto parts store/JCwhitney to charge a small lead acid battery, then power some l.e.d. x-mas lights from the battery. You can pick up a photo eye at the hardware store to turn it off and on.
Honestly sounds like a lot of money and effort for a 3ft tree, lol
Unless you have some experience in electronics, this is not something I would recommend.
First of all, you need to determine your load requirements. Assuming that the lights on your tree operate from 120 volts AC, 60 Hz, 1 phase, standard North American power, you need to know the amperage required by the tree’s lights.
Next, I don’t know where you live, but you need enough solar panels to provide the energy to run your tree all night if that’s what you want. You also need to calculate the amount of battery capacity you will need to store the charge from the solar cells and provide it to the lights at night.
You need to compensate for reduced sunlight on cloudy and rainy days. This means you need extra solar panels to give you this margin.
Finally, you need a 12 volt inverter to convert the battery power to North American residential power (120 volts AC). You need to determine the capacity of the inverter.
Finally, you need to find a 12 volt, DC photoswitch that will apply battery power to your inverter when the ambient light falls below a predetermined level (it gets dark).
Finally, I hope you have deep pockets, because this is going to cost you. I would estimate at least $ 1000 for all the components for your system.
Are you sure you wouldn’t rather just plug your lights into an outlet?
Buy solar rope lights