Hmmm. Lemme see if I got this right: you take the Power inverter, which produces 115 VAC powered by, let’s say, a 12 V car battery, and use it to power a battery charger whose output is connected to said 12 V car battery. Where does renewable energy enter into this scheme?
Energy leaves the battery to run the Power inverter, and some of this energy is lost to heat because the Power inverter isn’t 100% efficient in converting 12 VDC to 115 VAC. The remaining energy leaves the Power inverter to run the battery charger, but some more energy is lost to heat because the battery charger isn’t 100% efficient in converting 115 VAC to 12 VDC. And finally the output of the battery charger is connected to the battery, but alas! There isn’t enough energy left to replace from the original amount what was lost to heat. So, the result is less energy is put back into the battery than was taken out.
Conclusion? The battery will run down. No renewable energy here, nor perpetual motion motion machines either.
As another person who answered said, renewable energy is energy that nature provides in a renewable cycle, like falling water, tides, wind, and solar radiation. All such energy, as well as non-renewable energy like oil, coal, uranium, etc is ultimately provided by the sun or another star. The non-renewable energy sources take such a very long time period to evolve their energy that, from our point of view, they might as well be non-renewable rather than cyclic.
The way renewable energy works is you take from the environment only what the environment provides on a renewable basis and use what you take to produce energy. Energy produced in this way is said to be renewable.
Growing soy beans, for example, will produce a crop from which you can extract an oil useful as fuel. To be renewable and self-sustaining, the amount of fuel extracted must be considerably greater than the amount used to produce the crop and process it into fuel. The "considerably" is called profit. You can use part of the profit to buy more soy beans to plant as well as fuel to run the tractor used to till and plant and harvest the field of soy beans. Put aside some of the profit to buy the tractor and land you grow the soy beans on. Oh, and put aside some of the profit to buy food, clothing, and shelter for you and your family. And maybe put aside some more of the profit to purchase a good education for your kids. Maybe they will learn how to be soybean farmers too.