First off, what is the point of a solar system? To provide electricity for your home or business by taking the raw energy of the sun and transforming it into usable AC power.
Step 1: Sunlight hits the solar collector. Most often this is a flat panel whose surface is coated with silicon, a manufactured substance whose crystalline structure makes it a particularly good semiconductor. Pure silicon isn't actually a great semiconductor--the silicon in solar panels is doctored a bit to provide an imperfect crystalline structure which provides a more dynamic environment for the exchange of photons and electrons that actually produces your solar panel's electric current.
Step 2: Photons, the energy of sunlight, are absorbed by the solar collector. Electrons within the semiconductor material are essentially knocked out of place by the photons, and start floating around. Collector panels have built-in electric fields created by that doctoring of the silicon I mentioned, which goad these loose electrons into all moving the same direction--this is an electric current. FYI, the size of this electric current, multiplied by the size of the electric field (aka, voltage) built into the solar panel, is what determines the solar panel's wattage.
IMAGE (right): The blue surface is the modified silicon. The crisscross pattern is made up of the metal that draws off the electric current and sends it to the inverter.
Step 3: Metal built into the frame of the solar collector panels attracts the electric current that's just been generated, and presto! You have electricity. Alas, what you have is raw electricity, or "direct current" (DC). What you want and use in all applications in your home is "alternating current" (AC).
Step 3.5: In most home solar systems, there is no battery storage. It's so expensive it just isn't practical unless you live in the middle of nowhere, in which case it might be cheaper than convincing the local authorities to run power lines out to your Quonset hut on the Arctic tundra. If you do happen to have a battery (for the sake of argument), the DC power goes straight to the battery, making a brief pit-stop at a charge controller for safety reasons and general battery health. For use in your home, the electricity then proceeds to the inverter. With no battery component, the DC power moves directly from the metal of your solar panels a short ways to your inverter.
Step 4: Your DC power enters the inverter box and emerges on the other side as AC power, and marches itself smartly into your home's breaker panel. Your breaker panel, not knowing any better, uses this electricity exactly as it uses electricity pulled in from your utility.
Bonus step: In most states, the process of net-metering is available to users of solar electric systems. You might have heard of "electric buy-back", or of the grid "taking" your excess electricity. Net-metering means that when your solar panels are producing lots of electricity, but you're not using it (say, you're gone during a summer day and no lights or air conditioners are turned on), the electricity flows out to the municipal electric lines and becomes part of the utility's available power. It's perfectly safe; in power outages, your house gets "islanded" so that your power line isn't sneaking around live, waiting to zap some poor utility maintenance worker. And since the utility actually purchases this excess power from you and the same rate you pay for normal electricity, it's a win-win situation. They get power, you get money (you can think of it as offsetting what you pay for grid electricity during the hours your solar panels can't generate power).
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