What is the purpose of listing the power output (Wattage) from solar panel, without the energy/power specification of batteries or other electrical storage devices?
Do satellites often use the power directly from the panel?
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Solar panels are sized to meet the maximum power demands of a spacecraft at end of life. All satellites run power from the solar panels through power conditioning electronics that regulate the power supply to meet the demand.
On the ISS, there are a number of avionics boxes involved:
First is the Selective Shunt Unit (SSU). The ISS solar arrays are segmented into 82 strings on each of the eight wings. Each of these can be individually switched on and off to meet the power demand. This switching is performed by the SSU and turns the photoelectric power, which acts generally as a current source, into a power supply that acts like a voltage source.
Next is the Direct Current Switching Unit (DCSU), which handles -- among other things -- the handover from solar arrays to batteries to ensure that the power output is steady regardless of whether Station is insolated or eclipsed. Power from the DCSU goes to the Main Bus Switching Units, which are the master power controllers for all of Station.
Adjacent to the DCSU are three Battery Charge/Discharge Units (BCDUs), which handle the charging and discharging function for the battery units.
I don't have a ton of insight into how other satellites work, but I suspect the scheme is similar.