How much capacitance/joule/watt is needed on average household' energy storage system with supercapacitor?
Here's a quick calculation, using an example 500 F, 16.5 volt supercapacitor (https://www.mouser.com/datasheet/2/257/Maxwell_16VModule_DS_1009363-10-1179674.pdf)
Assume your converter electronics can work between 5 and 15 volts with a 90% efficiency.  At 5 volts, this capacitor would have energy ( 1/2 * C * V^2) of 12,500 joules.  At 15 Volts it would have an energy 112,500 joules.  Subtract and you would have 100,000 joules to work with if the capacitor was charged to 15V and discharged to 5V.

Since a joule is a watt-second, you have 100,000 watt-seconds, and at 9200 watts you have a theoretical 10.9 seconds (100,000 / 9200) of capacity in each capacitor of this size.  Throw in your 90% efficiency and you are just under 10 seconds of capacity for each 500 F, 16.5 volt capacitor.  So calculate the number of seconds you want to run the household, and you will see how many capacitors you need.