We know that demand for electricity is not constant. Power plants are not operated under full load conditions. What if power plants were operated under full load condition and excess electricity was stored in capacitors? I have read that capacitors of 10 kF capacitance are available. Could the use of such capacitors make it reasonable to operate power plants under full load at all times?
Capacitors are currently "rather too costly" for this purpose.
I've revised my estimated cost after some more research but you appear to be in the 'well over one hundred thousand dollars" range!
The dear way: If you were to assemble a 10kF 150 volt capacitor from available smaller capacitors now it would cost around 1 million dollars and store about 30 kWh of electricity - worth maybe 5 to 15 dollars retail depending where you are and a lot less wholesale.
Using 160 VDC rated parts, 1700 of these would cost about $2,000,000 (really), weigh about 9 tones and occupy about 17 cubic metres (!). You'd get a discount for quantity but overall they are not viable Datasheet here
One of 1700:
"Doing it yourself" is hardly cheaper..
In 1000 quantity these 3400 $\mu$F, 2.8fV cost a mere 53 dollars each. Each series string = 150/2.85 = 53 capacitors.
Capacitance in series divides by number of caps so C per spring = 3400/53 = 64F.
Number of strings = 10,000/64 = 156.
Total caps = caps/string x strings = 53 x 156 = 8268
Cost = 8268 x 53 = 438,204 dollars That's better than one million plus above - but that's a lot of mounting to do AND balancing circuitry will be essential.
1 to 2 million starts to look almost good.
Using smaller voltage high capacity units "off the shelf Alternatives include:
"Flow batteries" using eg Vanadium oxide liquid in various oxidation levels. "Tanks" of liquid are pumped through a cell to "charge" and stored in another tank for subsequent discharge. Large trial systems exist. Not yet mainstream. May or may not "make it" commercially.
Lithium Ion - as being used in Tesla cars and their Powerbank home storage technology. JUST becoming economic with careful timing of charge and discharge to buy cheap power and use it at peak cost periods. Large commercial installations exist in eg Germany - costs are about break even overall so far with advantages of continuity being a factor.
Lithium Titanium (a LiIon variant) - coming - used in eg Suzuki LEAF along with traditional LiIon cells. Dearerthan than standard LiIon but immensely fast charge rates and can have 5,000 - 10,000 usage cycles with due care.
Molten salt - used to store energy thermally and make power off peak - eg station at Guila-Bend near Phoenix. This is solar thermal heated but electric heating could be used.
Pumped storage as John mentioned. Some use but not very common. Efficiency overall about 60%. UK has a large system used for grid leveling applications.
Flywheels - investigated for many decades - good in theory but to get acceptable energy densities you need large masses )(tons) rotating at 10s of thousands of RPM. Mechanical failure is not pretty. So far many have tried but there are no significant working systems.
Others exist, but that gives a feel.
Capacitors typically store power over short periods of time, seconds or minutes. This is too short to be useful for the electrical power grid.
Typically peak power demand occurs during the day, often mid-afternoon. Excess power is available at night. To be useful, then, the energy must be stored for many hours. There are many possible technologies for storing energy but few are economical.
The most practical energy storage approach at the moment is pumped water storage. Excess electricity is used to pump water up to a reservoir. When power demand is high, the gravitational energy released when the water flows back downhill is used to generate electricity.
For capacitors to compete for practical power grid energy storage, they will need to have lower cost and higher leakage resistance.