I am making a water feature that will involve a stream fed by the basin of a fountain with a pump at the end sending water back into the fountain. To control the water flow rate through the stream and prevent flooding, I intend to use this valve controlled by an Arduino connected to a water level sensor. The nice thing about motorized ball valves is that they have very little head loss and can be left in a partially open position to throttle fluid flow.
For safety, I would like the valve to be able to fully shut from fully open in the event of a power loss. US Solid makes a variant of this valve with exactly this capability, unfortunately it does not have the ability to remain half open. Their documentation says the auto-return valves store energy in a capacitor that is used to shut the valve when power is cut off, but they don't give specifics on the size. I'd like to do my own custom set-up with the 3-wire version and my own capacitor, and I'm figuring out what size I need.
Their specs say it can operate in the 9 to 24 volt range, takes 3-5 seconds to close, and can draw up to 2 watts. Taking the worst case, 5 seconds at 2 watts, I need to be able to deliver 10 joules of energy between 9 and 24 volts. Taking stored energy as 1/2CV^2, I calculate that if I'm going from 24 volts to 9 volts, I need 1.3F of capacitance, or if going from 12V to 9V, I need 6.7F. A supercapacitor might work for this, but the closest I have been able to find with anything close to these specs that is not a complete beast is something like this one from Kemet. That one sells for $62, and given that the auto-return valve itself is only $45, I doubt that's what they're using.
Can anyone give me some guidance on selecting the right capacitor for this valve? Alternatively, I suppose I could use a rechargeable 9V battery as the backup power source, but then I would need to build a battery charger into my circuit, and that adds a whole other layer of complication as well.