Is it possible to construct a capacitor capable of storing the energy in lightning, then allowing that energy to flow gradually into the power grid?
Actually, the system of cloud and ground that produces lightning is itself a giant capacitor and the lightning is a failure of that capacitor. Like all capacitors, the system consists of two charged surfaces separated by an insulating material. In this case, the charged surfaces are the cloud bottom and the ground, and the insulating material is the air. During charging, vast amounts of separated electric charge accumulate on the two surfaces—the cloud bottom usually becomes negatively charged and the ground below it becomes positively charge. These opposite charges produce an intense electric field in the region between the cloud and the ground, and eventually the rising field causes charge to begin flowing through the air: a stroke of lightning.
In principle, you could tap into a cloud and the ground beneath and extract the capacitor’s charge directly with wires. But this would be a heroic engineering project and unlikely to be worth the trouble. And catching a lightning strike in order to charge a second capacitor is not likely to be very efficient: most of the energy released during the strike would have to dissipate in the air and relatively little of it could be allowed to enter the capacitor. That’s because no realistic capacitor can handle the voltage in lightning.
Here’s the detailed analysis. The power released during the strike is equal to the strike’s voltage times its current: the voltage between clouds and ground and the current flowing between the two during the strike. Voltage is the measure of how much energy each unit of electric charge has and current is the measure of how many units of electric charge are flowing each second. Their product is energy per second, which is power. Added up over time, this power gives you the total energy in the strike. If you want to capture all this energy in your equipment, it must handle all the current and all the voltage. If it can only handle 1% of the voltage, it can only capture 1% of the strike’s total energy.
While the current flowing in a lightning strike is pretty large, the voltage involved is astonishing: millions and millions of volts. Devices that can handle the currents associated with lightning are common in the electric power industry but there’s nothing reasonable that can handle lightning’s voltage. Your equipment would have to let the air handle most of that voltage. The air would extract power from the flowing current in the lightning bolt and turning it into light, heat, and sound. Your equipment would then extract only a token fraction of the stroke’s total energy. Finally, your equipment would have to prepare the energy properly for delivery on the AC power grid—its voltage would have to be lowered dramatically and a switching system would have to convert the static charge on the capacitors to an alternating flow of current in the power lines.