#7: Water Powered Batteries
I hope I’ve convinced you that some form of energy storage is required. Before we dig deeper into exactly how to store this energy, let’s first calculate how much energy we need to store.
Here is where we left off, with 5610.3 + 3208.5 TWh being supplied by unreliable sources.
Short term storage
Starting with solar energy, we have to assume that all of it will disappear every time the sun goes down, which happens every day. This typically happens between the hours of 7pm through to 7am (50% of the day). Assuming we used a fixed amount of energy per hour, we can approximately calculate the size of storage needed to cover our solar power usage as:
Short term solar storage = 5610.3 TWh / 365 days * 50% = 7.68 TWh
As for wind energy, proponents will say that while a single wind farm is unreliable, the average across many many wind farms will be reliable. I haven’t been able to find data on whether or not this is true in the US, but I have found data for the UK (which is obviously a much smaller country).
Wind farms across the UK had a few individual days, over a year, where the total output of wind across the entire country dipped below 5% capacity.
For argument's sake, let’s assume that average wind generation across sufficiently many wind farms will never dip below 10% capacity on any individual day, with an average capacity of 30%.
This represents a drop in of 66%.
Short term solar storage = 3208.5 TWh / 365 days * 66% = 5.8 TWh
This means we need about 13.5TWh of short term energy storage across the entire country.
Introducing pumped hydro
Pumped hydro is the most common method of storing excess power generation.
The idea is actually quite simple. When there is an over supply of energy, we will use the excess energy to push water up a hill into a reservoir. Then, when we need energy, we can the water to run back downstream and spin a turbine, to generate electricity.
The mathematics of pumped hydro
Pumped hydro relies on potential energy of water (how high up the water is) as its storage of power. When the water falls from high ground to low ground, that potential energy can be turned into electrical energy by turning a generator.
Thus, the theoretical amount of energy a pumped hydro plant can store can be calculated by:
Difference in height between upper and lower reservoir
Amount of water it stores
The formula for potential energy is
Here are some examples of hypothetical reservoir sizes, heights and their corresponding storage capacity.
This is by far the most common large scale energy storage system used in practice. Typically, they can recover about 80% of the energy that is generated.
How much pumped hydro do we have today?
According to Wikipedia, there is currently 0.25 TWh of pumped hydro installed in the United States, and 1.6 TWh in the entire world. This is a far cry from the 13.5 TWh of capacity we need. The challenge with pumped hydro is that they depend on a very unique geography, requiring a water and height.
The Bath County Pumped Storage Station is a pumped hydro facility in Virginia that is called the “largest battery in the world” and has a capacity of 24 GWh.
In order to store the 13.5TWh (13500 GWh), we would need about 560 of these facilities across the country.
Its a bit hard to get an exact measurement of the total acres of the reservoir, but from this crude google maps image, with the 1km scale at the bottom left, I would estimate total size to be about 5 km across and 8 km up, making it approximately 40 squared kilometers.
560 of these would be equal to about 22400 squared kilometers, about 5.5 million acres.
Going back to our visualization of how America uses its land, 5.5 million acres is equal to 22 of these squares (recall that each square is 0.25 million acres).