Back of the Envelope (3) – Batteries (Tesla Powerwall) to Store Renewables

Tesla_Powerwall

Tesla Powerwall (Image by Tesla Motors CC-I 4.0)

 

Summary: 375 MW of electricity is the amount currently provided by fossil fuel burning power plants for a population of about 320,000. To make this power with renewable sources (namely, solar PV) 2 GW must be generated: 375 MW for daytime use and 1.625 GW generated and stored for nighttime use. One option for storage is batteries. This amount of power can be produced by 1.5 million Tesla Powerwall (6.4 kWh) batteries. These could be distributed in residences and businesses with one Powerwall servicing roughly 460 square feet of building footprint. Alternatively, they could be housed in a few large warehouses following a more centralized utility model.

In the first Back of the Envelope we found that we need a 2 GW solar farm to replace the fossil fuel produced electricity currently used by a city such as Fort Collins, Loveland, Longmont, Estes Park, Colorado with a population of 320,000. 375 MW of that 2 GW will be used during the day and the rest, 1.625 GW, must be stored to be used at night. In the second Back of the Envelope we examined pumped hydro as the storage solution. While pumped hydro is the most prevalent form of storage today (99%), batteries are probably the most talked about solution to the storage problem. In this Back of the Envelope we will look at the solution offered by Tesla Motors with its Powerwall to see what level of implementation would be required to store the extra power produced by the 2 GW solar farm so we can make it through the night.

For this calculation we will use the home Powerwall, which is expected to cost $3000, can store up 6.4 kWh of electricity, and has dimensions of 33.9 inches x 51.2 inches x 7.1 inches (12,300 in3 or 0.2 m3). We need to store 1.625 GW x 6 hours or 9.75 GWh of electricity. That’s 9.75 million kWh. Divide that by the 6.4 kWh storage capacity of the Powerwall and you get 1.5 million Powerwall batteries taking up a volume of about 0.3 million m3 and costing $4.5 billion. If we can put them 6 high on a wall (about 8 m) in a warehouse that will require 37,500 m2 (400,000 square feet) of space. If we allowed 10x that space for access and cooling that would take up 375,000 m2 (4,000,000 square feet). That’s the size of about 20 large Walmart Supercenter buildings—not too bad for a utility scale centralized rollout. For such an installation we would probably use Tesla’s Powerpack or utility scale devices which have more capacity, but for this BOTE we will stick with the Powerwall batteries.

It is more likely that many or even most of these Powerwall devices will be distributed throughout town. The population density of Fort Collins is about 1000 people per km2; dividing 320,000 people by 1000 people per km2 gets us to  320 kmof area in Fort Collins, Loveland, Longmont, and Estes Park. Let’s assume that 20% of this is buildings (residences, businesses, schools, churches, etc.)—64 km2  (700 million square feet) of building footprint. If we need 1.5 million Powerwall batteries, that’s a Powerwall battery for every 460 square feet of building footprint.

  • An apartment with 1000 square feet needs one 1 or 2
  • An average size house of 2000 square feet needs 4 or 5
  • A church building with a 6000 square foot footprint needs 13
  • An office building with a 15,000 square foot footprint needs needs 30
  • A school building with a 140,000 square foot footprint needs 350

In its first year of production (2015-2016) Tesla plans to make around 100,000. 1.5 million are needed for the proposed 100% renewable solution. That’s 15 years worth just for Fort Collins. Obviously, that will need to scale up with an increased production rate and additional factories to make the devices. Because the “sample” city is only 1/1000 of the US population we will need 1.5 billion for the entire United States.

Lithium

Lithium floating on oil (Image by W. Oelen CC-BY-SA 3.0)

An estimate of the amount of lithium required is that 300 g Li metal is needed per 1 kWh of battery capacity. (Theoretical electrochemical considerations give a value of about 75 g Li per kWh; here we have multiplied by 4 to give a more realistic “real world” value.) Thus the 6.4 kWh Powerwall requires about 2 kg Li. For the 1.5 million needed in Fort Collins that’s 3.0 million kg of Li or 3,000 metric tonnes (3 million metric tonnes for the whole country). Global annual production of lithium is around 37,000 metric tonnes of lithium. Currently, only about 30% of the produced lithium is used for batteries (portable tools, laptops, cell phones, and the nascent electric vehicle (EV) market). A full, nation-wide rollout of this new market for batteries involves a 80x increase in the production of lithium. Of course, the EV market is also rapidly growing. A transition to EV of the over 250 million passenger vehicles in the US today, each one using 10x as much lithium as a Powerwall battery, would put significant pressure not only on lithium production but also on global reserves of lithium. The USGS estimates that there are 13 million metric tonnes of known reserves (i.e. currently economically obtainable) and only 39 million metric tonnes of lithium existing on the planet. For more information about lithium supply limits see this article from Green Tech Media. Perhaps a more serious resource limitation is the rare earth metals used in the DC to AC inverters. We’ll save that discussion for another BOTE.

The solar farm discussed in the first BOTE is already going to cost $2.5 billion with probably a 20 year lifetime. 1.5 million Powerwall batteries will cost another $4.5 billion. However, these only have a 10 year lifetime. Let’s say $5.75 billion for 2 GW of electricity for 10 years:

2 GW x 6 hr/day x 365 days/year x 10 years = 43,800 GWh = 43.8 billion kWh

The price of this electricity (not counting operation and maintenance) is $5.75 billion/43.8 billion kWh = $0.13/kWh–a bit pricey, but not far off from today’s prices. No doubt the price of batteries will go down as production scales go up, as technology improves, and with business and utility scale models incorporated into the implementation.

The most serious limitation at this point in time seems to be the rate of lithium production and the rate of battery production.

Check out Energy: What the World Needs Now by Terry M. Gray and Anthony K. Rappé.

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Back of the Envelope (2) – Pumped Hydro to Store Renewables

Summary: 375 MW of electricity is the amount currently provided by fossil fuel burning power plants for a population of about 320,000. To make this power with renewable sources (namely, solar PV) 2 GW must be generated: 375 MW for daytime use and 1.625 GW generated and stored for nighttime use. One option for storage is pumped hydroelectric power. This amount of power can be produced hydroelectrically by draining a reservoir (such as Horsetooth Reservoir near Fort Collins, Colorado) of 120 million m3 of water at night and pumping it back during the daytime. This would involve creating a lake downstream from the reservoir 6 m (20 ft) deep and 6 km (3-4 mi) on each side. Alternatively, 377 pairs of large tanks (500 ft in diameter 100 ft tall) slightly larger than the oil storage tanks located in Cushing, Oklahoma, one above ground and one below ground, could be filled and drained each day. Each tank takes up about 5 acres or just a bit more than 2 city blocks.

In the first Back of the Envelope we found that we need a 2 GW solar farm to replace the fossil fuel produced electricity currently used by a city such as Fort Collins, Loveland, Longmont, Estes Park, Colorado with a population of 320,000. 375 MW of that 2 GW will be used during the day and the rest, 1.625 GW must be stored to be used at night.  The only form of energy storage reported by the Energy Information Administration is pumped hydroelectric power. “Pumped hydro” is the only large-scale energy storage in use today–99% of all storage is pumped hydro. Water is pumped into a reservoir using excess energy production and then released later to generate electricity as in a hydroelectric power plant. Some pumped hydro facilities were developed in concert with nuclear power facilities. When power production exceeded demand, the excess was used to pump water into a reservoir rather than throttle the  amount of electricity produced by the nuclear power plant. This allows the nuclear power plant to operate an optimal level. This Back of the Envelope post will explore what would be required to provide overnight storage of daytime generated electricity using pumped hydro.

The important physics/engineering equation is that which calculates the power available in a reservoir of water. The equation is

Power (Watts) =
Efficiency x density of water (kg/m3) x flow rate (m3/s) x force of gravity (m/s2) x height (m)

Horsetooth Reservoir

Horsetooth Reservoir near Fort Collins, Colorado (Photo from the US Department of Interior Bureau of Reclamation)

Efficiency is the efficiency of conversion of hydropower to electrical power. We’ll assume 80%. The density of water is 1000 kg/m3. The force of gravity is 9.81 m/s2; we’ll call it 10 m/s2. The height will depend on our exact system. We’ll explore a couple of options.

Option 1: Horsetooth Reservoir

Horsetooh Reservoir is less than a mile away from the western edge of Fort Collins. There are four earthen dams that make up the reservoir. The reservoir holds 0.2 km3 (200 million m3, 157,000 acre-ft) of water. At the north end is a dam that is 155 feet high. How much electricity could we generate if we let the water out? In order to pump it back we have to store the water downstream somewhere. We’ll talk about that later. Let’s estimate the water level behind the dam to be 50 meters higher than in front of the dam. However, as we’ll see we will be changing that height significantly as the water is released even in a large reservoir like Horsetooth. (Technically, we should integrate as the water is released, but as a first approximation we’ll do the calculation using a static height of 1/2 of the initial height.) Let’s say that our actual head height is 25 meters. Now we can plug numbers into our equation. We need 375 MW of power.

375 x 106 W = 0.8 x 1000 kg/m3 x flow rate (m3/s) x 10 m/s2 x 25 m

Solving for flow rate gives us 1875 m3/s. We need to do this for 18 hours. 18 hours is 64,800 seconds.

Total volume needed is 1875 m3/s x 64,800 s = 121 million m3.

This is 60% of Horsetooth Reservoir drained out every night and pumped back in during the day. A flow rate of 1875 m3/s is comparable to the flow rate out of other large scale hydroelectric plants. Three 6-7 m (20 feet) diameter pipes could do the trick. Pumping the released water back during the daytime needs to occur 3x faster. The giant pumps that are being installed in New Orleans since Katrina can pump at near 625 m3/s. We would need nine of these monsters each costing $0.5 billion to pump all the water back each day.

Another problem is where to put the water. Without worrying for now about land use issues, let’s make a shallow lake downstream from the main dam. If it is 6 meters (20 ft) deep, we need a 33 million m2 area (33 km2,  82,000 acres). That’s a shallow lake 6 km or 3-4 miles on a side. Interestingly, that’s the size of the solar farm needed. Perhaps we can float the solar panels on the lake.

Option 2: Storage Tank Farm

Cushing, Oklahoma oil tank

An Enbridge oil tank at Cushing, Oklahoma (Photo by roy.luck CC-BY-SA 2.0)

The previous solution requires a specific geographical setting that may only be appropriate for certain locations, and since Horsetooth Reservoir is also a recreational facility, we may not want to drain it every night. Is there a way to make this work anywhere with artificial storage tanks? The oil storage facility in Cushing, Oklahoma comes to mind. What if we built large water storage tanks, one above ground and one below ground? What would it take to store enough power to get through the night? The largest of these tanks run about 400 feet in diameter and 70 feet tall. Let’s say we can stretch the limits a bit and get to 500 feet in diameter and 100 feet tall. That would be 150 meters in diameter and 30 meters tall. Each tank holds 530,000 m3 of water. The average height between the levels of water is now only 15 meters (rather than the 25 meters we had for Horsetooth Reservoir). Since we have only 60% of the head, we need 1.67x as much water. Using the number from the previous calculation (121 million m3) this gives us 200 million m3 of water.

Cushing, Oklahoma Oil Tank Farms

A satellite image of the Cushing, Oklahoma oil storage tank farms. The image is about 2 miles horizontal and 1.5 miles vertical.

At 530,000 m3 per pair of tanks, that means 377 pairs of tanks. Each tank takes up a 150 m x 150 m square (about 5 acres or 4 football fields or just over 2 city blocks). This ends up being a 10 km x 10 km (6 mi x 6 mi) water storage tank farm. That area is comparable to the area of Horsetooth Reservoir and the downstream lake that was created.

Feasible?

Either project is grandiose. And keep in mind that we have to do this times 1000 for the US alone. However, such projects are not necessarily engineering impossibilities. Geography might help in many instances. Coastal regions or those near the Great Lakes might be able to use the ocean or lake as the lower level storage tank. The bottom line is that this would be a massive enterprise. On the surface it looks doable, but the scale of the project makes it seem like other options might be better. These will be discussed in future BOTE blog posts.

Check out Energy: What the World Needs Now by Terry M. Gray and Anthony K. Rappé.