Backyard gravitational energy storage

 kw: analytical projects, energy, energy storage, batteries, gravitational energy storage

The Federal subsidy for installing solar panels on houses' roofs continues. I can't take advantage of it because the huge trees in my back yard shade too much of the roof too much of the time. I was told there is an extra subsidy to pay for removing big trees. Hmm, I wonder what the carbon "pollution" balance is between removing several 150-foot trees and using solar power…produced with panels that were manufactured using large amounts of fossil fuel-powered equipment. Is anybody producing solar panels using only solar power?

Anyway, at my latitude, I must use air conditioning about one-third of the year. On the warmest days, the A/C runs periodically all night long, particularly when the overnight low temperature is in the 80's (°F of course; that's about 30°C). It's no longer possible in most states to have the solar panels "run the meter backward" during the day, to build up an energy credit with the utility. Thus, I would have to purchase electricity to run my A/C, and the rest of the house, at night.

I'd like to store energy during the day to use at night. The Tesla Powerwall is one expensive option, and it is probably insufficient. Let's do some figuration.

My electricity bill shows monthly usage between 500 and 1,100 kwh/month. The smaller amount is characteristic of spring and autumn. My A/C unit is a heat pump, so my highest usage is actually in slightly warmer winters, when the heat pump usually runs rather than the backup oil furnace. Let's take 600 kwh/month as the top end of A/C-heat pump usage. That's about 20 kwh/day on the "worst" days, from an energy consumption perspective. Not every day is the same, so there are probably peak days with usage in the 30-40 kwh range. In the summer, more cooling is needed during the day; in winter, more heating is needed at night. Considering that these are very approximate figures, I can begin with the likelihood that an energy storage solution in the range of 20 kwh is appropriate.

First possible option: Tesla Powerwall 2. At a web page for This Old House, I find that the Powerwall 2 has a current (early 2023) price of $11,500 for one battery with a capacity of 13.5 kwh, and $18,500 for a unit with two batteries (27 kwh total). The warranty life is 10 years, with a guarantee of 70% remaining capacity at the end of 10 years. That brings the effective storage of an older unit as low as 9.45 kwh or 18.9 kwh. My benchmark figure of 20 kwh thus requires a two-battery system, with replacement needed 9-10 years down the road. Also, such a unit weighs about 500 pounds (230 kg).

If you're enough of a maker (we used to say "handyman"), what about buying a bunch of car batteries and wiring them together with a charger and a large inverter for converting the DC output to AC at 110 volts (or 220V, for your A/C)? Lead-acid batteries have an energy density of about 40 watt-hours per pound (wh/lb) or 88 (or 90) wh/kg. To achieve 20 kwh we need 500 pounds of car batteries. Hmm, that's about the same as the Tesla unit. Of course, adding the charger and inverter will probably add 100 lbs, and the supporting structure would be another hundred or so. A typical car battery costs $200 or more and weighs 45 pounds; we need 11 of these, perhaps 12 for good measure (even numbers are better for balancing charging and discharge circuits). Not knowing what large, fast chargers cost, nor large inverters, this is still looking pretty good at a battery cost of about $2,400.

That sets some sidebars on direct electricity storage. But I've been wondering about gravitational energy storage. This picture shows one company's proposal for using concrete cylinders and a six-arm crane that uses wind turbine-generated electricity to raise the cylinders, and generates electricity when they are lowered during periods of less wind. They claim overall efficiency of 90%.

The concept is by Energy Vault. The tower is 33 storeys tall (about 100 meters). However, I couldn't make much sense of the numbers in the report, which describes 5,000 concrete blocks with a total weight of 35 tons. That doesn't add up; it works out to 14 pounds per block. I suspect the actual weight of each block is 1,400 lb (640 kg). Such a cylinder would have a volume of a little less than a third of a cubic meter (or about 1/3 of a cubic yard), which is almost twice the volume of an oil drum. From the picture, that looks about right.

What kind of weight would I need to make a backyard gravitational power "tower"? In most neighborhoods, one cannot construct anything taller than a 2-story house; perhaps 30 feet (9 m) at the very most. More figuration is needed, to convert weight and distance to watt-hours.

• One horsepower is 33,000 ft-lbs per minute, or 550 ft-lbs per second
• One kilowatt = 1.36 HP = 738 ft-lbs/s
• 1 kwh = 738×3,600 = 2,692,800 ft-lbs = 372,400 kg-m
• 20 kwh comes to 7,448 Tonne-m (nearly 7½ million kg-m)
• Divide by 9: About 830 Tonnes (910 tons) raised to a 9 m height

Ok, just to run my overnight energy storage, I need to be able to raise and lower upwards of 900 one-ton blocks, using motors that can function as generators with a 4000-watt capacity. Standard concrete weighs 2,400 kg (2.4 Tonnes) per cubic meter, or 4,000 lbs (2 tons) per cubic yard. 830/2.4 = 346 cubic meters of concrete, a mass 18 by 19 meters, one meter thick (English units: 455 cubic yards, about 64 by 64 feet, and 3 feet thick).

My back yard is rather small, only 30 feet deep, though it's 90 feet wide. I do have a side yard that's plenty large enough. I wonder what my neighbors would think if I built a structure as tall as my house, with a footprint of more than 4,000 sq ft. And the big electric motors/generators would most likely whine when in use. I'd probably have to remove some soil and seat it 2-3 feet below grade (with drainage infrastructure for rainy weather) to keep the total height below 30 feet.

Maybe I can use iron (I can't afford 900 tons of lead!). Iron's density is 7,874 kg/cubic meter, or 3.28 times that of concrete. This would shrink the volume needed to 105.5 cubic meters or 138 cubic yards. Reducing the vertical depth to 2 feet means the footprint would be no longer 4,000 sq ft but 1,860 sq ft, or about 43 feet square. My 2,000 square-foot house is two storeys, so it's size is only 25 by 40 feet.

The picture is a bit ridiculous. The primary virtue of such a system is that its energy capacity doesn't reduce over time the way the Powerwall will. But it illustrates the amazing energy density of batteries, even lead-acid car batteries, compared to big blocks of iron or concrete and big motors to lift and lower them.

This is a fun mental exercise. It convinces me to wait for better batteries to be developed. Systems based on something besides lithium, for sure! Sodium-sulfur can have 2-4 times the energy density of lithium-ion, and sodium-ion is in the two-times range. Recent research has produced prototypes that don't have to be kept at 300°C (570°F) to operate efficiently. I can wait.