Energy Vault: A mashup of two of my interests

Image Credit: Energy Vault

My occupation is as an executive in a firm that provides materials testing, inspection, consulting, and engineering in the construction space. We deal with all aspects of the built environment with the exception of single family housing. As such, concrete is a fundamental area of my firm's expertise. And, as is clear, energy in all its aspects is a personal interest, not to say obsession, of mine. Finally, as I've elaborated in multiple posts, to bring renewable energy to the level of being able to provide base load power, I contend that relatively inexpensive energy storage will be needed.

Energy comes, basically, in two forms: kinetic; and potential. And while storage via kinetic energy is possible (think flywheels and thermal storage), most forms of storage utilize potential energy. Batteries utilize chemical potential energy, compressed air energy storage utilizes mechanical energy, etc. And finally, gravitational potential energy is utilized in various systems. In fact, most grid scale storage currently in place uses pumped hydro storage.

But any system of raising a mass against the force of gravity has the potential (get it?) to be used for storage. And a Swiss firm called Energy Vault has constructed a prototype of a storage solution using concrete lifted by tower cranes. It's clear that the technology for producing concrete is not new, and tower cranes are ubiquitous in the developed world. The innovation claimed by Energy Vault lies in the software to efficiently determine crane movements to optimize storage of excess energy and to deliver energy when needed.

In a previous set of posts (the last one is here), I estimated that a 3 MW nameplate capacity wind turbine combined with 40 MWh of storage could reliably provide 725 kW of base load power. What would 40 MWh of storage look like with the Energy Vault system? Energy Vault's web site states that an operational plant would have the capacity to store "between 10 and 35 MWh" of electrical energy and be able to deliver that energy at a rate of from 2 to 5 MW. Based on this claim, perhaps two such plants would be sufficient to provide storage for our hypothetical 735 kW plant and would be able to deliver the energy at the needed rate.

So as not to subject my readers to endless calculations, suffice it to say that the energy stored by lifting a mass against gravity is simply the product of the mass of the object lifted, the height to which it is lifted, and the local gravitational acceleration constant. Let's say we'll settle for two storage plants, each with a capacity of 20 MWh. For calculating purposes, we need to convert 20 MWh to the 7.2*10^10 J (joules, the SI unit of energy). 

We have two "knobs" that we can control to determine how much energy is stored in a storage system of the nature of that of Energy Vault. We can control the height to which our masses are lifted and we can control the amount of mass. And (net of losses), energy stored by lifting a mass against gravity is E=mgh, where E is the energy, m is the mass, g is the acceleration of gravity, and h is height. However, for the purposes of the physical logistics of our plant, we're really concerned about the volume of concrete so we'll use m=ρ*v where ρ is density and v is volume. This yields E=ρvgh. To isolate the knobs we can control, a little algebra yields E/(ρg)=vh. Concrete is typically quoted as having a density of 2,400 kg/m^3, g is 9.8m/s^2 and we need 7.2*10^10 J. Plugging these in, we see that we need v*h=7.2*10^10/(9.8*2,300)=3.06*10^6. This is the required product of height in meters times volume in meters^3.

In order to determine the feasibility we need to understand what an actual installation might look like, and Energy Vault helpfully includes an animated video of a hypothetical production facility.

While there's not a lot of information on the Energy Vault site with respect to tower height, plant radius, etc., Quartz has a writeup on the system that states that a tower would be on the order of 120 meters tall and the diameter of the installation would be around 100 meters. For our 40 MWh system, we need two of these.

It's also stated that each concrete block weighs about 35 metric tons (35,000 kg) and so the volume of each block would be 35,000/2,400 = 14.6m^3. Judging from the video, the concrete height is about 100 meters, and clearly it's not possible to have each block raised from the ground to 100 meters and lowered back to the ground, the blocks have to be stacked. I'd assume that it would be possible to have the average of the lift and drop to be 50 meters.

Does all of this make sense in comparison to the numbers from the earlier paragraph? We need height times volume to be 3.06*10^6 m^4. This means that we need about 3.06*10^6/50 = 61,200 m^3 of concrete. The video shows the beginning configuration to be basically a cylinder of concrete about 100 meters tall and a radius of, I estimate, 13 meters. This yields a volume of about 53,000m^3. This is not too bad, given the accuracy of estimates for height, radius, etc.

Now, in the U.S., we typically measure concrete volume in cubic yards, where a cubic meter is 1.308 cubic yards, so we're talking about a little over 80,000 yd^3 of concrete. Right now, a cubic yard of generic concrete costs around $80/yd^3 so the concrete cost alone (not counting concrete for the foundation) would be on the order of $6.4MM. However, Energy Vault claims to have developed the capability to use discarded materials as aggregate. Further, the concrete really needs very little compressive strength and so the cement requirement could be very low. Let's generously cut the $6.4MM by two thirds and call it $2.13MM. So we see that the concrete cost might be on the order of $2.13MM/20MWh = $156,500/MWh or $156.50/kWh. This is similar to the current cost of a lithium ion battery storage but doesn't include the cranes, the foundation, the construction, the control system, or the power electronics. To be fair, Li ion storage costs also are higher than strictly the battery costs.

Among the advantages of the Energy Vault solution are: negligible degradation of capacity over time; no use of rare elements; no toxic chemicals; no danger of thermal runaway. Is this the answer for turning our 3MW wind turbine into a reliable 725kW base load energy system? Well... as in so many things, it boils down to economics. I'll cover that in a future post at some yet to be determined future time.

Requiem for LightSail Energy

Image Credit: LightSail Energy

I've published multiple posts concerning LightSail Energy and its Chief Science Officer, Danielle Fong. I was enthusiastic about the the Lightsail Energy compressed air energy storage technology concept, wherein a water mist was to have been used during compression in order to produce a quasi isothermal compression process and consequently reducing thermal losses. And I wasn't alone in my enthusiasm, such notables as Vinod Khosla, Bill Gates, Peter Thiel, Total, and others invested somewhere in the vicinity of $80MM in LightSail.

But, despite the confidence of these very bright investors and the large amount of capital invested, LightSail Energy is, according to co-founder Stephen Crane, in a state of "hibernation." I follow Ms Fong on Twitter and, off and on, have corresponded with her. I haven't read anything from her with respect to the fate and apparent demise of LightSail, but the tenor of her Tweets is that she's moved on.

This saddens me because, the potential of near-term success of hydrogen fusion as an energy source notwithstanding, I am firmly convinced of the urgency of weaning ourselves from near-total reliance on fossil fuels for energy and saving those resources for applications for which substitution is extremely difficult such as transportation fuels (airlines, transoceanic shipping for example). Electricity is the low-hanging fruit here, albeit a pretty high low-hanging fruit! We have wind, solar, hydro, geothermal, and other ways to harvest energy that don't directly involve the burning of fossil fuels and all of them result in the generation of electricity.

But the most bountiful categories are solar and wind (hydro, while certainly a large contributor, has mostly been "built out," i.e., the best sources have already been exploited) and those are intermittent sources. In order for them to provide so-called "base load" power, a method of eliminating this intermittency must be employed. This can be accomplished in part by wide geographic dispersion, but the holy grail would be the ability to store energy when the wind blows and the sun shines.

Currently, nearly all new storage installations involve large lithium ion battery installations. But Li ion batteries, while good and continuing to improve, have downsides. They degrade over time, they require assiduous management both to preserve lifespan and to prevent issues of thermal runaway. And, in comparison to large scale pumped hydro storage (PHS) and compressed air energy storage (CAES), the energy capacity of Li ion battery installations is not as large (see chart below, note the log-log scale).

Image credit: unknown

Image credit: LightSail Energy

In the chart, you'll find the "Large CAES" installations in the upper right hand corner. However, the two installations plotted use underground caverns as their containment vessel and need natural gas heating in order to function. LightSail was developing modular units of much smaller size using above-ground storage in tanks. And, in what now seems to have been a last-ditch effort to continue, LightSail began an attempt to market the tanks they'd developed and, apparently, delivered at least one.

Unfortunately, the LightSail web site is gone and with it, I'm afraid, is the investors' money and the hopes and dreams of Danielle Fong.

How much storage is needed, part 4

Image credit: Unknown

My previous post in this series related some of the drawbacks of my simplistic analysis, the objectives I want to achieve, and a sketch of the methodology I've employed. Briefly, I've used a Monte Carlo simulation (yes, I linked to something other than Wikipedia, you're welcome Doctor Steve) to determine a likely outcome for generation of energy by a single hypothetical wind turbine in Dalhart, TX.

I ran 1000 simulations of 8760 data points of wind speed from what turned out to be a mixture distribution combining a normal and a Gamma distribution. This generated a total of 8,760,000 wind speeds. Each was delivered to an interpolating function generated from a digitized power curve of a 3MW nameplate capacity wind turbine. This resulted in 8,760,000 data points, each representing the average power delivered by the turbine for a hypothetical hour.

From there, finding the average power delivered was a simple process, and the result of this simulation was a mean power of 788 kW. This equates to a capacity factor of ~788*100/3000=26.3\%~. This is a surprisingly low number for the location and turbine chosen, given published figures at sites such as this that yield an implied capacity factor of 33.1%.  Further, the model estimate has no allowance for planned and unplanned maintenance outages. And, of course, the 33.1% number is ostensibly from measured data, so, as Dr. Steve might say, "who ya gonna believe, me or your lyin' eyes?"

All that said, perhaps Dalhart isn't the ideal location, perhaps the wind gradient is steeper than the model I used, perhaps they've used more highly optimized equipment, perhaps the measured year had, for some reason, particularly strong (but not too strong) winds. I'm going to proceed with my analysis based on the model data.

So, the next step is to determine the storage required for the ability to deliver a given power at, say, 99.99% reliability. That is, the system should be able to supply the specified power for all but ~8760/10000=0.876~ hours/year. This is actually less than the SAIDI*SAIFI (system average interruption duration index, measured as the average duration of outages*system average interruption frequency index, measured as the average number of outages per customer per year) and so sounds quite reasonable if not overly conservative.

One assumption will be that, when the turbine is delivering more than the power under consideration and the storage facility is "topped off," we can send the power to the grid. Another will be that, for the level of power being considered, the storage system is capable of delivering power at that level. As I've discussed in previous posts, there are two primary characteristics of an energy storage installation: the quantity of energy that the system can store; and the rate at which it can deliver that energy.

Of note, approximately 4.0% of the time, the wind is below the cut in speed of the turbine and thus all energy delivered by the system must come from storage. The modeled wind exceeded the cut out speed of the turbine a negligibly small 0.0004% of the time. But there are no black swan events in the distribution (think tornadoes).

It took me a little time to decide on an effective way to proceed, but ultimately I decided to start with a guess of storage and loop through each increment (i.e., each hour's worth) of power (since the power is in kilowatts and the increments are hours, no conversion is necessary). If the storage plus the increment minus the steady use exceeded the maximum available storage, the excess was discarded and the maximum was kept for the next iteration. If the sum was less, that was kept for the next iteration. Upon completion, determine the number of iterations at which storage was zero or less, adjust maximum storage if and as necessary and try again. Using the mean power from all of the trials, no amount of storage sufficed, but reducing it to 725kW gave me what I wanted.

And finally, the result: If our 3MW turbine plus storage system is committed to delivering 725 kilowatts and we can provide 40MWh* of storage, there's effectively zero chance of not having the committed power available. Of course, the system can deliver greater power than that when the wind blows and/or when plenty of energy is stored but committing to greater power than 725kW or installing less storage than 40MWh means that there will be times when the system cannot deliver. Obviously, installing it in an integrated grid system can offset this, but the goal here was to determine what storage will enable what level of reliable base load power for a single turbine so the result is likely to be conservative. This is a virtue in the world of engineering. Below is a chart showing the first 100,000 increments with increment number on the x-axis and energy stored on the y-axis.

One widely discussed concept in energy generation is "capacity value," a very different concept (and number) than capacity factor. Basically, this number represents how much other generating capacity can be avoided with the installation of a generator and, for wind in particular, it is typically much lower than the capacity factor. Since there are times when no wind is blowing and demand does not abate, for an unaided turbine, sufficient generating capacity must be available to meet the demand, even though it may only be used sporadically. The goal of adding storage in this analysis is to bring the capacity value of the wind turbine close to the capacity factor.

As I noted in my previous post (on another topic), most utilities are not looking for days of storage (my analysis above determined that 48 hours of storage at 24.2% of the turbine's nameplate capacity would provide that power continuously and reliably), they're looking for a few hours. And, of course, the myriad complexities of transmission constraints, demand side variability, planned and unplanned generator outages, etc. have not been considered. Others have taken some of these into account using a similar methodology (i.e., Monte Carlo simulation). None that I've found, however, incorporate storage into the analysis. If I were a professor at a research institution or an NREL researcher or, perhaps, if I worked for a turbine manufacturer or a storage technology firm, I'd implement a much more sophisticated model incorporating the above factors as well as a wind farm as opposed to a single turbine.

Next in this series (which, as readers may have noted, may be interrupted by posts on other topics) will be an analysis of the economics of such a system, or at least the beginning of such an analysis. I anticipate that the cost will be prohibitive without pricing the externalities of fossil fuel generation (i.e., without implementing a carbon tax).




*In several trials, 35MW would have sufficed with no increments less than 0, but this run had a particularly calm stretch and, even with 40MW, had 0.0088% of the increments less than 0. However, this met the criteria of 99.99% reliability at 99.9912%.

A box of rocks?

I've blogged on a few occasions regarding energy storage, most recently a "LightSail Energy redux" (though I'll be updating that in the near future to revise an inaccuracy with respect to LightSail's ability to produce commercially in their existing Berkeley facility). But there are lots of ideas for storage out there, from molten salt to bags of air beneath the sea and many others. But a new one caught my eye not too long ago that seemed out of cloud cuckoo land.

The firm touting this technology is Heindl Energy and their concept is to cut an annulus around rock and space beneath the rock, thereby creating a rock mass piston in a rock mass cylinder. Water would be pumped in to lift the rock when excess energy (or cheap energy if arbitrage is the name of the game) is available and let the rock descend, pumping the water through turbines when energy is needed or expensive.

The idea is that the piston diameter is equal to its length, and it would be raised and lowered a length equal to its radius, so half or more of the piston would always be beneath the ground surface.

One claimed advantage is that, unlike pumped hydro or underground compressed air energy storage, the geological feature necessary for the storage is more easily found (though, obviously, they can't be built just any old place).

Another is that the density of rock is greater than that of water and so a smaller volume of rock is needed for a given potential energy availability (though the factor is only about 2.5 or so).

It's easy to show that the available energy, ignoring efficiency losses of various kinds, is ~E=(2\rho_{r}+\frac{3}{2}\rho_w)\pi gr^{4}~  where ~\rho_r~ is rock density, ~\rho_w~ is water density, ~\pi~ is, well, ~\pi~, ~g~ is the acceleration of gravity, and ~r~ is the radius of the rock piston. Note that the length of the piston is ~2r~ and the height to which it's raised is ~r~. Thus, the storage available scales with the fourth power of the radius. But, since construction is really all about the surface of the piston, construction time and cost scales approximately with the square of the radius. So, in this case, size truly matters! Doubling the radius gives approximately 16 times the capacity for "only" four times the construction cost and difficulty.

A bit of an issue is that the Heidl site "Idea & Function" page gives the energy as ~(2\rho_r\frac{3}{2}\rho_w)\pi gr^{4}~. I'm sure it's a typo and I've emailed them to mention it but still, it doesn't lend confidence. Nevertheless, I used Wolfram Mathematica to check on the validity of the table shown on that page and it's actually conservative. They claim efficiency of 85% but I have to reduce efficiency to 57% or so to hit their numbers. Update: I received an email from Dr. Eduard Heindl recognizing the typo and stating that it has now been fixed. Dr. Heindl agreed that such an error on the technical page should not have taken place.

Unlike many storage scheme sites and descriptions, Heidl limits their discussion to quantity (gigawatt hours) and doesn't, as far as I could find, discuss power (the rate at which energy can be delivered by such a system). Both metrics are, of course, crucial and this site has the opposite of my typical frustration. They also provide no discussion of any load following capabilities.

We're talking here about a very large project. Using their numbers, 8 gigawatt hours of storage requires a 125 meter radius piston (250 meters or over 2 1/2 football fields across). Such a piston would weigh about 35.2 million (short) tons! To lift it would require water pressure of about 64 bar (though their table shows 52 bar).

Such pressures would demand a lot from the seals between the piston and cylinder walls, otherwise, the system would act as a 250 meter diameter circular fountain! Heidl discusses the seal system here and it appears to be quite innovative (a rolling seal against, apparently, a steel cylinder sleeve) but I see no indication that a pilot plant has confirmed that it will work. The devil, as always, is in the details.

Finally, how many? If a single 250 meter diameter rock piston can store 8 gigawatt hours, what is required to provide stable delivery from renewable sources so that the need for fossil fuel burning base load, spinning reserve, and peaker plants can be minimized with increasing penetration of intermittent renewable sources? According to Heidl's site, Germany currently needs 1,600 gigawatt hours of storage, of which only 40 have so far been provided. Therefore, Germany currently needs 195 such storage facilities!

In the Q & A, Heidl estimates that the system is of comparable cost to pumped hydro storage at a radius of 100 meters, and less expensive above that due to the scaling factors mentioned above. They also estimate a minimum of 2 years of planning and 3 to 4 years of construction per facility. And my experience is that the grander the scale of the project, the less likely it is to meet budget and schedule estimates. And this has never been tried.

While I think that it's a long shot that this type of system will ever see widespread use, the bigger picture is the scale of the undertaking needed to provide sufficient storage for deep grid scale intermittent penetration regardless of the system used. I think that distributed generation and local storage are key to providing a sustainable energy future through renewable sources.

Note: R.I.P. BB King.

California's storage mandate solved!

This post won't be the first time I've expressed my annoyance with the California Public Utilities Commission over their storage mandate of 1.325 "gigawatts of storage" (scare quotes because this is already mixing apples and oranges - it's analogous to saying "65 miles per hour of distance") by 2020.

The linked post gives my more detailed thinking, but this one is just a quickie to bring home the inadequacy of only giving the rate of delivery of electrical energy in the mandate with no reference to the period for which this energy could be delivered. It's obviously (as you'll see) an extreme, but I can meet the mandate as stated for a bit under $2M!

How? A photographer's flash unit takes electricity and stores it in a capacitor. When it's triggered, it quickly (quickly is the key here) discharges the capacitor through a flash tube. Here, we see the Elinchrom Pro HD 1000 flash unit. It can discharge 1000 W-s (photographers use "watt-seconds" but a watt-second is just another name for a joule) through the tube in 1/1430 second. This rate is 1000 watt*second/(1/1430 second)=1.43MW (megawatts). To get to 1.325 GW (gigawatts) I need 1,325/1.43=927 such units. I can purchase each for $1,049.88 ($964.88 if I order no later than January 31) for a total of $973,238.76. Of course, that doesn't include shipping and some rewiring, so double it.

Now, these units are set to power flash tubes but there's no requirement for that. They simply store energy and discharge it quickly. So, wired in parallel, they could supply the 1.325 gigawatts for about 2/3 of a millisecond. Problem solved!

Of course, the total energy delivered is a bit lacking. It's the 1000 joules*927 Elenchrom flash units=927,000 joules or a bit over a quarter of a kilowatt hour. Still, it meets the mandate and I bet I can have them delivered this year, beating the deadline by some five years.

It's rather shocking to me that our esteemed CPUC has managed to put this mandate in

place with no reference as to capacity. I will agree that rate is important (as I mentioned in the post linked above) but it's foolish to not also include capacity. However, I'm speculating that they aren't even aware of the problem. They are, after all, political appointees and, among the five of them, only Carla Peterman appears to have any sort of energy related experience or education. Mostly, it's attorneys. This is, after all, California!

If you know anyone from Southern California Edison, Pacific Gas and Electric, or San Diego Gas and Electric, please don't tell them. I want to get a good earnest money deposit on my simple solution to their storage mandate woes.

Rates vs. quantities - more unit confusion

It's widely accepted (though not universally) in the renewable energy/clean tech/green community that one of THE major problems in the widespread adoption of such renewable sources of electricity as solar and wind is their intermittent character. It's further believed that the ability to store the energy from these sources will enable their intermittency to be smoothed out, thus making them a reliable source of energy and enabling them to become much more easily integrated into the grid, possibly even a source of baseload power.

I read today that my state, California, has, through our Public Utilities Commission, set a goal of "1.3 gigawatts of energy storage by 2020." My state is certainly at the leading edge of sustainability with AB32, the Global Warming Solutions Act of 2006, the Cap and Trade Program, and many others. But I worry about people who make laws write regulations and yet aren't able to distinguish between rates and quantities.

Here's a link to the Assigned Commissioner's Ruling on this. Throughout the document, Carla Peterman discusses storage in megawatts. But a "watt" is a rate of energy utilization, or rate of performing work. A megawatt is a million joules per second. Certainly, the rate at which a storage system can deliver energy is important, but the key is the quantity that can be stored. This would be measured in watt hours, kilowatt hours, megawatt hours, gigawatt hours, terawatt hours, etc. Or, equivalently, in joules, megajoules, etc. Saying "we need 1.3 gigawatts of storage" is analogous to saying San Francisco is 80 miles per hour away from Los Angeles.

A typical gasoline pump will pump, conservatively, around five gallons per minute. Each gallon of gasoline has a chemical potential energy through oxidation of about 132 megajoules. Thus, when you fill your tank, you're delivering energy at the rate of 132*10^6 joules/gallon * 5 gallons per minute/60 seconds per minute or 11 megawatts. About 120 people filling their tanks are delivering energy at about the 1.3 gigawatts mentioned by the PUC. But this doesn't tell you a thing about how many miles these 120 drivers can travel. To know that, you need to know the capacity of the 120 tanks in gallons (along with the rate of fuel consumption of the vehicles).

To provide a bit of orientation as to the rates being discussed, in 2011, California generated or imported a total of about 292,454 gigawatt hours of electricity. This is a rate of about 33.36 gigawatts so the storage being discussed could deliver a bit under 4% of the average California rate of electricity usage.  Of course, the planned storage is divided between different utilities and geographical locations and would be deployed locally. But key to the discussion is FOR HOW LONG? A second? A minute? An hour? A day? Nothing in the document tells us.

Addendum, June 15, 2013: It's bad blog form to edit a posted blog without saying so. In reviewing the above, I realize that, while it's quite true that capacity is a fundamental metric of the viability and practicality of storage, rate is also important. I alluded to that above but I want to make it clear that I realize that vast capacity is not relevant if the rate at which it can be delivered isn't matched to the demand present in the area served.

This merits a bit of analysis of what sort of capacity might "match" a delivery rate of 1.3 gigawatts. For a starting point, let's take a look at the 4% calculated above. And I'll arbitrarily assume that we'd like to be able to "even out" the output from intermittent sources over a 24 hour period with a reserve capacity (no wind, cloud covered sky, whatever) for three days. In three days, on average, California might use (3/365)*29,2454 or about 2,400 gigawatt hours of electrical energy. 4% of this is 96 gigawatt hours.

Arguably, the storage method with the best combination of capacity, dispatchability, delivery rate, and efficiency is pumped hydro storage. If we assume a round trip efficiency of 75%, we'll need to store 128 gigawatt hours of energy. Hoover Dam delivered, at its 1984 peak, 10.348 terawatt hours so, in an average three day period in 1984, it delivered 10348*(3/365) = 85 gigawatt hours. So we're talking about something like one and a half Lake Mead/Hoover Dam storage schemes.

By the way, this goes to show just what an amazing resource gasoline is. 3032 gasoline pumps can deliver the energy equivalent to the entirety of California's average electrical consumption.

Update: The Blenheim-Gilboa Power Station in New York can deliver electricity at the rate of 1.6 gigawatts and, per a comment in a post on pumped hyrdo storage at one of my favorite sites, Do the Math, can deliver this for 16 hours for a total of 25.6 gigawatt hours. Another site says 1,000 megawatts for eight hours, or 8 gigawatt hours. In any case, storage of the magnitude specified is certainly achievable.

Also, as seen here, it's clear that pumped hydro plants are typically rated in rate in watts rather than capacity and, in fact, it's difficult to find the energy capacity in megawatt hours or gigawatt hours. In a comment in the article linked above, Ben K. say that this is because generating plants are rated in this way. But I don't see that this is a valid reason. A generating plant generates continuously as long as coal, natural gas, uranium, etc. is delivered - the amount of source material is not the issue. In a storage facility, the amount of source material (compressed air, battery chemical potential energy, water, flywheel rotational energy, capacitor electrical charge energy, whatever) is THE issue. After all, we look at battery storage capacity in terms of amp-hours which, at a fixed voltage, is a measure of quantity of energy.