From Watts Up With That?

Kevin Kilty

While reading the article “A Semi-Competent Report On Energy Storage From Britain’s Royal Society” by the Manhattan Contrarian a few days ago, I was reminded by Figure 1 of the variations in flow of the Nile River which was the inspiration for Mandelbrot’s development of fractals.[1] This naturally brought to mind Hurst’s algorithm for determining the required storage of a reservoir.[2]

Hurst’s explanation of the algorithm is very simple.

“For example, if a long-time record of annual total discharges from the stream is available, the storage required to yield the average flow, each year, is obtained by computing the cumulative sums of the departures of the annual totals from the mean annual total discharge. The range from the maximum to the minimum of these cumulative totals is taken as the required stornge(sic).”

If we think of energy conversion as equivalent to river inflow, electrical demand as equivalent to reservoir discharge and water storage behind a dam as the equivalent of chemical energy storage in a battery, then we can make use of this simple algorithm to explore the storage needed to get us through any hypothetical period with only intermittent wind or solar or some combination available to us. Hurst didn’t consider evaporation – we won’t consider inefficiency of charge/discharge.

Rather than base my analysis on seasonal weather from Monte Carlo modeling, I thought to take some of my own advice. I had made a suggestion in a public service commission hearing last January that a regional utility could do no better than to take the most inclement weather period of the last sixty or seventy years, real data in other words, and show us how their hypothetical energy system would fare. Thus, I decided to marry Hurst’s algorithm with data from this past summer gathered from the EIA hourly grid monitor for the Northwest region which is where I live.

I decided on the time period stretching from June 24, 2023 through September 30, 2023. This period includes the season of heavy demand for air conditioning and irrigation and probably the poorest wind resources overall.

Conditions of Analysis

Here are my assumptions for this first cut analysis:

• Wind energy only
• I assume wind can be scaled up to meet season demand without degrading capacity factor
• Storage level ends the season at the same level it began (one of Hurst’s conditions)
• Storage level is adjusted upward to avoid negative storage
• I include no losses from internal battery leakage, inefficiency of charge/recharge, no provision for line losses
• No provision for equipment outages or reserves
• No inter-balancing area transfers

Pattern of Demand

Figure 1 shows the pattern of demand in the Northwest. The EIA uses units of MWhr of demand during each previous hour. One might think of this more simply as the hourly average power in MW required from all sources to meet demand. There is a single daily peak that may rise above 60,000 MWhr each hour of the day when there is great demand for air conditioning and irrigation (these two sources of demand are highly correlated). The full daily swing in demand is typically around 20,000 MWhr per hour. On any given day this swing might have to be met with a combination of coal, natural gas, hydro, and solar – natural gas generally balances the swing in solar that occurs early and late in the day and has a rapid slew rate. Only gas turbines can follow it easily and it would wear a typical thermal plant to tatters to try to follow solar and wind each day. A combination of hydro, coal, and natural gas is needed to balance the fluctuation in wind generation.  The seasonal average demand is 42,661 MWhr each hour.

Wind Generation

Our analysis assumes wind generation alone. Figure 2 shows actual wind generation during our test period. The generation is highly variable.  It rises above 12,000 MW on some days but drops well below 1,000MW on others.The swing in output can take place in a matter of hours. Extended wind droughts lasted as long as 36 hours during the season.

The seasonal average wind generation is about 5,140 MW. Thus, in order to provide all demand in the Northwest, and not leave storage in any worse condition when the season is over, wind has to supply at a minimum the seasonal average demand (the actual figure turns out to be 42,735). Thus, current wind energy capacity has to be scaled up by a factor of about 8.32 to accomplish this. It is not very likely that this can be done without having to place wind farms in less than optimal locations. The best locations for wind production are very likely taken, or at least planned to be taken, already. So, this is a minimum figure.

An interesting calculation at this point is to estimate how much land area is required for this much wind generation and what the first cost, the cost of capital expenditure, is likely to be. Assuming an annual average capacity factor of one-third means we will have to install three times our 42,735 MW of actual capacity to reach a minimum needed nameplate rating. This is 128,205 MW of nameplate wind. A couple of the most recent applications for wind plants in Wyoming propose to use 125 acres per MW of nameplate rating. Thus the required wind would need something like a minimum of 16 million plus acres. For comparison this is a bit greater than one-fourth the State of Wyoming itself. The cost of constructing and equipping a wind farm I would have estimated at $1,200 per kW, but after the inflation reduction act (IRA) has raised costs this might be as high as $1,500 per kW. Total is then maybe between $150-192 billion dollars.

The Resulting Required Storage

With a few iterations of guess, assess and modify, I arrived at the following solution to the problem posed here. Average wind energy generation is 42,735 MW. By starting the season (on 6-24-2023) with 4,600 GWhr in storage, we will end the season at midnight on 9-30-2023 with  4,600 GWhr of storage. The maximum energy in storage over the season is 5,221 GWhr. This is 122 hours of average demand. The minimum is only 71,000 MWhr, which considering this has occurred during a lull in the wind and in mid-summer with air conditioning and irrigation demands is little more than an hour of reserve. During 172 hours of the season there is less than 24 hours of reserve. In other words, this is not a robust solution by any means. There is a lot more work to do. Figure 3 shows what goes on in this particular season. Storage rises a bit at first only to be whittled away as the wind dies and the season becomes hot and dry. As summer recedes, storage rises again to finish the period with the same storage it began.

What about cost? The last time I checked on lithium battery storage in the form of a Telsa Megapack it was $600 per kilowatt hour. This would put the cost of the maximum storage energy of 5,221 GWhr at around $3.13 Trillion (yes capital ‘T’ dollars).

Before any battery storage proponent tries to tell me that I am over-estimating because such batteries are only $200 per kWhr, let me state something about estimating industrial facilities. One does not just purchase batteries and wire them together. One needs a facility with all sorts of services in order to house said batteries – land, grading and foundations, roads and parking, a building, environmental control, safety systems, switching, transformers, AC/DC conversion, lines, labor and so on. The same is true of chemical plants or power plants or any major facility. Take the functional part of a facility and multiply its cost by around 1.5 for all this ancillary stuff. Take a GE quotation for a 300MW ultrasupercritical boiler and turbine of $240M (probably a bit too low after all the inflation reduction of the IRA); multiply by 1.5 and the rest of the power plant is probably $360M – $600M in total. Under-estimating costs is common – let’s not do it.

This estimate for an all-wind/storage system is not likely to be an order of magnitude in error. You see, 3.3 or so trillion dollars is probably an under-estimate considering my liberal assumptions. Storage needs equal to 122 hours of average network demand, or more, is something one should expect. It’s like 5 years worth of national savings just to supply energy for the Northwest with its roughly twenty million people (7% of the U.S.). In order to make a fantasy modern energy system work, a person needs a fantasy modern energy storage system too; and to pay for that a person needs modern monetary theory.

Making Better Estimates

Keep in mind that what I have done here is a first cut. I’d have to begin adding the complications that I assumed away early-on to do better. Maybe I could get a lower cost by adding solar energy and reducing wind. Maybe not. But keep in mind the big plan is to rely on wind/solar and storage only in the future. No coal. No gas. Even hydro is a target. Nuclear? What a horror. No way!

Also, this is just one realization of something that is a stochastic process. I’d get a bit more robust estimate by not only adding the losses of a real system, but by looking similarly at multiple seasons back in time. It takes about 25 years to gain another standard deviation of uncertainty. Thus, those 60 years worth of seasons I suggested to the PSC would reach around 2.5 standard deviations which translates to 99% certainty. Except, weather and climate don’t follow a gaussian distribution, but rather something like that of a fractal – a hyperbolic or power-law distribution. There have been weather events in the past which in their extremes of magnitude and persistence we have never observed before.

Beware. Expect surprises. Expensive ones.

References:

1. Benoit Mandelbrot, The fractal geometry of nature. 1982, ISBN: 0-7167-1186-9
2. Hurst, H.E., Long-Term Storage Capacity of Reservoirs, Transactions of the American Society of Civil Engineers Archive, Vol. 116, No. 1, January 1951.