# Storage Situation is Worse than Mearns and Rogers Calculated

The following graphs were prepared using data from the California Independent System Operator with one hour resolution. They show the net energy content (or deficit) in storage, assuming all supply came from renewable sources. They assume a system with unlimited but empty storage capacity at the beginning of the study period. The units of the vertical axis are watt hours in storage per average watt of demand.

In early sections, quantities in storage were calculated by assuming average renewable capacity is equal to average demand. In later sections, the effect of average renewable supply being larger than average demand is analyzed. Mearns and Rogers compared instantaneous renewable supply to average renewable output. Herein, renewable supply instantaneous output is compared to total instantaneous demand.

## Daily average for solar and wind

The top left graph shows that solar + wind output decreases at the time when demand increases — people come home from work, turn on the air conditioner, turn on the television, and cook dinner.

The bottom left graph shows the average daily trend for solar and wind output, as a fraction of average total demand during the period of analysis.

The top right graph shows what fraction of total demand would be satisfied by solar and wind, if they were the only sources.

The bottom right graph shows the amount of energy in storage. The vertical axis is watt hours in storage per watt of average solar + wind capacity. This rather rosy average-day picture is the basis for claims that only small amounts of storage are necessary. ## Energy in storage 2018-2020

When a time range longer than one day is considered, it is clear that the daily average is not an adequate description.

Some days are better than average, and some are worse. It is necessary to consider the cumulative effect of good and bad days, especially the cumulative effect of consecutive good and bad days. The "Solar+Wind only" line shows that with only solar and wind generators, to avoid blackouts, a storage system would need to have a capacity of about 1,000 watt hours per average watt of output. If such a system were started on January 1, 2018, it would need to have been pre-charged to about 500 watt hours per watt to avoid the first blackout. By about December 1, 2018, storage would have been depleted, the negative trend in storage content indicates that generation would not have satisfied demand, and there would have been blackouts.

The "All Renewables" line includes biogas, biomass, geothermal, hydro, solar, and wind sources. To avoid blackouts, the storage system would need a capacity of about 600 watt hours per watt of average output. If such a system were started on January 1, 2018, it would need to have been pre-charged to about 300 watt hours per watt to avoid the first blackout. By about January 1, 2019, storage would have been depleted, the negative trend in storage content indicates that generation would not have satisfied demand, and there would have been blackouts.

## How the graphs were computed

Let $$ represent the average value of A, and $\stackrel{}{A}=\frac{A}{}$ be the amount of A at each instant, normalized to its average. That is, when $\stackrel{}{A}$ = 1, the amount of A is equal to its average. When $\stackrel{}{A}$ < 1, the amount of A is less than its average. When $\stackrel{}{A}$ > 1, the amount of A is greater than its average.

Let R and T be the amounts of electricity produced by renewable sources, and the total amount produced, respectively. Further, assume T is equal to demand, i.e., non-renewable sources adjust their output to equal demand, a practice called load following. $\stackrel{}{R}$ and $\stackrel{}{T}$ are their amounts normalized to their averages. Then $\rho =\frac{\stackrel{}{R}}{\stackrel{}{T}}$ is the relationship of electricity produced by renewable sources to demand, assuming all electricity is produced by renewable sources, and the average amount produced by renewable sources is the average amount of demand.

When ρ > 1, production from renewable sources would be more than demand, and the excess could be stored. When ρ < 1, production from renewable sources would be less than demand, and energy would have to be withdrawn from storage to satisfy demand.

The amount of electrical energy in storage at time t is $S\left(t\right)=\underset{t1}{\overset{\mathrm{t2}}{\int }}f\rho \left(\tau \right) - 1d\tau ,$ that is, the accumulated difference between energy produced and energy withdrawn, from time t1 to time t2. f is the factor by which average generating capacity exceeds demand. Unless otherwise specified, f = 1, that is, average renewables' generating capacity is assumed to be equal to average demand.

## How to read the graphs

Where S(t) is increasing, ρ > 1, more electricity was produced than demand, and energy was flowing into storage. Where S(t) is decreasing, ρ < 1, less electricity was produced than demand, and energy was being withdrawn from storage. Where S(t) > 0, renewable sources plus stored electricity produced sufficient power to satisfy demand. Where S(t) < 0, renewable sources plus stored electricity did not produce sufficient power to satisfy demand, and blackouts would occur where S(t) is decreasing, for example, between November and March. This shows the necessity for non-renewable sources — coal, gas, and nuclear — or significant storage, in California's electricity systems.

Observe that in mid 2018 and mid 2019, total energy that would be in storage as a result of renewables having produced more than demand was about 300 watt hours per average watt of capacity. When the amount in storage is negative, for example between November 2018 and June 2019, any time that demand exceeds supply, i.e., ρ < 1, there would be blackouts.

## Including data from earlier dates

If data from 2016 and 2017 are included, the amount of energy in storage does not become positive until June 4, 2020, and the deepest deficit, for solar plus wind alone, is more than 3,000 watt hours per watt. The amount of storage necessary is so enormous that if average renewables' capacity were equal to average demand, it would have been impossible for renewables alone to have provided firm power during this interval.

For the period shown, using all renewables (the green line in the graphs), the maximum surplus would have been 334 watt hours per average watt of demand on August 12, 2020, and the maximum deficit would have been 2180 watt hours per average watt of demand on February 17, 2018.

The May 2020 price for Tesla PowerWall 2 is \$0.543 per watt hour of capacity, including associated electronics but not including installation. Individual installation costs are \$0.142 to \$0.214 per watt hour of capacity. Industrical scale systems might get price breaks.

An all-electric United States energy economy would have average demand of about 1.7 TWe. Assuming California average generating conditions from 2016 to 2020 apply to the entire nation, which is probably optimistic, the total cost for Tesla PowerWall 2 storage units, not including installation, with $2180×1.7×{10}^{12}=4.29×{10}^{15}$ watt hours' capacity would be $4.29×{10}^{15}×0.543$ = \$2 quadrillion, or about 100 times total US 2018 GDP (about \$20 trillion). Assuming batteries last ten years (the Tesla warranty period), the cost per year would be about ten times total US 2018 GDP. The cost for each of Americas 128 million households would be about \$130,000 per month.

Elon Musk would have more money than God.

## Effect of increasing average capacity above average demand

Data were analyzed again with average renewables' capacity increased to f = 1.22 times average demand, and a 500 Wh/W storage capacity. The "flat line" bounding the storage amount means that excess generation would be dumped. Wind output can be adjusted somewhat but solar output cannot. Assuming storage were pre-charged to about 250 Wh/W (the depth of the first deficit in the graph below), blackouts were eliminated if all renewables' capacity were increased by the same factor. Increase in hydro is unlikely. Increasing capacity for solar and wind alone by a factor of 1.22 did not eliminate blackouts. Early deficits cannot be explained by lesser penetration of the electricity system by renewable sources, because the data were analyzed under the assumption that renewable sources were the only sources, and demand is independent of source. There were better conditions for generation from renewable sources in 2019 and 2020.

Assuming solar and wind generation alone (the purple line in the graph below), if capacity is increased to f = 3 times average demand, and 12 hours' storage is provided, as is claimed to be sufficient by many environmentalists, power is not available 13.3% of the time. The cost for only twelve hours' storage, for an all-electric 1.7 TWe American energy economy, would be \$1.1 trillion, or about \$110 billion per year. The cost per American household would be about \$721 per month. And electricity would still be available only 86% of the time.

In order to show the relationship from autumn 2015 onward in detail, the negative extent of the ordinate is shortened. The deepest storage deficit was 1762 watt hours per watt of average capacity, not twenty watt hours, on February 10, 2012 at 2:00 PM.

If the average of all renewables' generating capacity (the green line) is increased to three times average demand, and 12 hours' storage is provided, firm power is available. July 16, 2011 is shown above without electricity from any renewable sources. There was none reported by the California Independent System Operator for that day.

Renewables provided 27.73% of California electricity in 2019 and 2020. Electricity satisfies about one third of total California energy demand. To provide all California energy from renewable electricity sources whose average generating capacity is three times average demand would require a capacity increase of 3200% above the capacity to satisfy all current California electricity demand. Increasing hydro at all, or increasing biogas, biomass and geothermal by 3200%, is unlikely. With solar and wind alone, blackouts are frequent.

## Conclusion

This discussion assumes that the period analyzed includes the deepest deficit that will ever occur — which is, of course, false. When Tambora erupts again, in another "year without a summer" such as 1816 there will be no times when ρ > 1. The trend of storage content will be everywhere downward. The deepest deficit will be far deeper than any shown here. No physically or economically feasible amount of storage could suffice. Renewable and storage capacity could not be increased sufficiently rapidly. There would be energy available for only a small fraction of demand. Hospitals, and politicians' homes, would have first priority. Civilization would collapse.

## References

Typos? Mistakes? Quibble with the analysis? Want the software I used?

van dot snyder at sbcglobal dot net.