The following graphs were prepared using data from the California Independent System Operator (CISO) with one hour resolution from 1 January 2011 until 30 November 2020, and five minute resolution thereafter, data from the Electric Reliability Council of Texas (ERCOT) with hourly resolution from 2 July 2018, nationwide data from the Hourly Electric Grid Monitor with one hour resolution since 1 July 2018, and data from EU for Denmark, Germany, and EU as a whole with hourly resolution from 1 January 2015 until 30 September 2020. They show the net energy content (or deficit) that would have been in storage, assuming all supply came from renewable sources and storage charge and discharge are 100% efficient. At first, the analyses assume a system with unlimited but empty storage capacity at the beginning of the study period. Analyses are repeated with bounded storage capacity.

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. The method of calculation used here is explained below.

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 and their average output were magnified to equal average demand.

The bottom right graph shows the average daily variation of the amount of energy that would be in storage if solar and wind were the only sources and their average output were magnified to equal average demand. The vertical axis is watt hours in storage per watt of average solar + wind production. This rather rosy average-day picture is the basis for claims that only small amounts of storage are necessary. But look carefully and you'll notice that the average daily deficit is four watt hours per watt, while the average surplus is three watt hours per watt: Storage is being continuously depleted.

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 graph below shows the amount of electrical energy that would have been in storage in California with an all-renewable energy system. The units of the vertical axis are watt hours in storage per watt of average demand, compared to the amount in storage on 1 January 2011.

The “Unweighted” (green) line multiplies the output of all renewable generators by the same factor so that their total average output is equal to average demand. It is unlikely that biomass, biofuel, and hydro can grow much. Environmentalists want to remove dams, and they complain that fracking for geothermal causes earthquakes.

The “Weighted Increase” (purple) line is computed by magnifying each renewable's output in proportion to the rate of change of that generation method's label capacity, with a different rate for each method in each year.

The maximum surplus calculated using “Weighted Increase” was 570 watt hours per watt on 22 August 2011. The deepest deficit was 687 watt hours per watt on 4 February 2021. To avoid outages and to avoid dumping power when more is available than demand, and storage is already charged to full capacity, a storage system would need to have a capacity of 570 + 687 = 1,257 watt hours per watt of average demand (more than 52 days), and to have been precharged to 673 watt hours per watt of average demand on 1 January 2011 to avoid outages. The effect of precharging would be to shift the graphs upward by 687 watt hours, and the “Weighted Increase” (purple) line would nowhere have been negative.

The yearly average maximum and minimum were 372.6 watt-hours per watt and -198.9 watt-hours per watt, an annual swing of 571.5 watt-hours per watt. The surplus-deficit cycle clearly has a period of a year. Although there would, on average, be daily charge-discharge cycles of about 7 watt hours per watt of average demand, during their ten year lifetimes, batteries would be nearly fully charged and discharged ten times. To break even on operating (not capital) costs, they would need to sell electricity at 57 times the usual rate. This assumes that batteries could hold the surplus for six months until it is needed, and wouldn't be damaged by deep discharge cycles.

Renewable sources provided 36% of electrical energy. Without storage and with
only renewable sources, when the trend of the amount was negative
(δ(*t*) below is less than 0), i.e., 23.7% of
the time, there would have been outages. With unlimited storage capacity, not
precharged, when the amount in storage was negative and the trend of the amount
was negative, i.e., 13.8% of the time, there would have been outages (see How the Graphs are Computed below). The industry definition
of *firm power* is 99.97% availability, or about two hours and forty
minutes of outage per year.

Total label generating capacity amounts, year by year, for each generation method, were obtained from the California Department of Energy.

The rate of change of total renewables has not changed significantly since 2012, when solar PV began increasing rapidly, and wind and solar thermal stopped increasing.

The largest surplus was 349 watt hours per watt of demand on 21 June 2022. The deepest deficit as of 1 December 2023 was 1,372 watt hours per watt of demand on 1 December 2023. The storage capacity required to avoid outages is 349 + 1372 = 1,722 watt hours per watt of average demand, i.e., 72 days of storage capacity would have been necessary.

Renewable sources provided 10.2% of nationwide electric energy, or about 3%
of total energy. Without storage and with only renewable sources, when the trend
of the amount was negative (δ(*t*)<0), i.e., 61.6% of the time,
there would have been outages. With unlimited storage capacity, not precharged,
when the amount in storage was negative and the trend of the amount was
negative, i.e., 36.9% of the time, there would have been outages.

The May 2020 price for Tesla PowerWall 2 was $0.543 per watt hour (not kilowatt hour) of capacity, including associated electronics but not including installation. Individual installation costs range from $0.142 to $0.214 per watt hour of capacity. Industrial scale systems might get price breaks.

Activists insist that an all-electric United States energy economy would have
average demand of about 1,700 GWe. Assume that the California requirement of
1,257 watt hours of storage per watt of average demand is adequate forever (this
is optimistic). The total cost for Tesla PowerWall 2 storage units, not
including installation, with
$\mathrm{1,257}\times \mathrm{1.7}\times {\mathrm{10}}^{\mathrm{12}}=\mathrm{2.1}\times {\mathrm{10}}^{\mathrm{15}}$
watt hours' capacity would be
$\mathrm{2.1}\times {\mathrm{10}}^{\mathrm{15}}\times \mathrm{\$0.543}=\$\mathrm{1.16}$
quadrillion, or about 58 times total US 2018 GDP (about $20 trillion). Assuming
batteries last ten years (the Tesla warranty period), the cost would be **5.8
times total US 2018 GDP per year.** The cost for each of America's 128 million
households would be about $907,100 per year. If the more pessimistic nationwide
analysis is used, the total cost would be **7.9 times total US 2018 GDP per
year,** and the cost per household would be $1,242,094 per year. Prices that
include installation would be 25-40% greater. This analysis assumes 100% battery
charge and discharge efficiency. They're closer to 90% (81% round-trip), so the
necessary capacity increase would add about 25% more. Taking both installation
and the necessary capacity increase into account results in a 75% cost increase
to about **13.8 times total GDP every year**.

Elon Musk would have more money than God.

California average electricity demand is 26 gigawatts. The 1,700 GWe average
demand that activists insist an all-electric American energy economy would have
is about 3.83 times total current average electricity demand of 444 GWe.
Assuming the same ratio for California, total electricity demand in an
all-electric California economy would be 99.6 GWe, so the total storage required
would be 99.6×10^{9}×1,233 = 123 trillion watt hours. The
cost for California would be $6.7 trillion per year, or “only” about
three times total California GDP every year, or about 5.25 times total
California GDP when accounting for installation and 81% round-trip efficiency.

The energy density of lithium ion batteries is 230 watt hours per kilogram. A
capacity of 1.9×10^{15} watt hours for the entire USA would weigh
8.26 billion tonnes. A
lithium ion battery contains the following ingredients (among others):

Metal's | Metal's Amount in | Metal's | ||||
---|---|---|---|---|---|---|

Proportion in | 8.26 billion tonnes | Global | ||||

Metal | Li-ion Battery | of Li-Ion Batteries | Reserves | Requirement | ||

(%) | (million tonnes) | (million tonnes) | ÷ Reserve | |||

Copper | 17.0% | 1,404 | 830 | 1.69 | ||

Aluminum | 8.5% | 702 | 32,000 | 0.022 | ||

Nickel | 15.2% | 1,256 | 89.0 | 14.1 | ||

Cobalt | 2.8% | 231 | 6.9 | 33.5 | ||

Lithium | 2.2% | 182 | 14.0 | 13.0 | ||

Graphite | 22.0% | 1,817 | 330.0 | 5.51 |

**Other than aluminum, the Earth does not contain enough
metals to make the first generation of necessary batteries for the United States
alone!** Batteries last about ten years, and are not completely recyclable.
Even if the first generation could be built, where would the second generation
come from?

Presented with these quantities, activists propose other methods, such as
pumping water up mountains. In California, where would we get the water and
where would we put it? The Oroville Dam at 771 feet or 235 meters is the highest
dam in the country. The area of Yosemite Valley is 6 square miles, or about 15
square kilometers. Assuming it's flat (which it isn't), building a 235 meter dam
across the entrance could impound 4.17 trillion liters, or 4.17 trillion
kilograms, of water. The mouth of the valley is 1,200 meters above sea level, so
the top of the full reservoir would be 1,435 meters above sea level. The
potential energy, in joules (watt-seconds), of a mass *m* lifted to a
height *h* in a gravitational field with acceleration *g* (9.8
meters per second squared at the surface of the Earth) is *mgh*. Assuming
a power plant at sea level, not at the base of the dam, the water in such a
reservoir would have potential energy of about
4.17×10^{12}×1200×9.8/3600 = 13.6 trillion watt hours.
The Betz limit for the efficiency of a turbine is 57%. California would need at
least 121 trillion / (0.57×13.6 trillion) = 15.6 of these reservoirs. If
the power plant were at the mouth of the valley instead of at sea level, about
97 would be required. The nation as a whole would need almost 1,500. All of
this assumes 100% efficiency (other than the Betz limit) and optimal conditions,
so in reality much more would be required.

Opportunities for reservoirs the size of Yosemite Valley are limited. The
*Snowy 2* project in Australia is to connect two reservoirs with capacity
of 920.6 million liters, separated by an elevation of 800 meters. Water is to be
pumped between the reservoirs in 27 kilometers of tunnels (Yosemite Valley is
250 kilometers from San Francisco Bay). The advertised storage capacity is 350
GWe-hours, but capacity as calculated above would be 2 GWe-hours, about 5.7
times larger, so they have accounted for losses not counted above for the
Yosemite Valley calculation. The United States would need 9,600 such systems.
There are currently 1,450 conventional hydroelectric power plants, and 40 pumped
storage plants, in the United States. The current budget for Snowy 2 is $AU 4.8
billion = $US 3.26 billion, but many expect the project to exceed $AU 20 billion
= $US 13.6 billion. The project is scheduled to be completed in 2028, but many
believe it will not be completed. The total cost for 9,600 such projects in the
United States would be $130 trillion — if we could find places for them
and water to use them.

Total rainfall in a particular river's watershed is cyclical. In 2022, Lake Mead was almost empty. Texas has a more difficult problem than California, with water in the East but no mountains, and mountains 1,000 miles to the West but no water. A statistical analysis of data from the Shuttle Radar Topography Mission showed that Kansas is indeed as flat as a pancake.

The next proposal is towing weights up mountains or old mine shafts. How many are required? The storage requirement is 1,722 Wh/W × 1,700,000,000,000 W × 3600 seconds/hour = 16.9 quintillion watt seconds, or joules. Assuming 100% efficiency, a ten tonne weight, and a one kilometer lift, the result is “only” 102 million such devices. Where would these be put? How much would they cost, per year, taking into account capital, amortization, operations, maintenance, safety, replacement, decommissioning, environmental effects, and disposal or recycling?

During the interval for which data were available, renewables provided 11.4% of electricity for EU as a whole, 46% for Denmark, and 28.3% for Germany. If solar and wind had been the only generators, for EU as a whole, the largest surplus in storage of unlimited capacity would have been 355 watt hours per watt of average demand, and the deepest deficit would have been 598 watt hours per watt.

To provide firm power without dumping energy when batteries are fully charged, 355 + 598 = 953 watt hours of storage capacity per watt of average demand would have been needed. Without storage and without other generation sources, there would have been outages 55.5% of the time, i.e., whenever the slopes of the lines in this graph are negative. Although the patterns for EU as a whole, and for Denmark and Germany alone, are different, the storage situation is almost identical for Germany: 969 watt hours of storage would be required, and there would have been outages 55.2% of the time without storage if the only generators were renewable sources. Denmark fared somewhat better, requiring only 783 watt hours storage, and would have had outages 54.9% of the time without storage and if the only generators were renewable sources.

The amount of energy in storage at time *t* since the beginning of the
analysis, in watt hours per watt of average demand, is then obtained by
accumulating the instantaneous power surplus (or deficit) δ(*t*) in
each measurement interval, multiplied by the interval length (energy = power
× time), i.e., computing the integral:

$S\left(t\right)=\underset{0}{\overset{t}{\int}}\delta \left(\tau \right)d\tau \approx \sum _{\mathrm{n=1}}^{N}\delta \left(\mathrm{tn}\right)\Delta \mathrm{tn}$

where δ(*t*) has units of watts of surplus (or deficit) per watt of
average demand, *N* is the number of measurement instants,
Δ*t _{n}* (the duration of a measurement interval) has
units of hours, and

Rectangular quadrature is justified by the fine resolution of measurements
— Δ_{n} was one hour for California from 1 January 2011
until 30 November 2020, and five minutes thereafter, and one hour for the other
data.

To use historical data to compute what δ(*t*) would have been if
all sources were renewable sources, it is necessary to increase measured
renewables' average production to match average demand. Let
$\stackrel{}{R}$
be current average renewables' production, and
$M\stackrel{}{W}$
be the additional average renewables' production needed to match average total
demand
$\stackrel{}{T}\left(t\right),$
where
$\stackrel{}{W}$
is a weighted average of renewables' production, and *M* is a
magnification factor. Then

$\stackrel{}{R}+M\stackrel{}{W}=\stackrel{}{T}$, or $M=\frac{\stackrel{}{T}-\stackrel{}{R}}{\stackrel{}{W}}.$

To compute the relationship of *S*(*t*) to average total demand,
that is, how much storage capacity is needed per watt of average demand, we need

$\delta (t)\; =\frac{R(t)\; +\mathrm{G\; M}W(t)}{\stackrel{}{T}}-\frac{T(t)}{\stackrel{}{T}}=\frac{R(t)}{\stackrel{}{T}(t)}+G\frac{W(t)}{\stackrel{}{W}(t)}\left((,1,-,\frac{\stackrel{}{R}(t)}{\stackrel{}{T}(t)},)\right)-\frac{T(t)}{\stackrel{}{T}}$

where *G* is a general growth factor that allows to increase the
weighted average of renewables' production above average demand,

$R\left(t\right)=\sum _{\mathrm{i=1}}^{N}\mathrm{Ri}\left(t\right),$ $W\left(t\right)=\sum _{\mathrm{i=1}}^{N}\mathrm{gi}\left(t\right)\mathrm{Ri}\left(t\right),$ and $\sum _{\mathrm{i=1}}^{N}\mathrm{gi}\left(t\right)=\; 1.$

As remarked above, *g _{i}*(

Because neither average demand nor average renewables' production are constant,
the “instantaneous” average demand and production were computed
using least-squares fits to *C ^{2}*-continuous cubic splines,
with constraints on the slopes (

The “Wt Average” line here is for the weighted average $\stackrel{}{W}\left(t\right)$.

An example of this method to compute the “instantaneous” average is illustrated for total demand. The end point yearly averages are anomalously large and small compared to other years because data are available for only a fraction of the year.

Observe that in mid 2020, total energy that would be in storage as a result
of all renewables being increased equally, and renewables having produced more
than demand, was about 400 watt hours per average watt of capacity. When the
amount in storage is negative, for example between November 2020 and June 2021,
any time that demand exceeds supply, i.e., δ(*t*) < 0,
there would be outages.

If an all-renewable generating system had been in place in California on 1 January 2011, with a storage system having capacity less than about 963 watt hours per watt of average demand, and had not been precharged to 296 watt hours per watt of average demand, there would have been prolonged outages.

The yearly periodic asynchronous relationship of renewables' output compared to demand is evident in the second graph above.

Phases of yearly variation were computed by fitting each phenomenon to
β_{1} sin ( ω *t* ) + β_{2} cos ( ω
*t* ), where ω = 2 π / 8765.81 (the number of hours per year),
and *t* is time in hours since the beginning of the period of analysis (1
January 2011). The phase of each phenomenon with respect to the beginning of the
period of analysis is then tan^{-1} ( β_{2} /
β_{1} ), and the difference in phases is 46 days, i.e., demand
begins to increase about 46 days after output from renewable sources begins to
decline.

With the limited amount of data available (twelve years), by fitting to
β_{1} sin ( ω *t* ) + β_{2} cos ( ω
*t* ) + β_{3} sin ( λ *t* ) +
β_{4} cos ( λ *t* ), where ω is as above and
λ is to be found, a longer term variation with a period of 8.24 years was
found. The phase differences of this variation, tan^{-1} (
β_{4} / β_{3} ), compared to demand, range from -28
days (wind) to +172 days (solar) to +515 days (hydro). The average phase
difference between demand and renewables is 45 days. Each time that more data
are used, the solved-for period ( λ / 2 π ) increases. Long-term
variation frequencies are probably related to the Sun's eleven year activity
cycle. There might be even longer term variations that are related to solar
activity cycles of about 70 and 1,500 years, but these cannot be measured by
using only twelve years of generation data.

California data were analyzed again with average renewables' generating
capacity increased to *G* = 1.25 times average demand, with the same
relative output magnifications *g _{i}*(

If average renewables' generating capacity were to have been increased to
*G* = 3 times average demand, and 12 hours' storage were provided, as is
claimed to be sufficient by many activists, there would have been outages 3.4%
of the time, i.e., when the slope of the line in this graph is negative.
6,300,000 gigawatt hours of output — 355% of total demand — would
have been dumped.

The cost for only twelve hours' storage, for an all-electric 1.7 TWe American energy economy, would be $11.1 trillion, or about $1.1 trillion per year, or 5.5% of total GDP. The cost for each of America's 128 million households would be about $8,654 per year for batteries alone.

Renewables provided 33.4% of California electricity between 1 January 2011 and 1 January 2023. 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 3 × 3 / 0.334 = 2695% above the capacity to satisfy all current California electricity demand. Increasing hydro at all, or increasing biogas, biomass and geothermal by 2695%, is unlikely.

As of 30 April 2023 | ||
---|---|---|

Storage | Outage | Dumped |

12 Wh/W | 46.8% | 1.69% |

100 Wh/W | 44.4% | 1.69% |

200 Wh/W | 41.9% | 1.58% |

300 Wh/W | 37.1% | 1.35% |

400 Wh/W | 31.6% | 1.12% |

500 Wh/W | 26.9% | 0.88% |

600 Wh/W | 18.1% | 0.65% |

Unlimited | 4.4% | 0% |

Dumping output reduces the energy return on energy invested (EROI). EROI at least seven is required for economic viability. With storage, and even without dumping, solar PV and wind are not viable without subsidies. Subsidies do not eliminate costs — they just hide them in your tax bill — so they do not actually make solar and wind viable. California appears to have stopped building solar thermal generators, and the EIA does not predict any increase in US solar thermal capacity.

(Solar CSP means

Daniel Weißbach, G. Ruprecht, A. Huke, K, Czerski, S. Gottlieb, and A. Hussein,Energy intensities, EROIs (energy returned on invested), energy payback times of electricity generating plants,Energy 52, 1 (April 2013) pp 210-221

Preprint at https://festkoerper-kernphysik.de/Weissbach_EROI_preprint.pdf

D. Weißbach, F. Herrmann, G. Ruprecht, A. Huke, K, Czerski, S. Gottlieb, and A. Hussein,Energy Intensities, EROI (energy return on invested), for energy sources,EPJ Web of Conferences 189, 00016 (2028) https://www.epj-conferences.org/articles/epjconf/pdf/2018/24/epjconf_eps-sif2018_00016.pdf

If 355% of total renewables' output were dumped, the EROI from solar PV would be reduced to 0.56, i.e., less energy would be produced than invested in the devices. Where would that extra required energy come from? The EROI from wind would be reduced to 1.13.

This discussion assumes that the period analyzed includes the deepest deficit
that will ever occur — which is, of course, false. When Mount Tambora on
the island of Sumbawa in Indonesia erupts again and produces another “year
without a summer” such as in 1816 — and it or another one as large
definitely will, the only question is when — there will be no times for
several years when δ(*t*) > 0. The trend of storage content will
always and everywhere be downward. The deepest deficit will be far deeper than
any shown here. No physically feasible or economically viable amount of storage
could suffice. Renewable generation capacity and storage capacity could not be
increased sufficiently rapidly. There would be energy available for only a small
fraction of demand. Politicians' homes, and (maybe) hospitals, would have first
priority. Civilization would collapse.

- Euan Mearns,
*Grid-Scale Storage of Renewable Energy: The Impossible Dream*,**Energy Matters**(November 20, 2017). - Norman Rogers,
*Is 100 Percent Renewable Energy Possible?*(May 25, 2018). - California Independent
System Operator Renewables and emissions reports (Updated daily). The format
was changed on 1 December 2020. Here are links to two representative dates:

http://content.caiso.com/green/renewrpt/20200820_DailyRenewablesWatch.txt

http://www.caiso.com/outlook/SP/history/20221205/fuelsource.csv - U.S. Energy Information Administration California State Profile and Energy Estimates (2018).
- Solar Reviews, Tesla Powerwall: Is it the best home battery? (July 24, 2020).
- Nationwide Hourly Electric Grid Monitor
- Nationwide yearly generating capacity predictions

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

van dot snyder at sbcglobal dot net.