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Written by Dr. Lars Schernikau and Prof. William H. Smith

Published November 2020, last updated February 2021 (the authors appreciated all received feedback leading to this substantially revised version).
Publicly available at Researchgate & SSRN

About the authors:

Dr. Lars Schernikau is an energy economist and entrepreneur in the energy raw material industry.

Prof. William Hayden Smith is Professor of Earth and Planetary Sciences at McDonnell Center for Space Sciences at Washington University.

DOI: 10.2139/ssrn.3730155

Disclaimer

This is a back-of-the-envelope calculation based on experience from existing PV plants in California and publicly available battery data and insolation data for Spain. The calculations can be adjusted using different assumptions.

Preface:

·         Power (in Watts, in German “Leistung”) is the horsepower of a car’s engine. Energy to drive a Tesla, for example, is derived from a battery. A Tesla S half-ton kWh battery powers a 192 kW electric motor to accelerate the 2,2-ton Tesla S.

·         Energy (in Watt/hour or Wh, in German “Arbeit oder Energie”) is how much work it takes to move the 2,2-ton car, for instance, for 1h at 100 km/h over a specified terrain. Energy is equivalent to “work”. In this case, energy varies with travel time, velocity, mass, aerodynamics, friction, and the power applied to overcome those “obstacles”. The half-ton Tesla S battery stores energy of 85 to 100 kWh.

·         Capacity Factor “CF” (in German “Nutzungsgrad”) is the percentage of power output achieved from the installed capacity for a given site, usually stated on an annual basis.

–        Capacity factor is not the efficiency factor. Efficiency measures the percentage of input energy transformed to usable energy.

–        Capacity factor assumes a stable photovoltaic response and measures the site quality, which varies with latitude, air mass, season, diurnal (24h sun cycle at that location), and weather.

–        In Germany, photovoltaics (“PV”) achieve an average annual capacity factor of ~10%, while California reaches an annual average CF of 25%3. Thus, California yields 2,5x the output of an identical PV plant in Germany.

–        It is important to distinguish between the average annual capacity factor and the monthly or better weekly and daily capacity factor, which is very relevant when we try to use solar for our daily power needs (See Figure 5).

1.      Abstract

Germany is responsible for about 2 % of global annual CO2 emissions from energy. To match Germany’s electricity demand (or over 15% of EU’s electricity demand) solely from solar photovoltaic panels located in Spain, about 7 % of Spain would have to be covered with solar panels (~35.000 km2). Spain is the best-situated country in Europe for solar power, better in fact than India or (South) East Asia. The required Spanish solar park (PV-Spain) will have a total installed capacity of 2.000 GWp or almost 3x the 2020 installed solar capacity worldwide of 715 GW. In addition, backup storage capacity totaling about 45 TWh would be required. To produce sufficient storage capacity from batteries using today’s leading technology would require the full output of 900 Tesla Gigafactories working at full capacity for one year, not counting the replacement of batteries every 20 years. For the entire European Union’s electricity demand, 6 times as much – about 40 % of Spain (~200.000 km2) – would be required, coupled with a battery capacity 6x higher.

To keep the Solar Park functioning just for Germany, PV panels would need to be replaced every 15 years, translating to an annual silicon requirement for the panels reaching close to 10% of current global production capacity (~135% for one-time setup). The silver requirement for modern PV panels powering Germany would translate to 30% of the annual global silver production (~450% for one-time setup). For the EU, essentially the entire annual global silicon production and 3x the annual global silver production would be required for replacement only.

There are currently not enough raw materials available for a battery backup. A 14-day battery storage solution for Germany would exceed the 2020 global battery production by a factor of 4 to 5x. To produce the required batteries for Germany alone (or over 15% of EU’s electricity demand) would require mining, transportation and processing of 0,4-0,8 billion tons of raw materials every year (7 to 13 billion tons for one-time setup), and 6x more for Europe. The raw materials required include lithium, copper, cobalt, nickel, graphite, rare earths & bauxite, coal, and iron ore for aluminum and steel. The 2020 global production of lithium, graphite anodes, cobalt or nickel would not nearly suffice by a multiple factor to produce the batteries for Germany alone.

It appears that solar’s low energy density, high raw material input and low energy-Return-On-energy-Invested (eROeI) as well as large storage requirements make today’s solar technology an environmentally and economically unviable choice to replace conventional power at large scale.

2.      Introduction and Assumptions

On 3rd July 2020, the German Minister for the Environment Ms. Svenja Schulze announced publicly (translated from German) that “Germany will be the first country to abandon coal and nuclear energy. We will rely completely on energy derived from solar and wind”. This statement as well as the IEA’s October 2020 proclamation that solar will become the “new king of the world’s electricity markets” led the authors to make the calculations herein.

The goal of this paper is to calculate how much solar installed capacity in Spain is needed to supply Germany’s electricity requirement 100% with solar energy produced in Spain, which equals replacing over 15% of EU’s electricity demand. We refer to this Spanish photovoltaic solar park as “PV-Spain”. Spain is Europe’s best location for solar power given its high direct normal irradiation (DNI, see Figure 1) and in fact, Spain has significantly more suitable sunshine than India or (South) East Asia.

In addition, this paper will calculate the backup capacity required in the form of batteries and address the subject of material input required for both the PV-Spain and the backup. The subjects of a Solar Park in the Sahara Desert as well as Hydrogen are also addressed. The multidimensional calculations herein demonstrate the complexity of energy economics, which is largely underestimated in the current debate on renewable energy.

Figure 1: Global Direct Normal Irradiation, based on long-term average kWh/m2.
Source: World Bank Group, accessed 4 Sep 2020 at this 
link

Simplifying assumptions

The authors’ calculations are based on the following simplifying assumptions which are on average quite generous. These assumptions can be replaced with the readers’ own:

A1. Average Electricity Demand: Germany has a measured average annual electrical energy demand of up to ~550 TWh, to simplify we assume ~45 TWh per month or ~1,5 TWh per day. For comparison, EU demand is 3.300 TWh p.a., 6 times larger[1].

A2. Peak Power Factor = 1,6x: Germany has average power demand of ~63 GW (550 TWh ÷ 8.760h). The actual peak power demand in the winter reaches 82 GW. Accounting for standard 20% safety margin increases required capacity for peak power to ~100 GW (100 ÷ 63=1,59).[2] Peak demand will likely rise because of electric vehicles and heat pumps. The Peak Power Factor adjustment converts average annual power demand to daily peak power demand including safety margin which is significantly higher than the average. For comparison, EU average power demand is ~375 GW, 6 times higher.

A3. Backup Peak Power Factor = 1,5x: Figure 4 illustrates the typical electricity demand curve and photovoltaic production during a day. The photovoltaic peak must be approximately twice the demand peak in order to allow the batteries to charge during the few sunny hours around noon. Figure 2 also illustrates that nearly all power is produced in only one-quarter of a 24h-period and nothing at night. The authors generously only assume a Backup Peak Power Factor of only 1,5x.

A4. DC/AC and Transmission loss = 30% or 1,3x: DC to AC conversion before consumption incurs a loss of 21-24%3 of direct current power produced. Transport of electricity to the German end user over approximately 1.500 km (air distance from Toledo to Frankfurt) will account for approx. 10% loss. Thus, total ~30% loss or a factor of about 1,3x.

A5. Average annual DNI in Spain located at 41 ºN latitude is normalized to data from the largest US solar park called “Solar Star[3] located in California, which is well documented.

a.     Solar Star is amongst the largest, most efficient and modern operating solar parks in the world employing large form-factor, high-wattage, high-efficiency, higher cost crystalline silicon solar panels/modules, mounted on single axis trackers. Solar Star produced 1,66 TWh/p.a. of DC electricity between 2017 and 2019. The park operates 747 MWDC total installed solar PV capacity covering 13 km2 using 1,7 million solar panels3, translating to 57,5 MW installed capacity per km2.

b.     The Direct Normal Irradiation (DNI) map in Figure1 accounts for sunny days in Spain. It adjusts for latitude, clouds, rain, as well as hours of day and night.

c.     ESP/CA DNI Factor = 1,5: The DNI for Southern Spain is ~1.900 W/m2/p.a., while the DNI in Southern CA is ~2.900 W/m2/p.a.[4], a factor of 1,53.

d.     Solar panels can be operated for 15 years before they have to be replaced[5].

A6. Winter Capacity Factor = 1,8:The 2017-2019 average annual capacity factor of Solar Star in California was measured at 24,8%3. This translates to 16,5% average annual capacity factor for Spain.

a.     The monthly capacity factors in California for 2018/2019 varied from 13,3% in December to 33,9% in June (see Figure 5), leading to a Winter Capacity Factor adjustment of 1,8x (24,8% ÷ 13,3% = 1,86).

b.     Figure 2 illustrates a typical PV sunny day output during winter and summer in Austria. The output varies also here by more than 3:1 between winter and summer.

A7. Gigafactory = 50 GWh Li-ion batteries: The annual production of a Tesla Gigafactory is anticipated to reach up to 50 GWh of Li-ion batteries.[6]

a.     Materials required to build today’s best battery technology include lithium, copper, cobalt, nickel, graphite, rare earths & bauxite, coal and iron ore (for aluminum and steel).

b.     It is estimated that optimistically 1-2 % of actual ore body mined ends up in the weight of the battery[7].

A8. Battery Storage Utilization Factor = 1,7: Li-ion rechargeable batteries can store energy over several months, and self-discharge ~5 % of stored energy in first 24h, and at ~2% per month thereafter.

a.     The efficiency of storing charge is 90%.

b.     Charging to 80% of capacity and discharge to 20% of capacity preserves battery life. Internal electronics maintain optimum internal operating temperature of 12-16 ºC, optimum discharge rate near 1C (refers to 1 Coulomb per hour discharge rate)[8], and protect batteries from too high or too low charge or discharge voltages which damage the batteries[9].

c.     Maintenance electronics consume 3% per month of the charge per cell. The diurnal discharge cycle must be controlled carefully to preserve battery life out to 7.000 cycles, equivalent to a 20-year lifetime[10].

d.     As a result, on average 50-60% of installed battery capacity can be used effectively, therefore a factor of 1,7x is assumed.

A9. Not considered by the authors are:

a.     Total energy consumption in Germany, which is ~5x higher than electricity demand (including non-electrical heating, transportation, etc.).

b.     Energy that Germany imports from other parts of the world because Germany consumes products that require energy to build (but they are built outside of Germany, for instance in China, India or the US).

c.     Alternate means of producing power, 100% solar from Spain is assumed for Germany which equals to over 15% of the EU.

d.     Alternate means of providing backup (other than battery backup), such as any conventional capacity from fossil, nuclear, hydro, or hydrogen. This assumption illustrates the backup requirement and focuses on batteries. Hydrogen is covered in Section 3.4.

e.     Total costs, energy required, materials needed or environmental impact of building transmission lines and transmission systems, building solar panels (silicon and silver requirements are mentioned, other materials not). Solar’s energy-Return-On-energy-Invested (eROeI) is estimated to be too low to support advanced societies[11].

f.      Costs and environmental impact of recycling or disposing of solar panels after their useful life. Also not included are costs of building, maintaining, and recycling or disposing the storage capacity which will need to be replaced every 20 years or sooner (estimation is given on materials required for construction of batteries).

g.     Cost for land used that includes but is not limited to animal life destroyed, crop land and forests, towns, streets, valleys, mountains that would have to be cut or eliminated (see Figure 3).

h.     The impact of large-scale solar PV farms on local temperatures in non-desert environments, which may have a substantial heating effect. Sunlight on vegetation (grass, trees) supports plant growth and plants support transpirational cooling. On areas covered with solar panels, 70-90 % of absorbed sunlight cannot be transformed to useful energy nor can it be absorbed by plants, thus, warming the surroundings (see Lu et al. Dec 2020 and Li et al. Sep 2018[12]).

i.       Positive side effects such as producing green hydrogen with excess capacity in the summer. Hydrogen is briefly addressed in section 3.4.

3.      Calculating the PV-Spain

The goal of this paper is to calculate how much installed solar capacity in Spain (PV-Spain) is required to supply 100% of Germany’s electricity requirement which equals just over 15% of EU’s demand. To accomplish this, the PV-Spain installed capacity has to be sufficient during winter months. During winter, however, solar energy is at its minimum while consumer demand is the highest. 

Figure 2: Typical PV sunny day output winter and summer (Austria during 2015 for illustration).
Source: elkemental Force, Austria, accessed 4 Sep 2020 at this 
link

3.1.      PV-Spain installed capacity and space requirement

For calculation purposes, the authors use the well-documented Solar Star3 Project in California. Solar Star produced on average 1,66 TWh/p.a. of DC electricity or 128 GWh/km2/p.a. (see A5.a) or 10,67 GWh/km2/month with 747 MW total and 57,5 MW/km2 installed capacity. German electricity demand is on average 45 TWh or 45.000 GWh per month (see A1).

Therefore, it appears at first sight that monthly 45.000 GWh ÷ 10,67 GWh/km2 = 4.220 km2 of solar panels in Spain should be sufficient. However, the following adjustments detailed above are required:

·         Adjusting for the Peak Power Factorof 1,6x (A2),

·         Adjusting for the Backup Peak Power Factor of 1,5x (A3)

·         Adjusting for DC/AC Conversion and Transmission loss of 30% (A4) or a factor of 1,3x,

·         Adjusting California’s higher solar irradiance to Spain’s lower solar irradiance with an ESP/CA DNI Factorof 1,5x (A5.c),

·         Adjusting the average capacity factor to the Winter Capacity Factorof 1,8x (A6).

Total required adjustments are 1,6 x 1,5 x 1,3 x 1,5 x 1,8 = 8,4x. Thus, the total required area of PV-Spain only for Germany becomes ~35.000 km2 (8,4 x 4.220 km= 35.448 km2). Since solar panels last on average 15 years, this translates to ~2.300 km2 of new solar panels to be built every year in perpetuity.

Considering that Solar Star in California has an installed capacity of 747 MWDC, then PV-Spain will have a total installed capacity of 2.000 GW or almost 3 times the 2020 installed solar capacity worldwide of 715 GW[13] (35.000 km2 x 57,5 MW/km2 = 2.013 GW). Please note that PV-Spain provides only for 1/5th of Germany’s total energy demand and that Germany accounts for 2% of global anthropogenic energy CO2 emissions not accounting for methane.

PV-Spain with an area of ~35,000 km2 is oversized to produce the electrical energy required for Germany in wintertime. Excess output is nominally zero in mid-winter and increases to a maximum in midsummer. Integrated over a year, generously about half of PV-Spain is producing excess power, albeit intermittently, which could be used for green-hydrogen or for other purposes such as smelting (see Section 3.4).

The authors would like to point out here that the area required of PV-Spain may be reduced substantially if the backup capacity would be increased by a factor of ten. This reduction would be possible if such backup – possibly also in the form of hydrogen – could store half a year of Germany’s electricity demand, such that the energy collected and stored in the summer can power a part of Germany’s winter demand. To match the European Union’s electricity requirements, the above numbers will all have to be multiplied by six.

3.2.      Storage Capacity or Backup

It is evident that all intermittent forms of power generation require a backup even if the sun shines “almost” every day or the wind blows “almost” every hour. The backup has to be such that the resulting power availability at the consumer is more than 99% reliable at all times. An economy that cannot provide reliable power all the time risks human life and loses its economic relevance in the global context.

We will make two calculations. A) Calculate the backup capacity required for one single day, assuming the sun shines every day in Spain. B) Calculate the backup for 14 days of cloudy weather, which happens rarely but has occurred in Spain in January 2021 with a 50 cm snowfall over several days, requiring several days more to melt from PV-panels as temperature were sub-zero. The reader should make his/her your own calculation.

One day of Germany’s demand equals 1,5 TWh (A1). It appears that storage matching this daily demand would suffice. However, again as specified above, the following adjustments are required:

·         Adjusting for the Battery Storage Utilization Factor of 1,7x (A8),

·         Adjusting for the DC/AC Conversion and Transmission loss of 30% (A4) or a factor of 1,3x,

·         Batteries last 20 years (A8.c).

Thus, Germany’s one-day energy demand of 1,5 TWh has to be multiplied by a factor of 1,7 x 1,3 = 2,2x. Therefore, the resulting required one-day storage capacity increases to ~3,3 TWh or the output of about 65 Gigafactories. Since batteries last for 20 years, more than 3 Gigafactories would have to produce 165 GWh of battery capacity annually in perpetuity just for one day storage capacity. During those production years, no Tesla could be produced.

A more realistic 14-day storage backup for Germany during the winter requires ~45 TWh of battery storage. The output of ~900 Gigafactories is required for construction of the batteries in one year, and then the output of ~45 Gigafactories or 2,25 TWh is required for annual replacement of batteries in perpetuity (45 TWh/50 GWh/20 yrs). For comparison, the replacement of batteries alone exceeds the current global battery production of 0,5 TWh in 2020 by a factor of 4 to 5x. To match the European Union’s storage requirements, the above numbers will have to be multiplied by six.

Figure 3: Global and Spanish Cropland Coverage, Fractional Cropland Area.
Sources: Ramankutty and Foley 1999, Cropland Intensity 1992, accessed 4 Sep 2020 at this link; Castillo et al., An Assessment and Spatial Modelling of Agricultural Land Abandonment in Spain (2015–2030), accessed 4 Sep 2020 at this link.

3.3.      Spain vs. Sahara vs. California

In May 2020, energypost.eu[14] announced that “10.000 km2 of Solar in the Sahara could provide all the world’s energy needs”. The energypost.eu author referenced the renowned book of MacKay: “Sustainable Energy – without the hot air”[15]. This statement is refuted by the author MacKay himself who states on page 178 that “To supply every person in the world with an average European’s power consumption (125 kWh/d), the area required would be two 1.000 km by 1.000 km squares in the desert”. That is 2.000.000 km2 not 10.000 km2.

The authors’ calculations for Germany powered from Solar PV in the Sahara, adjusting for A5.c and Figure 1 irradiation in the various regions, are as follows:

1.     Southern Spain ~1.900 W/m2/p.a.

2.     Southern California ~2.900 W/m2/p.a.

3.     Sahara ~2.300 to 2.600 W/m2/p.a.

4.     India ~1.300 to 1.900 W/m2/p.a.

5.     South East Asia <1.500 W/m2/p.a.
(example Indonesia, Vietnam, Thailand, Myanmar, Malaysia)

The first observation is that, on average, India and South East Asia have worse sunshine conditions than Southern Spain. This is primarily a result of the Monsoon. For the Sahara at 22 ºN latitude, the DNI map (Figure 1) illustrates that, except for a core region, the Sahara has a lower DNI than Southern California but is superior to Spain. However, neither MacKay nor the authors of the energypost.eu article considered the following key problems with the Sahara or, in fact, with any desert-based solar solution: lack of water, lack of infrastructure, high temperatures, haze, dust, and, most importantly, sandstorms.

Nomadd[16], founded at Saudi Arabia’s King Abdullah University of Science & Technology in 2012, has studied this subject intensively and concludes that “Dust build-up is the greatest technical challenge facing a viable, desert solar industry. A 0,4-0,8% per day baseline yield loss caused by dust. 60% energy yield losses during and after sandstorms are widely reported. If left more than a day, dust particles from organics, dew and sulfur adhere to the panels”. Solar Star in California requires almost 200.000 m3 of water annually to wash the panels for dust control[17]. If dust conditions in the Sahara were similar (they are much more stringent), then rainfall over about 250 km2 would need to be collected and used for washing, requiring storage and distribution facilities as well.

Numerous peer-reviewed studies researched the issue of sandstorms and large solar parks in the desert, but so far, no commercially viable large-scale solution has been found. The Saudi Arabian Nomadd, however, suggests that the Nomadd system16, itself can work without water and clean a solar panel within two hours. The system has not been implemented at large scale and costs/maintenance and abrasive effects on the panel surface are to be detailed. Electrostatic methods removing dust from PV elements, as planned by ACWA in Saudi Arabia, have been studied and offer promise. No moving parts or water would then be required[18]. These methods reduce the need for water-surfactant cleaning but may not eliminate it.

In addition, the desert regularly reaches temperatures of over 50 ºC. Coupled with heating by the absorbed solar energy, the panels’ efficiency drops by at least 0,5% per ºC above 0 ºC[19]. This means that the typical temperature rises from a typical morning temperature of 10 ºC to an afternoon temperature of up to 50 ºC will cause a loss of up to 20% in efficiency. This requires an even larger PV-Sahara to meet the world energy demands. Further, the constant expansion-contraction from diurnal cycles of over 35 ºC stresses the panels’ electrical and physical connections, leading to failure. Lifetimes for PV panels in the Sahara Desert are likely to be well below the typical 15 years. NASA[20] concludes that “Solar power in the desert brings some challenges. According to IEEE Spectrum, extremely high temperatures can sometimes damage inverters, which convert the DC power made by the photovoltaics into the AC power needed for the grid. High voltage transformers are also subject to high temperature loss of efficiency and failure.”

In conclusion, even if the authors assume dust, haze, and sandstorms are not problems and assume a Sahara/CA DNI Factorof 1,1x and reduce the Winter Capacity Factorto an optimistic 1,3, the following applies:

Total required adjustments compared to California are 1,6 x 1,5 x 1,3 x 1,1 x 1,3 = 4,5x. Thus, the total required area of PV-Sahara for Germany becomes~19.000 km2 (4,5 x 4.220 = 18.990 km2). If one now takes the world 27.000 TWh vs. Germany 550 TWh, one has to multiply the 19.000 km2 by 49x, or ~1.000.000 km2, to provide electricity for the entire world with solar photovoltaics in the Sahara. This is half the area required by MacKay because he assumed average European consumption for the entire world. Presently, over 600 million people in Africa have no access to electricity at all. However, it should be considered that above calculation and in fact also MacKay’s numbers are too optimistic because of lack of water, lack of infrastructure, high temperatures, haze, dust and most importantly, sandstorms.

A large-scale solar park in the Sahara would negatively impact the climate by warming the atmosphere noticeably by ~1 ºC as discussed by Lu et al. in their Dec 2020 study Impacts of Large-Scale Sahara Solar Farms on Global Climate and Vegetation Cover12. In addition, the task of storage and transmitting the power to the consumers around the word would be significantly more challenging and there would not be sufficient raw materials available under any scenario to construct the required solar panels for the world.

Concentrated Solar Power (CSP – essentially a “solar furnace” where sunlight is focused onto a target to heat it) does not appear to be a viable alternative as demonstrated by numerous efficiency issues with California’s CSP plants. A proposed hybrid PV-CSP system would use the remaining portion of the solar spectrum that silicon cannot absorb to boil water for a Rankine Cycle engine. Ivanpah and other CSP plants in California produce little power in winter due to a 7x seasonal decline in the capacity factor[21]. Thus, the use of only a small part of the solar spectrum will be even more inefficient. In the context of H2 production, a hybrid approach might be considered.

Figure 4: Typical electricity demand curve and photovoltaic production. The photovoltaic peak must be approximately twice the demand peak.
Source: Nominal electricity demand curve with photovoltaic production schematic by the authors, adapted from EnergyMag accessed 4 Sep 2020 at this link.

3.4.      Hydrogen and PV-Spain

H2 can be produced via electrolysis using PV-Spain’s excess electricity generation in summers. European governments suggest that “green Hydrogen“ will solve the intermittency problem of wind and solar via synthetic production of H2 as an energy carrier. However, with today’s technology hydrogen’s low volumetric energy density and high cost to transport is a barrier to the wide use of H2. Compressed H2 storage requires heavy duty storage cylinders of substances that do not become brittle as H2 permeates the material. More energy is required to compress or liquefy and transport H2 – energy which must also be derived from the excess energy from PV-Spain available during summer months.

On the subject of transport, Bossel et al.[22] concluded that “At 200-bar, a 40-ton truck delivers about 3,2 tons of methane, but only 320 kg of H2, because of low density of hydrogen and because of weight of pressure vessels and safety armatures. About 4,6 times more energy is required to move H2 through a pipeline than is needed for the same natural gas energy transport.” Natural gas pipelines may suffer from Htransport. H2 tends to permeate steel pipes, making them brittle and increase failure rates. ACWA in Saudi Arabia plans to produce ammonia in combination with H2 to ease the transportation burden of Hydrogen[23]. We have not considered the efficacy of this hybrid H2-NH3 concept.

It should be noted, however, that significant research and progress has been made in recent years in relation to so-called “Hydrogen Sponges” (see Morris et al. 2019, and Northwestern University as example[24]). Some candidates appear to reach 8% by weight of H2. The materials used are relatively inexpensive and abundant, such as transition metals and carbon lattices as a scaffold for the metals. In the not-too-distant future, this work promises to lead to an “H2-Revolution” allowing for an appropriate medium for storing H2 in a dense manner presenting a potentially viable alternative to lithium-ion battery storage. A 500 kg Tesla battery, for example, contains less than 100 kWh of energy. The metal-organic H2 ‘tank’ with 8% H2 by weight contains about 1.300 kWh of energy, or over 13x the energy density of the Tesla Li-ion battery. That would translate to a range of over 4.000 km. Refueling, therefore, would not be a daily task.

PV-Spain with an area of ~35,000 km2 is oversized to produce the electrical energy required for Germany in wintertime. Excess output is nominally zero in mid-winter and increases to a maximum in midsummer. Integrated over a year, generously about half of PV-Spain is producing excess power which can be used for hydrogen.

At an average annual capacity factor for Spain of 16,5% (see A6), PV-Spain with 2.000 GW installed capacity produces about 2.900 TWhDC of electricity (2.000 GW x 16,5% x 8.760h = 2.891 TWh). Instead of battery powered backup, hydrogen may be produced in Germany near the point of consumption. Electrolysis of H2O to H2 and then the use of H2 in a fuel cell may yield an overall net efficiency of ~40%. Then, there is the additional 30% AC/DC and transmission loss. Thus, PV-Spain would yield ~800 TWh of power in Germany annually via H2. This would replace the entire battery backup calculated above and would be sufficient for Germany’s entire electricity consumption plus a large portion of the energy requirements for the transportation sector. The other option is to use “only” the excess power produced in PV-Spain of ~1.450 TWh (half of 2.900 TWhDC) and convert this to ~600 TWh of usable hydrogen for the transport sector (assuming 30% AC/DC Transmission loss and 60% electrolysis efficiency). However, the physical challenges of transporting H2 effectively over larger distances remain and have been covered above.

The authors note that a hydrogen-based storage solution does not solve the underlying issues of solar installations illustrated in this paper, which are mainly high raw material input, low energy density, and low eROeI.

Figure 5: California solar photovoltaic capacity factor 2018-2020.
Note: Values for 2019 and prior years are final. Values for 2020 are preliminary. For 2020, only data from January to November is considered.
Source: EIA, accessed 3 Jan 2020 at this 
link

4.      Raw Material Requirements

For the solar panels: Global production of silicon has been about 7,5 million metric tons p.a. since 2010[25]. About 2-4 kg of Si are required per 1 kW nameplate 6-7 m2 solar panel[26]. The authors assume 2 kg and 7 m2 or 0,29 kg Si per mof solar panel.

This means the current global silicon production could yield 26.000.000.000 m2 or 26.000 km2 of solar panels annually (7.500.000.000 kg silicon ÷ 0.29 kg/m2). Since we need to build one time 35.000 km2 and then 2.300 km2 of solar panels every year in perpetuity just for Germany, this translates to one time ~10 million tons of silicon or 1,35x global silicon production and then ~660.000 tons of silicon annually or ~9% percent of current global silicon production in perpetuity. Of course, you would have far less silicon left to produce any other globally required silicon product such as computer chips or glass. On a side note, polycrystalline silicon thin films could allow a larger area of photovoltaic, but as of today would translate to half the quantum efficiency and lower stability requiring more frequent replacement.

Silicon has been addressed above, but high-quality silver which is produced primarily in Latin America and China is also a critical ingredient for solar panels. CRU estimates that in 2019 about 11% of global 27.000 tons silver production went into solar panels and that one solar cell requires about 0,1 mg of silver[27]. Assuming 72 cells per 2 m2 panel, this translates to about 7 g of silver per 2 m2 panel or 3,5 tons of silver per km2. Since we need to build one time 35.000 km2 and then 2.300 km2 of solar panels every year in perpetuity just for Germany, this translates to one time ~120.000 tons of silver or 4,5x global silver production and then ~8.000 tons of silver annually or ~30% of current global silver production in perpetuity. Recovery of silver from recycle panels would be essential. A similar conclusion was reached by Zoltan Ban[28] whose requirement is twice the amount of silver that the authors assumed. As per today, the use of alternate materials such as aluminum or organic conductors results in lower panel efficiency and shortened lifetimes of the panels. To match the European Union’s electricity requirements, the above numbers will have to be multiplied by six.

For the batteries: To calculate the approximate material requirement for a battery park with 45 TWh nameplate capacity using Tesla’s newest technology, the weight for one Tesla battery could be assumed to be about 500 kg with 85 kWh capacity, a factor of 5,9 kg per kWh[29]. However, to be generous the authors halve the battery weight to 250 kg, to a currently still impossible 2,9 kg per kWh, in further calculations.

Considering that 1-2 % of ore body mined end up in the battery (A7.a) and accounting for halving the battery weight, this would translate to 8-15 million tons of raw materials p.a. for one 50 GWh factory that need to be mined, transported and processed such as lithium, copper, cobalt, nickel, graphite, rare earths & bauxite, coal and iron ore (for aluminum and steel). In addition, the mining, transportation and processing of these raw materials requires significant energy.

In summary, the raw materials required for batteries to keep PV-Spain backed up for 14 days would translate to one time demand of 900 Gigafactories (45 TWh) or 7-13 billion tons and then 45 Gigafactories (2,25 TWh) or 0,4-0,7 billion tons of raw materials annually in perpetuity. For battery replacement alone, this equals 0,5-1% of all globally mined raw materials of 92 billion tons[30] just to create backup for Germany (a little over 15% of the EU), a country which is home to ~1% of the global population. To match the entire European Union’s storage requirements, the above numbers will have to be multiplied by six.

Other materials to build the required 2,25 TWh of battery capacity annually in perpetuity for Germany include[31]:

·         ~6x current global Lithium production (~880 tons Lithium per 1 GWh, 2020 production about 320.000 tons, ~70 % from China),

·         ~22x current global Graphite Anodes production (~1.200 tons Graphite anodes per 1 GWh, 2020 production about 210.000 tons, ~80 % from China),

·         ~2x current global Cobalt production (~100 tons Cobalt per 1 GWh, 2020 production about 120.000 tons, ~80 % from China), and

·         ~8x current global Nickel Sulphite production (~800 tons Nickel Sulphite per 1GWh, 2020 production about of 230.000 tons[32], ~60 % from China).

5.      Summary

Unless the safety, space, environmental, raw material, and energy considerations can be overcome, PV-Spain is a poor choice for solving Germany’s, Europe’s, or the global power dilemma. Alone the material requirements for the panels (see silicon and silver) or batteries cannot be met. Moreover, the energy required to build and maintain the batteries for such a large solar facility in Spain – also referred to as energy-Return-On-energy-Invested eROeI – have not yet been considered in this paper.

If it does not make sense to replace Germany’s power demand (or a little over 15% of EU demand) with solar from Spain, why would it make sense to replace alone a fraction of power requirement from solar panels installed further North of Spain or in India or Asia for that matter, where the natural sunshine conditions are worse?[33]

Alternatives to currently available solar photovoltaic technology, as well as more research to understand the material and energy input, are required for the proposed energy transition away from conventional power. Solar PV may be an environmental and economical choice for certain local power requirements without access to large scale grids, or to augment non-critical power requirements for selected – non-scale – power requirements.

Note: Silicon is produced essentially from silica (quartz stone), wood chips, and coal. Silicon is the second most abundant elementin the Earth’s crust, but so far only high-purity silica (quartz stone) is commercially viable. Metallurgical-grade silicon (MG-Si, about 98% purity) is manufactured at a process temperature of more than 2.000 ºC in electric arc furnaces that also require coal for reduction and energy. Both solar-grade silicon (SoG-Si, 99,9999% purity) and electronic-grade silicon (EG-Si, 99,9999999% purity) are then produced out of metallurgical-grade silicon in a refining process (“Siemens” or other processes) that again requires large amounts of energy and also chemicals.[34]


[1] Estimated data according to Agora and europa.eu, accessed 4 Sep 2020 at this link and this link.

[2] Germany’s actual peak power demand reaches up to 82 GW in the winter according to WikipediaAgoraBMWI,   and entso-e, accessed 3 Jan 2021.

[3] Facts on Solar Star and the World’s largest solar power parks, accessed 3 Jan 2021 at this link and this link.

[4] Solargis: Solar Irradiance Data, accessed 3 Jan 2020 at this link.

[5] Aleo Solar: Solar panel lifespan – The 6 things to know, accessed 3 Jan 2021 at this link.

[6] Nevada Gigafactory hoping to achieve 40 GWh output according to Rich Duprey, The Motley Fool, accessed 4 Sep 2020 at this link.

[7] Not much research has been done on this subject, this assumption seems realistic and conservative and has been vetted by the authors. Refer to Mark Mills, accessed 4 Sep 2020 at this link and this link.

[8] A 1C rate means the discharge current will discharge the entire battery in 1 hour. For a battery with a capacity of 100 Amp-hours, this equates to a discharge current of 100 Amps. A 5C rate for this battery would be 500 Amps, and a C/2 rate would be 50 Amps.

[9] Hagopian: Battery Degradation and Power Loss, BatteryEducation.com, April 2006, accessed 3 Jan 2021 at this link.

[10] BatteryUniversity: What’s the Best Battery?, March 2017, accessed 3 Jan 2021 at this link.

[11] Brook: The Catch-22 of Energy Storage, Energy Central on eROeI, August 2014, accessed 3 Jan 2021 at this link.

[12] Lu et al.: Impacts of Large-Scale Sahara Solar Farms on Global Climate and Vegetation Cover; AGU Research Letter, Dec 2020, accessed 15 Feb 2021 at this link; see also Li et al.: Climate model shows large-scale wind and solar farms in the Sahara increase rain and vegetation; Science Magazine, Sep 2018, accessed 15 Feb 2021 at this link

[13] Total global installed solar capacity in 2020 was 715 GW according to IEA, accessed 3 Jan 2020 at this link.

[14] Energy Post: 10,000 sq km of Solar in the Sahara, May 2020, accessed 5 Jan 2021 at this link.

[15] David MacKay: Sustainable Energy — without the hot air, November 2008, accessed 5 Jan 2021 at this link.

[16] NOMADD: The Desert Solar Challenge, accessed 5 Jan 2021at this link.

[17] BHE Renewables: Just the Facts – Solar Star Projects, March 2017, accessed 15 Jan 2021 at this link.

16 NOMADD: The Desert Solar Challenge, accessed 5 Jan 2021at this link.

[18] Kawamoto: Electrostatic cleaning equipment for dust removal from soiled solar panels, Journal of Electrostatics,

    Volume 98, March 2019, Pages 11-16, accessed 15 Jan 2021 at this link.

[19] Moharram et al.: Enhancing the performance of photovoltaic panels by water cooling, Ain Shams Engineering Journal, Volume 4, Issue 4, December 2013, Pages 869-877, accessed 5 Jan 2021 at this link.

[20] Nasa.gov: Catching Rays in the Desert, accessed 5 Jan 2021 at this link.

[21] Information on Ivanpah Solar Power Facility, accessed 15 Jan 2021 at this link.

[22] Bossel et al..: The Future of the Hydrogen Economy: Bright or Bleak?, Cogeneration and Competitive Power Journal Volume 18, Issue 3, 2003, accessed 10 Jan 2021 at this link.

[23] Air Products: ACWA Power and NEOM Sign Agreement for $5 Billion Production Facility, July 2020, accessed 18 Jan 2021 at this link.

[24] Northwestern University: Gas storage method could help next-generation clean energy vehicles, April 2020, accessed 10 Jan 2021 at this link; and Morris et al.: A manganese hydride molecular sieve for practical hydrogen storage under ambient conditions, Energy & Environmental Science, Issue 5, 2019, accessed 10 Jan 2021 at this link.

[25] Statista: Silicon production worldwide from 2010 to 2019, February 2020, accessed 4 Sep 2020 at this link.

[26] Stack Exchange, accessed 4 Sep 2020 at this link.

[27] The Silver Institute: Market Trend Report, June 2020, accessed 15 Oct 2020 at this link; and Statista: Global mine production of silver from 2005 to 2019, February 2020, accessed 15 Oct 2020 at this link.

[28] Zoltan Ban: Not Enough Silver To Power The World Even If Solar Power Efficiency Were To Quadruple, Seeking Alpha, February 2017, accessed 4 Nov 2020 at this link.

[29] Tesla’s Powerwalls designed for power backup have a capacity of 13,5 kWh and masses 114 kg including the frame. Assuming 100 kg is the net battery weight, this translates to 7,4 kg per kWh, so less effective than Tesla‘s car batteries, but the authors remain optimistic and overlook this.

[30] WU Vienna (2020): Material flows by material group, 1970-2017, accessed 4 Jan 2021 at this link.

[31] Benchmark Mineral Intelligence Data 2020, accessed 3 Jan 2021 at this link and this link.

[32] Despite the total nickel market being large (over 2,3 million tons) only a fraction is geared to making nickel sulphate chemical for lithium-ion battery usage, see also footnote 30 for more details.

[33] The latest 180 MW PV-park project in Germany by utility ENBW, located in Brandenburg, at over 50 ºN latitude, will not be able to achieve its purported energy production with realizable PV materials. The project is summarized by ENBW, accessed 20 Jan 2021 at this link.

[34] Bine Information Services, accessed 4 Sep 2020 at this link; and PV Education, accessed 4 Oct 2020 at this link.

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March 7, 2021 at 08:08AM