Capacity factors for electrical power generation from renewable and nonrenewable sources

Significance Capacity factor (CF) of an electrical generation plant is a direct measurement of the efficacy of this plant, or all power plants in a country, region, or the world. CF measures directly how much electrical power is produced by a plant relative to how much could possibly be produced at peak capacity. In view of a dire need to decarbonize and transition to clean energy, long-time average CFs provide a key component of reliable, unbiased insights into what is required to replace the current fossil fuel mix (coal, natural gas, and oil). CFs also are needed for an accurate quantification of the nominal generation capacity needed to replace and expand the current electricity infrastructure.

particular(8-10). Those wanting to use quantitative information for decision-making about complex issues therefore face the 23 standard predicament identified by Box(11): "all models are wrong, but some are useful". This does not mean that scientific 24 inquiry is useless. Even if "true models" do not exist (like the capacity factor model), we can still tell useful stories about 25 complex problems by selecting different perceptions of the system that we judge useful for our purpose (e.g., for guiding 26 action)(12). 27 From this point of view, the capacity factor model we present in this paper is a useful story that informs decision makers 28 about a key aspect of supplying uninterrupted electricity to end-users, and it cannot inform them about other aspects. Where 29 we seem to differ with some economists is that we are engineers, and focus on one subset of the problems 1 we deem to be 30 important, and economists seem to focus on another subset 2 . But this is not a mutually exclusive proposition. Our model 31 shows a very useful comparison of all sources of electrical power around the world, allowing people to make direct comparisons, 32 even if in a limited sense. The often unspoken and unreferenced differences among different tellers of the Green Transition Fig. S1. The common belief that "when the cost of the kWh of alternative sources will be lower than that of the conventional sources, the conventional producers will be forced out of the market" is simply not true. Power capacity related to intermittent sources grew dramatically in Germany, but the size of power capacity related to conventional sources remained largely unaffected. Due to a lack of an adequate storage capacity, conventional sources are still needed to guarantee biophysical viability, see the Patzeks' story in Section 10. As a matter of fact, before the arrival of alternative electric sources, the cost of producing electricity with "baseload end-uses" and "peak end-uses" was different, and still the two types of end-uses (techniques of production) coexisted without there being an issue. The red line shows actual power generation. Fig. 4 and text in(7). 104 The current decrease in the fossil fuel capacity factors could be associated with several interrelated causes. We explore two key 105 hypotheses: 106 Fig. S4. Total installed capacity for fossil fuels, i.e., coal, natural gas, and oil, and renewables, i.e., biomass, geothermal, hydro, solar, and wind. . a) Growth of electricity generated and GDP. b) Correlation between electricity growth and GDP growth. c) Electricity generated, the red line is historic data, the solid line is a projection based on real GDP growth, the dashed blue line is electricity generation based on the forecasted GDP. d) CF of fossil fuel sources; the red line denotes real values, the solid blue line is based on GDP growth, and the dashed blue line based on forecasted GDP. The blue shaded area represents the overestimate. The red shaded area is the mirrored values of the blue area, which illustrates the difference between the real GDP and current electricity values. The green area is difference remaining even if the overestimate is removed; in practice, it is a safety margin due to uncertainties.

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The following regional division was adopted 127

Capacity Factor by Region
165 Figure S7 shows a compilation of CFs by region. It allows a quick comparison of the suitability and/or importance of each 166 electricity source for the specific region. Each box plot summarizes data scatter. The weighted mean gives an insight into the 167 big electricity producers in each region and for all sources.  fig. S8a, which shows that while North America reduced its share of total electricity generated from biomass, the total capacity 173 installed grew over the investigated period.  Figure S9 shows the average CF and the weighted mean CF. It shows the distribution of capacity factors, and the weighted 175 mean illustrates performance of big producers. The discrepancy between the weighted mean and mean implies that some 176 countries in a given region have a strong reliance on biomass.  fig. S10 displays the full data, allowing us to observe the dynamic evolution. It indicates whether a given region is adopting or ditching the biomass technology. The missing points in the CIS region are due to low data quality, which necessitated 180 elimination of some data points.

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In the case of Oceania, it reflects Australia's capacity factor and China's dominance in Asia. These discrepancies can also be 190 due to the impact of more than one specific country with a strong reliance on fossil fuels.      D. Hydro. Figure S17 shows the information used to calculate CF. The historical data showed in fig. S17a show the predominant magnitude of electricity generated by water. Again, we can observe that Asia increased its installed capacity, consequently 209 increasing the electricity generated from hydropower, while the other regions were practically constant except Latin America 210 that saw a slight increase.   factor is dominated by Brazil, which is responsible for half of the hydroelectricity generated in the region. Africa has a handful 214 of countries, which are big producers that unbalance the weighted mean. In MENA, a considerable discrepancy between 215 countries with capacity factor near zero could be a consequence of political problems, and lack of river and lakes.      Figure S24 shows the average CF and the weighted mean CF. It shows the distribution of CFs, and the weighted mean 237 illustrates performance of big producers. Solar technology has few aspects that must be considered in the CF estimations.

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First, a broad expansion has occurred recently, implying that this technology will no longer be deployed at optimal locations, 239 and the solar PV CF will decrease as a consequence. Some regions are more suitable and do not suffer from severe impacts due 240 to seasonality, which explains the variance of reported values.  242 presents the full data, allowing us to observe the dynamic evolution. For solar PV, we observe that mean and weighted mean are close in the majority of the regions. In the case of Oceania, after 2010, more countries adopted solar power generation, but 244 as previously mentioned, Australia is the heavyweight in this region. North America has a higher mean because of the U.S.

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Virgin Islands that reports capacity factors in the range of 0.25. the magnitude of electricity generated by wind turbines. We observe that Europe was the leading region in installed capacity, 250 and was recently surpassed by Asia.  has notably less installed capacity, but and the share of electricity generated by wind is similar, which is caused by the higher 254 CF in comparison to Asia and Europe. It is a good illustration of how different technologies are suitable for each region.  the full data, allowing us to observe the dynamic evolution. Interestingly, in the majority of regions, the mean and weighted 257 mean close. In Oceania, the weighted mean is higher than the mean, which is opposite to Asia.  (0.57). In addition, other countries have CFs that seem to be out of range, and proper judgment should be applied before using 263 them. Figure S29 shows the data histograms for all sources. This figure should be consulted as a reference to identify outliers 264 mainly for solar PV and wind. For example, it is physically impossible to have an annual capacity factor for solar PV higher 265 than 0.42.

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Table S1. Capacity factor by countries

Country
Biomass Fossil Geothermal Hydro Nuclear Solar Wind       by Siemens for the second author. Its performance decreased by 10 % in 2020, compared with the other years. This efficiency 280 decline was caused mostly by an irradiance decrease in 2020. Its sun-tracking system needs to be properly maintained to 281 ensure a good performance. In this case, even a single six-month delay in cleaning the panels and tuning their tracking systems 282 impact the array's performance. 283 We should add, that the Càceres location in Spain is relatively dust-free and very sunny. The only serious dust comes from 284 the Sahara desert and from droughts.  Overall,these detailed data show that solar PV arrays are very sensitive to many environmental factors. Proper maintenance 290 is essential to keeping these arrays performing well. In one case, we could clearly see the drop in performance that occurred in 291 2020, due to lack of maintenance imposed by COVID-19. The ground arrays in Austin were washed twice in 2020 by the senior 292 author, who spent the COVID lockdown on his property. 297 Figure S33a shows the actual performance in Austin. The most recent array (Array 3) performs better than arrays 1 and 2.

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Overall, the arrays are delivering 64 % of the expected power output if we only consider incident radiation. Figure S33b shows 299 the actual performance for the array in Càceres. The initial observation is that in some months, the performance was above

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Our main points about economics can be summarized as follows:  2. There is a critical capacity factor below which energy return on investment becomes too small, say 3-5:1, to run current 310 complex infrastructure and physics destroys the system. Our case studies below show how this may happen. and giant electrical power storage/backup systems, renewables will continue to play an increasingly important role.

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As to the first bullet, for every "engine" (power supply system) ever constructed there are numerous factors that contribute

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We are engineers, jointly with 26 years of experience in designing, installing, monitoring, maintaining and using solar PV 323 panels. Thus, our own economic analysis is simplified, case-specific and applied to solar PV systems, but we will cite a few 324 definitive papers that analyze economics of green transitions. the average the Patzeks export roughly 50% of the electricity they produce, they really need external grid electricity at least 333 12h a day, and more during winter, see Figure S34.   (FiT) payment of around £20/MWh. This payment is funded by a levy on energy bills. Additionally they receive a Renewable similar to that in Càceres, but with 500 suns concentration and 37% efficiency cells (Càceres was 400 suns and 27% efficient), 387 but in no case, not one of the Amonix systems has performed as predicted so far, and only 100 MWp were sold worldwide by 388 academic theoreticians, who promised Energy Return on Investment (EROI) of 33 to 41:1, but never struggled with real life 389 systems. By 2022, most if not all of these systems were abandoned or replaced. This is just one of the many difficulties with 390 theoretical analyses that can be orthogonal to reality.   . This is what one must do when there is no or little grid, like in Puerto Rico, a failing US territory that seems to be comparable to Lebanon. overestimates that are frequently reported. 460 We are keenly aware that several economic aspects play a role in the decision to deploy a certain project. However, economic 461 analysis has its own shortfalls. Whenever we compare the prices of renewable and fossil electricity systems, we tend to forget 462 that these systems are fundamentally different. The real-life performance of all major electricity sources is based on their 463 physical limitations that will not change because the market is favorable. Potential material limitations, such as that of copper, 464 are mentioned in one sentence only, because they are outside of the scope of this paper. However, these potential material 465 constraints will force choices that guarantee the optimal performance of any device to be installed. The capacity factor tells us 466 how much we can rely on a source and the role that it can play.

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A great example is the current war in Ukraine and the pressure on certain countries to cut ties with Russia. The UK 468 answered these challenges by setting up a plan that will expand nuclear power capacity and give the energy fields of the North 469 ( †) The economist Joseph Stiglitz, a Nobel laureate, said(39) the market failed to accurately price in the risk -however unlikely it may have seemed at the time -that Russia could decide to reduce or withhold gas to apply political pressure. It would be like figuring the costs of building a ship without including the cost of lifeboats. "They didn't take into account what could happen," Mr. Stiglitz said.
energy is the energy that we do not have. Nuclear electricity will be the backbone of a robust energy transition in the UK. Two recent papers proposed a sophisticated analysis of energy returned on investment (EROI) for the static(41) and 477 dynamic(42) grid penetration by the variable output renewables. Here is a summary of the latter paper: "A novel methodology 478 is developed to dynamically assess the energy and material investments required over time to achieve the transition from fossil 479 fuels to renewable energy sources in the electricity sector. The obtained results indicate that a fast transition achieving a 100% One of the many economic outcomes of different green energy transition scenarios in this paper is shown in Figure S42. After 498 the initial stimulation of an economy by the high initial capital spending on a green transition, this economy goes invariably 499 into contraction caused by the low capacity factor of renewables (their low EROI). So, for the rich countries, the only long-term 500 answer to climate change is to continue with a green energy transition and consume much less fast. 501 Fig. S42. Figure 29 in(43) compares growth rates of an economy during the faster and slower transitions to a green economy. The main difference between the slower/faster transitions is that in the slower transitions the variations in particular variables (e.g. energy prices, unemployment, output growth) are smaller, but last for a longer period of time. However, the smaller variations but longer durations approximately offset each other, so that by the time the economy has returned to a steady state it is in roughly the same place (e.g. with regards to the level of output, unemployment, prices, the wage profit split, etc.). Figure reproduced with a permission from the authors.