### Introduction

Some EROI authors have suggested that renewable sources of energy have much lower EROI ratios than generally believed. The reason is that published EROI figures do not include**all**of the energy investments which were incurred. There are many small energy investments which are difficult to count, for example, the energy investments for smelting aluminum used to build metal fences around a power plant. Those tiny energy investments are omitted from EROI analysis. As a result, the EROI ratio is overstated for renewable sources of energy.

There are many small energy investments for any source of electricity, which are too numerous and too minor to count. For example, the EROI of solar power (commonly quoted as 10) does not include the energy investments to replace truck tires which wear out during the delivery of solar panels to solar farms. Nor does it include the energy investment of the steel-making equipment used to manufacture the steel for parts for that truck. And there are thousands of other little uncounted energy investments, such as energy investments for fences around the power plant, roads to the plant, security cameras, replacement of transportation equipment, electricity used in the plant office, and so on. Any one of those energy investments might be quite small, but taken together, they can add up to a lot, because there are so many of them. When those little energy investments are added up, the EROI of renewable electricity will be reduced considerably.

Of course, the same holds true for all sources of energy. The EROI of coal-fired electricity, for example, does not include the energy investments of building roads to the coal power plant, building a railway to the coal power plant, replacing locomotives which have worn out delivering coal to the power plant, and so on. Those energy investments could be considerable and could greatly reduce the EROI of coal-fired electricity.

As a result, EROI is overstated for all sources of electricity. The only way to get an accurate EROI value is to include all the small uncounted energy investments, or at least try to estimate them.

Dr Charles Hall has referred to this as "extending the boundaries" of EROI analysis. Prior EROI analyses have not included indirect energy investments such as degradation of transportation equipment. It was considered outside the scope of the EROI analysis. As we extend the boundaries of EROI analysis, we include more and more energy investments that occurred further up the supply chain.

The purpose of this article is to extend the EROI boundaries all the way, and to include

**all**energy investments for each source of energy, no matter how minor or indirect. This will be done for coal fired electricity, nuclear power, solar PV, and wind power. The result is a convergence of EROI values for different sources of electricity, as will be shown.

### Method of estimating extended EROI

The great difficulty with extending EROI boundaries is that it becomes more and more difficult to gather the information needed, the further you extend the boundaries. The uncounted energy investments become more numerous and smaller. As an example, a coal-fired power plant requires a railroad connection. That railroad connection requires railroad ties, which are made out of wood, which were taken from a tree, which was chopped down using a chainsaw, which has a plastic gasoline tank, and the plastic was made out of oil, which was extracted by an oil well, and the oil well was made out of steel, taken from a blast furnace. How do we account for the energy investment for the degradation of the blast furnace, which is fully seven degrees removed from the top of the supply chain?At some point, the energy investments are so far removed, and there are so many of them, and they are so little, that it becomes difficult to add them all up. It would be nearly impossible to track down all this information.

Hall and Prieto attempted to extend the EROI boundaries for a solar PV plant[1]. They accomplished this by adding up all the monetary costs for things like roads to the power plant, security cameras, fences, and so on. Prieto was a manager at a solar power plant, so he had access to the relevant accounting information and added up the prices for everything. Hall and Prieto then converted those prices to energy by means of a formula (6 megajoules per dollar, if I recall).

It was a good idea to estimate uncounted energy investments by looking at prices. That was a significant contribution of Hall's and Prieto's book.

However, it is not necessary to add up the prices of all these little things like roads to the plant, security cameras, and so on. All of those things are

**already included**in the final levelized price of wholesale solar electricity. For that matter, all monetary expenditures, along the entire supply chain, no matter how minor or indirect, are already included in the final levelized price of solar electricity.

The price of something includes all the monetary costs, along the entire supply chain, to obtain that thing. Each supplier in the supply chain keeps track of all its monetary costs, and passes along all those expenses to the supplier above it in the chain. All companies keep careful track of money and pass along all of their expenses. There is an army of accountants, spread throughout the economy, who do this. They pass along

**all**monetary costs, no matter how indirect. As a result, the final price of a thing, is a kind of summary of all prices paid to obtain it, throughout the entire supply chain.

Because of this, we can estimate the uncounted energy investments for a source of energy by just looking at the price of it. The price of electricity from solar PV, for example, includes the price of

**everything**needed to obtain it.

Thus, we can estimate the extended EROI of a source of electricity using the following algorithm:

- Obtain the levelized cost of electricity for a source (from Lazard[2], for example).
- Subtract the top-level interest expense, which is not an energy investment.
- Also subtract the money which was spent on obtaining energy for the counted energy investments. This can be done using published EROI figures. Those energy investments have already been counted, and we don't want to double-count them.
- What is left is the amount of money spent on everything else. We'll call this "miscellaneous expenses". It includes things like profits, salaries, taxes, interest paid on transportation equipment like trucks, and everything else, for every contractor and sub-contractor and supplier, up the entire supply chain. It also includes all money spent on obtaining energy, throughout the entire supply chain.
- We must estimate how much of this "miscellaneous" money was spent on energy, and how much was spent on everything else, using a factor. We'll refer to that factor as the "uncounted energy investment factor".
- We must multiply the uncounted energy investment factor by the amount of money spent on miscellaneous expenses.
- We then add that "uncounted" energy investment to the energy investment from published EROI figures. After which, we can calculate an "extended EROI" by just performing the division again using the energy investment with extended boundaries.

Let's try extending the boundaries for a typical solar PV plant. We'll assume that the levelized cost of wholesale electricity for solar PV is $0.05/kwh (as per Lazard), that 50% of that money is spent on interest (which is common for projects which involve almost the entire cost upfront and which last decades), and that the EROI of solar PV is 10. In which case, the amount of money for miscellaneous expenses for solar PV is $0.02/kwh (interest was $0.025, and counted energy investments were $0.05, and subtracting both of those leaves $0.02 remaining for miscellaneous expenses). Let's assume, as an initial estimate, that 10% of the miscellaneous expenses are payments for energy. We'll also assume that the price of the energy for investment is $0.01/megajoule. With a conversion factor of 0.10, $0.002 of the wholesale price was spent on uncounted energy investments. At $0.01/megajoule, that translates into 0.2 megajoules, or 0.0556 kilowatt hours. Thus, the counted energy investments for solar PV were 0.1 kwh

_{invest}/kwh

_{delivered}(or 1/eroi), and the uncounted were 0.0556 kwh

_{invest}/kwh

_{delivered}, leading to a total extended energy investment of 0.1556 kwh

_{invest}/kwh

_{delivered}, or an extended EROI of 6.43 for solar PV.

If we perform the same procedure for various sources of energy, we obtain the following extended EROI ratios:

Source | Extended EROI | Notes |

Solar | 6.43 | |

Coal | 5.29 | (assumes EROI of 20 after waste heat loss, $0.10/kwh, 40% interest) |

Nuclear | 6.22 | (assumes EROI of 30, $0.10/kwh, and 50% interest) |

Wind | 9.00 | (assumes EROI of 20, $0.04/kwh, and 40% interest) |

Of course, the above figures are dependent upon an uncounted investment factor of 0.10. In other words, we assumed that 10% of miscellaneous expenses are devoted to buying energy products. However, the choice of 0.10 was little more than a guesstimate.

At this point, we could estimate an accurate uncounted factor by looking at the economy as a whole. We could examine a first-world economy which gets most of its electricity from coal-fired plants and try to estimate how much of its energy expenditure is devoted to the energy industry itself, then subtract the the energy investments which had already been counted.

I suspect that the factor of 0.10 was too high. If coal-fired plants, for example, consume 18.9% of the energy they produce, then this would have been obvious in Sankey diagrams of the US economy back in the 1970s and 1980s. As a result, let's use a different factor of 5%. In which case, the extended EROI ratios for different sources of electricity are:

Source | Extended EROI |

Solar | 7.82 |

Coal | 8.37 |

Nuclear | 10.43 |

Wind | 12.34 |

We can use different estimates for the uncounted energy investment factor. With smaller factors, the EROI ratios of all sources of energy increase, and the ratios for coal and nuclear power increase by more.

### Interpretation of Results

Right away, it is obvious that the extended EROI ratios for different sources of electricity are fairly close together. This is totally unsurprising. The**monetary prices**of those sources of electricity are also somewhat close together. Any conversion of money into energy would cause the EROI ratios for different sources of energy, of the same price, to converge.

Furthermore, the high-EROI sources of electricity (such as coal-fired electricity and nuclear power) are also moderately more expensive. This implies that the "uncounted" energy investments are

**higher**for those sources of electricity than for renewables, using any consistent conversion of money into energy. As a result, extending EROI boundaries will reduce the EROI ratios for high-EROI sources of energy (such as coal and nuclear) the most. In turn, that will cause the EROI ratios of different sources of energy to converge

**even more strongly**.

The result is

**no large difference**between the extended EROI ratios of different sources of electricity.

Of course, we may have chosen an uncounted factor which was

**still**far too high, even after revising it downwards. In which case, extending EROI boundaries would make little difference for solar PV, and published figures are already fairly accurate. Using very small factors will result in less than a 10% adjustment of published figures for solar PV.

It is just not possible that solar PV has a drastically low extended EROI ratio while other sources of electricity have much higher extended EROI ratios. Solar PV is

**much cheaper**than alternatives, so any attempt to extend boundaries will cause a strong convergence of EROI values. This implies one of two things. If extending boundaries makes little difference, then the EROI of solar PV was fairly accurate beforehand and is above 9. If extending boundaries makes a large difference, then the EROI ratios of other sources of electricity will be reduced by more, and all sources of electricity will have similarly low extended EROI ratios. There is

**no possible**factor for uncounted energy investment which would yield a very low extended EROI for solar power and very high extended EROI ratios for other sources of electricity. The higher the factor, the more the extended EROI is reduced for coal and nuclear power compared to solar PV. Making assumptions of extremely high uncounted energy investments will result in

**lower**extended EROI ratios for coal and nuclear power than for solar PV.

One other conclusion from the above figures is that coal-fired electricity has much higher "uncounted" energy investments than other sources of electricity. This is also totally unsurprising. It has frequently been pointed out that solar PV plants require fences and security cameras, which incur energy investments that had not been counted. That much is clearly true. However, coal-fired plants require a railroad connection with a mile-long train full of coal arriving every few days, for the entire lifetime of the plant. That imposes massive "uncounted" energy investments, including fuel usage by locomotives, degradation and replacement of locomotives and rail cars, wear on the national rail network, and so on. Those energy investments are massive and

**ongoing**, and would obviously outweigh the trivial energy investments of installing cameras or fences once. Those much higher "uncounted" energy investments for coal-fired electricity are reflected in its higher price.

One final point bears mentioning. The extended EROI ratio of solar PV (indicated above) is considerably higher than that estimated by Hall and Prieto. Their analysis was useful, but it's years old. The field of solar PV moves quickly. Hall's and Prieto's estimate has fallen out of date.

Hall and Prieto estimated the extended EROI of a 1-megawatt solar plant. However, newer solar plants are much larger, frequently larger than 100 megawatts. There is an economy of scale when it comes to uncounted energy costs. Solar plants which are 100x larger do not require 100x as long of a road leading to the plant, or 100x as many employees, or 100x as long of a fence surrounding the plant, and so on (in fact, a solar plant which is 100x larger would require only 10x as long of a fence surrounding the plant, if we assume that all solar plants are laid out in a square shape, which implies a 90% reduction in energy investment for fences, per kilowatt-hour). As a result, Hall's and Prieto's analysis is out of date, and the actual extended EROI of solar PV would be significantly higher now, as indicated in the table above.

### Summary and Conclusion

Extending EROI boundaries as far as possible, while also assuming high uncounted energy investments, causes the EROI values for different sources of electricity to converge strongly. The result is no large difference between EROI values for different sources of electricity. If we assume that uncounted energy investments are extremely low, then published figures for the EROI of solar PV are already fairly accurate.**References**

[1]

*Spain's Photovoltaic Revolution*, Charles Hall and Pedro Prieto, Springer, 2013

[2] Lazard Levelized Cost of Energy, version 11.0. https://www.lazard.com/media/450337/lazard-levelized-cost-of-energy-version-110.pdf

**Errata**

This article was originally published with a minor arithmetic error which was corrected several hours after the initial publication.

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