EROI and the limits of conventional feasibility assessment—Part 2: Stocks, flows and power return on investment

Update, 24 July 2015: while doing some background work for a forthcoming post that draws on data presented here, I reconsidered the best basis to use for the PV comparison. The post has now been revised to reflect my updated thinking, specifically using a higher EROI for PV of 4.17:1, rather than the original of 2.45:1, by considering only a subset of Prieto and Hall’s energy costs. In the course of making this change, I also discovered an error in the original calculation, in the ratio of emplacement energy to operating & maintenance energy for PV (relatively minor impact only, from 0.59 to 0.55). This is also corrected here.


An important principle to bear in mind for inquiring into the ways that energy-related considerations influence human societies is that, by and large, economies are dependent for their present functioning not on the total stocks of energy sources they might have at their disposal, but on the current rate at which energy sources are supplied and utilised. This is a key distinction in understanding the phenomenon of peak oil. “Peak oil” for a given field or territory is taken to have occurred at the point in time for which the production rate for petroleum—appropriately defined, i.e. by grade or composition—reaches a maximum, and thereafter declines. But at such a time, as much as half of the ultimate resource may still be available. Peak oil doesn’t imply that we’re on the brink of “running out of oil”. What it means is that the production rate is at the highest level that will ever be achieved. It is the change in rate that is central for understanding the implications of the phenomenon for future social prospects, as a declining aggregate oil production rate (i.e. where a shortfall from one region cannot be compensated by increased production from others) implies greatly foreshortened prospects for further growth in the non-energy related economic activity enabled by that production, and in fact very likely implies commensurate economic contraction. The same principle applies to any resource that is ultimately stock-limited, but for which it is the supply rate upon which the present nature of the economic activity enabled by that resource depends.

A corollary of this is that in assessing the present feasibility and future prospects for an energy source, we need to focus on the achievable supply rate, rather than fixating on overall resource size. This applies whether the resource is ultimately stock-limited (fossil fuels and uranium) or rate limited (solar radiation, wind, hydrological flows etc). We see the implications of this illustrated clearly in the 3 to 4 orders of magnitude difference between incident solar radiation at the Earth’s surface, and estimates of technical potential for electricity from solar sources, discussed in Part 1. But it also helps to explain why extraordinarily large estimates of non-conventional fossil fuel resources have had greater success to date driving growth in financial markets than in physical economic output.

The physical processes by which goods and services are produced are affected not in the slightest by the stock of potential future inputs “in the ground”; what affects current performance and its ongoing expansion is the rate at which inputs are supplied, and how readily that rate can increase. There are no simple generalistaions that can be offered regarding correlations between resource size and achievable supply rate. Nonetheless, it’s certainly fair to say that a large energy resource provides no guarantee of commensurately high energy supply rate from that resource. In fact, supply rate is more directly dependent on the scale of physical and institutional capital—that is, the quantity of infrastructure, plant and equipment, and the extent of the social systems for their coordination—available to convert primary energy sources to fuels and electricity, and to distribute these to end users.

This distinction between the relative importance of resource size and capital investment is obvious when we consider that across the vast majority of human history, the energy sources that we are now burning through in a metaphorical blink of an eye remained almost entirely unexploited, despite many situations in which local populations were aware both of their presence and their fuel potential. A special report published recently by the International Energy Agency (IEA), World Energy Investment Outlook 2014, is especially relevant in this respect, and makes for sobering reading. Headline findings in the executive summary illustrate the strength of the relationship between capital investment and energy supply rate, but moreover, highlight the direction in which this relationship is heading:

  • More than $1 600 billion was invested in 2013 to provide the world’s consumers with energy, a figure that has more than doubled in real terms since 2000;
  • Over the period to 2035, the investment required each year to supply the world’s energy needs rises steadily towards $2 000 billion; and
  • Less than half of the $40 trillion investment in energy supply goes to meet growth in demand, the larger share is required to offset declining production from existing oil and gas fields and to replace power plants and other assets that reach the end of their productive life.[1, p.11]

The story told in the IEA report is starkly apparent: investment in maintaining current global energy supply rates is subject to sharply declining returns; we should expect the decline in marginal returns from further expansion of supply rates beyond current levels to be sharper still.

Power return on investment

There is a useful analogue between the principle that the size of a resource stock is not a good predictor of supply rate, and a limitation that applies to the analysis of energy supply systems on the basis of EROI or net energy. It’s this limitation that has previously led me to suggest (here and here) that to the essential analytical concept of energy return on investment, we need also to add the concept of power return on investment, or “PROI”. The analogue takes the following form: the EROI for an energy supply system tells us about the relationship between input energy and output energy, over the system’s full life-cycle (i.e. including manufacture, emplacement, operation & maintenance, and eventually, decommissioning). In quantifying the relationship between the lifetime gross and net energy that is potentially available from a supply system, EROI affords us a measure of the system’s overall “resource potential”. By expressing life-cycle performance in terms of a single value, though, we lose the considerable nuance associated with the rate of the energy flows into and out of the system, and how these change across its lifespan. As we’ll see, the staging of these flows has critically important implications for system viability when we’re interested not just in the addition of new supply sources at the margins of an existing system, but in transitioning entire energy supply systems from incumbent sources to alternatives—as is the case with proposals to replace fossil fuelled thermal electricity generation with generation primarily from solar and wind sources.

Readers who’ve been following for a while may note a recurring theme arising again here: EROI, in reducing system performance to a single variable, entails an extreme level of abstraction. As with any such process of abstraction, this has the benefit of making associated data sets more manageable, and enables straightforward comparison of alternative means for achieving given ends. With these benefits, though, comes the disadvantage of losing the ability to resolve finer details that might have important implications for the comparisons we wish to make. A key principle associated with this is that the value of the findings from any analysis methodology depends on the extent to which we keep the “methodological context” in mind when considering the findings—especially, being aware of the methodology’s underlying assumptions, and recognising that it will both “reveal and conceal” aspects of the situation in which we’re interested. Knowing what a particular analytical approach conceals is just as important as knowing what it reveals. I’ll refer back to this in Part 3, when I close out this series by looking briefly at Jacobson & Delucchi’s response to Trainer’s critique of their feasibility assessment (mentioned briefly in Part 1) for providing all global energy from wind, water and solar power.

Kessides & Wade’s dynamic EROI analysis

In the most general terms, the issue that I’m highlighting here arises due to the relationship between the energy required to emplace a supply system, the quantity of energy that this system then makes available, and the time-frame over which this energy is delivered. The argument for considering rates of energy investment and return, as well as the way that these vary over a system’s life-cycle, is established in detail by Ioannis Kessides and David Wade, in an article titled “Deriving an Improved Dynamic EROI to Provide Better Information for Energy Planners” published in the journal Sustainability.[2] Their principal interest is in developing a basis for assessing the capacity of a given energy supply system to “fund”, in energy terms, further emplacement of similar systems.

The authors note that energy payback period—the time for which an installation must operate in order to supply a quantity of energy equivalent to that required to emplace it—is often used alongside EROI to assess the net energy performance of supply infrastructure, but that these parameters alone are inadequate for assessing “self-funded” growth potential. To address this, they introduce as an additional parameter the doubling time for an installation—the time that it would take for it to provide sufficient energy to emplace further nameplate generation capacity equivalent to its own nameplate capacity. The model that they develop allows them to:

(i) identify the essential constraints on feasible rates of growth; and (ii) clarify why the single numerical values of the EROI are not by themselves sufficient for assessing the growth potential of alternative energy infrastructures–i.e. that it is important to analyze and understand the structure and time dependencies of the energy investments that are required for emplacing and maintaining these infrastructures.[2, p.2351]

In their conclusions, Kessides & Wade note that:

When the growth rate for a specific supply option is specified by societal need or by policy, the necessary energy input for growth of the chosen supply option will be diverted from societal usage – either by increasing its indigenous energy plowback fraction or by subsidizing its energy requirement from another supply option. While an EROI value well in excess of unity is necessary for self-supplied infrastructure growth, it is not sufficient; capacity factor and energy necessary for emplacement and for operation and time lags for licensing and construction also play an important role.[2, p.2354]

In arriving at this view, they present a comparison—based on IEA data for life-cycle assessment of a range of electricity generation sources in Japan—of a coal-fired plant and wind facility, each with nameplate capacity of 1,000 MW. Each installation has the same EROI (6:1) and operating life (30 years). An energy plowback rate of 20 percent is set for each. This means that 20 percent of the electricity generated is directed at all times towards the emplacement of further generation capacity of the same type. Despite having an operating & maintenance plowback rate a little over half that of the coal-fired plant, the doubling time for the wind facility is 28.5 years compared to only 1.3 years for coal. This contrasts with energy payback periods of 3.39 and 0.15 years respectively. The doubling time is dominated by the much lower emplacement energy per unit of nameplate capacity for coal compared with wind (coal=0.094 watt-years per watt; wind=0.637 watt-years per watt), and the much higher capacity factor for coal (coal=75%; wind=20%).

The data that Kessides & Wade use is from prior to 2002, and since then the emplacement energy for wind has declined significantly, while that for coal will have changed little. Higher capacity factors for wind are also now common—though there are basic limits to how much higher these can go. On this basis, the doubling time for wind is now likely to be considerably lower. On the other hand, an EROI of 6:1 for coal is far lower than is typically found in other studies. With this in mind, the significance of the example will likely be apparent: despite identical EROI for coal and wind in the original IEA study, wind’s capacity to scale up production using its own output energy is severely limited compared with coal. In fact, the doubling time for wind is only 18 months less than the plant’s operating life. Consider the implications of this: at an energy plowback rate of 20 percent, the wind facility will have only just enabled its own replacement by the end of its life. The doubling time can be reduced by increasing the plowback rate, but at the expense of electricity available for the supply system’s primary purpose of enabling other economic activity.

Given that the doubling time in Kessides & Wade’s analysis is a function of the endogenous energy plowback rate, it might be argued that the implications for viability of wind generated electricity are not as significant as the comparison figures suggest, because the option to divert exogenous energy flows (from conventional sources) towards the initial infrastructure build out, and then to operate the wind infrastructure under steady state (zero growth) conditions, remains open to us. The point that I make above about the doubling time for wind being only slightly less than the operating life is central to addressing this objection. For while Kessides & Wade’s original interest was in establishing a basis for assessing and comparing the endogenous growth potential for different energy supply systems, their general approach is also relevant for assessing a supply system’s potential to maintain a given level of nameplate generating capacity in perpetuity, by “funding”, in energy terms, its own replacement. For instance, using their model we could determine the energy plowback rate required to allow a supply system to pay back its emplacement energy costs over its operating life.

Over-sizing plants for self-funded replacement: a comparison of coal, wind and solar

Another way of considering this may be more useful though: taking a slightly different approach to Kessides & Wade, we can calculate the amount by which an installation of given nameplate capacity must be over-sized in order to provide sufficient excess net output energy over its life so that by end of life, it has “funded” new installations of equivalent capacity to its own. Assuming a constant rate of depreciation—i.e. that the installation “pays forward” each year an amount of energy equal to its own emplacement energy cost divided by the number of years for which it is designed to operate—the 1000 MW nameplate capacity wind facility must be over-sized by 127 MW, and the coal facility by only 5 MW. For comparison, using Prieto & Hall’s data for solar PV in Spain (partial energy input EROI=4.17, operating life=25 years, capacity factor=16%), a 1000 MW facility would need to be over-sized by 174 MW.

Calculations for each of these situations are available here (Excel spreadsheet). Note that the oversize capacity is sufficiently large to also replace itself, over the facility design life. So, after 30 years, the coal facility would emplace 1,005 MW nameplate capacity, the wind facility 1,127 MW and the solar PV facility 1,174 MW. It may be tempting to assess the significance of these figures by considering the amount of oversize capacity relative to the base nameplate capacity. So for instance, the wind facility oversize at 12.7 percent of the base capacity may not appear particularly onerous. This, however, would miss the principal insight revealed by the analysis, which is arrived at not by comparing oversize to base capacity for a given energy source, but by comparing the oversize capacities for different sources. It is the fact that the wind facility requires more than 25 times the oversize capacity of that for coal that is of real significance.

This still provides only a partial view though: the above comparison is based on a given nameplate capacity, but this does not take into account the consequences of intermittency—and in the case of solar PV, seasonal variation in insolation—for overall plant availability. We can get a rough idea of the significance of this by considering the lifetime average power output for the coal, wind and solar PV installations, and correcting the total installed capacity to bring this into alignment across the three sources. Taking this approach, we find that matching the coal installation’s 1,005 MW total nameplate capacity (628 MW lifetime average output across the facility boundary, after deducting operating & maintenance load) requires a wind installation of 3,768 MW total, or a solar PV installation of 5,649 MW total. To match the 5 MW oversize capacity needed by the coal installation to self-fund its replacement, the wind installation now requires oversize capacity of 426 MW (85 times the coal allowance), and the solar PV installation 780 MW (156 times the coal allowance).

The relative magnitude of these figures might give us some pause for reflection. Our current global socio-economic arrangements have evolved in the context of a very particular mix of fossil energy sources, including coal. The analysis I’ve presented suggests that the proportion of a fossil fuelled economy’s energy sector that is needed to service the sector’s own replacement could increase by several orders of magnitude in a transition to high levels of renewable energy. This starts to give some sense of the capital implications associated with high emplacement energy cost, and why it is that EROI alone gives us an incomplete picture. And this brings us finally to my proposal that, in comparing the relative viability of different energy sources to meet a given supply task, we might do well to look beyond energy return on investment to also consider power return on investment.

Two specific indicators that may be useful in this respect are power return on energy investment (PROEI); and power return on power investment for replacing an installation over its operating life (PROPI). My analysis extending the illustrative example from Kessides & Wade readily allows both of these to be calculated. The results are presented in Table 1 below, which also summarises the other data presented throughout the preceding section.

Parameter Coal Wind Solar PV
EROI 6 6 4.17
Operating life (years) 30 30 25
Capacity factor (%) 75 20 16
Equivalent lifetime average power output per 1000 MW installed nameplate capacity, after deducting operating & maintenance load (MW) 628 188 130
Energy to emplace a unit of installed nominal capacity (PJ/GW) 3 20 16
Operating & maintenance energy plowback as proportion of gross output (%) 16 6 11
Oversize capacity per 1000 MW nameplate capacity required for installation to self-fund energy for own replacement over operating life (MW) 5 127 174
Total installed capacity, including oversize to self-fund replacement, required to match lifetime average power output of coal installation with 1000 MW base nameplate capacity (MW) 1,005 3,768 5,649
Oversize capacity to self-fund replacement that is included in figures above (MW) 5 426 780
Total emplacement embodied energy for installed capacity sufficient to match lifetime average power output of coal installation with 1000 MW base nameplate capacity, including oversize capacity for self-funding replacement over operating life (PJ) 3 76 92
Power return on energy investment (PROEI) (MW/PJ) 210 8.29 7.30
Power return on power investment (for replacing an installation over its operating life) (PROPI) 200 7.84 5.76

 Table 1: Comparison of data related to “power return on investment” for coal and wind installations, based on example presented by Kessides & Wade to illustrate the implications of taking a dynamic view of EROI, and extending to consider solar PV (based on data from Prieto & Hall).

I’d like to emphasize here that these figures are illustrative only. The point of this exercise is to show how widely the relative physical capital requirements of different energy sources can vary, even where EROI is similar in magnitude. To be clear though, what these results should emphatically not be taken to imply is that “the typical PROEI of coal generated electricity is 210 MW/PJ” (and this applies equally to generalisations based on the wind and solar PV figures). The illustrative figures here are situation specific. Nonetheless, the findings suggest strongly that, if our interest is in transitioning modern industrial economies from incumbent energy systems to alternatives, wind and solar PV generated electricity face significant impediments, given that the viability of such economies depends on maintaining sufficiently high rates of energy supply, rather than on achieving a particular level of net energy return.

Next week, in Part 3, I will continue the line of inquiry commenced here by considering the capital implications of intermittency and seasonal variation. I will then conclude the three part series by looking at some broad questions relating what all of this might mean for assessing and comparing the economic feasibility of different approaches to electricity supply.


[1] IEA (2014), World Energy Investment Outlook, International Energy Agency, Paris.

[2] Kessides, Ioannis N. & Wade, David C. (2011), “Deriving an Improved Dynamic EROI to Provide Better Information for Energy Planners”, Sustainability, Vol. 3 No. 12, pp. 2339-57.

11 thoughts on “EROI and the limits of conventional feasibility assessment—Part 2: Stocks, flows and power return on investment

  1. Josh: really interesting series. I have a bunch of questions I’d like to ask offline about some of the concepts but more the calculations. and I don’t want to gum things up. if you are willing to talk, would you email me? I would really appreciate it. Or provide me with your email here…

    Hope to hear from you.

  2. Josh: I actually answered most of my own questions, once I looked at your spreadsheet. What accounts for the “much lower emplacement energy per unit of nameplate capacity for coal compared with wind (coal=0.094 watt-years per watt; wind=0.637 watt-years per watt).” Your calcs in wind section of spreadsheet, lines 25-6?

    • Hi Gregory, thanks for taking the time to look at the details–I appreciate having another set of eyes over the calcs. The data comes from Table 3, p.2354 in the Kessides & Wade paper (, specifically the parameter q=E/Pnp (so dimension is time). Kessides & Wade in turn take their data from this IEA report: IEA (International Energy Agency). Environmental and Health Impacts of Electricity Generation; The International Energy Agency–Implementing Agreement for Hydropower Technologies and Programmes, 2002. Available online: (accessed on 4 December 2011). I only had a cursory look over their source when writing the post, as the point was really to get a sense of how much PROI might vary for electricity sources with same EROI, rather than to propose “definitive” PROI values for wind, coal etc. The data is taken from section 8.2 “Net energy analysis and energy payback time”, starting on p.159. Kessides & Wade describe their method for deriving the Table 3 data from the IEA report on p.2353. The values for q are back-calculated from the IEA data, rather than taken directly from equivalent figures presented in the source. I haven’t done a detailed check on Kessides & Wade’s calcs though. The usefulness of the illustration I’ve presented obviously depends on the validity of that underlying data, so if you spot any issues with that, I’d be pleased to revisit my own calculations.
      So with all this in mind, I could only answer your question in very general terms, rather than with reference to the details of the original LCA (the IEA report only provides summary findings there–the specific answer to your question depends on their LCA methodology, boundaries & inputs etc). In general terms though, my understanding is that this essentially follows from the very large difference in power density for the primary energy sources–high-temperature coal combustion and low-altitude air mass movement respectively. The physics involved simply means that wind generation simply needs (much) more plant & equipment per unit of energy transformed per second. This post is my attempt to illustrate this in more concrete terms (no pun intended). Does this help?

      • Yes. It helps a lot. another question. putting aside the likelihood that in fact coal EROIs are higher, if we take equal EROIs for coal and wind, is this largely due to coal’s fuel costs? Initially, I was puzzled by the combination of nearly order of magnitude superiority on doubling time along with equal EROIs. But when I thought about it, this all makes sense given coal’s fuel cost, which enters on EROI but not on emplacement of plant and equipment. Is this about right?

        I’m not a scientist. a humanities professor with a serious citizen’s interest in this stuff. As I am writing on the material with a scientist coauthor, I want to make sure and get things right.

        • Actually, EROI by definition does not include the energy associated with the primary source as an input. The final electrical energy output divided by primary energy input provides a measure of the installation’s energy conversion efficiency, which is quite distinct from EROI–and will always be less than 1. So just to be clear, operating & maintenance energy plowback does not include primary energy input associated with fuel’s heating value. For a comprehensive analysis, the energy required to supply the fuel should be included in the inputs. I assume that this must be a significant contributor to the low EROI for coal-fired electricity in Japan i.e. the fuel has to be imported by sea–but I haven’t confirmed this.
          The reason that the EROI for coal & wind is the same in the Kessides & Wade example, despite wind requiring much higher energy for emplacement per unit of nameplate capacity and having much lower capacity factor, is that wind also has a much lower operating & maintenance energy plowback rate than coal. It’s the relationship between the initial emplacement energy and the total operating & maintenance energy use over an installation’s lifetime that is the key to making sense of the situation. A wind installation with same nameplate capacity as a coal-fired plant produces much less electricity over its lifetime–but it also uses energy for operation & maintenance at a much lower rate. For wind, total energy use is dominated by the installation fraction; for coal, total energy use is dominated (and to a much larger extent) by the operating & maintenance fraction.

          • thank you. very helpful. I make many mistakes studying this stuff. best to get them on the table!!!

  3. Hi Josh,

    It seems that by ignoring the energy input costs for the coal plant you make wind an solar look quite a bit worse than they are and that is before we consider the environmental consequences of burning coal. You need to take a look behind the curtain of the coal input into the coal plant and all the upfront investment and ongoing investment in coal mines and transportation facilities that must take place to enable that. It is not only the oil industry that requires continued investment to make energy available, the coal and natural gas industries require this investment as well and it continues to become more and more expensive as the fossil fuel reserves are depleted.

    So the question becomes should we invest more in coal plants and natural gas plants and coal mines and natural gas wells which will (in the case of mines and wells) become increasingly expensive over time, or should we invest in wind, solar and nuclear and greater efficiency in the use of energy?

    • Hi Dennis,

      I’m not sure how you got the impression that I (or rather, the authors of the IEA report from which Kessides and Wade draw their data) ignored energy input costs for the coal plant. See “Energy to emplace a unit of installed nominal capacity” in Table 1.

      If you have a look at the contextualising comments that I make immediately after the table, you’ll see that the point of this exercise is not to offer definitive values of what I’ve termed “power return on investment” for each of the three generating technologies, but to show how widely these vary even when EROI is similar (bearing in mind that the coal and wind data all comes from the original IEA report, and is based on consistent methodology — whereas the PV data, from Prieto & Hall, is obviously based on very different boundaries, and so the EROI figure there isn’t directly comparable).

      The analysis isn’t presented as an argument for continued investment in coal and natural gas — it’s simply exploring an issue that needs to be taken into account in considering energy transitions more generally, and that is additional to energy return on investment.


  4. Pingback: An integrated view of energy transition: what can we learn? | Beyond this Brief Anomaly

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