A deeper dive on PV ‘EROI’

In this post I give a quick overview of recent goings on in the world of Beyond this Brief Anomaly, and then take a far more detailed look at the basis for the input values relating to PV EROI in the Insight Maker net energy return model: Prieto & Hall’s field study of utility-scale photovoltaic electricity generation for Spain over the period 2009-2011.[2] Having spent quite a bit of time examining this source previously and in the run up to writing this post, I anticipated that the post would simply be a fairly dry technical document. For most folks, this is indeed an apt description. But for that small community aware of the controversies surrounding Prieto & Hall’s book, there’s a surprise in store.  If you’re such a reader (and especially if you followed Ugo Bardi’s blog posts related to this a little while back here and here), then there’s a dramatic twist ahead. Yesterday in writing this post, closer scrutiny of Prieto & Hall’s study alongside the meta-study of PV EROI by Bhandari et al. (that I first learned about from those posts at Cassandra’s Legacy–thank you Ugo) brought to light something quite unexpected. But no spoilers — you’ll need to read on for the details.

And if anyone thinks I’m off the mark with this ‘discovery’, please weigh in to let me and other readers know. I’m really scratching my head over why this hasn’t come to light previously–it seems rather obvious in hindsight.

In recent months, work relating to Beyond this Brief Anomaly’s ongoing inquiry has centred on opportunities to share the findings from last year’s dynamic net energy return modelling more widely. The first of these was an article published in The Conversation at the start of May, co-authored with my Understandascope colleague Anthony James. And then more recently, this led to an invitation to present the findings as part of an event on energy transition at the University of Melbourne’s Carlton Connect Initiative. The event was co-organised by the EU Centre for Shared Complex Challenges, the Australian-German Climate & Energy College and The ASTRA network (Australia-based Sustainability Transitions Researchers Alliance).

A brief aside: Ronan Bolton from the University of Edinburgh’s School of Political and Social Science gave the headline presentation at this event. Ronan’s work ‘examines the interconnected policy, market and regulatory challenges of transforming carbon based energy systems and enabling the development of lower carbon energy infrastructure’, from an approach based in science, technology and innovation studies. Ronan described transitions in electricity supply-demand systems as complex, co-evolutionary processes influenced in important ways by effects associated with technology lock-in and path dependency. An implication is that such processes entail far higher uncertainty about how transition pathways might unfold than many of the popular ‘revolutionary visions’ of energy system change often imply. Regular readers here would likely find Ronan’s outlook resonant with Beyond this Brief Anomaly’s systemic view. The introduction and framing sections of his recent article ‘Infrastructure transformation as a socio-technical process — Implications for the governance of energy distribution networks in the UK’ (co-authored with Timothy Foxon) are particularly relevant to themes explored here. I recommend reading and considering.[1]

The posts here last year on the dynamic energy return modelling went to significant lengths to set out the context for that work. I emphasised that the purpose was to learn about the significance of net energy effects, and to encourage closer attention to their implications, rather than to make concrete predictions about how energy futures will play out. And the modelling itself was exploratory, with much scope for development and refinement if the initial inquiry supported its relevance.

If you’re reading about the work here, and you miss some of the contextual nuance, then it’s probably fair for you to shoulder a greater share of the responsibility. But if I’m promoting it through other public channels, the weight of responsibility shifts back my way. In reporting the work via a 1000 word media article or a twenty minute talk for an audience including non-specialists, it’s perhaps less fair to expect that the findings will be encountered as originally intended.

For this reason, I spent quite a bit of time going over the model structure and inputs for my own satisfaction that they hold up to scrutiny. This led to some improvements to the structure:

  • Most significantly, I’ve added a dynamic calculation for global mean conversion efficiency from primary energy to work & heat. This is now used to convert from self-power demand to self-demand for work & heat for each energy source. Previously, the model used the global mean conversion efficiency from final energy to work & heat for this purpose. Since the generally accepted convention is that energy inputs (the denominator) for EROI calculations be in the form of primary energy equivalent, this resulted in the self-demand for work & heat being too high.
  • Inclusion of historical emplacement of wind and PV capacity, with emplacement from the start of the transition period then being additional to this base capacity.
  • Tidy-up of the growth in biomass, hydro and nuclear, so that these more accurately reflect the intended ‘doubling in capacity during the transition phase’.

A new iteration of the model, version 2.6, incorporates these changes.

I then also gave significant further consideration to some of the principal input parameters used in the reference scenario. The most pertinent—and consequential—are those that contribute directly to the net energy return for wind and PV. In the remainder of this post I discuss the PV-related parameters in greater detail. In a later post, I’ll look at the wind parameters.

1. The controversial world of photovoltaic ‘EROI’

The reference (or default) parameter values that affect PV net energy return (operating life, capacity factor, emplacement energy use, and operating and maintenance (O&M) energy use) used in the Insight Maker model are based on Prieto & Hall’s field study of utility-scale PV in Spain for the period 2009-2011.[2] (Subsequently referred to as P&H.)

PV EROI studies typically consider the PV modules plus the basic equipment necessary to provide an AC electricity output to the grid, at the appropriate voltage for the type of facility. The boundary for the analysis is the ‘factory gate’ i.e. energy inputs up to the equipment leaving the manufacturing facility. Standardised insolation regimes (level of solar irradiance; annual and diurnal insolation pattern) and operating lives are used to harmonise conditions across different systems and analyses. A meta-analysis by Bhandari et al. published in 2015 provides a thorough overview of this typical approach.[3] This is generally in line with the PV net energy analysis methodology guidelines published by the IEA Photovoltaic Power Systems Programme, the most recent version of which was published in January 2016 with Marco Raugei as lead author.[4]

P&H’s study takes this as its starting point, and then expands the analysis boundary on the energy input side to include a range of energy costs without which utility-scale PV plants—for Spain during the study period, at very least—would not be able to fulfil their electricity supply function. They also take into account a range of attenuating factors on the energy output side that are not included in standard studies, but are found from field experience to be relevant and significant. P&H state that their baseline EROI finding of 2.45:1 corresponds with the input and output boundaries that Murphy et al. define as the ‘standard’ boundaries  (EROIstnd) in this article’s Table 1 (input boundary 1; output boundary 2).[5]

Now, to be very clear, P&H’s study is regarded as controversial, to say the least, by some of the most highly credentialed researchers in the PV net energy area. Marco Raugei and Vasilis Fthenakis are perhaps the most outspoken critics – see this article and report, and also this review of P&H (with comments in response from Raugei here and here, from Fthenakis here, here and here, and from Hall here).[4],[6] The major criticisms seem to be as follows:

  1. Due to the way that P&H’s methodology relies on a mix of ‘project [or facility] level’ and ‘society level’ energy inputs, the figure that they present as a mean ‘EROI’ for utility-scale PV in Spain for the period 2009-2011 isn’t really equivalent to the life-cycle EROI for a single facility. As such it is not consistent with the IEA Photovoltaic Power Systems methodological guidelines and so shouldn’t be compared with EROI assessments made in accordance with those guidelines. It should really be described as something different to ‘EROI’.
  2. Exception has been expressed with respect to P&H’s findings being represented as a ‘true EROI for PV’ with broader relevance for the global context (and presumably this is seen as implying that other PV EROI studies with narrower boundaries are erroneous), rather than relating to a specific time period for Spain.
  3. A number of energy inputs are inferred by converting financial costs to energy equivalents. The approach taken is viewed as not methodologically sound (or at least, not sufficiently rigorous). There also seem to be concerns expressed about methodological inconsistency in this area.

On issue 1 above, I think the point made is quite fair and should be considered closely. If PV EROI is taken to mean what the researchers carrying out comparative studies of PV modules and basic “balance of system” (BOS) equipment mean by it, then using the same term for the index that P&H calculate for mean utility-scale PV performance in Spain from 2009-11 is potentially confusing. Then again, with their study findings P&H wish to draw attention to the fact that the index conventionally termed PV EROI, and for which reported values are higher, doesn’t tell the full story in terms of PV electricity generation’s role in displacing other sources. And so from that point of view, it would also be confusing to not link their index with the EROI concept.

Considering also issue 2 above, the problem arises when the respective indices are taken to be dealing with equivalent boundaries, with the implication then being that P&H’s figure poses a challenge to the accuracy of module + BOS EROI studies on their own terms. So to be very clear here: P&H’s figure of 2.45:1 should not be compared directly with module + BOS EROI values on a like-for-like basis, the range for which is reported by Bhandari et al. as approximately 5-17:1 for mono- and poly-crystalline silicon (mono-Si and poly-Si) modules that make up well over 90 percent of all capacity deployed to date.[3] (The minimum and maximum values in the range are based on one standard deviation below the mean for mono-Si and one standard deviation above the mean for poly-Si respectively—see figure 7 in [3].) Studies based on a PV module + BOS boundary deal with a particular sub-set of the inputs included by P&H.

Some careful clarification is required at this point–and this is where the dramatic turn flagged in the opening paragraph of the post enters the story. The IEA PV Power Systems Programme methodological guidelines specify that the numerator in EROI calculations (the energy returned to society) should be specified in either units of electricity, or in primary energy equivalent units, using the life cycle conversion efficiency from primary energy to electricity for the location in question.[4] Energy inputs (the denominator in the EROI calculation) are always expressed in terms of primary energy equivalent. Bhandari et al. explicitly adopt the primary energy equivalent option for the numerator, with a default conversion efficiency of 0.35 where this is not specified in the original studies included in their review. P&H, on the other hand, adopt the electricity unit option for their energy return figures (with energy inputs expressed in terms of primary energy equivalent, in line with the IEA PVPS guidelines). This means that an adjustment is required, either to the P&H figure or the Bhandari et al. range above, in order to compare the respective module + BOS EROI figures. Here, I will take P&H’s chosen convention as the basis for harmonising the figures, and so the Bhandari et al. figures must be multiplied by 0.35. With this adjustment, the reported module + BOS range of 5-17:1 translates to 1.75-5.95:1.

Figures reported by Bhandari et al. are based on an assumed operating life of 30 years.[3] P&H use an energy input value for module + BOS equivalent to an EROI of 8.33:1, based on a 25 year operating life and what the authors regard as an industry-typical energy payback time (EPBT) of 3 years. It’s of particular note that this is 40 percent higher than the high-range figure from the Bhandari et al. meta-study (and is equivalent to 23.8:1 on a primary energy equivalent energy return basis). Adjusting for a 30 year operating life would bring the P&H figure up to 10:1 (electricity unit energy return basis), almost 70 percent higher than the high-range figure from Bhandari et al. For the record, whether the operating life should be set at 25 or 30 years (or something else again) as a wide-scale and long-term mean is an area of some contention. It seems to me this will only be resolved through field studies over coming decades. In the context of P&H’s overall study, it’s a minor issue: by assuming 30 years, their reference value increases from 2.45:1 to 2.59:1.

From the figures above, it might be inferred that P&H have taken a particularly generous approach to setting the PV module + BOS energy input. Based on Bhandari et al.’s reported data, it would be reasonable to have adopted a mid-range figure of around 3.85:1 in place of their figure of 8.33:1. I wonder, though, if this might have been inadvertent. It occurs to me that in selecting an industry standard EPBT of 3 years, P&H may have overlooked that this corresponds with an energy return defined in units of equivalent primary energy, not units of electricity. If this is in fact the case, then making the appropriate adjustment (assuming with Bhandari et al. a life cycle conversion efficiency from primary energy to electricity for the relevant electricity system of 0.35) would reduce their figure for PV module + BOS EROI from 8.33:1 to 2.92:1 (or an EPBT of 8.57 years). This would mean a significantly increased energy input for this component, with the effect of reducing their overall EROI figure from 2.45:1 down to just 1.59:1.

For the purpose of this review, I’ll proceed on the assumption that the figures reported by P&H are actually correct as stated, and that the authors’ treatment of PV module + BOS energy input is simply very favourable. An advantage of this is that it reduces any concerns about the future-relevance of P&H’s figures, when using them as the basis for inputs to the Insight Maker model.

Regarding the concern about extrapolating findings to the global situation (issue 2), one critic states that ‘presenting [P&H’s study] as a book describing the global PV reality was a disservice,’ and ‘presenting one’s view as the view for the world [would] hinder the growth of solar.’ On the strength of their findings for a three year period in Spain, P&H do indeed explore questions related to broader global energy transition. More fundamentally though, their study is set in the context of questions about the extent to which solar PV is subsidised, in energy terms, by fossil fuels. But the book is titled Spain’s Photovoltaic Revolution, and having read it fairly closely, I don’t come away with the impression that the authors go too far in considering broader implications of their findings. Their approach to this is suitably measured, and is limited to the introductory and concluding sections. It seems relevant to set the work in that context, and the style in which this is addressed strikes me as appropriately circumspect.

On the matter of their study being interpreted in such a way that it discourages investment in PV, P&H write in their conclusion:

Finally the low EROI that we derived is not an argument to “kill” the expansion of photovoltaic systems. For one thing such detailed analyses have not been undertaken for other energy systems, whose EROI’s generally are developed using a less comprehensive analysis than what we do here. So maybe the evaluation that we provide of an operational PV system’s EROI should be evaluated against perhaps half of the EROIs of conventional fossil fuels, which might be a ballpark estimate of the values derived if such comprehensive analyses were done for coal, oil and so on…Certainly there must be a much more comprehensive, objective such analysis undertaken if we are to understand well what energy choices are before us.[2](pp. 118-9)

P&H’s intent appears quite clear here. If someone chooses to interpret their findings as a case for not investing in PV, then it seems that’s hardly the responsibility of the authors. Their interest seems to me to genuinely relate to important questions about large-scale energy futures and the societal implications.

On issue 3, relating to methodological concerns about inference of energy inputs from financial expenditure, I think it’s probably clearest to simply present what P&H say on this (in the Discussion section of their concluding chapter):

We are certain that many of our readers will be critical of the broad inclusiveness in our energy costs and of the methods by which we derive energy costs. We believe that the absence of any I-O [input-output] analysis of the Spanish economy—let alone adding in energy analysis—makes it very difficult to come up with much better numbers. But we would be happy to see someone do a better job and will take no offense if our preliminary analyses are shown to be in substantial error, although we think this is quite unlikely.[2] (pp. 117-8).

It seems to me that any criticism in relation to this issue would perhaps be more helpful if it at least referenced P&H’s own prior acknowledgement of the matter. Some may have done so, though I’m not aware of it. Criticisms seem to imply that P&H are just methodologically naïve (or ignorant). Clearly this is not the case.

Notably, on the matter of being too broadly inclusive with energy inputs, pre-empted by P&H above, I haven’t seen any specific concerns expressed (at least by the most prominent critics from the PV EROI research area; I’m leaving aside random blog comments here, such as this one). Carbajales-Dale et al. do state in relation to input data sources that ‘it appears that anecdotal worst cases of installations were generalized by the authors.’[6](p. 996) They don’t substantiate the charge, or offer any specific examples of where they believe this to be the case. So on the whole, it seems that there’s little contention regarding the relevance of the energy input categories that P&H include, even if they go beyond what is typically included in EROI studies conducted by others. In fact, P&H indicate that they identified additional relevant energy inputs, but chose to omit these due to a lack of suitable data for estimating values.

On the basis of this, it seems that there’s broad agreement that energy inputs required in order for PV electricity supply systems to function extend well beyond the module + BOS embodied energy. There are questions regarding just how far this extends, but overall, these seem to be methodological questions about the way the energy inputs are assessed, rather than substantive challenges to their underlying relevance (though given the level of acrimony apparently surrounding the study, I wouldn’t be surprised if, having now pointed this out, someone weighed in wishing to express a different view).

But let’s be very clear here. In the complete absence of further energy inputs beyond the ‘factory gate’, the PV modules and other core equipment remain sitting on pallets in the manufacturing facility’s warehouse or dispatch yard, and we would then know the actual energy return on investment with great precision: it would then be exactly zero.

2. Sensitivity analysis for Prieto & Hall’s reference EROI finding

On the basis that P&H’s energy inputs and attenuating energy output factors are broadly legitimate, but that due to methodological and data availability limitations, the actual figures on the input side are subject to some uncertainty, I’ll now assess the sensitivity of their overall finding to variations in input factors. The results that I present here take into consideration P&H’s own sensitivity analysis in their concluding chapter. What I’m particularly interested in identifying is a plausible ‘outer bound’ for the energy inputs—an envelope within which these can be expected to fall with significant confidence, at least for PV deployment and operation of a similar character to Spain’s (which seems as a guide to be broadly relevant to conventional outlooks for other situations). This can then be used in turn to test sensitivity of consequential behaviour in the Insight Maker dynamic net energy return model.

For the purpose of the Insight Maker model’s reference (or default) inputs, P&H’s data is used to derive component input values for emplacement energy investment, O&M energy use and capacity factor, with the operating life assumed to be the same (25 years). This requires that each of their inputs be allocated to either emplacement or O&M. The allocation is shown in Table 1 below (based on [2], Table 6.18, pp. 111-2). The original data set with all inputs included is designated here as Case A. This corresponds with P&H’s reference EROI finding of 2.45:1. For the purpose of the sensitivity assessment, I’ll present the findings as overall EROI ratios that can be compared directly with this figure.

Case A: Prieto & Hall’s original case
Factor Description Category allocation for all energy investments included in original study Emplacement energy investment (GJ/year) (for operating life of PV modules) O&M energy investment (GJ/year)
Energy used on site
a1 Accesses, foundations, canalizations and perimeter fences Emplacement 203760
a2 Energy investments of evacuation lines and rights of way Emplacement 16920
a3 Operation and maintenance energy costs O&M 1418400
a4 Module washing and/or cleaning O&M 40320
a5 Self consumption in plants O&M 101520
a6 Security and surveillance O&M 498960
Energy used off site to manufacture ingots/wafers/cells/modules and some equipment
a7 Modules, inverters, trackers and metallic infrastructure (labor excluded) Emplacement 2188800
Other energy expenses for on site and off site sine qua non activities for solar PV plants
a8 Transportations. From local manufacturers to China Emplacement 345600
a9 Premature phase out of unamortized manufacturing and other equipment O&M 534240
a10 Associated energy costs to injection of intermittent loads: pump up costs and/or other massive storage systems, if applied O&M 0
a11 Insurances O&M 71640
a12 Fairs, exhibitions, promotions, conferences, etc. O&M 95040
a13 Administration expenses O&M 123480
a14 Municipality taxes, duties and levies (2-4% total project) O&M 50400
a15 Cost of land long term rent or ownership O&M 31320
a16 Circumstantial and indirect labor (not included in direct labor activities) O&M 79200
a17 Agent representative or market agent Emplacement 21600
a18 Equipment stealing and vandalism O&M 42840
a19 Communications, remote control and management O&M 61200
a20 Pre-inscription, inscription, registration bonds and fees Emplacement 0
a21 Electrical network/power lines restructuring Emplacement 640800
a22 Faulty modules, inverters, trackers O&M 142560
a23 Associated energy costs to injection of intermittent loads: network stabilization associated costs (combined cycles) Emplacement 712800
a24 Force majeure acts of god and others: wind storms, lighting, storms, flooding, hail O&M 0 0
Total 4130280 3291120

Table 1: Energy input factors from Prieto & Hall’s study, with each factor allocated to either emplacement or O&M

Case B comprises the inputs used to derive the reference (default) input parameter values for the Insight Maker model (version 2.6). This is not shown here in detail, as it simply omits the emplacement factors a21 and a23 (refer to Table 1). I left these out on the basis that (very conservatively) they may be less relevant when intermittency is compensated with battery buffering. The equivalent EROI value for Case B is 3.01:1.

Case C is shown in detail in Table 2. This extends Case B by omitting a range of further input factors that P&H identify as potentially controversial (a11-15,17,20). Factors a8-10 are discounted according to P&H’s sensitivity analysis. I have elected to omit factors a16, relating to circumstantial and indirect labour, and a19, relating to communications, remote control and management. Several other factors relating to on-site energy use have been heavily reduced (a3-4,6). The resultant EROI for Case C is 4.59:1.

Case C: Case B with additional inputs omitted, to test sensitivity to omission of “controversial” factors as per P&H sensitivity discussion (and beyond).
Factor Description Category allocation for all energy investments included in original study Proportion included: 1 = fully included; 0 = fully omitted Emplacement energy investment (GJ/year) (for operating life of PV modules) O&M energy investment (GJ/year)
Energy used on site
a1 Accesses, foundations, canalizations and perimeter fences Emplacement 1 203760
a2 Energy investments of evacuation lines and rights of way Emplacement 1 16920
a3 Operation and maintenance energy costs O&M 0.5 709200
a4 Module washing and/or cleaning O&M 0.25 10080
a5 Self consumption in plants O&M 1 101520
a6 Security and surveillance O&M 0.25 124740
Energy used off site to manufacture ingots/wafers/cells/modules and some equipment
a7 Modules, inverters, trackers and metallic infrastructure (labor excluded) Emplacement 1 2188800
Other energy expenses for on site and off site sine qua non activities for solar PV plants
a8 Transportations. From local manufacturers to China Emplacement 0.5 172800
a9 Premature phase out of unamortized manufacturing and other equipment O&M 0.5 267120
a10 Associated energy costs to injection of intermittent loads: pump up costs and/or other massive storage systems, if applied O&M 0.25 0
a11 Insurances O&M 0 0
a12 Fairs, exhibitions, promotions, conferences, etc. O&M 0 0
a13 Administration expenses O&M 0 0
a14 Municipality taxes, duties and levies (2-4% total project) O&M 0 0
a15 Cost of land long term rent or ownership O&M 0 0
a16 Circumstantial and indirect labor (not included in direct labor activities) O&M 0 0
a17 Agent representative or market agent Emplacement 0 0
a18 Equipment stealing and vandalism O&M 1 42840
a19 Communications, remote control and management O&M 0 0
a20 Pre-inscription, inscription, registration bonds and fees Emplacement 0 0
a21 Electrical network/power lines restructuring Emplacement 0 0
a22 Faulty modules, inverters, trackers O&M 1 142560
a23 Associated energy costs to injection of intermittent loads: network stabilization associated costs (combined cycles) Emplacement 0 0
a24 Force majeure acts of god and others: wind storms, lighting, storms, flooding, hail O&M 1 0
Total 2582280 1398060

Table 2: Energy input factor values and allocations for Case C (heavily reduced energy input case)

Case D is an extension to Case C (details not shown). Here, the PV module + BOS EROI (factor a7) is reduced to the mid-range figure from Bhandari et al. for mono-Si and poly-Si, adjusted for energy return in units of electricity. The corresponding EROI value for that basic equipment, as noted in the previous section, is 3.85:1. The resultant overall EROI for Case D is 2.79:1.

And finally, Case E makes the same adjustment as for Case D, but this time using all of the energy inputs from the original study. In other words, Case E is a modification of Case A, with PV module + BOS EROI (factor a7) set to 3.85:1. The resultant overall EROI for Case E is 1.83:1.

For the purpose of exploring limit cases within which EROI can be expected to fall, it is also interesting to consider what happens if the PV module + BOS energy input goes to zero (in other words, as the EROI for these core components approaches infinity). This is useful for thinking about the implications of future PV technology developments, and better appreciating how factors other than this core equipment affect net energy. Findings for this are presented in Table 3 below, along with the findings described above. Note 1

As a further extension, it’s interesting to consider how the attenuating energy output factors identified by P&H affect the PV module + BOS EROI, and corresponding with this, the overall EROI. If the energy payback time (EPBT) for these components is based on the nominal rated output for the equipment under standard test conditions, and if this nominal output omits (in whole or part) any of the factors identified by P&H, then the actual EPBT will be longer than the nominal value. If we assume that P&H’s attenuation factors are indeed additional to or greater than those typically taken into account in manufacturers’ performance ratings, then the EROI for the basic equipment will reduce accordingly.

I’m not sure to what extent these conditions apply in practice, and P&H do not make any such adjustment in their study (other than perhaps taking this into account in converging on a three year EPBT as representative for Spain as a whole over the study period). But if this adjustment is applied, the result is that a PV module + BOS EROI of 8.33 reduces to 6.38; 3.85 reduces to 2.94. This is also shown in Table 3, along with the corresponding values for overall EROI.

Case A Case B Case C Case D Case E
PV module + BOS EROI 8.33 8.33 8.33 3.85 3.85
Overall EROI 2.45 3.01 4.59 2.79 1.83
Overall EROI as PV module + BOS EROI → ∞ 3.49 4.71 10.20 10.20 3.49
PV module + BOS EROI adjusted for net energy output attenuation factors identified by P&H 6.38 6.38 6.38 2.94 2.94
Overall EROI corresponding with PV module + BOS EROI adjusted for net output attenuation factors identified by P&H 2.26 2.71 3.93 2.28 1.60

Table 3: Summary of findings from sensitivity analysis

3. Conclusions

The overall finding from the sensitivity analysis is that we can say with a high degree of confidence that the EROI for PV electricity supply, under any conditions, will be less than 10.20:1 on an electricity unit energy return basis. This is an upper bound, before taking into account the embodied energy for the actual energy conversion and supply equipment. It takes into account only a small subset of energy inputs required for current (and plausible future) ‘real world’ functionality. We could view this as a possible best-case under conditions of ‘science fantasy technology’ (zero-cost PV module + BOS) and utopian socio-economic conditions in which most of the institutional requirements and many of the practical and technical requirements for operating utility-scale PV systems have been circumvented (somehow or another).

Once PV module + BOS energy inputs are included, this upper bound for overall EROI comes down to just 4.59:1 (assuming P&H’s perhaps inadvertently very generous allowance of 8.33:1) or perhaps more realistically, 2.79:1 (assuming Bhandari et al.’s mean figure for mono-Si and poly-Si PV cells, on an electricity unit energy return adjusted basis, of 3.85:1). These figures can be compared with P&H’s all-inputs-included reference figure of 2.45:1, which we now see has a significant degree of ‘future proofing’ built in, given that the mean module + BOS input figure from Bhandari et al. would see this reduced to just 1.83. Further reductions in EROI would be seen if we took into account some portion of the additional energy output attenuation factors identified by P&H.

On the strength of this assessment, I conclude that the reference (or default) input parameter values used in version 2.6 (and earlier versions) of the Insight Maker energy transition model, collectively corresponding with an overall EROI figure of 3.01:1 (electricity unit energy return basis), are robust. In fact, when we take into account that these figures are based on the favourable insolation conditions for Spain, but are applied in the model as global means, they can probably be considered quite generous. This is particularly so when we take into account the fact that the PV module + BOS EROI is 40 percent higher than Bhandari et al.’s output adjusted high-range figure. From this I think it’s reasonably safe to infer that the input parameter values used in the Insight Maker model include significant allowance for future performance and manufacturing improvements.

One final point in closing: P&H used an operating life of 25 years. I have followed suit with the PV operating life in the model. Some may wish to argue that the operating life should be longer. I think the analysis I’ve presented here makes this a somewhat moot issue. The generous treatment of the module + BOS energy inputs (i.e. significantly lower than Bhandari et al.’s reported data) should override any concern with the operating life.


Note 1: There’s an important caveat here, that only occurred to me belatedly while reading Vaclav Smil’s most recent book, Power Density: A Key to Understanding Energy Sources and Uses.[7] This relates to the role that the numerator in the EROI ratio plays in technology-driven increase in EROI with time. I’ve looked here at the extreme limit case as EROI for PV module + BOS goes to infinity, but the underlying intent is to consider the range within which the extended boundary EROI can be expected to lie, as the core equipment improves. This can take form of both manufacturing improvements and improvements in performance. If the energy inputs for manufacturing reduce, then this will increase the EROI for the core equipment, but for the most part won’t affect the other extended boundary inputs (reduction in mass of core equipment is one area where we could expect a reduction in some extended inputs). In the case of performance improvements though, if these increase the power density of electricity supply (electricity output per unit of land area), then most of the extended energy inputs would also see some corresponding level of decrease, and so the extreme limit EROI (extended EROI as PV module + BOS EROI → ∞)  would also increase. How much difference this could make depends on the potential for PV cell efficiency to increase. A doubling in efficiency could mean something in the order of half the extended boundary energy inputs.


[1]  Bolton, R., & Foxon, T. J. (2015). Infrastructure transformation as a socio-technical process — Implications for the governance of energy distribution networks in the UK. Technological Forecasting and Social Change, 90, Part B, 538-550. doi: http://dx.doi.org/10.1016/j.techfore.2014.02.017

[2] Prieto, P. A., & Hall, C. A. S. (2013). Spain’s Photovoltaic Revolution: The Energy Return on Investment. New York: Springer.

[3] Bhandari, K. P., Collier, J. M., Ellingson, R. J., & Apul, D. S. (2015). Energy payback time (EPBT) and energy return on energy invested (EROI) of solar photovoltaic systems: A systematic review and meta-analysis. Renewable and Sustainable Energy Reviews, 47, 133-141. doi: http://dx.doi.org/10.1016/j.rser.2015.02.057

[4] Raugei, M., Frischknecht, R., Olson, C., Sinha, P., & Heath, G. (2016). Methodological guidelines on Net Energy Analysis of Photovoltaic Electricity, IEA-PVPS Task 12, Report T12-07:2016, viewed 19 July 2016 at http://iea-pvps.org/index.php?id=349&eID=dam_frontend_push&docID=3001

[5] Murphy, D. J., Hall, C. A. S., Dale, M., & Cleveland, C. (2011). Order from Chaos: A Preliminary Protocol for Determining the EROI of Fuels. Sustainability, 3(10), 1888-1907, http://www.mdpi.com/2071-1050/3/10/1888

[6] Carbajales-Dale, M., Raugei, M., Fthenakis, V., & Barnhart, C. (2015). Energy Return on Investment (EROI) of Solar PV: An Attempt at Reconciliation [Point of View]. Proceedings of the IEEE, 103(7), 995-999. doi: 10.1109/jproc.2015.2438471, http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7128485

[7] Smil, V. (2015). Power Density: A Key to Understanding Energy Sources and Uses. Cambridge, Massachusetts: The MIT Press.

9 thoughts on “A deeper dive on PV ‘EROI’

  1. Wow, this is fantastic stuff! I haven’t looked into it in detail but can I quickly ask, are all the input energy requirements of canal digging, O&M costs etc, in electricity energy demand or primary demand (I would expect primary demand)? If they are primary energy demand and they are delivered (hypothetically & fantastically) somehow by PV, wouldn’t then these inputs be significantly lower?

    • Hi Nick, yes all the energy inputs are expressed as primary energy equivalents. The question you ask is a very important one. The great hope is that, yes, electrification leads to overall reduction in the primary energy required to deliver the same quantity of energy services in the form of work & heat (plus lighting, if you wish to distinguish that). This is on the basis that conversion of electrical energy to work & heat can be done at a higher efficiency than conversion of chemical energy in fuels to work and heat, due to the fundamental thermodynamic limits to which heat engines (devices that convert heat to work) operate. Expectations of future absolute decoupling of economic output from energy inputs hinge on this (in large part at least).
      Problem is, it depends on an exceedingly abstract view of the role of energy in economic systems, in which the only important characteristic of an energy source is its heating value in joules: a classic ceteris paribus assumption. In the ‘real’ world, of course, all other things are not equal. Heavy transport and many basic industrial processes are not readily (or at all) amenable to electrification. And if fossil fuels are replaced with synthetic fuels with renewably generated electricity as the primary source, the efficiency improvement reverses and becomes an efficiency penalty. I highly recommend Richard Heinberg and David Friedly’s new book Our Energy Future in relation to these issues (http://ourrenewablefuture.org/#the-book). But also see other posts here — the issues that arise when energy questions are treated at too great a level of abstraction is a key theme of this project.
      All that said, the energy transition modelling referred to in this post does in fact take into account this very issue. This is achieved by converting all energy outputs from supply sources to flows of work & heat in order to aggregate them, and also converting the demand for energy inputs for each source (for emplacement of new capacity and for O&M) to a work & heat demand which is deducted from the total pool from all sources. So you could run the simulation to see how this plays out. The model is still operating at a very abstract level, but goes some way in addressing this by recognising the potential for fuels and electricity to be converted to work and heat with different efficiencies. The model doesn’t address the broader issue of the substitutability of fuels and electricity in economic processes though.

      • Thanks Josh, you’re too right on the difficulty of electrification, though I suppose many of the societal factors that Prieto use could reasonably be considered electric (insurance, security etc?) or able to be converted to electric. I’ve read a couple of the sections of Our Energy Future (particularly those on renewables & EROI) none of which hasn’t made me particularly any more optimistic!

        In some respects, I think one of the easy conclusions of the somewhat scary low numbers out of the Prieto & Hall study would be that we really need to be attempting to optimise & reduce all those other factors as much as possible if we are trying to sensibly & rationally deploy renewables.

        In regards to your point regarding the Prieto & Hall study being less a typical EROI for apples vs apples comparison as much as a “societal EROI” – to me this somewhat points towards a conclusion that we may actually have been functioning on a much lower “societal EROI” than what we commonly think, or would you disagree? For example most typical EROIs of say oil at around EROI of 20 or so would not be taking into account these societal factors which they would be subject to (if not more so than a solar farm), which would likely result in much lower final or societal EROIs than what we typically think we are operating at in our fossil fuelled society. E.g. I saw one of Hall’s presentations suggest our current society currently requires/functions on something of the order of EROI20+ etc? Perhaps it is not so high??

        Anyway again thanks for the article & model and look forward to delving into the rest of your articles further.

        • I think one significant point that Prieto & Hall bring home with their study is the extent to which fossil fuels are implicated in (or rather, contextual for) every societal factor. Any of the factors they include is directly enabled by the full spectrum of present energy sources, but in differing proportions depending on the activity. But then if you extend the analysis boundary upstream from the direct energy inputs, there’s decreasing differentiation between the energy sources that the activity relies on.

          Your point about the ‘societal EROI’ of all current energy sources being lower than commonly(!) understood is another important point — one of the block quotes from Prieto & Hall in the post discusses exactly that issue. I don’t think EROI analysis provides any easy answers on that front — at least in terms of interpreting the significance of a single all-in ratio. Hence the body of opinion that it’s best used to compare different versions of otherwise equivalent systems (e.g. poly-Si and thin film PV systems). But I see this as a starting point for thinking about the relationship between energy context and societal futures, rather than ever being the last word.

  2. Hi Josh,

    Thanks for your good article. I may quote some parts of it shortly over at Peak Oil Barrel, which, recently seems to have suffered a dropoff in comment-numbers since changing owners.

    (‘Nick B’, incidentally, sounds like ‘Nick G’ over at Peak Oil Barrel and I wouldn’t be surprise if it was they or someone from their ‘office’, ostensibly pushing a continuation of ‘BAU’– something like a so-called ‘renewable’ economy continuing to operate on the grid and running electric cars full of continued wage-slaving coercively-taxed sheeple.)

    In any case, if you factor in true or pure democracy into technology– (What’s the point of technology anyway? To improve our lives for all or to merely serve the system and the ‘crony-capitalist plutarchies’ or the so-called ‘1%’ or ‘elite’?)– into how it is derived and implemented, etc., things seem to kind of fall apart– perhaps much like what civilizations have done in the past, and what may be starting to happen now.
    Dennis Meadows of Limits To Growth fame; the HANDY study (University of Maryland?); and Jay Hanson, among others, touch on this crucial, if remarkably, generally ignored, issue.

    Technology is not supposed to make the world worse for humans, but better. If it’s making things worse, then honest, objective, transparent and rigorous EROEI analyses, etc., need to be part of the picture, if we’re going to be serious about it.

    ~ Caelan

  3. Just a minor elaboration to my previous comment:

    I meant that the variables of equality and/or real/pure/direct democracy and/or anarchy (the ‘equality’ and ‘freedom from illegitimate/coercive leadership’ kind) need to be factored into a proper analyses of technology for more accurate results.

    Nuclear energy, for example, takes a tax-hostaged public, and AFAIK, only Finland has seriously done anything with regard to its waste– a can so far kicked down the road. This is supposedly very dangerous in light of a serious collapse scenario.

    ~ Caelan

  4. Very interesting work. It is a very interesting time we live in where models are getting so complex. I recently read this very interesting paper modeling the economic adoption costs of adapting renewable energy. It does not look good. I wonder if the models could be incorporated off each other at all. http://www.sciencedirect.com/science/article/pii/S0921800916301343?np=y

    As far as I can tell the only way we have any chance at avoiding 2C warming is using LFTR’s which no one seams in any hurry to fund. Sigh. Hell in a hand basket.

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