Exergy and Power Plants

By Andy May

Key question: Can renewables ever replace fossil fuels and nuclear?

Understanding the value of renewables, vis-à-vis fossil fuels and nuclear power, requires that we consider that all energy is not equal in value. In fact, the quantity we call energy can be misleading and many experts prefer the quantity called “exergy,” which is defined in economics as (source Exergy Economics):

The maximum useful work which can be extracted from a system as it reversibly comes into equilibrium with its environment.”

Or it can be thought of as the measure of potential work embodied in a material or device. As Ayres, et al. (1998) argue exergy is a more natural choice as a measure of resource quantity than either mass or energy. Even today it seems BTU’s, a measure of heat of combustion, or MToe, million tonnes of oil equivalent, are commonly used and mislabeled energy (see the Exxon Outlook, 2017 or the BP Energy Outlook, 2017). In a previous post (here) I discussed EROI, or energy returned from energy invested. I complained in that post about the inconsistency and inaccuracy in current EROI and LCOE (Levelized cost of electricity) calculations. The problems mostly stemmed from comparing energy or electricity output from different sources (solar, wind, natural gas, coal, nuclear) as if all produced energy was equally valuable, which it isn’t. While comparing the heat of combustion or million tonnes of oil equivalent is clearly incorrect, Rud Istvan and Planning Engineer show that comparing the cost of producing megawatts of electricity, like the IEA and EIA do, is also incorrect, see here and here. Since exergy is a measure of useful work, it helps get around that problem. In a comment to that post, Captain Ike Kiefer posted a reference to Weißbach, et al. (2013) which has a much more valid EROI comparison (see figure 2) of conventional and renewable electricity sources in Germany. Since Germany is, in many ways, a testbed of renewable energy sources for the world; this is very helpful.

EROI is computed in many ways that make it difficult to compare different energy sources. Weißbach, et al. (2013) improve the calculation by using the system input and output exergy in the calculation rather than energy. Thus, now EROI becomes the ratio of the exergy returned and the exergy expended. Put another way, the ratio of the work we get out of a source of energy divided by the work that went into making it. In Weiβbach, et al., they take exergy delivered as equivalent to electricity delivered. Thus, how the electricity is used by the customer is not considered. One other important concept is that the study must include the full life cycle of the power plant, from the very beginning to the end, this is called “LCA.” LCA and exergy are discussed in full by Ayres, et al. (1998).

We will not get into all the ways that EROI has been misused in the past, but the reader can go to Giampietro and Sorman for more on this topic. However, one EROI misuse is worth mentioning as an example. EMROI is the money returned on invested energy, excluding labor and carrying costs. It is not a measure of EROI, but is sometimes presented as EROI which can be very confusing, to see the difference compare figures 1 and 2 and notice the scale change. Our economy runs on energy of different qualities, thermal energy and electrical energy. Currently, thermal energy power plants have an efficiency of 33%, meaning that they are one third as efficient as sources that produce electricity directly, like solar PV (photovoltaic) panels. We are comparing apples and oranges, thermal and electrical; and exergy and LCA can help do this in a valid way.

A modern economy needs electricity on demand, 24 hours a day, without fail. A period without electrical power is called a disaster for a reason. Because demand for electrical power rises and falls constantly there is a need to store energy so power generation can rise to meet increased demand. Fossil fuels, biofuels and nuclear are their own storage, so they have this capability naturally. Wind and solar do not have built-in storage, so it needs to be provided, and this is a cost that must be accounted for. Inexplicably, both the IEA and the EIA (see my previous post here) ignore this cost in their LCOE (levelized cost of electricity) calculations. For example, from the IEA guidelines for LCA (life cycle analysis) assessments (page 10):

“Back-up systems are considered to be outside the system boundary of PV LCA [photovoltaic solar life cycle assessments]; if a back-up system is included, it should be explicitly mentioned.”

This makes no sense, in a modern economy electricity must be available on demand or chaos ensues. Demand cannot be adjusted to cloudiness, so for solar (or wind) to work at all, it must be backed up. The backup (batteries, molten salt storage, fossil fuel, pumped hydro, whatever) must be part of the system. We will not discuss the other problems with IEA assessments here, but will mention that Giampietro and Sorman do a very good (and often hilarious) job of detailing the problems with the IEA assessments in their jewel of a paper entitled “Are energy statistics useful for making energy scenarios?

Using fossil fuel power plants as a backup creates a conundrum, if the fossil fuel plants must run all the time, but they are not selling power when the solar and wind facilities are providing power, who pays for the fully staffed and idling plants? It turns out the government must subsidize them with “capacity payments” to keep them from going out of business and closing down due to lack of revenue. If they did close, the grid would quickly become unstable as third world grids often are.

In figure 1 we see a Weißbach, et al. (2013) histogram of their exergy calculated EMROI by energy source. The yellow bars include the cost of backup (“buffered”) and the blue bars do not (“unbuffered”). The data used to compute the values shown in the figures can be downloaded as a spreadsheet here.

Figure 1, German EMROI (money returned from an energy investment) of various energy sources. Source Weißbach, et al. (2013), data: source

Figure 2 uses the same data as figure 1, but EROI is plotted. The scale is reduced for figure 2 due to the smaller numbers. To compute EMROI a weighting factor of three is used in this case, see the spreadsheet for the details. The weighting factor is based on the production cost ratio of electricity to thermal energy. The economic threshold of 7:1, for Germany, is shown in gray. The biomass plotted is corn, the wind generation location is in Germany, coal transportation costs are not included and the type of coal is the German mix (roughly 42% hard coal and 58% lignite). Nuclear is based on 83% centrifuge and 17% diffusion refining. The solar PV values are all rooftop solar values. The commercial solar values are computed as if from the Sahara Desert, but the grid connection to Europe is not included in the cost.

Figure 2, German EROI (energy returned on energy invested) of various energy sources (source: Weißbach, et al. (2013) , data: source

How is an energy source “buffered” or “backed-up”

Fossil fuel, biofuel and nuclear power plants backup themselves, one simply stores the fuel itself. Hydro power plants can increase the amount water behind the dam to a certain extent to provide some backup, but more is needed. Solar and wind power plants require a separate facility to store power or they require another source of power at the ready. The data plotted in figures 1 and 2 comes from Germany, a country with many contiguous countries that can supply it with emergency power (from fossil fuels, biofuels or nuclear sources) when wind and/or solar fail. They are very dependent upon German coal and lignite power plants for emergency power, currently 45% or so of Germany’s power comes from coal and lignite. In some cases, they have had to return paid taxes to coal power plants to keep them from going bankrupt.

But, this post is not about using fossil fuels to backup wind and solar power plants. Fossil fuel backup is the cheapest backup today and for the foreseeable future. The question we ask is can renewables replace fossil fuels? That requires non-fossil fuel storage of energy. Our charts and figures in this post only apply to Germany today, so does the rest of the discussion. As Weißbach, et al. (2013) write:

“No direct LCA [power plant life cycle assessments] studies could be found for storage systems but pump storage systems are very similar to hydroelectricity plants with storage capabilities. Alternative storage techniques like hydrogen electrolysis and gas storage are much more uneconomic anyway. Here, the Australian Benmore station with an energy demand … of 24,000 TJ has been selected and slightly scaled up (30,000 TJ) in order to fit the planned German Atdorf pump storage system with a projected lifetime of … 100 years. The material and working demands are similar, strongly dominated by the dam’s energy input. Atdorf’s storage capacity is about … 52 TJ … It should, however, be kept in mind that if no favorable topology is available the necessary geo-engineering elevates the energy investment substantially.”

Thus, the authors chose the most economical energy storage system (except for fossil fuel backup) to use for their calculation of the EROI of wind and solar. They chose to store 10 full load days of power for rooftop solar and 2 days for the desert commercial solar facility. They decided only two days would be required for the Sahara Desert facility based on weather history. We should add that topology is not the only problem with pumped hydro storage, land is also an issue. This storage method uses a lot of land, which is not a small cost and it displaces people, never an easy thing to accomplish.


According to Weißbach, et al., a common mistake in EROI comparisons between electricity sources is using inaccurate power plant lifetimes, this problem is discussed by Planning Engineer and Rud Istvan also. Wind and solar energy sources are reported to have a lifetime of 20 to 30 years, although much shorter lifetimes have also been observed. In the case of wind, rotor and bearing fatigue limit the life and in the case of solar it is silicon degradation. However, it is common for combined cycle gas turbines to last more than 40 years and for coal power plants to last more than 50 years. Nuclear plants often last more than 60 years (the current US planned life) and hydroelectric facilities can last more than 100 years. It is very important for the plant lifetime to be accurate because the EROI (or levelized cost) scales directly with it. Consider then the US EIA statement (page 3) quoted below about lifetime and LCOE (levelized cost of energy). See also 2018 Levelized Costs AEO 2013, page 2:

“The levelized cost shown for each utility-scale generation technology in the tables in this discussion are calculated based on a 30-year cost recovery period, using a real after tax weighted average cost of capital (WACC) of 6.6 percent. In reality, the cost recovery period and cost of capital can vary by technology and project type.”

So, they know the various plant lifetimes are different. Presumably they know that the levelized cost of a 60-year nuclear plant could be as low as one half the cost of their assumed 30-year plant, yet they use 30 years anyway.


For the most part this post is a summary of Weißbach, et al. and I refer the reader to that excellent paper and their supplementary spreadsheet for more details. Here we only hit the highlights. They note that only a uniform mathematical procedure based on exergy makes it possible to compare all power generating systems accurately. They have done this using mostly data from Germany, the numbers will be different for different locations.

Solar PV, the most efficient rooftop solar, is not economic in this study. Wind energy is only economic when not backed up or “buffered.” Biofuels require no buffering, but it makes no difference, the huge cost of producing the fuels make them uneconomic. Commercial solar is economic in deserts, so if transmission lines can be built and if suitable backup storage is built, this is a renewable possibility. Unfortunately, the best backup is pumped hydro and this is often not possible in deserts. Weißbach, et al. do mention that, in their opinion, molten salt energy storage is not economic.

The most egregious flaws in previous EROI studies are:

  • Upgrading the output inappropriately for solar and wind generation because their output is electricity. That is renewable EMROI is computed, then compared with the EROI of conventional plants. Apples and oranges again! See also Giampietro and Sorman on this topic, page 10.
  • Using inappropriate power plant lifetimes.
  • Counting all output, that is using wind and solar capacity for calculations and ignoring the need for “buffering” or backup. Virtually all other assessments do this and the difference is huge.

Weißbach, et al. have corrected the errors in previous studies and seem to have computed the most robust set of numbers I’ve seen to date. So, what is the answer to the question at the top of the post? It seems that Germany is very unlikely to replace fossil fuels and nuclear with renewables. Weißbach, et al. have shown that, in Germany, all renewables, except commercial solar installed in the Sahara Desert, are currently uneconomic. This means that renewables must be subsidized indefinitely, unless a major technical breakthrough in energy storage appears. Currently, the cheapest form of “buffering” are the existing German coal and natural gas power plants. Other buffers, like pumped hydro and molten salt are uneconomic. However, since renewable fuels must be purchased by the grid, by German law, fossil fuel plants will probably not sell enough electricity to break even. Thus, fossil fuel plants will also need to be subsidized for grid stability. The alternative is for Germany to import all their emergency power from neighboring countries. But, in the latter case, they may need to subsidize the added necessary, and presumably fossil fuel, power surplus their neighbors will need. Germany is apparently burning Euro notes for power and, fairly large denomination Euro notes at that.

March 17, 2017

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