Should-Cost Nuclear and Human Stupidity

In an earlier piece we discussed the tradeoff between nuclear power's cost and plant radiation release frequency, and how the NRC's valuation of the two dimensions is quite different from society's. The NRC regards a release to be intolerable which moves the NRC far up the cost/release tradeoff curve, preventing society from enjoying anything close to the full benefits of nuclear power. In particular, the capital cost of nuclear ends up five to ten times the should-cost of less than $2000/kW. This is not the NRC's fault. It is ours.

Let's talk about another tradeoff: CO2 emissions versus electricity cost. Figure 1 summarizes the GKG's study of the German grid. Vertical axis is cost; CO2 emissions are on the horizontal.

Figure 1. German Power Costs vs CO2 emissions for a range of nuke CAPEX

Unlike our discussion of nuke cost versus release frequency, these are not made up tradeoff curves. They are based on multiple runs of the GKG Grid Model. In these runs, the basic rule was the program had to supply the actual hourly German demand for electricity for every hour from the beginning of 1993 to the end of 2000. The peak hourly demand in that 8 years was 101 GW. The average over that period was 62 GW. In each run, the model comes up with that combination of onshore wind, offshore wind, PV solar, batteries, hydrogen, open cycle gas turbine, closed cycle gas turbine, coal or nuclear that minimizes the sum of the grid cost and the CO2 emissions cost. Each of the curves in Figure 1 were created by fixing the nuke overnight CAPEX at the numbers shown in the legend and varying the dollar cost to society of an additional ton of CO2 emissions from $1600/ton CO2 at the left upper end of the curve to zero dollars per ton at the right lower end of the curve.

The official name for this dollar cost is the Social Cost of Carbon (SCC). If the Social Cost of Carbon is very high, the societal optimum for any given nuclear CAPEX is near the left end of the curve. If the SCC is near zero, the societal optimum is near the right end of the curve.

Nobody knows what the Social Cost of Carbon is; but that has not stopped people from making guesses at it. The US EPA has been using $51/ton CO2; but recently the EPA proposed increasing the legal SCC by nearly a factor of four to $190/ton.\cite{epa-2023} Other estimates range from negative to over $1000/ton. It is easy to concoct hypothetical scenarios that support either end of that range and anything in between. I repeat: we do not know what the social cost of CO2 is. Anybody who claims to know what the SCC is is either a liar or a fool.

The should-cost of nuclear is around $2000/kW. The first thing that hit me when I saw Figure 1 is how tiny the light-blue, should-cost curve is. Even if the social cost of CO2 is zero, the program comes up with a low 59 gCO2/kWh grid. Even if the social cost of CO2 is a very high $1600/ton, the model comes up with an affordable 56 $/MWh grid. Should-cost nuclear is resilient against human ignorance and stupidity. Even if the Social Cost of CO2 is very high and we don't account for that cost in building our grid, we will be in pretty good shape. Even if the Social Cost of CO2 turns out to be nearly zero and we act as if it's very high, we will not have impoverished humanity unnecessarily, at least as far as the grid goes.

It turns out that the slope of the tradeoff curve at any point is the SCC that produced that point. Moreover, if society's SCC is say $190/ton, then the optimal grid for that society is at the point where the slope of the trade off curve is $190/ton.¹ I have marked the point on the curves that corresponds to a $200/ton SCC. As we increase nuclear's CAPEX from $2000/kW up to $8000/kW, things deteriorate rapidly; but it is mostly in the form of increased grid cost. Above $8000/kW nuke, the model shifts hard right and down. Above $8000/kW, the model pretty much stops using the prohibitively expensive nuclear.² With nuclear, very low CO2 pretty much comes for free. Without nuclear, reducing CO2 becomes far more expensive. The best the model can do is accept a much higher CO2 intensity in return for a lower grid cost. Put another way, the $200/ton CO2 slope on the $16000/kW CAPEX curve is well to the right and below the $200/ton CO2 slope on the $8000/kW. In plain English, it is exceedingly expensive to get below 100 gCO2/kWh without nuclear.

Once we are above $8000/kW nuclear, Germany's choices (and our choices) are pretty stark. At one end, she can have $60/MWh and 717 gCO2/kWh electricity from a coal grid with gas peaking. At the other end, she can have $167/MWh and 37 gCO2/kWh power from a wind, solar, hydrogen, and gas grid. To pick out the optimum from that wide span, ranging from planet frying to tragically unnecessary impoverishment, she needs to guess the Social Cost of CO2, and she (and us) had better get it right. Good luck with that.

Unnecessary appendix: Additional Insights from these Runs

In a rational world, all this blather would be unnecessary. Nuclear would be down at its should-cost of $2000/kW or less. We'd be down on the light blue curve. Nobody would be concerned about CO2 from power plants. But the light blue line is not an all nuclear grid, not even the far left end. Table 1 drills down on the $2000/kW CAPEX $1600/ton SCC grid,

Table 1. GKG Model Run, Nuke CAPEX $2000/kW, SCC = $200/ton CO2

Focus on the blue box. At $2000/kW unit CAPEX and $1600/ton SCC, the program chose to install 84 GW's of nuke. The nukes did considerable load following. The nuke capacity factor was 66.7%, considerably less than the assumed availability of 90%. The nuke capacity provided 99.9% of all the electricity consumed over the 8 year period. But the model also installed 4.5 GW of Combined Cycle Gas Turbine (CCGT) and nearly 17 GW of Open Cycle Gas Turbine (OCGT). In total, 34% of the average demand. Then it used that capacity very sparingly!!! The CCGT capacity factor was a paltry 1.4% and the OCGT capacity factor was a miniscule 0.1%.

This behavior is a product of both the cheapness of gas turbine capacity and the extremely high cost of carbon emissions. If the model has installed more nuke, that marginal nuclear capacity would have had the same very low capacity factor as the gas turbines. But it would have been more costly and it would have produced more CO2.

The GKG model is smart enough to divide CO2 emissions into fixed and variable.³ The fixed CO2 comes from providing the capacity. The variable CO2 is almost all fuel. Nuclear has a much smaller variable CO2 intensity (4.7 g/kWh) than gas (700 g/kWh for OCGT) but a much higher fixed CO2 (131 kg/kW versus 11.5). These assumptions show up in the red box. If the capacity factor is small enough, the marginal nuke will be more CO2 intensive than the marginal gas. For the Table 1 numbers and a 6% discount rate, the breakeven capacity factor is 0.0012. By installing some OCGT capacity, the program was able to save some money and reduce CO2 emissions. On the right side of the blue box, you can see that nuke is creating almost all the CO2 emissions, in this very low carbon grid.

Now I know what is in your evil little minds. The five or six synapses therein are slowly forming the but-this-is-not-a-zero-carbon-grid pattern. There is no such thing as a zero CO2 grid. All the lines in Figure 1 turn vertical before they get to zero. Not only is there no such thing as a zero CO2 grid, any real attempt to impose one would be a cataclysmic disaster for humanity, starting with the poor. The goal here is not zero CO2 emissions. The goal is maximizing humanity's well being. As soon as we get to the point where the cost of further decreasing CO2 emissions is more than the social cost of CO2, we must stop. By the same token, if we overstate the cost of CO2 and reduce emissions based on that over-estimate, we will not be maximizing human welfare.

To get a little insight into the tradeoff, consider Table 2, which is a run in which everything is the same as Table 1, except the social cost of CO2 has been reduced to $200/ton, a bit more than EPA's proposed number.

Table 2. GKG Model Run, Nuke CAPEX = $2000/kW, SCC = $200/ton CO2.

The model's overall results are in the green box. Thanks to the reduction in the SCC, the optimal carbon intensity has risen from 6 grams CO2/kWh to 13. Still a very low number. The intensity of the current German grid is about 400 gCO2/kWh. The market cost of the power has dropped from $57/MWh to $53/MWh. Over the 8 year period, this grid emits 30 million tons more CO2, but consumes 14 billion dollars less resources. The German people are 14 billion dollars wealthier. If the Social Cost of CO2 really is $190/ton as the EPA claims, the German people are better off with Table 2 and worse off with Table 1. Even if you are a CO2 freak, that 14 billion dollars almost certainly could reduce more CO2 elsewhere.

Figure 2 compares the two grids graphicly.

The fact that the model can afford to buy a lot of gas and then use it very sparingly should tell us something about how the USA should organize her grid. This will be the subject of an upcoming piece.

1. In Figure 1, the slope in $/ton CO2 has to be adjusted for the units being displayed. An SCC of $200/ton is a slope of 0.2 on the figure, to go from grams to tons and MWh to kWh.

2. Above $8000/kW CAPEX, all the $200/ton CO2 points fall on top of each other, making a mess of my beautiful artwork.

3. Any model of CO2 emissions that does not do this (which as far as I know means all of the non-GKG models) can and usually will produce misleading results.