The Impact of Learning 107 

So far, analyses of fuel cycle decisions have assumed that LWR and FR costs are constant over the entire simulation. While the methodology does model uncertainty in the relative FR cost, once this uncertainty is resolved, there are no further changes. We know the assumption of perfectly constant costs (for any type of nuclear reactor over time) to be

inaccurate. Costs may change for any system in the nuclear fuel cycle, but for purposes of this discussion, capital costs are the primary focus because they are the strongest driver of nuclear electricity cost.

Capital costs for either reactor type could increase over time, depending on

macroeconomic factors like commodity costs, or regulatory delays. At least one study, for example, has concluded that nuclear reactors costs actually increased in real terms over the main buildup of the French fleet, because of escalation in complexities of reactor design and

construction processes.(Grubler, 2009) The U.S. fleet, with far less standardization than that present in the French fleet, has also surely seen a real escalation in nuclear costs.

It is possible, however, that for the large number of builds envisioned in many of these growth scenarios, the capital costs of plants will come down due to learning effects, and indeed other studies have found positive learning rates for the nuclear industry. The University of Chicago performed an extensive economic analysis of nuclear power, focusing mostly on LWR technology; among their investigations is a survey of literature on nuclear learning rates.(The University of Chicago, 2004) They conclude that a learning rate of 3-10% cost improvement with each doubling of units built is a fair estimate, and they provide conditions under which various points along that range are appropriate.

The actual learning rate for LWRs, and for less economically-understood FRs, is a subject of intense debate. For purposes of this study, estimates within the 3-10% range are

applied to LWR and FR costs, in order to determine the basic effect on learning decision analysis results. A 3% learning rate is assumed for LWRs (intended to reflect the likelihood of near-term slow growth), while a 5% learning rate is assumed for FRs (because FRs are built later in the century and generally at a faster, more continuous pace, allowing for higher worker retention and better construction learning). The initial cost premiums of FRs are increased, because the 55% and 5% cost premiums were based on an assumption of an “nth of a kind” plant. Now, the first

108

FR will cost 100% more than a LWR at the high range, and 25% at the low range, but the learning curve will bring those costs down as more FRs are built.

Learning is implemented in FANTSY by tracking the number of each reactor type built, and calculating the cost adjustment factor (CAF) for year y by:

1 ⁄

where d is the learning rate, and n is the number of reactors built up to the beginning of year y (equation adapted from (The University of Chicago, 2004)). The CAF for year y is then multiplied by the initial capital cost of the reactor, and that cost is used for all reactors built in year y. For the particular learning rates assumed and at the highest-growth scenario, fast reactor costs reach 60% of their initial cost by the end of the simulation. This represents the most extensive cost reduction due to learning of all pathways in the analysis.

The new cost model is applied to the five-option decision tree that includes the option of building FRs or EUFRs at 10% of the allowed rate (tree depicted in Figure 5-10). The results for decision desirability across the range of cost weights and period 1 growth probabilities are shown in Figure 5-33. The dark purple region shows the growth and cost weight conditions under which building 10% TFRs was desirable before, given constant reactor costs (the assumptions of

section 5.3). When learning is included as described above, the 10% TFR space expands out to the blue area.

109

Figure 5-33: Increased desirability of building 10% TFRs given learning

We would expect TFRs to become more desirable in general if the learning curve brings the cost of fast reactors closer to the cost of LWRs. In fact, for this particular set of assumptions, the cost gap between FRs and LWRs is greater than it was in section 5.3, and for most decisions throughout the tree, FRs become less desirable than they were in previous studies. For the second period decisions that follow the best first period options, the decrease in FR desirability is small but evident.

Figure 5-34 shows the impact of learning on the first period decision for a value function incorporating the relative heat output of each type of waste (a more full explanation of the differences between value functions is presented in section 6.1). A comparison of the results for learning vs. no learning elucidates a seeming contradiction: the space favoring 100% TFR builds

110

shrinks when learning is considered, but the space favoring 10% TFRs grows. As mentioned above, it makes sense that the space favorable to TFRs shrinks, because the particular

assumptions about learning mean that FRs are especially expensive relative to LWRs throughout the simulation.

Figure 5-34: Effect of learning on the first-period decision, for heat metric value function

In fact, the 10% TFR decision responds differently to learning because of the particular pattern of FR construction in that scenario. Figure 5-35 shows the FR construction pattern for the three decision options represented in Figure 5-34 (all at high growth only). The three sets of data represent three different first period decisions, modeled along with the optimum second period decision. For both the LWR and 100% TFR scenarios, the optimal second period decision is to build TFRs at 100%. The graph shows that “clumped” construction results, whereby many

111 reactors are built in short bursts. For the 10% TFR decision, the optimal second period choice is to build 50% TFRs, and the result includes slightly more total TFRs built than for the other two scenarios in addition to a much smoother build pattern.

The learning factor is calculated each year. This means that when FRs are built smoothly across many years, more reactors are built at lower cost. Rather than build 15 reactors in a single year at one point on the learning curve, those 15 reactors are stretched across several years and the cost decreases each year. Ultimately, this means that the 10% TFR scenario comes out with a slight cost advantage relative to its position when learning is not considered.

It is of note, however, that inclusion of a learning cost model overall has only a small impact. Even with dramatic assumptions about initial costs, learning rates, and growth rates, learning by doing has a tiny effect on the optimal decision space. These results do confirm, however, that sustained, smooth building is preferable to a “bunched” build profile in order to maximize the effects of learning. Further exploration of the relationship between the building curve shape and decision results is presented in section 6.5.

112

5.9 Key Takeaways from Learning Curve Analysis

Assuming that nuclear reactor costs will decrease over time due to learning effects has only a small effect on the decision space. The effect is to increase the overall desirability of building traditional fast reactors at 10% of the allowed pace and increasing the pace later, because this particular configuration allows for the smoothest building curve. Given that learning is likely to disseminate relatively slowly (under long construction times), spreading reactor builds out across more years allows better leverage of learning cost reductions.

113