Development of the Mathematics of Learning Curve Models for Evaluating Small Modular Reactor Economics
The cost of nuclear power is a straightforward yet complicated topic. It is straightforward in that the cost of nuclear power is a function of the cost to build the nuclear power plant, the cost to operate and maintain it, and the cost to provide fuel for it. It is complicated in that some of those costs are not necessarily known, introducing uncertainty into the analysis. For large light water reactor (LWR)-based nuclear power plants, the uncertainty is mainly contained within the cost of construction. The typical costs of operations and maintenance (O&M), as well as fuel, are well known based on the current fleet of LWRs. However, the last currently operating reactor to come online was Watts Bar 1 in May 1996; thus, the expected construction costs for gigawatt (GW)-class reactors in the United States are based on information nearly two decades old. Extrapolating construction, O&M, and fuel costs from GW-class LWRs to LWR-based small modular reactors (SMRs) introduces even more complication. The per-installed-kilowatt construction costs for SMRs are likely to be higher than those for the GW-class reactors based on the property of the economy of scale. Generally speaking, the economy of scale is the tendency for overall costs to increase slower than the overall production capacity. For power plants, this means that doubling the power production capacity would be expected to cost less than twice as much. Applying this property in the opposite direction, halving the power production capacity would be expected to cost more than half as much. This can potentially make the SMRs less competitive in the electricity market against the GW-class reactors, as well as against other power sources such as natural gas and subsidized renewables. One factor that can potentially aid the SMRs in achieving economic competitiveness is an economy of numbers, as opposed to the economy of scale, associated with learning curves. The basic concept of the learning curve is that the more a new process is repeated, the more efficient the process can be made. Assuming that efficiency directly relates to cost means that the more a new process is repeated successfully and efficiently, the less costly the process can be made. This factor ties directly into the factory fabrication and modularization aspect of the SMR paradigm—manufacturing serial, standardized, identical components for use in nuclear power plants can allow the SMR industry to use the learning curves to predict and optimize deployment costs. Thus, SMR deployment cost estimates can be modeled using learning curve theory to provide some insight into how and when SMRs would be competitive with both the GW-class reactors and other mutual competitors. However, assuming static learning curve behavior for all aspects of SMR construction is likely an invalid approach—not all components and systems in SMRs will be subject to learning, and those that are subject to learning may not learn at the same rate. A learning curvebased model must be capable of tracking these unique behaviors. At the same time, the behavior of the aggregated and integrated SMR deployment is a more useful metric for discussion and comparison—ultimately, the most useful learning curve information is that which describes power plant deployment as a whole. Therefore, the goal of SMR component and systems learning modeling includes a method to produce an overall power plant learning model. This report describes the mathematics of learning curves that can be used for estimating unit cost in future production for individual components and aggregated systems. All necessary assumptions are provided to support the derivations presented. Future work will demonstrate the implementation of this methodology and provide example calculations of SMR cost