Friday, April 4, 2014

The Truth About Nuclear Power – Part Eight

Subtitle: No Benefits From Smaller Modular Nuclear Plants

Are there any benefits from small, modular nuclear power plants?    As background, this series on nuclear power has shown that large, “cathedral” nuclear power plants of 1,000 MWe or greater cost as much as $10 billion each to construct.  The high capital costs require a high power sales price, making the new generation of nuclear power plants uneconomic.  See Part Two,  Part Three, and  Part Six for particulars.   This article explores the costs that can be expected if smaller, modular nuclear power plants are installed.  There is a contingent of nuclear power proponents that insists that costs per kW can be reduced by building smaller plants, more of them, and building them in controlled factory conditions.   But, are those assertions true?
Modular Small Nuclear Plant
The short answer is, No.  Supposedly, the benefits are shorter construction times, less inflation, less interest on loans, all of which lead to lower costs.  But, loss of economy of scale overwhelms such benefits.  Consider 1200 MWe vs 600, 400, 300, and note that Dept of Energy defines Small Modular Reactors as 300 MW or less.  Each of the smaller size plants must be delivered much more quickly to achieve any savings in materials inflation and interest on construction loans.    A shorter construction period very likely cannot be done due to fabrication and delivery of large items: the reactor, steam generators, turbines, and pumps. 
There is, perhaps, a case for some capital savings for a smaller plant if only one steam generator can do the job instead of two or more.  For example, the 1600 MW plant under construction in Finland has four steam generators for its one reactor.  The recently-closed plants in California at San Onofre each produced a bit more than 1000 MW, and each reactor has two steam generators.   Those steam generators, at approximately 500 MW per steam generator, caused problems that led to the plant shutting down.  Therefore, a 600 MW plant with one steam generator probably cannot be done, or at least, no one would take that risk.  But, a 400 MW plant could have one reactor and one steam generator and still remain within the proven size of approximately 400 to 500 MW per steam generator.  That single bit of savings, however, would not be enough to overcome the cost increase per kW created by the loss of economy of scale.
The initial premise is that a 1,000 MWe nuclear plant would cost $4,000 per KW as its overnight cost (the cost to construct if it could all be built in one month, or “overnight”), and materials and labor escalation or inflation over six years increases the cost by $3,000 per kW, and finally, interest on the construction loan increases the cost by another $3,000 per KW.  The total is then $10,000 per kW.    The sources for these costs is explained in detail in Part Three.   (Note, EIA shows 2013 overnight costs for a new nuclear plant as $5,530 per kW).  See Table 2 from  this link
Costs for a smaller plant can be expected to follow the “Point 6” power rule for economy of scale, such that the cost of Unit B is found by the formula 
Cost B = Cost A x (Size B / Size A) ^0.6.   
An example illustrates using overnight costs only, where Size B is 400 MW, Size A is 1200 MW, and Cost A is $4,800.  Then,

Cost B = $4,800 x (400/1200)^0.6  = $2,483 per kW overnight cost.

Then, for a total power output of 1200 MW, three of the 400 MW plants are required.   The total overnight costs for the three plants is then 3 x 2483, or $7,449 per kW.    The goal here is to have a final cost less than $12,000, which is the single-plant size of 1200 MW times the cost per kW of 10,000.   With the overnight cost already at $7,450 (rounded slightly, which is fine using such rough numbers), one is left with only 4,550 available for inflation and escalation, plus interest.   If we make the very rough allocation of escalation or inflation is the same as interest on the loan, that then results in each category being half of 4,550, or 2,275.   
Then, we can compute the number of years that the modular plant must require for construction, at inflation of 5 percent per year.   Calculations show that approximately 5.5 years at 5 percent per year yields the desired result.  To save any on the final costs, then, the modular plants must be built in less than 5.5 years.   Stated another way, savings are realized only if the plant can be brought online in 3 or 4 years from notice to proceed. 
The question is, then, can it be done?  Once again, the nuclear industry is scrambling, trying to find a way to justify itself.   Small, modern design, modular-constructed nuclear power plants have never been built in the US, indeed, they are not even approved by the NRC.   The first projects would suffer all the problems of first-of-a-kind projects, and likely have no cost reductions at all. 
The same analysis can be performed for smaller plants, such as 300 MW, where four plants would be required to produce 1200 MW of power, and 200 MW, where six plants would be required.  The results are as follows.  The 300 MW plants must be constructed in 4 years to have zero savings, with any savings produced only if construction time is 2 or 3 years.  The 200 MW plants must be constructed in 2.1 years to have zero savings over the cathedral design.    It seems highly unlikely that small, modular plants can be built on such short timescales.  
The analysis is dependent on the inflation or escalation rate for equipment, labor, and services over the life of the project.  If the inflation rate is higher, as many forecasters predict must be the case, then the situation is worse.  The amount of time required to build the plant and yield a cost savings will be less and less as the inflation rate increases.
There are no benefits to the smaller, modular nuclear power plants that some nuclear power proponents advocate.   The loss of economy of scale requires much shorter construction times for any savings to be had. 

Update: 4/17/14 - Modular reactor developer cuts development, funding by 90 percent due to lack of customers and lack of investors.  (Imagine that...)  "Babcock & Wilcox will slash its spending on the mPower small modular reactor project, having failed to find customers or investors."  also, from same article:   "In February this year (2014) Westinghouse announced it would scale back its development of its 225 MWe small modular reactor design, having lost out in the DoE competition."  see link from World Nuclear News, 4/14/14  -- end update

Update 2-   4/19/14: - Navy-style small reactors are mentioned by nuclear advocates as proof that smaller reactors are viable.  Those reactors do indeed function for the purpose.  However, the issue is one of cost and the price require for electric power on a grid powered by nuclear reactors.  The US Navy has many nuclear powered ships and submarines that work very well.  Those reactors are not designed like commercial power plants.  Also, the economy of scale applies here.  It appears that the largest of the military reactors are approximately 165 MWe, however the USS Ronald Reagan, a new aircraft carrier, has two nuclear reactors each producing just under 100 MW of shaft power.   Such small reactors would require very high-priced electricity.   -- end update 2
Previous articles in The Truth About Nuclear Power can be found at the following links. 

Roger E. Sowell, Esq.
Marina del Rey, California

1 comment:

Anonymous said...

You are right: cost is proportional to the surface (materials), power is proportional to the volume of the core. But the same rule is applicable to the passive cooling efficiency:

Cost_B = Cost_A x (Size_B / Size_A)^n
PCE_B = PCE_A x (Size_B / Size_A)^n

PCE - Passive cooling efficiency
n = 0.5 - 0.7

300 MW nuclear power station is more costly than 1200 MW, but smaller reactor is safer. Deterministic safety is achievable for all small enough reactors. Alvin Weinberg pointed out already 50 years ago that probabilistic safety is nice, but deterministic safety is a real safety. Moreover playing with probabilistic safety the reactors are getting safer and safer but they are more and more expensive, they have more and more safety systems.

It is high time to come back to small reactors and deterministic safety concepts.