Showing posts with label San Onofre. Show all posts
Showing posts with label San Onofre. Show all posts

Sunday, September 13, 2015

US NRC Stops Study of Cancer Risks near Reactors

Subtitle: $8 Million Is Too Costly to Study Nuclear-Caused Cancer

The NRC has cancelled an $8 million study that would have determined, then published, the statistics on greater-than-normal incidences of diseases among persons, especially children, living within close distances of nuclear power plants.   The technology and data is available for the study, but NRC chose not to allocate funding to the study.  Predictably, nuclear advocates cheered, and nuclear opponents are disappointed.  see link to the article.   
An earlier (1991) study of health effects near nuclear plants was fatally flawed by design, and its results are not surprising.   

Quoting the article: "Among the 1991 study’s many problems, according to scientists who were designing the new probe:

•"It tracked mortality rates based on where people died, rather than where they lived before getting cancer. That makes it hard to determine true lifetime exposure.

• "It tracked deaths, rather than total cancer cases. That may downplay the full health impact of living near a reactor, since many cancer patients survive.

• "It used countywide data to reach conclusions – a blunt instrument that may again downplay the impact on those living closest to a reactor. Residents in La Habra and San Clemente live in the same county – but few would argue that they had the same exposure to San Onofre.  (Note, San Clemente is only a few miles from SONGS, while La Habra is approximately 40 miles away.)

"To remedy all that, the NRC asked the NAS (National Academy of Science) to evaluate cancer diagnosis rates, not just cancer deaths; and to explore how to divide the areas around nuclear facilities into geographical units smaller than counties. The NAS made no bones about the effort being difficult and time-consuming, but said it could be done."   

This is certainly an area where citizen volunteers - qualified and motivated - should step forward to perform this study pro-bono.   However, it is a shame that the US government cannot find the $8 million to perform the initial study of 7 reactors.   In an era where government spending, and borrowing, is full of studies for irrelevant issues, this one is certainly deserving of funding.

See this link for a more detailed article on nuclear power and radiation health effects. 

Roger E. Sowell, Esq.
Marina del Rey, California
Copyright (c) 2015 by Roger Sowell, all rights reserved


Monday, June 30, 2014

The Truth About Nuclear Power - Part 24

Subtitle: St. Lucie Ominous Tube Wear

Tube wear in steam generators at the twin-reactor nuclear plant at St. Lucie, Florida, is the subject of this article 24.  St. Lucie in on a barrier island, a few miles north of Palm Beach.  (see photo).  There are no cooling towers, but inlets to the Atlantic Ocean are
St. Lucie Nuclear Unit 1 and 2, Florida
Atlantic Ocean on right, two containment domes in left-center
photo from Google maps - 6/29/2014
clearly visible.   This plant has the pressurized-water reactor technology, hence it has steam generators very similar to the ones that failed in 2012 at San Onofre in southern California.   The leaking tubes at St. Lucie have been in the news recently, with public concern growing over fears that they, too, may be irradiated when a tube bursts and spews radioactive steam into the skies. (see link, and link, and link for news articles.)

Background

A steam generator is nothing more than a heat exchanger, typically with U-tubes in a vertical configuration.  Hot water from the reactor is pumped through the tubes, flowing in at the bottom, up through the tubes, around the U-bend, and back down and out again at the bottom. (this is somewhat simplified).   On the outside of the tubes, the shell-side, boiler feedwater is pumped in at the bottom.  The boiler feedwater rises in between the tubes and is heated as it rises.  At some point in the upward journey, the water begins to boil.  Steam rises to the top of the steam generator and flows out the top to the steam turbine. 

The point of concern is where the water begins to boil.  The steam bubbles exert pressure in all directions, some of it upward, some downward, and some to the sides.  Since water is incompressible (at least at these conditions), the downward pressure has essentially no effect.  The upward pressure has the most effect, because the mixture of water and steam above the boiling zone is much less dense.  Therefore, steam bubbles push water upward, and rather strongly.   However, it is the horizontal force that is of most concern.  As the water and steam mixture rises, one can imagine that the amount of water decreases while the amount of steam increases.  Therefore, water is also forced horizontally by the steam bubbles.  The tubes, which as already mentioned are vertical, resist the horizontal force and bend to some extent.  The tubes are not rigid, but have thin walls.  The tubes also are not very far apart, perhaps one-quarter inch spacing between tubes.  With violent boiling occurring, the tubes can vibrate and hit each other.  To minimize this banging, manufacturers install stability bars or stabilizer bars.  However, the tubes can also rub against the stabilizer bars. 

None of this is new and surprising, as heat exchanger designers have known this for decades.  The goal is to design and manufacture a steam generator that sustains the tube collisions and rubbing for 20 to 30 years, and continues to produce quality steam without releasing radioactivity to the atmosphere.  It is a very good thing, then, that nuclear reactors take a shutdown to refuel and inspect equipment approximately every 18 months.   Part of the inspection procedure is to pressure test the steam generator tubes, and to perform visual inspections to identify any worn spots or places that fail during the pressure test.  With approximately 9,000 tubes in a single steam generator, it is acceptable to plug a few tubes so that no water flows through those tubes.  This is not limited to nuclear plant steam generators, as pressure testing heat exchanger tubes and plugging those that leak is a common practice in many industries.  For many heat exchangers, more tubes are added in the manufacturing stage than are actually required to meet the heat transfer goal.  The over-design, or safety factor, allows some tubes to be plugged as the years go by, and the heat exchanger continues to serve satisfactorily.

Implications on Safety and Cost

With that as background, the St. Lucie plant is noteworthy due to the unusual number of steam generator tubes with wear.  NRC inspectors are reportedly aware of the steam generator tube condition and are monitoring the plant closely.    The NRC has not required the plant to shut down for safety concerns, at least not as of this writing (June 30, 2014).    The steam generators in Unit 2 were replaced in late 2007, so they have been in service for barely more than 6 years.   The original steam generators lasted 24 years, from 1983 to 2007.    An article with photos and describing the steam generator replacement process is available – see link.

The safety implications are a concern, and if the new steam generators fail prematurely, then there are cost issues also.  As Part 23 in the series showed, southern California utility customers are being asked to pay billions for faulty equipment that resulted in two shutdown reactors.   The people of Florida would also be outraged if this happens to them. 

Until a report is issued by NRC on the tube wear at St. Lucie Unit 2, which is expected late in 2014, it is perhaps best to sit and watch.  Perhaps the people of Florida will be lucky, and their St. Lucie nuclear plant will continue to run without catastrophic tube failure.  Perhaps the utility spokesperson is correct, and the tube wear is slowing down. 

This article will be updated as conditions warrant. 

Previous Articles

The Truth About Nuclear Power emphasizes the economic and safety aspects by showing that (one) modern nuclear power plants are uneconomic to operate compared to natural gas and wind energy, (two) they produce preposterous pricing if they are the sole power source for a grid, (three) they cost far too much to construct, (four) use far more water for cooling, 4 times as much, than better alternatives, (five) nuclear fuel makes them difficult to shut down and requires very costly safeguards, (six) they are built to huge scale of 1,000 to 1,600 MWe or greater to attempt to reduce costs via economy of scale, (seven) an all-nuclear grid will lose customers to self-generation, (eight) smaller and modular nuclear plants have no benefits due to reverse economy of scale, (nine) large-scale plants have very long construction schedules even without lawsuits that delay construction, (ten) nuclear plants do not reach 50 or 60 years life because they require costly upgrades after 20 to 30 years that do not always perform as designed, (eleven) France has 85 percent of its electricity produced via nuclear power but it is subsidized, is still almost twice as expensive as prices in the US, and is only viable due to exporting power at night rather than throttling back the plants during low demand, (twelve) nuclear plants cannot provide cheap power on small islands, (thirteen) US nuclear plants are heavily subsidized but still cannot compete, (fourteen), projects are cancelled due to unfavorable economics, reactor vendors are desperate for sales, nuclear advocates tout low operating costs and ignore capital costs, nuclear utilities never ask for a rate decrease when building a new nuclear plant, and high nuclear costs are buried in a large customer base, (fifteen) safety regulations are routinely relaxed to allow the plants to continue operating without spending the funds to bring them into compliance, (sixteen) many, many near-misses occur each year in nuclear power, approximately one every 3 weeks, (seventeen) safety issues with short term, and long-term, storage of spent fuel, (eighteen)  safety hazards of spent fuel reprocessing, (nineteen) health effects on people and other living things, (twenty) nuclear disaster at Chernobyl, (twenty-one) nuclear meltdown at Three Mile Island, (twenty-two)  nuclear meltdowns at Fukushima, (twenty-three) near-disaster at San Onofre, (twenty-four) the looming disaster at St. Lucie, (twenty-five)  the inherently unsafe characteristics of nuclear power plants required government shielding from liability, or subsidy, for the costs of a nuclear accident via the Price-Anderson Act, and (twenty-six) the serious public impacts of large-scale population evacuation and relocation after a major incident, or "extraordinary nuclear occurrence" in the language used by the Price-Anderson Act.  Additional articles will include (twenty-seven) the future of nuclear fusion, (twenty-eight) future of thorium reactors, (twenty-nine) future of high-temperature gas nuclear reactors, and (thirty), a concluding chapter with a world-wide economic analysis of nuclear reactors and why countries build them.  Links to each article in TANP series are included at the end of this article. 


Additional articles will be linked as they are published. 













Part Twenty Three - San Onofre Shutdown Saga
Part Twenty Four - this article

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




Sunday, June 29, 2014

The Truth About Nuclear Power - Part 23

Subtitle:  San Onofre Shutdown Saga

The twin-reactor nuclear power plant at San Onofre, California, known as SONGS (San Onofre Nuclear Generating Station), is now shutdown after a project to replace worn steam generators resulted in premature tube leaks that released a small amount of radioactive steam to the atmosphere.  The plant's majority owner, Southern California
SONGS Nuclear plant aerial view
Pacific Ocean at bottom, Interstate 5 at top
source: Wikipedia
Edison, SCE, chose to shut down the plant permanently rather than determine the cause of the premature failure and correct the problem.   More on the details of the technical side may be found in Part Ten, see link,   and in Part 16, see link.  


The reasons for choosing a different design for the worn steam generators, and the economic aftermath for ratepayers and utility shareholders are the subject of this article, Part 23 in the series. 

Choosing a Bad Design

The NRC has two separate paths for allowing replacement parts at a nuclear power plant: 1) like-for-like, where the new part is so nearly identical to the old part that a comprehensive design review is not required, and 2) differences between the new and old parts are substantial, and a comprehensive design review is required.    SCE informed NRC that the new steam generators, two each for each reactor at SONGS, were like-for-like.  That turned out not to be true.   A couple of differences were 1) more tubes in the new steam generators, and 2) each tube had a slightly smaller internal diameter.   

A utility company is in business for profit, and tries to make more profit where it can and is legally permitted to do so.   Even at a nuclear plant, opportunities occur to increase profits.  One way to increase profit is to increase the plant's output.  As with most process plants, it is normally not economically attractive to replace a constraining part because the increased benefits are small while the added costs for replacing the part are large.   A constraining part in a nuclear power plant could be, for example, a steam generator or steam turbine.  

That economic computation changes, however, when a part is so worn that it must be replaced to stay in business.  At that point, engineers can perform an incremental project analysis to determine if the part can be replaced with a somewhat larger part that produces more profit.  Due to economies of scale, making the part only a few percent larger can cost very little extra.  For example, making a steam generator 5 percent larger in surface area could produce perhaps 5 percent more electrical output.   This is not a hypothetical, as some nuclear plants across the US have increased their generating capacity to a few percent above the design capacity.   This is very likely what SCE was trying to accomplish at SONGS.  

Where SCE erred was choosing the new design for the steam generators.  The design turned out to have more vibration so that adjacent tubes banged into each other, rubbing metal away so that tube walls thinned and holes formed.  The holes allowed the radioactive water to leak into the steam system.   Safety was compromised, and the NRC was correct in stopping SCE from running the plants until the problem was resolved.  

Economic Consequences

This entire episode was also described in a newspaper article which is actually not badly written.  (This is high praise from me, as most newspaper articles on technical subjects get it very wrong.)  see link   

The utility wanted approximately $4.7 billion in compensation from the California Public Utility Commission, CPUC, for making the utility whole.  The customers, or ratepayers, would pay the entire amount in the utility's request.  However, ratepayer advocates negotiated a reduced amount - but not by much.   The settlement agreement provides for $1.4 billion reduction, leaving $3.3 billion for ratepayers.   The CPUC will make a decision on who pays how much for what.   The basics of the proposed settlement can be found here -- see link

The higher, policy argument is this: should a monopoly utility be rewarded for making stupid economic decisions?  In this case with SONGS, the amount in question is only $4.7 billion.  SCE is a huge utility, with a bit more than $12 billion in annual revenue, $45 billion in assets, 5 million customer accounts serving 14 million customers, transmission peak of 22,500 MW, and employing approximately 13,000 people.  (source: SCE Annual Report 2013)

As the LA Times article (linked above) noted, this proposed settlement is akin to bailing out the banks in the economic crisis of 2008-2009.   As ratepayer advocates stated, it is simply wrong to reward bad behavior by a utility.  In my own words, somebody should give a utility reason to pause, think it over, and realize that jobs will be lost and the company will suffer for taking such a great risk.   SCE could have easily ordered identical new steam generators, the same as the ones that ran perfectly well for 20-plus years.   That would have been the no-risk alternative.  Instead, the new design was chosen (perhaps) to increase plant output and profit.   

It is the CPUC's job to look out for the ratepayer.     One hopes that the settlement agreement is not accepted, and the utility is forced to bear the entire costs of making a stupid decision.  


Previous Articles

The Truth About Nuclear Power emphasizes the economic and safety aspects by showing that (one) modern nuclear power plants are uneconomic to operate compared to natural gas and wind energy, (two) they produce preposterous pricing if they are the sole power source for a grid, (three) they cost far too much to construct, (four) use far more water for cooling, 4 times as much, than better alternatives, (five) nuclear fuel makes them difficult to shut down and requires very costly safeguards, (six) they are built to huge scale of 1,000 to 1,600 MWe or greater to attempt to reduce costs via economy of scale, (seven) an all-nuclear grid will lose customers to self-generation, (eight) smaller and modular nuclear plants have no benefits due to reverse economy of scale, (nine) large-scale plants have very long construction schedules even without lawsuits that delay construction, (ten) nuclear plants do not reach 50 or 60 years life because they require costly upgrades after 20 to 30 years that do not always perform as designed, (eleven) France has 85 percent of its electricity produced via nuclear power but it is subsidized, is still almost twice as expensive as prices in the US, and is only viable due to exporting power at night rather than throttling back the plants during low demand, (twelve) nuclear plants cannot provide cheap power on small islands, (thirteen) US nuclear plants are heavily subsidized but still cannot compete, (fourteen), projects are cancelled due to unfavorable economics, reactor vendors are desperate for sales, nuclear advocates tout low operating costs and ignore capital costs, nuclear utilities never ask for a rate decrease when building a new nuclear plant, and high nuclear costs are buried in a large customer base, (fifteen) safety regulations are routinely relaxed to allow the plants to continue operating without spending the funds to bring them into compliance, (sixteen) many, many near-misses occur each year in nuclear power, approximately one every 3 weeks, (seventeen) safety issues with short term, and long-term, storage of spent fuel, (eighteen)  safety hazards of spent fuel reprocessing, (nineteen) health effects on people and other living things, (twenty) nuclear disaster at Chernobyl, (twenty-one) nuclear meltdown at Three Mile Island, (twenty-two)  nuclear meltdowns at Fukushima, (twenty-three) near-disaster at San Onofre, (twenty-four) the looming disaster at St. Lucie, (twenty-five)  the inherently unsafe characteristics of nuclear power plants required government shielding from liability, or subsidy, for the costs of a nuclear accident via the Price-Anderson Act, and (twenty-six) the serious public impacts of large-scale population evacuation and relocation after a major incident, or "extraordinary nuclear occurrence" in the language used by the Price-Anderson Act.  Additional articles will include (twenty-seven) the future of nuclear fusion, (twenty-eight) future of thorium reactors, (twenty-nine) future of high-temperature gas nuclear reactors, and (thirty), a concluding chapter with a world-wide economic analysis of nuclear reactors and why countries build them.  Links to each article in TANP series are included at the end of this article. 


Additional articles will be linked as they are published. 













Part Twenty Three - this article

Part Twenty Four - St. Lucie Ominous Tube Wear





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


Thursday, May 15, 2014

San Onofre Nuclear Power Plant Threatened by Wildfire

Subtitle: Power Outage Doomed Fukushima - is San Onofre Next? 

The nuclear power plant in San Onofre in Southern California, now shut down permanently, today announced it was evacuating non-essential personnel in advance of a wildfire that threatens the plant.  see link.

From the article, "The fires do not pose a safety issue at San Onofre at this time, but we continue to coordinate with regional agencies to ensure we remain apprised of evolving conditions."   This is code-speak for "these wildfires can get out of hand quickly, with the high temperatures and high winds."

With the San Onofre plant shut down, there are still electrical loads to maintain cooling water pumps in service that keep spent fuel in the cooling pools sufficiently cool.  This was a problem at Fukushima, as they had no electrical power after the earthquake and tsunami, and their emergency generators were flooded.  

It would not take much for the wildfires to burn near or under the transmission lines that bring power to the San Onofre plant.  It is certainly hoped that this does not happen.  But, if it were to happen, it is also hoped that the plant management has ample supplies of diesel fuel with which to run the emergency generators to keep the spent fuel properly cooled.  

The last thing California needs is a nuclear radiation release from San Onofre, with the resulting evacuation of millions of local residents. 

Someone should put in a call to Chevron, or ExxonMobil, or one of the other oil companies, and order up a couple of tank-trucks of diesel fuel to be brought on-site and kept there just in case.   

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


Wednesday, April 9, 2014

The Truth About Nuclear Power - Part Ten

Subtitle: Nuclear plants require costly upgrades after 20 to 30 years
Steam generators inside containment structure
Purple-cutaway view.
source: NRC
One of the favorite arguments of the nuclear proponents is that, even though a nuclear plant costs more to build, it lasts for 60 years.  The second part of the statement is not true, although the first part is definitely true.  Equipment wears out, and must be replaced at significant cost.  As an example, the pressurized water reactors, PWR, have an expensive heat exchanger – the steam generator – that suffers tube degradation over time. see image.  NRC requirements cause these steam generators to be replaced when tube degradation reaches a certain level.  For some plants, the replacement works.  At California’s San Onofre plant – SONGS – however, four replacement steam generators failed recently very soon after startup.  The plant owner, Southern California Edison, SCE, elected to shut down the plant permanently rather than complete the steps required by the NRC to ensure the steam generators could be repaired and operate safely. 
Details of the SONGS steam generator troubles can be found at the NRC website: see link.  
The NRC described the tube degradation as “unexpected.”  Apparently, the type of tube wear and degradation is one that has never been witnessed before.   The tube wear was due to adjacent tubes rubbing against each other, and tubes rubbing against retainer bars.    The safety concern, unique to nuclear power plants using the PWR design, is a sudden loss of main steam header pressure.   In the words of the NRC, this is a main steam line break.   The reason this is a safety concern is that radioactive hot water under high pressure flows on the inside of the tubes in the steam generator.  At a somewhat lower pressure, water flows on the outside of the tubes.  The water on the outside of the tubes is heated, boils, and turns to steam (hence the name, steam generator).  The tube walls must retain their strength to prevent leaks of the radioactive water through the tubes and into the steam system.  The steam system's pipes run outside the containment building, into the steam turbine, and from there steam flows into the condenser.   With both systems operating normally, pressurized radioactive water on the inside of the tubes, and lower pressure water/steam on the outside, the tubes have an easier task in keeping the two water systems separate.  But, if a main steam line breaks, the pressure difference across the tube walls increases suddenly and dramatically.  Weak tubes would, of course, fail and send radioactive water and steam into the atmosphere.  This is unacceptable, but is a natural consequence of choosing to generate power using nuclear fission as the heat source.
Indeed, this is exactly what happened at SONGS when the new steam generators sprung a leak, radioactive water entered the steam system, and a small amount of radioactive steam was released into the atmosphere.  See link  As required, SCE shut down the plant to investigate. 
The sticking point in the order from NRC to SCE was this: “SCE will determine the causes of tube-to-tube interaction and implement actions to prevent recurrence of loss of integrity in the Unit 3 steam generator tubes while operating.”   That is a most reasonable requirement, find out what happened, and implement steps to make sure it does not happen again.  SCE, however, either could not, or would not take the time and expense to determine the causes.  Instead, SCE shut down both reactors in the plant.
It should be noted that minor tube wear is normal and expected.  Indeed, with the more than 9,000 individual tubes in one steam generator, a tube that is near failure due to excessive wear can be plugged to remove it from service.  The difference in this case was the rapid tube wear so very soon after the new steam generators were placed in service.   The original steam generators lasted not quite 30 years, as the SONGS reactors came online in 1983 and 1984, and the steam generators were replaced around 2010.  The radioactive steam leak occurred in January, 2012. 
There is much more to the story of the leaking tubes at SONGS.  As time permits, that story will be told.  It involves SCE trying to obtain an extension to the operating permit by claiming the replacement steam generators were sufficiently similar to the original equipment to qualify for "like-for-like" status, when the new steam generators were not "like-for-like."   A United States Senator became involved.  A re-licensing procedure would have been lengthy and the plant would be shut down for the duration of that procedure.   
In addition, the 2000 MW of electricity was lost to the grid, and had to be replaced somehow.  A part of that story is related at this link.  The good news is that at least 75 MW of the power must be from energy storage systems.  That will provide a significant boost to the grid-scale energy storage firms.  
Other nuclear plants also have been in the news due to tube wear and degradation, including the St. Lucie plant in Florida.  See link   Also, the Watts Bar plant has suffered tube wear and has ordered replacement steam generators.   Finally, the Davis-Besse nuclear plant in Ohio is replacing its steam generators, also.
It’s an exciting time.  How many more nuclear plants will go the way of SONGS, due to faulty replacement steam generators that have tubes wear on each other? 
Conclusion
It can be seen, then, that the nuclear power plant in California lasted a bit less than 30 years, not the 50 or 60 years as nuclear proponents claim.   Nuclear plants require costly upgrades after 20 to 30 years, but the anticipated added life does not always appear.  


Previous articles in the Truth About Nuclear Power series are found at the following links.  Additional articles will be linked as they are published. 












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

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
source: Energy.gov
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.
Conclusion
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