HTGR reactor physics and fuel cycle studies

Nuclear Engineering and Design236(2006)

615–634

HTGR reactor physics and fuel cycle studies

J.C.Kuijper a,?,X.Raepsaet b,J.B.M.de Haas a,W.von Lensa c,U.Ohlig c,H.-J.Ruetten c,

H.Brockmann c,F.Damian b,F.Dolci b,W.Bernnat d,J.Oppe a,J.L.Kloosterman e,

N.Cerullo f,G.Lomonaco f,A.Negrini g,J.Magill h,R.Seiler i

a NRG,Westerduinweg3,P.O.Box25,NL-1755ZG Petten,The Netherlands

b Commisariat`a l’Energie Atomique(CEA),Saclay/Cadarache,France

c Forschungszentrum J¨u lich(FZJ),J¨u lich,Germany

d Universit¨a t Stuttgart,Institut fuer Kernenergetik und Energiesysteme(IKE),Stuttgart,Germany

e Delft University o

f Technology(TUD),Delft,The Netherlands

f Universita di Pisa(UNIPI.DIMNP),Pisa,Italy

g Ansaldo Energia S.p.A.,Genova,Italy

h European Commision,Institute for Transuranium Elements(JRC-ITU),Karlsruhe,Germany

i Paul Scherrer Institut(PSI),Villigen,Switzerland

Received6October2004;received in revised form21October2005;accepted31October2005

Abstract

The high-temperature gas-cooled reactor(HTGR)appears as a good candidate for the next generation of nuclear power plants.In the“HTR-N”project of the European Union Fifth Framework Program,analyses have been performed on a number of conceptual HTGR designs,derived from reference pebble-bed and hexagonal block-type HTGR types.It is shown that several HTGR concepts are quite promising as systems for the incineration of plutonium and possibly minor actinides.

These studies were mainly concerned with the investigation and intercomparison of the plutonium and actinide burning capabilities of a number of HTGR concepts and associated fuel cycles,with emphasis on the use of civil plutonium from spent LWR uranium fuel(?rst generation Pu)and from spent LWR MOX fuel(second generation Pu).Besides,the“HTR-N”project also included activities concerning the validation of computational tools and the quali?cation of models.Indeed,it is essential that validated analytical tools are available in the European nuclear community to perform conceptual design studies,industrial calculations(reload calculations and the associated core follow),safety analyses for licensing,etc., for new fuel cycles aiming at plutonium and minor actinide(MA)incineration/transmutation without multi-reprocessing of the discharged fuel. These validation and quali?cation activities have been centred round the two HTGR systems currently in operation,viz.the HTR-10and the HTTR.The re-calculation of the HTTR?rst criticality with a Monte Carlo neutron transport code now yields acceptable correspon-dence with experimental data.Also calculations by3D diffusion theory codes yield acceptable results.Special attention,however,has to be given to the modelling of neutron streaming effects.For the HTR-10the analyses focused on?rst criticality,temperature coef?cients and control rod worth.Also in these studies a good correspondence between calculation and experiment is observed for the3D diffusion theory codes.

?2006Elsevier B.V.All rights reserved.

1.Introduction

The European Research and Development(R&D)activities on high-temperature gas-cooled reactors(HTGR)concentrate

?Corresponding author at:NRG,Fuels,Actinides&Isotopes Group, Westerduinweg3,P.O.Box25,NL-1755ZG Petten,The Netherlands. Tel.:+31224564506;fax:+31224568490.

E-mail address:kuijper@https://www.wendangku.net/doc/0210857398.html,(J.C.Kuijper).on HTGR-related key technologies and innovation potentials with the objective to consolidate and advance modular HTGR technology for industrial application in the next decade and to explore new applications like hydrogen production and waste transmutation in the long-term.As the HTGR is a promising concept for the next generation of nuclear power reactors and nuclear process heat,the European nuclear community must have analytical tools capable to perform conceptual design stud-ies,industrial calculations(reload calculations and the associ-

0029-5493/$–see front matter?2006Elsevier B.V.All rights reserved. doi:10.1016/j.nucengdes.2005.10.021

616J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

ated core follow),safety analyses for licensing etc.for new fuel cycles aimed at plutonium and minor actinides(MA)transmu-tation by ultra-high burn-up without multi-reprocessing of the discharged fuel.As part of the European Union Fifth Framework Program the“HTR-N”project and the complementary activi-ties in“HTR-N1”(HTR-N/N1Contracts,2000/2001)deal with high-temperature reactor nuclear physics,waste and fuel cycle studies and include14partner organisations.For simplicity the projects/contracts mentioned above will be further referred to as “HTR-N”in this article.An overview of the full set of activities within the projects mentioned above can be found in von Lensa et al.(2003).

This article focuses on the quali?cation,validation and improvement of computational tools and models for the anal-ysis and design of HTGR cores,as well as on the application of these tools and models to analyse several HTGR concepts with different fuel cycles.The?rst subject is mainly centred around the two HTGR systems currently in operation,viz.the HTR-10 and the HTTR,and is also concerned with the in?uence of uncer-tainties in nuclear data and with the applicability of the codes for plutonium-based HTGR fuel at very high burn-up.The second subject concerns the analysis of some more advanced HTGR concepts and applications,e.g.the incineration of plutonium.

2.Contribution to core physics code and data

quali?cation

The HTGR appears to be a promising concept for the next generation of nuclear power reactors.In this context,the Euro-pean scienti?c community needs analytical tools to perform conceptual design studies and industrial plant sizing as best esti-mate or reference calculations.This implies in a near future, besides Monte Carlo codes,to develop methods based on multi-group diffusion and transport codes able to model the HTGR core with its inherent characteristics whichever the fuel cycle and core concept(pebble or prismatic).

A survey on the inherent HTGR characteristics shows that they have a strong impact on the core modelling related issues. Several points can be identi?ed:

?The use of helium gas as coolant in HTGR leads to an impor-tant void fraction in the core and to a large neutron streaming effect.

?Due to the use of graphite as moderator,a large part of the neutron spectrum is epi-thermal.Therefore,the classical self-shielding treatment of the resonances ampli?es the existing imperfections of the models,which conversely represent well-mastered uncertainties for other reactors.?Compared to a cladded fuel pin,the fuel dispersion in micro-particles(coated kernels)has the potential to exploit(also taking advantage of the epi-thermal spectrum)very high burn-up.Uncertainties in fuel depletion calculations must be addressed.

?It is often mentioned that the HTGR is highly?exible and can ful?l a wide range of diverse fuel cycles through different physical parameters such as the fuel loadings(particle volume fraction in the graphite),the type of fuel,the burnable poisons,

?ssile/fertile fuel particle fraction,etc.The resulting core con-

?gurations are often strongly heterogeneous with important

space dependent variations of the neutron spectrum.?Finally,the fuel in a form of dispersed particles on the one hand and,the treatment of the pebble-bed core on the other,

impose a stochastic approach of the geometry in the Monte

Carlo calculations.This may con?ict with the requirement

of the absolutely unbreakable reference that constitutes the

Monte Carlo method.

Core physics calculation tools are available today both for

pebble-bed and block-type core.In order to take into account

all the characteristics detailed above in the HTGR core physics

studies,some calculation schemes have been developed in the

past and continue to be improved.However,these codes and

methods are validated for the former HTGR concept conditions

and for a limited set of fuel types,such as uranium or U/thorium.

Additional requirements appear today because the HTGR design

evolutions and changes lead today to some new core con?gura-

tions for which references do not exist,e.g.:

?Annular core geometry;

?Type of fuel(plutonium&minor actinides burning,waste minimization strategy);

?Ultra-high burn-up(e.g.up to more than700GWd/t).

Therefore,validation and quali?cation steps are always needed in order to be able to take into account these additional require-ments.So the activities in this part of the“HTR-N”project are aiming at:

?Code validation;

?Quali?cation and improvement of the methods for modelling the HTGR.

HTTR and HTR-10are two reactors recently started-up in Japan(1998)and in China(2000).Both reactors are representa-tive of the HTGR concepts that are envisaged today:block-type and pebble-bed reactors.On the basis of these reactors activities have been performed demonstrating the capabilities of the Euro-pean code systems as well as identifying the calculation method de?ciencies or the lack of theoretical models.These activities have been reported in an earlier article(Raepsaet et al.,2003). Besides the activities concerning the HTTR and HTR-10,also re-calculations have been performed on the HTR-PROTEUS experiment at PSI,Villigen,Switzerland.Furthermore,studies have been performed on the in?uence of basic nuclear(cross-section)data,and on the applicability of the applied HTGR reactor physics code systems for HTGR plutonium-based fuel at very high burn-up.In the following sections the main results of these studies are presented.Further note that nothing is available today for qualifying the codes on plutonium or minor actinides fuels in an HTGR.A?rst step in his quali?cation process is presented by the“HTR Plutonium Cell Burnup Benchmark”,an activity within the“HTR-N”project,which is described else-where(Kuijper et al.,2004).

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634617

2.1.HTTR

The high temperature engineering test reactor(HTTR)con-structed at the JAERI-site at Oarai in Japan is a graphite moder-ated and helium gas-cooled reactor with an outlet temperature of950?C and a nominal thermal power of30MW(IAEA-TECDOC-1382,2003).It is build to gain and upgrade the technology for high temperature reactors to be built in the future. It became critical at the end of1998.

The active hexagonal core(d=2.30m and h=2.90m)con-sists of30fuel columns and7control rod guide columns and is surrounded by a re?ector(d=4.25m and h=5.26m),which also contains9control rod columns and3irradiation columns.All is contained in a reactor pressure vessel measuring13.2m high and5.5m in diameter.The columns consist of stacks of hexago-nal blocks58cm high and36cm wide and are made of graphite.

A fuel block has33holes,which contain sleeves with fuel,leav-ing a gap to let pass the helium coolant along the fuel.The fuel is of the coated fuel particle type(TRISO,UO2)embedded in graphite compacts,which are mounted in the sleeves.Up to12 different enrichments,ranging from3.3to9.8w/o in U-235,are in use over the core.To control the over-reactivity burnable poi-son has been applied in the fuel blocks.The reactor operates in batch mode,so after each cycle part of the fuel will be replaced. The reactor is controlled by means of chains of cans with boron carbide,lowered into the holes in the control rod guide blocks. Helium at395?C and40bar is blown from the top downwards through the core.

As far as the HTTR is concerned,the activities within the “HTR-N”project have been launched following the great dis-crepancies observed on the international results of the HTTR-FC benchmark(IAEA-TECDOC-1382,2003)in which the num-ber of fuel columns to achieve criticality had to be predicted. The fuel columns were gradually loaded one after another from the outer region of the core.In these conditions,a thin annu-lar core con?guration was obtained in the course of loading(18 columns),the rest of the core being loaded with dummy fuel blocks.This speci?c geometry is very close to the one that can be encountered in current HTGR designs proposed today,i.e. GTHTR-300,GT-MHR and PBMR-SA.It represents one of the ?rst opportunities to model such a core geometry and to be able to compare with the experiment.Finally,the excess reactivity for18,24,and30fuel columns in the core had to be evalu-ated and formed(or forms)also the subject of the benchmark HTTR-EX(IAEA-TECDOC-1382,2003).It is noteworthy that an important analysis and interpretation of the former HTTR-FC benchmark results have been done in order to tentatively explain the discrepancies with the experiment.Then,different strong assumptions or physical hypothesis in the HTTR mod-elling have been identi?ed and their effects quanti?ed by the partners.A very good coherence has been observed between the code systems for quantifying the impact of three common phys-ical effects.These investigations have been extensively reported in an earlier article(Raepsaet et al.,2003).

However,it must be pointed out that the observed discrep-ancies for the thin core decreased with increasing number of fuel columns in the core.Due to the large experimental error at30fuel columns loading(full core),the differences between the calculations and the experiment are within the error interval, whereas at the thin annular core assembly the discrepancies are still signi?cant.

As a concluding remark,one could say that,based on the revised data of the HTTR benchmark,the re-calculation of the ?rst criticality with the TRIPOLI-4Monte Carlo code allowed to reduce the discrepancy by about a factor of two(from～2to 1% k/k).On the other hand,the results obtained for the fully loaded core con?guration is quite acceptable taking into account the uncertainties associated with the experimental values.The remaining deviation for the thin annular core(?rst criticality) may be explained by the uncertainties of the graphite impurities for which the impact is very important in this core con?guration (dummy fuel blocks of pure graphite,with impurities,in the central part of the core).

Finally,the following procedures seem to be necessary for a better approach to the experimental results:

?Take into account the detailed heterogeneity of the burnable poisons-and fuel region in the whole core calculation;?Use?ne-group constants in the whole core diffusion calcula-tion(FZJ)or consider the actual environment of the fuel bocks in the transport cell calculations(NRG)in order to accurately describe the core/re?ector coupling;

?Consider the axially heterogeneous distribution of the burn-able poisons by2D cell calculations(FZJ)or by3D diffusion calculations(CEA and NRG);

?Improve the treatment of the enhanced neutron streaming either by an adaptation of the diffusion constants to Monte Carlo calculations(FZJ)or by a leakage model combined with an analytical model(CEA).

The HTTR of JAERI will be operated at temperatures between850and950?C and a thermal output of30MW.The HTTR calculations presented so far have been performed at room temperature of the core,only.Additional calculations on the HTTR to be carried out in the“HTR-N”project had to take into account temperature feedback effects.Indeed,HTTR crit-ical core con?gurations at elevated,homogeneously distributed temperature may be available in the near future.They represent a succession of critical states in which temperature feedback effects become more and more important.

However,before modelling these HTTR core con?gura-tions at different reactor power levels taking into account these temperature feedback effects can take place,?rstly,con-trol rod modelling related problems must be solved and then, a good accordance has to be achieved between the partners on the evaluation of the obtained reactivity worth for an homogeneous temperature variation in the reactor at a hot zero power(isothermal temperature coef?cient).Therefore,the following activities have been carried out in the“HTR-N”project:

?Evaluation of the control rod worth for different core con?gu-rations at Hot Zero Power condition.Many con?gurations are available:scram reactivity of all the control rods,and scram

618J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

Table1

Control rod worth in the HTTR(k eff and k/k)

Control rod position KENO TRIPOLI4CITATION CRONOS PANTHER Experimental 178.9cm 1.0093±0.0006 1.00117±0.00024 1.0031 1.00020 1.0088Critical 177.6cm0.99972±0.000380.99840

Scram of re?ector CRs0.9178±0.0005(9.88%)0.92215±0.0004(8.56%)0.86535(15.87%)0.90245(10.83%)12%(±1.2) Scram of all CRs0.6809±0.0005(47.78%)0.68396±0.0003(46.32%)0.67937(47.50%)0.63982(56.31%)0.7317(37.5%)46%(±4.6) reactivity of the re?ector control rods only(Raepsaet et al.,

2004a);

?Calculation of isothermal temperature coef?cients on the fully

loaded core con?guration at Hot Zero Power with?xed con-

trol rod position.The temperature coef?cients have been

determined for temperatures between280and480K by cal-

culating the effective multiplication factors at280,300,340,

380,420,460and480K.The following expression was used

to calculate the isothermal temperature reactivity coef?cient

at the mid-point temperatures(so at290,320,360,400,440

and470K,respectively)(Raepsaet et al.,2004b):

α12(T1,2)=(k T1?k T

2

)/k T

1

k T

2

T1?T2with T1,2

=

T1+T2

2

The control rod(“CR”)worth calculations at hot zero power conditions(30fuel columns con?guration)have been performed by the codes KENO(at IRI/TUD),TRIPOLI4and CRONOS2 (at CEA),CITATION(at FZJ),WIMS/CITATION(at UNIPI) and PANTHER(at NRG).The main results are listed in Table1.

It should be noted that criticality in the experiment was obtained with all the CRs inserted at178.9cm.In this con?gu-ration the calculated k eff is slightly above1for all codes applied, which is favourable from a safety point of view(conservative calculation).

The re?ector control rod worths are all in good agreement with the values given by the other international participants of the IAEA benchmark,nevertheless an underestimation of the con-trol rod worth could be underscored compared to the experiment in case a scram of re?ector CRs.Especially the3D PANTHER calculations yield a very low control rod worth in comparison with the other codes.However,this can be explained by neutron streaming in the control rod holes and is to be recalculated by means of an isotropic cross-sections/diffusion coef?cients.

Moreover,these results underscore the fact that discrepancies exist between the CR worths,as obtained from diffusion theory and Monte Carlo calculations and experiment,especially in this case where no equivalence factors have been used in order to respect either the?ux or the absorption rates between the multi-group transport calculations and the broad group diffusion core calculations.Consequently,it is obvious that further investiga-tions must be carried out in a near future in order to improve the CR modelling related problem especially for rods inserted in the re?ector of an HTGR.

Concerning the calculation of the isothermal temperature coef?cients it is found that these coef?cients range from?15 to?16pcm/K between300and480K.In Table2a comparison is shown(at T1,2=400K)between the results obtained by the different code systems used by the project partners.It is note-worthy that the results are in relatively good accordance with the

experiment where the values are comprised between?13and ?14pcm/K at the same temperature.One can conclude that the isothermal temperature coef?cients are overestimated by about

10%on average by the different codes.

2.2.HTR-10

The HTR-10is a high temperature reactor build at the site of

the Institute of Nuclear Energy Technology(INET)near Beijing

in China(IAEA-TECDOC-1382,2003).The reactor is of the

pebble-bed type and has a thermal power of10MW.It reached

criticality at the end of2000and full power in January2003with

an outlet temperature of700?C.After the?rst phase of reactor

experiments it is the intention to install,in the second phase,a

direct gas turbine power generation unit in the primary loop to

develop nuclear helium turbine technology.

The pebble-bed in the core cavity(d=1.80m and h=1.97m)

consists of fuel pebbles,graphite balls(d=6cm)dispersed with

coated fuel particles(TRISO,UO2).Each pebble contains5g

of uranium enriched to17w/o in U-235.

The core cavity is a void in the re?ector with an effective

thickness of1.00m,all is contained in an RPV11.15m high and

4.20m in diameter(see Fig.1).In the side re?ector are holes,

which guide the control rod system.In the bottom re?ector is

a50cm wide chute to carry off the fuel pebbles in a continues

reload operation,in which pebbles are taken away at the bottom

of the core and if still below the burn-up limit returned at the top

of the reactor,else they are discarded and a fresh pebble will be

added on the top.The helium coolant with an inlet temperature

of250?C and pressure of30bar?ows from the top downwards

through the pebble-bed at a rate of4.3kg/s.

To achieve?rst criticality,the fuel discharge tube and the

cone of the core bottom has been?lled with graphite pebbles,

only.Thus,the active core has de facto a cylindrical shape when

adding fuel and graphite pebbles from the top except a conical

heap-up on the surface of the pebble-bed core.

The core was?lled with fuel pebbles from Chinese fabrica-

tion because the transport from FZJ to INET of the residual

A VR pebbles used in the Swiss PROTEUS experiment was

Table2

Isothermal temperature coef?cients of the HTTR at400K

Temperature(K)KENO

(pcm/K)

PANTHER

(pcm/K)

CRONOS

(pcm/K)

CITATION

(pcm/K) 400?14.7?15.2?16.2?17.2

CR group C,R1and R2inserted(178.9cm).

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

619

Fig.1.HTR-10core view.

delayed due to licensing problems.Nevertheless,the type of fuel and the core geometry in HTR-10and PROTEUS is rather comparable.PROTEUS was charged with pebbles in different arrangements to investigate the in?uence of pebble relocations. In contrary to PROTEUS,HTR-10will also deliver data on higher temperatures to determine the temperature coef?cient for LEU fuel.

Despite the small power size of HTR-10,it is a nearly1:1 scale test for a modular HTGR because the radial dimensions of the re?ector blocks are identical to the commercial size.There-fore,HTR-10can be seen as a representative test for the passive decay heat removal and for veri?cation of codes especially with regard to the effectiveness of the shutdown systems.

Due to the similarities of HTR-10and PROTEUS,no big deviations were expected for the cold?rst criticality.The Chi-nese partners predicated16759pebbles from calculations based originally on European codes.The reactor?nally got critical with16890pebbles,which corresponds to an effective core height of123.1cm,assuming a pebble packing fraction of0.61.

The?rst benchmark task was to evaluate the amount of peb-bles,or the level of core loading,at which the reactor became critical.Loading started at the upper level of the bottom cone, which itself was?lled with dummy(graphite only)balls.

For the benchmark all control rods were withdrawn.The orig-inal benchmark was de?ned before the actual?rst core criticality and has been revised for the real experimental con?guration as the deviated benchmark(IAEA-TECDOC-1382).The differ-ences are:

?Core temperature:20instead of15?C;

?Graphite density dummy balls:1.73instead of1.84g/cm3;?B-impurity in dummy balls:1.30instead of.0.125ppm;?Core atmosphere:helium instead of humid air.

The code systems in use by the“HTR-N”partners NRG,FZJ and CEA were PANTHER,VSOP(CITATION)and TRIPOLI, respectively.PANTHER and VSOP are both codes based on3D diffusion theory whereas TRIPOLI is a3D Monte Carlo code. At INET also a version of VSOP has been used.Results for the Table3

Critical core level of the HTR-10

Code/model Core level(cm)

Original

benchmark

Deviated

benchmark Diffusion with VSOP(2D)124.2121.0 Diffusion with VSOP(3D)126.8123.3 Diffusion with PANTHER125.3122.1 Monte Carlo with TRIPOLI(cubic)–117.4 Monte Carlo with TRIPOLI(hex)–122.7 Experimental–123.1

different institutes are summarized in Table3and show a good agreement with the experimental value.

The difference between the2D and3D VSOP calculations is that in the latter the control rod guide holes and shutdown KLAK holes has been considered explicitly.This gives an impression of the neutron streaming in those holes.

And the difference between the cubic and hexagonal TRIPOLI calculations is an adapted face-centred-cubic lattice (74%)of the pebbles in the core or a column hexagonal point-on-point arrangement of the pebbles(60.46%of packing fraction). The latter turns out to be more representative of the pebbles ran-dom distribution and highlights the in?uence of the pebble-bed description in the core model.Results are tabulated in Table3 and show a good agreement with the experimental value.More detailed information on Monte Carlo modelling of the HTR-10?rst criticality can be found in Chang et al.(2004).

Further calculational benchmark exercises concerned the isothermal temperature coef?cient and the control rod worth. It should be noted that for the?rst item no experimental data have been made available yet,whereas only limited experimental information(at somewhat deviating state parameters)is avail-able on the second item.

The benchmark calculations were to be performed with the entire reactor at the same(isothermal)temperatures of20,120 and250?C and a core height of180cm(full core)(IAEA-TECDOC-1382,2003).By calculating the corresponding mul-tiplication factors,the temperature coef?cients could be calcu-lated in the same way as was done for the HTTR(see Section 2.1).Results are listed in Table4.

As no measured values are available,a comparison can be made with the values for the isothermal temperature coef?cient as obtained by INET,the owner of the HTR-10.INET values for the original benchmark were obtained by means of VSOP.The

Table4

HTR-10isothermal temperature coef?cients

T(?C)INET CEA FZJ NRG

k eff for the different temperatures

20 1.119747 1.14737 1.12665 1.11759 120 1.110435– 1.11331 1.10846 250 1.095961– 1.09588 1.09629 Isothermal temperature coef?cient

20–120?7.49E?5–?1.06E?4?7.37E?5 120–250?9.15E?5–?1.10E?4?7.70E?5

620J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

NRG values agree rather well with the values of INET,especially at lower temperature.The FZJ values agree rather well at higher temperatures,but at low temperatures it is rather high compared with the other participants.No reason could be given yet.The differences between the values at low and high temperature are about the same for FZJ and NRG and are small compared to the difference in the values of INET,leading to a stronger decline of coef?cient with temperature.

Concerning the calculation of the control rod worth two dif-ferent benchmark situations were proposed and performed:?With the core level at180.0cm(full core)and a uniform reac-tor temperature of20?C;the insertion of all control rods ran from119.2to394.2cm;

?And with the core level at126cm(critical level)and a uni-form reactor at of20?C;the insertion of all control rods ran from119.2to394.2cm as well.

Also two different core situations with the core level at126and at180.0cm and with the reactor at20?C,a series of calculations has been done for different insertion fractions of only one control rod.

As the experimental condition of the reactor differed from the stated original benchmark condition,INET,CEA and FZJ performed these benchmark items for the experimental situa-tion(the so-called deviated benchmark(IAEA-TECDOC-1382, 2003)).A summary of the obtained results is presented in Table5.

As there are no experimental values known yet for the10 control rod worths,a comparison can be made with the MCNP calculations done by INET,the owner of the HTR-10.If these MCNP calculations are taken as reference calculations the values of FZJ do compare very well with INET.The values of NRG are too low which can be attributed to the in?uence of neutron streaming in the rather wide holes which contain the control rods and the KLAK shut down system.FZJ values are corrected for this effect.In the CEA calculations,the neutron streaming effect cannot be invoked to explain the discrepancies.The CR worth has been calculated from the Cubic core model already used for the evaluation of the?rst criticality(shown in Table3).That core model led to a reactivity overestimation of1.5%due to the speci?c description of the arrangement of the pebbles in the core cavity.It is then obvious that the neutron spectrum near at the core/re?ector interface and in the re?ector itself is in?uenced by the pebble-bed model and can be far from the actual one,leading to differences in the CR worth estimation.

For the single control rod worth a value of1.437%was mea-sured for a core height of123.86cm and the deviated benchmark conditions.INET calculated the single rod worth as1.448%, which is in very good agreement with the experiment,which gives con?dence to these reference calculations.As for the scram reactivity the same applies for the single rod worth as concerns the neutron streaming to arrive at a lower rod worth for NRG.

2.3.HTR-PROTEUS

Benchmark calculations and cold critical experiments for fresh LEU-HTR pebbles were done at PSI in the critical facility PROTEUS(see Fig.2)in the time period1992–1997.The main goal of the program was to provide integral data for small and medium-sized LEU-HTR-systems related to:

?Reaction rate distributions and criticality;

?Worth of absorber rods which are located in the side re?ector;?The effects of accidental water ingress;

?Neutron streaming on the neutron balance.

The experimental results have been analyzed mainly with the MICROX-2/TWODANT calculational route.However,some shortcomings especially in calculating the reaction rate traverses have been identi?ed.

In the framework of the“HTR-N”project,new calculations with the Monte Carlo code MCNP4B have been performed with respect to criticality and reaction rate distributions for two ref-erence core con?gurations(de Haas et al.,2004;Seiler,2004). Monte Carlo calculations with MCNP have already been per-formed during the HTR-PROTEUS program,but with poor

Table5

Control rod worth in the HTR-10

Number of rods INET CEA FZJ NRG Rod worth for the full core(180cm)and original benchmark(% k/k)

1016.56±0.3113.44±0.2616.6011.86 1 1.413±0.265 1.31±0.29 1.563–Rod worth for the critical core(126cm)and original benchmark(% k/k)

1019.36±0.4413.80±0.2020.5513.67 1 1.793±0.3710.28±0.10 1.969–Number of rods INET FZJ

Rod worth for the full core(180cm)and deviated benchmark(% k/k)

1015.3115.73

1 1.343 1.48

Rod worth for the critical core(126cm)and deviated benchmark(% k/k)

1018.2819.31

1 1.571 1.86

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

621

Fig.2.Vertical cross-section of the HTR-PROTEUS con?guration(dimensions in mm,top)and top view of the pebble-bed(bottom).

statistics in the low?ux regions(lower and upper re?ector). In the meantime,the measurements to estimate the absorption cross-section of the re?ector-graphite were re-analyzed result-ing in an increase of the graphite absorption cross-section from 4.09to4.47mbarn.With new MCNP4B calculations,the sta-tistical error could be reduced by a factor of two by calculating 5million histories.

The cavity was partially?lled with mixtures of modera-tor(pure graphite)and fuel(containing16.7%enriched UO2 TRISO-coated particles)pebbles,loaded either in deterministic or random arrangements to form the reactor core.Both pebble types had an outer diameter of6.0cm and a fuel region with a diameter of4.7cm.The“Arbeitsgemeinschaft Versuchsreak-tor”(A VR)in Germany supplied the pebbles.Each fuel pebble contained about1g of235U in～9400particles.

The presently reported results were calculated for the HTR-PROTEUS Cores5and7.Core5has a rhombohedral pebble-lattice geometry with a fuel-to-moderator(F/M)pebble ratio of2:1,corresponding to a C-to-235U ratio of about5670.This so-called column hexagonal point on point(CHPOP)pebble-bed arrangement had a?lling factor of0.6046,which is only slightly lower than a stochastic arrangement with a?lling factor of0.62.In order to improve the homogeneity of the core region, an ABCABC...loading scheme was adopted in which the layer pattern repeats every fourth layer.The packing frequency ABC was repeated up to layer22.Each layer consists of241fuel pebbles and120moderator pebbles,however the position of the pebbles differed from layer to layer[9,10].The arrangement of the23rd layer(top layer)was changed because too few fuel peb-bles remained to form a complete layer.Therefore the remaining 138fuel pebbles were arranged in a2:1lattice in the centre of this layer,with the surrounding area being?lled with moderator pebbles.

Core7was similar to Core5but the vertical channels con-tained polyethylene rods(total of654rods)in order to simulate accidental moderation increase in terms of higher hydrogen den-sity.The pebble-bed core height was reduced from23layers to 18layers to yield a critical con?guration.The pebble-layers of Core7were identical to those of Core5up to layer17,and the top layer18similar to the top layer23of Core5.

The deterministic models for the calculation of Cores5and7 were based on use of the2D transport-theory code TWODANT. The necessary macroscopic cross-sections for the doubly hetero-geneous pebble-bed-lattices were derived using the MICROX-2 cell code in conjunction with its JEF-1based data library.Cor-rections for inter-pebble streaming effects were made,in each case.

The Monte Carlo code MCNP4B was employed along with its ENDF/B-V based continuous-energy cross-section library. For Cores5and7a very detailed model was developed with the 12-sided polygon,absorber rod channels and the top re?ector modelled in detail.Thereby,heterogeneity effects in the core region(particles/matrix/shell for the fuel pebble,moderator/fuel pebble arrangement for the lattice,and polyethylene rods in the case of Core7)were all treated explicitly.But certain detailed aspects of the HTR-PROTEUS con?gurations have been omitted in order to facilitate a more straightforward modelling of the experiments.The most important single item,in this context, is represented by the partly inserted control rods which have not been described and had an experimentally determined worth (inserted)of about84and48cents in Cores5and7,respectively. Considering the other detailed features(e.g.the instrumentation channels,etc.),which have been omitted,one has estimated that corrections of1109and670pcm(TWODANT)and834and 505pcm(MCNP)need to be applied for the two con?gurations. The“experimental”k eff values to be used as reference for the presently described TWODANT/MCNP-models for Cores5and 7(without any shutdown rod inserted)are thus1.0111/1.0083 and1.0067/1.0051,respectively.

Tables6and7show the comparison of calculated and mea-sured values for the system reactivity k eff.As mentioned before, the reactivity was calculated for a system without partially inserted control rods.Only the absorber rod channels and the air gaps of the driver-fuel channels in the side re?ector have

622J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

Table6

Calculated and Measured k eff values for cores5and7(HTR-PROTEUS) Core Experimental TWODANT MCNP4B Measured and calculated k eff values

5 1.0111/1.0083±0.00050.9980.99502±0.00044 7 1.0067/1.0051±0.0005 1.010 1.00268±0.00033 been modelled for the MCNP calculations,the experimental k eff values were corrected accordingly.It can be seen that the calcula-tions agree well with the experiments in Core7but underestimate k eff of Core5.This could be an indication that the polyethylene rods can be smeared into the inter-pebble void,but that stream-ing corrections,which have to be applied for the core region,are not treated correct in the deterministic model.

A comparison of calculated with experimental axial reaction rate distributions shows a good agreement with MCNP4B(see Fig.3)and a satisfactory agreement with TWODANT,especially in the low-?ux regions(lower and upper axial re?ectors).The distributions were normalised to unity in the centre of the pebble-bed.

2.4.Conclusions—core physics codes and data

quali?cation

From the calculations and re-calculations of the HTTR and HTR-10(benchmark)con?gurations it can be learned that Monte Carlo codes are sensitive to the way the in principle stochastic“lattice”of the pebbles in the core are modelled in a more regular lattice(HTR-10).The adaptation of a highly compact cubic lattice(74%)by randomly removing pebbles to achieve the actual packing fraction(61%)can lead to high inter-pebble streaming in the pebble-bed(pseudo cavity)or local moderating ratio different than in the experiment especially at the core/re?ector interface,leading to differences in core reac-tivities.For the diffusion codes care has to be taken on how big holes,like control rod guide holes,are modelled.These holes also give rise to pronounced neutron streaming inside and affect the control rod worth(HTTR and HTR-10).Also care has to be taken on how the core heterogeneities have to be modelled.This is the case for the burnable poison rods in the HTTR,where axial detail has to be taken into account.There is a tendency that tem-perature coef?cients and single control rod worths are slightly overestimated by diffusion/transport codes compared to Monte Carlo or measurements(HTTR and HTR-10).All together do streaming effects in voids play an important role in graphite re?ectors so further investigations have to be performed in the future.

Table7

Comparison of calculated and measured k eff values for cores5and7(HTR-PROTEUS)

Core Experimental TWODANT MCNP4B Measured and calculated/experimental k eff values

5 1.0111/1.0083±0.00050.9870.987±0.00044 7 1.0067/1.0051±0.0005 1.0030.998±

0.00033Fig.3.Experimental and calculated(MCNP4B)axial reaction rate traverses of ?ssion in235U(F5)and239Pu(F9)in Core5(closed points denote experimental data,open points denote calculations).

Deterministic and stochastic calculations have been per-formed with MICROX/TWODANT and MCNP4B for an HTR-PROTEUS core con?guration with(Core7)and without(Core 5)simulated water ingress.The system reactivity(k eff)could be well calculated for Core7,but was underestimated for Core5. This can be an indication that water ingress can be well simu-lated with(heterogeneous)polyethylene rods.The axial reaction rates calculated with MCNP4B are in good agreement with the measurements especially in the lower re?ector.The calculations with TWODANT were less satisfactory,indicating the need for an exact modelling of the core/re?ector region at the bottom of the pebble-bed.

Two other activities within the“HTR-N”project concern a ?rst step towards the quali?cation of HTGR core physics codes for the use of Pu-based fuel at high burn-up(“HTR Plutonium Cell Burnup Benchmark”),and the investigation of the in?uence of uncertainties in nuclear data,respectively.Results form these activities have been reported elsewhere(Kuijper et al.,2004; Oppe and Kuijper,2004;Dolci,2003;Bernnat et al.,2003a,b; Di?lippo et al.,2002;Young and Huffman,1964),but for com-pleteness their main conclusions are listed below.

Concerning the“HTR Plutonium Cell Burnup Benchmark”, generally a good agreement,up to a burn-up of approximately

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634623

600MWd/kgHM,is found between the results of three out of four participants,representing four out of?ve code systems.The reasons for deviations of the single partner have been identi?ed, and meanwhile corrected.The remaining differences in results between the three participants can be largely attributed to differ-ences in modelling of reaction paths in the different code sys-tems,which are ampli?ed by the unusually high?ux levels typ-ical to this particular benchmark exercise(Kuijper et al.,2004).

Investigations on the in?uence of nuclear data uncertainties on results of calculational reactor physics analyses lead to the conclusion that,for the calculation of criticality parameters,a good agreement is obtained between JEF-2.2and JENDL-3.2 based calculations for a broad range of moderation ratios, whereas ENDF/B-VI(release5)based calculations lead to an underestimation for low moderation ratios.From sensitivity and uncertainty calculations both at low and high burn-up of the fuel it can be concluded that the uncertainty in calculated reactivity is about0.6%for weapon grade(WG)Pu fuel.A need for actualized covariance data was found since there rather few reliable processed data available for thermal systems.Observed large differences in scattering law and frequency distribution data for the scattering of thermal neutrons have no signi?cant in?uence on calculated neutron spectra and integral parameters (Dolci,2003;Bernnat et al.,2003a,b;Di?lippo et al.,2002; Young and Huffman,1964).

3.Several HTGR concepts with different fuel cycles

An important part of the activities within the“HTR-N”project was dedicated to the analyses,by the code systems also used for the analyses presented in Section2,of several HTGR concepts.These studies were mainly concerned with the investigation and intercomparison of the plutonium and actinide burning capabilities of a number of HTGR concepts and asso-ciated fuel cycles,with emphasis on the use of civil plutonium from spent LWR uranium fuel(?rst generation Pu)and from spent LWR MOX fuel(second generation Pu).Two main types of HTGRs under investigation are the hexagonal block-type reactor with batch-wise reloading and the continuously loaded pebble-bed reactor.In conjunction with the reactor types also a number of different fuel types(e.g.Pu-based and Pu/Th-based) and associated fuel cycles have been investigated.In addition, studies have been conducted on the optimization of the power size of pebble-bed HTGRs(employing an annular core geome-try),the optimization of burnable poison particle designs(mainly required for batch-loaded HTGRs)and the more exotic concept of the spectrum transmitter.

3.1.Reference core and fuel designs

For a meaningful assessment and intercomparison of HTGR concepts a common basis has been de?ned and agreed upon by the partners in the“HTR-N”project(Kuijper et al.,2002).This common basis includes the de?nition of a reference pebble-bed reactor(“?at bottom”“HTR-MODUL”)with continuous re-loading(“MEDUL”)of fuel elements(Reutler and Lohnert, 1983),the de?nition of a reference hexagonal block-type reactor Table8

General parameters of PuO2-containing coated particle fuel

Kernel diameter of coated particle0.240mm

Kernel material(fuel)PuO2

Density of kernel material10.4g/cm3

Coating materials(inner to outer)C/C/SiC/C

Coating thickness(inner to outer)0.095/0.040/0.035/0.040mm Density of coating material(inner to outer) 1.05/1.90/3.18/1.90g/cm3 Table9

Isotopic composition of?rst and second generation plutonium in the HTR Pu cell burn-up benchmark(wt.%)

Isotope First generation

(original)“A”

First generation

(alternative)“B”

Second

generation“C”238Pu1 2.59 4.9

239Pu6253.8526.9

240Pu2423.6634.3

241Pu813.1315.3

242Pu5 6.7818.6

(“GT-MHR”)(General Atomics,1996),the de?nition of a reference TRISO coated particle(kernel diameter,composition and thickness of coatings),the de?nition of reference?rst and second generation Pu-composition and the de?nition of a set of transmutation(plutonium and minor actinide reduction)and safety related common output parameters to be calculated for each of the concepts and cases under study by the partners (Kuijper et al.,2002).

A common feature for the pebble-bed and block-type HTGR designs is the use of coated particle(CP)fuel.Main parameters of the PuO2-loaded CP fuel are given in Table8.Detailed infor-mation on other CP fuel types,which have been investigated in these studies,can be found in Kuijper et al.(2002).The assumed initial isotopic composition of?rst and second generation Pu is presented in Table9.

The main dimensions and other parameters of the reference continuous reload pebble-bed reactor are presented in Fig.4 and Table10.This reference reactor is a simpli?ed version of the“HTR-MODUL”design(Reutler and Lohnert,1983).For example the conically shaped defuelling chute is not modelled and consequently a uniform vertical?ow velocity distribution

Table10

General parameters of the HTR-MODUL-based reference reactor

Nominal power200MWth

Power density in the core 3.0MW/m3

Thermal ef?ciency40%(assumed in FZJ

calculations)

Core height9.43m

Core diameter 3.0m

Number of pebbles5394per m3

He core inlet temperature250?C

He core outlet temperature700?C

System pressure60bar

He mass?ow rate85.55kg/s

Basic graphite density(in re?ectors) 1.80g/cm3

Pebble diameter 6.0cm

Diameter of fuel zone(matrix/coated

particles)

5.0cm

Graphite density(matrix and outer shell) 1.75g/cm3

624J.C.Kuijper et al./Nuclear Engineering and Design236(2006)

615–634

Fig.4.Main dimensions and material regions of the calculational model of the HTR-MODUL.Dimensions are in centimetre.The core is a random stacking of the well-known6cm fuel balls(‘pebbles’).The conical defuelling chute below the core is not modelled.Other(more or less homogenised)material regions in the model are:(1)re?ector(graphite);(2)void(so He gas);(3)homogenised void and graphite;(4)re?ector(graphite);(5)carbon bricks;(6)re?ector with coolant channels;(7)re?ector with control rod channels;(8)re?ector(graphite). of the pebbles over the entire radius of the core is assumed.In fact there is a rather uniform velocity distribution from the top of the pebble-bed to the bottom,except for the conical region but this is an area with a relative low power density,thus jus-tifying the“?at bottom”option as a simpli?cation.As in the original HTR-MODUL design,in our analyses the“MEDUL”(German:“MEhrfach DUrchLauf”–multi-pass)fuelling strat-egy was assumed as well.

The investigation of fuel cycle studies for block-type HTGR cores was performed on the basis of the gas turbine modular Table11

General parameters of the GT-MHR-based reference reactor

Power600MWth

Thermal ef?ciency48%(assumed in CEA calculations) Loading factor0.85(assumed in CEA calculations) Power density in active zone 6.6MW/m3

Inlet/outlet temperature490/850?C

Height of active zone8m

Equivalent diameter of active zone 2.96/4.84m

Height of axial re?ectors 1.3m

Number of columns in the annular core102

Standard fuel elements720(10per column)

Control fuel elements300(10per column)

Control rods in core12(start-up)and18(shutdown) Control rods in re?ector36(core operation)

Type of fuel loaded into core PuO x

Fuel composition Only one type of particle helium-cooled reactor(GT-MHR)concept.The main features of the GT-MHR core(General Atomics,1996)are indicated in Table11and Fig.5.The core of the GT-MHR consists of102 columns of fuel comprising72standard element columns and30 control element columns.The re?ector and fuel columns consist of stacks of prismatic blocks with a height of80and36.0cm across opposite sides.The core of the GT-MHR also includes a re?ector at the top and the bottom with a height of130cm.

3.2.Continuous reload pebble-bed type HTGR

Starting from the reference pebble-bed reactor,NRG and FZJ investigated on the feasibility of burning of?rst and second generation plutonium in such a reactor.By3D reactor cal-culations,combining neutronics and pebble-bed HTGR core thermal-hydraulics,several loading schemes,including some containing mixtures of fuel pebbles containing different CP fuel types,were investigated,focusing on Pu incineration capabili-ties and parameters concerning the safety of a reactor loaded as such(e.g.maximum power densities and temperature reactivity coef?cients).The investigations by IKE concerned the optimiza-tion of the power size of the reactor,considering a number of different core layout designs.

3.2.1.Plutonium incineration capability

The NRG analyses on the Pu-loaded HTR-MODUL pre-sented in this report were performed by means of the WIMS/PANTHERMIX code system.Since a number of years NRG is developing the HTGR reactor physics code system WIMS/PANTHERMIX,based on the well-known lattice code WIMS(versions7and8),the3D steady-state and transient core physics code PANTHER and the2D R-Z HTGR thermal-hydraulics code THERMIX-DIREKT.At NRG the PANTHER code has been interfaced with THERMIX-DIREKT to enable consistent core follow and transient analyses on both pebble-bed and block-type HTGR systems.Further information can be found in de Haas and Kuijper(2005).

NRG has implemented the reference pebble-bed reactor (“HTR-MODUL”)in their PANTHERMIX code system and has performed some initial studies on the OTTO(once through then out)loading scheme with UO2fuel(7.8%enriched)and?rst generation(pure)PuO2,with7g per pebble of initial heavy

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

625

Fig.5.Geometry of the600MWth GT-MHR core,with details of a standard fuel element and a control element.

metal mass.It was concluded that in the equilibrium state,after 2000days of operation,415(fresh)pebbles are needed per day to maintain criticality.In this state the maximum power density in the core is11.84MW/m3,the maximum burn-up in the core is 77.5MWd/kg and the maximum(fuel)temperature in the core is1072.5K.

Further studies have been executed concerning the use of?rst and second generation(pure)Pu in an HTR-MODUL in contin-uous recycling mode,focussing on the in?uence of the heavy metal mass per pebble and the selected discharge burn-up on the values of the common parameters agreed upon.The pebble circulation rate was kept constant at3kg(initial)Pu per day, throughout all NRG calculations.Some results from these stud-ies are shown in Table12.In this table the calculated“case”is described by the coding“Pu-x-mass-mod”,in which“x”indi-cates the Pu type(1—?rst generation,2—second generation),“mass”indicates the amount of Pu per fresh(unit:grams)and “mod”the number of admixed moderator pebbles(pure graphite) per fuel pebble(either1or0).For?rst generation Pu a further distinction is made between composition“A”(70%?ssile)and “B”(67%?ssile)(see Table9).Further information can be found in de Haas and Kuijper(2005).

From these investigations it can be concluded that the reactor can be made critical at beginning of life with all investigated fuel types containing?rst generation Pu.However,only the fuel pebbles containing2g Pu,without admixed moderator pebbles,lead to a suf?ciently negative temperature coef?cient in the equilibrium situation.For the?rst generation Pu cases the average burn-up of the permanently discharged pebbles is about750MWd/kg.An appreciable reduction of about85%of the original plutonium can be achieved.Note that quite simi-lar results are found for the two types of?rst generation Pu, which indicates a relative insensitivity of the results to the exact plutonium vector.

For second generation plutonium the situation is somewhat less favourable.The burn-up of the permanently discharged peb-bles has to be reduced to about440MWd/kg in order to retain a negative temperature coef?cient at equilibrium.In this case,the

Table12

Results from calculations,by NRG,on the use of pure?rst and second generation Pu(oxide)in a pebble-bed HTR in continuous reload operation mode

Case Pu-?ss

(%)Pu feed

(g/d)

BU cycle

(GWd/t)

BU disc

(GWd/t)

k eff(BOL)k eff(equiv.)α(T)(BOL)α(T)(equiv.)Rem.HM(%)Rem.Pu(%)

Pu-1-1.00-070.0255.8373781.8 1.2825 1.0717?3.25E?05?4.01E?0623.418.0 Pu-1-2.00-170.0255.8373781.8 1.2931 1.0705?2.95E?058.73E?0723.418.1 Pu-1-2.00-070.0254.1361787.0 1.1892 1.0353?5.41E?05?4.60E?0523.315.9 Pu-1-1.00-067.0266.3384751.1 1.2961 1.0706?1.94E?05 1.64E?0523.416.7 Pu-1-2.00-167.0266.3384751.1 1.3044 1.0686?1.72E?05 2.08E?0523.516.8 Pu-1-2.00-067.0270.1366740.4 1.2111 1.0575?4.17E?05?3.28E?0523.414.8 Pu-2-0.75-042.2256.0376781.4 1.16470.8411 2.58E?059.80E?05

Pu-2-1.00-042.2256.2363780.7 1.14360.8991 6.10E?07 5.43E?0522.6 6.6 Pu-2-2.00-142.2266.3383751.1 1.15090.87899.66E?067.54E?0522.6 6.7 Pu-2-1.50-042.2256.3377780.4 1.09640.9192?2.40E?057.10E?0622.6 6.8 Pu-2-3.00-142.2268.2382745.8 1.11240.9156?1.71E?05 2.07E?0522.6 6.9 Pu-2-2.00-042.2271.0379738.0 1.05600.9250?4.64E?05?2.32E?0522.7 6.9 Pu-2-3.00-042.2282.9358706.9 1.00130.9210?7.35E?05?4.87E?0522.77.5 Pu-2-1.50-042.2456.6195438.1 1.0964 1.0068?2.40E?05?2.39E?0554.846.5 Pu-2-2.00-042.2444.6197449.8 1.05600.9831?4.64E?05?4.17E?0555.144.9

626J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

Table13

Fuelling strategy of the HTR-MODUL reactor for burning?rst generation LWR Pu

(a)High Pu-burning ratio(b)Low residual Pu in discharged fuel

Pu-FE(50%)U/Th-FE(50%)Pu-FE(50%)U/Th-FE(50%) Pu3g3g–

Th–18g–16.7g

U(HEU)–2g– 3.3g

Incore time7.3F.P.years11.0F.P.years Fractional power production65%35%52%48%

HM-burn-up595MWd/kg58MWd/kg700MWd/kg116MWd/kg Average128MWd/kg192MWd/kg

reduction of only about50%of the original plutonium can be achieved.

Similar investigations concerning?rst and second generation plutonium have been conducted by FZJ.The numerical inves-tigations within this study have been performed by means of the V.S.O.P.(99)code.In the FZJ calculations concerning?rst generation plutonium pebble-bed core is assumed to be fuelled according to the two-pebble concept(see Table13).One type of pebbles(Pu-FE)contains PuO2-coated particles with a diame-ter of0.24mm having a total of3g plutonium per pebble(?rst generation Pu,composition“A”,see Table9).The assumed max-imum attainable burn-up of this particle is800MWd/kg.The second pebble type(U/Th-FE)contains20g(HEU-Th)O2in the form of larger coated particles(diameter0.5mm).The assumed maximum attainable burn-up of this particle is120MWd/kg.On the one hand the addition of uranium to the thorium is necessary to sustain criticality–depending on the desired burn-up of the fuel–,and,on the other hand,in order to achieve a prompt tem-perature increase of the resonance absorber,thorium,in case of an increase of the neutron?ux,thus causing a prompt negative reactivity feedback.The uranium is highly enriched(93%)in order to minimize the build-up of Pu.

A strategy for burning Pu can be optimised in view of two principal objectives.Today’s main goal probably should be to reduce the separated amounts of Pu as soon as possible.This–in other words–means to maximize the amount of Pu depleted in nuclear reactors per unit of produced energy,which is equiv-alent to maximizing of the fractional power production by Pu in the reactors.Another important aspect,however,comes up with a view to intermediate storage of burned fuel and to?nal disposal of fuel without Pu-separation,as well as with respect to the non-proliferation aspect.From these points of view the min-imization of residual Pu in the discharged fuel elements should be the main goal of the fuelling strategy.Here,the high burn-up, which is achievable in case of HTGR fuel elements,is a feature of particular importance.The positive features of this fuelling strategy,of course,imply the need to handle highly enriched uranium.

In Table13a comparison is shown of the two fuelling strate-gies indicated above(cases“a”and“b”)for the incineration of spent?rst generation LWR-Pu in the considered HTGR core. The?rst strategy is designed to achieve a high Pu-burning ratio, the second one to achieve an especially small amount of resid-ual Pu in the discharged fuel elements.Table14displays the corresponding mass balance of the plutonium and of the?ssile uranium.Detailed further information can be found in Ruetten and Haas(2002).

Both cases apply two kinds of fuel elements,as it has been described above.About half the reactor power is produced by ?ssions of the Pu.The charged Pu is depleted by81%(Table14, case“b”)and about500kg Pu are incinerated per GWa of produced electrical energy,assuming the ef?ciency0.4for the HTGR power plant.In case“a”the burn-up period of the fuel elements is reduced from11down to7.3years of full power, and thus the average burn-up of the fuel is lowered to a standard operation value of the German A VR reactor.In consequence the amount of Pu burned per GWa el increases by30%.On the other hand,the residual Pu of the discharged fuel also increases from 19to31%of the initial amount.The requirement of uranium is similar in both cases.

A parametric study on the temperature coef?cients of an HTGR for Pu-burning showed the need for a relatively large Pu-

Table14

Mass balances for the HTR-MODUL burning?rst generation LWR Pu

(a)High Pu-burning ratio(b)Low residual Pu in discharged fuel

Pu-FE(50%)U/Th-FE(50%)Pu-FE(50%)U/Th-FE(50%) Pu charged(kg/GWa el)929–615–

Pu discharged(kg/GWa el)265239326

Pu burned(kg/GWa el)664?23522?26

641net496net

Pu burned/Pu charged0.690.81

U235charged(kg/GWa el)–578–624

U235discharged(kg/GWa el)–251–171

U233produced(kg/GWa el)–161–116

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634627

load of the fuel elements,favourably about3g Pu.The result is a“hard”thermal neutron spectrum,which favours the parasitic absorption of neutrons in the resonance of the240Pu-absorption cross-section at the energy1eV.Its increase with the moderator temperature dominates some others–partly contrary–spectral effects.Thus,the value of the moderator coef?cient is strongly in?uenced by the fraction of240Pu in the fuel.Nevertheless,the temperature reactivity coef?cients of the reactor(both Doppler and moderator coef?cient)were found to be suf?ciently negative over the whole applied range of reactor operation.

Second generation plutonium contains a distinctly lower frac-tion of?ssile plutonium(about40–50%)compared to plutonium of the?rst generation(about70%)(also see Table9).Follow-ing their investigations concerning?rst generation plutonium, FZJ has concluded a study on continuous reload pebble-bed reactors loaded with a mixture of second generation PuO2and (U-Th)O2,comparing a number of different fuelling strategies. These strategies involved different combinations of the follow-ing fuel element types:

?Pu,Type1:3g plutonium2.Generation/fuel element;?Pu,Type2:1g plutonium2.Generation/fuel element;?Pu,Type3:0.5g plutonium2.Generation/fuel element;?Th,Type1:20g(Th+HEU)-MOX/fuel element;

?Th,Type2:10g(Th+HEU)-MOX/fuel element;

?U:10g U(20%235U)/fuel element.

Some results of these investigations are shown in Table15. The composition of the second generation plutonium differs (238/239/240/241/242=5/36/35/10/14wt.%)slightly from the de?nition in the“Common Parameters”document(Kuijper et al.,2002).However,the results,as presented in Table15,show a good agreement with those from the NRG studies,for the pure(“100%”)Pu case.The combination of thorium and pluto-nium allows for a slightly higher burn-up of the permanently discharged second generation Pu fuel elements,leading to a somewhat higher reduction of the initial Pu content.

Pu incineration by means of a use of low-enriched uranium as basic fuel turns out to be the by far most unfavourable variant of the regarded fuelling strategies.Here,the production of new plutonium by the breeding effect of238U is nearly as big as the destruction rate by?ssions.As consequence,the amount of plutonium in the unloaded fuel elements is lower by only14% compared to the start of the irradiation.3.2.2.Maximum power size

IKE has adopted and actualized the ZIRKUS program system to model pebble-bed reactors with annular core and performed fuel cycle equilibrium calculations with different core sizes and reload cycles with uranium oxide fuel.The goal of investi-gations is the optimization of power of a pebble-bed HTGR under constraints of limitation of maximum fuel temperature during a depressurisation accident.Starting point of the investi-gation was the HTR-MODUL reactor with200MWth and LEU fuel.Further calculations were performed for annular cores with increased power up to400MWth.

The maximisation of the power size of modular pebble-bed HTGRs under the constraints that de?ned temperatures of fuel and structure components will not be exceeded even under all kinds of loss of coolant accidents is an important task for devel-oping of inherent safe and economic nuclear reactors.For HTR pebble-bed reactors the maximum power under these constraints can be achieved by several design and reload concepts:?Reload strategy of fuel or moderator spheres;?Annular core with inner re?ector column of moderator

spheres;

?Annular core with solid inner re?ector column;

?Core height;

?Thermal isolation of the core to limit the temperature of the pressure vessel during LOCA.

For all concepts additionally to the main constraints requested from inherent safety principle,all safety related parameters such as reactivity coef?cients,shutdown margin,maximum fuel tem-perature etc.must lie inside of distinct limits to guarantee safety under operating and accidental conditions.The power conver-sion can be realised by a RANKINE or a BRAYTON cycle.The coolant will be in all cases He.Typical mayor design parameters for pebble-bed HTRs are given in Table16.

The HTR-MODUL and PBMR designs with dynamic mid-dle column only need one outlet for the operating elements(fuel or moderator elements),The concept with compact solid inner re?ector needs at least three outlets.The difference between the MODUL concept and the PBMR concept with dynamic inner column is the reload strategy.The PBMR concept reloads into the inner cylindrical part of the core pure moderator elements, which allows a total higher power since the maximum fuel tem-perature under DLOCA conditions is lower compared to the

Table15

Comparison of different fuelling strategies for the incineration of second generation plutonium in pebble-bed HTGRs

Fuel elements Heavy metal

burn-up(MWd/t)Average burn-up

(MWd/t)

Pu charged

(kg/GWa el)

Plutonium burned

(kg/GWa el)

Ratio Pu burned/

Pu charged(%)

50%Pu,Type152200017400068345066 50%Th,Type1122000

50%Pu,Type1495000200500104864361 50%Th,Type2112000

100%Pu,Type2428000–2050102050 100%Pu,Type3416000–209396846 50%Pu,Type114500055000372550314 50%U30000

628J.C.Kuijper et al./Nuclear Engineering and Design 236(2006)615–634

Table 16

Overview of major design parameters for selected modular HTGR concepts Reactor

HTR-MODUL PBMR dynamic inner column

PBMR solid inner column

Thermal power (MW)200

302

400

Core layout

Cylindrical Annular core with dynamic middle column Annular core with compact middle column Outer diameter of core (m)3 3.7 3.7Inner diameter of core (m)–22Height of core (m)9.49.311Diameter of RPV (m)

6

6.2

6.2

Inlet/outlet temperature (?C)250/700500/900500/900Coolant

Helium

Helium

Helium

MODUL concept with cylindrical active core.The MODUL concept can only vary the reload strategy or the core height to increase the total power.The in?uence of the number of reloads of fuel elements on the maximum fuel temperature is shown Fig.6.

The larger the number of reloads,the lower is the peaking factor of the axial power distribution and hence the lower the maximum temperature after a DLOCA accident.This means the power can be increased if 15instead of 5reloads are planned.For the case of a strategy,which reloads into the inner part fuel elements with higher burn-up and into the annular part,fresh fuel and fuel elements with lower burn-up,the radial power distribu-tion can be ?attened and correspondingly the radial peak factors kept lower than in the original MODUL concept.This allows also to increase the total power while the maximum fuel tem-perature under DLOCA conditions remains below the limit.The disadvantage is the necessity of more feed channels compared to the one of the MODUL.The maximum power,however,can be achieved if the inner part of the core is inactive.The disadvan-tage is the radial temperature pro?le in the core during operation and the very high thermal ?ux in the thermal column,which can be problematical if a fresh fuel element enters this region.A variable reload concept with higher irradiated fuel in the middle column avoids this problem and the problem of mixing of very different He temperatures at core

outlet.

Fig.6.Maximum fuel temperature as a function of time after depressurisation for different recycle passes for HTR-MODUL (200MWth).Comparing concepts with dynamic and solid inner columns with inactive material regarding the maximum fuel tempera-ture after DLOCA an advantage for the solid inner part can be seen.For both designs under considerations,the behaviour is quite similar.The reactor starts to heat up due to the decay heat.The initial temperature pro?le under operating conditions,with maximum temperatures at the core exit,is transformed in an axi-ally essentially symmetric pro?le imposed by the heat source distribution.The maximum temperatures in the core continu-ously increase,until they reach a maximum around 2.5days (see Fig.7),when the decreasing decay heat can be removed from the core region by heat conduction and radiation.The time,when the maximum fuel temperature is approached,marks also a transition from transient to quasi-steady behaviour.This can especially be seen from the radial temperature pro?le in the core.During heat-up,the temperatures in the unheated middle column lag behind the temperatures in the annular core.When the maximum temperature is approached,the radial pro?le over the central column vanishes.The subsequent cool-down then follows a quasi-steady behaviour,in which the developed tem-perature pro?le is practically maintained.

For the DLOCA case,the differences between the designs with dynamic and ?xed middle column are relatively small.The maximum fuel temperature remains within acceptable lim-its.The higher temperatures reached in the case with dynamic middle column are mainly caused by the lower thermal

iner-

https://www.wendangku.net/doc/0210857398.html,parison of maximum fuel temperature versus time for pebble-bed HTGR designs with annular core in the DLOCA case.

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634629

tia of the pebbles compared to a massive graphite column. Thus,the maximum temperature is reached at an earlier time,when the decay heat to be removed is still at a higher level.

In the case of a failure of the circulation of coolant is assumed and the reactor is supposed to be shut down but remains under pressure(PLOCA).A natural convection?ow develops under the in?uence of driving temperature differences,which in con-trast to the DLOCA case strongly affects the decay heat redistri-bution.Due to a large initial radial temperature gradient,which results from operational conditions with cooled middle column and hot core annulus,a strong natural circulation loop has devel-oped after4s.Helium rises in the outer hot annulus,heating up the upper parts,and?ows downwards through the central part, releasing heat to the cold middle column.As a result,the hot spot moves from its initial position at the bottom towards the top of the core.

While the radial temperature difference between core and middle column is successively reduced,a second convection loop develops due to the increasing radial temperature gradi-ent between core and re?ector,which is cooled by conduction and radiation.The heat?ux redistributed through the two loops exceeds at around2.6h the local decay power in the hot spot region,resulting in the?rst peak and subsequent decrease of the maximum fuel temperatures.Finally,the?rst circulation loop practically disappears due to the continuous heat up of the mid-dle column.With only the re?ector as major heat sink,the heat redistribution by convection is less effective.This leads to an at?rst renewed increase of the maximum temperature,until the core?nally cools down with decreasing decay power.Although the fuel temperature remains within pre?xed limits during the DLOCA accident the reference design with425MWth can-not be considered as optimum in terms of inherent safety.The mechanical stability of the reactor pressure vessel e.g.cannot be guaranteed if it is exposed to too high temperatures for a long time.At this point a second safety criterion regarding this fact is needed.A design with a thermal isolation of the re?ec-tor,keeping both the maximal accident temperature of the fuel and the maximal temperature of the RPV below distinct limits. More details of these investigations are shown in Ben Said et al. (2004).

3.3.Batch-wise reload hexagonal block-type HTGR

For the GT-MHR-based reference reactor,CEA investigated the Pu(and minor actinide)incineration capability.It is notewor-thy that to give information such as cycle length,mass balance, peak power,core?ux distribution,etc.for a speci?c block-type HTGR loaded with plutonium fuels suppose an important opti-mization stage of the core:use burnable poison or not,?attening the?ux distribution in the annular zone(different?lling frac-tion in the compact close to the re?ector,different enrichment, burnable poison in the re?ector,etc.),number of the control rods, etc.Moreover,this optimization stage must be based on an equi-librium fuel cycle assuming a speci?c fuel-reshuf?ing scheme. For the present analysis,simplest methods than3D core burn-up calculations were employed.2D transport detailed calculations allowed to compute the fuel depletion.Nevertheless,in order to get the fuel element discharged burn-up,the core reactivity was calculated during fuel depletion using a simpli?ed2D annu-lar core con?guration on which also transport calculations have been done.It is important to note that all these calculations have been performed without taking into account temperature feed-back.The same2D annular core con?guration was used for the temperature coef?cient estimations.The plutonium and minor actinides balances were calculated considering a thermal ef?-ciency of48%and a loading factor of0.85.

Intimately connected to the batch-wise reload(hexago-nal block-type)HTGR is the use of burnable poison,e.g. to?atten the reactivity-to-time behaviour of the core or to improve the temperature reactivity coef?cients.A detailed study was performed on the optimization of the burnable poi-son particle design,in combination with different HTGR fuel types.

3.3.1.Plutonium incineration capability

The investigation of fuel cycle studies for block-type HTGR cores was performed for?rst generation and second generation plutonium-based fuel cycles.The core neutronic analysis pre-sented here is essentially based on a speci?c calculation process employing the APOLLO2transport code.The formalism used to solve the multi-group Boltzmann transport equation is either the integral-equation(P ij:collision probability1D and2D)or integral-differential-equation(S n:discrete ordinates and nodal methods in2D).The standard172-group cross-section library issued mainly from JEF2.2is used in the present study.Detailed information can be found in Damian and Raepsaet(2004a).

The calculations have been performed in fundamental mode (critical buckling),considering a linear anisotropic collision hypothesis for the calculation of the graphite diffusion coef?-cient.In order to evaluate the fuel element discharged burn-up, the core k eff needs to be calculated.The core reactivity during fuel depletion is calculated using a simpli?ed2D core con?gura-tion.Although the calculations are performed using a simpli?ed modelling,it allows making an accurate calculation of the radial leakage during core depletion.After all,the core volumic leak-age(3D leakage)was evaluated using the radial leakage issued from the simpli?ed core calculation and considering a constant axial leakage value(1500pcm in all cases).For the different fuel types feeding the reactor,the discharged burn-up was deter-mined in order to achieve a reactivity margin of2000pcm at the end of cycle(k eff=1.02)embracing the possible uncertainties.

Preliminary investigations showed that:

?The fuel cycle length increases linearly with the mass of plu-tonium loaded into the core;

?There is an optimum for the fuel fed into the core with respect to the discharge burn-up,which allows using at best the plu-tonium(see Fig.8;case“A”is?rst generation,case“B”is second generation).

Indeed,an increase of the total mass fed into the core has been analyzed for both types of plutonium fuel.All the results are gathered in Table17.Whatever the plutonium isotopic content

630J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

Table17

Plutonium and minor actinides balance for?rst and second generation plutonium fuel in batch-wise fuelled hexagonal block-type HTGR

Type of fuel First generation plutonium(66.2%)

Mass of fuel loaded into the core(kg)701900120015001800 Plutonium balance

%?67.4?71.3?74.4?75.4?75.1 Pu f/Pu total at EOL(%)28.328.630.032.736.7 Minor actinides balance

In percentage of metal burnt8.39.210.211.112.0 Type of fuel Second generation plutonium(42.2%)

Mass of fuel loaded into the core(kg)7009001100 Equilibrium cycle length180234275

Average discharged BU460.7468.0450.7

Plutonium balance

%?56.1?58.2?57.6

kg/TWhe?107.4?110.3?113.5

Pu f/Pu total at EOL(%)19.3522.427.0

Minor actinides balance

Americium(kg/TWhe)+13.57+14.88+16.93

Curium(kg/TWhe)+3.90+5.29+6.43

Total(kg/TWhe)+17.47+20.17+23.36

In percentage of metal burnt16.318.320.5

is,the fuel cycle length is proportional to the total mass loaded into the core.The higher the plutonium loaded into the core, the longer the fuel cycle length.Nevertheless,an increase of the plutonium loaded into the core will be limited by technological and physical criteria.For example,the particles volume fraction in the compact represents a technological limit to the plutonium loading capacity.Besides,the reactivity margin at the beginning of cycle appears as a physical limit to the use of highly degraded plutonium or important fuel loading.In fact,higher plutonium loading imply an increase of great absorbers like240Pu in a similar core geometry and reduce the reactivity margin although the?ssile isotopes content increases.By increasing the loaded fuel mass,the neutron spectrum becomes harder and favours the neutron absorption in the fertile isotopes.It should be noted that if the plutonium balance reaches an optimum with respect to the plutonium loaded into the core,it is not the case with the minor actinide balance,which increases linearly with the mass of plutonium.One could have thought that maximize the burn-up should minimize both discharged masses of Pu and minor actinides.In fact,as shown in Table17,the production of minor actinides raises continuously with the Pu-loading.Consequently, the optimum burn-up obtained from the critical calculations, which leads to an optimum of the plutonium consumption with respect to the fuel loading,can be explained as follow:?Despite a smaller initial reactivity,the increasing of the Pu-loading leads to a neutron spectrum hardening that will enhance the Pu conversion and thus increase the cycle length (then the burn-up);

?At a certain level of Pu-loadings a too hard neutron spectrum (deteriorating the?ssion rate)and the important amount of minor actinides in the fuel will limit again the cycle length and thus the burn-up.Therefore,for each isotopic Pu-composition,an optimum Pu-loading exists that maximizes the burn-up and then minimizes the Pu-discharge despite a constant MA-discharge mass increas-ing.

Finally,as far as the?rst generation plutonium is concerned, the temperature effect(Doppler and moderator)has also been evaluated on the fuel element geometry(see Table18).The Doppler coef?cient given in the table is an average value between 20and900?C.As far as the moderator temperature coef?cient is concerned,the calculated value is an average between20and 500?C.Despite the strong decrease of the moderator tempera-ture coef?cient during fuel irradiation,the results have shown that the global core temperature effect is negative and there-fore self-stabilizing,with a fuel management by1/3rd where the average core burn-up ranges roughly from200and400GWd/t between the beginning and the end of cycle.

Further studies have also been conducted concerning the incineration of minor actinides in prismatic block HTGRs.Final conclusions on this application cannot be drawn yet,as the assembly based calculations do not provide for suf?cient accu-racy(Damian and Raepsaet,2004b).

Prismatic block-type HTGRs have a?exible core that can ful?l a wide range of diverse fuel cycles.The use of a wide spec-trum of plutonium isotopic compositions prove HTGR potentials to use at best the plutonium as fuel without generating large amounts of minor actinides.However,the analysis has been done without really taking into account the common fuel par-ticle performance limits(burn-up,fast?uence,temperature). It is obvious that such long cycles and associated high level of Pu-destruction will be possible only if burn-ups as high as 700GWd/t and?uences in the order of12n/kb(a factor2with the common requirements)sustained by the fuel particles will be technologically feasible.The use of high-burn-up plutonium

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

631

Fig.8.Dependence of burn-up on core loading of the batch-wise loaded hexago-nal block-type HTGR(case“A”is?rst generation plutonium,case“B”is second generation).

particles cannot be regarded as proven technology today and important fuel characterisation program including irradiation will be required to demonstrate that a burn-up of about80%“?ssions per initial metal atom”(FIMA)can be achieved for the Pu-particles without an inadmissible failure rate of the fuel coating.

It should be stressed that precaution must be taken with regard to the preliminary results given in the previous section.Indeed, the indicated mass balances have not been estimated from3D full core calculations and remain to be con?rmed.Nevertheless, such a3D core calculation is inferred that a core optimization approach close to conceptual design studies is needed for a block-type reactor fully loaded with plutonium fuel.This has not been carried out in the present analysis.

Moreover,it is noticeable that further detailed core physic analyses will be required in the future in order to assess the dynamic features of such a reactor,as is also the case for the pebble-bed HTGR(Section3.2.1).Additional studies concern-ing also the reactivity control aspects,the temperature coef?-cients,the decay heat associated with plutonium fuel,the appro-priate fuel management and the associated power distributions related issues(especially important in the case of the plutonium use)should allow to precise that pure plutonium cycles will respect the current high level of safety of the HTGR.

3.3.2.Optimization of burnable poison design

A batch-wise fuel load scheme in HTGRs can be combined with a burnable poison in a heterogeneous way by mixing burn-able poison particles(small spherical particles made of burnable poison,in the remainder abbreviated as BPPs)in the fuel ele-ments.By varying the diameter of the BPPs and the number of these particles per fuel pebble,it is possible to tailor the reactivity-to-time curve.

Such a batch-loading scheme in HTGRs combined with BPPs has some attractive properties not offered by the continuous loading scheme.Burn-up calculations have been performed on a standard HTGR fuel pebble with a radius of3cm containing 9g of enriched uranium or1g of?rst-grade plutonium,together with spherical BPPs made of B4C highly enriched in10B or Gd2O3containing natural Gd.The calculations aim at obtaining a?at reactivity-to-time curve for a batch-wise-loaded HTGR by varying the radius of the BPP and the number of particles per fuel pebble.

With BPPs mixed in the fuel of an HTGR,it is possible to control the excess reactivity present at beginning of life.For 8%enriched UO2fuel,mixing1070BPPs containing B4C with radius of75?m through the fuel zone of a standard HTGR

Table18

Doppler and moderator temperature coef?cient for the?rst generation Pu in batch-wise fuelled hexagonal block-type HTGR

Burn-up(GWd/t)701kg900kg1200kg1500kg1800kg Doppler coef?cient(pcm/?C)

Without erbium

0?2.76?3.13?3.49?3.67?3.70?0.98?1.00?0.92?1.04?1.14 Variable625GWd/t650GWd/t650GWd/t650GWd/t650GWd/t Graphite temperature coef?cient(pcm/?C)

Without erbium

0?2.29?2.14?1.91?1.69?1.46 +8.15+6.33+4.47+2.86+1.74 Variable625GWd/t650GWd/t650GWd/t650GWd/t650GWd/t

632J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634

fuel pebble with outer radius of3cm,the reactivity swing is 2%at a k∞of1.1.This means the burnable poison occu-pies a volume60,000less than that of the fuel pebble(FVR= 60,000).

Using Gd2O3as a burnable poison gives an optimum radius of about840?m and an FVR of only5000.This latter number corresponds to9BPPs per fuel pebble.The low number for the FVR re?ects the fact that the natural Gd in the particle absorbs fewer neutrons despite the fact that the thermal cross-sections of the155Gd and157Gd isotopes are much larger than that of the 10B.This is due to the relatively large microscopic absorption

cross-section of10B in the epi-thermal range and the high atomic number density of the boron in B4C.For the Gd2O3particles, the resulting reactivity swing is3%,which is very similar to that obtained with the B4C particles.The bigger size of the Gd2O3 particles could be advantageous for the manufacturing process of the BPPs.

The B4C particles used in UO2fuel(radius between70and 90?m)can also be used to reduce the reactivity swing in PuO2 particles.The reactivity swing at a target k∞of1.1is about 4%for BPPs with radius of85?m and an FVR of27,500 (corresponding to1600BPPs per fuel pebble).The uniform temperature coef?cient is comparable to that of the UO2fuel (?7to?8pcm/K).More results can be found in Kloosterman (2003a,b).

3.4.Spectrum transmitter

The disposal of nuclear waste is one of the major problems to be solved to guarantee a future for the nuclear industry.For this reason,the incineration of plutonium and minor actinides(MA) is probably the most interesting and effective option in reducing the radio-toxicity of the wastes produced by the nuclear fuel cycle.

An alternative solution to fast reactor or ADS is to make use of thin?ssile?lms as?ux converters to generate regions with fast?uxes inside a thermal reactor and thereby improve their incineration capabilities.The basic idea is to isolate some regions inside the reactor by de-coupling them from the main core with a?ux converter.Provided that no moderating material is present inside these regions,the?ux there will be prevalently fast and allow a more effective incineration of minor actinides.

The scope of this work is to analyse the feasibility of fast islands in thermal reactor,by giving a rough estimation on basic dimensioning,?ux conversion and incineration perfor-mances.Presently,the main conclusions are as follows(Magill and Peerani,2001a):

?It is possible to obtain fast islands inside the cores of thermal reactors by coating special assemblies with thin?lms of?ssile material.These special assemblies have to be moderator-free.?The special assemblies could be loaded with minor actinides to enhance the incineration rates in the fast spectrum.?The fast?ux inside the thermal islands is improved by a factor ranging from2to10,depending on the reactor type and on the?lm material and thickness.This improves considerably the capabilities of MA transmutation.?In a PWR the realization of a fast island with the same dimen-sions of a standard fuel element is possible from the neutronic point of view.Nevertheless,since in this kind of reactor water is both coolant and moderator,the condition requiring no moderator inside the fast island leads to a severe heat removal problem.

?Intrinsic to the HTGR concept is the fact that the moderator (graphite)and the coolant(gas)are distinct.It follows that heat can be easily removed without introducing any signi?cant neutron moderation.

?The pebble dimension in pebble-bed HTGR is not optimal for the fast island concept.In fact,since the minimum thickness of the?ssile?lm is imposed by neutronic conditions to be at least 1mm,the fast island should have reasonably large dimensions in order to keep as low as possible the ratio between the?ssile mass in the?lm and the MA loaded in the fast island.?Block-type HTGR seems to offer the best conditions for an optimal design of a fast island.

?Typical incineration rates in fast islands are two to three times higher than the corresponding rates in thermal reactors.

Following the above results it seems worthwhile to go on the analysis to assess de?nitely the feasibility of the fast island con-cept.The most immediately required further steps are:?Optimization of the MA assembly geometry;?Analysis of the local effects close to the interface due to the ?ux perturbation induced by the presence of the fast island and of the?ssile layer;

?Thermal-hydraulic analysis to verify the capability to remove the heat produced inside the fast island and in the?ssile layer;?Investigation of the impact on the main reactor safety param-eters(feedback effects,dynamic behaviour).

A world patent has been granted on the spectrum transmitter concept(Magill and Peerani,2001b).

3.5.Conclusions—HTGR concepts

A number of conceptual HTR designs were analyzed with respect to their capability to incinerate plutonium and minor actinides,while maintaining favourable safety characteristics. The basis for these investigations was provided by two ref-erence reactors,representing the two main HTR designs,viz. HTR-MODUL(continuous reload pebble-bed)and GT-MHR (batch-wise reload hexagonal block).The investigations show quite promising results concerning the incineration(reduction) of especially?rst,but also of second generation plutonium,for both HTR concepts.It should be noted,however,that only an indication of the favourable safety characteristics was calculated in the form of suf?ciently negative temperature reactivity coef-?cients.Future R&D work should address the actual dynamic properties of such Pu-loaded HTR cores under both operational and accident conditions.

Furthermore,in the analysis of the Pu-burning capabilities of the several HTR concepts it was assumed that the fuel is able to withstand very high burn-ups,in the range of700MWd/kg

J.C.Kuijper et al./Nuclear Engineering and Design236(2006)615–634633 Table19

Comparison of the Pu incineration in the different studies

First generation NRG(pebble-bed)FZJ(pebble-bed)CEA(batch-wise)

High rate Low residual

Discharge burn-up(MWd/kg)750595700640

Pu-balance(%)85698164

Features Pure Pu(2g Pu)Pu+(Th+HEU)Pu+(Th+HEU)Erbium BP Second generation NRG(pebble-bed)FZJ(pebble-bed)CEA(batch-wise)

Pu+(Th+HEU)Pure Pu

Discharge burn-up(MWd/kg)445495428470

Pu-balance(%)55615058

Features Pure Pu(2g Pu)3g Pu/pebble1g Pu/pebble Erbium BP

or higher.However,as in particular the use of high burn-up plutonium particles cannot be regarded as proven technology, an irradiation program will be required to:?Demonstrate that a burn-up equal about80%“?ssions per

initial metal atom”(FIMA)can be achieved for the Pu-loaded coated particles without an inadmissible failure rate of the fuel coating;

?Investigate the?ssion product retention of both the fuel ele-ment variants at a temperature level,which might occur in a loss-of-coolant accident.

For batch-wise(re-)loaded HTRs the use of burnable poison enables?attening of the reactivity-to-time behaviour of the reac-tor and the improvement of temperature reactivity coef?cients. The investigations demonstrate the capabilities of burnable poi-son particles,containing either boron or gadolinium in the form of either small spheres or cylinders,to achieve these goals.Opti-mization of the behaviour is quite well possible by varying the diameter of the particles and/or the number of particles per fuel element.

A comparison of the Pu incinerating capacities of the differ-ent fuelling strategies of the of the pebble-bed and batch-wise fuelled reactors can be seen in Table19,with the Pu-balance as Pu burned/Pu charged,showing a slight decrease in capa-bility for the batch-wise fuelled reactor because of the neutron consumption by the burnable poison.

Investigations concerning the more exotic concept of the“spectrum transmitter”(thermal reactor containing“fast islands”—assemblies coated with thin?ssile material)show that the block-type HTR seems to offer the best conditions for an optimal design of a fast island,and that the typical incinera-tion rates in fast islands are two to three times higher than the corresponding rates in thermal reactors.

Acknowledgement

The work presented in this article was partly funded by the European Union Fifth Framework Program,under contract nos.FIKI-CT-2000-00020“HTR-N”and FIKI-CT-2001-00169“HTR-N1”.References

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电抗器基本知识介绍

电抗器基本知识介绍 一、干式电抗器的种类与用途 电抗器是重要的的电力设备，在电力系统中起补偿杂散容性电流、限制合闸涌流、限制短路电流、滤波、平波、启动、防雷、阻波等作用。根据电抗器的结构型式可分为空心电抗器、铁心电抗器与半心电抗器。 补偿杂散容性电流的电抗器主要有并联电抗器与消弧线圈。并联电抗器的作用是限制电力传输系统的工频电压升高现象，工频电压升高的原因在于空载长线的电容效应、不对称对地短路故障与突然甩负荷。消弧线圈通常应用在配电系统，它的作用是使得单相对地短路电流不能持续燃烧，导致电弧熄灭。消弧线圈通常具有调谐功能，可根据电力系统的杂散电容与脱谐度改变其电感值。 串联电抗器或称阻尼电抗器的作用是限制合闸涌流。串联电抗器与电力电容器串联使用，用于限制对电容器组合闸时的浪涌电流，通常选取电容器组容量的6%。 限流电抗器是串联于电力系统之中，多用于发电机出线端或配电系统的出线端，起限制短路电流的作用。为了与其他电力设备配合，其实际阻抗不能小于额定值。 滤波电抗器与电容器配合使用，构成LC谐振支路。针对特定次数的谐波达到谐振，滤除电力系统中的有害次谐波。 平波电抗器应用在直流系统中，起限制直流电流的脉动幅值作用。在设计平波电抗器时须注意线圈中的电流是按电阻分布的，设计时最好采用微分方程组计算。若按交流阻抗设计可能造成线圈出现过热现象，且阻抗值未必准确。 启动电抗器用于交流电动机启动时刻，限制 防雷线圈通常用于变电站进出线上，减 阻波器与防雷线圈的应用场合相仿，线 用于阻碍电力 便于将通讯载波提

取出来，实现电力载波的重要设备。 户外空心干式电抗器是20世纪80年代出现的新一代电抗器产品，如图1.1所示。它是利用环氧绕包技术将绕组完全密封，导线相互粘接大大的增加了绕组的机械强度。同时利用新的耐候材料喷吐于包封的表面，使得产品能够满足在户外的苛刻条件下运行。包封间由撑条形成气道，包封间与包封内绕组多采用并联连接以便满足容量与散热的要求。为了满足各个并联支路电流合理分配的需要，采用分数匝来减少支路间的环流问题。为了能够形成分数匝，采用星形架作为绕组的出线连接端。绕组的上下星架通过拉纱方式固定，固化后整个产品成为一个整体。这种结构的电抗器与传统方式的电抗器相比较具有可以直接用于户外、电感为线性、噪音小、防爆、使用维护方便等特点，因而对于某些此产品有可能正逐步取代其他形式的电抗器。 由于受到绕组结构的限制，户外空芯干式电抗器通常不适合电感量（>700mH ）较大或电感较小(<0.08mH)但电流较大的场合，否则就会造成体积过于庞大或者支路电流极不平衡。在这两种极端条件下，需要适当改变线圈的绕线形式。此外，空心电抗器通常占地面积最大、对外漏磁最严重，这是这类电抗器的主要缺点。 干式铁心电抗器主要是由铁心和线圈组成的，如图1.2所示。干式铁心电抗 器主要由铁心、线圈构成。铁心可分为铁心柱与 铁轭两部分，铁心柱通常是由铁饼与气隙组成。 线圈与铁心柱套装，并由端部垫块固定。铁心柱 则由螺杆与上下铁轭夹件固定成整体。对于三相 电抗器常采用三心柱结构，但对于三相不平衡运 行条件下，需采用多心柱结构，否则容易造成铁 心磁饱和问题。干式铁心电抗器的线圈通常采用 浇注、绕包与浸漆方式。由于铁磁介质的导磁率极高, 而且其磁化曲线是非线性的, 故用在铁心电抗器中的铁心必须带气隙。带气隙的铁心,其磁阻主要取决于气隙的尺寸。由于气隙的磁化特性基本上是线性的, 所以铁心电抗器的电感值取决于自身线圈匝数以及线圈和铁心气隙的尺寸。由于干式铁心电抗器是将磁能主要存贮于铁心气隙当中，铁心相当于对磁路短路，相当于只有气隙总长度的空心线圈。因此铁心电抗器线圈的匝数较少， 从而图1.2 干式铁心电抗器

电力系统中目前使用的变压器 电抗器多含有有 、.

简 介 电力系统中目前使用的变压器、电抗器多含有有载调压机构，分接头的位置是变压器、电抗器的重要信息。测控单元在采集分接头位置信号时，通常提供的开关量位置较少，因此通常对分接头位置进行编码，转换成与测控系统相适应的 BCD 方式输出。 该装置是配合变电站实现电力调度自动化、无人值班化的一种自动监测仪器。它将来自主变压器有载调压分接开关的升、降、停调压控制、档位机械分接点位置监测、远方/就地控制等功能集于一体。可以在就地位置实现升、降、停操作，也可以与综合自动化系统的测控装置接口，进行远方遥控操作，并且遥测档位位置。 该装置可以满足三种输入方式：（1）一对一（每个档位对应一付空接点）；（2）编码方式（1-9分别对应一付空接点，10位对应一付空接点）；（3）BCD 输入方式。 输出方式：BCD 或HEX 输出。 结构上采用了屏柜安装方便快捷。 技术参数 额定工作电压： DC220V/110V 编码输出类型： BCD 或HEX 输出 输入最大档位数：19档(更多档位订货时注明) 档位输入类型： 一对一的输入、编码输入、BCD 输入 装置端子定义图 输出方式： 空接点输出 输出接点容量： 载流容量 5A 接点断弧容量： 60W(220VDC)；2000VAC 安装方式： 柜面开孔安装

装置电原理图 装置典型使用接线 接线图如下： 1一对一输入的接线方式 2 编码输入的接线方式（仅适用于BCD输出方式时） 3 BCD输入的接线方式（仅适用于BCD输出方式时） 装置操作说明

运行指示灯：档位控制器上电，运行正常时运行灯点亮(绿色)。 远方、就地选择开关 远方位置：允许测控装置通过档位控制器进行调压机构遥控操作。 就地位置：允许通过装置面板上的升、降按钮进行调压机构操作。 升、降、停按钮 升、降按钮：就地操作时，通过面板上的升、降按钮可以实现调压机构的就地升降；档位控制器面板上的按钮只在就地位置时，升、降才有效。 停按钮：按下停按钮时，切断调压机构电源，禁止调压操作；停接点不受远方就地的控制。 码制转换（√表示输入相应档位时该接点与BCOM为通路） BCD码输出：用跳帽将J2、J4、J8、JA跳至“BCD”位置 BCD码输出逻辑23~44 输入档位数码管显示 1 2 4 8 A 无输入00 档位1 01 √ 档位2 02 √ 档位3 03 √√ 档位4 04 √ 档位5 05 √√ 档位6 06 √√ 档位7 07 √√√ 档位8 08 √ 档位9 09 √√ 档位10 10 √ 档位11 11 √√ 档位12 12 √√ 档位13 13 √√√ 档位14 14 √√ 档位15 15 √√√

铁心电抗器电感计算公式【通用

铁心电抗器电感计算公式 铁心电抗器电感计算公式 当有气隙时，其磁阻主要取决于气隙尺寸。由于气隙的磁化曲线基本上是线性的，所以其电感值仅取决于自身线圈匝数、铁心截面和气隙的尺寸。 主磁通所产生的电感LM LM=ψ/ I =μ0W2 SM / n d=1.257 W2 SM / n d×10 – 8 (H) 式中： ψ─磁通量（Wb） I ─电流（A） μ0 ─空气中的导磁率= 0.4π×10 – 6 = 1.257×10 – 6 (H/m) W ─线圈匝数 SM ─气隙处总有效截面积(cm 2 ) n ─气隙个数 d─单个气隙尺寸(cm ) SM ─气隙处总有效截面积计算 选择单个气隙尺寸d=0.5~3 cm 计算行射宽度E E=d/π ln ((H+d) /d) cm π=PI() 圆周率 H—铁饼高度,一般5 cm

计算行射面积(圆形铁心时)SE SE=2E×(AM+BM+2E) cm 2 AM—叠片总厚度cm BM—最大片宽cm (矩形铁心时)SE SE=2E×(AM+BM) cm 2 AM—叠片总厚度cm BM—片宽cm 计算气隙处总有效截面积 SM=SF / KF +SE cm 2 SF—铁芯截面 KF—叠片系数 漏磁通所产生的电感Ld Ld= 1.257 W2 Sdρ/ H1×10 – 6 (H) 式中： W —线圈匝数 Sd —总漏磁链 ρ—洛氏系数 铁心电抗器电感计算公式 H1 —线圈高度cm Sd=2π/3 F RF +πRn2 - SF / KF ρ=1- 2（RW - RO）/（πH1）

式中： F —线圈幅向尺寸cm RF —线圈平均半径cm Rn —线圈内半径cm RW —线圈外半径cm RO —铁芯半径cm H1 —线圈高度cm 线圈总电感 L= LM + Ld 线圈匝数W计算 ∵ I L = W φ = W B S ∴ W = I L /（B S） 程序计算步骤： 输入：I1，L 1. 计算容量P = I1 ^ 2* L / 1000 2. 参考铁心截面积QC = 15 * P ^ 0.5 3. 参考片宽DOOL =（QC / 1.5）^ 0.5 * 10 4. 参考铁心厚DOOS = DOOL * 1.5 5. 铁心截面积QC = Int(DOOL * DOOS * KQ) / 100 6. 初设磁密BMM =9000 7. 匝数N1 = Int(2 ^ 0.5 *I1 * I1*L * 10 ^ 5 / (BMM * QC))

kV干式铁心并联电抗器技术规范书

招标编号：xxxxxxx-xx-xx 江苏省电力公司工程 35kV铁芯并联电抗器 招标文件 第二卷技术规范书 江苏省电力公司 200x年x月

目录 1. 总则 2. 工作范围 2.1 供货范围 2.2 服务范围 2.3 技术文件 3. 技术要求 3.1 标准 3.2 使用环境条件 3.3 技术要求 4. 质量保证 5. 试验 6. 包装、运输和储存 7. 制造厂应提供的数据及资料 8. 卖方应填写的主要部件来源、规范一览表 附表1: 35kV铁心并联电抗器供货表 附表2: 投标差异表(格式)

1. 总则 1.1 本设备技术规范书适用于 35kV铁心并联电抗器, 它提出了该电抗器本体及附属设备的功能设计、结构、性能、安装和试验等方面的技术要求。 1.2 本设备技术规范提出的是最低限度的技术要求。凡本技术规范中未规定，但在相关设备的国家标准或IEC标准中有规定的规范条文，卖方应按相应标准的条文进行设备设计、制造、试验和安装。对国家有关安全、环保等强制性标准，必须满足其要求（如压力容器、高电压设备等）。 1.3 如果卖方没有以书面形式对本规范书的条文提出异议, 则意味着卖方提供的设备完全符合本规范书的要求。如有异议, 不管是多么微小, 都应在报价书中以“对规范书的意见和同规范书的差异”为标题的专门章节中加以详细描述。 1.4 本设备技术规范书所使用的标准如遇与卖方所执行的标准不一致时, 按较高标准执行。 1.5 本设备技术规范书经买、卖双方确认后作为订货合同的技术附件, 与合同正文具有同等的法律效力。 1.6 本设备技术规范书未尽事宜, 由买、卖双方协商确定。 1.7 卖方在应标技术规范中应如实反映应标产品与本技术规范的技术差异。如果卖方没有提出技术差异，而在执行合同的过程中，买方发现卖方提供的产品与其应标技术规范的条文存在差异，买方有权利要求退货，并将对下一年度的评标工作有不同程度的影响。 1.8 卖方应充分理解本技术规范并按本技术规范的具体条款、格式要求填写应标的技术文件，如发现应标的技术文件条款、格式不符合本技术规范的要求，则认为应标不严肃，在评标时将有不同程度的扣分。

电抗器技术协议(国网)

国网四象限电抗器技术协议 1．概述： 本电抗器是四象限电压源变流器滤波使用的电感，采用的是铁芯电抗器技术，线圈和铁心采用水冷板冷却技术，温升低。 2．执行标准 GB10229-1988 《电抗器》 GB1094.1-1996 《电力变压器》 GB1094.3;.5-1985 《电力变压器》 GB6450-1986 《干式变压器》 GB7449 《电力变压器和电抗器的雷击冲击波和操作冲击波试验导则》 GB7328-1987 《变压器和电抗器的声级测定》 3．主要技术参数 3.1环境条件 3.1.1环境温度：－25℃～＋40℃ 3.1.2 进口水温：-25℃～＋55℃，进水流量：≥6L/min，工作压力：≥3Kg 3.1.3 水的电导率：1×10-6 MΩ 3.2电性能要求 3.2.1相数：三相 3.2.2额定电流：1000A（有效值），1.5倍额定电流不饱和 3.2.3工作电压：690V；基波频率50Hz，峰值电压1300V 3.2.4 直流电阻:2mΩ±10%(20℃) 3.2.5总损耗:12.5KW,水路每组 4.3KW 3.2.6开关频率：450~1050HZ 3.2.7额定电感量：320uH；容许误差-5%~+5%；相间误差±2% 3.2.8匝间耐压及相间耐压：≥5KV，对地耐压≥5KV 3.3热性能要求

3.3.1 水的温升≤15K（流量在6L/min时） 3.3.2 电抗器温升≤50K（流量在6L/min时） 3.3.3 电抗器的流阻≤2Ba（流量在6L/min时） 备注：因相关参数是根据产品实物及经验提供的技术参数,有可能乙方提供产品与原实物存在差异,允许进行修正. 4．.对外接口 4.1 外形及安装尺寸见附图 4.1.1外形尺寸：见附图 4.1.2机械安装尺寸：400×320 4-14×24 4.2电连接：6处4-φ13，具体尺寸见附图。 4.3水路连接3进3出G 3/8’管螺纹，φ8×1水管，安装尺寸见附图。 5、试验内容：试验内容如表1所示： 6．额定工况下仿真波形：

电抗器的基本结构

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各种电抗器的计算公式

各种电抗器的计算公式 The manuscript was revised on the evening of 2021

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铁心电抗器设计

电磁装置设计原理课程设计（二） 铁心电抗器设计 班级：

主要参数 B(mm)一、 技术要求： 1、 额定容量KVA S N 360= 2、 线两端电压KV U l 10= 3、 额定电压V U N 381= 4、 相数3=m 5、 额定电流A I N 315= 6、 损耗W P P k 40000≤+ 7、 线圈温升K T K 09< 二、 铁芯参数选择 铁芯直径m m S K D D 189.03/36057.0/44=?==，选择m D 3 10190-?= 采用30133-DQ 硅钢片，查表（5-1）得： 铁芯叠压系数：95.0=dp K 心柱有效截面面积：2 4 105.238m A z -?= 轭有效截面面积：24104.258m A e -?= 角重：kg G 0.62=?

铁芯最大片宽：m B M 185.0= 铁芯总叠厚：m M 16.0=? 铁轭片高：m b em 17.0= 三、 设计线圈时电压、电流的选择 每段电抗值Ω===210.1315/381/1N N k I U X ， 设计线圈时的电压和电流分别是V U N 381=，A I N 315= 四、 线圈匝数 初选48.0,89.0'==m k T B ， 匝7.8610 5.23889.0502381 48.0'24 =?????== -ππZ m A fB V k W ，取整得：匝86=W 五、 主电抗计算 1、 初选单个气隙长度m 3105.7-?=δ，初选铁芯饼高度m H B 3 1008-?= 2、 气隙磁通衍射宽度：m H B 3 31065.55700.008.05700.0ln 105.7)ln(--?=?? ? ??+?=+=πδδπδε 3、 气隙磁通衍射面积： 23621003.410)16018565.52(65.52)2(2mm b A M M --?=?++??=?++=εεδ 4、 气隙等效导磁面积： 221029.01000/30.495 .002385 .0mm A K A A dp Z =+=+= δδ 5、 主电抗，取n=7,Ω=??????=?=-160.110 105.770292 .0865081087 322722πδπδn A fW X m 6、 主电抗压降V X I U m N m 2.203160.1315=?== 7、 磁密T V fWA U B Z m 0.8902385 .0865022.20321=???= = ππ 六、 线圈设计 1、 线圈高度估计值： m H n H n H A B l 224.011.05700.0708.0)17()1(=-?+?-=-+-=δ 2、初选导线：23363.29,108.51055.3mm S mm b mm a L =?=?=--，

电抗器与变压器是一样的产品吗

电抗器与变压器是一样的产品吗 电抗器也叫电感器，一个导体通电时就会在其所占据的一定空间范围产生磁场，所以所有能载流的电导体都有一般意义上的感性。然而通电长直导体的电感较小，所产生的磁场不强，因此实际的电抗器是导线绕成螺线管形式，称空心电抗器；有时为了让这只螺线管具有更大的电感，便在螺线管中插入铁心，称铁心电抗器。电抗分为感抗和容抗，比较科学的归类是感抗器（电感器）和容抗器（电容器）统称为电抗器，然而由于过去先有了电感器，并且被称谓电抗器，所以现在人们所说的电容器就是容抗器，而电抗器专指电感器。 什么叫变压器？ 变压器是一种用于电能转换的电器设备，它可以把一种电压、电流的交流电能转换成相同频率的另一种电压、电流的交流电能。 变压器几乎在所有的电子产品中都要用到，它原理简单但根据不同的使用场合（不同的用途）变压器的绕制工艺会有所不同的要求。变压器的功能主要有：电压变换；阻抗变换；隔离；稳压（磁饱和变压器）等，变压器常用的铁心形状一般有E型和C型铁心。 一、变压器的基本原理 当一个正弦交流电压U1加在初级线圈两端时，导线中就有交变电流I1并产生交变磁通ф1，它沿着铁心穿过初级线圈和次级线圈形

成闭合的磁路。在次级线圈中感应出互感电势U2，同时ф1也会在初级线圈上感应出一个自感电势E1，E1的方向与所加电压U1方向相反而幅度相近，从而限制了I1的大小。为了保持磁通ф1的存在就需要有一定的电能消耗，并且变压器本身也有一定的损耗，尽管此时次级没接负载，初级线圈中仍有一定的电流，这个电流我们称为"空载电流"。 如果次级接上负载，次级线圈就产生电流I2，并因此而产生磁通ф2，ф2的方向与ф1相反，起了互相抵消的作用，使铁心中总的磁通量有所减少，从而使初级自感电压E1减少，其结果使I1增大，可见初级电流与次级负载有密切关系。当次级负载电流加大时I1增加，ф1也增加，并且ф1增加部分正好补充了被ф2 所抵消的那部分磁通，以保持铁心里总磁通量不变。如果不考虑变压器的损耗，可以认为一个理想的变压器次级负载消耗的功率也就是初级从电源取得的电功率。变压器能根据需要通过改变次级线圈的圈数而改变次级电压，但是不能改变允许负载消耗的功率。 二、变压器的损耗 当变压器的初级绕组通电后，线圈所产生的磁通在铁心流动，因为铁心本身也是导体，在垂直于磁力线的平面上就会感应电势，这个电势在铁心的断面上形成闭合回路并产生电流，好象一个旋涡所以称为"涡流"。这个"涡流"使变压器的损耗增加，并且使变压器的铁心发

电抗器计算公式和顺序

电抗器计算公式和步骤 S=1.73*U*I 4% X=4/S*.9 1. 铁芯直径D D=KPZ0.25 cm K—50~58 PZ—每柱容量kVA 2.估算每匝电压ET ET=4.44fBSP×10-4 V B—芯柱磁密 0.9~1T SP—芯柱有效截面

cm2 3. 线圈匝数 W=UKM/（ET×100）KM—主电抗占总电抗的百分数 U—总电抗电压 V 4. 每匝电压及铁芯磁密 ET=UKM/（W×100） V BM=ET×104/（4.44fSP） T 5. 主电抗计算 选择单个气隙尺寸δ=0.5~3cm 计算行射宽度E E=δ/πln((H+δ)/δ) cm H—铁饼高度,一般5cm 计算行射面积SE

SE=2E×(AM+BM+2E) cm2 AM—叠片总厚度 cm BM—最大片宽 cm 计算气隙处总有效截面积 SM=SF/KF+SE cm2 SF—铁芯截面 KF—叠片系数 计算气隙个数 n=(7.9fW2SM)/(X NδKM×106) XN—电抗Ω 计算主电抗 XM=(7.9fW2SM)/(nδ×108) 如果XM≈X N KM/100则往下进行，否则重新选择单个气隙长度，重复上述计算。 6.

漏电抗计算 Xd=(7.9fW2Sdρ)/(H×108) Ω Sd=2π/3FRF+πRn2-SF/KF ρ=1-2×（RW-RO）/（π×H）式中： F—线圈幅向尺寸 cm RF—线圈平均半径 cm Rn—线圈内半径 cm RW—线圈外半径 cm RO—铁芯半径 cm

H—线圈高度 cm 总电抗X N X N=XM+Xd Ω 附：串联电抗器参数与计算 一基本技术参数 1 额定电压UN （电力系统的额定电压kV） 并联电容器的额定电压U1N 2 额定电流I1 3 额定频率f 4 相数单相三相 5 电抗器额定端电压U1当电抗器流过额定电流时一相绕组二端的电压6 电抗器额定容量P

电抗器设计

07
级
《电磁装置设计原理——电抗器的设计》
设 计 报 告
姓 学
名 号
专业班号
指导教师 日 期

1
480KV/10KV 电 抗 器 设 计
一．电抗器的额定值和技术要求：
1、 额定容量 S N = 480 KVA 2、 额定电压 U N = 10 KV 3、 阻抗压降 U 1 = 381V 4、 相数 m = 3 5、 额定电流 I N = 419 A 6、 损耗 PCU + PFe ≤ 7000W 7、 线圈温升 TK < 125K 电抗器的主要参数选择结果
二．电抗器的参数计算选择
1． 铁芯参数设计选择
1.1 铁芯直径选择
D = K D 4 S / m = 0.06 × 4 480 / 3 = 0.206m ，
选择 D = 210 × 10 ?3 m ，采用 DQ133 ? 30 硅钢片，查表（5-1）得： 铁芯叠压系数： K dp = 0.95

2
铁芯柱有效截面面积： Az = 291.8 × 10 ?4 m 2 轭有效截面面积： Ae = 321.3 × 10 ?4 m 2 角重： G? = 84.8kg 铁芯最大片宽： BM = 0.2m 铁芯总叠厚： ? M = 0.178m 铁轭片高： bem = 0.19m 1.2 矩形铁芯长宽确定 举行铁芯的面积由上面查表得到的数据确定，又要求 a/b 为 3， 则可选取长 a=300mm，宽 b=100mm。 有效铁芯截面积等于铁芯面积 X 叠压系数： A S =0.95*300*100=28500 mm 2
2． 线圈参数设计选择
电抗额定值
X1 =
VN
IN
= 381
419
= 0.909
设计后，要满足电抗器的电抗的标幺值为 1~1.025 线圈匝数 初选 B ' = 0.81T , k m = 0.81 ，
W=
k mV 2πfB' AZ
=
0.81× 381 = 60匝 ，取整得： W = 60匝 2π × 50 × 0.87 × 300 × 10 ?4
主电抗计算
初选单个气隙长度 δ = 6.5 × 10 ?3 m ，铁芯饼高度 H B = 50 × 10 ?3 m

输出电抗器技术参数

变频器输出电抗器（1%压降） 1、作用 ◆降低电机的噪音，降低涡流损耗。 ◆降低输入高次谐波造成的漏电流。 ◆用于平滑滤波，降低瞬变电压dv/dt，延长电机寿命。 ◆保护变频器内部的功率开关器件。 2、 技术参数 1、额定工作电压：380V/50Hz或660V/50Hz 2、额定工作电流：5A至1600A@40℃ 3、抗电强度：铁芯-绕组3000VAC/50Hz/5mA/10s无飞 弧击穿(工厂测试) 4、绝缘电阻：1000VDC绝缘阻值≥100MV 5、电抗器噪音：小于65dB（与电抗器水平距离点 1米测试） 6、防护等级：IP00 7、绝缘等级：F级以上 8、产品执行标准：IEC289:1987电抗器 GB10229-88 电抗器(eqv IEC289:1987) JB9644-1999 半导体电气传动用电抗器

出线电抗器型 号变频器 调速器 功率KW 额定 电流 （A） 外形尺寸 长*宽*高 mm 安装 尺寸 mm 绝缘 等级 压 降 孔 径 OCL-80.75(1.5)8140*80*14075*60F，H1%6 OCL-10 2.510140*80*14075*60F，H1%6 OCL-10 3.7(4.0)10140*80*14075*60F，H1%6 OCL-15 5.515140*80*14075*60F，H1%6 OCL-207.520170*130*13578*75F，H1%6 OCL-301130170*130*13578*75F，H1%6 OCL-401540210*130*170112*75F，H1%8 OCL-5018.550210*130*170112*75F，H1%8 OCL-602260210*130*170112*75F，H1%8 OCL-803080210*160*170112*90F，H1%8 OCL-11037110210*160*170112*90F，H1%8 OCL-12045120210*160*170112*90F，H1%8 OCL-150*********200*210133*120F，H1%10 OCL-20075200240*200*210133*120F，H1%10 OCL-25090250300*220*240172*130F，H1%10 OCL-280110280300*220*240172*130F，H1%10 OCL-300132300310*230*250190*130F，H1%10 OCL-400160400320*230*270190*130F，H1%10 OCL-450187450330*240*270210*135F，H1%10 OCL-500200(220)500330*250*270210*135F，H1%10

电抗器参数计算公式

电抗器参数计算公式 加载其电感量按下式计算:线圈公式 阻抗(ohm) = 2 * 3.14159 * F(工作频率) * 电感量(mH)，设定需用360ohm 阻抗，因此： 电感量(mH) = 阻抗(ohm) ÷(2*3.14159) ÷F (工作频率) = 360 ÷(2*3.14159) ÷7.06 = 8.116mH 据此可以算出绕线圈数： 圈数= [电感量* { ( 18*圈直径(吋)) + ( 40 * 圈长(吋))}] ÷圈直径(吋) 圈数= [8.116 * {(18*2.047) + (40*3.74)}] ÷ 2.047 = 19 圈 空心电感计算公式 空心电感计算公式：L(mH)=(0.08D.D.N.N)/(3D+9W+10H) D------线圈直径 N------线圈匝数 d-----线径 H----线圈高度 W----线圈宽度 单位分别为毫米和mH。。 空心线圈电感量计算公式: l=(0.01*D*N*N)/(L/D+0.44) 线圈电感量l单位: 微亨 线圈直径D单位: cm 线圈匝数N单位: 匝 线圈长度L单位: cm 频率电感电容计算公式: l=25330.3/[(f0*f0)*c] 工作频率: f0 单位:MHZ 本题f0=125KHZ=0.125 谐振电容: c 单位F 本题建义c=500...1000pf 可自行先决定,或由Q 值决定 谐振电感: l 单位: 微亨 线圈电感的计算公式 1。针对环行CORE，有以下公式可利用: (IRON) L=N2．AL L= 电感值（H) H-DC=0.4πNI / l N= 线圈匝数(圈) AL= 感应系数 H-DC=直流磁化力I= 通过电流(A) l= 磁路长度（cm) l及AL值大小，可参照Micrometal对照表。例如: 以T50-52材，线圈5圈半，其L值为T50-52(表示OD为0.5英吋)，经查表其AL值约为33nH L=33．(5.5)2=998.25nH≒1μH

电抗器规范

第一章总则 第1.0.1条并联电容器用串联电抗器（以下简称电抗器）的设计选择必须执行国家的技术经济政策，并应根据安装地点的电网条件、谐波水平、自然环境等，合理地选择其技术参数；做到安全可靠、经济合理。 第1.0.2条本标准适用于变电所和配电所中新建或扩建的6～63KV并联电容器装置中电抗器的设计选择。 第1.0.3条本标准所指电抗器是串联于高压并联电容器回路中的电抗器，该电抗器用于限制合闸涌流，减轻电网电压波形畸变和防止发生系统谐波谐振。 第1.0.4条电抗器的设计选择，除应符合本标准的规定外，尚应符合国家现行有关标准的规定。 第二章环境条件 第2.0.1条电抗器的基本使用条件： 一、安装场所：户外或户内； 二、环境温度：－40℃～+40℃； －25℃～+45℃； 三、海拔：不超过1000m； 四、相对湿度：对于户内电抗器月平均相对湿度不超过90%，日平均不超过95%； 五、地震裂度：设计地震基本裂度为8度；即水平加速度0.3g，垂直加速度0.15g； 六、户外式最大风速为35m/s； 七、电抗器的外绝缘泄漏比距不应小于2.5cm/KV。对于重污秽地区可以取3.5cm/KV。 第2.0.2条选用电抗器时，应按当地环境条件校核，当环境条件超出其基本使用条件时，应通过技术经济比较分别采取下列措施： 一、向制造厂提出补充要求，制造符合当地环境条件的产品； 二、在设计中采取相应的防护措施，如采用户内布置、水冲洗、减震装置等。

第三章技术参数选择 第一节电抗率的选择 第3.1.1条电抗率的选择，应使装置接入处n次谐波电压含量和电容器上n次谐波电压值均不超过有关标准规定的限值。 第3.1.2条当仅需要限制合闸涌流时，宜选用电抗率为0.1%～1%的电抗器。 第3.1.3条为抑制5次及以上谐波电压放大，宜选用电抗率为4.5%～6%的电抗器；抑制3次及以上谐波电压放大，宜选用电抗率为12%～13%的电抗器。 第3.1.4条在电力系统谐波电压较大时，应由非线性用电设备所属单位负责采取限制谐波的措施，在采用交流滤波电容器装置时，电抗器应按滤波电抗器的要求选择。 第二节额定值 第3.2.1条电抗器的基本额定参数，应选择下列规定值： 一、额定频率：50Hz； 二、相数：1Φ或3Φ； 三、系统额定电压：6KV，10KV，35KV，63KV； 四、额定电抗率（K）：0.1%～1%，4.5%～6%，12%～13%。 第3.2.2条电抗器的额定电流应和与其串联组合的电容器或电容器组的额定电流相等。 第3.2.3条电抗器的额定端电压应等于与其串联组合的一相电容器额定电压的K倍，其值见表3.2.3。 第3.2.4条电抗器的额定容量，应等于与其串联组合的电容器或电容器组额定容量的K倍。

电源电压为1 100 V及以下的变压器、电抗器、电源装置和类似产品的

I C S29.180 K41 中华人民共和国国家标准 G B/T19212.17 2019 代替G B/T19212.17 2013 电源电压为1100V及以下的变压器二电抗器二电源装置和类似产品的安全第17部分:开关型电源装置和开关型电源装置用变压器的特殊要求和试验 S a f e t y o f t r a n s f o r m e r s,r e a c t o r s,p o w e r s u p p l y u n i t s a n d s i m i l a r p r o d u c t s f o r s u p p l y v o l t a g e s u p t o1100V P a r t17:P a r t i c u l a r r e q u i r e m e n t s a n d t e s t s f o r s w i t c hm o d e p o w e r s u p p l y u n i t s a n d t r a n s f o r m e r s f o r s w i t c hm o d e p o w e r s u p p l y u n i t s (I E C61558-2-16:2013,S a f e t y o f t r a n s f o r m e r s,r e a c t o r s,p o w e r s u p p l y u n i t s a n d s i m i l a r p r o d u c t s f o r s u p p l y v o l t a g e su p t o 1100V P a r t2-16:P a r t i c u l a r r e q u i r e m e n t s a n d t e s t s f o r s w i t c hm o d e p o w e r s u p p l y u n i t s a n d t r a n s f o r m e r s f o r s w i t c hm o d e p o w e r s u p p l y u n i t s,MO D) 2019-10-18发布2020-05-01实施 国家市场监督管理总局