Nghiên cứu tối ưu thay đảo nhiên liệu lò phản ứng hạt nhân VVER 1000ư

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGYVIETNAM ATOMIC ENERGY INSTITUTE TRAN VIET PHU STUDY ON FUEL LOADING PATTERN OPTIMIZATION FOR VVER-1000 NUCLEAR REACTO

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE

TRAN VIET PHU

STUDY ON FUEL LOADING PATTERN

OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR

DISSERTATION FOR THE DOCTOR DEGREE OF PHYSICS

Hanoi - 2022

BỘ GIÁO DỤC VÀ ĐÀO TẠO BỘ KHOA HỌC VÀ CÔNG NGHỆ

VIỆN NĂNG LƯỢNG NGUYÊN TỬ VIỆT NAM

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE

TRAN VIET PHU

STUDY ON FUEL LOADING PATTERN

OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR

DISSERTATION FOR THE DOCTOR DEGREE OF PHYSICS

Major: Nuclear and Atomic Physics

Code: 9.44.01.06

1 Assoc Prof Dr TRAN Hoai Nam

2 Prof Dr YAMAMOTO Akio

Hanoi - 2022

1.1 General introduction 1

1.2 Description of fuel LP optimization problem 3

1.3 Overview of methods applied to fuel LP optimization 8

1.4 Overview of VVER reactor 12

1.5 Purposes of this dissertation 18

1.6 Dissertation outline 19

2 Methods and development 21 2.1 Introduction 21

2.2 VVER-1000 MOX core benchmark 22

2.3 Data preparation for core calculations 25

2.4 Development of LPO-V code for core physics calculations 28

2.4.1 Steady-state multi-group diffusion equations 28

2.4.2 Finite difference method for spatial discretization 30

2.4.3 Boundary conditions 34

2.4.4 Successive over-relaxation method 36

2.4.5 Core modeling by LPO-V code 41

2.4.6 Verification of core calculations 43

Contents ii

2.5 Development of ESA method 46

2.5.1 SA and ASA methods 46

2.5.2 ESA method 48

2.6 Development of a discrete SHADE method 52

2.6.1 Classics Differential Evolution 52

2.6.2 SHADE operators 54

2.6.3 Success-history based adaptation 57

2.6.4 Discrete SHADE method 60

2.7 Fitness functions 62

2.8 Mann-Whitney U Test 65

2.9 Conclusions 67

3 Loading pattern optimization of VVER-1000 reactor 68 3.1 Introduction 68

3.2 LP optimization of VVER-1000 core using ESA method 69

3.2.1 Selection of ESA method 69

3.2.2 Comparison among SA, ASA and ESA 71

3.2.3 LP optimization of the VVER-1000 MOX core using ESA method 76 3.3 LP optimization of VVER-1000 reactor using SHADE method 77

3.3.1 Determination of control parameters 77

3.3.2 LP optimization of the VVER-1000 MOX core using SHADE method 79

3.4 Optimal core loading pattern of SHADE and ESA 87

3.5 Conclusions of Chapter 3 88

4 Conclusions and future work 91 4.1 Conclusions 91

4.2 Future works 94

Declaration of Authorship

I certify that this dissertation entitled "STUDY ON FUEL LOADING TERN OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR" is my own origi- nal work except where otherwise clearly indicated I confirm that the dissertation sub- mitted to the Nuclear Training Center, Vietnam Atomic Energy Institute was mainly done during my candidature for a PhD degree under the supervision of Assoc Prof.

PAT-Dr Tran Hoai Nam and Prof PAT-Dr Yamamoto Akio.

TRAN VIET PHU

This dissertation presents a long-term work in an interesting field of nuclear and atomic physics The dissertation was performed with great supports from my colleagues and the encouragements of my relatives together with my individual endeavor.

To my wife and sons, who have constantly supported me throughout challenging years.

To my parents, my younger sister, who are always next to me with love.

Tóm tắt

Luận văn này trình bày nghiên cứu về tối ưu thay đảo nhiên liệu cho lò phản ứng VVER Một chương trình mô phỏng vùng hoạt (LPO-V) đã được phát triển cho các lò phản ứng VVER, cùng với các phương pháp tìm kiếm tối ưu hóa Chương trình này giải các phương trình khuếch tán trong ô mạng tam giác dựa trên phương pháp sai phân hữu hạn Việc xác minh chương trình LPO-V được thực hiện dựa trên một bài toán chuẩn của lò VVER-1000 nạp tải nhiên liệu MOX Kết quả cho thấy chương trình có độ chính xác đảm bảo và hiệu suất tốt hơn mô-đun CITATION.

Hai phương pháp tối ưu hóa tiên tiến đã được phát triển cho bài toán tối ưu nạp tải nhiên liệu của lò phản ứng VVER-1000: Phương pháp mô phỏng tôi kim tiến hóa (ESA) và phương pháp tiến hóa vi phân dựa trên lịch sử thành công (SHADE) Phương pháp ESA được cải tiến từ phương pháp mô phỏng tôi kim nguyên bản (SA) bằng cách sử dụng các toán tử trao đổi chéo và đột biến để tạo ra các cấu hình nạp tải thử nghiệm mới Phương pháp SHADE sử dụng cơ chế thích ứng dựa trên lịch sử của các tham số điều khiển thành công, tức là tỷ lệ đột biến F và tỷ lệ trao đổi chéo

CR, để cải thiện thuật toán tiến hóa vi phân (DE) ban đầu Do đó, thay vì ba tham

số điều khiển trong DE ban đầu, phương pháp SHADE bao gồm hai tham số là kích thước quần thể N P và kích thước bộ nhớ lịch sửH Để áp dụng phương pháp SHADE cho bài toán tối ưu thay đảo nhiên liệu, phương pháp tiếp cận chỉ số vị trí tương đối

đã được triển khai để chuyển đổi các biến thực thành các biến số nguyên Các tính toán đã được thực hiện để chọn các thông số điều khiển phù hợp của SHADE cho bài toán tối ưu thay đảo nhiên liệu của lò phản ứng VVER-1000 nạp tải MOX.

Tóm tắt vii

Các tính toán số cho bải toán tối ưu thay đảo nhiên liệu của lò VVER-1000 nạp tải MOX đã được thực hiện bằng các phương pháp ESA và SHADE, có so sánh với SA, mô phỏng tôi kim thích ứng (ASA) và DE Một hàm mục tiêu đã được chọn để tối đa hóa kef f, đồng thời làm phẳng phân bố công suất hướng tâm Kết quả cho thấy

kef f của cấu hình tối ưu lớn hơn của cấu hình tham chiếu khoảng 1580 pcm Trong khi đó, hệ số đỉnh công suất xuyên tâm (P P F ) của cấu hình tối ưu nhỏ hơn khoảng 2,4 % so với cấu hình tham chiếu Sự khác biệt thống kê giữa các phương pháp này cũng được đánh giá dựa trên phương pháp Mann-Whitney U-test Kết quả cho thấy rằng phương pháp ESA và SHADE có hiệu suất tương đương với DE và lợi thế hơn so với SA và ASA.

Việc phát triển thêm các phương pháp và mở rộng ứng dụng của chúng cho các vấn đề khác về tối ưu thay đảo nhiên liệu vẫn sẽ được tiếp tục nghiên cứu trong tương lai.

This dissertation presents a research on optimization of fuel loading pattern (LP) for VVER reactor A core physics calculation code (LPO-V) has been developed for VVER reactors, and coupled with optimization search methods This code solves diffusion equations in triangular meshes based on finite difference method Verification for the LPO-V code was performed based on the VVER-1000 MOX benchmark core

in comparison with MCNP4c calculations The results show that the code has a high accuracy and better performance than the CITATION module.

Two advanced optimization methods have been developed for the problem

of fuel loading optimization of VVER-1000 reactor: Evolutionary Simulated ing (ESA) method and discrete Success-History based Adaptive Differential Evolution (SHADE) method The ESA method which was improved from the original simulated annealing (SA) by using crossover and mutation operators to generate new trial load- ing patterns The SHADE method uses an adaptive mechanism based on a historical record of successful control parameters, i.e mutant scale F and crossover ratio CR, to improve the original Differential Evolution (DE) algorithm Therefore, instead of three control parameters in the original DE, the SHADE method consists of two parameters

Anneal-of population size N P and memory size H To apply SHADE method to the fuel

LP optimization, a relative position indexing approach was deployed to convert real variables into integer variables Calculation surveys was performed to select suitable control parameters of the SHADE for the LP optimization problem of the VVER-1000 MOX core.

Numerical calculations for optimizing fuel LP of the VVER-1000 MOX core have been conducted using the ESA and SHADE methods in comparison with Sim- ulated Annealing (SA) and Adaptive Simulated Annealing (ASA) A fitness function was chosen to maximize the kef f, while flattening the radial power distribution The results show that the kef f of the optimal LP is greater than that of the reference core by about 1580 pcm Whereas, the radial power peaking factor (P P F ) of the optimal LP

Abstract ix

is about 2.4% smaller than that of the reference core Statistical differences between these methods were also evaluated based on the Mann-Whitney U test The results show that the ESA and SHADE methods are advantageous over SA and ASA.

Further development of the methods and extension of their application to other problem of fuel loading optimization are being continued in the future work.

List of Abbreviations

ENDF Evaluated Nuclear Data File

ESA Evolutionary Simulated Annealing

kef f Effective Multiplication Factor

LPO-V Loading Pattern Optimization of VVER

Abstract xi

RPI Relative Position Indexing

SCWR Supercritical Water-Cooled Reactors

SHADE Success-History based Adaptive Differential Evolution

SOR Successive Over-Relaxation

VVER Vodo-Vodyanoi Energetichesky Reaktor

VVER-TOI Vodo-Vodyanoi Energetichesky Reactor Tipovoi

Optimizirovanniy Informatizirovanniy

List of Figures

1.1 Diagram of a nuclear reactor cycle 5

1.2 Three LP samples of VVER-1000 MOX core 7

1.3 Sample of local and global optimums 9

1.4 Main components of a VVER reactor [87] 13

1.5 VVER reactor vessel [88] 14

1.6 Sample VVER assembly (a) and VVER reactor core (b) 15

1.7 Fuel designs of VVER-1000 (TVS-2) and VVER-1200 (TVS-2006) [92] 17 2.1 Structure and dimensions of the VVER-1000 benchmark core [5] 23

2.2 VVER-1000 benchmark core with 30% MOX fuel loading Each hexag-onal block shows the identification number of the fuel assembly (upper) and the fuel type (lower) 25

2.3 UO2 and MOX assemblies of the VVER-1000 benchmark core [5] 26

2.4 Fuel cell, Central tube/Guide tube cell and absorber rod cell of the VVER-1000 benchmark [5] 26

2.5 one-sixth model of VVER-1000 assembly 27

2.6 2D triangular mesh (a) and mesh’s neighbours (b) in the FDM 34

2.7 Form of the matrix A in 2D model of the FDM 35

2.8 Free surface boundary condition 37

2.9 Reflective boundary condition 37

2.10 Periodic boundary condition 37

2.11 VVER-1000 core model with 24 triangular meshes per assembly in the LPO-V code 42

2.12 kinf as function of burnup in U O2 and MOX assemblies 43

2.13 Comparison of the power distributions in states S1 (a) and S4 (b) ob-tained from LPO-V and MCNP4c calculations 45

2.14 Crossover 1 (C1) exchanging two assemblies randomly between the parents 49 2.15 Crossover 2 (C2) exchanging a random block between the parents 49

2.16 Example of the relative position indexing (RPI) approach to convert a real vector to an integer vector 61

2.17 Flowchart of the discrete SHADE method for the problem of LP opti-mization 63

List of Figures xiii

2.18 Survey for selecting the weighting factors wp (a) and wf (b) The values

of kef f, P P F and F latness were taken as the average of 20 independent runs using SA (α = 0.9) wf = 0.0 was set in the survey of wp, and

wp = 2.5 was set in the survey of wf The values of wp = 2.5 and

wf = 0.006 were selected 65 3.1 fitness function F 1 obtained with 50 independent runs of the ESA methods 70 3.2 fitness function F 2 obtained with 50 independent runs of the ESA methods 70 3.3 Comparison of the convergence of the ESA, ASA and SA methods with the use of fitness function F 1 The values were taken as the average of

50 independent runs 73 3.4 Comparison of the convergence between ESA, ASA and SA with the use

of F 2 The value is taken as the average of 50 independent runs 74 3.5 Comparison of the convergence of ESA, ASA and SA with the use of F 2 and the stop criterion for the best LP of 10000 trial LPs The value is taken as the average of 50 independent runs 76 3.6 Evolution of the k ef f and P P F (a), and F latness (b) obtained by the ESA with the use of fitness function F 2 The values were taken as the average of 50 independent runs 77 3.7 A survey of control parameters N P and H The values of N P = 20 and

H = 6 were selected for further optimization process 79 3.8 Distribution of the individuals and trials in the initial, 400th and 750th generations 80 3.9 Evolution of the fitness function with the number of generations in ten independent runs The average curve is taken as the average of 50 inde- pendent runs 81 3.10 Evolution of the fitness function with the number of generations The value is taken as the average of 50 independent runs 82 3.11 Evolution of the kef f as a function of the number of generations The value is taken as the average value of 50 independent runs 82 3.12 Evolution of the PPF as a function of the number of generations The values are taken as the average of 50 independent runs 83 3.13 Evolution of the F latness as a function of the number of generations The value was taken as the average of 50 independent runs 83 3.14 Evolution of F and CR with the number of generations The values were taken as the averages of 50 independent runs 84 3.15 Comparison of the optimal fitness functions obtained from 50 indepen- dent runs of SHADE, DE and ESA 85 3.16 Optimal core LP (a) and its relative radial power distribution (b) in comparison with the reference one 88

List of Tables

1.1 kef f and assembly PPF of three sample LPs 6

1.2 Number of LP of VVER-1000 MOX-core 8

1.3 Specification of VVER types 16

2.1 Reactor state descriptions of the Benchmark [5] 24

2.2 Fuel assemblies and burnup levels in the 1/6th VVER-1000 MOX bench-mark core 25

2.3 Comparison of the kef f values calculated with the LPO-V and MCNP4c codes for five states (S1–S5) of the VVER-1000 MOX benchmark core 44 3.1 Comparison of ten approaches of the ESA method using the two fitness functions The results were taken as the average of 50 independent runs The Mann-Whitney U Test is used to compare ESA-C1A4 with other ESA methods 71

3.2 Comparison of the SA, ASA and ESA methods with the use of fitness function F 1 in reproducing a reference LP 72

3.3 Comparison of the SA, ASA and ESA methods using the Mann-Whitney U Test with the fitness function F 1 73

3.4 Comparison of the performance of the SA, ASA and ESA methods 75

3.5 Comparison of the SA, ASA and ESA methods with fitness function F 2 using the Mann-Whitney U Test P > 0.05 means that two methods are not significant different P < 0.05 means that the second method is better than the first one 75

3.6 Comparison of SHADE with DE and ESA 87

3.7 Comparison of the optimal LP obtained from the search process with the reference one 88

A.1 Dimension of the cell zones [5] 118

A.2 Material names used in the fuel assemblies [5] 119

A.3 Isotopic composition of fuel U_4.2, atoms/barn ∗ cm 2 [5] 119

A.4 Isotopic composition of fuel TVEG_5, atoms/barn ∗ cm 2 [5] 120

A.5 Isotopic composition of fuel U_3.7, atoms/barn ∗ cm 2 [5] 121

A.6 Isotopic composition of fuel PU_3.6, atoms/barn ∗ cm 2 [5] 122

A.7 Isotopic composition of fuel TVEG_4, atoms/barn ∗ cm2 [5] 123

A.8 Isotopic composition of fuel PU_2.7, atoms/barn ∗ cm2 [5] 124 A.9 Isotopic composition of fuel PU_2.4, atoms/barn ∗ cm2 [5] 125 A.10 Isotopic composition of the structural material, atoms/barn ∗ cm 2 [5] 125 A.11 Moderator and water in reflector materials, atoms/barn ∗ cm 2 [5] 126 B.1 Four groups structure with three fast groups and one thermal group 126 B.2 Four groups cross sections of fuel assemblies 127 B.3 Four groups cross sections of non fuel materials 128

1964, i.e Beloyarsk Nuclear Power Station (using boilling water graphitechannel reactor technology) and Novovoronezh Nuclear Power Plant - unit

1 (using Russian PWR technology: veda-vodyanoi energetichesky reaktor

- VVER) In addition, countries such as France and Canada also startedoperating commercial reactors around this time [1]

Development of nuclear power has undergone several times of clines and stagnation due to severe accidents, i.e the Three Mile Island

de-accident (1979), the Chernobyl de-accident (1986) and the Fukushima dent (2011) in the most recently However, nuclear power still plays animportant role in the global energy system so far In 2019, about 10%

acci-of the world’s total electricity was generated by more than 440 nuclearreactors There are about 50 power plants under construction, that isequivalent to 15% of the current total capacity [2]

There are still a number of reasons for that nuclear power remains

an important source of energy in the future The first reason is the ing demand for electrical energy around the world, especially in developingcountries The second is the importance of energy security for each coun-try, so that each country needs to ensure the capacity for electricity supplywith an affordable and stable price, meeting the demand anytime and any-

change

In nuclear power technology, there are two main concerns: safetyand cost The recently constructed nuclear power plants are mostly be-longing to the III+ generation, and the IV generation are being researchedand developed These generations have added active and passive safetyfeatures Therefore, they are much safer than the previous ones, espe-cially in comparison with those of the above mentioned severe accidents (Iand II generations) The cost of nuclear power includes construction cost,operating cost and fuel cost Whereas the construction cost, accountingfor about 70% in whole nuclear power cost [3], depends on the technologyand the supplier, and are usually fixed at the preparing for constructing

a nuclear power plant The operating cost and fuel cost can be optimizedduring the operation of the nuclear power plant In the case, the fuel costs,

accounting for about 15-25% [3], have a great impact on the cost of clear power The cost of fuel mainly depends on three factors, includingthe type of reactor, the characteristics of the fuel and the in-core fuel man-agement (ICFM) method In this dissertation, the reduction of fuel costs

nu-by improving the ICFM will be focused

In ICFM, the main task is to determine the optimal fuel loadingpattern Fuel loading pattern is an arrangement of the fuel assemblies inthe reactor core An optimal arrangement can give the best fuel efficiency,for the maximum total energy generated in a cycle while ensuring safetyrequirement In a reactor core, there are many types of fuel assemblieswith different enrichments and burnup levels Therefore, the loading pat-tern optimization problem is a complex problem with a large number ofpossible loading patterns This dissertation focuses on the development

of advanced method for fuel loading pattern optimization of VVER-1000reactor VVER is Russian PWR technology, and was considered for Viet-nam’s nuclear power program before 2016

1.2 Description of fuel LP optimization problem

ICFM, i.e fuel loading pattern (LP) optimization, is an importanttask in designing a nuclear reactor core, and is performed after each fuelcycle for most nuclear reactors For current light water reactors (LWRsincluding PWR, BWR, VVER), the operation time of each fuel cycle isusually 1 or 1.5 year The reactor is then stopped for maintenance andreplacement apart of the old fuels before starting a new cycle Fig 1.1shows the main stages of a fuel cycle of LWR In the "fuel inspection"step, about 1/3 of the old fuel bundles are removed and put into the used

fuel storage The remaining 2/3 of the burnt fuel bundles together withthe fresh fuel bundles will be used in the "loading pattern design" step

to design a new LP for the active core The important task here is todetermine the optimal arrangement of the fuel bundles within the core toachieve the objectives of neutronic characteristics and safety of the core,and the best fuel efficiency simultaneously The process of determining theoptimal arrangement of the fuel bundles is known as the LP optimizationproblem This is a very complex multi-objective problem, in which manycharacteristic parameters tend to change in opposite directions In theICFM problem, two main objectives are typically considered [4]:

(1) maximization of fuel cycle length

(2) maintaining safety criteria during operation

The cycle length maximization means increasing the efficiency offuel utilization, and consequently minimization of fuel cycle cost Whereas,the safety criteria should be maintained during operation to ensure thesafety of nuclear reactors One of the most basic safety criterion is mini-mization of power peaking factor (PPF) This criterion results in the de-crease of fuel failure possibility and the enhancement of safety margin

To have the maximization of the cycle length, that means ing the amount of leakage neutrons, or the neutron flux in the outer region

minimiz-is small However, thminimiz-is means that the heat generation in the outer area

is small, so the heat generation in the inner area will be larger to ensurethe heat generation of the whole active area Therefore, this target is con-trary to the target of the minimization of PPF Since then, when designingthe active core, there will be a need for a balance between the safety andeconomy of the reactor

Figure 1.1: Diagram of a nuclear reactor cycle.

For example, Fig 1.2 shows three sample of LPs of VVER-1000MOX core with fuel inventory given in [5] In this figure, the fuel assemblysymbols include the first character to indicate the fuel type including U

indicate the burn-up of the fuel assembly The details of assemblies were

radial assembly PPF in the rest of this dissertation) of the three LPs aresummarized in Table 1.1 Normally, the safety limit of radial assemblypower peaking factor of PWR is about 1.5 Therefore, the (a) core violates

the safety limit because the PPF is 1.640 The PPF of (b) core and (c)core are 1.313 and 1.348, respectively They satisfy the safety criteria on

(c) core is higher than that of the (b) core

Table 1.1: k ef f and assembly PPF of three sample LPs.

kef f 1.15235 1.13627 1.15828

The objective of maximization of cycle length usually is replaced

cycle (BOC) This replacement makes the calculation speed much faster

by not having to perform the burn-up calculation On the other hand,the second objective of maintaining safety criteria usually simplified by

a constraint condition of the PPF, so that PPF have to be lower than agiven safety limit This constraint ensures the balance of the safety andthe economy of the reactor as mentioned above In this dissertation, thePPF is at BOC without burnup considering because infinite multiplicationfactors of all fuel assemblies decrease with burnup (see Section 2.4.5)

In general, the objectives are combined into a fitness function (FF)for searching optimal solutions A nuclear reactor simulator is used todetermine typical parameters of the core those are used to calculate the

FF value of a LP The best FF values of all LPs corresponds to the optimum

LP for the reactor Nevertheless, A typical LWR consists of about 150–200fuel assemblies, and therefore, the possible number of fuel LPs would beenormous even when geometrical symmetry and constraints are considered.Table 1.2 estimates the number of possible LPs and calculation time for theVVER-1000 MOX core One can see that it is impossible to calculate all

Figure 1.2: Three LP samples of VVER-1000 MOX core

possible LP Therefore, many optimization methods have been developedand applied to the LP optimization problem.

Table 1.2: Number of LP of VVER-1000 MOX-core.

(time* (year)

No symmetry, do not consider the

similarity of the fuel assemblies 1.2E+289 3.9E+280

No symmetry, consider the similarity

1/6 symmetry, do not consider the

1/6 symmetry, consider the similarity

*: The average calculation time is assumed 10 LPs/second.

1.3 Overview of methods applied to fuel LP optimization

The problem of LP optimization has received attention from the ginning of nuclear reactor technology Many efforts have been contributed

be-to solve the problem of ICFM with the development and application of

a number of optimization methods Initially, some classical search ods were used such as Direct search (DS) and Binary exchange (BE) [6].The advantage of these algorithms is that the number of calculated LPs

meth-is small, and the search converges quickly to a local optimum However,these algorithms have the disadvantage of being unable to escape from thelocal optimum Along with the development of computer technology, ad-vanced stochastic optimization methods were developed and applied to the

LP optimization problem These methods need to calculate a larger ber of LP, but it is capable of escaping from local optimums and reachingglobal optimum (Fig 1.3)

num-Figure 1.3: Sample of local and global optimumsThese methods can be classified into two categories: Neighborhood-based algorithms and population-based algorithms Examples of neighborhood-based algorithms include Simulated Annealing (SA) [6–15], Tabu Search(TS) [16–24] Typical population-based algorithms are Genetic Algorithms(GA) [25–34], Evolution Methods (EM) [35–43], Particle Swarm Optimiza-tion (PSO) [44–53], Ant Colony Optimization (ACO) [54–60], DifferentialEvolution (DE) [61–69], and so on.

One of the earliest adopted methods for ICFM was SA method Theadvantage of the SA method is an ability to escape local optima due to anacceptance probability of a worse solution However, the disadvantage ofthe SA method is a slow convergence Due to a slow convergence, the num-ber of calculated LPs in the SA search process is usually large The mainissue of the original SA is that the convergence speed should be decreased

in order to increase the probability to reach the global optimum Thisresults in a large number of candidate solutions to be evaluated around

this point The performance of the SA method depends on the hood structure and/or the generation of a new trial solution [70] AdaptiveSimulated Annealing (ASA) method was developed to enhance the conver-gence speed by improving the annealing schedule and the generation ofnew trial LPs [9, 10, 70–72] The generation of a new trial LP in the ASAmethod is binary or ternary exchange combined with one of the two follow-ing strategies The first strategy is known as "return to the best" [70, 71].

neighbor-It means that if the current best LP does not change after a number oftrial LPs, the current best LP is reused as a base LP The second one isthe application of a transition probability matrix or restriction LP lists Atransition probability matrix approach was developed to make the anneal-ing system adaptive by recording the impact of rejected solutions and biasthe system away such solutions in the search space [72] The lists includetrial and base LPs, which have been previously examined When a newtrial LP is generated, it is compared with the lists If the new trial LP isalready included in the lists, it will not be used or will be reused with adescending probability

In the case of population-based algorithms, DE is one of the highestefficiency method The DE algorithm was first proposed by [73], which isbased on a common concept of simulating the evolution of a populationusing mutation, crossover and selection operators DE has been applied

in various engineering fields and exhibited advantageous performance inconvergence and robustness [74–76] It was demonstrated that DE has astrong possibility to explore the search space and approach to a globaloptimum compared to GA and other EMs [77] A comprehensive review ofthe development and application of DE algorithms was performed by [78]

A number of advanced DE variants has been investigated, such as JADE,

CoDE, SHADE, and so on Success-History based Adaptive DifferentialEvolution (SHADE) method is an advanced DE variant proposed by [79],which uses a parameter adaptation mechanism based on a historical record

of successful parameters It was shown that SHADE is advantageous overother DE variants such as JADE, CoDE and EPSDE [79]

The DE algorithm was originally developed for continuous variableproblems [73] Since the problem of LP optimization handles integer vari-ables, it needs a strategy to convert real variables to integer ones Severalattempts have been conducted to apply DE to the problem of fuel LP opti-mization [62, 63, 80–82] In a previous work, a discrete DE algorithm wasdeveloped and applied to the problem of fuel LP optimization of a researchreactor [63] This is a pool-type research reactor with the power output of

500 kW [83, 84] The core were loaded with 100 fuel bundles with variousburnup levels and asymmetrical geometry Therefore, the problem of aresearch reactor is even more complicated with a much larger search spacethan that of a power reactor The performance of a classical DE variantwas found advantageous over the GA on the same problem [63]

In this dissertation, two advanced methods have been developed andapplied to solve the LP optimization for VVER reactor, i.e an Evolution-ary Simulated Annealing (ESA) method and a discrete SHADE method.Numerical calculations have been performed based on a VVER-1000 MOXfuel core using the two new methods in comparison with the performance

of the SA, ASA and DE methods The ESA method is improved by ing a crossover of two base LPs for generating a new trial LP, instead ofbinary or ternary exchanges in the original SA and ASA This crossover

us-is similar to that used in GA Two fitness functions (FFs) were used toevaluate the performance of the ESA method in comparison with the SA

and ASA methods The first one aimed at comparing the possibility inreproducing a reference core LP of the three methods The second one was

flatten-ing the radial power distribution A statistical significance test, so-calledMann-Whitney U Test, was also conducted to compare the performanceamong the three methods Comparison of the objective parameters of theoptimal core LP obtained from the ESA and SHADE search process withthat of the reference core is presented

1.4 Overview of VVER reactor

The nuclear power reactors operating in the world are mainly PWRand BWR types, in which PWR accounts for more than 2/3 The PWRtechnologies have been developed in many countries, i.e CNP, CPR-1000and ACPR-1000 of China, EPR of AREVA - France, AP-1000 of Westing-house - USA, OPR-1000 and APR-1400 of Korea, VVER of Russia and so

on [85] Among PWR technologies, The VVER reactors are the most mon reactor type in the world [86, 87] VVER is the Russian pressurizedwater reactor technology designed with the characteristics of hexagonalassemblies and reactor core Fig 1.4 and Fig 1.5 shows the main compo-nents of a VVER-1000/1200 plant and main structure of the reactor vessel.The reactor core loaded by hexagonal assemblies is shown in Fig 1.6 TheVVER have some significant differences from the other PWRs as follows:

com Using hexagonal fuel assemblies with triangular grid arrangement

of the fuel rods

- Using horizontal steam generators

Figure 1.4: Main components of a VVER reactor [87]

- Using high-capacity pressurizers

- Avoiding bottom penetrations in the pressure vessel

Until recent, 67 VVER reactors have been constructed since 1960s,and 14 reactors are under construction [87] Table 1.3 shows main spec-ifications of the VVER types [86, 87, 89, 90] The VVER was first builtbefore the 1970s In the early stage, the most popular design deployed wasthe VVER-440 model V230 with the power of about 440MW electricity.Another version of the VVER-440 is the V213 model that added an emer-gency cooling system and an auxiliary water supply system, as well as anupgraded fault localization system After 1975, VVER-1000 technologywas developed with four cooling circuits placed inside the reactor building

Figure 1.5: VVER reactor vessel [88]

This generation of technology was designed in detail to incorporate tomatic control systems, passive safety system corresponded to the thirdgeneration of Western technology Recently, the III+ generation of VVERhave been developed and constructed in Russia with many models Thesetechnologies are upgraded safety systems especially passive safety systems

au-In addition, the III+ generation extends the fuel burnup to 70 GWd/tand service life to 60 years In 2017, Novovoronezh Nuclear Power Plant

II started commercial operation the first generation III+ nuclear reactor

Figure 1.6: Sample VVER assembly (a) and VVER reactor core (b)

in the world using 1200 V-392M An additional version of

VVER-1200 is V-491 developed simultaneously with V-392M, that also have beencommercially operated in Leningrad II nuclear power plant in 2018 and

2021 [91] The power of these version is upgraded by extending the activelength of fuel assemblies (Fig 1.7)

Recently, the newest constructing version is VVER-TOI (typicaloptimized, with enhanced information), an upgrade of the V-392M Thereare two VVER-TOI under construction in Kursk Nuclear Power Plant andmany of this plant to construct This version is planed to be standard ofRosatom for new projects in Russia and worldwide [91]

Following generation III+, the VVER generation IV version is alsobeing researched and developed in Russia A generation IV version calledVVER-SCWR is being developed in collaboration with the Generation

IV International Forum [91, 93, 94] The VVER-SCWR (SupercriticalCoolant Water Reactor) is cooled by water of supercritical pressure Themain version named VVER-1700, V393 is 3830 MWt and 1700 MWe, with

Table 1.3: Specification of VVER types.

Coolant flowrate through reactor (m3/h) 41000 84800 86000 Coolant temperature at reactor outlet (C) 300 320 328.9 Coolant temperature at reactor inlet (C) 270 290 298.2

Number of Control rod assemblies/clusters 37 61 121

Dy2O3TiO Fuel enrichment (Fuel cycle length (month) 12 12 12(18)

Reactor vessel designed life time (year) 30 40 60

higher heat utilization efficiency (43% - 45%) and a higher breading ratio(0.9 - 0.95) As a result, it will be possible to significantly reduce thenuclear fuel cost Rosatom plans to commercialize this technology in 2030and they will replace the current technologies

Many efforts have been spent on fuel loading pattern optimizingfor VVER reactors using Perturbation method, Genetic method, ParticleSwarm algorithm and so on, combined with reactor simulators [44, 46, 95–101] Since 1994, the OPTIMAL program using binary exchange method(BE) and ATHENA program using random method were developed tooptimize the fuel loading for the Czech VVER-440 Dukovany reactor [95,96] In 2013, a research on combining weighting methods, genetic methodand ant colony method was carried out for the problem of loading pattern

Figure 1.7: Fuel designs of VVER-1000 (TVS-2) and VVER-1200 (TVS-2006) [92]optimization of VVER-1000 Bushehr reactor of Iran [97] This problem wasalso performed using LONSA tool based on neural network and SA method.The optimal results were quite good [98] Some optimal search tools usinggenetic methods such as SCAM-W, CIGARO in combination with reactorphysics calculation tools have been used for the problem of loading patternoptimization of VVER reactors, and applied to some reactors of the CzechRepublic such as the VVER-440 Dukovany and VVER-1000 Temelin [99].However, the researches on the LP optimization are still ongoing, because

no method or calculation program can guarantee a completely optimalsolution to the problem of LP optimization

In Vietnam, VVER technology was considered for Ninh Thuan 1nuclear power plant However, Vietnam’s nuclear power program was can-celed in 2016 by the National Assembly There were a number of researches

for VVER reactors carried out at Nuclear Energy Center [102–104] search on LP optimization for VVER was also carried out in a ministerialproject in 2015-2016 by the PhD student [105] A part of the results of theresearch are also presented in this dissertation.

Re-1.5 Purposes of this dissertation

The issue of the ICFM problem is that the search space is too large,

so the developed optimization search processes can not confirm that thefinal found solution is global optimal one Therefore, the current opti-mization studies focus on improving the convergence speed of the searchprocess in order to find better and better solutions with the same num-ber of trials This study will address the issue by considering, improvingand applying advanced optimization methods to enhance the convergencespeed for solving the LP optimization problem The two objectives of thisdissertation are as follows:

1) Investigation of advanced optimization methods to the problem

of loading pattern optimization of nuclear reactors

As mentioned above, the optimization problem has a very largesearch space Therefore, advanced optimization methods will save the com-putational cost a lot, and at the same time have a high chance of escapingthe local optimum and approaching the global optimum Therefore, thedevelopment and application of advanced optimal methods are a researchdirection of interest in ICFM in the world recently

2) Development of a calculation tool for optimizing the loadingpattern for the VVER reactor

To calculate a very large number of configurations for the LP mization problem (10000 to 100000), it is necessary to have a core physicssimulator with fast calculation speed and guaranteed accuracy Therefore,this research aims to develop a reactor physics code that meets the re-quirement of the optimization study This code will be combined with theadvanced optimization methods to create a search tool for the VVER re-actor This tool will be useful in training as well as evaluation for reactorswith hexagonal fuel bundles such as VVER or research reactors Furtherapplication of this tool can be extended to other reactor types.

opti-1.6 Dissertation outline

Chapter 1 describes briefly overview of the nuclear reactor nologies, LP optimization problem and optimization methods, and theobjectives of the dissertation

tech-Chapter 2 presents the methods and developments of advanced timization methods and a core physics code The VVER-1000 MOX core

op-is used to illustrate the application of the advanced optimization methodsfor solving the LP optimization of VVER reactors A core physics code,LPO-V, has been developed based on finite difference method for solvingmulti-group diffusion equations in triangular meshes to calculate neutroniccharacteristics of VVER reactor, and to evaluate the fitness functions ofthe LP optimization problem Verification calculations shows that thecode has guaranteed accuracy and fast calculation speed, suitable for therequirements of the LP optimization problem

Two advanced methods have been developed, i.e the ESA method

SA method by using crossover operator similar to GA SHADE has beenproven as a high performance advanced method with many optimizationproblems In this dissertation, a discrete SHADE has been developed andapplied to the LP optimization problem Finness functions based on power

the optimal one A Mann-Whitney U test also applied to compare theefficiency of the optimization methods

Chapter 3 presents the numerical calculations for VVER-1000 MOXcore applying ESA and SHADE methods The results of ESA method werecompared with SA and ASA Statistical differences between these methodswere also evaluated based on the Mann-Whitney U test The results showthat the ESA method is advantageous over the SA and ASA The results

of discrete SHADE method is also comparable with the ESA method Thefound optimal LP by the two method are identical The results show that

optimal LP is about 2.4% smaller than that of the reference core

Chapter 4 summarizes the results of this dissertation and providessome future plans

and power distribution of the core These results are used to calculatethe fitness function in the LP optimization problem Verification of theLPO-V code has been performed based on the VVER-1000 MOX core incomparison with MCNP4c [5].

Two advanced optimization methods have been developed: ESAand discrete SHADE The ESA method is improved by using a crossover

of two base LPs for generating a new trial LP, instead of binary or ternaryexchanges in original SA The discrete SHADE applies a discrete strategybased on a relative position indexing approach to convert real variables

to integer ones Two types of fitness function were used to evaluate LPsand efficiency of the optimization methods A statistical significance test,so-called Mann-Whitney U Test, was also conducted to compare the per-formance among the optimization methods

In this research, numerical calculations for LP optimization havebeen performed based on a VVER-1000 benchmark core loaded with 30%MOX fuel The VVER-1000 benchmark core was proposed by OECD/NEA

verifying computational codes and methods [5] In this benchmark, sixdifferent states of the core were considered as described in Table 2.1 Theisotopic compositions of fuels, water and steel structures have been shown

in the appendixes

The core includes 163 assemblies surrounded by water and steel sel The structure and dimensions of the reactor core are shown in Fig 2.1.The reference 1/6th core configuration consists of 28 fuel assemblies, in-

15, 32 and 40 MWd/kg as listed in Table 2.2 Whereas, 9 MOX assembliesare divided into three burnup levels of 0, 17 and 33 MWd/kg The fuelregion is surrounded by a water gap, steel baffle with water holes, steelbarrel, down-comer (water) and reactor vessel The 1/6th core model has