Application of Evolutionary Simulated Annealing Method to Design a Small 200 MWt Reactor Core

Nội dung text: Application of Evolutionary Simulated Annealing Method to Design a Small 200 MWt Reactor Core

1. Nuclear Science and Technology, Vol.10, No. 4 (2020), pp. 16-23 Application of Evolutionary Simulated Annealing Method to Design a Small 200 MWt Reactor Core Tran Viet Phu1*, Tran Hoai Nam2, Hoang Van Khanh1 1Institute for Nuclear Science and Technology, VINATOM 2Institute of Fundamental and Applied Sciences, Duy Tan University Email: *tvietphu@gmail.com (Received 10 November 2020, accepted 28 December 2020) Abstract: This paper presents the application of an evolutionary simulated annealing (ESA) method to design a small 200 MWt reactor core. The core design is based on a reference ACPR50 reactor deployed in a floating nuclear power plant. The core consists of 37 typical 17x17 PWR fuel assemblies with three different U-235 enrichments of 4.45, 3.40 and 2.35 wt%. Core loading pattern (LP) has been optimized for obtaining the cycle length of 900 effective full power days, while minimizing the average U-235 enrichment and the radial power peaking factor. The optimization process was performed by coupling the ESA method with the COREBN module of the SRAC2006 system code. Keywords: Small reactor, core design optimization, ESA method. I. INTRODUCTION application of various optimization methods. Most of the methods are based on the In recent years, interest in small module simulation of natural systems such as reactors (SMR) has been increasing due to simulated annealing (SA) 0-0, generic their flexibility in power generation for wider algorithms (GA) 0, 0, 0, 0, evolution method ranger users, locations and applications. They 0, particle swarm optimization method (PSO) also show an enhanced safety performance 0, 0, 0, differential evolution 0 and so on. through passive safety systems and updated Although many attempts have been done, it technologies [1]. Currently there are more than is still a complicated multi-objective task 0. 50 designs of SMR under development in the In the present work, an evolutionary world [2]. Because of flexibility and safety simulated annealing (ESA) method has been features of SMRs, researches in this applied to design a small 200 MWt reactor technology are very necessary to energy core. The ESA method is developed to improve development strategy in Viet Nam. One of the the original SA by using crossover and first tasks of the research in SMRs is reactor mutation operators to generate new trial core design and its loading pattern. solutions, instead of binary or ternary Fuel loading optimization is one of the exchanges in the original SA 0. The crossover important tasks in designing a nuclear reactor and mutation operators are similar to that used core, which is performed after every cycle of in GA. The reactor core is designed based on a a nuclear reactor. The problem of fuel reference ACPR50S reactor deployed in a loading pattern (LP) optimization has floating nuclear power plant (FNPP) using received attention from the beginning of typical PWR fuel assemblies [2], 0, 0. The core nuclear reactor technology with the design is targeted to attain a cycle length of ©2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
2. TRAN VIET PHU et al. about 900 effective full power days (EFPDs) base LP and the trial LP; T is the similar to the reference ACPR50S, while temperature of the search. minimizing the U-235 enrichment and radial (4) A new trial LP is generated from two base power peaking factor. Core physics LPs using crossover and mutation operators. calculations were performed using the (5) The temperature T(n) is decreased as T(n+1) COREBN module of the SRAC2006 code = αT(n), α < 1, after a number of calculated system. The ESA method has been coupled trial LPs with constant T, known as with the COREBN module to perform the Malkov length. optimization process. (6) The convergence criteria is checked, and the II. METHODOLOGY search is stopped if the convergence criteria are met. Otherwise, step (2) is repeated. A. ESA method In the ESA method, the two base LPs are Simulated annealing (SA) method has referred to as parents, and the new trial LP is been soon applied to the problem of fuel LP an offspring. The crossover is executed by optimization 0. The SA method has ability to exchanging two assemblies between the escape local optima due to an acceptance parents as displayed in Fig. 1. Then, a new trial probability of a worse solution. However, due LP is generated from the offspring by applying to a slow convergence, the number of the mutation with a probability of 0.5. The calculated LPs is usually large. In a previous crossover is performed as follows: work, the ESA method was developed to i) In the father LP, two locations L1 and improve the original SA by using crossover L2 are randomly selected, and the and mutation to generate trial solutions. The corresponding assemblies at the locations L1 advantages of ESA over SA and ASA have and L2 are identified as F1 and F2. been examined 0. The procedure of ESA is described as follows: ii) A temporary offspring is generated by copying the mother. (1) Starting with an initial trial LP iii) The assemblies F1 and F2 are located (2) Core physics calculation of the trial at the locations L1 and L2 of the offspring. At LP is performed, and the fitness the same time, the assemblies at the locations function is evaluated. L1 and L2 of the offspring are moved to the (3) Comparison of the fitness function with locations L3 and L4, where the assemblies F1 that of the current base LPs is performed. and F2 are formerly located. The base LPs are updated if: The fitness value of the trial LP is greater than or equal to that of the base LP. The fitness value of the trial LP is less than that of the base LP, the base LP is updated by an acceptance probability: ). Where, is the ) difference of the fitness between the Fig. 1. Crossover operator used in the ESA method 17
3. APPLICATION OF EVOLUTIONARY SIMULATED ANNEALING METHOD TO The mutation is performed in two steps. | | First, two or three assemblies of the offspring (1) are selected and exchanged randomly to ) generate a new trial LP. Second, an assembly of the offspring is selected randomly and ∑ (2) replaced by a random assembly with different ∑ U-235 enrichment by a probability of 0.5. Where, C is cycle length; E is the The two base LPs are updated by average enrichment of loaded assemblies, Ei is replacing the worse base LP by a better trial. enrichment of fuel assembly type i and ni is the Therefore, the best current LP is always number of loaded fuel assembly type i; and selected as one of the two base LPs. Since PPF is the radial power peaking factor. C0 = the offspring contains more characteristics of 900 effective full power days (EFPDs), P0 = the mother than that of the father, the 1.5 are chosen as constants. wc = 0.00333, we = selection of the mother from the two base 0.1 and wp = 10 are weighting factors. The LPs would have a significant effect on the cycle length is determined when the keff performance of the crossover. Thus, to decreases to unity. A better LP corresponds to increase the diversity of the search process, a larger value of Fitness. the worse base LP is chosen as the mother. C. Description of the core The convergence criteria were set to stop the calculation loop if the current base LP is The core is designed based on typical remained unchanged after 100 trial solutions PWR assembles similar to the reference or the current best LP is remained unchanged ACPR50 core as shown in Fig. 2. The core after 1000 trial solutions. consists of 37 fuel assemblies with 1/4th symmetrical geometry. The assemblies are B. Objective function typical types of PWR, with 17x17 lattice, A fitness function has been used to containing 264 rods, 24 guide tubes and a design the core for achieving a cycle length of instrumentation tube. Three types of fuel about 900 EFPDs, which is similar to the cycle assemblies corresponding to the U-235 length of the reference ACPR50 reactor. The enrichments of 4.45, 3.40 and 2.35 wt%, average U-235 enrichment and radial power respectively, are considered for loading into peaking factor are minimized. Therefore, the the core. The main design parameters of the fitness function is written as: core are given in Table 0, 0, 0. Fig. 2. Core configuration (a) and a typical 17x17 PWR fuel assembly (b) 18
4. TRAN VIET PHU et al. Core physics and burnup calculations and fuel lattices were generated using the PIJ have been performed based on a 2D full-core module of the SRAC2006 code. The model using the COREBN module of the COREBN calculations were performed for SRAC2006 code system and the JENDL-3.3 obtaining the effective multiplication factor data library. The core is reflected by water as (keff) and power distribution during the shown in Fig. 2. The eight-group burnup. Then the cycle length (C) and the macroscopic cross-section set of reflector maximum PPF are determined. Table I. Main parameters of the small modular reactor core based on the reference ACPR50 reactor [2], 0 Parameters Values Reactor thermal power [MW] 200 Cycle length [day] 900 Number of assembly [-] 37 Assembly pitch [cm] 21.4173 Assembly height [cm] 220 Fuel rod pitch 1.2598 Fuel pellet radius [cm] 0.4096 Fuel inner cladding radius [cm] 0.4178 Fuel outer cladding radius [cm] 0.475 Fuel enrichment [%wt U235] 4.45, 3.40, 2.35 Operation pressure [MPa] 15.5 Inlet coolant temperature [K] 572.6 Outlet coolant temperature [K] 595.1 Fuel temperature [K] 1145 III. RESULTS AND DISCUSSION fitness function whereas the number of searching LP in each run is lower than 2000. A. Core design and optimization The initial temperature T were selected as 15.0 In the optimization process using the to ensure the initial acceptance probability ESA method, the control parameters have to be approximate unity. Due to the 1/4 symmetry of chosen firstly. A survey has been conducted to the core, the calculation model consists of 10 determine the values of α and Malkov length. fuel assemblies with three types of U-235 In this survey, the values of α and Malkov enrichments of 4.45 %wt (F445), 3.40 %wt length were varied in the ranges of [0.85, 0.95] (F340) and 2.35 %wt (F235), respectively, and [20, 50] with steps of 0.5 and 5, loaded in the 1/4th core geometry. The search respectively. The values of α = 0.9 and Malkov processes were performed with ten length = 25 have been selected to maximize the independent runs 0, 0, 0, 0. 19
5. APPLICATION OF EVOLUTIONARY SIMULATED ANNEALING METHOD TO Fig. 3. Evolution of the fitness (a), cycle length (b), PPF (c) and average enrichment with the number of calculated LPs in ten independent runs Table II. Optimal objective parameters obtained by ESA method in ten independent runs Cycle length Enrich-ment run Fitness PPF (EFPDs) (wt%) 1 -0.35127 900.2 1.377 3.505 2 -0.35127 900.2 1.377 3.505 3 -0.35268 899.3 1.370 3.505 4 -0.35127 900.2 1.377 3.505 5 -0.35515 898.6 1.497 3.505 6 -0.35127 900.2 1.377 3.505 7 -0.35128 900.2 1.377 3.505 8 -0.35128 900.2 1.377 3.505 9 -0.35268 899.3 1.370 3.505 10 -0.35127 900.2 1.377 3.505 Average -0.35194 899.9 1.387 3.505 20
6. TRAN VIET PHU et al. Fig. 3 shows the change of the fitness beginning of cycle shows that the PPF of function and other objective parameters in ten 1.377 appear near the core central at the independent runs. Once can see the assembly with the enrichment of 3.40 wt%. improvement of the Fitness occurs throughout Fig. 5 shows the change of keff and PPF the search process. The objective parameters during the burnup. The PPF is decreased such as cycle length, PPF and average during the EFPDs, and the keff is unity at enrichment are also converged to stable values about 900 days. together with the convergence of Fitness Several main parameters of the optimal function. Table summaries the optimal LP have been calculated and summarized in objective parameters obtained in ten Table . One can see that two parameters of the independent runs. The PPFs are converged to core included PPF and EFPDs satisfy the the values of about 1.387, while the average requirements of the ACPR50S reactor those are enrichment is 3.505 wt%, and the cycle length PPF < 1.377 and EFPDs = 900 days. The is approximate 900 EFPDs. temperature coefficients of moderator and fuel B. Optimal core LP are negative also. Furthermore, the average Fig. 4 shows the optimal core LP of the enrichment of the ACPR50S core is estimated small 200 MWt reactor selected from the ten at 3.505 wt%. The number of loaded fuel types independent runs of the optimization process. are nine assemblies of F235, 12 assemblies of The relative radial power distribution at the F340 and 16 assemblies of F445. Fig. 4. Optimal loading pattern and relative power distribution of the small reactor core Fig. 5. Evolution of the keff and PPF of the optimal core as functions of burnup 21
7. APPLICATION OF EVOLUTIONARY SIMULATED ANNEALING METHOD TO Table III. Parameters of the optimal core Parameters Values Cycle length (days) 900 Average enrichment [wt% U-235] 3.505 Maximum PPF [-] 1.377 Maximum keff 1.22417 Fuel temperature coefficient [pcm/K] -2.564 Moderator temperature coefficient [pcm/K] -104.3 Number of fuel assembly F235 9 Number of fuel assembly F340 12 Number of fuel assembly F445 16 IV. CONCLUSIONS REFERENCES The ESA method was applied to design [1]. Nuclear Development, Small Modular a small 200 MWt modular reactor core based Reactors: Nuclear Energy Market Potential for on the reference ACPR50S reactor. The Near-term Deployment, OECD-NEA, 2016. COREBN module of the SRAC2006 code [2]. IAEA, “Advances in Small Modular Reactor system was for core physics and burnup Technology Developments”, IAEA booklet, 2018. calculations, which was coupled with the ESA [3]. Yamamoto A., “A quantitative comparison of method for performing the design process. loading pattern optimization methods for in- The core consists of 37 typical PWR fuel core fuel management of PWR”, Nucl. Sci. assemblies with the enrichments of 4.45, 3.40 Eng., 34, 339, 1997. and 2.35 wt%. The target designs are to obtain [4]. Mahlers Y P., “Core loading pattern the core cycle length of about 900 EFPDs, optimization based on simulated annealing and while minimizing the PPF and the average U- successive linear programming”, Ann. Nucl. 235 enrichment. The optimal core is obtained Energy, 22, p 29, 1995. with the number of F445, F340 and F235 [5]. J. G. Stevens J G., Smith K S, Rempe K R, assemblies of 16, 12 and 9, respectively. The Downar T J, “Optimization of pressurized cycle length of the optimal core is 900 EFPDs, water reactor shuffling by simulated while the PPF is 1.377 and the average annealing with heuristics”, Nucl. Sci. Eng., 121, p 67, 1995. enrichment is 3.505 wt%. Negative fuel temperature and coolant temperature [6]. Sikander M M, Aneela A, Nasir M M., coefficients have been confirmed. “Adaptive Simulated Annealing Methodology for Fuel Loading Pattern Optimization”, Nucl. Sci. J., 37, p 340, 2000. ACKNOWLEDGMENTS [7]. Hyun C L, Hyung J S, Chang H K., “Parallel This research is funded by Vietnam computing adaptive simulated annealing National Foundation for Science and scheme for fuel assembly loading pattern Technology Development (NAFOSTED) under optimization in PWRs”, Nucl. Technol., 135, p grant 103.04-2019.37. 39, 2001. 22
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