Loading pattern optimization for a PWR using Multi-Swarm Moth Flame Optimization Method with Predator

ABSTRACT

This paper aims to propose a new methodology for optimizing fuel loading pattern in a nuclear reactor which is important for its higher safety and economic efficiency. Previous researches have proposed various methodologies to decide better loading patterns automatically. However, the processes still require manual operations of engineers to automatically design actual loading patterns. Swarm intelligence algorithm has currently gained interest as a solution to seek the patterns. Although these methodologies generate better patterns, they sometimes struggle with getting out from local optima and fails to complete the optimization. Large and multimodal solution space sometimes captures worse solutions due to local optima. The conventional methodologies struggle with setting proper parameters to get out from local optima. This research focuses on Multi-Swarm Moth Flame Optimization with Predator (MSMFO-P), an improved Moth Flame Optimization (MFO) by applying the concepts of predator and multi-swarm, as new methodologies. The method of MSMFO-P was applied to solve a loading pattern problem and compared with the conventional optimization methods such as simulated annealing (SA), Hybrid genetic algorithm (GA), and particle swarm optimization (PSO). The results of our experimental works indicated that MSMO-P generates better loading patterns than the conventional methodologies.     

考虑燃料组件内燃耗非均匀效应的最优化换料程序的研究

本文研究了燃料组件内燃耗非均匀性对堆芯内燃料最佳化布置的影响,提出了堆芯换料时所应遵循的某些新规则。介绍了由作者编制的自动换料计算机程序。     

Optimization studies of fuel loading pattern for a typical Pressurized Water Reactor (PWR) using particle swarm method

A three dimensional multi-energy group computer model PRISHA, which solves the neutron diffusion equations using finite difference method is developed for Pressurized Water Reactor (PWR). This computer code can find an optimum loading of a group of fresh fuel assemblies along with fuel assemblies of different exposures. The successive line over relaxation (SLOR) method is used to solve neutron diffusion equations. After validation of this part of computer code against an IAEA – PWR benchmark problem with 177 fuel assemblies in the core, particle swarm optimization (PSO) method is incorporated in the code for finding the optimum fuel loading pattern. A typical PWR core with 157 fuel assemblies, where 289 fuel pins are arranged in 17 × 17 rectangular arrays in a fuel assembly, was analyzed using this computer model for two cycles using PSO method. Different numbers of particles and iterations were used in PSO method. The results are found to be not very sensitive to either the number of particles or the number of iterations used in PSO method for considered case. However, a number of experiments have to be performed to arrive at the best global fitness parameter. Reasonably low power peaking factors were obtained for both the cycles.     

用于堆芯换料优化的遗传算法的改进及检验

文章采用年龄代、相似度和价值函数等新技术对用于堆芯换料优化的遗传算法加以改进,其中年龄技术赋予了算法及时总结前一阶段方案搜索"经验"、引导算法更好地在局部最优邻域内进行搜索的能力;在对方案进行杂交之前首先评估方案的相似度,避免了对两个过于相似的方案进行杂交,从而防止算法早熟;价值函数的运用赋予算法依据较优方案共性特征的统计来产生新方案的能力.针对一个两环路堆芯换料优化基准题的数值检验说明,经改进的遗传算法可显著提高算法的搜索效率,同时也使优化解的质量得以提高.     

Development of a new approach,evolutionary harmony search algorithm,for the LPO problem

This paper proposes a new variant of harmony search (HS) algorithm i.e. evolutionary harmony search (EHS), for exploiting in the loading pattern optimization (LPO) problem. The main innovations of EHS are the consideration of current best harmony vector in creating the new solution vector in any iteration and applying a pitch adjustment approach using a mutation strategy borrowed from the realm of the differential evolution (DE) algorithms, both with dynamic probabilities. Reactor core pattern optimization has been done using EHS for two test cases including KWU PWR and VVER-440. In order to represent the EHS capability to gain improved results in the LPO problem, a comparison is performed between results of EHS and a recent developed HS algorithm i.e. self-adaptive global best harmony search (SGHS). Numerical results show a major and distinctive enhancement of the proposed approach, EHS, in obtaining convergent results in comparison to SGHS approach. As a result, I can recommend the checking of EHS performance in other optimization problems.     

A class-based search for the in-core fuel management optimization of a pressurized water reactor

The In-Core Fuel Management Optimization (ICFMO) is a prominent problem in nuclear engineering, with high complexity and studied for more than 40 years. Besides manual optimization and knowledge-based methods, optimization metaheuristics such as Genetic Algorithms, Ant Colony Optimization and Particle Swarm Optimization have yielded outstanding results for the ICFMO. In the present article, the Class-Based Search (CBS) is presented for application to the ICFMO. It is a novel metaheuristic approach that performs the search based on the main nuclear characteristics of the fuel assemblies, such as reactivity. The CBS is then compared to the one of the state-of-art algorithms applied to the ICFMO, the Particle Swarm Optimization. Experiments were performed for the optimization of Angra 1 Nuclear Power Plant, located at the Southeast of Brazil. The CBS presented noticeable performance, providing Loading Patterns that yield a higher average of Effective Full Power Days in the simulation of Angra 1 NPP operation, according to our methodology.     

Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (fp) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain fp. The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the fp of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the fp increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on fp. The increase of Reynolds number and Jakob number causes the increase of fp, and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors.     

An estimation of an operator's action time by using the MARS code in a small break LOCA without a HPSI for a PWR

To estimate the success criteria of an operator's action time for a probabilistic safety/risk assessment (PSA/PRA) of a nuclear power plant, the information from a safety analysis report (SAR) and/or that by using a simplified simulation code such as the MAAP code has been used in a conventional PSA. However, the information from these is often too conservative to perform a realistic PSA for a risk-informed application. To reduce the undue conservatism, the use of a best-estimate thermal hydraulic code has become an essential issue in the latest PSA and it is now recognized as a suitable tool. In the same context, the ‘ASME PRA standard’ also recommends the use of a best-estimate code to improve the quality of a PSA. In Korea, a platform to use a best-estimate thermal hydraulic code called the MARS code has been developed for the PSA of the Korea standard nuclear power plant (KSNP). This study has proposed an estimation method for an operator's action time by using the MARS platform. The typical example case is a small break loss of coolant accident without the high pressure safety injection system, which is one of the most important accident sequences in the PSA of the KSNP. Under the given accident sequence, the operator has to perform a recovery action known as a fast cooldown operation. This study focuses on two aspects regarding an operator's action; one is how they can operate it under some restrictions; the other is how much time is available to mitigate this accident sequence. To assess these aspects, this study considered: (1) the operator's action model and (2) the starting time of the operation. To show an effect due to an operator's action, three kinds of control models (the best-fitting, the conservative, and the proportional-integral) have been assessed. This study shows that the developed method and the platform are useful tools for this type of problem and they can provide a valuable insight related to an operator's actions.     

Safety analysis of LBLOCA in BDBA scenarios for the Bushehr's VVER-1000 nuclear power plant

This paper presents the results of thermal-hydraulic calculations of a large break loss of coolant accident (LBLOCA) analysis for a VVER-1000/V446 unit at Bushehr nuclear power plant (BNPP). LBLOCA is analysis in two different beyond design basis accident (BDBA) scenarios using the RELAP5/MOD3.2 best estimate code. The scenarios are LBLOCA with station blackout (SBO) and LBLOCA with pump re-circulation blockage which have been evaluated in the final safety analysis report (FSAR) of BNPP. A model of VVER-1000 reactor based on Unit 1 of BNPP has been developed for the RELAP5/MOD3.2 thermal-hydraulics code consists of 4-loop primary and secondary systems with all their relevant sub-systems important to safety analysis. The analysis is performed without regard for operator's actions on accident management. The safety analysis is carried out and the results are checked against the acceptance criteria which are the possibility of using water inventory in the emergency core cooling system (ECCS) accumulators and the KWU tanks for core cooling and the available time to operators before the maximum design limit of fuel rod cladding damage is reached. These kinds of analyses are performed to provide the response of monitored plant parameters to identify symptoms available to the operators, timing of the loss of critical safety functions and timing of operator actions to avoid the loss of critical safety functions of core damage. The results of performed analyses show that the operators have 2.9 and 3.1 h for LBLOCA with SBO and LBLOCA with pump re-circulation blockage scenarios, respectively, before the fuel rod cladding rupture. The results are also compared with the BNPP FSAR data.