Axial offset control of PWR nuclear reactor core using intelligent techniques

Improved load following capability is one of the main technical performances of advanced PWR (APWR). Controlling the nuclear reactor core during load following operation encounters some difficulties. These difficulties mainly arise from nuclear reactor core limitations in local power peaking, while the core is subject to large and sharp variation of local power density during transients. Axial offset (AO) is the parameter usually used to represent of core power peaking, in form of a practical parameter. This paper, proposes a new intelligent approach to AO control of PWR nuclear reactors core during load following operation. This method uses a neural network model of the core to predict the dynamic behavior of the core and a fuzzy critic based on the operator knowledge and experience for the purpose of decision-making during load following operations. Simulation results show that this method can use optimum control rod groups maneuver with variable overlapping and may improve the reactor load following capability.     

Application of Fuzzy Logic Controller to Load-Follow Operations in Pressurized Water Reactors

The fuzzy logic controller was developed to control load-follow operations in pressurized water reactors. The reactor core characteristics change according to different fuel cycles or core exposures, thus making a nonlinear time-varying control problem. This proposed method, however, does not require a mathematical model to design the controller, and so avoids redesigning or tuning controller gain for various cores. Clearly, this method is very suitable for reactor load-following operation control. The control system has two subsystems: one is to track the desired power, and the other is to keep axial offset close to the target value. Both controllers use fuzzy logic: one is the conventional type, and the other uses fuzzy logic to tune the parameters of the controller so the controller can correspond to various core characteristics. Simulation results show that the control system performs well for different cores, and so this system is useful for load-follow operation.     

Improvement of core control strategy for CPR1000: Load follow without boron adjustment

This paper presents the study of load follow operations without boron adjustment for CPR1000. To enable the CPR1000 to perform load follow maneuvers without changing soluble boron concentration, the worth of Rod Cluster Control Assemblies (RCCAs) are reconfigured with their amount and location unchanged according to the reactivity variations during the load follow transient. To ensure the real-time ability of the reactor core, the target axial offset (AO) during load follow operations is set to the same value with that in based load, and the Delta-I is maintained within the special trapezoidal shaped target band around its target value.For the simulation of the reactor core, the time-dependent one-dimensional two group diffusion equations with the reactivity feedback of moderator temperature, Doppler and xenon–iodine are used. The transverse buckling is adjusted at each time interval so that the one-dimensional model can match the average characteristics of the three-dimensional reactor core accurately. To show the superiority of the improved core control strategy for CPR1000 reactor, the load follow results employing the purposed boron-adjustment free control strategy are compared to those obtained with the typical MODE-G control strategy. It has been demonstrated by the simulation results that the load follow capability of CPR1000 reactor is greatly improved due to the elimination of boron concentration adjustments during load change transients. Full load follow capability of the reactor has been extended from the initial 80% of cycle life to more than 90% of cycle life. Thus, the boron adjustment free improvement on the MODE-G core control strategy is feasible for CPR1000, which can improve the economical performance of the plant and simplify the operational process during power maneuvers.     

A neuro-fuzzy controller for axial power distribution an nuclear reactors

A neuro-fuzzy control algorithm is applied for the core power distribution in a pressurized water reactor. The inputs of the neural fuzzy system are composed of data from each region of the reactor core. Rule outputs consist of linear combinations of their inputs (first-order Sugeno-Takagi type). The consequent and antecedent parameters of the fuzzy rules are updated by the backpropagation method. The reactor model used for computer simulations is a two-point xenon oscillation model based on the nonlinear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation having nonlinear power reactivity feedback. The reactor core is axially divided into two regions, and each region has one input and one output and is coupled with the other region. The interaction between the regions of the reactor core is treated by a decoupling scheme. This proposed control method exhibits very fast response to a step or a ramp change of target axial offset without any residual flux oscillations between the upper and lower halves of the reactor core.     

Power control of CANDLE reactor by coolant flow rate

CANDLE reactors do not require control rods for burn-up control. Such reactors can achieve the excellent features of previously-considered CANDLE reactors such as constant power shape and reactivity feedback coefficients during the entire operation period at the rated power level. By eliminating control rod use for power level control, the CANDLE reactor can be operated in a load-following mode and its utility will expand dramatically.By numerical calculations, power control by coolant flow rate was studied for the sodium-cooled metallic fuel large CANDLE reactor. The effect of thermal expansion of the core support structure shows considerable contribution toward achieving negative reactivity feedback to improve the power controllability. We employ HT-9 and SUS316 for core support structures. Since the maximum cladding temperature reaches its design constraint, power level cannot be decreased less than its lower limit, which is 66% for HT-9 and 57% for SUS316.     

基于钒探测器补偿的轴向偏移控制设计

机械补偿控制是基于控制棒调节反应堆功率并进行轴向功率偏移控制的先进技术,频繁移动的控制棒对传统堆外校准后的轴向功率偏差测量精度有较大的负面影响,采用能给出准确堆内功率分布的钒基自给能探测器的信号可对其进行校正。为补偿钒探测器较长的响应时间,设计了超前/滞后控制器,提出了用补偿后的信号对堆外测量得到的轴向功率偏差信号进行修正的方法。仿真结果表明,该方法能有效应对控制棒移动对轴向偏移控制的影响,可提高控制精度。对该方法的安全相关影响、可实施性及性能分析表明,其具有较高的实用价值。     

CNP650压水堆不调硼负荷跟踪可行性研究

海南昌江核电厂等CNP650压水堆采用Mode-A控制模式,该模式采用黑体控制棒,有很好的基负荷运行能力,但负荷跟踪能力相对较差。而对一些具有小电网的国家或地区,负荷跟踪运行能力具有一定的市场需求。不调硼负荷跟踪通过棒控系统自动完成,大大减轻了操纵员负担;负荷跟踪过程基本不需要频繁地调硼操作,允许简化化学和容积控制系统设计,减少了废液处理成本。为此,在CNP650压水堆上进行了不调硼负荷跟踪研究。负荷跟踪过程主要有两个控制任务:一是反应性补偿;二是功率分布控制。根据不调硼负荷跟踪的控制任务,重新进行了控制棒的设计、分组和布置,设置两套独立控制的控制棒组(功率补偿棒组和轴向偏移控制棒组),分别用于堆芯反应性控制和轴向功率分布控制,以实现不调硼负荷跟踪。使用SCIENCE程序包进行典型的12h~3h~6h~3h、100%—50%—100%功率水平的日负荷循环计算来进行不调硼负荷跟踪分析。计算步骤为:进行三维堆芯模型计算;根据三维堆芯模型建立一维堆芯模型;在一维模型基础上,进行模拟计算。完成了海南昌江核电厂平衡循环寿期末典型的日负荷循环不调硼运行分析,模拟计算结果表明在CNP650压水堆上不调硼负荷跟踪运行模式是可行的。     

Robust nonlinear model predictive control for nuclear power plants in load following operations with bounded xenon oscillations

One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In this paper, a robust nonlinear model predictive control for the load-following operation problem is proposed that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to maintain xenon oscillations to be bounded. The constant AO is a robust state constraint for load-following problem. The controller imposes restricted state constraints on the predicted trajectory during optimization which guarantees robust satisfaction of state constraints without restoring to a min-max optimization problem. Simulation results show that the proposed controller for the load-following operation is so effective so that the xenon oscillations kept bounded in the given region.     

基于Dragon与Donjon程序的液态熔盐实验堆临界计算与分析

基于组件输运程序Dragon与堆芯节块法程序Donjon,对包含有上下熔盐腔室、控制棒、实验孔道与中子源孔道的液态熔盐实验堆堆芯进行了计算与分析,给出了液态熔盐实验堆不同组件的等效均匀化模型。根据液态熔盐实验堆特性将中子能群划分为5种少群能群结构,基于所划分的每一种少群能群结构,对单根控制棒与不同控制棒组插入堆芯后的有效增殖因数和控制棒价值进行了计算分析。结果表明,7群能群结构具有更好的计算结果。基于7群能群结构开展了堆芯径向与纵向功率分布,以及控制棒拔出后堆芯的温度反应性系数计算分析,其计算结果与MCNP5计算结果相近,证明了模型等效的合理性以及Dragon和Donjon程序对液态熔盐实验堆的适用性。     

The three-dimensional power distribution control in load following of the heating reactor

A new optimizing objective (three-dimensional power distribution control) for the load-following problem in nuclear reactor is presented. To realize such an objective, a combination of Harmonic Synthesis Method and Nodal Method has been practiced on the numeric calculation for optimizing problem on the 200 MW Heating Reactor, in which the control rods serve as the only control variables. In contrast, most of the load-following problems have been solved under a one-dimensional neutron model. And it seems that such a model is not suitable for the reactor core whose power was controlled only by control rods. In this case, the control rod causes a strong absorption of neutron in a local area thus makes the radial power distribution play a much more important role in the load-following process. As the 3-dimensional model is used and the corresponding method is performed, both of the total power level and power distribution are controlled well. For example, the power peak-factor is lower about 4% than that with one-dimensional method.     

Sliding mode observer design for a PWR to estimate the xenon concentration & delayed neutrons precursor density based on the two point nuclear reactor model

One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In other hands, precursors produce delayed neutrons which are most important in control of nuclear reactor, but xenon concentration & precursor density cannot be measured directly. In this paper, non-linear sliding mode observer which has the robust characteristics facing the parameters uncertainties and disturbances is proposed based on the two point nuclear reactor model to estimate the xenon concentration & delayed neutron precursor density of the Pressurized-Water Nuclear Reactor (PWR) using reactor power measurement. The stability analysis is given by means Lyapunov approach, thus the system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications. This estimation is done taking into account the effects of reactivity feedback due to temperature and xenon concentration. Simulation results clearly show that the sliding mode observer follows the actual system variables accurately and is satisfactory in the presence of the parameters uncertainties & disturbances.     

用硼中毒法进行脉冲堆控制棒效率和总后备反应性测量

本文介绍了在脉冲堆零功率物理实验中,利用硼中毒法测量反应性的原理和方法,给出了脉冲堆堆芯的硼微分价值、控制棒效率和总后备反应性的实验结果。还利用硼中毒法和脉冲中子源法配合进行脉冲堆控制棒之间反应性干涉效应的实验研究,取得了初步结果。     

HFETR占栅元铍中孔控制棒物理特性研究

研究了高通量工程试验堆(HFETR)占栅元铍中孔控制棒物理特性。首先,采用CELL程序计算各组件的少群截面参数;然后分别对占栅元控制棒和占栅元铍中孔控制棒进行了堆芯物理计算,并对反应堆轴向热中子注量率分布、60Co产量以及控制棒价值做了比较。研究结果表明,占栅元铍中孔控制棒完全可以用于HFETR的反应性控制,而且可以提高反应堆的安全性和经济性。     

神经网络-遗传复合算法在压水堆堆芯换料设计中的应用

基于大规模数据的训练,神经网络模型能迅速准确预测堆芯的有效增殖因数（k_eff）、组件功率峰因子（Rad）和棒功率峰因子（FΔH）,并以这3个参数作为衡量换料方式优劣的标准,构造改进的遗传算法从大量堆芯燃料方案中迅速搜索出最优排布方案,解决了在大量堆芯换料方案中选择最优方案费时的问题。堆芯装载方式建模时,设计二进制向量作为输入参数,有效减少了网络复杂度、提高了预测精度;最优方案搜索时,具有独特交叉算子、选择算子的遗传算法保证了搜索结果在可行域内,并提高了搜索效率。理论分析和数值实验结果表明,包含1个隐藏层的单隐层自适应BP网络可很好预测k_eff数据,包含3个隐藏层的自适应BP神经网络可较好地预测Rad和FΔH数据,再运用遗传算法快速搜索出了较理想的换料方案,为人工智能算法在核工业中的进一步深入应用提供参考。     

A Solution of a Material Balance Equation of Channeling Stage Model for a Simple Case of a Water Distillation Column

Xenon oscillations in large PWRs are well understood and there have been no operational problems remained. However, in order to suppress the oscillations effectively, optimal control strategy is preferable. Generally speaking in such optimality search based on the modern control theory, a large volume of transient core analyses is required. For example, three dimensional core calculations are inevitable for the analyses of radial oscillations. From this point of view, a very simple 3-D model is proposed, which is based on a reactor model of only four points. As in the actual reactor operation, the magnitude of xenon oscillations should be limited from the view point of safety, the model further assumes that the neutron leakage can be also small or even constant. It can explicitly use reactor parameters such as reactivity coefficients and control rod worth directly. The model is so simplified as described above that it can predict oscillation behavior in a very short calculation time even on a PC. However the prediction result is good. The validity of the model in comparison with measured data and the applications are discussed.     

Calculation of the power peaking factor in a nuclear reactor using support vector regression models

Local power density (LPD) at the hottest part of a hot nuclear fuel rod should be estimated accurately to confirm that the rod does not melt. The power peaking factor (PPF) is defined as the highest LPD divided by the average power density in the reactor core. In this paper, the PPF is calculated by support vector regression (SVR) models using numerous measured signals from the reactor cooling system. SVR models are regression analysis models using a kernel function for artificial neural networks. Their neural network weights are found by solving a quadratic programming problem under linear constraints. SVR models are trained using a training data set and then verified against another test data set. The proposed SVR models were applied to the first fuel cycle of the Yonggwang nuclear power plant unit 3. The root mean square errors of the SVR model, with and without in-core neutron flux sensor signal inputs, were 0.1113% and 0.0968%, respectively. This level of errors is sufficiently low for use in LPD monitoring.     

大型压水堆机械补偿控制策略仿真研究

机械补偿（MSHIM）运行的优点之一是实现了堆芯功率和轴向功率偏移（AO）在控制手段方面的部分解耦，但原始控制策略设计并未充分利用该优点。本研究通过理论分析提出了一种新的改进型MSHIM控制策略，同时基于节点反应堆模型开发了MSHIM控制系统仿真平台，并利用该平台对西屋公司原始控制策略、西屋公司Drudy的改进控制策略和本研究提出的改进控制策略进行仿真研究和比对。结果表明，本研究提出的改进型MSHIM控制策略能够显著地提高AO的控制精度，并能减少控制棒的移动，明显地改善了AP1000核电机组的运行效果，可在工程中参考使用。      

压水堆核电厂负荷跟踪建模与控制方法研究

压水堆核电厂负荷跟踪模式能够有效协调机组产能与电网需求,延长燃料的循环寿期,提高机组运行的经济性能。反应堆系统具有高度复杂、非线性、时变等特点。通过合理简化,建立了反应堆系统集总参数模型,设计了负荷跟踪控制策略。引入负荷阶跃变化扰动和线性变化扰动,对反应堆负荷跟踪控制系统特性进行仿真。结果表明,控制特性与实际基本一致,控制系统能够满足负荷跟踪性能要求。     

Azcatl-CRP: An ant colony-based system for searching full power control rod patterns in BWRs

We show a new system named AZCATL-CRP to design full power control rod patterns in BWRs. Azcatl-CRP uses an ant colony system and a reactor core simulator for this purpose. Transition and equilibrium cycles of Laguna Verde Nuclear Power Plant (LVNPP) reactor core in Mexico were used to test Azcatl-CRP. LVNPP has 109 control rods grouped in four sequences and currently uses control cell core (CCC) strategy in its fuel reload design. With CCC method only one sequence is employed for reactivity control at full power operation. Several operation scenarios are considered, including core water flow variation throughout the cycle, target different axial power distributions and Haling conditions. Azcatl-CRP designs control rod patterns (CRP) taking into account safety aspects such as k_eff core value and thermal limits. Axial power distributions are also adjusted to a predetermined power shape.     

状态微分反馈控制与压水反应堆功率现有两种控制系统的等价性研究

本文提出了一种新型的反馈控制--状态微分反馈控制,并用于设计负荷跟随运行模式下的反应堆控制系统。设计过程依赖于控制棒位置的积分控制和控制棒速度的状态微分反馈控制两种控制系统之间的等价性,这一关系被证明并总结为定理。数值仿真结果表明,所设计的反应堆功率的状态微分反馈控制系统具有很好的负荷跟随模式性能。