On-line extraction of the variance caused by burn-up in in-core three-dimensional power distribution

In most of PWRs, the ex-core ion-chambers are the sole real-time sensors to respond to in-core power and its axial offset. However, the calibration coefficient of the ion-chambers depends on the (3D) power distribution and varies with the burn-up. People expect to know the variance in distribution caused by burn-up directly from the signals of ion-chambers. This expectation is not realized as yet, because an ion-chamber almost only responds to its nearest fuel assemblies. The authors then developed a two-step method for burn-up characteristic extraction: the harmonics synthesis method and harmonics’ burn-up grouping. Using the extracted burn-up characteristics, the relationship between the readings of the ex-core ion-chambers and the in-core 3D power distribution is set up. Through the simulation on the heating reactor, the method of burn-up characteristic extraction is verified under engineering conditions. It is possible to on-line extract the variance caused by burn-up in 3D power distribution.     

钒自给能探测器中子响应计算方法

钒自给能探测器被广泛用作核动力反应堆的堆内固定式探测器,为堆芯中子注量率分布测量连续不断地提供信息。研究钒自给能探测器的响应电流计算方法,为堆芯在线功率分布监测与探测器设计优化提供理论依据。首先描述钒自给能探测器的响应机理与特性,然后基于Warren提出的理论模型,详细介绍中子响应电流控制方程及电子逃脱概率的计算方法,最后根据公开报道的典型钒探测器规格与实验数据进行数值模拟分析。结果显示,单位长度热中子灵敏度计算值与测量值相对偏差在±5%以内,论证了该方法的有效性与计算精度。     

基于贝叶斯推断的堆芯功率分布重构

基于贝叶斯推断理论,实现了一种有效融合堆内中子探测器实际测量值与中子学理论计算值两类信息的堆芯功率分布重构方法。应用大亚湾核电站1号机组的测量数据对贝叶斯推断方法的功率分布重构精度进行了验证,并将贝叶斯推断方法与卡尔曼滤波方法以及耦合系数法进行了精度对比。验证结果显示,贝叶斯推断方法在整个循环寿期内的均方根误差、最大相对误差、功率峰重构误差分别不大于0.31%、1.64%和0.07%,且重构精度优于卡尔曼滤波方法以及耦合系数法。重构精度以及计算速度表明贝叶斯推断方法有潜力被应用于功率分布在线监测系统。      

Diagnostics of core barrel vibrations by in-core and ex-core neutron noise

Diagnostics of core-barrel vibrations has traditionally been made by use of ex-vessel neutron detector signals. We suggest that in addition to the ex-core noise, also the in-core noise, induced by core barrel vibrations, be also used. This would enhance the possibilities of diagnostics where the number of the ex-core detectors is not sufficient or their positions are disadvantageous for effective diagnostics, especially for shell-mode vibrations.

To this order, the theory of in-core noise induced by a fluctuating core boundary has been elaborated and applied to the diagnostics of beam and shell mode vibrations. The formulas were tested on some measurements taken in the Ringhals PWRs. The results confirm the validity of the model itself, and the possibilities for enhanced diagnostics were demonstrated. A more effective use of these novel possibilities requires more in-core detectors and/or better detector positioning.     

基于BP神经网络的堆芯三维功率重构方法研究

堆芯功率分布包含了堆芯内的大量信息,由于在反应堆运行过程中无法直接测量堆芯内所有位置的功率,因此需通过其他方法得到堆芯三维功率分布的情况。本文以秦山一期工程为对象,利用堆外中子探测器在不同棒位和不同功率下的计数及BP神经网络对堆芯三维功率分布进行重构计算,并利用REMARK程序对该计算结果进行验证。结果表明,该功率重构方法能在反应堆运行的50%～100%功率范围内,较好地呈现堆芯三维功率分布。     

一种用芯内中子探测器读数校准燃耗后堆芯截面参数的方法

燃耗后的反应堆堆芯截面参数偏离了原来的数值,尽管用燃耗表对其进行了修正,但由于修正过程中的近似,仍使得截面参数的可靠性受到怀疑。文中提出：在用芯内中子探测器读数重构出“测量的”全堆热群中子通量密度分布的基础上,约束堆芯截面参数,并采用节块格林函数法对其进行校准的一套完整方法。截面参数经校准后,可以使理论模型计算结果与实际测量值相一致。仿真结果说明了此方法的可行性。     

最小二乘支持向量机在堆芯功率分布重构中的应用

应用最小二乘支持向量机(LS-SVM)进行了堆芯轴向功率分布重构的研究,通过6节堆内中子探测器的信号重构出堆芯轴向18个节块的功率。使用ACP-100模块式小堆的7 740套轴向功率分布对LS-SVM重构算法进行了验证,实验结果表明:LS-SVM算法的重构精度远优于交替条件期望(ACE)算法,且LS-SVM算法具有良好的鲁棒性。     

堆外探测器读数与堆内功率分布的关系研究

通常认为堆外探测器读数与反应堆总功率之间存在正比关系,这其实很不合理,在实际运行过程中会出现很大的偏差。堆芯功率分布和堆外探测器读数的映射关系可以通过空间响应函数来更好地表达。论文介绍了空间响应函数的计算方法,压水堆的堆外探测器空间响应函数的特点、影响因素,以及其在反应堆功率重构中作用。     

In-core coolant flow monitoring of pressurized water reactors using temperature and neutron noise

Noise measurements were performed at the Loss-of-Fluid-Test (LOFT) and Sequoyah-1 pressurized water reactors (PWRs) in order to investigate the possibility of inferring in-core coolant velocities from cross-power spectral density (CPSD) phases of core-exit thermocouple and in-core neutron detector signals. These noise measurements were used to investigate the effects of inlet coolant temperature, core flow, reactor power, and random heat transfer fluctuations on the noise-inferred coolant velocities. The effect on the inferred velocities of varying in-core neutron detector and core-exit thermocouple locations was also investigated. Theoretical models of temperature noise were developed, and the results were used to interpret the experimental measurements.Results of these studies indicate that the neutron detector/thermocouple phase is useful for monitoring core flow in PWRs. Our results show that the interpretation of the phase between these signals depends on the source of temperature noise, the response times and locations of the sensors, and the neutron dynamics of the reactor. At Sequoyah-1 we found that the in-core neutron detector/core-exit thermocouple phase can be used to infer in-core coolant velocities, provided that the measurements are corrected for the thermocouple response time.     

An on-line fuel management method using in-core detector readings for CANDU reactors

An on-line fuel management method for a CANDU reactor has been developed. In the method, the in-core detector readings are used for channel power generation for refueling channel selection. The in-core detector readings are converted to measured mesh readings, and the Kalman filtering technique is applied to reduce calculation and measurement errors of the mesh readings. Then, the estimated channel powers are fed into the refueling channel selection process, in which the channels are refueled so that the difference of zone power from the reference one is minimized. The performance of the method has been demonstrated against the operating data of CANDU 6 reactor. Also, it is found that the core tracking fuel management could be implemented, so that the proposed method would contribute to economic and safe operation of the reactor.     

Kalman Filter Applied to Estimation of Neutron Flux Distribution and Optimum Allocation of In-Core Detectors

Estimation of the spatial distributions of prompt neutrons and delayed neutron precursors has been studied by analyzing the output signals of in-core neutron detectors. In this paper, application of distributed Kaiman filter is attempted for a one-dimensional core model having statistical fluctuations. Assuming that their statistics are determined by Schottky formula, the error covariance matrix of estimation is computed in order to evaluate the filter performance. In the computation of this matrix, the algebraic Riccati equation is solved by generalized Newton-Raphson method.

From the viewpoint of estimation accuracy, it is also an important problem to optimize the detector locations. Considering the cases where estimation is focussed on a specified quantity related to prompt and delayed neutrons, the optimum allocations of two detectors are searched numerically. It is inferred that the optimized allocation has a considerable effect on estimating the shapes of the distributions where higher terms of spatial harmonics cannot be neglected.     

Nuclear reactor power and flux distribution fitting from a diffusion theory model and experimental data

Power and flux tracking in nuclear reactor cores are normally done using diffusion codes. These codes take into account geometric characteristics, compositions, operative conditions and eventually thermohydraulic feedbacks. However, due to operating requirements, in some cases these reactor are instrumented with in-core neutronic flux detectors. This information is usually used in order to verify instantaneous calculations, but it can also be used to fit the theoretical model and then to produce an improved solution. A scheme like this will fit into some extend with the deficiencies of the mathematical problem definition. In this work the integration between a theoretical model and experimental data is searched. It starts with a synthesis method called flux mapping and then its elements are studied. This is the minimization of a functional and selection and construction of expansion functions. For the first expansion function the solution of a diffusion code is chosen, while the other ones are built from Helmholtz equation solutions for a reactor having the same dimensions and boundary conditions. Flux mapping is then tested in a real reactor, a CANDU-600, for several reactivity device configurations. The set of measurement data available even from different physics principles made it suitable to perform the verifications. Comparison with experimental data in the zone at which flux detectors were located shows, for flux mapping, agreements of 2.4%, but 3.2% for the diffusion code used as standard for this reactor. Comparisons throughout the core shows agreements of 3.4 and 5.0%, respectively.     

Neural network correlation for power peak factor estimation

This paper proposes a method, based on the artificial neural network technique, to predict accurately and in real time the power peak factor in a form that can be implemented in reactor protection systems. The neural network inputs are the position of control rods and signals of ex-core detectors. The data used to train the networks were obtained in the IPEN/MB-01 zero-power reactor from especially designed experiments. The relative error for the power peak factor estimation ranged from 0.19% to 0.67%, an accuracy better than what is obtained performing a power density distribution map with in-core detectors. The networks were able to identify classes and interpolate the power peak factor values. It was observed that the positions of control rods bear the detailed and localised information about the power density distribution, and that the axial and the quadrant power differences, obtained from signals of ex-core detectors, describe its global variations in the axial and radial directions. In the power reactor environment, the neural networks would require in the input vector the position of control rods, and axial and quadrant power differences. The results showed that the RBF networks produced slightly better results than the MLP networks, but, for practical purposes, both can be considered of similar accuracy. The results indicate that they may allow decreasing the power peak factor safety margin by as much as 5%.     

Optimized gadolinia concepts for advanced in-core fuel management in PWRs

Utilities operating LWRs require fuel assemblies and in-core fuel management service, which ensure safe, flexible and cost-effective production of electricity. Because the reliability of the fuel has always been the most important requirement, advanced measures to minimize fuel cycle costs are receiving increasing attention in the light of the pressure on costs within the deregulated power generation markets. The role of in-core fuel management in supporting the goal to minimize fuel cycle costs consists in the development of more demanding core loading strategies, i.e. in the first place, more advanced low leakage loading patterns. A prerequisite for this type of loading pattern is the use of an optimized burnable absorber design. Gadolinia (Gd) as integrated burnable absorber is a very effective means for limiting the critical boron concentration and power peaking factors. Current development efforts for optimizing Gd-fuel are focused on the reduction of the inherent penalties of today's Gd-FA designs, i.e. reduced average fuel assembly (FA) enrichment and heavy metal content, as well as the residual reactivity binding. The most effective way to overcome these drawbacks is the reduction of the Gd₂O₃ concentration to values of ≈2 w/o, for which, according to recent measurements of the heat conductivity of modern Gd-fuels, the reduction of the fissile content in the Gd-rods is no longer necessary. Various feasibility studies have been performed to evaluate the consequences of FA designs with low Gd-concentrations (low-Gd designs) for Siemens PWRs and non-Siemens PWRs, for which more restrictive boundary conditions with respect to critical boron concentration and peaking factors have to be fulfilled. These studies, as well as operation experience of reactor cycles using low Gd-FA reload designs, confirm that the in-core fuel management can handle the different Gd burnout characteristics without problems. The economical benefits of low-Gd designs compared to conventional Gd designs are comparable to those achievable by distinctly more costly and complex alternatives, like the use of enriched gadolinia.     

Investigation of the two-phase flow in a boiling water reactor using neutron-noise technique

In this paper, the fluctuations of the neutron flux (“neutron noise”) of the Mühleberg BWR are investigated. Above 2 Hz, the noise measured by the in-core neutron detectors is driven exclusively by local fluctuations of the void fraction. Characteristic changes of the neutron-noise signature along the axis can be attributed to changes of flow pattern. By measuring the phase lag between pairs of axially placed neutron detectors, the transit time of the steam between the detectors can be evaluated. The measured transit times are applied to the study of two-phase flow in the core. The neutron-noise method has the advantage of providing in-core information under operational conditions.     

2D/1D耦合的堆芯实测功率分布快速重构研究

针对三代核电压水堆在线监测系统需要快速准确进行实测3D功率重构的需求,本文提出了一种2D/1D耦合的3D功率重构方法。首先采用耦合系数法对探测器层的功率进行了2D实测功率重构;其次针对每个组件,采用二次样条函数拟合方法进行了轴向1D实测功率重构,最后得到了全堆3D实测功率分布。该方法计算流程简单,占用内存少。针对华龙一号开展的4个典型例题的数值验证结果表明,该方法具备很高的精度,满足三代核电在线监测系统实测功率重构对精度和速度的要求。     

Reactor noise measurements in the safety and regulating systems of CANDU stations

Reactor noise measurements of safety and regulating system intrumentation are performed in the CANDU nuclear power stations of Ontario Power Generation (OPG) and Bruce Power. Station signals included in the noise measurements are in-core flux detectors (ICFD), ion chambers (I/C), flow transmitters, pressure transmitters, and resistance temperature detectors (RTD). Their frequency dependent noise signatures are regularly measured during steady-state operation, and are used for parameter estimation and anomaly detection.

The specific applications include the following areas:

Flux noise measurements to detect and characterize (a) anomalies of in-core flux detectors, ion chambers and their electronics, (b) mechanical vibration of fuel channels and in-core detector tubes induced by coolant/moderator flow.

Pressure and flow noise measurements to estimate the in-situ response times of flow/pressure transmitters and their sensing lines installed in the reactor's coolant loops.

Temperature noise measurements to estimate the in-situ response times of thermal-well or strap-on type RTDs installed in the reactor's coolant and moderator loops.

基于EFEN-SP3方法的pin-by-pin中子动力学计算方法研究

为能直接给出安全分析所需的最热棒功率而不引入组件均匀化近似和精细功率重构近似,本文研究了基于栅元均匀化的pin-by-pin中子动力学计算方法。通过全隐式向后差分对多群时空中子动力学方程组的时间变量进行离散,采用指数函数展开节块-SP₃（EFEN-SP₃）方法求解含裂变介质的多群中子固定源方程组,通过高阶源展开技术消除了中子源分布与缓发中子先驱核分布形状不一致的问题。采用Ks因子、LW外推和粗网再平衡等加速技术提高计算效率。三维pin-by-pin中子动力学问题的数值结果表明：pin-by-pin中子动力学计算能直接给出单棒功率密度分布;高阶源展开技术可有效抑制计算偏差随时间步的累加效应;加速技术可将SP₃动力学计算的求解速度提高134.9倍。