球床式高温气冷堆由于连续流动的球床堆芯和高温环境，堆芯内无法安装探测器，无法由堆芯内的探测器直接测量堆芯三维功率分布。本论文试图利用数量有限的布置在堆芯外的中子探测器，实现高温气冷堆的堆芯三维功率分布的在线监测，以便更好地指导高温气冷堆的运行，而这从未被实现或被证明。 谐波综合法给出了解决此难题的可能途径，即在各个物理因素影响下变化的堆芯功率分布可用一组预先确定的、数量有限的特征分布的组合表示，形成堆芯功率分布的约束公式；然后由探测器读数确定各个特征分布的份额，实现三维功率分布的在线监测。针对高温气冷堆，研究的难点在于能否找出合适的特征分布，能否由数量很少的芯外探测器确定所有特征分布的份额。 论文以模块式高温气冷堆核电站示范工程HTR-PM为参考对象。首先，利用不连续因子修正的扩散方程和控制棒区的局部均匀化，建立了准确、高效的堆芯三维模型，为研究各物理因素对功率分布的影响规律和特征分布的确定提供模型基础。其次，采用共轭输运离散纵标法准确计算芯外探测器的空间响应函数，分析了堆芯状态变化对响应函数的影响，建立了功率分布和探测器读数之间的响应关系。然后，利用谐波综合法、谐波分组法、谐波系数多项式展开法，以及直接拟合的方法实现了各个物理因素（包括控制棒运动、堆芯温度变化、氙动态）的特征分布抽取与优化，获得了多物理因素耦合作用时的堆芯功率分布以及芯外探测器读数的约束公式，实现了由芯外探测器在线监测功率分布。最后，分析了监测过程的鲁棒性；分析了探测器读数噪声对结果的影响；基于现有的探测器布置方案，优化了监测方案的精度和鲁棒性；分析了增加探测器数量的可行性和好处；给出了探测器空间响应函数随堆芯状态的修正方法。 大量的数值试验证明了该方法的可行性。针对反应堆可能的运行工况，正向计算出各种物理因素影响下的堆芯功率分布（理想分布），和对应该分布的芯外探测器读数，仅根据探测器读数，重构出堆芯功率分布，然后比较重构分布和理想分布的吻合程度。验算结果表明，对于高温气冷堆，由芯外探测器能监测堆芯功率分布，还能监测控制棒位等堆芯状态，并具有实时、实测的优点。
Because of the movable pebbles and high temperature environment in the reactor core, it is not impractical to install the detectors in the core of pebble bed high-temperature gas-cooled reactor (HTR). The in-core power distribution (IPD) which is the essential reactor parameter can not be obtained directly from the in-core detectors. In the thesis, effort was made to realize the on-line IPD surveillance for HTR by ex-core detector readings (EDRs) whose number is limited, in order to provide useful information for HTR operation. But this task is not realized nor proven before. The harmonics synthesis method provides one possibility to solve this problem. In this method, the IPD variance induced by various physical causes is proposed to be expressed by the combination of a finite number of characteristic distributions, which can be pre-obtained from reactor physical analysis and calculation. This represents the restriction equation of IPD. And the portion of each characteristic distribution in the restriction equation can be determined by the detector readings. As a result, on-line 3D IPD surveillance is achieved. Concerning the particularity of HTR, the key task of this research is to find out the appropriate characteristic distributions and to prove that it is possible to determine the portion of each characteristic distribution through limited number of ERDs. The model used in this thesis is derived from the Chinese design of High-Temperature gas-cooled Reactor-Pebble-bed Module (HTR-PM). Firstly, based on the localized homogenization of control rod region and the diffusion model corrected by the discontinuity factor theory, an accurate and efficient three-dimensional (3D) reactor model is setup. This 3D model is the basis to analyze the influence law of each physical cause on IPD, and to obtain characteristic distributions of each physical cause. Then the adjoint discrete ordinate method is adopted to accurately calculate the spatial response function of ex-core detectors, the characteristics of the spatial response function are analyzed. Especially, the effect of reactor state variables on spatial response function is evaluated. The spatial response functions establish the relationship between IPD and EDRs. In third step, the characteristic distributions for each physical cause, including control rods movement, the change of temperature distribution in the core and xenon dynamic procedure, are determined and optimized by the harmonics synthesis method, harmonics grouping method, harmonics’ coefficients polynomial expansion method and the directly fitting method. The restriction equation of IPD, also the restriction equation of EDR, is established, even for the case that all physical causes are taken into account at same time. As a result, the surveillance of IPD via EDR is realized. In the end, the robustness of IPD surveillance procedure is analyzed. The effect of random noise in EDR on surveillance result is analyzed. One optimization scheme concerning both the precision and robustness is proposed based on the current arrangement of ex-core detectors. The possibility and the benefit by increasing the number of ex-core detectors are evaluated. Because the spatial response function of ex-core detector will be influenced slightly by reactor state variables, a correction method is proposed and verified. The feasibility to surveillance HTR IPD via ex-core detectors is demonstrated and verified by large amount of numerical experiments. Contraposing the most possible reactor operation conditions, the theoretically ideal IPD used as reference and the EDRs responding to this reference IPD are generated by forward calculation. Then an IPD can be reconstructed just from the calculated EDRs by the method proposed in the thesis. The comparison between reconstructed IPD and the reference IPD is carried out. For HTR, these results indicate that, not only the IPD, but also other reactor state variables such as control rod positions, can be monitored through EDRs, in real-time, and directly based on measurement.
