Open Access

ARTICLE

Study on Higher-Order Harmonic Calculation of Neutron Diffusion Equation and Its Application in Core Power Monitoring of the Gas-Cooled Microreactor

Kui Hu, Peng Zhang^*, Xiang Xiao, Yuan Xu, Yunhuang Zhang, Yuan Yuan, Zhiyuan Feng
China Nuclear Power Engineering Co., Ltd., Beijing, China
* Corresponding Author: Peng Zhang. Email:
(This article belongs to the Special Issue: Neutronic and Thermal-Hydraulic Analysis of Advanced Nuclear Reactors)

Energy Engineering https://doi.org/10.32604/ee.2026.078340

Received 29 December 2025; Accepted 16 March 2026; Published online 05 May 2026

Abstract

The rapid development of gas-cooled microreactors (GMRs) for remote and modular power supply necessitates highly efficient and autonomous core power monitoring systems. Traditional monitoring systems, such as those deployed in commercial power plants, rely on dense in-core instrumentation, whereas due to the limitation of space and simplicity in hardware designs, only sparse ex-core detectors are employed in microreactor designs. To address this challenge, this study proposes an advanced online power reconstruction approach based on the higher-order harmonic expansion. A dedicated higher-order harmonic calculation module was developed within a multi-group diffusion framework, capable of executing rapid three-dimensional core simulations at any core state. The proposed methodology utilizes signals from a limited set of ex-core detectors to inversely solve for the harmonic expansion coefficients of the power distribution. Unlike data-driven or fission-matrix-based techniques, our diffusion-theory-based approach eliminates the need for extensive pre-computed snapshot libraries, thereby enhancing adaptability to various transient operational states. Numerical validations were conducted using a representative GMR model, where the reconstructed power distributions were compared against high-fidelity Monte Carlo reference solutions. Under typical operating conditions, the results demonstrate that the maximum relative deviation remains within ±1.5%, affirming the high precision of the methodology. Furthermore, a comprehensive sensitivity analysis was performed to evaluate the robustness of the reconstruction against measurement uncertainties and detector configurations. The investigation reveals that the stability of the inverse solver is highly dependent on the condition number of the detector response matrix. It is quantitatively established that maintaining detector reading deviations below 0.2% is a critical threshold to satisfy stringent nuclear engineering design margins. By incorporating these findings, the developed code provides a powerful tool that bridges the gap between theoretical neutronics and practical reactor instrumentation. This work not only meets the current computational speed and accuracy demands for GMR power monitoring but also offers a scalable framework for integration into future digital twin systems and autonomous control architectures.

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Keywords

Higher-order harmonic; power monitoring; diffusion theory; gas-cooled micro-reactors

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