• Nuclear Engineering and Technology
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• 제53권6호
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• pp.1731-1735
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• 2021

The operation of the nuclear reactor requires accurate and fast methods and techniques for analysing its kinetics. These techniques become even more important when the MOX-fuel is used due to the lower value of delayed neutron fraction 𝛽 for ²³⁹Pu. Based on a Birth-and-Death process review, the mathematical model of thermal reactor core has been proposed different from existing ones. The analytical method for thermal point-reactor parameters evaluation is described within this work. The proposed method is applied for analysis of the unsteady transient processes taking place in a thermal reactor at its start-up or shutdown power change, as well as during small accidental power variation from the rated value. Theoretical determination of MASURCA reactor core reactivity through the analysis of experimental data on neutron time spectra was made.

• 시스템엔지니어링학술지
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• 제18권2호
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• pp.58-74
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• 2022

Deterministic accident analysis plays a central role in the nuclear power plant (NPP) safety evaluation and licensing process. Traditionally the conservative approach opted for the point kinetics model, expressing the reactor core parameters in the form of reactivity and power tables. However, with the current advances in computational power, high fidelity multi-physics simulations using real-time code coupling, can provide more detailed core behavior and hence more realistic plant's response. This is particularly relevant for transients where the core is undergoing reactivity anomalies and uneven power distributions with strong feedback mechanisms, such as reactivity initiated accidents (RIAs). This work addresses a RIA, specifically a control element assembly (CEA) withdrawal at power, using the multi-physics analysis tool RELAP5/MOD 3.4/3DKIN. The thermal-hydraulics (TH) code, RELAP5, is internally coupled with the nodal kinetics (NK) code, 3DKIN, and both codes exchange relevant data to model the nuclear power plant (NPP) response as the CEA is withdrawn from the core. The coupled model is more representative of the complex interactions between the thermal-hydraulics and neutronics; therefore the results obtained using a multi-physics simulation provide a larger safety margin and hence more operational flexibility compared to those of the point kinetics model reported in the safety analysis report for APR1400. The systems engineering approach is used to guide the development of the work ensuring a systematic and more efficient execution.

• Nuclear Engineering and Technology
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• 제50권8호
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• pp.1277-1288
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• 2018

In this work, the reactor kinetics capability is used to compute the design safety parameters in a PWR due to complete loss of coolant flow during protected and unprotected accidents. A thermal-hydraulic code coupled with a point reactor kinetic model are used for these calculations; where kinetics parameters have been developed from the neutronic SRAC code to provide inputs to RELAP5-3D code to calculate parameters related to safety and guarantee that they meet the regulatory requirements. In RELAP5-3D the reactivity feedback is computed by both separable and tabular models. The results show the importance of the reactivity feedback on calculating the power which is the key parameter that controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core melt. In addition, extending modeling capability from separable to tabular model has nonremarkable influence on calculated safety parameters.

• Nuclear Engineering and Technology
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• 제47권1호
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• pp.94-101
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• 2015

This paper presents findings on the second-order sliding-mode controller for a nuclear research reactor. Sliding-mode controllers for nuclear reactors have been used for some time, but higher-order sliding-mode controllers have the added advantage of reduced chattering. The nonlinear model of Pakistan Research Reactor-1 has been used for higherorder sliding-mode controller design and performance evaluation. The reactor core is simulated based on point kinetics equations and one delayed neutron groups. The model assumes feedback from lumped fuel and coolant temperatures. The effect of xenon concentration is also considered. The employed method is easy to implement in practical applications, and the second-order sliding-mode control exhibits the desired dynamic properties during the entire output-tracking process. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness, and stability.

• 시스템엔지니어링학술지
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• 제19권2호
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• pp.46-58
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• 2023

Deterministic safety analysis is a crucial part of safety assessment, particularly when it comes to demonstrating the safety of nuclear power plant designs. The traditional approach to deterministic safety analysis models is to model the nuclear core using point kinetics. However, this simplified approach does not fully reflect the real core behavior with proper moderator and fuel reactivity feedbacks during the transient. The use of Multi-Physics approach allows more precise simulation reflecting the inherent three-dimensionality (3D) of the problem by representing the detailed 3D core, with instantaneous updates of feedback mechanisms due to changes of important reactivity parameters like fuel temperature coefficient (FTC) and moderator temperature coefficient (MTC). This paper addresses a CEA ejection accident at hot full power (HFP), in which the underlying strong and un-symmetric feedback between thermal-hydraulics and reactor kinetics exist. For this purpose, a multi-physics analysis tool has been selected with the nodal kinetics code, 3DKIN, implicitly coupled to the thermal-hydraulic code, RELAP5, for real-time communication and data exchange. This coupled approach enables high fidelity three-dimensional simulation and is therefore especially relevant to reactivity initiated accident (RIA) scenarios and power distribution anomalies with strong feedback mechanisms and/or un-symmetrical characteristics as in the CEA ejection accident. The Systems Engineering approach is employed to provide guidance in developing the work in a systematic and efficient fashion.

• Nuclear Engineering and Technology
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• 제56권9호
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• pp.3571-3584
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• 2024

Reactor core transient calculation is very important for the reactor safety analysis, in which the kernel is neutron kinetics calculation by simulating the variation of neutron density or thermal power over time. Compared with the point kinetics method, the time-space neutron kinetics calculation can provide accurate variation of neutron density in both space and time domain. But it consumes a lot of resources. It is necessary to develop a surrogate model that can quickly obtain the temporal and spatial variation information of neutron density or power with acceptable calculation accuracy. This paper uses the time-varying characteristics of power to construct a time function, parameterizes the time-varying characteristics which contains the information about the spatial change of power. Thereby, the amount of targets to predict in the space domain is compressed. A surrogate method using the machine learning is proposed in this paper. In the construction of a neural network, the input is processed by a convolutional layer, followed by a fully connected layer or a deconvolution layer. For the problem of time sequence disturbance, a structure combining convolutional neural network and recurrent neural network is used. It is verified in the tests of a series of 1D, 2D and 3D reactor models. The predicted values obtained using the constructed neural network models in these tests are in good agreement with the reference values, showing the powerful potential of the surrogate models.

• Nuclear Engineering and Technology
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• 제54권3호
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• pp.940-947
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• 2022

Meta-heuristic algorithms have found their place in optimization problems. Henry gas solubility optimization (HGSO) is one of the newest population-based algorithms. This algorithm is inspired by Henry's law of physics. To evaluate the performance of a new algorithm, it must be used in various problems. On the other hand, the optimization of the proportional-integral-derivative (PID) gains for load-following of a nuclear power plant (NPP) is a good challenge to assess the performance of HGSO. Accordingly, the power control of a pressurized water reactor (PWR) is targeted, based on the point kinetics model with six groups of delayed-neutron precursors. In any optimization problem based on meta-heuristic algorithms, an efficient objective function is required. Therefore, the integral of the time-weighted square error (ITSE) performance index is utilized as the objective (cost) function of HGSO, which is constrained by a stability criterion in steady-state operations. A Lyapunov approach guarantees this stability. The results show that this method provides superior results compared to an empirically tuned PID controller with the least error. It also achieves good accuracy compared to an established GA-tuned PID controller.

• Nuclear Engineering and Technology
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• 제54권4호
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• pp.1253-1260
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• 2022

This paper reports the control method for the core power of the China initiative Accelerator Driven System (CiADS) facility. In the CiADS facility, an intense external neutron source provided by a proton accelerator coupled to a spallation target is used to drive a sub-critical reactor. Without any control rod inside the sub-critical reactor, the core power is controlled by adjusting the proton beam intensity. In order to continuously change the beam intensity, an adjustable aperture is considered to be used at the Low Energy Beam Transport (LEBT) line of the accelerator. The aperture size is adjusted based on the Proportional Integral Derivative (PID) controllers, by comparing either the setting beam intensity or the setting core power with the measured value. To evaluate the proposed control method, a CiADS core model is built based on the point reactor kinetics model with six delayed neutron groups. The simulations based on the CiADS core model have indicated that the core power can be controlled stably by adjusting the aperture size. The response time in the adjustment of the core power depends mainly on the adjustment time of the beam intensity.

• Nuclear Engineering and Technology
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• 제19권3호
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• pp.192-197
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• 1987

다량의 중수반사체를 가진 조밀한 노심에서는 핵분열시 발생하는ｒ선과 중수소와의 (ｒ,n) 반응에 의해 지발 광중성자가 다량 생성되므로 이러한 계통을 기술하기 위하여 광중성자와 그 모핵종의 공간적 분리에 역점을 두어 2-점노 운동방정식을 정립하였다. 여러 반응도를 주입하여 출력 천이를 모사계산하므로써 노심과 반사체사이의 관련 효과를 조사하였다. 이 모델에 의한 모사계산 결과와 공간 종속 운동방정식에 의한 계산결과를 비교하였다. 반사체 영역에서의 광중성자 효과가 포함되므로써, 이를 포함하지 않은 모델에 비해 출력 천이현상을 감소시켰다. 실제로 출력을 측정하는 계측기는 이러한 공간적 분리영 향을 제거하기 위하여 노심 내부에 위치하여야 한다.

• Nuclear Engineering and Technology
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• 제35권5호
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• pp.399-411
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• 2003

A model predictive control method is applied to design an automatic controller for thermal power control in a reactor core. The basic concept of the model predictive control is to solve an optimization problem for a finite future at current time and to implement as the current control input only the first optimal control input among the solutions of the finite time steps. At the next time step, the second optimal control input is not implemented and the procedure to solve the optimization problem is then repeated. The objectives of the proposed model predictive controller are to minimize the difference between the output and the desired output and the variation of the control rod position. The nonlinear PWR plant model (a nonlinear point kinetics equation with six delayed neutron groups and the lumped thermal-hydraulic balance equations) is used to verify the proposed controller of reactor power. And a controller design model used for designing the model predictive controller is obtained by applying a parameter estimation algorithm at an initial stage. From results of numerical simulation to check the controllability of the proposed controller at the $5\%/min$ ramp increase or decrease of a desired load and its $10\%$ step increase or decrease which are design requirements, the performances of this controller are proved to be excellent.