3D Power Distribution Research Articles

Application of new axial power distribution synthesis method using in-core detector signal in digital core protection system

ABSTRACT A new method for the generation of axial power distributions using artificial neural network (ANN) technique and real-time measured planar radial peaking factor, Fxy (hereinafter ‘Live Fxy’) method for digital core protection system of pressurized water reactors is presented. ANN with Simulated Annealing (SA) technique to find global optimum solution was used to calculate core average axial power distribution. In Live Fxy method, axial node-wise Fxys were calculated by multiplying pin/box factors to the measured assembly powers inferred from in-core detector signals without calculating detailed 3D power distributions. The hot pin power distribution for DNBR and LPD was then obtained by multiplying the core average axial power distribution and Fxys at axial nodes. The validation of the method was performed for various core conditions (e.g. core power levels, control rod positions, etc.) of Korean OPR1000 power plant. The result showed a decrease in RMS errors by 2.2% ~ 7.0% (3.6% on average), and the minimum thermal margins for DNBR and LPD were increased by 6.4% and 15.6%, respectively. The application of the method would improve the accuracy of axial power distribution and thermal margin, contributing to the operability and safety of digital core protection system.

Circular SAR Incoherent 3D Imaging with a NeRF-Inspired Method

Circular synthetic aperture radar (CSAR) has the potential to form 3D images with single-pass single-channel radar data, which is very time-efficient. This article proposes a volumetric neural renderer that utilizes CSAR 2D amplitude images to reconstruct the 3D power distribution of the imaged scene. The innovations are two-fold: Firstly, we propose a new SAR amplitude image formation model that establishes a linear mapping relationship between multi-look amplitude-squared SAR images and a real-valued 4D (spatial location (x, y, z) and azimuth angle θ) radar scattered field. Secondly, incorporating the proposed image formation model and SAR imaging geometry, we extend the neural radiance field (NeRF) methods to reconstruct the 4D radar scattered field using a set of 2D multi-aspect SAR images. Using real-world drone SAR data, we demonstrate our method for (1) creating realistic SAR imagery from arbitrary new viewpoints and (2) reconstructing high-precision 3D structures of the imaged scene.

Simulating self-powered neutron detector responses to infer burnup-induced power distribution perturbations in next-generation light water reactors

Understanding how 3D power distribution will be monitored throughout reactor core volumetric space in next-generation nuclear power reactors is crucial to the design, deployment, and licensing of these reactors. Although numerous techniques exist for 3D power distribution monitoring based on the response of both in situ and ex situ sensors currently implemented or proposed for use in the US reactor fleet, crucial details about these techniques are often unclear. The publicly available documentation does not include information such as how well these techniques are characterized and optimized in their implementations and the levels of uncertainty in the inferred 3D power distribution. The work described herein investigated a recently developed 3D power distribution inferencing method as applied to two next-generation reactor simulations: (1) the NuScale small modular reactor design and (2) the Westinghouse AP1000 design, both of which contain in-core strings of vanadium self-powered neutron detectors (SPNDs). This investigation considered a range of SPND string sensor densities, as well as a range of 3D power distribution axial segment sizes. SPND response simulation is informed by neutron flux calculations in representative homogenized cores. For the different sensor densities and power distribution axial segment sizes in these simulations, the average solution error, solver iterations, and run time were tracked to parameterize the sensor-core configuration.

Artificial neural network reconstructs core power distribution

To effectively monitor the variety of distributions of neutron flux, fuel power or temperatures in the reactor core, usually the ex-core and in-core neutron detectors are employed. The thermocouples for temperature measurement are installed in the coolant inlet or outlet of the respective fuel assemblies. It is necessary to reconstruct the measurement information of the whole reactor position. However, the reading of different types of detector in the core reflects different aspects of the 3D power distribution. The feasibility of reconstruction the core three-dimension power distribution by using different combinations of in-core, ex-core and thermocouples detectors is analyzed in this paper to synthesize the useful information of various detectors. A comparison of multilayer perceptron (MLP) network and radial basis function (RBF) network is performed. RBF results are more extreme precision but also more sensitivity to detector failure and uncertainty, compare to MLP networks. This is because that localized neural network could offer conservative regression in RBF. Adding random disturbance in training dataset is helpful to reduce the influence of detector failure and uncertainty. Some convolution neural networks seem to be helpful to get more accurate results by use more spatial layout information, though relative researches are still under way.

Validation results of the BIPR-8A code, the new module of the software package KASKAD

Abstract The BIPR-8A executable module is a main component of the BIPR 2007 code. This module is intended for three-dimensional coarse mesh calculation of the VVER reactor cores. This paper presents the results of validation of the BIPR-8A executable module. Validation is based on comparison of the calculated results with the operating data of power plants with the VVER-440, VVER-1000 and VVER-1200 reactors, and with the results of calculations obtained by using Monte Carlo codes. The results of comparison of the following values at HZP (hot zero power) power level and operational power level are presented: critical concentration of boric acid, temperature reactivity coefficient, efficiency of the control rods system, relative power distribution of fuel assemblies and 3D power distribution, effective multiplication factor.

MTL-based modeling and analysis of the effects of TSV noise coupling on the power delivery network in 3D ICs

With the application of heterogeneous integration and advanced packaging technologies, the use of through-silicon vias (TSVs) to deliver the power supply has become popular in the design of stacked chips in three-dimensional integrated circuits. High-density vertical interconnections offer higher speed and bandwidth, but the electromagnetic coupling effect among TSVs becomes more serious. Therefore, investigation of the noise coupling among TSVs and analysis of its impact on the power supply become important considerations. An analytical model based on the theory of multiconductor transmission lines (MTLs) is presented herein to discuss such TSV noise coupling. The method can accurately and quickly estimate the noise coupling coefficient among a large number of TSVs and offers good practicability for similar structures and even the TSVs of complex structures. Further, the influence of TSV noise coupling and simultaneous switching noise from switching circuits on the supplied power voltage is discussed. Finally, the parameters of an actual Intel chip are taken as an example to analyze the supplied power voltage that reaches complementary metal–oxide–semiconductor (CMOS) circuits through the three-dimensional (3D) power distribution network after considering the power supply noise. The presented model is validated by comparing the calculation results with those obtained from a full-wave simulator. The runtime and memory consumption requirements are lower than those of the full-wave simulator.

Predicting Ex-core Detector Response in a PWR with Monte Carlo Neutron Transport Methods

An approach for calculating ex-core detector response using Monte Carlo code MCNP was developed. As a first step towards ex-core detector response prediction a detailed MCNP model of the reactor core was made. A script called McCord was developed as a link between deterministic program package CORD-2 and Monte Carlo code MCNP. It automatically generates an MCNP input from the CORD-2 data. A detailed MCNP core model was used to calculate 3D power distributions inside the core. Calculated power distributions were verified by comparison to the CORD-2 calculations, which is currently used for core design calculation verification of the Krško nuclea power plant. For the hot zero power configuration, the deviations are within 3 % for majority of fuel assemblies and slightly higher for fuel assemblies located at the core periphery. The computational model was further verified by comparing the calculated control rod worth to the CORD-2 results. The deviations were within 50 pcm and considered acceptable. The research will in future be supplemented with the in-core and ex-core detector signal calculations and neutron transport outside the reactor core.

Full core 3D simulation of the BEAVRS benchmark with OpenMOC

The Method of Characteristics (MOC) has seen wide interest in reactor physics because of its accuracy and efficiency in computing lattice physics problems. While most of its use has been in solving 2D problems, there has been recent interest in extending MOC to 3D in order to more accurately calculate 3D power distributions in LWRs. While the method is naturally extensible to 3D, it presents significant computational difficulties. OpenMOC, an open source MOC simulator, has been extended from 2D to 3D capabilities. Simulation results are presented in this study for the full core 3D simulation of the BEAVRS benchmark, adequately resolved in space and angle.

Validating COMSOL multiphysics for VVER-1000 whole-core-steady-state via AER benchmark problem

In this work, a full core, three-dimensional, multi-group model of VVER-1000 reactor core is developed using specifications of the Schulz benchmark. This paper presents a new 3-D full core solution, and simulates the neutronic behaviour of the VVER-1000 reactor by predicting the system criticality, power distribution, and the neutron flux distribution. Multi-group constants are applied to the COMSOL model to perform neutronics calculations using finite element method with adaptive mesh refinement. The study found that the calculated effective multiplication factor (keff) compares well with the reference value. Furthermore, the fission rates 3D power distributions and axially averaged 2D power distribution are in good agreements with reported reference results. The thermal neutron spectrum is also calculated by the COMSOL model as presented in this paper. This study allows us to validate the COMSOL calculation schemes for VVER-type reactors and to compare our solutions with reference solutions at steady state.

Validation and Application of MCNP and TORT Source Generation Codes

Primary Shielding Calculation (PSC) plays an important role in reactor shielding design and analysis. In order to facilitate PSC, a source generation code is developed to generate cumulative distribution functions (CDF) for the source particle sample code of the MCNP code, and a source particle sample code is developed to sample source particle directions, types, coordinates, energy and weights from the CDFs. A source generation code is developed to transform three dimensional (3D) power distributions in xyz geometry to source distributions in rθz geometry for the TORT code. Validation on PSC model of Qinshan No.1 nuclear power plant (NPP), CAP1400 and CAP1700 reactors are performed. Numerical results show that the theoretical model and the codes are both correct.

Research on Primary Shielding Calculation Source Generation Codes

Primary Shielding Calculation (PSC) plays an important role in reactor shielding design and analysis. In order to facilitate PSC, a source generation code is developed to generate cumulative distribution functions (CDF) for the source particle sample code of the J Monte Carlo Transport (JMCT) code, and a source particle sample code is deveoped to sample source particle directions, types, coordinates, energy and weights from the CDFs. A source generation code is developed to transform three dimensional (3D) power distributions in xyz geometry to source distributions in r θ z geometry for the J Discrete Ordinate Transport (JSNT) code. Validation on PSC model of Qinshan No.1 nuclear power plant (NPP), CAP1400 and CAP1700 reactors are performed. Numerical results show that the theoretical model and the codes are both correct.

Monte Carlo and nodal neutron physics calculations of the IAEA MTR benchmark using Serpent/DYN3D code system

As part of recent efforts to utilize NPPs computational methodologies to safety analysis of research reactors, the Serpent and DYN3D codes were extensively compared with a variety of static and burnup calculations as defined in the IAEA benchmark for 10 MW MTR pool-type reactor. These calculations include unit cell calculations and few group constants generation, unit cell and full core k-eigenvalue and burnup calculations, and full core 3D flux and power distributions. The Serpent code capabilities as a lattice code for MTR plate-type fuel assemblies were evaluated and compared with EPRI-CELL and WIMS-D4 results and reference solutions for full 3D core models were compared with MCNP5 and OpenMC results. The DYN3D nodal diffusion code capabilities in modeling full 3D MTR cores were also evaluated using few group cross sections and assembly discontinuity factors obtained by Serpent unit cell calculations. The DYN3D results were compared with Serpent, MCNP5 and OpenMC.

Research on intelligent monitor for 3D power distribution of reactor core

A real-time monitor for 3D reactor power distribution is critical for nuclear safety and high efficiency of NPP’s operation as well as for optimizing the control system, especially when the nuclear power plant (NPP) works at a certain power level or it works in load following operation. This paper was based on analyzing the monitor for 3D reactor power distribution technologies used in modern NPPs. Furthermore, considering the latest research outcomes, the paper proposed a method based on using an ex-core neutron detector system and a neural network to set up a real time monitor system for reactor’s 3D power distribution supervision. The results of the experiments performed on a reactor simulation machine illustrated that the new monitor system worked very well for a certain burn-up range during the fuel cycle. In addition, this new model could reduce the errors associated with the fitting of the distribution effectively, and several optimization methods were also obtained to improve the accuracy of the simulation model.

Application of Virtual Visualization in Smart Power Distribution System

With the increasing development of the power system, particularly, with the proposing of smart grid and the applying of distributed generation technology, the traditional geographic information system (GIS) which relies on the tables, graphs, has become more and more difficult to meet the needs of power system equipment management, and planning. Three-dimensional (3D) GIS has developed to meet the requirement appropriately. In this paper, we choose ArcGIS as the development platform, ESRI CityEngine 2011 and Google SketchUp as the 3D modeling software. By combining the virtual reality(VR) technology and image synthesis technology, a 3D power distribution system is established, which realizes the 3D physical simulation of the transmission lines, electrical equipment, power distribution stations, and distributed generators. This methodology provides a new vision for the modernization of the power distribution system management.

Neutronics and thermal hydraulic coupling analysis of integrated pressurized water reactor

SUMMARY In this paper, three-dimensional (3D) power distribution of newly designed small nuclear reactor core has been achieved by using neutron kinetic/thermal hydraulic (NK/TH) coupling. This is pressurized water reactor-based small nuclear reactor in which plate type fuel element has been used and the core of the reactor has hexagonal type geometry. This paper depicts the design of the reactor core by using coupling approach of neutronics(Neutron Kinetic) and thermal hydraulic studies. For this purpose, neutronic analysis has been obtained by using lattice physics code, i.e. HELIOS and neutron kinetic code, i.e. REMARK. HELIOS code gives the cross-section data which is being used as input to the REMARK code. At the same time, THEATRe code was used for the thermal hydraulic analysis of the reactor core. In the coupling process, some data (fuel temperature, moderator temperature, void fraction, etc.) from THEATRe code has been used in conjunction with HELIOS and REMARK codes. After finalizing the NK/TH coupling, 3D evaluation of the power distribution of the reactor core has been achieved and is included in the paper. The purpose of this paper is to evaluate the design and get the normal operational behavior of the reactor core by NK/TH coupling approach. Copyright © 2012 John Wiley & Sons, Ltd.

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.