As a follow-up to the paper previously published by the authors detailing the hybrid finite element (HYBFEM) solution of the SP3 equations, in this paper, besides a semi-analytical solver verification with an analysis on the applied source fitting polynomial order, three-dimensional WER-440, and WER-1000 benchmarks are reproduced with the continuous Galerkin (CGFEM) and HYBFEM SP3 modules of the SPNDYN code. The effect of the applied axial nodalisation and radial element order on the calculation results is discussed. The HYBFEM solver extended with a discontinuity factor (DCF) calculation module based on Serpent 2 output parameters is verified on a two-dimensional WER-1000 benchmark. The SPNDYN CGFEM and HYBFEM results show very good agreement. We also verify that by introducing DCFs in SP3 calculations, the reference transport solution can be reproduced with high accuracy. We high-light the effect of using scalar flux weighted linearly anisotropic scattering matrices in higher-order transport calculations. (C) 2022 The Authors. Published by Elsevier Ltd.

Targeting ultimate fidelity reactor physics calculations the Dynamic Monte Carlo (DMC) method simulates reactor transients without resorting to static or quasistatic approximations. Due to the capability to harness the computing power of Graphics Processing Units, the GUARDYAN (GpU Assisted Reactor DYnamic ANalysis) code has been recently upscaled to perform pin-by-pin simulations of power plant scale systems as demonstrated in this paper. A recent rod drop experiment at a VVER-440/213 (vodo-vodyanoi enyergeticheskiy reaktor) type power plant at Paks NPP, Hungary, was considered and signals of ex-core detectors placed at three different positions were simulated successfully by GUARDYAN taking realistic fuel loading, including burn-up data into account. Results were also compared to the time-dependent Paks NPP in-house nodal diffusion code VERETINA (VERONA: VVER Online Analysis and RETINA: Reactor Thermo-hydraulics Interactive). Analysis is given of the temporal and spatial variance distribution of GUARDYAN fuel pin node-wise power estimates. We can conclude that full core, pin-wise DMC power plant simulations using realistic isotope concentrations are feasible in reasonable computing times down to 1–2% error of ex-core detector signals using current GPU (Graphics Processing Unit) High Performance Computing architectures, thereby demonstrating a technological breakthrough.

The C-PORCA reactor physics code of the Paks Nuclear Power Plant performs three-dimensional, two-group diffusion calculations applying parametrized group constants generated by the HELIOS code. To improve the accuracy of the calculations, the C-PORCA code was extended with a simplified spherical harmonics module. This paper presents the applied finite-element-based solution algorithm of the SP3 equations in response matrix formalism. Radially primal mixed-hybrid finite element method is used for response matrix calculation with the inclusion of Lagrange multipliers to enforce nodal balance on each element. The axial solution is analytically performed connecting the axial and radial directions through radial leakage with transverse integration. Coupling between the adjacent volumetric elements is performed with node-to-node axial and radial partial current-like moment iterations, that enables the application of SP3 discontinuity factors and the parallelization of the calculation process. The accuracy of the SP3 solution algorithm is demonstrated on academic benchmark and VVER-440 core calculations. (C) 2021 The Author(s). Published by Elsevier Ltd.

Abstract This work deals with the \Full-Core" VVER-1000 calculation benchmark which was proposed on the 26th Symposium of AER [1]. Recently, the calculation benchmarks \Full-Core" VVER-440 [2] and its extension [3] have been introduced in the AER community with positive response [4, 5]. Therefore we have decided to prepare a similar benchmark for VVER- 1000. This benchmark is also a 2D calculation benchmark based on the VVER-1000 reactor core cold state geometry, explicitly taking into account the geometry of the radial reflector. The loading pattern for this core is very similar to the fresh fuel loading of cycle 9 at Unit 1 of the Temelin NPP (Czech Republic). This core is filled with six types of fuel assemblies with enrichment from 1.3%w 235U to 4.0%w 235U with up to 9 fuel pins with Gd burnable absorber per FA. The main task of this benchmark is to test the pin-by-pin power distribution in fuel assemblies predicted by macro-codes that are used for neutron- physics calculations especially for VVER reactors. In this contribution we present the overview of available macro-codes results.

The C-PORCA/HELIOS models have been used at NPP Paks as basic core neutron physics calculation tools for many years. C-PORCA is a node-wise diffusion model for the purpose of 3D core analysis. HELIOS is a well-known neutron transport code. Its utilisation at Paks NPP has a dual use. This code is a basic tool for preparation of homogenised few-group neutron cross sections inside fuel nodes and areas without fuel and the flexibility of HELIOS allows using it for testing. During the last decade some new kind of fuel assemblies were utilised in Paks. In order to ensure the accuracy and performance requirements of the off-line core analysis and in-core monitoring, continuous development and testing of the codes have been performed. In this paper the main characteristics of the diffusion solver applied in the C-PORCA model are described. The accuracy of this solver is also demonstrated on the basis of comparisons with different international references available in hexagonal geometry. The C-PORCA results have been compared against benchmark data produced in the framework of the AER (Atomic Energy Research) community in recent decades. All presented comparisons illustrate that the accuracy of the C-PORCA diffusion solver is excellent.

After a preparation period with VERONA upgrade and lead test assembly program, a new fuel type was introduced at MVM Paks NPP Ltd. This 4.7% average uranium enriched assembly type, together with the former 4.2% uranium enriched fuels, allowed us to lengthen the operating cycles to 15 months. Both fuel types contain gadolinium burnable poison, in six and three pins respectively. All of the four units have been converted to the C15 cycles, and have been being operated without any problems in the last few years. In this paper the test results of core design code HELIOS/C-PORCA, which is the basic model of VERONA, are outlined. C15 cycles were entirely investigated with the comprehensive study of measured and predicted (calculated) values of different reactor states. At first step, in order to prove the capability of the reactivity calculation of the nodal diffusion model, critical boric acid concentrations of different burnup and start up states were calculated and compared with measured values. During the next step of the verification process local in-core parameters were investigated. Measured neutron flux distributions (SPND signals) and coolant outlet temperatures were examined. SPND and thermo couple (TC) signals were predicted as a part of the monitoring system. The results of statistical investigations (average differences and standard deviations) for the applied fuel types are also presented.

This work deals with "Full-Core" VVER-440 extended calculation benchmark which was proposed on the 24th Symposium of AER in October 2014 [2]. This benchmark is based on calculation benchmark defined by SKODA JS a.s. on the 21st Symposium of AER in 2011 PI This benchmark differs from the first "Full-Core" VVER-440 benchmark in use of control rods from group No. 6. Reason why these benchmarks exist is problematic validation of power distribution predicted by macro-code on the pin by pin level against experimental data. This new benchmark is also a 2D calculation benchmark based on the VVER-440 reactor core cold state geometry with taking into account the geometry of explicit radial reflector. Loading pattern for this core is very similar to the first pattern of the Mochovce NPR This core is filled with fief assemblies with enrichment of 1.6 %w U-235, 2.4 %w U-235 and 4.25 %w U-235 The main task of this benchmark is to test the pin by pin power distribution in fuel assemblies predicted by macro-codes that are used for neutron-physics calculations especially for VVER reactors. The reference solution has been calculated by MCNP6 code using Monte Carlo method and the results have been published in the AER community. The results of reference calculation were presented on the 27th Symposium of AER in 2017 [3]. In this paper is presented comparison of available macro-codes results for this calculation benchmark.

Abstract In Paks Nuclear Power Plant the VERONA core monitoring system is being used. In this article there is a new way presented to determine the precision of VERONA calculations during power transients. In that case VERONA uses a sophisticated method to follow the changes of the core. During a transient many online measured parameters cannot be used to determine the precision of the model due to their insufficient accuracy. However the change of the calculated boric acid concentration can be used for this purpose. If there is no inlet of boric acid or clean condense during the transient, at the end, the calculated boric acid concentration value should be equal to that, which was determined at the beginning of the power transient. However there is often a difference between these two values, which difference denotes the precision of the calculating model. This precision is heavily influenced by the heat conduction model, used between the fuel and the coolant. During the work five different conduction models were investigated, to determine which one offers more precise results. There was also a way examined to determine the uncertainty of the fuel temperature coefficient based on the outcome of the examined power transitions.

Factory acceptance tests (FAT) of the new refuelling neutron monitoring and reactivity measurement system (Hungarian acronym ANEREM) for Paks NPP were performed in April 2018. ANEREM is a combined system carrying out both refuelling neutron monitoring and start-up measurements. In order to increase the reliability of the new system it contains six autonomous measurement chains covering the whole neutron flux range from 1 cps to 1010 cps and comprises two redundant signal processing subsystems. The new system will be installed in two phases in order to guarantee the highest safety and availability. Phase 1 will be achieved in February 2019 at Unit 4. Redundancy for the refuelling as well as the validation of the new system will be provided by one of the subsystems of the old refuelling neutron monitoring system. The old reactivity monitoring system will be kept in operation during this phase with the aim of helping in the validation of the start-up measurements. Finalization of the new system with its full 6-detector installation will be achieved in Phase 2 in May 2020.

Abstract The Refueling Neutron Monitoring System and the Reactivity Monitoring System for startup measurements are both aged, the development of a new combined system fulfilling both functionalities has therefore been started. The new system is based on 6 autonomous measurement chains covering the whole neutron flux range and uses fixed fission chambers. The signals of the measurement chains are received by two redundant processing systems continuously providing measured and calculated data for external systems like the VERONA core monitoring system. The system generates emergency signals and events for the operators of the Main Control Room and the Refueling Machine. The pilot measurement chain has been tested at Units 2 and 3 of Paks NPP. The first implementation of the new system is planned to be installed at Unit 3 by the middle of the following year.

The core monitoring and surveillance system of Paks nuclear power plant has been replaced recently with a new version of the system VERONA utilizing virtualization technology and GPU accelerated numerical computations. In the new system, the process variables are monitored by the visual engine of a new simulation platform SIMTONIA (SIMulation TOols for Nuclear Industrial Application). In this paper the hardware and software architecture of the new system is presented in details enlighten the advantages of the application of stateof- art computational technologies.

Nowadays the installation of a new modernized VERONA core monitoring system (version V7.0) is in process at the NPP Paks. The most important steps of the current improvements are as follows: complete replacement of the hardware and the local area network; application of a new operating system and "virtual machine" (VM) technology; implementation of a new human-system interface; and last but not least, introduction of improved reactor physics calculations. Basic novelty of the modernized core analysis is the application of general purpose graphical processing units (GPGPU) in the on-line core-follow module. This new technology has allowed of performing the real-time node-wise core analysis by standard Paks NPP core design codes HELIOS/C-PORCA. The present paper gives a brief overview of the system version (V7.0), focusing to the models of reactor physics and results of validation. Main characteristics of new approaches of the modified on-line reactor physics calculations are also described.

The Reactivity Monitoring System and the Refuelling Neutron Monitoring System of Paks NPP are aged and need to be reconstructed. Since both systems are based on neutron flux measurements, the new system is to be served by the same detectors and measurement instrumentation. In order to provide data during refuelling, start-up and at full power, a full range system is required, i.e. the detectors and the associated instrumentation should cover the full range of neutron flux measurements from 0% to 100% of reactor power. Additionally, the new system is required to operate continuously, to maintain a measurement archive, and to provide data for the Process Computer and the VERONA core monitoring system. In order to cover the full neutron flux range, Photonis CFUL08 type fission chamber was chosen. The interface module will serve all three operation modes of the detector: pulse, Campbell (AC) and current (DC) modes. In order to obtain high reliability and dependability, the system will be built from independent and redundant components.

Between 2003 and 2007 the Hungarian Paks NPP performed a large modernization project to upgrade its VERONA core monitoring system. The modernization work resulted in a state-of-the-art system that was able to support the reactor thermal power increase to 108% by more accurate and more frequent core analysis. Details of the new system are given in Végh et al. (2008), the most important improvements were as follows: complete replacement of the hardware and the local area network; application of a new operating system and porting a large fraction of the original application software to the new environment; implementation of a new human-system interface; and last but not least, introduction of new reactor physics calculations. Basic novelty of the modernized core analysis was the introduction of an on-line core-follow module based on the standard Paks NPP core design code HELIOS/C-PORCA. New calculations also provided much finer spatial resolution, both in terms of axial node numbers and within the fuel assemblies. The new system was able to calculate the fuel applied during the first phase of power increase accurately, but it was not tailored to determine the effects of burnable absorbers as gadolinium. However, in the second phase of the power increase process the application of fuel assemblies containing three fuel rods with gadolinium content was intended (in order to optimize fuel economy), therefore off-line and on-line VERONA reactor physics models had to be further modified, to be able to handle the new fuel according to the accuracy requirements. In the present paper first a brief overview of the system version (V6.0) commissioned after the first modernization step is outlined; then details of the modified off-line and on-line reactor physics calculations are described. Validation results for new modules are treated extensively, in order to illustrate the extent and complexity of the V&V procedure associated with the development and licensing of the new calculations running in version V6.22 of VERONA. Some details on the experience collected during the operation of the new reactor physics calculations are also discussed. Finally conceptual plans for the next system modification phase are outlined briefly; these changes are induced by the forthcoming introduction of 15 month long fuel cycles (instead of the present 12 month long cycles).

Because of the difficulties with experimental validation of power distribution predicted by macro-code on the pin by pin level we decided to prepare a calculation benchmark named "FULL-CORE" VVER-440. This benchmark is a two-dimensional (2D) calculation benchmark based on the VVER-440 reactor core cold state geometry with taking into account the geometry of explicit radial reflector. The main task of this benchmark is to test the pin by pin power distribution in fuel assemblies predicted by macro-codes that are used for neutron-physics calculations especially for VVER-440 reactors. The proposal of this benchmark was presented at the 21st Symposium of AER in 2011. The reference solution has been calculated by MCNP code using Monte Carlo method and the results have been published in the AER community. The results of reference calculation were presented at the 22nd Symposium of AER in 2012. In this paper we will compare the available macro-codes results of this calculation benchmark.

High-resolution gamma-spectrometry (HRGS) has been used for monitoring burn-up of VVER-440 spent fuel assemblies. The objective is to support burn-up calculations by an independent experimental method. Measurements were carried out using a collimator tube built into the concrete wall of the service pit in the reactor block at the Paks Nuclear Power Plant. Fuel assemblies were sunk down into the service pit, positioned in front of the collimator, and moved down and up under water by the refueling machine. The measured Cs-134/Cs-137 activity ratio is in good correlation with the calculated burn-up of the assemblies. Experimental results were simulated by model calculations and excellent agreement was found between calculation and measurement.

Abstract Measurement of rod efficiency is an important part of nuclear reactor safety. In case of operating power reactors it is usual to measure all rod efficiency at beginning of cycle hot zero power condition. Measurement of all rod efficiency is technically complicated because the measured “dynamic” reactivity cannot be compared directly to calculated “static” value of control rod efficiency. At Paks Nuclear Power Plant a new method was established to solve this problem. A static computer code used for reload safety analysis was extended to calculate core kinetics as well. Using the developed code the rod drop measurement itself is simulated and the time dependence of flux is determined. In addition, using Monte Carlo calculations weight functions are determined to describe the detector signal response to neutron flux changes in the reactor core. Using this combined system the detector signal itself can be simulated to the actual cycle and condition. Thus the measurement directly can be compared to simulation and the result can be evaluated. The method is under introduction to NPP Paks measurement practice and the first results – which are shown in the paper, are very promising.

The paper deals with two recently developed, high-precision nuclear measurement systems installed at the VVER-440 units of the Hungarian Paks NPP. Both developments were motivated by the reactor power increase to 108%, and by the planned plant service time extension. The first part describes the RMR start-up reactivity measurement system with advanced services. High-precision picoampere meters were installed at each reactor unit and measured ionization chamber current signals are handled by a portable computer providing data acquisition and online reactivity calculation service. Detailed offline evaluation and analysis of reactor start-up measurements can be performed on the portable unit, too. The second part of the paper describes a new reactor noise diagnostics system using state-of-the-art data acquisition hardware and signal processing methods. Details of the new reactor noise measurement evaluation software are also outlined. Noise diagnostics at Paks NPP is a standard tool for core anomaly detection and for long-term noise trend monitoring. Regular application of these systems is illustrated by real plant data, e.g., results of standard reactivity measurements during a reactor startup session are given. Noise applications are also illustrated by real plant measurements; results of core anomaly detection are presented.

In 2002 the Hungarian Paks NPP started a large-scale reconstruction project to upgrade its core monitoring system called VVER On-Line Analysis (VERONA). The main reason for the reconstruction decision was the planned reactor thermal power increase from 1375 MW to 1485 MW (108%), in order to achieve 500 MW electric power output. Considering safety margins and operation limits the basic approach was to keep all previously valid limits at 108%, as well. However, increased core power and a new type of fuel required a more accurate and more frequent core analysis; therefore modernization of the VERONA system was necessary and unavoidable. At this moment Unit 3 and Unit 4 are served by the new system. The reconstruction project is planned to be fully completed in 2008, when all Paks units will have a modernized core analysis system, providing state-of-the art services and operator support.The paper first presents a brief overview of the reconstruction process, and then main design principles and functions of the new VERONA system are outlined. Details of the new system architecture, hardware devices and software tools are also given, and then elements of the new human-machine interface are described and illustrated. A special emphasis is devoted to the new core analysis software with a detailed description of the validation methods and results. The process of reaching 108% power at Unit 4 is discussed; core behavior is illustrated by real data taken during the power increase procedure. Finally experience related to the development and operation of the new system is discussed briefly. (C) 2007 Elsevier B.V. All rights reserved.