Large Pressurized Water Reactor Research Articles

Predicting Model Biases of the APOLLO3 Neutronics Code Using Machine Learning: Toward a Multiscale and Multifidelity Approach

As part of the verification, validation, and uncertainty quantification process applied to neutronics deterministic codes, there is a requirement to expand the validation domain, especially to accommodate new third-generation reactors. The objective of the present work is to estimate the numerical biases arising from the several approximations used in deterministic codes and across different points in the phase space. Typically, this is accomplished by comparing the deterministic code to be validated with a Monte Carlo or stochastic reference code (without significant approximations). Since these reference calculations are computationally expensive, this paper proposes an alternative approach for predicting model biases of the APOLLO3® deterministic code for third-generation pressurized water reactors using machine learning algorithms. Three types of metamodels are employed (polynomial regression, kriging, and neural networks). Two scales are investigated, from a single assembly to a cluster of 3 × 3 assemblies [small two-dimensional (2-D) core], with model biases evaluated for APOLLO3 schemes with various levels of accuracy (lattice and core solvers, with high- to low-fidelity approaches). For the small 2-D core, numerical biases are observed for reactivity and power peak, representing both global and local quantities of interest. Throughout the study, the best results are achieved using kriging or neural networks, even if polynomial regression provides satisfactory predictions in some cases. The possibility of predicting biases for different quantities is also introduced. In conclusion, this paper discusses the prospects of extending the applicability of these metamodels to small and large third-generation pressurized water reactor cores, the idea being to potentially use these metamodels to support safety demonstrations for the new reactors in the long term.

Experimental analysis of boron dilution transient flow mixing characteristics based on planar laser induced fluorescence measurement

In Reactor Pressure Vessels (RPV), flow mixing between high and low concentration coolants will cause uneven distribution of boric acid. Severe cases will lead to boron dilution transient and re-criticality safe operation accident. Therefore, accurate measurement of coolant flow mixing characteristics and boron concentration distribution in RPV and study of the mechanism affecting the mixing process are of great significance to improve reactor operation safety. Based on the structural characteristics of large advanced pressurized water reactor pressure vessel, a large-scale visual experimental device was built by 1:6 scale modular design. Optical path correction scheme is used to solve the problem of optical path distortion existing in PLIF technology, and improved ratio calibration method is used to reduce the experimental error of concentration field distribution measurement. Flow mixing process and boron concentration field distribution in pressure vessel under single loop conditions were obtained based on plane laser induced fluorescence technique (PLIF). The influence of Reynolds number on boron diffusion behavior was studied. The experimental results show that during single loop operation, the localized eddy current formed in the left area of the lower head will result in a high concentration retention zone and a V-shaped boric acid concentration distribution in the core. With the increase of the ratio of cold tube flow to injection flow, the time when the high concentration coolant reaches the core hardly changes with the boric acid solution flow rate. The mixing diffusion behavior of boron concentration is the best when the ratio of injection to Reynolds number in the cold tube is at a certain value.

A neural-network based variable universe fuzzy control method for power and axial power distribution control of large pressurized water reactors

This paper proposes a neural network-based variable universe fuzzy controller (NN-VUFC) for power and axial power distribution control of large pressurized water reactors (PWRs). First, a two-node reactor kinetics model is introduced, and the fuzzy inference rules are formulated for the reactor power and axial power distribution control according to their deviations from corresponding setpoint values. Then, based on the idea of variable universe, the scaling factor of the input fuzzy universe is designed to maximize the utilization of fuzzy rules. Finally, a neural network is designed to optimize the proportionality coefficient of the scaling factor online to further improve the fuzzy control performance. Simulation results of the CPR1000 reactor under typical transient conditions show that the NN-VUFC can realize good control of both the reactor power and axial power distribution, and its control performance is effectively improved compared to traditional fuzzy controllers.

Study on Thermal Shock Failure Characteristics of RPV During IVR System Start-Up for Typical Advanced PWR

When the large pressurized water reactor in-vessel retention (IVR) system is put into operation, the outer wall of the reactor pressure vessel (RPV) will experience severe temperature fluctuations and be subjected to high internal pressure loads at the same time. In order to ensure the structural integrity of the RPV under such conditions, first, through the severe accident system program, the case that has the greatest impact on the pressure-bearing thermal shock of the outer wall of the reactor pressure vessel was selected under the station blackout (SBO) accident. Then, based on this case, the fracture mechanics finite element method was used to calculate and evaluate the pressure thermal shock (PTS) of the RPV, and the final crack size at the end of the life of the core barrel and the lower head was obtained by fatigue crack expansion calculation. The maximum ratio of the stress intensity factor correction value and corresponding limit value under the PTS transient load is about 0.874, which meets the requirements of RCC-M specification. The results of the study indicate that the RPV will not experience fracture failure when the IVR system is put into service during the station blackout accident for the HPR1000 nuclear power plant.

A boron-adjustment-free control strategy for large pressurized water reactors

This paper proposes an advanced boron-adjustment-free (BAF) control strategy for large pressurized water reactors (PWRs). The strategy combines the advantages of fast power compensation of the boron-adjustment Mode-G control strategy with the closed-loop axial offset (AO) control through control rods in the Mechanical Shim (MSHIM) control strategy. It can achieve fast power compensation, exact coolant average temperature control, and automatic AO control through three independently-moving control banks, respectively. Also, to avoid mutual interference between the core power and AO control, a novel blocking logic for the three control banks was developed. Simulation results of a large PWR implementing the BAF control strategy indicate satisfactory load-follow capabilities of the reactor without the need to adjust boron concentration. Moreover, the proposed blocking logic can provide better AO control without compromising reactor power control than that referring the blocking logic of reactor power and AO control banks in the MSHIM control strategy.

Bifurcation Analysis of Xenon Oscillations in Large Pressurized Heavy Water Reactors with Spatial Control

Large nuclear reactors operating in the thermal spectrum are prone to both global and regional oscillations in power due to variation of 135Xe concentration. These power oscillations are self-stabilizing up to a certain operating power level, beyond which spatial power control becomes necessary for suppressing these oscillations. Especially for large pressurized heavy water reactors (PHWRs), which are natural uranium–fueled reactors using heavy water as coolant and moderator, the modes of xenon instabilities decide the extent and scheme for spatial power control. In this paper, the effect of spatial control on the bifurcation characteristics is demonstrated using a two-region model. The error signal for movement of the reactivity device has a global component for bulk power control and a local component for regional power control. The amount of regional power control determines the power level at which the spatial xenon oscillations stabilize. Using bifurcation analysis, it is found that in case of limited regional control, both supercritical and subcritical Hopf bifurcations exist, whereas in the case of increased regional control only supercritical Hopf bifurcations exist. However, these supercritical Hopf oscillations are due to time lag in control and have short timescales and lower amplitudes as compared to xenon oscillations. Hence, a proper choice of spatial control enables a PHWR to operate at rated full power capacity without any spatial Xenon instability.

A neural network predictive control method for power control of small pressurized water reactors

Compared with large pressurized water reactors (PWRs), small PWRs have flexible operating conditions and complex operating environment, putting forward higher requirements on the power control system. Considering the low model identification accuracy of the widely-used model predictive control algorithm in reactor control, a neural network predictive (NNP) power control method is proposed for small PWRs in this paper. The local models under five typical operating conditions are weighted by a multi-model method to establish a core multi-model system, based on which a global NNP power control system is designed. The neural network is used to identify the core model first, and then a performance criterion function is optimized to determine the optimal control input to the reactor core. Simulation results of a small PWR core under typical transient conditions demonstrate the good load-following performance and strong anti-interference capability of the proposed NNP power control method for small PWRs.

Capital cost estimation for advanced nuclear power plants

The first-of-a-kind (FOAK) nuclear plants built in the last 20 years are 2X over budget and schedule in the US and some European countries. One of the nuclear industry's proposed remedies is the small modular reactor (SMR). SMR designs leverage five factors to be more economically competitive than large reactors: 1) multiple units; 2) increased factory production and learning; 3) reduced construction schedules; 4) plant design simplification and 5) unit timing. There are currently no bottom-up studies that quantitatively account for these factors and compare different near-term light water reactor SMRs with Gen III + large plants. This work presents a nuclear plant cost estimating methodology using a detailed bottom-up approach for over 200 structures, systems, and components. The results compare relative costs for two large pressurized water reactors, one with active safety and one with passive safety, to two SMR designs, one with multiple reactor power modules and one with a single reactor module. Passive safety systems showed noticeable savings at both the large and small-scale reactors. The power uprating of an SMR by 20% resulted in ∼15% savings in the overnight unit capital cost. Overall, if built by an inexperienced vendor and work force, the two SMRs' overnight costs were higher than large reactors, since significant on-site labor still remains while losing economy of scale. However, the single-unit SMR had significantly less total person-hours of onsite labor, and if built by an experienced workforce, it could avoid cost-overrun risks associated with megaprojects.

Uncertainty and Sensitivity Analysis of the In-Vessel Hydrogen Generation for Gen-III PWR and Phebus FPT-1 with MELCOR 2.2

In this study, uncertainty and sensitivity analyses were performed with MELCOR 2.2.18 to study the hydrogen generation (figure-of-merit (FoM)) during the in-vessel phase of a severe accident in a light water reactor. The focus of this work was laid on a large generation-III pressurized water reactor (PWR) and a double-ended hot leg (HL) large break loss of coolant accident (LB-LOCA) without a safety injection (SI). The FPT-1 Phebus integral experiment emulating LOCA was studied, where the experiment outcomes were applied for the plant scale modelling. The best estimate calculations were supplemented with an uncertainty analysis (UA) based on 400 input-decks and Latin hypercube sampling (LHS). Additionally, the sensitivity analysis (SA) utilizing the linear regression and linear and rank correlation coefficients was performed. The study was prepared with a new open-source MELCOR sensitivity and uncertainty tool (MelSUA), which was supplemented with this work. The FPT-1 best-estimate model results were within the 10% experimental uncertainty band for the final FoM. It was shown that the hydrogen generation uncertainties in PWR were similar to the FPT-1, with the 95% percentile being covered inside a ~50% band and the 50% percentile inside a ~25% band around the FoM median. Two different power profiles for PWR were compared, indicating its impact on the uncertainty but also on the sensitivity results. Despite a similar setup, different uncertainty parameters impacted FoM, showing the difference between scales but also a significant impact of boundary conditions on the sensitivity analysis.

Bifurcation Analysis of Spatial Xenon Oscillations in Large Pressurized Heavy Water Reactors Using Multipoint Reactor Kinetics with Thermal-Hydraulic Feedback

Conventionally, the stability of xenon oscillations is estimated by solution of the time-dependent neutron diffusion equation, coupled with iodine and xenon equations, by finding out the damping ratios in each case. This is performed for different initial perturbations and core burnup conditions and is a very time-consuming and tedious process. Some earlier studies include linear stability estimation, which is valid for small perturbations, but not much work has been done in nonlinear stability analysis for spatial xenon oscillations in particular. In this paper, an approach for carrying out bifurcation analysis of xenon oscillations in large pressurized heavy water reactors (PHWRs) is demonstrated using reduced-order models. The reduced-order model for studying spatial xenon oscillations consists of multipoint kinetic equations coupled with xenon and iodine equations along with explicit fuel and coolant temperature feedback. Both subcritical Hopf bifurcation and supercritical Hopf bifurcation in different parameter planes exist, which leads to unstable limit cycles in the linearly stable region (subcritical Hopf bifurcation) and stable limit cycles in the linearly unstable region (supercritical Hopf bifurcation). The stability map provides a total picture of the stability of the out-of-phase oscillations in a PHWR. Depending on the value of the fuel temperature coefficient of reactivity and coolant temperature coefficient of reactivity, one can determine the operating power level above which the out-of-phase xenon oscillations start to grow. This model can be used to analyze nonlinear stability characteristics without spatial power control, which is helpful in identification of stable/unstable regimes in different parameter spaces and is likely to aid in reactor design.

Numerical Investigation of Water Film Evaporation with the Countercurrent Air in the Asymmetric Heating Rectangular Channel for Passive Containment Cooling System

Passive containment cooling system (PCCS) is an important passive safety facility in the large advanced pressurized water reactor. Using the physical laws, such as gravity and buoyancy, the water film/air countercurrent flow is formed in the external annular channel to keep inside temperature and pressure below the maximum design values. Due to the large curvature radius of the annular channel, one of the short arc segments is taken out, as a rectangular channel, to analyze the main water film evaporation heat transfer characteristics. Two numerical methods are used to predict the water film evaporative mass flow rate during the heat transfer process in the large-scale rectangular channel with asymmetric heating when the water film temperature is not saturated. At the same time, these numerical simulation results are validated by the experiment which is set up to study water film/air countercurrent flow heat transfer on a vertical back heating plate with 5 m in length and 1.2 m in width. It is shown that the maximum deviation between numerical simulation and experiment is 30%. In addition, the influences on these parameters, such as heat flux, evaporative mass flow rate, and water film thickness, are evaluated under the different tilted angles of the rectangular channel and horizontal plane, water/air inlet flow rates, water/air inlet temperatures, heating surface temperatures, and air inlet relative humidities. All these results can provide a good guidance for the design of PCCS in the future.

Making Construction Cost Estimate of Nuclear Power Plants Credible: Assessing Impact of Unknown Unknowns

Credibility requires predictability. Nuclear power plant (NPP) construction projects tend to be large and expensive, sometimes with high cost overruns far beyond those that might have been expected or predicted due to usual and recognized uncertainties and variations (e.g., in labor and materials costs combined with multiyear duration and complex construction logistics). This unaccounted for uncertainty brings the credibility of new NPP build projects into question and may prevent future projects from going forward. It is believed that the high initial capital cost of nuclear power is less of a hindering factor than the uncertainty about that cost. For nuclear power to regain credibility and enable future NPP construction projects, this unexpected uncertainty, or unknown unknown, needs to be assessed. Regular (expected) uncertainties (known unknowns) were addressed previously in a paper where the Iman-Conover method was used to account for correlated uncertainties. This paper addresses the impact of unexpected events (unknown unknowns), such as the Three Mile Island Unit 2 (TMI-2) accident. For this purpose, NPP construction in the United States is divided into two periods: pre-1979 (NPPs completed before the 1979 TMI-2 accident), and post-1979 (NPPs under construction when the accident happened and completed later). The latter group experienced significant schedule and budget overruns due to the change in regulation imposed after NPP construction was already under way. Analyzed a posteriori, this event and the escalated cost for the second group of NPPs was used to study the impact of a representative unexpected event. An approach was developed to assess the range of potential risks, including those due to such unexpected events, and thus enable assigning appropriate contingencies. A traditional large four-loop pressurized water reactor [PWR12-Better Experience (BE)] was considered. With the inputs derived from the pre-1979 data, the expected total capital investment cost (TCIC) mean value for the PWR12-BE is found to be $3.3 billion, with a contingency of $1.3 billion, which corresponds to 39.4% of the TCIC mean. If the unknown unknowns are taken into account based on the post-1979 data, the TCIC mean value increases to $9.4 billion, with a cost contingency that is 108% of the TCIC mean derived for the pre-1979 NPPs. Based on the experience-based assumed probability of unexpected events with large financial impact, it is then possible to derive an adequate contingency. The presented analysis offers a possible approach to treat unknown unknowns and to assess their impact on cost, providing the required contingency, as well as uncertainty in the construction time. In a broader context, this may provide quantitative tools to support making long-term energy policy decisions of new considered nuclear power projects.

Experimental and Numerical Investigation of Temperature Distribution on Reactor Pressure Vessel Support under Operating Conditions

Reactor pressure vessel (RPV) support is a key safety facility which is categorized as Class 1 in the ASME nuclear safety design. The temperature distribution of RPV support is one of the key considerations for the concrete safety contacting with the bottom of the support. So it is necessary for accurate evaluation on the temperature field characteristics of RPV support, especially the bottom of support. This paper investigates the temperature field characteristics of modified RPV support which will be applied to a large advanced pressurized water reactor. A support entity is manufactured in a ratio of 1:1, and its temperature distribution is measured under simulated reactor operating conditions. Numerical simulation is also used to validate the results by the developed CFD model. The results show that under the operating conditions, of which the inlet cooling air temperature is 35.35°C and the velocity is 6.25 m/s, the temperature distribution of modified RPV support bottom is uneven, and the highest temperature is around 38°C, which is much lower than the demanding design temperature 93.3°C. Therefore, the design of the modified RPV support is reliable. In addition, the results of numerical simulation agree well with the experimental results with the error less than ±4°C, which ensures the reliability of the conclusion. The effects of inlet cooling air temperature and velocity on the RPV support temperature distribution are further studied. Both the temperature decrease and velocity increase can reduce the RPV support temperature. But the effect of inlet cooling air temperature is more obvious than inlet cooling air velocity. So the best way to improve air cooling capacity is to decrease the support inlet cooling air temperature. The results can provide a good guidance to the design of RPV support for the subsequent large advanced pressurized water reactor.

Automatic generation control for the flexible operation of multimodular high temperature gas-cooled reactor plants

To balance the intermittent renewable energy (IRE) and to realize its deep penetration, it is necessary for nuclear power plants (NPPs) to operate with enough flexibility. This necessity leads to the concerned questions such as which types of nuclear reactors are suitable for flexible operation and how to realize the operational flexibility of NPPs. In this paper, based on literature review and related analysis, it is shown that the modular high temperature gas-cooled reactor (MHTGR) is suitable for balancing IRE because of the advanced features such as robust fuel elements, online fuel handling, low power density and full-power-range temperature negative feedback effect. Due to the low power density, the power rating of a single MHTGR is lower than those large commercial pressurized water reactors (PWRs). To balance IRE by MHTGRs in a scalable manner, it is recommended to develop NPPs with high rated power based on multimodular scheme, i.e. multiple MHTGR-based nuclear steam supply system (NSSS) modules providing superheated steam for a common turbine. Further, to realize the flexible operation of MHTGR for deep IRE penetration, the automatic generation control (AGC) of multimodular MHTGR plants should be developed. In this paper, two AGC methods including both the adaptive AGC and extended-state-observer (ESO) based AGC are proposed, where the former one has a simple proportional-integral (PI) structure, and the latter one has an additional feedforward compensating action determined by the ESO. The corresponding control system of multimodular MHTGR plants is also designed, which is composed of the units of NSSS control, multimodular coordination control, turbine speed governor (TSG) and AGC. The AGC methods as well as the plant control system design with AGC function are then applied to two modular MHTGR plant HTR-PM. Numerical simulation results show that the newly-built multimodular control system can well stabilize the grid frequency by properly performing the power-level maneuver and maintenance of NSSS modules, and also show that the ESO-based AGC has a better frequency stabilization performance than the adaptive AGC does.

Generalized Partitioned Matrix Acceleration for Variational Nodal Diffusion Method

The Generalized Partitioned Matrix (GPM) acceleration method for the Variational Nodal Method (VNM) with diffusion approximation is presented. In the GPM method, the vectors of expansion coefficients of the scalar flux, source, and partial currents are divided into low-order and high-order terms. For each outer iteration, the low-order terms of the flux, fission source, and partial currents are first solved with fixed higher-order terms from the preceding outer iteration, and then a full matrix sweep through the energy groups is performed to update the full set of expansion coefficients. The GPM method increases the CPU time per outer iteration but reduces the overall computational time significantly by reducing the number of outer iterations required for convergence. The GPM acceleration method has been implemented in the NODAL code, and its performance was compared with that of the traditional Partitioned Matrix (PM) acceleration scheme for four problems: two- and three-dimensional C5G7 problems, a NuScale modular core problem, and a large pressurized water reactor problem. The numerical results show that the PM acceleration consistently reduces the computational time by a factor of 2.0 and the GPM acceleration yields two to three times higher speedup than with PM acceleration by reducing the number of outer iterations. The GPM speedups over the unaccelerated VNM range between 4.3 and 6.3. Moreover, the speedup ratio achieved with the GPM acceleration increases with an increasing dominance ratio of the problem since the required number of outer iterations increases with an increasing dominance ratio.

New monitoring procedure of axial xenon oscillation in large pressurized water reactors

Xenon oscillation is caused by imbalance of xenon distribution in nuclear reactors. Procedures have been developed in the past to dampen these oscillations. One of the procedures is known as quite simple and effective, which uses several constants obtained from reactor modeling codes in the analysis of xenon oscillations (not from actual data of the plant). This causes uncertainties in the solutions obtained and the need for an improved approach becomes apparent. This paper discusses a new methodology that allows the utilization of actual reactor data in the procedure’s analysis to dampen xenon oscillations. Moreover, it has been shown that only two constants are needed to fully express the xenon oscillation behavior.

Implication of LOCA characteristics of large PWR and SMR for future development of intelligent nuclear power plant control system

Operation with reduced number of operators is considered as an important operational mode to improve economics of a nuclear power plant (NPP) in the future and it will be more important for the small modular reactors (SMRs). To control NPPs efficiently and safely with a reduced number of operators, an intelligent operation system can be very useful. However, reduced number of operators will result in larger consequence in human error due to simultaneous multi-unit failures are now more probable than the conventional operational mode. Thus, to decrease the probability of human error occurrence for the reduced number of operators, the development of an autonomous operation system with certain level of intelligence is inevitable. The prediction capability of system’s behavior as well as understanding the root cause for the current situation should be an essential function of the designed autonomous operation system. The authors propose to use the current system thermal–hydraulic (STH) analysis code platform to develop such intelligence. As a demonstration of the suggested method, the authors used the STH code to track the accident initiator of both large pressurized water reactor (PWR) and SMR. The discussions on how this method can be useful for future NPP operation and how generic differences in system design actually influence the system behavior are presented.

Use of Dynamic Event Trees and Deep Learning for Real-Time Emergency Planning in Power Plant Operation

An initiating event that disrupts regular nuclear power plant (NPP) operation can result in a variety of different scenarios as time progresses depending on the response of standby safety systems and operator actions to bring the plant to a safe, stable state, or the uncertainties in accident phenomenology. Depending on the severity of the accident and potential magnitude of release of radioactive material into the environment, off-site emergency response such as evacuation may be warranted. An approach that could be used for real-time emergency guidance to support the declaration of a site emergency and to guide off-site response is presented using observable plant data in the early stages of a severe accident. The approach is based on the simulation of the possible NPP behavior following an initiating event and projects the likelihood of different levels of off-site release of radionuclides from the plant using deep learning (DL) techniques. Training of the DL process is accomplished using results of a large number of scenarios generated with the Analysis of Dynamic Accident Progression Trees/MELCOR/Radiological Assessment System for Consequence Analysis (RASCAL) computer codes to simulate the variety of possible consequences following a station blackout event (similar to the Fukushima accident) for a large pressurized water reactor. The ability of the model to predict the likelihood of different levels of consequences is assessed using a separate test set of MELCOR/RASCAL calculations.

Architectural model driven dependability analysis of computer based safety system in nuclear power plant

Abstract The most important non-functional requirements for dependability of any Embedded Real-Time Safety Systems are safety, availability and reliability requirements. System architecture plays the primary role in achieving these requirements. Compliance with these non-functional requirements should be ensured early in the development cycle with appropriate considerations during architectural design. In this paper, we present an application of system architecture modeling for quantitative assessment of system dependability. We use probabilistic model checker (PRISM), for dependability analysis of the DTMC model derived from system architecture model. In general, the model checking techniques do not scale well for analyzing large systems, because of prohibitively large state space. It limits the use of model checking techniques in analyzing the systems of practical interest. We propose abstraction based compositional analysis methodology to circumvent this limitation. The effectiveness of the proposed methodology has been demonstrated using the case study involving the dependability analysis of safety system of a large Pressurized Water Reactor (PWR).

The RAPID Fission Matrix Approach to Reactor Core Criticality Calculations

The Real-time Analysis for Particle transport and In-situ Detection (RAPID) code uses a unique, extremely fast, fission matrix–based methodology to compute the eigenvalue, and three-dimensional, pinwise fission source distribution for reactor, spent fuel pool, and spent fuel cask problems. In this paper, the RAPID fission matrix method is described and analyzed for application to several large pressurized water reactor problems, based on the Organisation for Economic Co-operation and Development/Nuclear Energy Agency Monte Carlo Performance Benchmark problem. In the RAPID methodology, fission matrix coefficients precalculated using the Serpent Monte Carlo code, are then coupled together and solved for different core arrangements. A boundary correction method is used to obtain more accurate fission matrix values near the radial and axial reflectors. Eigenvalues and fission source distributions are compared between RAPID and Serpent reference calculations. In most cases, the eigenvalue differences between methods are less than 10 pcm. For a uniform core model, pinwise fission distributions between the methods differ by a root-mean-square value of , compared to a Serpent uncertainty of . The pinwise, axially dependent (100 axial levels) differences are , compared to a similar Serpent uncertainty of . To achieve these levels of uncertainty, the RAPID calculations are over 2500 times faster than Serpent, not counting the precalculation time.