Dynamics and Control of Nuclear Reactors

Thomas W. Kerlin, Belle R. Upadhyaya

• Publisher: Academic Press
• Year: 2019
• Print ISBN: 9780128152614
• eBook ISBN: 9780128152621
• Topic: Technology & Engineering
• Subtopic: Energy Industry
• Index: Technology & Engineering

Dynamics and Control of Nuclear Reactors presents the latest knowledge and research in reactor dynamics, control and instrumentation; important factors in ensuring the safe and economic operation of nuclear power plants. This book provides current and future engineers with a single resource containing all relevant information, including detailed treatments on the modeling, simulation, operational features and dynamic characteristics of pressurized light-water reactors, boiling light-water reactors, pressurized heavy-water reactors and molten-salt reactors. It also provides pertinent, but less detailed information on small modular reactors, sodium fast reactors, and gas-cooled reactors.- Provides case studies and examples to demonstrate learning through problem solving, including an analysis of accidents at Three Mile Island, Chernobyl and Fukushima Daiichi- Includes MATLAB codes to enable the reader to apply the knowledge gained to their own projects and research- Features examples and problems that illustrate the principles of dynamic analysis as well as the mathematical tools necessary to understand and apply the analysis Publishers Note: Table 3.1 has been revised and will be included in future printings of the book with the following data: Group Decay Constant, li (sec-1) Delayed Neutron Fraction (bi) 1 0.0124 0.000221 2 0.0305 0.001467 3 0.111 0.001313 4 0.301 0.002647 5 1.14 0.000771 6 3.01 0.000281 Total delayed neutron fraction: 0.0067

Chapter 1

Introduction

Abstract

This book addresses the approaches for the analysis of dynamic systems and control design. In addition to the discussion of current reactor systems, an overview of next generation nuclear plants (NGNP), small modular reactors (SMR), and instrumentation systems are presented. Treatments of individual topics progress from introductory to advanced levels. For use in undergraduate engineering courses, the coverage may be limited to the simpler and less rigorous portions that appear in the first part of pertinent chapters. Several chapters are totally devoted to introductory topics and some to advanced topics. Appendices are included to provide details of subjects whose inclusion in the text would interrupt the flow of information needed for a student's learning. The appendices are an integral part of the book.

Sample problems are solved in the text and many exercises are provided for students to solve. Some problems require computer solutions, including student-prepared computer codes.

Keywords

Nuclear reactor dynamics; Reactor control; Plant dynamics simulation; Next generation nuclear plant (NGNP); Small modular reactor (SMR); International Atomic Energy Agency (IAEA)

1.1 Introduction

The power level of a nuclear reactor at any time is expected to be as desired by the plant operator. These plants undergo transients that are induced by operator actions, by actions initiated by an automatic control system, or by a component failure. Designers and operators must understand the transient behavior in order to achieve desired operation and safety.

The first step is to understand the transient operation of a reactor that operates at a low power level, so low that there are negligible increases in temperature because of fission heating. Such a reactor is usually called a zero-power reactor. The power is not actually zero, but is so low that significant heating does not occur, and temperature related feedback effects are negligible. Many research reactors are zero-power reactors.

A power reactor, on the other hand, operates at power levels high enough to cause major temperature increases. The temperatures of reactor components change along with reactor power during transients and these temperature changes, in turn, affect reactor power (a feedback loop). Also, power reactors that contain a compressible fluid undergo pressure changes during a transient. These pressure changes also affect reactor power (another feedback loop).

Transients are usually accompanied by control actions. Control systems monitor selected plant parameters (such as power, temperature, pressure, flow rate) and change appropriate controllable actions (such as control rods and valve positions).

Creating a set of mathematical equations and parameters (coefficients) in those equations to be used to analyze reactor transients is called modeling. Creating a solution to those equations is called system simulation.

Nuclear reactor simulations generally have one of three purposes: obtaining a basic understanding of reactor behavior during transients, analysis of transients during normal maneuvering and response during accident conditions, and operator training. Each of these functions has different requirements for the level of detail in the model.

Reactor simulation efforts started in the early days of reactor operation. Early simulation involved hand calculations and rudimentary calculators. Shortly thereafter, reactor simulation turned to computers for implementation, and simulation technology matured as the capabilities of computer technology evolved. Analog computers were used extensively in early simulations. These computers used electrical circuits to mimic reactor operation. Next came hybrid computers. They used digital computations along with analog components. The digital components handled computations that were not possible or practical with analog components. As digital computers became more powerful and faster, they came to dominate reactor simulation activities.

Computer simulations may be performed on personal computers for some applications. Some solve model equations and provide numerical and/or graphical results. Other, more sophisticated personal computer simulations provide screen displays that mimic actual reactor control room displays.

Simulators for operator training include full-scope simulators that duplicate the control room for the reactor being simulated. The displays provide computed results for all of the variables monitored in the actual plant and include capability for simulating all operator actions.

Reactor accident analyses involve very detailed models that are implemented on large, high-performance computers. Simulations deal with large disturbances with potentially large consequences. Analyses include major accident scenarios such as loss of coolant and control rod ejection.

This book addresses modeling and simulation of nuclear reactors, both zero-power reactors and power reactors. Modeling options include a wide range of possibilities, each with very different levels of complexity. Modeling and simulation is not a “do it and be finished” activity. Reactor constituents change continuously during operation and immediately at restart after refueling. These changes cause changes in the quantities that determine the reactor's dynamic behavior. So, there is no such thing as model or simulation that defines the reactor at all times. Furthermore, even trying to evaluate the parameters needed in a model is complicated by the need to know neutronic and heat transfer properties that depend on position in the core and the burnup history of the fuel and are difficult to evaluate. The importance of simulation is to provide a way to understand what goes on in a reactor and why it happens rather than a precise determination of reactor dynamic response behavior for a specific disturbance on a specific day.

There is very little in the book that requires detailed knowledge of reactor physics, but familiarity with reactor physics at least at the introductory level is helpful.

1.2 System dynamics and control design

Power generating units (such as a nuclear power plants, fossil-fueled power plants, etc.) and large industrial facilities are complex systems. The design of these systems requires extensive analysis that uses dynamic models and simulation of their operation under various conditions. Because of mathematical methods developed over the past two centuries and computer capability developed since the 1950s, powerful techniques exist for analysis of dynamic systems and for design of control systems. It is now possible to predict the way a system will respond to external disturbances and to develop a control strategy that will cause the system to perform as desired. The ability to describe the system dynamics using a variety of models is crucial to achieve a good engineering design. The control or regulation of a power plant requires critical measurements of process parameters (and neutron power measurements in a nuclear power plant). As a result, a typical large nuclear plant employs a few thousand measurements. These are used by control systems, plant safety (protection) systems, and by monitoring systems. Thus, instrumentation and control play a critical role in safe and reliable operation of commercial nuclear power plants.

Dynamic performance is an important issue in many industrial systems. The key issues in dynamic system performance are the following:

• • Can the system be moved from one desired value (set point) to another in an acceptable manner? That is, without deviating from limits of variation and within an acceptable time interval.
• • Can the system respond in a stable manner without exceeding safety limits when subjected to unplanned disturbances (possibly due to an accident, an external disturbance, failure of a component, or human error)?

The latest development to enhance the power and usefulness of digital simulation is modular modeling software. Modular modeling software provides a menu of models of commonly encountered systems (reactor kinetics, fuel-to-coolant heat transfer, hot and cold leg volumes, steam generators, feed water heaters, pressurizers, steam turbine, condenser, moisture separators, steam reheaters, pumps, valves, etc., including their control modules) and an automated means for linking them together and running simulations. Because the model for each component is used in many different analyses, great effort by highly qualified experts to develop and check the software is warranted.

Several vendors market new simulation and control design software systems. The International Atomic Energy Agency (IAEA) also provides simulators for most types of power reactors to qualified organizations in member countries. These are used quite extensively for training in industry and universities. Ref. [1] provides the procedure for requesting IAEA simulation software. Recommendation by the IAEA representative for the country of the requester is required.

In this book, we emphasize the use of the software system MATLAB and its Toolboxes. A companion system called Simulink is used for the simulation of large processes, such as a nuclear power plant. These software systems are designed for implementation in personal computers (PCs) and (larger) mainframe computers. The MATLAB, Simulink, and the toolboxes are comprehensive collections of functions (software modules) and are developed and marketed by The MathWorks, Inc.

We recommend strongly that the students familiarize themselves with MATLAB, Simulink and the associated Toolboxes [2, 3]. ‘MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment. The name, MATLAB, stands for matrix laboratory’[4]. An open source simulation platform based on the Modelica modeling language is a popular resource for system modeling and simulation [5].

This book addresses the approaches for the analysis of dynamic systems and control system design. In addition to the discussion of current reactor systems, an overview of next generation nuclear plants (NGNP), small modular reactors (SMR), and instrumentation systems are presented. Treatments of individual topics progress from introductory to advanced levels. For use in undergraduate engineering courses, the coverage may be limited to the simpler and less rigorous portions that appear in pertinent chapters. Several chapters are totally devoted to introductory topics and some to advanced topics. Appendices are included to provide details of subjects whose inclusion in the text would interrupt the flow of information needed for a student's learning. The appendices are an integral part of the book and the reader is encouraged to review the material.

Sample problems are solved in the text and exercises are provided for students to solve. Some problems require computer solutions, including student-prepared computer codes.

Exercises

1. 1.1. Go to the IAEA web site (see Ref. [1]), determine all of the reactors for which simulation software is available, and document your review

References

[1] International Atomic Energy Agency: Website: https://www.iaea.org/topics/nuclear-power-reactors/nuclear-reactor-simulators-for-education-and-training/, Email: [email protected].

[2] Klee H. Simulation of Dynamic Systems with MATLAB and Simulink. Boca Raton, FL: CRC Press; 2007.

[3] MATLAB and Simulink User Guides, The MathWorks, Inc., Natick, MA.

[4] Moler C. The Origins of MATLAB. ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Acknowledgments
• Chapter 1: Introduction
• Chapter 2: Nuclear reactor designs
• Chapter 3: The point reactor kinetics equations
• Chapter 4: Solutions of the point reactor kinetics equations and interpretation
• Chapter 5: Subcritical operation
• Chapter 6: Fission product poisoning
• Chapter 7: Reactivity feedbacks
• Chapter 8: Reactor control
• Chapter 9: Space-time kinetics
• Chapter 10: Reactor thermal-hydraulics
• Chapter 11: Nuclear reactor safety
• Chapter 12: Pressurized water reactors
• Chapter 13: Boiling water reactors
• Chapter 14: Pressurized heavy water reactors
• Chapter 15: Nuclear plant simulators
• Chapter 16: Nuclear plant instrumentation
• Appendix A: Generation II reactor parameters
• Appendix B: Advanced reactors
• Appendix C: Basic reactor physics
• Appendix D: Laplace transforms and transfer functions
• Appendix E: Frequency response analysis of linear systems
• Appendix F: State variable models and transient analysis
• Appendix G: Matlab and Simulink: A brief tutorial
• Appendix H: Analytical solution of the point reactor kinetics equations and the prompt jump approximation
• Appendix I: A moving boundary model
• Appendix J: Modeling and simulation of a pressurized water reactor
• Appendix K: Modeling and simulation of a molten salt reactor
• Index