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Understanding time-dependent behaviors of nuclear reactors and the methods of their control is essential to the operation and safety of nuclear power plants. This book provides graduate students, researchers, and engineers in nuclear engineering comprehensive information on both the fundamental theory of nuclear reactor kinetics and control and the state-of-the-art practice in actual plants, as well as the idea of how to bridge the two. The first part focuses on understanding fundamental nuclear kinetics. It introduces delayed neutrons, fission chain reactions, point kinetics theory, reactivity feedbacks, and related measurement techniques. The second part helps readers to grasp the theories and practice of nuclear power plant control. It introduces control theory, nuclear reactor stability, and the operation and control of existing nuclear power plants such as a typical pressurized water reactor, a typical boiling water reactor, the prototype fast breeder reactor Monju, and the high-temperature gas-cooled test reactor (HTTR). Wherever possible, the design and operation data for these plants are provided.



Erratum: Nuclear Reactor Kinetics and Plant Control

Without Abstract
Yoshiaki Oka, Katsuo Suzuki

Nuclear Reactor Kinetics


Chapter 1. Delayed Neutron and Nuclear Reactor Kinetics

Introduction Reactor power changes when the temperature and position of the control rods of a nuclear reactor are changed. This change is unique to each reactor, and its characteristics are called “nuclear reactor kinetics.”
The control rods are made of strong neutron-absorbing materials, and when they are inserted into the reactor, the reaction rate of neutron absorption increases. The reactor becomes subcritical and its power decreases. Conversely, the reaction rate of neutron absorption decreases when the control rods are withdrawn; the reactor becomes supercritical and its power increases. The reaction rate of neutron absorption changes when the reactor temperature is changed and, therefore the reactor power changes.
The reactor power is proportional to the number of fission reactions per second in the nuclear reactor. As fission reactions are caused by neutrons, the number of their reactions is proportional to the total number of neutrons in the reactor. However, the number of neutrons varies depending on the neutron production rate due to the fission reactions, the rate of neutron absorption by the nuclear fuel and reactor structure materials, and the rate of neutron leakage from the reactor.
Yoshiaki Oka

Chapter 2. Point Reactor Kinetics

To describe the reactor kinetics, the number of neutrons and the number of delayed neutron precursors that change with time are considered. The following ordinary differential equations can be gotten if the space dependence of these variables is ignored and the neutron energy is handled in one group. This is called the point reactor kinetics model. Actually, the reactor is not treated as a single point but the assumption is made that the space distribution of parameters does not change with time. When a slow disturbance is treated in spatial asymmetry, the point reactor kinetics model can be used by weighting the reactivity feedback amount determined with the importance function. Generally, the point reactor approximation can be used to approximate a slow change of the space distribution of parameters. It can be applied to many transient events that contain the disturbance to be handled by reactor control. In contrast, when handling a local and fast (that is, approximately 0.1 s or less) reactivity disturbance, the space-dependent kinetics model must be used. An example is the accident that may occur if asymmetric control rods are quickly withdrawn.
Yoshiaki Oka

Chapter 3. Temperature Effect of Reactivity

In Chap. 2, it was assumed that effective multiplication coefficient k eff and reactivity ρ do not depend on reactor power n, and the point reactor kinetics equations were solved. Their solutions are applicable to the reactor having almost zero power or zero number of neutrons. It is called the “zero-power reactor” and its reactor temperature does not change. In the actual reactor, however, when its number of neutrons numbers (or its power) changes, the temperature of the reactor changes and therefore, the k eff and ρ values change. These changes affect reactor power. This reactivity change is called the temperature effect of reactivity. The reactivity changes with reactor temperature and moderator density, etc. The reactor power changes with the reactivity. Therefore, this reactor power change is called the reactivity feedback effect.
Yoshiaki Oka

Chapter 4. Kinetics Parameters and Reactivity Measurement Experiments

Introduction To analyze reactor kinetics, we need to know the kinetics parameters of the reactor. Also, we build the reactor, operate it in the critical state, and determine the reactivity of each control rod. This chapter explains the primary steps of these operations.
Yoshiaki Oka

Actual Nuclear Reactor Plant Control


Chapter 5. Control System Basics and PID Control

The first automatic control system is said to be the governor (a speed regulator) for the steam engine, invented by James Watt. The speed regulator enabled the steam engine to be used as a practical power source, starting the industrial revolution. “Control” is defined as “adding required operation to an object so that it can be adapted for a certain purpose” (JIS automatic control terms). Control can be divided into two main categories: automatic and manual. Automatic control is divided into feedback control, feed-forward control, sequential control, and others. Automatic control can be implemented by control systems among which single-variable control systems (single-input, single-output systems) are one type.
Katsuo Suzuki

Chapter 6. Reactor Stability Study

Usually, the one-point core dynamic approximation model can be expressed by the following equation system
Katsuo Suzuki, Hiroshi Ono, Shuhei Miyake

Chapter 7. Actual Operation Control of Boiling Water Reactor

The boiling water reactor (BWR) is divided into two main systems: the nuclear steam supply system (NSSS) that generates steam, and the turbine system (or turbine island) that uses the stream to rotate turbo-generator and generate electric power. The NSSS consists of various subsystems and equipments. They include basically the reactor pressure vessel that houses fuel, control rods, and other nuclear reactor equipments, a reactor auxiliary system that handles circulation of coolant, generated steam, and feed water returned from turbines, the engineered safety features that are required for securing safety, and a reactor auxiliary system that is required for operating the plant. The fuel handling and storage equipment, the instrumentation and control system, and the electrical system, as well as the radioactive waste treatment system that is unique to nuclear power station are also included in the NSSS. The turbine system consists mainly of turbines, generators, the condenser that condenses steam, the feed-water system that resupplies the reactor with the condensate. Figure 7.1 shows the overview configuration of BWR systems.
Koichi Kondo, Yasuo Ota, Hiroshi Ono, Masahiko Kuroki, Yuji Koshi, Masayoshi Tahira

Chapter 8. Actual Operation and Control of Pressurized Water Reactor

The operation control of a power plant maintains or changes the generator power or the volume of electricity supplied steadily to the grid system as appropriate. Various types of automatic control systems are installed to maintain the processing volume of the plant equipment stably within an appropriate range when the power plant is operated under operation control. The pressurized water reactor (PWR) has automatic control systems built for the reactor and turbine systems separately because the primary and secondary coolants of the reactor and turbine systems are separated from each other by the steam generator.
Shuhei Miyake, Toshihide Inoue, Satoshi Hanada

Chapter 9. Actual Operation and Control of Fast Reactor

A fast breeder reactor has several features that make it different from a light water reactor. The fuel is plutonium and uranium-mixed oxide, the reactor core enables breeding mainly by reaction of fast neutrons, and it has high power density and burn-up levels. In addition, sodium is used as the coolant and the operating temperature is far below the boiling point (approximately 880°C at 1 atmospheric pressure). So, the reactor cooling system is designed to operate at low pressure and high temperatures. Sodium is active chemically, and the sodium liquid surface has to be covered with inactive gas.
Hidetaka Takahashi, Kiyoshi Tamayama

Chapter 10. Actual Operation and Control of High-Temperature Engineering Test Reactor

The high-temperature engineering test reactor (HTTR) (Fig. 10.1) is the first high-temperature gas-cooled reactor in Japan. It first attained criticality in November 1998, and the reactor outlet temperature reached 850°C in December 2001, and 950°C in June 2004, both world firsts.
Shigeaki Nakagawa

Chapter 11. New Control Theory and Its Application

The PID control system design method based on transfer functions was established in the 1950s and has since made contributions to automation processes in various industrial fields. Transfer functions have features that make you aware of rough characteristics of input–output responses based on the positioning of the poles and zero point and also discuss frequency responses and the stability of the control system using their Bode diagram. Now we will once again review the restrictions required to express dynamic characteristics of the control target with transfer functions.
Katsuo Suzuki, Kunihiko Nabeshima


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