Dynamics and Control of Nuclear Reactors

Cover
Dynamics and Control
of Nuclear Reactors
Copyright
Dedication
Preface
	Communication with authors
Acknowledgments
1
ntroduction
	Introduction
	System dynamics and control design
	References
2
Nuclear reactor designs
	Introduction
	Generation I reactors
	Generation II reactors
	Generation III reactors
	Generation III+ reactors
	Generation IV reactors
	Advanced reactors
	Early twenty-first century construction
	References
	Further reading
3
The point reactor kinetics equations
	Neutronics
	Delayed neutrons
		Delayed neutrons from fission products
		Photoneutrons from nuclei excited by gamma rays
	Development of the point reactor kinetics equations
	Alternate choices for the neutronic variable
	Perturbation form of the point kinetics equations
	Transfer functions
	Frequency response function
	Stability
	Fluid-fuel reactors
	References
	Further reading
4
Solutions of the point reactor kinetics equations and interpretation
	Evolution of simulation methods
	Numerical analysis
	Maneuvers in a zero power reactor
	Analytical solutions
	Solutions for small perturbations
	Sinusoidal reactivity and frequency response
	Fluid fuel reactor response
	The inhour equation
	References
	Further reading
5
Subcritical operation
	The neutron source
	Relation between neutron flux and reactivity in a subcritical reactor
	The inverse multiplication factor
	Responses during startup
	Power ascension
	Further reading
6
Fission product poisoning
	The problem
	Dynamics of xenon-135
		Xe-135 production
		Xe-135 losses
		Equations for Xe-135 behavior
		Steady state Xe-135
		Xe-135 poisoning
		Behavior of Xe-135 after Startup
		Xe-135 after Shutdown
		Xe-135 poisoning after a power increase
		Xe-135 poisoning after power maneuvers
		Coupled neutronic-xenon transients
		Xenon-induced spatial oscillations
		Xenon in molten salt reactors
	Samarium-149 poisoning
	Summary
	References
7
Reactivity feedbacks
	Basics
	Fuel temperature feedback in thermal reactors
	Moderator temperature feedback in thermal reactors
	Pressure and void coefficients in thermal reactors
	Fission product feedback
	Combined reactivity feedback
	Power coefficient of reactivity and the power defect
	Reactivity feedback effect on the frequency response
	Destabilizing negative feedback: A physical explanation
	Explanation of stability using state-space representation
	References
8
Reactor control
	Introduction
	Open-loop and closed-loop control systems
	Basic control theory
		Manual control
		On-off controller
		Proportional controller
		Integral controller
		Differential controller
		Combined controllers
		An example of proportional and integral controller for a first order system
			Proportional controller
			Integral controller
		Advanced controllers
	Control of a zero-power reactor
	Control options in power reactors
	Effect of inherent feedbacks on control options
	Load following operation
	The role of stored energy
	Steady-state power distribution control
	Important reactivity feedbacks and control strategies for various reactor types
	References
9
Space-time kinetics
	Introduction
	Diffusion theory
	Multi-group diffusion theory
	Calculation requirements
	Computer software
	Models and computational methods
		Finite difference methods
		Finite element method (FEM)
		Modal methods
		Quasi-static methods
		Nodal methods
	References
10
Reactor thermal-hydraulics
	Introduction
	Heat conduction in fuel elements
	Heat transfer to liquid coolant
	Boiling coolant
	Plenum and piping models
	Pressurizer
	Heat exchanger model
	Steam generator model
		U-Tube steam generator (UTSG)
		Once-through steam generator (OTSG)
	Balance-of-Plant (BOP) system models
	Reactor system models
	References
	Further reading
11
Nuclear reactor safety
	Introduction
	Reactor safety principles
	Early accidents with fuel damage
		Accidents
		Assessment
	Analysis of potential reactor accidents
	Accidents in Generation-II power reactors
		Three mile Island [14]
		Chernobyl [15]
		Fukushima Dai-ichi [16]
	Consequences and lessons learned
	References
12
Pressurized water reactors
	Introduction
	PWR characteristics [1-3]
	The reactor core
	The pressurizer
	Steam generators
		U-tube steam generator (UTSG)
		Once-through steam generator (OTSG)
		Horizontal steam generator
	Reactivity feedbacks
	Power maneuvering
	Steady-state programs for PWRs
		Heat transfer in a steam generator
		Fuel-to-coolant heat transfer
		Equivalence between reactor power and power delivered to the steam generator at steady state
		Energy change in the coolant
		Development of a steady-state program
		Steady-state program for PWRs with once-through steam generators (OTSG)
	Control rod operating band and control rod operation
	Feedwater control for PWR with U-tube steam generators [2, 4, 5]
	Control of a PWR with once-through steam generators [3]
	Turbine control
	Summary of main PWR controllers
	PWR safety systems
	Example of a PWR simulation
	References
	Further reading
13
Boiling water reactors
	Introduction
	History of BWR design evolution
		BWR-1
		BWR-2
		BWR-3
		BWR-4
		BWR-5
		BWR-6
		ABWR
	Characteristics of BWRs
		General features of a BWR
		Recirculation flow and jet pumps
		Other features of BWRs
	Reactivity feedbacks in BWRs
	Reactivity and recirculation flow
	Total reactivity balance
	BWR dynamic models
	BWR stability problem and impact on control
	The power flow map and startup
	On-line stability monitoring
	Power maneuvering
	BWR control strategy
	BWR safety
	Advantages and disadvantages
	References
	Further reading
14
Pressurized heavy water reactors
	Introduction
	PHWR characteristics
	Neutronic features [3]
	Temperature feedback in heavy water reactors
	The void coefficient
	Reactivity control mechanisms
	Control systems
		Unit power regulator
		Reactor regulating system
		Pressure and inventory control
		Steam generator level control
		Steam generator pressure control
	Maneuvering
	Reactor dynamics
		Modeling strategy
		Reactor power response to reactivity insertion
	References
15
Nuclear plant simulators
	Introduction
	Types of simulators and their purpose
		Simulator games
		Desk-top simulators
		Control room simulators
	Desk-top simulators
		Introduction
			PC simulation
			Using an IAEA simulator
		Simulation of PWR and BWR plant transients
			PWR simulation
			BWR simulation
		How to obtain an IAEA simulator?
		Internet-based desk-top simulators
	Control room simulators
	References
16
Nuclear plant instrumentation
	Introduction
	Sensor characteristics
		Neutron and gamma ray detectors
			Ionization chambers
			Fission detectors
			Self-powered neutron detectors
			Scintillation detectors
			Gamma thermometers
			Nitrogen-16 measurement
		Temperature sensors
			Resistance thermometers
			Thermocouples
			Thermowells and bypass installation
			Advanced temperature sensors
		Pressure sensors
		Flow sensors
			Flow vs. pressure drop
			Advanced flowmeters
		Level sensors
			Differential pressure
			Bubbler
		Actuator status sensors
	PWR instrumentation
	BWR instrumentation
	CANDU (PHWR) reactor instrumentation
	High temperature reactor instrumentation
		Liquid metal fast breeder reactor (LMFBR) instrumentation
		High temperature gas-cooled reactor (HTGR) instrumentation
		Molten salt reactor instrumentation
	References
	Further reading
APPENDIX A
Generation II reactor parameters
	Pressurized water reactor (PWR)
	Boiling water reactor (BWR)
	Pressurized heavy water reactor (PHWR): CANDU reactor
	References
APPENDIX B
Advanced reactors
	Introduction
	Design possibilities
	A note about reactors that use thorium
	Advanced reactor marketplace
	Large evolutionary reactors
		Pressurized water reactors
		Boiling water reactors
		Pressurized heavy water reactors
	Large developmental reactors
		Gas-cooled reactors
		Liquid metal fast breeder reactors
		Molten salt reactors
		Heavy water reactors
	Small reactors
		Introduction
		Incentives
		Small reactor list
	Dynamics of advanced reactors
	References
APPENDIX C
Basic reactor physics
	Introduction
	Neutron interactions
	Reaction rates and nuclear power generation
	Nuclear fission
	Fast and thermal neutrons
	Relation between specific power and neutron flux
	Neutron lifetime and generation time
	Multiplication factor and reactivity
	Computing effective multiplication factor
	Neutron transport and diffusion
	References
APPENDIX D
Laplace transforms and transfer functions
	Introduction
	Defining the Laplace transform
	Calculating Laplace transforms
	The inverse Laplace transform
		Method of residues
		Inverse transform using partial fractions
	Transfer functions
	Feedback transfer functions
	The convolution integral
	Laplace transforms and partial differential equations
	References
APPENDIX E
Frequency response analysis of linear systems
	Frequency response theory
	Computing frequency response function
	Systems with oscillatory behavior
	Systems with time delay dynamics
	Frequency response of distributed systems
	Frequency response measurements
	References
APPENDIX F
State variable models and transient analysis
	Introduction
	State variable models
	General solution of the multiple-input multiple-output (MISO) linear
		Definition of multiple-input multiple output (MIMO) systems
		Transfer function representation of MIMO systems
		Transient response of MIMO systems
		The state transition matrix
	The matrix exponential solution
	Sensitivity analysis
	Numerical solutions of ordinary differential equations
		Euler's method
		Runge-Kutta order-two method
	Solutions for partial differential equations
		Examples of partial differential equations
		Solution of partial difference equations using the finite difference method
			Introduction
			Formulation of grids and nodes [8]
			FDM solution of the two-dimensional heat conduction problem [8]
		Solution of partial difference equations using the finite element method
	References
APPENDIX G
Matlab and Simulink: A brief tutorial
	Introduction
	Getting started with simulink
	Simulation of a single-input single-output (SISO) system
	Simulation of a closed-loop system with P-I controller
	Solving linear differential equations using state-space models
	Computing step response using a transfer function
	Computing eigenvalues and eigenvectors
	References
APPENDIX H
Analytical solution of the point reactor kinetics equations and the prompt jump approximation
	Introduction
	Analytical solution of the point kinetics equations
	The prompt jump
	An example
APPENDIX I
A moving boundary model
	Introduction
	Development of a moving boundary model
APPENDIX J
Modeling and simulation of a pressurized water reactor
	Introduction
	Linearized isolated core neutronic model
	Numerical values of coefficients in the isolated core neutronic model
	Fuel-to-coolant heat transfer
	Numerical values of coefficients in the isolated core thermal-hydraulic model
	State space representation of dynamic equations
	Simulation of PWR isolated core dynamics response
	Frequency response characteristics of reactor core dynamics
	PWR NSSS dynamics
		Neutronics
		Core thermal-hydraulics
		T-average controller
		Piping and plenums
		Pressurizer and its controller
		U-tube steam generator modeling and control
		NSSS model
	Plant system parameters used in the models
	NSSS simulated response to a steam valve perturbation
	References
	Further reading
APPENDIX K
Modeling and simulation of a molten salt reactor
	Introduction
	Molten salt reactor experiment (MSRE)
	Lumped parameter model of the MSRE
		Sub-system models and characteristics
		Nodal model of the MSRE system
		Equations describing neutronics and reactor heat transfer
		Parameters used in simulation models
	Results of simulation of MSR dynamics
	References
	Further reading
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Z
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