Control Rod Pattern Research Articles

On-Line Critical Control Rod Pattern Prediction Algorithm for BWR Plant Startup.

This paper describes an on-line algorithm for predicting the critical control rod pattern, which has been developed to reduce the mental strain on operators while withdrawing control rods in the BWR plant startup operation. The proposed algorithm estimates a target eigenvalue (eigenvalue bias) for a three-dimensional neutron kinetics model with a neutron source incorporating actual neutron detector readings. The critical control rod pattern is then predicted based on the estimated eigenvalue bias. The algorithm has been verified using data obtained from an actual startup operation on a BWR model-5 plant, and the estimated eigenvalue bias agreed well with the effective multiplication factor at the criticality actually determined from the operator's judgement.

A Rule-Based Expert System for Automatic Control Rod Pattern Generation for Boiling Water Reactors

This paper reports on an expert system for generating control rod patterns that has been developed. The knowledge is transformed into IF-THEN rules. The inference engine uses the Rete pattern matching algorithm to match facts, and rule premises and conflict resolution strategies to make the system function intelligently. A forward-chaining mechanism is adopted in the inference engine. The system is implemented in the Common Lisp programming language. The three-dimensional core simulation model performs the core status and burnup calculations. The system is successfully demonstrated by generating control rod programming for the 2894-MW (thermal) Kuosheng nuclear power plant in Taiwan. The computing time is tremendously reduced compared to programs using mathematical methods.

High-Order Finite Difference Nodal Method for Neutron Diffusion Equation

A nodal method has been developed which accurately and rapidly solves the three-dimensional neutron diffusion equation in both Cartesian and hexagonal geometries. To reduce the number of unknowns in comparison with the interface current method in favor of short computation time and a small computer memory requirement, this method employs the finite difference method (FDM) as its global neutron balance solution method. In the global neutron balance solution, the coupling coefficients are modified in such a way as to conserve the nodal interface neutron currents which are obtained by a local neutron balance solution method fit to each geometry. To validate the method developed here, it has been applied to neutron diffusion calculations for reactor cores, typical of Cartesian and hexagonal geometries, with different core sizes, assembly pitches, core configurations, control rod patterns, etc. For a large FBR (hexagonal geometry), for example, errors in power distribution and control rod worth by the method are less than 1/2 and 1/10, respectively, compared to an ordinary FBR core design method, while the computation time is 1/8 that of the latter method.

High-order finite difference nodal method for neutron diffusion equation.

A nodal method has been developed which accurately and rapidly solves the three-dimensional neutron diffusion equation in both Cartesian and hexagonal geometries. To reduce the number of unknowns in comparison with the interface current method in favor of short computation time and a small computer memory requirement, this method employs the finite difference method (FDM) as its global neutron balance solution method. In the global neutron balance solution, the coupling coefficients are modified in such a way as to conserve the nodal interface neutron currents which are obtained by a local neutron balance solution method fit to each geometry. To validate the method developed here, it has been applied to neutron diffusion calculations for reactor cores, typical of Cartesian and hexagonal geometries, with different core sizes, assembly pitches, core configurations, control rod patterns, etc. For a large FBR (hexagonal geometry), for example, errors in power distribution and control rod worth by the method a...

Knowledge Based System for Control Rod Programming of BWRs

A knowledge based system has been developed to support designers in control rod programming of BWRs. The programming searches through optimal control rod patterns to realize safe and effective burning of nuclear fuel. Knowledge of experienced designers plays the main role in minimizing the number of calculations by the core performance evaluation code. This code predicts power distribution and thermal margins of the nuclear fuel. This knowledge is transformed into ‘if-then’ type rules and subroutines, and is stored in a knowledge base of the knowledge based system. The system consists of working area, an inference engine and the knowledge base. The inference engine can detect those data which have to be regenerated, call those subroutine which control the user's interface and numerical computations, and store competitive sets of data in different parts of the working area. Using this system, control rod programming of a BWR plant was traced with about 500 rules and 150 subroutines. Both the generation of control rod patterns for the first calculation of the code and the modification of a control rod pattern to reflect the calculation were completed more effectively than in a conventional method.

Knowledge based system for control rod programming of BWRs.

A knowledge based system has been developed to support designers in control rod programming of BWRs. The programming searches through optimal control rod patterns to realize safe and effective burning of nuclear fuel. Knowledge of experienced designers plays the main role in minimizing the number of calculations by the core performance evaluation code. This code predicts power distribution and thermal margins of the nuclear fuel. This knowledge is transformed into ‘if-then’ type rules and subroutines, and is stored in a knowledge base of the knowledge based system. The system consists of working area, an inference engine and the knowledge base. The inference engine can detect those data which have to be regenerated, call those subroutine which control the user's interface and numerical computations, and store competitive sets of data in different parts of the working area. Using this system, control rod programming of a BWR plant was traced with about 500 rules and 150 subroutines. Both the generation of ...

A Mathematical Method for Boiling Water Reactor Control Rod Programming

A new mathematical programming method has been developed and utilized in OPROD, an existing computer code for automatic generation of control rod programs as an alternative inner-loop routine for the method of approximate programming. The new routine is constructed of a dual feasible direction algorithm, and consists essentially of two stages of iterative optimization procedures Optimization Procedures I and II. Both follow almost the same algorithm; Optimization Procedure I searches for feasible solutions and Optimization Procedure II optimizes the objective function. Optimization theory and computer simulations have demonstrated that the new routine could find optimum solutions, even if deteriorated initial control rod patterns were given.

Optimization of Boiling Water Reactor Control Rod Patterns Using Linear Search

A computer program for searching the optimal control rod pattern has been developed. The program is able to find a control rod pattern where the resulting power distribution is optimal in the sense that it is the closest to the desired power distribution, and it satisfies all operational constraints. The search procedure consists of iterative uses of two steps: sensitivity analyses of local power and thermal margins using a three-dimensional reactor simulator for a simplified prediction model; linear search for the optimal control rod pattern with the simplified model. The optimal control rod pattern is found along the direction where the performance index gradient is the steepest. This program has been verified to find the optimal control rod pattern through simulations using operational data from the Oyster Creek Reactor.

The Development of the Reactor Management System

The Reactor Management System (RMS), an on-line system with a minicomputer, has been in operation at a boiling water reactor (BWR) nuclear power plant since 1977. The objectives of this system are to perform detailed monitoring and prediction of the core status and to make reactor operation more efficient, simpler, and easier. One of the features of the system is that the RMS utilizes process computer calculated data (such as power distribution and exposure distribution in the core) transferred through the data link, as well as the plant data (such as local power range monitor readings and control rod positions) transferred through the process input/output system. Based on operational experience at the BWR plant, calculation models have been improved to achieve higher accuracy, and new functions have been added to fulfill the operator's demands. The system has now become a useful tool for the operator. For instance, the power level prediction function has become essential for plant operation at the control rod pattern change.

Simple Method to Predict Power Level and Core Flow Rate of Boiling Water Reactors by Using One-Point Core Model

A simple one-point core model has been developed to predict startup and load following features of boiling water reactors (BWRs). The variables used in this model are core thermal power, core flow rate, xenon concentration and control rod pattern, where the last variable is expressed in terms of the corresponding thermal power at the rated core flow. The number of parameters to be identified is only three, and they are determined by flow control line, xenon reactivity coefficient and power reactivity coefficient. These parameters can be adjusted by using the actual operating data of BWR plants. The accuracy of the one-point core model was evaluated in some typical startup operations of a reference 800 MWe class BWR. The prediction errors of the model were within 2% of relative power in comparison with results of a three-dimensional BWR core simulator and within 3% in comparison with the operating data. Use of this one-point core model, with xenon-iodine maps, should successfully predict reactor conditions, even when employing only simple hand-calculations.

Principles for Control Rod Withdrawal Strategy During the Startup of Boiling Water Reactors

Control rod withdrawal strategy during boiling water reactor startup is explored and verified by examples simulated with a three-dimensional nuclear-thermal-hydraulic coupled computer code with xenon dynamics included. The study leads to the following two general principles. 1. Use of the shallow control rods should be minimized in the intermediate pattern insofar as the power peak near the bottom is within the limits for the xenon transient control. 2. Every control rod should be withdrawn at least once to the same depth or to more than that of the rated pattern, and use of two different control rod patterns is necessary for the effective stretching out of the preconditioned envelope.

Simple method to predict power level and core flow rate of boiling water reactors by using one-point core model.

A simple one-point core model has been developed to predict startup and load following features of boiling water reactors (BWRs). The variables used in this model are core thermal power, core flow rate, xenon concentration and control rod pattern, where the last variable is expressed in terms of the corresponding thermal power at the rated core flow. The number of parameters to be identified is only three, and they are determined by flow control line, xenon reactivity coefficient and power reactivity coefficient. These parameters can be adjusted by using the actual operating data of BWR plants. The accuracy of the one-point core model was evaluated in some typical startup operations of a reference 800 MWe class BWR. The prediction errors of the model were within 2% of relative power in comparison with results of a three-dimensional BWR core simulator and within 3% in comparison with the operating data. Use of this one-point core model, with xenon-iodine maps, should successfully predict reactor conditions...

A new method of startup planning for boiling water reactors.

Based on a heuristic approach, a practically applicable startup process for BWR's that minimizes the xenon transient effects has been derived, which answers this highly nonlinear complex multi-stage optimization problem, while satisfying the current constraints imposed for fuel integrity. The resulting PCP (Pre-Conditioning with Peripheral Rod Operation) method features an intermediate control rod pattern, with central region identical with the rated control rod pattern and with certain control rods fully inserted in the peripheral region. This method has been successfully applied to the initial startup of a commercial BWR, and the expected performance was confirmed from operating data.

Computer based systems in boiling water reactors

This paper describes the application of computers to the General Electric Company's Boilling Water Reactor (BWR) type nuclear power plants. In the GE BWR plants, computers are used for Real Time Process Monitoring, Nuclear Steam Supply Systemn Performance and Core Limit Evaluation, Balance of Plant Performance Evaluation, Historical Recording, and Control Rod Pattern Enforcement. These functions are performed by different systems and subsystems each consisting of one or more computers. This paper discusses the following:Basic design objectives of each System Major Functions performed by each system simplified systems configurations system operation system evaluation and testsThis paper concludes with a brief discussion of computer control and comments on a few anticipated control applications. It suggests that the architecture of the display control system is adaptable to control applications.

Boiling Water Reactor Control Rod Programming Using Heuristic and Mathematical Methods

OPROD, a computer code for automatic generation of control rod programming that has successfully been applied to an older boiling water reactor (BWR), has experienced some difficulties when applied to a BWR of larger power density and stronger heterogeneity. To improve the performance, a heuristic algorithm that is derived from accumulated experience has been introduced to search for a feasible rod pattern that satisfies all constraints. Application of this algorithm to an initial cycle of an 800-MW(e) BWR of high heterogeneity has been very successful. It has been demonstrated that the proposed algorithm is capable of finding a feasible rod pattern, even starting from an all-rods-out pattern. Some improvement was also made in the method of approximation programming (MAP) algorithm. The temporal constraint relaxation method is shown to be effective in finding an optimal control rod pattern in MAP starting from a guess pattern that is not feasible.

Reactivity Worths of Annular Control Rods in a Pressure-Tube-Type Heavy Water Lattice

The control rod effect has been experimentally studied in the Deuterium Critical Assembly (DCA) by using annular absorbers that simulate control rods of the FUGEN reactor, a prototype heavy-water-moderated, boiling-light-water-cooled, pressure-tube-type reactor. The DCA cores for this experiment are of the 1.2 percent-/sup 235/U-enriched UO/sub 2/ lattices, and consist of 28-pin fuel clusters arranged in a square array of 22.5-cm lattice pitch. The experiment has been carried out with various control rod patterns and with varying coolant void fraction. Experimental results were analyzed by the absorption method, which was employed in the FUGEN control rod design calculations. The calculated reactivity worth agreed with the experiment within +-10 percent. The calculations somewhat overestimated the absorber worths in the nonvoided core and underestimated them in the voided core. This tendency was found to be greatly improved by considering the anisotropy effect in the migration area of the cluster lattice. The experimental results were also analyzed by the logarithmic derivative method. This method more poorly predicted the worths, but described better the flux shape around the rods.

A Method for Generating a Control Rod Program for Boiling Water Reactors

The OPROD computer code has been developed to generate a long-term control rod program, a series of control rod patterns that optimize a cycle length within various operational constraints. In the algorithm, the optimization problem is decomposed into two hierarchies. In the inner loop, a time-invariant target power distribution is assumed, and a control rod pattern is determined so as to best fit the power distribution to the target within the constraints at each burnup step. The target is then improved in the outer loop to achieve a longer cycle length. The code consists of two major parts: a three- dimensional boiling water reactor (BWR) core simulator and MAP, the method of approximate programming. It readily generates a long-term control rod program of BWRs without trial search by core-management engineers. The OPROD has therefore facilitated prompt response to varying operating conditions and the investigation of a conflicting relationship between the thermal limitation and the cycle length. (auth)

Non-Destructive Gamma-Ray Spectrometry on Spent Fuels of a Boiling Water Reactor

The spent fuels from the JPDR-I reactor were measured by means of a γ-scanning facility installed in the fuel storage pool. The spatial distributions of the fission products (134Cs and 137Cs) were measured and analyzed in reference to the effects of control rod pattern. The ratios holding between the products of neutron capture and of direct fission (134Cs/137Cs and 154Eu/137Cs) were also examined for its relevance to non-destructive burnup determination. The activity ratios of the fission products can be expressed by a linear function of burnup, provided that corrections are made to account for differences in irradiation history and for spatial variations in the neutron spectrum.

A Search Technique of Control Rod Pattern for Smoothing Core Power Distributions by Fuzzy Automaton

This paper deals with a new search technique for optimum using a fuzzy automaton, which has been developed for the purpose of determining a desirable rod pattern for smoothing the core power distribution. Using the algorithm thus developed, the optimal input vector applied to a controlled system whose characteristics are unknown is determined automatically from a learning operation of the fuzzy automaton when an initial guess and a hypothetical range of optimal input vector are given. The characteristics of this algorithm are examined for an example of its application to a simple problem. The optimal control rod pattern for smoothing the core power distribution is also determined by this algorithm in a simulation study using the three-dimensional boiling water reactor simulator “FLARE”. It is concluded that optimum points are obtained with sufficient convergence and with only a small increase in the number of iterations and computation time accompanying an increase in the number of components of the input vector. The predicted optimal control rod pattern in the simulation study can be considered reliable.

A Search Technique of Control Rod Pattern for Smoothing Core Power Distributions by Fuzzy Automaton

A Search Technique of Control Rod Pattern for Smoothing Core Power Distributions by Fuzzy Automaton