Axial Power Distribution Control Research Articles

Design of Fractional Order Sliding Mode Adaptive Fuzzy Switching Controllers for Uncertain ACP1000 Nuclear Reactor Dynamics

Advanced Chinese Pressurized Water Reactor (ACP1000) is a third generation load following nuclear reactor. ACP1000 is designed to control the reactor power by a sophisticated control rod mechanism under the base load normal operation of a nuclear power plant in Mode-G. To extend the normal operation of ACP1000 for load following condition, boron adjustment control is used in manual configuration. In this research work, model based two new controllers are designed for ACP1000 reactor dynamics. A nonlinear two-point reactor kinetics model is developed for two halves of the reactor core designated as top and bottom of reactor core. Reactor feedbacks model for two-point reactor kinetics model is developed with fuel temperature, moderator temperature, Xenon concentration, G-Bank control rod position, R-Bank control rod position and boron concentration feedbacks under normal operation of ACP1000. Two problems of the large reactor core of ACP1000 are Xenon oscillations and axial offset in core power distribution. To address these problems, two new controllers are designed for normal load following operation of ACP1000. One controller is designed to replace G1-Bank and R-Bank in Mode-G for reactor power control. The second controller is designed to replace G2-Bank in Mode-G for reactivity control and axial power distribution control. Originally, both reactor coolant average temperature controller and reactor power controller were adaptive controllers. Therefore, both new controllers are designed based on an optimized sliding algorithm using a dedicated fractional order sliding mode control oriented adaptive fuzzy logic control (FO-SMC-AFLC) synthesis scheme. The performance of the proposed closed loop controllers is evaluated for design step and ramp power transients. Both proposed controllers are validated against benchmark results reported in Preliminary Safety Analysis Report (PSAR) of ACP1000. The novel control design scheme is proved satisfactory for normal load following operation of ACP1000, and all the results are found well within design limits.

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.

Research for axial power distribution control of a space nuclear reactor based on nonlinear model

During the operating process of a space nuclear reactor, once the local overload of heat energy occurs in the core, the corresponding fuel elements would be damaged and the lifespan of the reactor would be seriously reduced. In fact, the heat flux at any point in the core is proportional to the neutron flux density. A sufficiently flat axial neutron flux density distribution can protect the fuel assembly from frequent load changes. It is so clear that the axial power distribution control is crucial for the safe and stable operation of the space nuclear reactor. However, the space nuclear reactor is a distributed parameter system, which brings great challenges to the traditional lumped parameter control methods. In this paper, a distributed parameter control method is proposed to suppress the initial neutron flux peaks and realize the exponential stability of the neutron flux distribution control system. First of all, the spatiotemporal model of the reactor core based on the neutron diffusion equation is established. Then, the stability analysis of the control law for the neutron flux distributed parameter control problem is performed by constructing the Lyapunov function. The optimization technique based on the spatial differential linear matrix inequality is used to approximate the solution of the suboptimal integral control law. The control law is implemented by rotating drum, and the flat distribution of the axial power of the core is realized by the distributed parameter control. Finally, the numerical results are provided to validate the feasibility of the proposed control scheme.

Research on non-uniform control rod system of PWR

In order to improve the axial power distribution control performance of PWR power control system and simplify the control strategy, three non-uniform power control rod systems based on the novel non-uniform power control rod and their decoupling mode control strategy (mode D) are proposed. The types A, B, and AB non-uniform control rod systems of Qinshan nuclear power plant in China are established by MCNP5. These three non-uniform power control rod systems adopt mode D to control the core power. The radial and axial neutron flux densities of three non-uniform control rod systems at four rod positions are separately calculated. The simulation results show that types A, B, and AB non-uniform control systems adopting the mode D have good power level control performance, and type AB non-uniform control system has the best axial distribution performance. Compared with the other four control strategies, the mode D is simpler.

Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects

Load-following control of a nuclear reactor core is very crucial. The main challenge in examining power distribution control of the reactor core is to perform axial power distribution control rather than handling radial power distribution.In this work, a new model consisting of fractional order derivatives and two nodes of the reactor core with reactivity feedbacks is presented named as the two-point fractional neutron point kinetics (TPFNPK) model. According to neutron diffusion phenomena, this modeling method has a better physical interpretation for a quick change of neutron flux in load-following operation mode.For load-following control, a fractional order PID controller is implemented. Optimization of the parameters of this controller (KP, KI, λ, KD, and μ) is carried out utilizing a genetic algorithm (GA) which is an evolutionary algorithm.The objective is the minimization of the weighted sum of the integral of time-weighted absolute error (ITAE), and the overshoot or the undershoot (MP).The new reactor core model is simulated in a MATLAB/SIMULINK environment coupled with a genetic algorithm.Different load patterns (the assumed tracking signal) considering different values of the model parameter (α) are introduced to address the effectiveness of the implemented control method.The simulation result demonstrates that the optimized control methods (GA-PID and GA-FOPID) have satisfactory and suitable functionality during load pattern tracking for all selected values of the model parameter. However, the GA-FOPID controller has a relatively better performance compared to the GA-PID controller. In all cases, it has lower costs and faster convergence. In addition, core normalized axial offset (AO) is always maintained within a certain limit during load-following operation for all the cases. Furthermore, in all the cases, the normalized axial xenon oscillation index (AXOI) remains bounded during the power transient.

Axial power distribution control in fast nuclear reactor based on proportional spatial-derivative method

Axial power distribution control is one of the key issues for Nuclear Power Plant (NPP) operation. In the most of NPPs, the axial power distribution control is realized by the Lumped Parameters Control (LPC) method, which often takes the axial power difference between adjacent nodes as the controlled object. However, the nuclear reactor core has a typical distributed parameters feature. With the number of discrete nodes increases, the control system design is more and more complex. Therefore, it is necessary to develop the Distributed Parameter Control (DPC) method. In this work, a DPC method based on the Proportional Spatial-Derivative (PSD) controller is presented. Experiments show that the power distribution control system based on the PSD control method can inhibit the power peak. Meanwhile, the comparison between the PSD and PID controllers shows that the DPC system based on the PSD method has better dynamic performance than LPC system.

Observer based adaptive robust Feedback-linearization control for VVER-1000 nuclear reactors with bounded axial power distribution based on the validated multipoint kinetics reactor model

In nuclear reactor, spatial oscillations in neutron flux distribution resulting from xenon reactivity feedback are a matter of concern. If the oscillations in power distribution are not controlled, power density and rate of change of power at some locations in the reactor core may exceed their respective limits causing the nuclear power plant instability. Therefore, during the design stages of any Pressurized Water Nuclear Reactor (P.W.R), it is necessary to identify the existence of xenon oscillation and to design suitable control strategy for regulating the spatial power distribution. In each nuclear power plant, Load-following control is one of the most important techniques for nuclear reactor regulation. A novel nonlinear controller called observer-based adaptive robust feedback-linearization controller for VVER-1000 nuclear reactors is presented in this paper. This novel control strategy is then applied to the Axial power distribution control during load following operation in the VVER-1000 nuclear reactors.The reactor core is simulated based on the validated four nodes kinetics reactor model and three groups of delayed neutron precursor’s concentration based on the Skinner-Cohen model. Considering the limitations of the xenon concentrations and delayed neutrons precursor’s densities physical measurement, an adaptive sliding mode observer is designed to estimate their values and finally adaptive robust feedback-linearization based on the adaptive sliding mode observer and nodal kinetics reactor model is presented to AO control during load following operation for nuclear reactors. The stability analysis is given by means Lyapunov approach, thus the designed control system is guaranteed to be stable within a large range.Simulation results show that robust control and state estimation with adaptive robust feedback-linearization and adaptive Sliding mode methodologies can be achieved in nuclear plant systems with diverse applications including control and estimation in the presence of model uncertainties and external disturbances. One significant finding to emerge from this paper is that the Observer based Adaptive robust feedback-linearization control method provides a robust, high-performance and automatic control mechanism at all the power ranges of operation for P.W.R control system.

Effect of Axial Distribution of Gadolinium Burnable Poison in Advanced Pressurized Water Reactor Assembly

The radial and axial power distribution in power reactors are determined mainly by the patterns of the fuel assembly and the burnable absorber at the beginning of cycle. In Advanced Pressurized Water Reactor (APWR), gadolinium burnable absorber is used to decrease the relative power of fresh fuel assemblies. In this paper, the effect of the axial distribution of gadolinium (Gd) on the power of the APWR assembly is studied. Three models of APWR assemblies are simulated using MCNP6 code. In the first model, UO2 fuel is distributed uniformly in all the fuel rods. In the other two models some of the UO2 fuel rods are replaced by UO2-Gd2O3 rods in part length distribution. Two gadolinium concentrations 6% and 10% are used. The main neutronic parameters are estimated for the three models: the multiplication factor (K-infinity) as a function of burnup (GWd/MTU), the radial and axial power distributions. The results show that the distribution of the gadolinium absorber in the central region of fuel rod (part-length absorber) leads to flattening of axial power, which means additional axial power distribution control.

A Combined Method for Predicting the Boron Deposited Mass and the CIPS Risk

CIPS is a shift in the axial power towards the bottom half of the core, also known as axial offset anomaly (AOA), which results from the deposited of corrosion products during an operation. The main reason of CIPS is the solute particles especially boron compounds concentrated inside the porous deposit. The impact of CIPS is that the axial power distribution control may be more difficult and the shutdown margin can be decreased simultaneously. Besides, it also requires estimated critical condition (ECC) calculations to account for the effects of AOA. In this article, thermal-hydraulic subchannel code and boron deposit model have been combined to analyze the CIPS risk. The neutronics codes deal with the generation of homogenized neutron cross section as well as the calculation of local power factor. A simple rod assembly is analyzed with this combined method and simulation results are presented. Simulation results provide the boron hideout amount inside crud deposits and power shapes. The obtained results clearly show the power shape suppression in regions where crud deposits exist, which is a clear indication of CIPS phenomenon. And the CIPS effects on CHF have also been investigated. Result shows a margin of DNBR decrease in the crud case.

A decoupled Mechanical Shim core control strategy for a pressurized water reactor using feedforward compensation and a multimodel approach

The advanced Mechanical Shim (MSHIM) core control strategy employs two separate and independent control rod banks, namely the MSHIM control banks (M-banks) and axial offset (AO) control bank (AO-bank), for automatic reactivity/temperature and axial power distribution control respectively. The M-banks and AO-bank are controlled by two closed-loop controllers, independently, called the coolant average temperature (Tavg) controller and the AO controller. Since the motion of the M-banks and AO-bank can both affect the Tavg and AO, an interlocking design between the Tavg controller and the AO controller is adopted in the MSHIM control strategy to avoid the interference between the two controllers during power maneuvers. This design can enhance the stability of the MSHIM control system by avoiding the simultaneous movement of the M-banks and AO-bank and keeping the priority of the M-bank movement. However, the AO control performance is degraded at the same time. In the present study, a feedforward compensation decoupling method and a multimodel approach have been used to eliminate the coupling effect between the two controllers in the MSHIM control system during a wide range of power maneuvers. A multiple feedforward compensation system has been designed with integration of the feedforward compensators for the Tavg and AO controllers at five equilibrium conditions using the multimodel approach. By implementing it in the MSHIM control system, the interlocking between the M-banks and the AO-bank can be released to realize the independent and decoupling control between the Tavg and AO. The effectiveness of the decoupled MSHIM control strategy has been verified by comparing its control performance with that of the original MSHIM control strategy during typical load change transients of the AP1000 reactor. The obtained results show that superior and decoupling control of the Tavg and AO can be achieved using the proposed decoupled MSHIM control strategy.

Design of a decoupled AP1000 reactor core control system using digital proportional–integral–derivative (PID) control based on a quasi-diagonal recurrent neural network (QDRNN)

The control system of the AP1000 reactor core uses the mechanical shim (MSHIM) strategy, which includes a power control subsystem and an axial power distribution control subsystem. To address the strong coupling between the two subsystems, an interlock between the two subsystems is used, which can only alleviate but not eliminate the coupling. Therefore, sometimes the axial offset (AO) cannot be controlled tightly, and the flexibility of load-following operation is limited. Thus, the decoupling of the original AP1000 reactor core control system is the focus of this paper. First, a two-node disperse dynamic model is established for the AP1000 reactor core to use PID control. Then, a digital PID control system based on a quasi-diagonal recurrent neural network (QDRNN) is designed to decouple the original system. Finally, the decoupling of the control system is verified by the step signal and load-following condition. The results show that the designed control system can decouple the original system as expected and the AO can be controlled much more tightly. Moreover, the flexibility of the load following is increased.

Control parameter optimization for AP1000 reactor using Particle Swarm Optimization

The advanced mechanical shim (MSHIM) core control strategy is implemented in the AP1000 reactor for core reactivity and axial power distribution control simultaneously. The MSHIM core control system can provide superior reactor control capabilities via automatic rod control only. This enables the AP1000 to perform power change operations automatically without the soluble boron concentration adjustments. In this paper, the Particle Swarm Optimization (PSO) algorithm has been applied for the parameter optimization of the MSHIM control system to acquire better reactor control performance for AP1000. System requirements such as power control performance, control bank movement and AO control constraints are reflected in the objective function. Dynamic simulations are performed based on an AP1000 reactor simulation platform in each iteration of the optimization process to calculate the fitness values of particles in the swarm. The simulation platform is developed in Matlab/Simulink environment with implementation of a nodal core model and the MSHIM control strategy. Based on the simulation platform, the typical 10% step load decrease transient from 100% to 90% full power is simulated and the objective function used for control parameter tuning is directly incorporated in the simulation results. With successful implementation of the PSO algorithm in the control parameter optimization of AP1000 reactor, four key parameters of the MSHIM control system are optimized. It has been demonstrated by the calculation results that the optimized MSHIM control system parameters can improve the reactor power control capability and reduce the control rod movement without compromising AO control. Therefore, the PSO based optimization method can be used to optimize MSHIM control system parameters to provide much better reactor control capabilities.

O.190 Laser information technologies in the oncological surgery

Axial power distribution control is one of the key issues for Nuclear Power Plant (NPP) operation. In the most of NPPs, the axial power distribution control is realized by the Lumped Parameters Control (LPC) method, which often takes the axial power difference between adjacent nodes as the controlled object. However, the nuclear reactor core has a typical distributed parameters feature. With the number of discrete nodes increases, the control system design is more and more complex. Therefore, it is necessary to develop the Distributed Parameter Control (DPC) method. In this work, a DPC method based on the Proportional Spatial-Derivative (PSD) controller is presented. Experiments show that the power distribution control system based on the PSD control method can inhibit the power peak. Meanwhile, the comparison between the PSD and PID controllers shows that the DPC system based on the PSD method has better dynamic performance than LPC system.

A Receding Horizon Controller with a Parameter Estimator for Nuclear Reactor Power Distribution

A receding horizon control method is used to solve on-line, at each time step, an optimization problem for a finite future interval and to implement the first optimal control input as the current control input. The receding horizon control method is combined with a parameter estimator to overcome the problems of the linear modeling and time-varying characteristics of a process. It is a suitable control strategy for time-varying systems, in particular, because the parameter estimator identifies a controller design model recursively at each time step, and also the receding horizon controller recalculates an optimal input at each time step by using newly measured signals. The proposed controller is applied to the axial power distribution control in a pressurized water reactor. The reactor dynamics model used for computer simulations is a two-point xenon oscillation model in which the reactor core is axially divided into two regions (upper and lower halves) and each region is assumed to have a single input and a single output and to be coupled with the other region. It is shown from numerical simulations that the proposed controller exhibits very fast tracking responses due to the step and ramp changes of axial target shape and also works well in a time-varying parameter condition.

Design of a Receding Horizon Control System for Nuclear Reactor Power Distribution

A receding horizon control method is applied to the axial power distribution control in a pressurized water reactor. The basic concept of receding horizon control is to solve on-line, at each sampling instant, an optimization problem for a finite future and to implement the first optimal control input as the current control input. Thus, it is a suitable control strategy for time-varying systems. The reactor model used for computer simulations is a two-point xenon oscillation model based on the nonlinear xenon and iodine balance equations and a one-group, one-dimensional, neutron diffusion equation with nonlinear power reactivity feedback that adequately describes axial oscillations and treats the nonlinearities explicitly. The reactor core is axially divided into two regions, and each region has one input and one output and is coupled with the other region. Through numerical simulations, it is shown that the proposed control algorithm exhibits very fast tracking responses due to the step and ramp changes of axial target shape and also works well in a time-varying parameter condition.

00/03300 Improvement of the axial power distribution control capabilities in VVER-1000 reactors

00/03300 Improvement of the axial power distribution control capabilities in VVER-1000 reactors

Improvement of the axial power distribution control capabilities in VVER-1000 reactors

This article describes an automatic reactor power control system for VVER-1000 reactor and reports simulation analysis results for a typical daily load follow operation. The associated reactor control algorithm is called “mode G” that uses a heavy-worth bank (H-bank) dedicated to axial power shape control and the light-gray banks (G-banks) for reactor power change and reactivity compensation. The simulation results for daily load follow operation in three burnup states of first cycle illustrate that the load follow capability of VVER-1000 reactors using this algorithm will be improved.

Advanced Designs and Operating Strategies to Enhance the Safety, Operability, and Efficiency of VVER-1000 Reactors

Advanced fuel, burnable absorber, and control rod designs along with advanced fuel management and power distribution control strategies will be implemented in the first operating cycle of the Czech Republic`s Temelin VVER-1000 nuclear power plants. These improvements increase safety margins, enhance operability, and improve fuel efficiency. The Westinghouse VVANTAGE 6 fuel assembly design incorporates many proven advanced fuel and core design features used extensively in western pressurized water reactors. The fuel assembly incorporates mixing vane structural grids, radial enrichment zoning, ZrB{sub 2} integral fuel burnable absorbers, axial blankets, and Zircaloy guide thimbles and structural grids. Low-leakage loading patterns are also used to reduce radial neutron leakage. The rod cluster control assembly (RCCA) design incorporates two absorber materials. The absorber tip uses silver-indium-cadmium material while the remainder of the absorber material is B{sub 4}C enriched in {sup 10}B. This design increases control rod worth as well as the usable lifetime of RCCA. The Westinghouse constant axial offset control operating strategy, improved RCCA design, modified RCCA overlap, and replacement of part-length RCCA by full-length RCCA are used to improve the axial power distribution control capability for VVER-1000 reactors. These design improvements provide thermal margin benefits, increase shutdown margin by almost 1.0% {Delta}{rho},more » reduce fuel cycle costs by nearly 30%, and improve axial power distribution control.« less

Fuel Cycle Extension by Part-Length Control Rod Removal at Rancho Seco

The Babcock and Wilcox Company (B&W) normally uses part-length axial power shaping rods (APSRs) for core axial power distribution control. The development and implementation by B&W and the Sacramento Municipal Utility District of a procedure for extending cycle length by removing the APSRs at the end of cycle 3 of Rancho Seco Nuclear Generating Station is explained. Increased core reactivity and hence greater cycle length were successfully achieved. Neither the reactor protection system nor normal operating limits were violated during the APSR withdrawal procedure. Further, pellet-cladding interaction was avoided, and primary coolant feedand bleed requirements were within the capacity of the plant evaporators. During the 22 h at less than full power, the average capacity factor was 81.1%, a reasonable tradeoff in light of the extension of cycle 3 by 10 effective full-power days (EFPDs). Successive use of this technique over following cycles yields average gains of 5 EFPDs per cycle.