Reactor Power Control Research Articles

Reactor power control system design and dynamic simulation for load maneuvers over full range and entire lifetime of an integrated supercritical CO2 reactor plant

Due to advantage of high efficiency, low carbon, and flexible operation, the integrated supercritical CO2 reactor plant has promising prospect in energy supply. This paper aims to clarify performance of the reactor plant and establish a reactor power control strategy through numerical modeling. Firstly, performance on separated components is evaluated to provide guidance for control strategy development. Secondly, influence of control methods, controller schemes, and saturation models on control strategy are discussed. Thirdly, dynamic response of reactor plant with proposed control strategy is confirmed via load change transients. Results show that passive control method is infeasible at EOL and load demand below 50 %FP, and active control method must be considered. The proposed control strategy adopts coupled temperature-channel and power-channel scheme and soft saturation model. It ensures safe operation of the plant over full load range in whole lifetime. These results can provide helpful guidance on part-load operation for this system.

A computational- experimental model of reactor kinetic for investigating the linearity response of in-core neutron detectors of a low power research reactor

In this study, the linear response of fission chamber (FC) neutron detectors in Isfahan miniature neutron source reactor (MNSR) is investigated through experiments and calculations at different powers of the reactor. The linearity of the response of the main neutron detector in the MNSR is important due to its safety functions in reactor power control. Additionally, determining the linear response region of this detector presents a linear neutron dosimetry field even outside of the reactor core, i.e. at the outlet of external beam tubes. Moreover, it is very difficult to remove and calibrate this neutron detector that has been installed in the reactor core for a long time. For this purpose, an alternative method for measuring the linearity of the response of a neutron detector is extended by investigating the kinetic behavior of reactor. The aim of this method is to calculate the delayed neutrons population in the reactor core and compare with the FC detector response. In this method, the numerical solution method is used to solve the point kinetic equation with 15 delayed neutron groups (6 delayed neutron groups and 9 photo-neutron groups) after inserting a large negative reactivity into the MNSR core by considering temperature and xenon reactivity feedbacks during a coupling procedure. To obtain the xenon reactivity feedback, xenon concentration is calculated by coupling the 135Xe and 135I production equations and the εpPFnlPTnl parameter is obtained by an experimental method. Furthermore, the value of fission cross section (Σf) is calculated using a validated model in the Dragon code. The large reactivities are inserted at two initial power of 150 W and 30 kW to investigate the response of the main FC neutron detector in a cold xenon-free condition and by considering temperature and xenon reactivity feedbacks, respectively. The results demonstrate that the response of the MNSR FC detector is linear in the neutron flux range between 5 × 107 to 1 × 1012 n.cm−2.s−1, which is equivalent to reactor power of 1.5 W to 30 kW. This innovative method can be applied to calibrate the neutron detectors in other research and power reactors.

Research on nuclear reactor power control system of VVER-1000 with thermal energy supply system

Cogeneration nuclear power plants (NPP) can reduce carbon emissions and improve the economy to deal with climate problems. However, after adding the thermal energy supply system (TESS), the nuclear reactor power control system (NRPCS) is affected by the change in the relationship between energy supply and load. Therefore, the NRPCS of VVER-1000 with TESS (Ts-VVER) is studied. In this paper, first, the simulation model of Ts-VVER is established, with the extraction of steam from the main steam header. Second, dynamic characteristic analysis, coupling characteristic analysis, and energy balance relationship analysis are studied to evaluate the influence of Ts-VVER. Then, the NRPCS modified scheme is designed, and the new nonlinear feedforward gain curve is gotten from the original curve by translation. Finally, the designed NRPCS modified scheme is verified by typical conditions simulation. The modified scheme can offer a reference for the design of the NRPCS of other cogeneration NPPs.

Design of control strategy for reactor power control system of LBE cooled Actinide Burner Reactor (ABR) using system analysis code NUSOL-LMR

The power control strategy for the Lead–Bismuth Eutectic (LBE) cooled Actinide Burner Reactor (ABR) has been designed to assess the closed-loop performance of newly developed control blocks that were not modeled in the NUSOL-LMR code before this research effort. After establishing a sustainable model of ABR in NUSOL-LMR, validation of the model in light of the already-published research is performed. The said closed-loop control strategy (consisting of the power and temperature control blocks) is evaluated under different transient scenarios (reactivity insertion, primary coolant pump fault, and change in demand power levels). The power and temperature control blocks concurrently control reactor power during any transient occurrence. The coupling effect of the primary coolant temperature deviation on the reactor power has been minimized by the proportional and integral (PI) controller in the temperature control block. The simulation results demonstrate that the closed-loop performance of the ABR under the controller action during transient events is quite satisfactory. The closed-loop power regulation performance of the conventional sliding mode controller (SMC) with a PI sliding surface (PISM) in the power control block of NUSOL-LMR is better than that of a simple proportional, integral and derivative (PID) controller. The asymptotic stability of the closed-loop system with the PISM controller has been ensured using the Lyapunov stability theory.

Adaptive neural network sliding mode controller design for load following of nuclear power plant

The power control and load following of nuclear reactors have always been a research topic of concern in the field of nuclear power. In order to improve the control system performance and load following performance, this paper proposes a sliding mode control method based on adaptive RBF neural network (RBFNN) for pressurized water reactor (PWR) power control and load following. Firstly, based on the operation mechanism and energy transport process of PWR, the PWR power model is established based on the point-reactor equation. Then, based on Lyapunov stability theory, an ideal sliding mode controller is designed for a general nonlinear second-order model. Secondly, considering that some state variables in the actual PWR model cannot be directly measured, which leads to the problem that the actual control law cannot be directly applied, RBFNN is used as the controller, and its output is used to replace the actual control law and approximate the ideal control law. Adaptive algorithm is adopted to improve the approximation effect of RBFNN. Finally, the simulation results show that the proposed control method can achieve the PWR load following task well under the set working conditions, and has good robustness to disturbances. Compared with the traditional sliding mode control (TSMC) method, this method can effectively eliminate chattering phenomenon and greatly improve the control performance of the sliding mode controller.

An inherently fault tolerant control of sodium cooled fast reactors and its stability analysis using particle swarm optimization

In this study we propose a simple, yet inherently fault-tolerant and robust controller utilizing a combination of both feedforward and feedback control schemes. Feedback controllers are known to be robust, but feedforward controllers can be reliable in the context of safety as they can be less dependent on measurements. Though, many combined feedforward and feedback controllers have been proposed in the literature, to the best of our knowledge a controller tolerant to the failure of power feedback signal is nowhere demonstrated. In this scheme, major corrections are effected by a model predictive forward control unit, while bounded uncertain part is corrected by a feedback control unit. The feedforward control is implemented using the inverse equations of the nuclear reactor point kinetics model. The bounded error control is effected by a simpler limited Proportional–Integral–Derivative (PID) feedback controller. Stability analysis of the controller is carried out numerically by Lyapunov’s direct method with the help of Particle Swarm Optimization (PSO) technique. The proposed controller (referred to as Inverse Dynamics Corrected Control (IDCC)), is studied for reactor power control with model error plus uncertainty and a principal feedback signal failure case ( i.e. power sensor failure). It is shown that the IDCC has excellent load tracking performance for a challenging demand profile with model error, in comparison to Sliding Mode Controller (SMC) and a manually tuned PID controller. For the loss of principal feedback signal case, there is a trade off between the tracking performance of IDCC and safety aspects. While both PID and SMC drive the reactor power to unsafe levels, IDCC maintains the reactor power within a safer bound.

Output feedback Model Reference Adaptive Control of nuclear reactor

This paper presents an output feedback Model Reference Adaptive Controller (MRAC) for controlling the total power of a nuclear reactor. It ensures set point tracking and estimation of unmeasurable states in the presence of unknown external disturbances and parametric uncertainties. A mathematical model of reactor core based on normalized point kinetic equations, with six groups of delayed neutron precursors, is considered along with reactivity feedbacks due to lumped fuel and coolant temperature. Parametric variations in thermal feedback coefficients are taken as uncertainties, reactivity disturbance is considered as a matched external disturbance and change in inlet coolant temperature is considered as an unmatched disturbance. The desired setpoints for reactor power control are generated by choosing a stable reference model based on LQR theory. An observer is designed based on the asymptotic properties of LQG/LTR for the estimation of unmeasurable states as well as external disturbances. Adaptive laws based on output error are developed to compensate for the effect of matched uncertainties and external disturbances. Further, a feedforward controller is augmented to the adaptive laws to compensate for unmatched disturbances. Overall stability and ultimate boundedness of the closed loop signals are analyzed with Lyapunov theory. Performance of the proposed controller is demonstrated through dynamic nonlinear simulations.

Control of small pressurized water reactors under single-loop operation based on MFAPC theory

Small pressurized water reactors can supply power to ships, and single-loop operation is adopted to improve maneuverability under some abnormal conditions. Large key parameter fluctuations and the potential risk of human errors occur in conventional single-loop operation. Therefore, an automatic rapid power reduction method is proposed to improve the control performance of single-loop operation. An automatic rapid power-reduction method based on conventional control systems was tested. Poor power control performance and large fluctuations in steam generator water level were observed. Reactor power and steam generator water level control systems improved by the model-free adaptive predictive control (MFAPC) theory were developed, and the parameters of the MFAPC controller were optimized by the differential evolution method. The simulation results under single-loop operation show that the improved control systems reduce the overshoot of the reactor power and effectively suppress the water level fluctuation of the steam generator.

Backstepping based model reference adaptive control for nuclear reactor with matched and unmatched uncertainties

In this work, a Backstepping Model Reference Adaptive Controller (BMRAC) is designed to control the total power of a Pressurized Water Reactor (PWR). It ensures robustness against matched and unmatched parameter uncertainties and disturbances. Reactor core dynamics based on normalized point kinetics equations with six delayed neutron groups is considered, while parametric variations in thermal feedback coefficients, control rod worth and heat transfer coefficients are considered as uncertainties. Reactivity disturbance is considered as unmatched disturbance and external disturbances that enter from control input are considered as matched disturbance. A stable reference model is designed using linear quadratic regulator (LQR) theory to generate setpoints for reactor power control. The disturbances and uncertainties are estimated by comparing reactor dynamics with a stable predictor model. Matched parameter uncertainties and disturbances are compensated with robust MRAC. To compensate for unmatched disturbance, an integrator backstepping is designed. Projection-based adaptive laws are used to provide robustness to the designed controller. The ultimate boundedness of all signals is verified through Lyapunov analysis. Efficiency of the proposed controller is demonstrated through simulation studies, controller performance is compared with conventional LQR controller and adaptive MRAC controller.

Development of nickel alloy based hardfacing procedure for fast breeder test reactor control rod sheath using conventional gas tungsten arc welding process and metal cored alloy grade ERC Ni Cr – B

Fast Breeder Nuclear Reactors (FBR) will play a vital role to fulfill the power scarcity of developing India. The main products of the reactor assembly are manufactured using austenitic stainless steel - nuclear grades of AISI 316L. This material has excellent resistance to corrosion, better creep strength at higher temperature, and resistance to impact. Few reactor components are designed to perform rotation and translation movement for operation and control of reactor power. The relative motion between the components may lead to wear. Also, there is a possibility of self welding of these components due to high temperature and presence under a hot sodium working environment. Control rod sheath houses the control rod in a nuclear reactor which is used for raising or lowering the reactor output power. During operation of a nuclear reactor the control rod will move in and out. Due to this movement the control rod sheath will experience wear and tear. To reduce the wear and self welding problems throughout the operating period of the reactor, the components are designed with a layer of hard faced metal. Nickel based hard facing alloy is widely used for hard face coating in the nuclear reactor components. Since, it has high wear resistance under elevated temperature in the nuclear reactor. The process is done using Gas Tungsten Arc Welding (GTAW) by using the metal cored filler wire of grade ERC Ni Cr-B. Efforts have been put through this project for developing GTAW hard facing procedure and to observe the micro structure including micro hardness, macro hardness on coating as well as fusion zone and base metal.

LQG/LTR Controller Design for Power Control of Small Pressurized Water Reactors Under Four Feedback-Controlled Strategies

To improve the economy and safety of small pressurized water reactors (SPWRs) with flexible operating characteristics, the reactor power control system should process excellent robustness to provide satisfactory control performances at different operating conditions. This paper proposes four control strategies for reactor power control of SPWRs based on the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) robust control method, including the single-loop reactor power feedback control (RPFC), single-loop average temperature feedback control, dual-loop feedback control, and modified dual-loop feedback control (MDFC) strategies. The corresponding LQG/LTR controllers in the reactor power control system of a SPWR were designed to assess the performance of the four control strategies. The simulation results show that the LQG/LTR controller with the MDFC strategy can provide good control performances for both reactor power and average coolant temperature among the four control strategies while the controller-based single-loop feedback control shows poor control of the reactor power or average coolant temperature. Meanwhile, compared with the existing conventional reactor power control system, the designed robust control system employing the MDFC strategy can provide better control performance for the reactor power and average coolant temperature in full-power operation of 100% to 90% rated power and low-power operation of 25% to 35% rated power with the differential control rod worth taken as 4 pcm/step and 24 pcm/step, indicating its effectiveness and superiority.

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.

A boron-adjustment-free control strategy for large pressurized water reactors

This paper proposes an advanced boron-adjustment-free (BAF) control strategy for large pressurized water reactors (PWRs). The strategy combines the advantages of fast power compensation of the boron-adjustment Mode-G control strategy with the closed-loop axial offset (AO) control through control rods in the Mechanical Shim (MSHIM) control strategy. It can achieve fast power compensation, exact coolant average temperature control, and automatic AO control through three independently-moving control banks, respectively. Also, to avoid mutual interference between the core power and AO control, a novel blocking logic for the three control banks was developed. Simulation results of a large PWR implementing the BAF control strategy indicate satisfactory load-follow capabilities of the reactor without the need to adjust boron concentration. Moreover, the proposed blocking logic can provide better AO control without compromising reactor power control than that referring the blocking logic of reactor power and AO control banks in the MSHIM control strategy.

Model predictive and fuzzy logic controllers for reactor power control at Reaktor TRIGA PUSPATI

The Reaktor TRIGA PUSPATI (RTP) rely extensively on a core power control system for control reactivity to fulfilment the fundamental safety function for a nuclear reactor. It is technically challenging to operate within tight multiple parameter constraints and keep the core power output stable. At present, the power tracking performance of the system could be considered unsatisfactory which produces a relatively long settling time and high control effort. Hence, a study of a model predictive control (MPC) strategy by integrating the current Power Change Rate Constraint (PCRC) using fuzzy logic which is part of the core power control design is conducted. In this paper, the MPC design based on mathematical models of the reactor core included point kinetics model, thermal-hydraulic model, reactivity model and dynamic rod position model help to enhance core power control. The power tracking performance of the proposed control method and previous Feedback Control Algorithm-Fuzzy PCRC is compared via computer simulation with different power range operations. Overall, the results show the MPC-Fuzzy PCRC strategy provides a greater level of operational safety and optimum operation of the TRIGA reactor.

NSGA-II algorithm-based LQG controller design for nuclear reactor power control

The design of reactor power control system is closely related to the safety and economy of nuclear power plants. To improve its power control performance, this study takes a pressurized water reactor as the research object. The nonlinear dynamic mathematical model and its state space model were first derived; Then the Linear Quadratic Gaussian (LQG) optimal control method was adopted to design the reactor power controller; Furthermore, the multi-objective optimization of the linear quadratic regulator (LQR) weighting coefficient is carried out based on the elitist nondominated sorting genetic algorithm version II (NSGA-II). The results show that the LQG controller optimized based on NSGA-II method not only has fast response, high control accuracy and good stability, but also has good robustness and can obtain superior reactor power control performance.

Gradient descent-particle swarm optimization based deep neural network predictive control of pressurized water reactor power

A pressurized water reactor (PWR) is an integrated system of various interdependent subsystems that show highly nonlinear behavior, and each component is prone to uncertainties and malfunctions that initiate potential accidents. In contrast, PWR needs to be continuously monitored for stable and safe operation over a service time. In this study, a gradient descent-particle swarm optimization hybrid algorithm-based deep neural network (GD-PSO-based DNN) approach is proposed to monitor the PWR core power and outlet temperature. The Gaussian noise is introduced to the input signal, and the PWR core stability conditions are examined by using Lyapunov analysis. The simulation results verified under different conditions, in which the proposed control approach tracks the reference inputs successfully and enhances the stability as compared with the sliding mode control, linear quadratic regulator, and proportional-integral-derivative methods. The controller is validated by using the data from RELAP5 system codes, and the performance is examined using the mean square error, integral square error, integral absolute error, integral time square error, and integral time absolute error criterion functions. This study gives the benefit to apply the GD-PSO-based DNN control method for other nuclear engineering fields for system identification, prediction, and control.

Optimization of control rod travel for a small pressurized water reactor

The flexible operating conditions of small pressurized water reactors (SPWRs) demand frequent movement of control rods, causing a serious problem of control rod wear and tear. This study focused on the optimization of the control rod travel for an SPWR. Three optimization strategies were proposed to improve the reactor power control scheme by introducing proportional-derivative, lead–lag, and incomplete differential control modules in the power deviation channel, and a weighting factor in the temperature deviation channel. The parameters of the three control modules and the weighting factor were tuned using the non-smooth optimization algorithm in MATLAB. The optimization strategies were implemented in a control simulation platform of the SPWR, based on which dynamic simulations of the SPWR were performed under typical load change transients at different power levels. The results demonstrate that the optimization strategies can significantly reduce the control rod travel of the SPWR with satisfactory control performance.

Robust controller design for small pressurized water reactors using non-smooth optimization

The flexible operating conditions of small pressurized water reactors (SPWRs) under parameter uncertainties require highly robust control systems. This paper presents a robust controller design for an SPWR using non-smooth optimization. First, nonlinear mathematical models of the SPWR nuclear steam supply system were adopted and linearized to obtain the corresponding transfer function models. Then, sensitivity analysis of the SPWR physical and thermodynamic parameters was conducted to determine the critical uncertainty parameters for the robust controller design. Subsequently, the reactor power and steam generator feedwater robust control systems were designed under large uncertainties in the identified critical parameters. Finally, simulation studies of typical transients for the SPWR under high- and low-speed operating conditions of the main pump were performed. The results indicate that the designed robust control systems for the SPWR exhibit good performance and excellent robustness under large parameter uncertainties during various load change transients.

A fuzzy-PID series feedback self-tuned adaptive control of reactor power using nonlinear multipoint kinetic model under reference tracking and disturbance rejection

In this work, a series feedback combination of fuzzy and PID controllers is designed to resolve the reactor power control problem for VVER-1000 PWR.A nonlinear multipoint kinetic model based on neutron diffusion, thermal hydraulics, spatial neutronics and poison effect developed for dynamic simulation with three groups of delayed neutrons. PID controller design is accompanied with the variable gains depending upon the reactor power level and error power concerning a defined reference value. Piece-wise linearity and curve fitting is used to find a linear variation of gainsand incorporated in the fuzzy control design.The optimum values of PID gains are based on the Matlab Tools,desired performance indices of response andthe critical limitations of control output for accommodating the actuator motorboundaries. The proposed fuzzy-PID adaptive control model found preferable in load tracking application and disturbance rejection conditions in comparison with PID and fuzzy controllers in standalone configuration.