基于LMIs的核电站蒸汽发生器水位控制策略研究

核电站蒸汽发生器水位常因多种干扰而具有不确定性,因此传统线性水位控制系统较难满足核电站运行要求。针对具有一定不确定性的核电站蒸汽发生器水位模型,根据其特性,借助线性矩阵不等式(LMIs)设计状态反馈H^∞控制器、基于极点配置的H^∞控制器以及H^∞跟踪控制器。在不同稳定工作点下通过仿真试验对上述控制器的效果进行验证和比较,得出了不同稳定工作点下控制策略的特性。     

Estimate of the parameters of feedback on power and the stability of IBR-2 for different average power levels

Experimental and model studies of the parameters of fast feedback on power as a function of the average power of IBR-2 have been performed. Transient power processes caused by square fluctuations of reactivity have been investigated. The changes in the parameters are estimated for average power ranging from 0.5 to 1.5 MW. The results obtained are compared with data from previous experiments performed in 1984–1996. It is noted that the influence of feedback on power decreases as the reactor operating time increases. The model of a reactor with parameters of feedback on power which correspond to one series of experiments is investigated for stability by the frequency method. It is shown that at the regular average power level 1.5 MW a reactor in a self-regulating regime (i.e., without an automatic regulator) possesses an adequate margin of stability. __________ Translated from Atomnaya énergiya, Vol. 103, No. 2, pp. 89–93, August, 2007.     

核反馈实时模拟程序

为了在堆外实验中实现核反馈实时模拟,用C 语言开发了核反馈模拟程序.该程序由3个主要模块组成:反应性反馈模拟、功率控制系统模拟及反应堆模拟.采用的主要物理模型有:点堆模型、一维均匀流体模型、瞬态导热模型等;堆功率控制系统模拟方案为平均温度控制方案;其他辅助计算包括物性参数、几何参数的计算.用Retran-02计算分析数据对模拟程序进行了测试,结果表明,模拟程序的数学模拟正确,运算速度快,计算准确.     

A new approach to plasma profile control in ITER

Advanced tokamak operation in ITER, such as the steady-state and hybrid modes, requires an active real-time feedback control of plasma profiles to achieve the advanced regimes for sustained operation. In this work, we have explored a potentially robust control technique that simplifies the active real-time control of electron temperature and safety factor profiles in ITER. As a new and simple approach, static responses of the plasma profiles to power changes of auxiliary heating and current drive are modelled and updated in real-time, differing from the techniques which use a dynamic model deduced from identification experiments, or even a simplified explicit model. To allow real-time update of the plasma profile response model, the underlying physics is simplified with several assumptions. The electron temperature profile response is modelled by simplifying the electron heat transport equation. The safety factor profile response is modelled by directly relating it to the changes of source current density profiles. The required actuator power changes are calculated using the singular value decomposition technique, taking the saturation of the actuator powers into account. The potential of this control technique has been tested by applying it to simulations of the ITER hybrid mode operation using CRONOS. In these simulations, the electron temperature and safety factor profiles were well controlled either independently or simultaneously.     

核动力堆热功率跟踪系统的多步模型算法控制仿真研究

动力堆控制系统是一带不确定参数及干扰的复杂非线性系统,采用常规的古典控制很难保证其势功率精确跟踪负荷的变化。本工作利用系统开环脉冲响应序列建立了一非参数模型,并应用多步模型算法控制原理提出了一种动力堆热功率跟踪数字控制方法。该方法跟踪调节性能好、鲁棒性强、能消除不可测干扰。通过仿真检验和调试证明了该方法的正确性和有效性,并实现了热功率-负荷的高精度匹配。     

Modeling aspects in linear stability analysis of a self-pressurized, natural circulation integral reactor

The stability of a self-pressurized natural circulation integral reactor is studied by means of a linear approach, taking the CAREM-25 reactor as reference.A thermohydraulic code has been improved for analysis of linear stability, great emphasis having been placed on the minimization of numerical diffusion and integration errors. A linearization method is implemented by means of numerical perturbations. The results are obtained within the frequency domain. The code is compared to a simpler analytical model, by contrasting stability maps obtained from both models for a test configuration, showing good agreement.In this type of reactor, oscillations are promoted by the two-phase regime in its long riser, and take place due to the counteraction between mass flow and buoyancy force.The stability of the system is strongly influenced by the steam-dome dynamics. Condensation in the steam zone, together with reactor power, determines the dynamical state of the system.The phase-lag introduced by the core dynamic regarding the riser timing, together with the sensitivity of the buoyancy force due to flow changes, determines the sustainability of the oscillation. A parametric study is carried out, gradually increasing the complexity of the model, to analyze the influence of different factors on the oscillation sustainability, concerning physical process and modeling approaches. The analysis includes the relative velocities between phases, the axial power profile along the core, the buoyancy force due to subcooled density changes, the flashing effect, the core dynamic and the pressure feedback due to self-pressurization. The steam-dome-pressure feedback is identified as a stabilizing effect, as long as it decreases the sensitivity of the buoyancy force.     

Analysis of non-stationary fluctuations in a nuclear power reactor with temperature feedback

We analyse the behaviour of the neutron density and temperature fluctuations of a non-linear power reactor model during the transient regime. The equations for both fluctuations are derived by applying the system-size expansion method to the master equation which models the system. The behaviour of the fluctuations, assuming a temperature feedback effect, is analysed.     

核电工程设备监理经验反馈体系的构建

介绍了经验反馈体系的组建原则、工作流程及报告要求;阐明了核安全管理当局、核电业主及设备监理单位各自的职能以及在经验反馈工作中的作用.给出了事件信息采集、分析、反馈与跟踪过程等规范性工作要求;事件报告与经验反馈报告特点与方式.着重强调了在信息分析方面应采用重大事件专项分析与整体分析相结合的方式,并将经验反馈工作与设备监理技术开发相结合和与当前工程设备制造紧密结合,从而最大限度地利用经验反馈信息,以进一步提高经验反馈工作的针对性和有效性.     

Nonlinear stability analysis of a reduced order model of nuclear reactors: A parametric study relevant to the advanced heavy water reactor

In this paper, we perform a parametric study of the nonlinear dynamics of a reduced order model for boiling water reactors (BWR) near the Hopf bifurcation point using the method of multiple scales (MMS). Analysis has been performed for general values of the parameters, but the results are demonstrated for parameter values of the model corresponding to the advanced heavy water reactor (AHWR). The neutronics of the AHWR is modeled using point reactor kinetic equations while a one-node lumped parameter model is assumed both for the fuel and the coolant for modeling the thermal-hydraulics. Nonlinearities in the heat transfer process are ignored and attention is focused on the nonlinearity introduced by the reactivity feedback. It is found that the steady-state operation of the AHWR mathematical model looses stability via. a Hopf bifurcation resulting in power oscillations as some typical bifurcation parameter like the void coefficient of reactivity is varied. The bifurcation is found to be subcritical for the parameter values corresponding to the AHWR. However, with a decrease in the fuel temperature coefficient of reactivity the bifurcation turns to supercritical implying global stability of the steady state operation in the linear stability regime. Moreover slight intrusion into the instability regime results in small-amplitude limit cycles leaving the possibility of retracting back to stable operation.     

Experimental study of natural circulation instability with void reactivity feedback during startup transients for a BWR-type SMR

The natural circulation boiling type SMR can experience flow instability during the startup transients due to the void reactivity feedback. A BWR-type natural circulation test loop has been built to perform the nuclear coupled startup transient tests for Purdue Novel Modular Reactor (NMR). This test loop is installed with different instruments to measure various thermal hydraulic parameters. The testing process can be monitored and controlled through PC with the assistance of LabVIEW procedure. The effects of power ramp rate on the flow instability during the nuclear coupled tests were investigated by controlling the power supply based on the point kinetics model with coolant void reactivity feedback. Two power ramp rates were investigated and the results were compared with those of the thermal hydraulic startup transients without void reactivity feedback. The time trace of power supply, system pressure, natural circulation rate, and void fraction profile are used to determine the flow stability during the transients. The results show that nuclear coupled startup transients also experience flashing instability and density wave oscillations. The power curves calculated from point kinetics model for startup transients show some fluctuations due to void reactivity feedback. However, the void reactivity feedback does not have significant effects on the flow instability during the startup procedure for the NMR.     

Impact of core electron temperature on current profile broadening with radio-frequency wave heating and current drive in EAST

In recent EAST experiments, current profile broadening characterized by reduced internal inductance has been achieved by utilizing radio-frequency current drives (RFCD). In contrast to previous density scan experiments, which showed an outward shift of the current density profile of lower hybrid current drive (LHCD) in higher plasma density, the core electron temperature (Te(0)) is found to affect the LHCD current profile as well. According to equilibrium reconstruction, a significant increase in on-axis safety factor (q0) from 2.05 to 3.41 is observed by careful arrangement of RFCD. Simulations using ray-tracing code GENRAY and Fokker–Planck code CQL3D have been performed to thoroughly analyze the LHCD current profile, revealing the sensitivity of the LHCD current profile to Te(0). The LHCD current density tends to accumulate in the plasma core with higher current drive efficiency benefiting from higher Te(0). With a lower Te(0), the LHCD current profile broadens due to off-axis deposition of power density. The sensitivity of the power deposition and current profile of LHCD to Te(0) provides a promising way to effectively optimize current profile via control of the core electron temperature.     

Space dependent slow power transients in high-temperature pebble-bed reactors

An outline of the space-time xenon behaviour in HTR pebble-bed reactors is given. For reactors of about 600 MW_e and more, detection and control of azimuthal transients have to be provided. For pebble-bed reactors with OTTO-fuel-management, the xenon and power density transients induced by load-following are reported. The asymmetric axial profile of the power density in that reactor proves to be very stable during electrical load changing.     

Calibration of new I&C at VR-1 training reactor

The paper describes a calibration of the new instrumentation and control (I&C) at the VR-1 training reactor in Prague. The I&C uses uncompensated fission chambers for the power measurement that operate in a pulse or a DC current and a Campbell regime, according to the reactor power. The pulse regime uses discrimination for the avoidance of gamma and noise influence of the measurement. The DC current regime employs a logarithmic amplifier to cover the whole reactor DC current power range with only one electronic circuit. The system computer calculates the real power from the logarithmic data. The Campbell regime is based on evaluation of the root mean square (RMS) value of the neutron noise. The calculated power from Campbell range is based on the square value of the RMS neutron noise data. All data for the power calculation are stored in computer flash memories. To set proper data there, it was necessary to carry out the calibration of the I&C. At first, the proper discrimination value was found while examining the spectrum of the neutron signal from the chamber. The constants for the DC current and Campbell calculations were determined from an independent reactor power measurement. The independent power measuring system that was used for the calibration was accomplished by a compensated current chamber with an electrometer. The calculated calibration constants were stored in the computer flash memories, and the calibrated system was again successfully compared with the independent power measuring system. Finally, proper gamma discrimination of the Campbell system was carefully checked.     

弱耦合堆芯功率调节系统的稳定性

对两个弱耦合堆芯的功率调节系统的稳定性作了分析研究,由一个简单物理模型得到了弱耦合堆芯之间的耦合反馈系数和反馈传递函数,建立了弱耦合堆芯的功率调节方块图,对系统作了稳定性分析,得出了堆功率的稳定范围,分析了系统参数变化对稳定功率阈值的影响,结果表明,在一定的耦合条件下,超过某个功率阈值将导致系统不稳定;随着两个堆芯区域之间的耦合减弱,这一功率阈值变低,反应堆只能在较低功率水平下稳定运行。     

Controlled magnetohydrodynamic mode sustainment in the reversed-field pinch: Theory, design and experiments

A novel control system design for magnetohydrodynamic (MHD) resistive-wall mode (RWM) stabilization is developed from the viewpoint of process control. The engineering approach assumed consists of system identification, selection of feedback interconnections, and subsequently, associated feedback gain tuning. A design for general output tracking is devised, implemented and experimentally verified to be capable of sustaining MHD modes in the reversed-field pinch (RFP) machine EXTRAP-T2R. In principle, by active feedback, the plasma column boundary is forced to ‘user-specified’ helicities of prescribed amplitudes and phases. Experimental success is mainly attributed to careful identification of local magnetic field diffusion time-constants, and individual actuator channel peripheral dynamics. Addition of functionality and key features of this new MHD feedback system software might provide a versatile tool for experimental plasma dynamics and innovative MHD stability research.     

Paralleling Inverters Study of EAST Vertical Stability Coil Power Supply

Experimental advanced superconducting tokamak vertical stability (VS) coil power supply is a large capacity single phase inverter power supply. To meet the requirement of large current and fast response, multi-inverters in parallel is presented, which based on carrier phase-shifted modulation technology. In parallel inverter system, the disperse circuit parameters and phase-shift carriers between parallel inverter units will cause circulating current, which contains fundamental component and a large number of harmonic components. In this paper, the model of circulating current is analyzed when VS coil power supply is working in voltage given mode, and an instantaneous current sharing control strategy is proposed based on the combination of current sharing inductor and instantaneous circulating current feedback control. Parallel inverter units are connected together through current sharing inductors which can change the impedance characteristic of the circulating impedance and well restrain the high-frequency circulating current. Then, the real part of the circulating impedance will be increased and the ability to restrain the low-frequency circulating current will be advanced by introducing virtual resistance, which is realized in the instantaneous circulating current feedback routine. The designations of the current sharing inductor and the virtual resistance are provided. The results of simulation and experiment verify that this current-sharing strategy is available and efficient.     

Design and implementation of power and phase feedback control system for ICRH on EAST

Ion cyclotron wave resonance heating(ICRH) is one of the most important auxiliary methods to heat plasma in the Experimental Advanced Superconducting Tokamak(EAST). Several megawatts of power is transmitted through separate coaxial lines and coupled with the plasma through arrays of loop antennas. The parameters of the ICRH system, including the injected power and phasing between antenna straps, are critical to the coupling efficiency of the power as well as the resulting impact on the heating efficiency. In this paper, we present a system for feedback control of the phase between the current straps and the ICRH power on EAST. The feedback control system was tested using both a matched dummy load and a plasma load, and it successfully maintained stable operation in the 2016 EAST campaign. Good control of the injected power and wave phases was achieved during edgelocalized mode operation.     

Pulsed Turbulence of the Neutron Field in Nuclear Reactors

It is shown on the basis of a one-group diffusion model with delayed neutrons that if the pulsed feedback function is negative and nonmonotonic and the gain of the feedback is large, an autooscillatory regime of spatiotemporal chaos, called the regime of pulsed turbulence of the neutron field, arises in small reactors. It consists in the fact that neutron bursts with random intensity arise at random times in local regions of the reactor, whose size, shape, and arrangement in the core vary irregularly with time. It is indicated that this regime is possible and could be desirable in reactors with a gaseous core.     

Synthesis of Digital Control Systems for Nuclear Reactors, (II)

Abstract

The purpose of this paper is to elaborate a closed-loop digital control system to regulate a reactor during commanded changes of power level, making use of the optimal control and trajectories derived in the previous paper. Simple application of this optimal control scheme alone would not permit satisfactory control of the reactor, on account of various external disturbances that would affect the control in actual practice. This difficulty has been overcome by linearizing the system equations around the optimal control and trajectories derived as above, and thereto applying modern control theory.

The feedback control system is first examined for a case where all requisite state variables are accessible. Then for the case where not all state variables are thus accessible, a method is devised for estimating the inaccessible variables. The estimates are obtained by detecting the accessible state variables a given number of times during each control stage, using the generalized inverse.

A closed-loop system is constituted by incorporating this method of estimation into the feedback circuit. The resulting system is shown to provide amply satisfactory performance in terms of response time and the accuracy.