Small Modular Reactor Reactivity Disturbance Suppression Method Based on Core Coolant Flow Control

Nuclear reactors may suffer from various disturbances during operation. These disturbances can cause core power deviates from the set parameters, and affect the power level of reactors. Due to the limited internal space of the reactor, the number of control rods is small. It is difficult to set up control rod groups dedicated to reactive compensation for modular reactor of medium or small size. Therefore, it is necessary to study a set of reactivity compensation measures that do not rely on control rods according to the actual needs of modular reactors to compensate for the power deviation caused by reactivity disturbances. A disturbance suppression method based on coolant flow control is proposed in the study. This method takes advantage of the Doppler effect of the coolant temperature, and changes the coolant flow rate to affect its temperature when reactive disturbances occur, thereby compensating for fluctuations of reactivity. Numerical experiments show that this method can effectively suppress the power deviation caused by reactive disturbances, and has engineering application value.


I. INTRODUCTION
Small modular nuclear reactors have been developed widely during recent years. For ensuring safe and effective operation, a desirable core power control system is necessary for small modular reactors [1,2]. The core power control system should have two critical functions: core power level control (figure 1), and reactivity disturbances suppression [3].
For the core power level control, there are some advanced methods are developed gradually. Including Model Reference adaptive control [4][5], model predictive control [6][7][8], fuzzy logical control [9], linear quadratic gaussian with loop transfer recovery [10][11], sliding mode control [12][13][14], and fractional order control [15,16]. Some of them have gradually become mature methods for power level control. Besides on the adjustment of power level, nuclear reactors may suffer from various reactivity disturbances during operation. These disturbances can cause core power deviates from the set parameters, and affect the power level of reactors. However, for modular reactors, the internal space is limited, so that there may be not enough control rods for reactivity disturbances suppression in modular reactors. Therefore, it is necessary to study a set of reactivity compensation measures that do not rely on control rods according to the actual needs of modular reactors to compensate for the power deviation caused by reactivity disturbances.
For the purpose of reactivity disturbances suppression in modular nuclear reactors, a reactivity disturbances suppression method without control rods movement or boron concentration adjustment was developed in this work. Considering the Doppler effect of coolant and fuel temperature, a disturbance suppression method based on coolant flow control is proposed. This method changes the coolant flow rate to affect its temperature when reactive disturbances occur, thereby compensating for fluctuations of reactivity.
The rest of this paper is organized as follows: Firstly, a common NPP dynamic model containing neutron kinetic and thermal-hydraulic was built; and then the formulation of control problem about uncertain reactivity disturbances was presented; after that, based on the analysis of zero-poles, the disturbance suppression scheme based on flow control was designed. at last, the effectiveness of the reactivity disturbances suppression method is verified.

II. Reference Design
In order to establish a simulation model and verify the effectiveness of the method in this study, the SNCLFR-100 is regarded as the reference design.
SNCLFR-100 is a typical modular reactor with only a small number of control rod groups for power level adjustment, and no boron adjustment equipment or control rods for reactivity compensation. Although the primary circuit coolant of the SNCLFR-100 is lead, the method proposed in this article is also applicable to coolants such as water and carbon dioxide.
SNCLFR-100 is a 100 MWth lead-cooled small modular reactor with a passive cooling feature to both normal and abnormal operations, was proposed by University of Science and Technology of China (USTC). The reactor is well suited as a remote power source because of its compact size, as well as because it has a refueling interval of 10 years without assembly reconfiguration. The major parameters of SNCLFR-100 are listed in Table 1 [17]. The primary cooling model of SNCLFR-100 is fully natural circulation, which is not conducive to core coolant flow control.
Therefore, this article improves the design of the SNCLFR-100, which is named SNCPWR-100, four non-seal centrifugal pumps are used to regulated the flow, and the type of coolant changed from lead to pressurized water with 15.5MPa. The major parameters of SNCPWR-100 are listed in Table 2.

III. Modeling
The following lists the calculation equations of neutron kinetic and Thermal-hydraulic models, and the detailed deduction of these equations was presented in the paper of Liming Zhang [3].

A. Neutron Kinetic
The linearized neutron kinetic model as follows: (1) And the total reactivity is the control rod reactivity combined with the feedbacks described as follows:

B. Thermal-hydraulic
(1) Core The increment form of core heat transfer process can be given as: (

2) Steam Generator
The increment form of steam generators heat transfer process can be given as:

C. Coupling Process
In the SMR model, (Δ , Δ ) , (Δ , Δ ) , and MATLB/Simulink software is used to simulate the above model, and the figure 2 is the simulation flow chart of the model. The simulation results are shown in figure 3 to figure 5. In the case of power perturbation, the steady-state power of the reactor changes, although the reactor has good sub-stability (lost 5% of our power). If reactivity compensation is not carried out, the output power will be affected.

Control
Due to the small number of control rod groups in modular reactors, additional reactivity compensation schemes need to be developed to suppress the effects of reactivity disturbances. Considering the significant negative temperature Doppler feedback effect in the core coolant, the reactivity can be compensated from the temperature by changing the core coolant temperature in reverse to maintain the constant power level.
The overall disturbance suppression strategy designed is shown in figure 6. In this strategy, the reactor core power is used as feedback, and the core flow rate is changed through the regulation of the controller, so as to affect the coolant temperature in the core, and then the introduction of reactivity is changed through the Doppler effect. And the controller adopts common PID controller as follow: ΔG = ΔP + K ∫ ΔPdt 0 (11) In order to ensure that the reactor power can completely converge to the initial state, the integral coefficient K is introduced. In order to speed up the adjustment process, differential terms are not used.
The overall stability of the reactor system can be further ensured by the zero-pole distribution under the action of the above mentioned PID controller, that is, after the addition of the above mentioned PID controller, as is shown in figure 7, all the poles of the system are in the left half-open plane of the complex plane (L.H.C.P) [18]. The inhibition effect of the controller designed in this paper on the reactivity disturbance is shown in figure 8 (including power, core temperature and steam generator temperature).    In conclusion, the disturbance suppression scheme based on flow control can effectively regulate the stability of reactor power, core temperature and evaporator temperature.

VI. Conclusion
When modular nuclear reactors suffer from uncertain reactivity disturbance, core power may deviate from the set parameters, and affect the power level of reactors. Due to the limited internal space of modular nuclear reactors, the number of control rods is small. It is difficult to set up control rod groups dedicated to reactive compensation for modular reactor of medium or small size. In the future, we will continue to verify the disturbance suppression method based on full scope simulator of NPPs.
Moreover, the couple mode between the disturbance suppression method and power level control method also needs to be researched.

ACKNOWLEDGMENT
We thank the great help from Southeast University in this research.