According to the mechanism analysis and simulation of power control system of MSHIM in AP1000, a modified MSHIM (Mechanical Shim) control strategy is presented, which employs the error between the reactor coolant average temperature and its reference value as the unique control signal with a Pcontroller added. The modified MSHIM control strategy is verified by simulations of three typical working conditions. The results show that the modified power control system satisfies the needs of reactor core power control and power distribution control. The conclusions have reference value for the engineering practice.
AP1000 is a twoloop pressurized water reactor (PWR) developed by Westinghouse, which uses the forces of nature and simplicity of design to enhance plant safety and reduce construction costs [
Compared to traditional reactor control strategies, the AP1000 adopts a different core control strategy, called Mechanical Shim (MSHIM) [
When it comes to the power control system, a threechannel controller is adopted in MSHIM, which is disposed from the traditional PWRs control system. In MSHIM control system, the AO control system is mainly reformed, but the power control system is similar to that in traditional PWR’s control system. Many scholars have been studying the control system of AP1000 and mainly focus on
As far as we know, the studies on the power control system in the MSHIM are very scarce. The present study aims at this purpose. This paper shows two main contributions of our work. Firstly, according to the simulation and analyzing of the original MSHIM control strategy, the power control system in MSHIM is modified. Secondly, the modified power control system is verified by three representative transient conditions.
The remaining of this paper is organized as follows. Section
In this paper, a simulation platform called Reactor Core Fast Simulation Program (RCFSP), which is developed in the MATLAB/SIMULINK environment based on the nodal method, is used for simulation and verification of the original and improved control strategy [
For detailed models containing the core physics calculations, thermalhydraulic analysis and burnup optimization are too costly for the dynamic simulations of the nuclear reactor because they are very complex and need tremendous calculation work. Therefore, a nodal method is used to describe the global power and axial power distribution of AP1000 reactor core here. The nodes are treated as independent cores coupled with each other through neutron flux. It is assumed that the neutron flux and material composition in each node are uniform. Thus, the neutron flux and other neutronic parameters in each node are represented by the respective average values integrated over its volume [
Figure
Nodalization of the AP1000 reactor core in the axial direction.
As described before, the nodal core model contains the neutron kinetic equations as (
The simulation flow diagram of RCFSP in SIMULINK is shown in Figure
RCFSP, simulation platform of AP1000 in MATLAB/SIMULINK environment.
The RCFSP is mainly made up of five parts: the power demand part, the Mbanks control system for power control, the AObank control system for axial power control, the reactivity calculation part, and the reactor core. The power demand part provides the target power for MSHIM operations. The Mbanks control system accounts for the core reactivity changes due to changes in power level and xenon concentration by the Mbanks position adjustment. The AObank control system maintains the core thermal margin within operating and safety limits through the motion of AObank. The motion of control rods would cause a change in the reactivity introduced into the reactor core. The reactor core calculates the variations of main physical and thermalhydraulic parameters with the variable step size solver Ode15s.
The simulation process of RCFSP is described in Figure
Simulation flow chart of RSFSP.
This simulation platform is developed in MATLAB/SIMULINK version R2014a. And this study is performed in a PC with CPU 2.30 GHz, ROM 8 GB, and Windows 8.1 operating system.
For nuclear reactor cores, the function of the power control system is to control and balance the core power and the load of turbine. Usually, the power control system is also referred to as the reactor coolant average temperature control system, whose function is implemented based on the threechannel nonlinear controller, as shown in Figure
Block diagram of the power control system of MSHIM in AP1000.
From Figure
As shown in Figure
The signal of power error is added to the control signal through the differential circuit, the variable gain (
One of the drawbacks of using the average temperature of the coolant as the control system is that it has a significant time delay and thus introduces a large lag into the feedback loop. In this way, the power mismatch pulse should be involved to enhance the response speed of the system. However, there are some problems when the power mismatch pulse is involved. Firstly, the nuclear reactor core is a selfstabilizing system. Although the response speed of the control system can be enhanced using the power error signal, the control rods may respond too quickly in the event of a perturbation in the power signal, which reduces the efficacy of the negative feedback on the core itself. This can easily cause the loss of control rods due to fatigue. Secondly, since the time constant of the neutron kinetic equation is small, the neutron flux level is more likely to be influenced by the perturbation. Thus, the noise of the power mismatch channel is too large for its use as the differential advanced control channel. On the other hand, if a large time constant of the filter in the channel is selected, the speed and amplitude of the signal will be decreased, which is not suitable for the initial purpose of controlling in advance.
To assess the feasibility and performance of the improved MSHIM control strategy, the original and improved MSHIM strategies are applied to AP1000 in RCFSP. The control signals of coolant average temperature error and power error are analyzed first.
AP1000 has been demonstrated to be able to perform the MSHIM operation during a wide range of anticipated operational scenarios. Among these scenarios, three typical conditions are performed in this paper.
Power level decreases from 100% to 50% FP (full power) at a rate of 5% FP/min. The simulation duration is 1500 seconds, and, in the first 200 seconds, the reactor core is 100% FP stable. The desired power is reduced to 50% FP with a velocity of 5% FP/min from 200th second; subsequently, it is 50% FP until the end of the condition.
Power level steps down from 100% to 90% FP. The simulation duration is 1500 seconds, and, in the first 200 seconds, the reactor core is 100% FP stable. The desired power is reduced to 90% FP at 200th second; subsequently, it is 90% FP until the end of the condition.
Power level varies from 100% to 50% in 3 h, holds at 50% for 6 h, and then rises to 100% in 3 h. The simulation duration is 96 hours, and, in the first 24 hours, the reactor core is 100% FP stable. The desired power is reduced to 50% FP from 24th hour in 3 hours, holds at 50% FP for 6 hours, and then rises to 100% FP in 3 hours; subsequently, it is 100% FP until the end of the condition.
The control signals of coolant average temperature error and power error under Conditions 1, 2, and 3 are illustrated in Figures
Comparison of two control signals under 5% FP/min ramp load decrease condition.
Comparison of two control signals under 10% FP step load decrease condition.
Comparison of two control signals under load follow condition.
As shown in Figure
As shown in Figure
From Figure
From these comparisons, under three conditions, it can be seen that the power error signal is much smaller than the coolant average temperature error signal in most of conditions, and the power error signal is large within a short period of time only in the step load change condition but still smaller than the coolant average temperature error signal.
According to the analyzing of the control signals in the original power control system of MSHIM, a modified one is presented in this paper. Considering the smaller value of power error signal in the original system, the power error signal is eliminated. Meanwhile, for the compensation of the control speed under the step load change, a Pcontroller is added in the coolant average temperature error signal.
As a result, the modified power control system of MSHIM is a twochannel power controller, as shown in Figure
Modified power control system of MSHIM in AP1000.
The most important criterion to evaluate the stability of the control system is the fast and accurate control of the power level around the target value. Additionally, the AO value should be controlled within the control objective band. For quantitative analysis, 5 suitable performance indices are used to assess the performance of the original and modified MSHIM control strategies.
The squared integral of the relative power mismatch is defined as
The squared integral of the AO mismatch is defined as
The power peak factor is defined as
In addition to these three parameters,
As mentioned above, three typical load change transients are simulated to assess the feasibility and performance of the original and modified control strategies. The simulation parameters are listed in Table
Parameters of the power control system simulation.
Parameters  Value 


5 

40 

5 

30 

50 

2 
The 5% FP/min ramp load decrease simulation results of the original and modified control strategy are shown in Figure
Five performance indices from the 5% FP/min ramp load decrease simulation of the original and modified power control system in MSHIM.
Performance indices 



MSteps  AOSteps 

Original  196.27  5.43  1.1605  540  9 
Modified  24.72  5.38  1.1602  578  9 
The 5% FP/min ramp load decrease simulation results obtained with the improved MSHIM control strategy: (a) desired and real nuclear powers (% FP), (b) AO (%), (c) Mbank position (Step), and (d) AObank position (Step) (the prefixes “ORI” and “MOD” denote the “original” and “modified,” resp.).
From Figure
This condition shows that the modified control system can control the core power and the axial power offset well in the 5% FP ramp load decrease. However, such improvement is based on the tradeoff to increase the motion of the control rods.
The 10% FP step load decrease simulation results of the original and modified control strategy are shown in Figure
Five performance indices from the 10% FP step load decrease simulation of the original and modified power control system in MSHIM.
Performance indices 



MSteps  AOSteps 

Original  257.04  3.02  1.1590  152  7 
Modified  113.70  3.20  1.1571  171  7 
The 10% FP step load decrease simulation results obtained with the improved MSHIM control strategy: (a) desired and real nuclear powers (%FP), (b) AO (%), (c) Mbank position (Step), and (d) AObank position (Step).
Figure
This condition shows that, based on the tradeoff to increase the motion of the control rods, the modified control system can control the core power and the axial power offset well in the 10% FP step load decrease.
The load follow simulation results of the original and modified control strategy are shown in Figure
Five performance indices from the load follow simulation of the original and modified power control system in MSHIM.
Performance indices 



MSteps  AOSteps 

Original  233.81  12.88  1.1431  2477  352 
Modified  135.18  9.94  1.1447  3073  416 
The load follow simulation results obtained with the improved MSHIM control strategy: (a) desired and real nuclear powers (%FP), (b) AO (%), (c) Mbank position (Step), and (d) AObank position (Step).
From Figure
In this paper, a modified MSHIM control system is introduced and verified by theoretical and simulation analysis. In the new control system, the coolant average temperature error signal is used to control the power level in the reactor core. The proposed method has been verified by dynamic performance simulation and compared to the original control system. The calculation results showed that the modified control system has simplified the control logic and enhanced the control performance at the same time.
Relative concentration of the delayed neutron precursor
Diffusion coefficient
Center distance of the neighboring nodes
Difference between the relative power and the target power
Difference between the real and target AO
Power peak factor
Fraction of the core power generated in the fuel
Control component
Relative concentrations of iodine
Squared integral of the relative power mismatch
Squared integral of the AO mismatch
Variable gain
Nonlinear gain
Product of mass flow rate and the heat capacity of the coolant
Relative neutron concentration
Power
Temperatures
Relative concentrations of xenon.
Reactivity coefficients
Fraction of the delayed neutron group
Fission yields
Node height
Average neutron generation time
Decay constant
Heat capacities
Reactivity
Microscopic cross section
Time constant
Neutron flux
Transfer coefficient between the fuel and coolant.
Average value
Error
Reference value
Node number
Steadystate value
Fuel
Coolant
Iodine
Xenon.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Science Foundation of China under Grant 11405125, China Postdoctoral Science Foundation Funded Project under Grant 2014M562420, and the Fundamental Research Funds for the Central Universities of China under Grant 2015gjhz09.