The best estimation process of AP1000 Nuclear Power Plant (NPP) requires proper selections of parameters and models so as to obtain the most accurate results compared with the actual design parameters. Therefore, it is necessary to identify and evaluate the influences of these parameters and modeling approaches quantitatively and qualitatively. Based on the best estimate thermalhydraulic system code RELAP5/MOD3.2, sensitivity analysis has been performed on core partition methods, parameters, and model selections in AP1000 Nuclear Power Plant, like the core channel number, pressurizer node number, feedwater temperature, and so forth. The results show that core channel number, core channel node number, and the pressurizer node number have apparent influences on the coolant temperature variation and pressure drop through the reactor. The feedwater temperature is a sensitive factor to the Steam Generator (SG) outlet temperature and the Steam Generator outlet pressure. In addition, the crossflow model nearly has no effects on the coolant temperature variation and pressure drop in the reactor, in both the steady state and the loss of power transient. Furthermore, some fittest parameters with which the most accurate results could be obtained have been put forward for the nuclear system simulation.
Nowadays, sensitivity analysis (SA) is becoming increasingly widespread in many fields of engineering and sciences, encompassing practically many computational modeling and process simulation activities. The sensitivity analysis is to study how the variation in the output of a model (numerical or otherwise) can be apportioned, qualitatively or quantitatively, to different sources of inputs, and how the given model depends upon the information fed into it. Furthermore, sensitivity analysis studies the relationships between information flows in and out of the model [
According to Saltelli et al. (2000) [
The global sensitivity analysis (GSA) methods explore the whole distribution range of the model inputs and the effects of their mutual combination, which quantify the effect of all uncertain input parameters simultaneously over their ranges of variations.
Several sensitivity analysis techniques are available from the simplest of scatter plots to more sophisticated sensitivity analysis techniques, which are listed in Hoseyni et al. (2014) [
The Pearson (or sample) correlation coefficient (CC) between inputs
Apart from these quantitative sensitivity analysis measures for the parameters, sensitivity importance evaluation could also be implemented qualitatively for model selection and nodal partition methods so as to make the most suitable models and simulation processes with which the most accurate computational results could be obtained compared with the system design values [
As is known, conflicting and contradictory claims are often made about the relative models and parameter selections during the simulation processes of Nuclear Power Plants, which may cause some unpredictable influences on the code outputs. For example, when using RELAP5 code to simulate the AP1000 NPP systems, as is shown in Figure
AP1000 reactor coolant system and passive core cooling system.
Within the AP1000 systems, the development of a RELAP5 input model started in 1999; during these years the model has been continuously improved and updated to reflect the actual plant configuration, culminating in the model documented in Ansaldo Nucleare S.p.A. (2010) [
AP1000 RELAP5 model simplified scheme.
Figure
Reactor core division models of AP1000 Nuclear Power Plant.
Three core channels’ model
Five core channels’ model
As can be seen from Figure
During the simulation procedure of AP1000 NPP systems, different node division methods may have different influences on the code output; thus sensitivity analysis on core channel node number in the axial direction should be carried out during the system simulation process. According to [
The influence of core channel node number on the coolant temperature variation.
Node number  Reactor inlet temperature (K)  Reactor outlet temperature (K)  Calculated temperature variation (K)  Designed temperature variation (K)  Fractional error 

5  554.516  593.6928  39.1768  40.4  3.03% 
10  554.3637  594.7499  40.3862  40.4  0.03% 
15  554.2802  595.3843  41.1041  40.4  1.74% 
20  554.1759  596.17845  42.00255  40.4  3.97% 
30  553.95  597.64  43.69  40.4  8.14% 
40  553.8906  598.1865  44.2959  40.4  9.64% 
50  553.8235  598.3517  44.5282  40.4  10.22% 
The influence of core channel node number on the reactor pressure drop.
Node number  Reactor inlet pressure (MPa)  Reactor outlet pressure (MPa)  Calculated reactor pressure drop (MPa)  Designed reactor pressure drop (MPa)  Fractional error 

5  15.7545  15.3944  0.3601  0.43  16.26% 
10  15.8342  15.4213  0.4129  0.43  3.98% 
15  15.8947  15.3997  0.495  0.43  15.12% 
20  15.9516  15.4006  0.551  0.43  28.14% 
30  16.0739  15.6097  0.4642  0.43  7.95% 
40  16.1328  15.6315  0.5013  0.43  16.58% 
50  16.1675  15.6589  0.5086  0.43  18.28% 
According to the design parameters of AP1000 Nuclear Power Plant, the reactor entrance and outlet coolant temperatures are 554.37 K and 594.77 K, respectively [
The influence of core channel node number on the fractional error between calculated and designed coolant temperature variation.
As can be seen from Table
In reference to the design documents of AP1000 NPP (AP1000 Design Control Document, 2010), the overall drop of coolant pressure in the reactor is
The influence of core channel node number on the fractional error between calculated and designed reactor pressure drop.
As can be seen from Table
According to Figure
The influence of core channel number on the coolant temperature variation.
Core channel number  Reactor inlet temperature (K)  Reactor outlet temperature (K)  Calculated temperature variation (K)  Designed temperature variation (K)  Fractional error 

1  554.3814  594.6475  40.2661  40.4  0.33% 
3  554.3778  594.6639  40.2861  40.4  0.28% 
5  554.3637  594.7499  40.3862  40.4  0.03% 
10  554.295  594.965  40.67  40.4  0.67% 
20  554.2796  595.0128  40.7332  40.4  0.82% 
The influence of core channel number on the reactor pressure drop.
Core channel number  Reactor inlet pressure (MPa)  Reactor outlet pressure (MPa)  Calculated reactor pressure drop (MPa)  Designed reactor pressure drop (MPa)  Fractional error 

1  15.8223  15.4123  0.4100  0.43  4.65% 
3  15.8250  15.4166  0.4084  0.43  5.02% 
5  15.8342  15.4213  0.4129  0.43  3.98% 
10  15.891  15.6085  0.2825  0.43  34.30% 
20  15.8647  15.5125  0.3522  0.43  18.09% 
In the best estimate analysis procedure of AP1000 Nuclear Power Plant, the core channel number has a direct influence on the complex level of simulation models. Overall, onechannel model is most simple, the threechannel model is most widely applied during simulation, and other multichannel models are more meticulous and comprehensive compared with these two models. Table
The influence of core channel number on the fractional error between calculated and designed coolant temperature variation.
In reference to Table
From Table
The influence of core channel number on the fractional error between calculated and designed reactor pressure drop.
Table
Statistical results of reactor inlet pressure.


Valid  5 
Missing  0 
Mean  15.8474 
Std. error of mean  .01324 
Median  15.8342 
Std. deviation  .02961 
Variance  .001 
Range  .07 
Minimum  15.82 
Maximum  15.89 
Nonparametric tests summary of reactor inlet pressure.
Hypothesis test summary  

Null hypothesis  Test  Sig.  Decision  
1  The distribution of Reactor_inlet_pressure is normal with mean 15.847 and standard deviation 0.03  Onesample KolmogorovSmirnov test  .200^{1,2}  Retaining the null hypothesis 
Asymptotic significance is displayed. The significance level is .05. 1: Lilliefors corrected. 2: this is a lower bound of the true significance.
Statistical results of reactor outlet pressure.


Valid  5 
Missing  0 
Mean  15.4742 
Std. error of mean  .03837 
Median  15.4213 
Std. deviation  .08581 
Variance  .007 
Range  .20 
Minimum  15.41 
Maximum  15.61 
Nonparametric tests summary of reactor outlet pressure.
Hypothesis test summary  

Null hypothesis  Test  Sig.  Decision  
1  The distribution of Reactor_outlet_pressure is normal with mean 15.474 and standard deviation 0.09  Onesample KolmogorovSmirnov test  .076^{1}  Retaining the null hypothesis 
Asymptotic significance is displayed. The significance level is .05. 1: Lilliefors corrected.
During the AP1000 Nuclear Power Plant simulation process, pressurizer simulation also has a direct influence on the best estimation results of nuclear systems. In particular, within the primary system of Nuclear Power Plant, pressurizer is employed to maintain the pressure of the primary loop; thus pressurizer node number may have a direct influence on the code output. According to [
The influence of pressurizer node number on the primary loop pressure.
Node number  Calculated pressure of primary loop (MPa)  Designed pressure of primary loop (MPa)  Fractional error 

1  15.7916  15.5  1.88% 
3  14.9463  15.5  3.57% 
6  15.5322  15.5  0.208% 
12  15.5565  15.5  0.365% 
18  15.0693  15.5  2.78% 
The influence of pressurizer node number on the coolant temperature variation.
Node number  Reactor inlet temperature (K)  Reactor outlet temperature (K)  Calculated temperature variation (K)  Designed temperature variation (K)  Fractional error 

1  550.56  591.8925  41.3325  40.4  2.31% 
3  551.7598  592.07125  40.3115  40.4  0.22% 
6  554.3637  594.7499  40.3862  40.4  0.03% 
12  554.3674  594.7526  40.3852  40.4  0.04% 
18  551.62  591.96  40.34  40.4  0.15% 
Table
The influence of pressurizer node number on the fractional error between calculated and designed primary loop pressure.
As is shown in Table
Table
The influence of pressurizer node number on the fractional error between calculated and designed coolant temperature variation.
As is reported by Table
The statistical results of reactor inlet temperature.


Valid  5 
Missing  0 
Mean  552.5342 
Std. error of mean  .77591 
Median  551.7598 
Std. deviation  1.73498 
Variance  3.010 
Range  3.81 
Minimum  550.56 
Maximum  554.37 
Nonparametric tests summary of reactor inlet temperature.
Hypothesis test summary  

Null hypothesis  Test  Sig.  Decision  
1  The distribution of Reactor_inlet_temperature is normal with mean 552.534 and standard deviation 1.73  Onesample KolmogorovSmirnov test  .200^{1,2}  Retaining the null hypothesis 
Asymptotic significance is displayed. The significance level is .05. 1: Lilliefors corrected. 2: this is a lower bound of the true significance.
As is demonstrated above, the pressurizer has a direct influence on the primary loop pressure, so the pressurizer node number may also have some effects on the reactor pressure drop, which are shown in Table
The influence of pressurizer node number on the reactor pressure drop.
Node number  Reactor inlet pressure (MPa)  Reactor outlet pressure (MPa)  Calculated reactor pressure drop (MPa)  Designed reactor pressure drop (MPa)  Fractional error 

1  15.8587  15.4125  0.4462  0.43  3.77% 
3  15.4805  15.0491  0.4314  0.43  0.33% 
6  15.8342  15.4213  0.4129  0.43  3.98% 
12  15.8819  15.4365  0.4454  0.43  3.58% 
18  15.4929  15.0131  0.4798  0.43  11.58% 
The influence of pressurizer node number on the fractional error between calculated and designed reactor pressure drop.
According to Table
As is known, the feedwater in the secondary side is heated by the primary loop coolant; thus the steam is produced and used to propel the turbines after flowing through the moisture separatordryer. Consequently, the feedwater temperature has direct influences on the steam properties.
According to [
The influence of feedwater temperature on the steam output.
Feedwater temperature (K)  Calculated steam output (kg/s)  Designed steam output (kg/s)  Fractional error 

494.85  970.2  943.6111  2.818% 
496.85  970.19  943.6111  2.817% 
499.85  970.18  943.6111  2.816% 
502.85  970.18  943.6111  2.816% 
504.85  970.17  943.6111  2.815% 
The influence of feedwater temperature on the fractional error between calculated and designed steam output.
As can be seen from Table
Table
The influence of feedwater temperature on the SG outlet temperature.
Feedwater temperature (K)  Calculated SG outlet temperature (K)  Designed SG outlet temperature (K)  Fractional error 

494.85  546.12  546.1  0.00367% 
496.85  546.14  546.1  0.00732% 
499.85  546.18  546.1  0.0146% 
502.85  546.22  546.1  0.0220% 
504.85  546.24  546.1  0.0256% 
The influence of feedwater temperature on the fractional error between calculated and designed SG outlet temperature.
In reference to Table
Table
The influence of feedwater temperature on the SG outlet pressure.
Feedwater temperature (K)  Calculated SG outlet pressure (MPa)  Designed SG outlet pressure (MPa)  Fractional error 

494.85  5.766085  5.764  0.0362% 
496.85  5.76833  5.764  0.0751% 
499.85  5.771655  5.764  0.133% 
502.85  5.774995  5.764  0.191% 
504.85  5.777175  5.764  0.229% 
The influence of feedwater temperature on the fractional error between calculated and designed SG outlet pressure.
According to Table
Overall, the coolant in the reactor core flows in the axial direction, while there exits crossflow between the different channels. In the simulation process of the primary system based on RELAP5 platform, the singlechannel model treats the core as an integration system; the water flows homogeneously in the core channel; in this case, the crossflow phenomenon could not be demonstrated. In regard to the multichannel core model, there exits crossflow phenomenon in reality, and whether considering the crossflow between different channels or not may have different influences on the coolant flow, coolant temperature, pressure drop in the reactor core, and some other system parameters.
According to the design parameters of AP1000 Nuclear Power Plant, the water temperature rise through the reactor coolant channels is 42.83 K. Table
The influence of crossflow model on the coolant temperature variation.
Crossflow model  Core inlet temperature (K)  Core outlet temperature (K)  Calculated temperature variation (K)  Designed temperature variation (K)  Fractional error 

None  554.4102  596.6464  42.2362  42.83  1.39% 
Having  554.4102  596.6468  42.2366  42.83  1.39% 
As can be seen from Table
In reference to the design documents of AP1000 Nuclear Power Plant, the designed pressure drop through the reactor core is
The influence of crossflow model on the pressure drop in the reactor core.
Crossflow model  Core inlet pressure (MPa)  Core outlet pressure (MPa)  Calculated pressure drop in reactor core (MPa)  Designed pressure drop in reactor core (MPa)  Fractional error 

None  15.9615  15.6468  0.3147  0.298  5.60% 
Having  15.9618  15.6470  0.3148  0.298  5.63% 
As can be seen from Table
In reference to the design documents of AP1000 Nuclear Power Plant, the core coolant mass flow is 14301.0 kg/s. Table
The influence of crossflow model on the core coolant mass flow.
Crossflow model  Calculated core coolant mass flow (kg/s)  Designed core coolant mass flow (kg/s)  Fractional error 

None  14304.73  14301.0  0.026% 
Having  14304.46  14301.0  0.024% 
As can be seen from Table
The loss of power transient is caused by a complete loss of the offsite grid accompanied by a turbinegenerator trip. During the loss of power transient, core decay heat removal is normally accomplished by the startup feedwater system if available, which is started automatically when low levels occur in the Steam Generator. If the startup feedwater system is not available, emergency core decay heat removal is provided by the PRHR heat exchanger. Upon the loss of power to the reactor coolant pumps, coolant flow necessary for core cooling and the removal of residual heat is maintained by natural circulation in the reactor coolant and PRHR loops [
Figure
The influence of crossflow model on core coolant mass flow.
As can be seen from Figure
Figure
The influence of crossflow model on PCT.
According to Figure
The best estimation process of AP1000 NPP requires proper selections of parameters and models so as to obtain the most accurate results compared with the actual design parameters. Based on the thermalhydraulic system code RELAP5/MOD3.2, sensitivity analyses on various of the parameters and models have been performed in this paper to provide reference to the simulation process of nuclear power systems. Main results obtained in this study are summarized as follows.
During the best estimation process of AP1000 NPP, the simulation results, especially the coolant temperature variation and pressure drop in reactor, are sensitive to both the number of core channels and the node number of each channel within the best estimation model. With the variation of core channel number, the reactor inlet and outlet pressures and the reactor inlet temperature are normally distributed. In addition, the best estimation results of coolant temperature variation and pressure drop through the AP1000 NPP reactor are about the most accurate when the node number and channel number are 10 and 5, respectively, compared with the other conditions.
The pressurizer node number has apparent influences on the primary loop pressure, coolant temperature variation, and pressure drop in reactor. In addition, the best estimation results of primary loop pressure and coolant temperature are about the most accurate when the node number is 6, while the corresponding node number of reactor pressure drop is 3.
Both the SG outlet temperature and pressure are susceptible to feedwater temperature, but the steam output is on the contrary. Besides, both of the fractional errors of SG outlet temperature and pressure compared with the corresponding designed values rise straightforward with the increase of feedwater temperature within its range.
Whether considering the crossflow model or not, the simulation results of AP1000 NPP, such as coolant temperature variation, pressure drop, and coolant mass flow, remain stable both at steady state and during loss of power transient.
Number of samples
Response
Model output
Mean value of the
Mean value of model output.
Correlation coefficient
Global sensitivity analysis
Nuclear Power Plant
Peak Cladding Temperature
Passive Residual Heat Remove
Rank correlation coefficient
Reactor Excursion and Leak Analysis Program
Sensitivity analysis
Steam Generator.
The authors declare that they have no conflicts of interest.