# Digitalization of the Ex-Core Neutron Flux Monitoring System for APR1400 Nuclear Power Plant
## 3 Simulation
### Estimation of Reactor Power by MSV and Current Mode Calculations  
The performance of MSV and current mode signal processing in terms of rejecting the influence of signals generated by gamma ray interactions and electric noise for the estimation of reactor power level were compared through simulations. Two detector signals were assumed, one signal generated by neutron interactions only while the other signal includes components of neutron and gamma interactions as well as electric noise. For MSV mode signal processing, the detector current signal pass through the amplifier and the band-pass filter, and then the mean values of the currents are calculated. In terms of current mode signal processing, the detector current signals also pass through preamplifier and low-pass filter, and then the mean values of the currents are calculated. The block diagram for MSV and current mode signal processing simulation is given in Figure 6 wherein gamma ray interactions are assumed to occur at the rate of \(3.3\times 10^{6}\) [events/sec] and produce a pulse current per interaction with an amplitude of 0.42 micro-amperes and a pulse width of 50 [nsec].  
Figure 5: The pulse height distributions.  
It can be seen in Figure 7a that the mean squared current values at interaction rates higher than \(3\times 10^{5}\) [events/sec] are almost the same between the detector current signals with and without gamma ray interactions and electric noise. Although the elements of gamma ray interactions and electric noise are dominant when the rates are lower than \(1\times 10^{5}\) [events/sec]. Therefore, the reactor power can be reliably estimated through MSV calculation at levels corresponding to the interaction rates higher than \(3\times 10^{5}\) [events/sec.]. The simulated values of the MSV which are only by neutron interactions, are smaller than expected at interaction rates lower than \(2\times 10^{4}\) [events/sec] because the pulses are not adequately overlapped at the range of rates. Pulses are considered sufficiently overlapped when the product of pulse rate and pulse width exceeds one.  
On the other hand, Figure 7b shows that the mean values of current at interaction rates higher than \(1\times 10^{7}\) [events/sec] are also almost the same between the detector current signals with and without including gamma ray interactions and electric noise. Elements of the gamma ray interactions and electric noise are dominant when the rates are lower than \(1\times 10^{6}\) [events/sec]. Therefore, the reactor power can be estimated reliably by mean of current calculation at levels corresponding to the interaction rates higher than \(1\times 10^{7}\) [events/sec.]. The RMSE values for each calculation of Mean, MSV and Average MSV for both neutron only interaction and neutron plus gamma ray with noise is given in Table 3.  
Figure 6: Block diagram of the MSV and current mode signal processing simulation.  
The comparison between true mean squared values and the averaged magnitude squared values is given in Figure 8. For neutron interaction rates over \(5\times 10^{5}\) [events/sec.], the average magnitude squared values by neutron interactions only are about 63.5 % of the true mean squared values, and the ratio decreases sharply when the neutron interaction rate is lower than \(1\times 10^{5}\) [events/sec]. Therefore, the use of digital ENFMS in calculating the true mean squared values can increase the effective range of signal linearity by one decade compared to analog ENFMS which calculates the averaged magnitude squared values.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reactor Power State** & **Mean (Current)** & **MSV (Voltage)** & **Average MSV (Voltage)** \\ \hline Neutron interaction only & 0.0005 & 0.1018 & 0.4784 \\ Neutron + Gamma Rays + Noise & 0.0087 & 0.2273 & 0.1134 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean (Current), MSV (Voltage) and Average MSV (Voltage) RMSE.  
Figure 7: Current with respect to neutron interactions.