Keywords

1 Introduction

The core quadrant power tilt ratio (QPTR) is defined as the ratio of the average power of a certain quadrant of the core to the average power of the whole reactor, which is an index to measure the asymmetry of radial power distribution of the core (referring to 1/4 symmetry). In the actual core, except some accident conditions, due to manufacturing tolerance, installation tolerance, loop asymmetry, operation history effect and other reasons, the physical quantities affecting power distribution in the core can not be completely symmetrical in practice, that is, there is a phenomenon of core quadrant power tilt.

In the PWR nuclear power plant, there are many quadrant power tilt related alarm signals. One of the alarm signal is the quadrant power tilt rate which is defined as the difference between the maximum and minimum nuclear power displayed in four RPN power range channels, and is set in LOCA monitoring system (LSS) after filtering process. The alarm signal variable is defined as RPN430KA, and the alarm logic diagram is shown in Fig. 1. The alarm threhold is set to 3%. When the RPN430KA signal is greater than 3%, the alarm will be triggered.

Fig. 1.
figure 1

Logical figure of RPN430KA alarm signal

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In which:

  • Pr(max): Maximum power of four power range channels

  • Pr(min): Minimum power of four power range channels

  • Pth(avg): Average thermal power in LSS system

  • AS = 1: the alarm is triggered with DPazn (rel) parameter which equals to the ratio of maximum quadrant tilt rate to relative average thermal power

  • AS = 0: the alarm is triggered with DPazn (max) parameter which equals to the difference of maximum nuclear power and minimum nuclear power.

Unit X (AS is set to 0) of a PWR nuclear power plant has flashed RPN430KA alarm several times during normal operation in the middle and late life of a certain cycle. When the cycle burnup reaches to 65%, the alarm trigger frequency is about once in month. After burnup of 80% EOL, the trigger frequency increases, and the alarm trigger frequency has reached once a day or even many times a day.

2 Root Cause Analysis

According to Fig. 1, the triggering of RPN430KA is mainly affected by several aspects. First, the nuclear power signal measured by RPN will trigger an alarm if the nuclear power deviation in different quadrants is large. Second, the process of filtering can reduce the number of alarm triggering if the filtering effect is good. This paper analyzed the cause from these two aspects.

2.1 RPN Measurement Data Analysis

Theoretically, the nuclear power of the four power range channels are all the same, but due to quadrant power tilt, neutron noise and other factors, the nuclear power mean values of the RPN four channels are different and fluctuate in a certain extent. So data analysis of RPN power of X unit in different cycles and different burnups is needed.

Figure 2 shows the standard deviation comparison of nuclear power fluctuation under the burnup of about 17000MWd/tU at the end of cycle life of X unit with different RPN measurement channels in different cycles.

It can be found that the fluctuation of nuclear power in cycle C02 is similar to that in cycle C03, and the fluctuation in cycle C04 is slightly larger, which is consistent with the phenomenon that RPN430KA alarm phenomenon is more frequent at the end of cycle C04 1.

Marcus Seidl studied the neutron noise phenomenon of nuclear power fluctuation [2, 3]. The research showed that the fluctuation amplitude of nuclear power increases with the increase of the absolute value of moderator temperature coefficient, Generally speaking, the absolute value of moderator temperature coefficient is larger at the end of cycle life, so the fluctuation amplitude of nuclear power is larger than that of beginning of cycle.

Figure 3 shows the variation of the absolute value of moderator temperature coefficient in different cycles of X unit with burnup. It can be seen from the figure that the absolute value of moderator temperature coefficient in cycle C04 is larger than that in cycle C03 at the same burnup. In the same cycle, the absolute value of temperature coefficient of moderator at the end of life is larger than that of beginning of cycle. This is consistent with the fact that the nuclear power fluctuation of cycle C04 is larger than that of cycle C03 and the nuclear power fluctuation of cycle C04 is larger at the end of cycle than that of beginning of cycle.

Nuclear power fluctuation or neutron noise fluctuation is a very complex phenomenon, which has been studied in the world and is still being further studied [4, 5].

Therefore, from the data analysis of RPN measurement, it can be seen that the large fluctuation of nuclear power at the end of cycle C04 is a promoting factor for the alarm of quadrant power tilt rate signal (RPN430KA).

Fig. 2.
figure 2

Neutral flux fluctuation amplitude under different cycles at EOL

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Fig. 3.
figure 3

Change of absolute value of MTC with burnup

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2.2 Filtering Effect Analysis

According to the logic diagram of RPN430KA alarm, the difference between the maximum value and the minimum value of nuclear power signal is processed by a filter. The transfer function of the first-order filter is 1/(1 + τs), in which τ is the filter time constant. After discretization, the transfer function can be written as follows:

$$ {\text{tNewOutput}} = {\text{ a}} \times {\text{tLastOutput}} + {\text{b}} \times {\text{tLastInput}} + {\text{c}} \times {\text{tNewInput}} $$
(1)

  • in which:

  • tNewOutput: output result of current time step after filtering;

  • tLastOutput: output result of last time step after filtering;

  • tLastInput: input data of last time step;

  • tNewInput: input data of current time step.

Where a, b and c are weight coefficients. Through proper weighting processing of the original signal at current and last time step and the filtered signal at the last time step, the current filtered output result is finally obtained. The choice of weight coefficient greatly affects the filtering effect, which is defined as follows:

  • a = 1.0−(SampleTime/d);

  • b =  −a + (Tau/d);

  • c = 1.0−(Tau/d);

  • d = Tau + (SampleTime/2.0) + (SampleTime/(12.0 × Tau × Tau)).

Where Tau is the time constant (Ï„), and its initial design value is 20 s, SampleTime is the time of sampling.

The filtering time constant and SampleTime jointly determine the weight coefficient. In principle, the SampleTime depends entirely on the frequency at which the original signal is collected. If the sampling frequency of a system is determined, the filtering effect can only be modified by time constant.

Assuming a group of input signals, the deviation signal DPazn (max) between the maximum value and the minimum value of RPN core power changes as the input signal in Fig. 4 (note that this input signal amplitude is larger than the actual value onsite, and it is only assumed for the convenience of observing the filtering effect). In order to monitor the effect of filtering, the time interval of the input signal is 50 ms, and the values of Tau are 20s and 0.5s. The input signal and output effect at different SampleTime are shown in Fig. 4 below.

It can be seen from the comparison that when the filtering time constant Tau is 20s, the setting of SampleTime has a great influence on the filtering effect. When the SampleTime setting is consistent with the time interval of the input signal (both are 50 ms), the filtering effect is better, while when the SampleTime setting is larger, the filtering effect is worse.

When SampleTime is set to 50 ms and the filtering time constant is 0.5 s, the filtering effect is basically the same as that when Tau is set to 20 s and SampleTime is set to 2 s.

After onsite inspection, in order to shorten the response time of the system, the SampleTime for calculating the weight coefficient was modified in the design of Unit X, which was inconsistent with the physical sampling frequency of the system. Its effect on the weight coefficient is equivalent to changing the filtering time constant without changing the SampleTime.

Therefore, the main reason for the RPN430KA alarm is that the SampleTime in the discretization calculation of LSS system of Unit X is inconsistent with the physical sampling time, and a larger SampleTime is set.

Fig. 4.
figure 4

Output of filter with different Tau and SampleTime

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3 Research in Solution

The purpose of setting RPN430KA alarm in LSS system is to monitor the power tilt of core quadrant and the operation state of core during normal operation. For noise signals, effective filtering means should be used. According to the cause analysis, it can be solved from two aspects for the alarm:

One method is the effective filtering setting. This method includes setting a suitable filtering time constant Tau and setting a sampling time (SampleTime) which is the same as the physical sampling frequency during discrete processing. Tau = 20s and SampleTime = 50 ms are recommended for unit X.

The second method is to reduce the fluctuation amplitude of nuclear power as much as possible. The reason of nuclear power fluctuation is complex, and it is closely related to the temperature coefficient of moderator from the phenomenon. Therefore it can be considered to optimize the temperature coefficient of moderator as much as possible in the design of fuel management, especially for the end of life. From the reason analysis of current research, the fluctuation of nuclear power is closely related to the fluctuation of core inlet flowrate. So in the design of a new reactor type, it is necessary to optimize the flow distribution device as much as possible to reduce the flow fluctuation of core inlet flowrate. For the in-service unit, because its flow distribution device has been finalized, it needs to be considered from other aspects.

In view of the first solution, this paper investigates the RPN430KA alarm of Y unit. For the same cycle, under almost similar fuel management strategies, the nuclear power fluctuation standard deviations of Unit X and Unit Y under the same burnup at the end of cycle are shown in Fig. 5. It can be seen that the fluctuation amplitude of cycle C03 of Unit X is equivalent to that of Unit Y, and the fluctuation range of cycle C04 of Unit X is slightly larger at the end of life. According to RPN430KA alarm statistics, the SampleTime of Unit Y is consistent with the physical sampling time, and there is no alarm during normal operation, but there is a certain alarm phenomenon of Unit X. It can be seen that this scheme has a good effect on solving the alarm of quadrant power tilt rate RPN430KA in normal operation.

Fig. 5.
figure 5

Comparison of neutral flux fluctuation amplitude

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4 Conclusions

In this paper, the quadrant power tilt rate alarm phenomenon of a PWR nuclear power plant is studied. Based on its alarm logic, the root cause is analyzed, and the solution is determined. Research shows that:

  1. (1)

    The main reason of the quadrant power tilt rate alarm is that the sampling time (SampleTime) is not consistent with the physical sampling time when the LSS system discretizes the filter link. The contributing factor is that the nuclear power of the unit fluctuates greatly at the end of the cycle.

  2. (2)

    In terms of solution, the abnormal alarm phenomenon of the unit can be well solved by optimizing the setting of SampleTime. At the same time, in order to reduce the fluctuation amplitude of nuclear power, for in-service units, the temperature coefficient of moderator can be optimized by optimizing fuel management scheme, and for new units, the flow distribution device should also be optimized to reduce the fluctuation of inlet flow.

The research results of this paper can also be used as relevant good experience (RGP) of a new reactor design. Appropriate alarm setting is of great significance for monitoring quadrant power tilt and ensuring stable operation of the unit.