Keywords

1 Introduction

Two circulating water pumps (CRF pumps) are equipped in the three loops of the nuclear power plant in order to provide cooling water and thus to realize the heat removal [1]. During a cold source failure or CRF pump failure, a rapid core power reduction to a lower power level is demanded based on the available CRF pump cooling capacity. During the power reduction process and the stay of the low-power platform, the core axial power distribution is disturbed, and the axial power deviation of the core (ΔI) is relatively hard to control, which is likely to cause a reactor trip. Consequently, it is vital to study the ΔI control strategy in order to achieve a compromise between the CRF pump cooling capacity and ΔI control. It is also of importance for core safety and plant economics.

In the process of rapid power reduction, many problems appear in ΔI control. The power reduction methods in nuclear power plants can be divided into two types: boronization and rod insertion. As for the method of boronization, the power distribution is less perturbed. However, due to the limitation of the boronization speed, the power change rated is relatively low, which is difficult to satisfy the rapid reduce power requirements at some time. Meanwhile, when using the boronization method to reduce power, ΔI is likely to continue increasing. As the power difference is so large until exceeding the right boundary the operation diagram. It will cause a reactor trip. The safety and economy performance of the unit are infected. As far as the way of rod insertion is concerned, the power reduction process can be realized within a short period of time by a rapid introduction of negative reactivity. Nevertheless, the rod insertion method disturbs largely the core power distribution. Meanwhile, The GN rods must be fully extracted out of the core within a certain period of time after the operating technical specifications which strictly restricts on rod insertion time. During the GN rod withdrawal, it is likely for ΔI to exceed the right boundary. In addition, during the rapid power reduction, the core ΔI is also significantly related to the core burnup and the magnitude of the power reduction, that’s why the core control strategy research is challenging.

In this paper, the SCIENCE program is utilized to simulate the variation of ΔI in the process of rapid power reduction. The control strategy of ΔI, which involves fuel burnup, low-power platform, and power-reduction methods, is optimized with the help of SOPHORA program. At the same time, the control rod action sensitivity analysis is also completed in this paper. Suggestions for ΔI control strategy in the process of rapid power reduction are given.

2 Research Background of Rapid Power Reduction

Researchers have carried out a lot of explorations and researches on the problem of ΔI control strategy of the rapid power reduction process. Among them, qualitative analysis has been given from the perspective of core characteristic including burn up, burnable absorber, control rod position, fuel type and moderator temperature in a large number of literatures [2,3,4,5,6,7,8,9,10]. At the same time, power reduction types, such as power reduction to hot shutdown, daily power reduction or augmentation, extended low power operation (namely ELPO), stretch out operation, are also described qualitatively [5]. Nevertheless, literature related to rapid power reduction is relatively scarce, especially the quantitative analysis. The difficulty of ΔI control is mentioned [9] in a case that the reactor realize a reduction of power rapidly by a speed of 50 MW/min due to cooling source failure. Therefore, the power is forced to reduce to below 30% FP in order to prevents load rejection action due to the uncontrollable ΔI. On the basis of previous research, quantitative and in-depth research on the impact of different factors in the process of rapid power reduction is meaningful to the ΔI control and to the matching between the low-power platform and the cooling capacity of the cold source pump, thus ensuring the safety and economy performance of the reactor operation.

3 Research Methods

In order to ensure the safe operation of reactor, the operating diagram limitations on ΔI must be met. In addition, operation technical specifications are also mandatory considering the operation factors. Under the condition of meeting these limitations, SCIENCE and SOPHORA programs are utilized to study the influence of difference factors, such as burnup, low-power platform, power reduction method and control rod action on ΔI control in the process of rapid power reduction.

3.1 Operation Technical Specifications

As one of the main bases for the operator to control the reactor, the operation diagram shows the relationship between the allowable value of ΔI and the relative reactor power. During the rapid power reduction process, the operator must ensure that ΔI satisfies the operation diagram. In addition, the ΔI performance also needs to meet the operation technical specification in which the operation diagram is defined. Related operating technical specifications are listed: when PΔIref is determined and the power of the core is reduced from high power to 50% or less, control rod insertion time is limited to 12 h in any 24 h period in region I and ΔI is limited at region I. In the case of a capacity of a quick return to high power levels, the control rod insertion limitation time can be extended to 24 h. When all the power compensation rods(GN rod) are completely drawn out, ΔI is able to leave the area I after 6 h of stable operation.

3.2 SCIENCE and SOPHORA Software

SCIENCE graphical software package, which invoked by the Copilote graphical user interface is used in this paper for calculations. SMART programs is used for 3D homogenized cores calculation. SOPHORA program is utilized for ΔI control strategy optimization.

3.3 Overall Control Strategy

Under the condition of meeting the demands of operation technical specifications, two periods related to rapid power reduction, which is the period of rapid power reduction and the low power platform is respectively considered in order to evaluate various influencing factors in this article.

Concerned the strategy of rapid power reduction period, the control of ΔI is achieved in two ways. One is to insert the GN rod according to the G9 curve, while the power decrease at a speed of 10MW/min until reaching the low power platform. The other is to increase the boron concentration of the core firstly, at the same time, the power decrease at a rate of 3 MW/min until 80%FP. Then, GN rods is inserted in order to reduce the power at a relatively high speed of 10 MW/min. As for the strategy of low power platform, the core is boronized in order to withdraw all GN rods while R rod is used to control ΔI in order to meet the requirements of operating technical specifications in Sect. 3.1 (the time limitation for rod insertion).

In order to study the ΔI control strategy of reducing power to different low-power platforms at different fuel burnup points, a certain 18-month refueling cycle was selected for research at 150 (BLX), 6000, 11000 (ΔI most negative burnup point), 14000 (MOL), 16000 (80%EOL), 18000MWd/tU and EOL. Low power platform of 50%, 60%, 65%, 70%, 80% FP are studied and the ΔI control strategy is carried out in case of reactor cold source failure.

4 Optimization Results

The ΔI control strategy optimization results of rapid power reduction is researched by mainly focusing on three factors: fuel burnup, reached low power level platform, and the power reduction method. The comprehensive impact evaluation of the three factors is also studied. Then, this paper introduces the sensitivity analysis of the control rod action in the process of rapid power reduction, and gives the ΔI control strategy conclusion of the rapid power reduction process.

4.1 Influence of Fuel Burnup

During the reactor normal operation, the temperature of the lower part of the core is lower than that of the upper part. Due to the negative feedback of temperature, the core ΔI is generally negative. Along with the deepening of burnup, the burnup in the lower part of the core is gradually larger than that of the upper part, therefore, ΔI tends to increase due to the influence of the burnup effect. In this research, after the GN rods are extracted, a larger ΔI is unfavorable for core control. Worse, the xenon oscillation effect manifest more negative effects at EOL than BOL.

In order to study the influence of the fuel burnup effect, the GN rod is inserted to reduce the power to 50% PN during the rapid power reduction period and the ΔI variation is compared at BLX, MOL and EOL. R rod is used to control ΔI only at the low power platform. The variations of ΔI are shown in Fig. 1:

Fig. 1.
figure 1

Burnup influence for ΔI control

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It can be seen from Fig. 1 that ΔI exceeds zone I when the GN insertion time is limited to 12h for all three burnup points. Therefore, we can draw that for the whole cycle, it’s likely to exceed zone I when the power is reduced to 50%FP rapidly. We also note that ΔI will not exceed the right boundary at operation diagram at BLX; Nevertheless, at MOL and 80% EOL burnup, the xenon oscillates more violently and ΔI tends to be bigger, thus it exceeds the right boundary. ΔI control is influenced significantly by fuel burnup.

4.2 Impact of Low-Power Platforms

In addition to fuel burnup, the low power level reached by the core after a rapid power reduction also has a considerable impact on ΔI control. When the core power is reduced from 100% to 80% FP or more, ΔI is easy to control due to the small variations in power. Additionally, if the core power is reduced to 30% FP or even less, although power distribution go worse, ΔI may still be controllable thanks to the lower power levels. However, as the power is reduced to 30%–80% FP, ΔI is the most difficult to control.

ΔI variations for three low-power platforms (80%, 60% and 50%FP) is compared at burnup of 11000 MWd/tU in this section. R rod is not inserted at the power reduction period. At the low power platform, the core is boronized in order to extract GN rods. Meanwhile, R rod is inserted to control ΔI. The variation of ΔI for the three low-power platforms is shown in the Fig. 2:

Fig. 2.
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Low-power platform influence for ΔI control

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As shown in Fig. 2, when the power is reduced to a low-power platform which is greater than 50% PN, the greater is the power reduction, the greater is the ΔI oscillation caused by the xenon oscillation. When the power is decreased to the 80% FP, ΔI varies slightly within zone I. While the power is reduced to 60% or 80% FP, ΔI exceeds zone I. Therefore the low-power platform also affects largely the ΔI control.

4.3 Influence of Boronization and Rod Insertion

It can be obtained from Sect. 3.3. That two methods can be used for rapid power reduction: one is direct rod insertion and the other is boronization to 80%FP and then rod insertion. The power drops rapidly in the upper part of the core because of the rod insertion, and thus ΔI becomes more negative. The boronization power reduction method disturbs less to the core ΔI than rod insertion method, and it leads to a more positive ΔI. In order to compare the effects of two power reduction methods on ΔI control, the core ΔI elevation of the two cases is compared.

It can be seen from Fig. 3 that the ΔI performance is slightly improved by adopting the method of boronizing and then inserting the rod. At the same time, studies have shown that if boronization itself is used to reduce power to 50% PN, not only the power change rate is limited, but ΔI is easy to exceeds the right boundary. The ΔI oscillation can be slightly reduced by using the rapid power reduction strategy of boronization and then insertion the control rod.

Fig. 3.
figure 3

Boronization and rod insertion influence for ΔI control

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4.4 Comprehensive Feasibility Analysis of Fuel Burnup, Low Power Platform and Boronization

It can be drawn from Sect. 4.1–4.3 that fuel burnup, low power platform and power reduction method have major influence on ΔI control. A comprehensive analysis contains the ΔI control strategy optimization at different fuel burnups to different low-power platforms and by using different methods. We also note that the criteria of feasibility for rapid power reduction strategy is that ΔI does not exceed the operation diagram.

The power reduction analysis is based on two assumptions to facilitate the calculation. The first is that, at a higher fuel burnup, if the core power can be reduced to a certain power level without exceeding the right boundary, the core power can also be reduced to that level without exceeding the right boundary at a relatively lower burnup. The other is that, if the direct insertion of control rod method is feasible to reduce the power without exceeding the right boundary, the power reduction method of boronization and then rod insertion will also be feasible. These two assumptions correspond to the conclusions in Sects. 4.1 and 4.3, respectively. On the basis of these two assumptions, the conclusion of whether ΔI is controllable can be obtained for different fuel burnups (the unit of fuel burnup is %EOL), with different power reduction method (use direct rod insertion, boronization without stay at 80%FP and rod insertion, and finally boronization with stay at 80%FP and rod insertion) to different power platform including 80%, 70%, 65%, 60% and 50% FP. The result is shown in Fig. 4:

Fig. 4.
figure 4

Combined influence of burn-up, low power platform and power reduction method for the feasibility of rapid power reduction

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From Fig. 4, the boundary between controllable and uncontrollable power is obtained. When the fuel burn-up is less than about 50% EOL (about 11GWd/tU), ΔI does not exceed the operation diagram if the power is reduced rapidly to 50%. However, as the fuel burn-up increases, in order to prevent ΔI from exceeding the operation diagram, the power reduction magnitude should be gradually reduced. When the fuel burn-up is high enough, a direct rod insertion to reduce the power may cause the ΔI exceeding the right boundary. In this case, the power can be reduced by boronization followed by rod insertion, and a stay of 80%FP may be necessary to avoid ΔI oscillation. The matching of cooling capacity and core power can be achieved with help of the strategy.

5 Sensitivity Analysis of Control Rod Motion

To limit ΔI oscillations during rapid power reduction, the R-rod action can be manually optimized. In addition, after reaching the low power platform, the GN rod is supposed to be raised in 12h, the GN rod action is flexible in time and in speed. Therefore, it is also of importance to carry out the analysis of the influence of the control rod action on ΔI during the rapid power reduction and the low-power platform.

Considering the power reduction method of direct insertion of control rod, according to the time and logical sequence, the sensitivity analysis of control rod action can be divided into: R rod action in power reduction process, GN rod action at low-power platform and R rod action low-power platform. The sensitivity analysis is simulated at a burnup of 80%EOL.

5.1 Sensitivity Analysis of R Rod Action During Power Reduction Process

During the power reduction process, GN rod needs to be inserted according to the known G9 curve, ΔI is generally more negative. In this process, the R rod can be properly raised in order to leave an insertion margin for the ΔI control when the GN rod is extracted for the low-power platform. In this section, the influence of whether to extract R rod out of the core during the power reduction process so as to leave a insertion margin in the low-power platform is researched.

Two case during power reduction process, which is firstly R rod is gradually extracted out of the core during power reduction and secondly R rod keeps still, is studied. At lower-power platform, R rod is evenly inserted into the core to its lower limit. ΔI variation at low-power platform is shown in Fig. 5:

Fig. 5.
figure 5

Sensibility study of for the withdrawal of R bank

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It can be drawn from Fig. 5 that in the process of power reduction, an extraction of R rod for more insertion margin has no significant optimization effect on the ΔI control strategy. ΔI raises as the GN rod is extracted, and finally exceeds the right boundary. The value of final ΔI is basically the same in both cases.

5.2 Sensitivity Analysis of GN Rod Motion of Low Power Platform

In order to meet the requirements of the operation technical specifications, the GN rods must be extracted of the core within 12 h. During the low-power platform, when GN rods are extracted, studies of its action include: extraction speed, beginning time and time interval of GN rod withdrawal.

For the analysis of extraction speed of GN rods, three cases of GN rod extraction at low-power platform are simulated. The result of ΔI is shown in Fig. 6:

Fig. 6.
figure 6

Influence of the withdrawal speed of GN bank on ΔI

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It can be seen from the above figure that the maximum ΔI is positively correlated with the GN rod extraction rate, but both ΔI are far beyond the right boundary.

For the beginning time of the GN rod extraction, at low-power platform, due to the Xe effect, ΔI tends to decrease in the low-power platform from 0 to 10 h in which is favorable for GN rods extraction. The GN rods are selected to be extracted at 2, 4, 6, and 8 h, and all of the cases are fully extracted at the 12th hour. The R rod keeps still, and the comparison of ΔI changes is shown in Fig. 7:

Fig. 7.
figure 7

Influence of the withdrawal time of GN bank on ΔI

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From Fig. 7, we observe the changes of ΔI In all four cases, the xenon oscillation causes ΔI to exceed the right boundary. However, by adjusting the time of GN rod withdrawal, the peak value of ΔI can be slightly reduced and the time to exceed right boundary can be delayed.

As shown in Fig. 8, after the rapid power reduction of the core, the ΔI variation is simulated for different stay times of 2h and 6h after reaching low-power platform in a real specific case. Compared with the 2h stay condition, the maximum value of ΔI after extraction the GN rods is lower and does not exceed the I zone for 6h-stay case. The operation technical specification is obeyed. Therefore, the beginning time optimization of GN rod has a positive effect on ΔI control.

Fig. 8.
figure 8

Influence of the withdrawal time of GN bank on ΔI for Daya Bay unit at middle of cycle

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For the sensitivity analysis of the extraction time interval of the GN rod, after the power is rapidly reduced, R rod keeps still, and GN rod is extracted at different time interval, as shown in Fig. 9:

Fig. 9.
figure 9

Influence of the withdrawal time interval of GN bank on ΔI

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From the above figure, ΔI attains the same value in the end. The extraction time interval of the GN rod does not affect greatly the variation of ΔI. Consequently, the GN rod can be evenly raised on the power platform.

5.3 Sensitivity Analysis of R-rod Motion of Low-Power Platform

In the low-power platform, during the process of the extraction of GN rod, the R rod needs to be inserted to control ΔI. The R rod can be either evenly inserted to its lower limit, or inserted once at a certain moment or inserted at different time. This section is to study the effect of the R rod action.

Fig. 10.
figure 10

Influence of the R bank action on ΔI at reduced power level

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As can be seen from Fig. 10, the R rod adopts different insertion strategies, none of them can control the ΔI within the right boundary. There is no significant correlation between R rod insertion method and final ΔI value. The later is mainly affected by the final position of R rod (namely the low-low limit).

5.4 Summary of Sensitivity Analysis

In this section, at the 80% EOL burn-up point, the sensitivity analysis of the control rod action to ΔI in the process of rapid power reduction and low-power platform is carried out, including the analysis of the R rod action in the process of the GN rod insertion, the action of the GN rod and R-rod at the low-power platform. We can basically conclude that the control rod motion improves slightly the ΔI performance, but it has no decisive effect on the core control. The fuel burnup, low power platform and power reduction method keeps the main factor affecting ΔI during the rapid power reduction.

6 Conclusion

Based on SCIENCE software, this article describes the effects of different factors such as fuel burnup, low power platform, power reduction method and control rod action on rapid power reduction. Aimed at the three main factors, the comprehensive feasibility analysis is carried out and based on a specific cycle, a rapid power reduction ΔI control strategy is given: when the fuel consumption is less than approximately 50% EOL, ΔI is controllable when the power is quickly reduced to 50% FP. As the fuel burnup deepens, in order to keep ΔI within the operation diagram, the power reduction should be gradually reduced to 70% FP. When the fuel burn-up is high enough (80% EOL), using the direct rod insertion method to reduce the power will cause the ΔI to exceed the right boundary. The power can be reduced by boronization and then rod insertion. When the fuel burnup deepens to 90% EOL, in order to quickly reduce the power to 50% FP, it is recommended to stay for a certain time after boronization. When the fuel consumption reaches EOL, if the core reduces the power rapidly to 70%PN, no matter how long it stays, ΔI is uncontrollable. At this time, it is recommended that the unit be reduced to more than 80% FP. The quantitative research of this paper is carried out between the CRF pump cooling capacity and the core power. It is of reference value for core control for rapid power reduction during CRF pump and cold source response failure.