Introduction

Floating nuclear power plants (FNPPs) have recently gained increasing attention owing to their flexible deployment and ability to provide heat, electricity, and water cogeneration for remote islands/regions [1-3]. To meet the needs of offshore platforms, an integrated pressurized water reactor (IPWR) that is compact, small, and has muscular mobility is usually selected as the FNPP, such as the ACP100 (Advanced China Power 100). As a small modular reactor (SMR), the safety system of ACP100 adopts a passive design concept to achieve reactor safety under accidents owing to natural forces, which reduces the dependence on external water sources, power supplies, and personnel intervention. The following key engineered passive safety systems are included: core cooling, residual heat removal, and containment air cooling. The design system follows a single-failure principle, and no human intervention is required 72 h after an accident [2, 4]. A potential deployment site was selected in Yantai in the Bohai region. Prior to formal testing, a probabilistic safety analysis (PSA) of an FNPP is crucial for project development.

Owing to the currently limited deployment of FNPPs, studies regarding their safety have mainly focused on deterministic analyses, including thermal-hydraulic characteristics [5], structural stresses [6], and severe accident analyses [7]. Studies regarding probabilistic analyses, especially those concerning external events, are limited, with current research primarily focusing on ship collisions [8]. According to meteorological data, heavy snowfall occurred in Yantai, where the FNPP was deployed. Considering the integrity of the safety assessment, it is necessary to consider the impact of extreme snowfall on an FNPP. In addition, incorporating extreme snowfall as an external event into the probabilistic safety assessment will have potential benefits for the design of an FNPP and the identification of risks for other nuclear power plants along the Bohai coast. This study aims to evaluate the impact of extreme snowfall on an FNPP using meteorological data within the framework of a risk assessment of an external event and to provide risk insights for the design of an FNPP.

Experts have typically used the general analysis framework of an external event [9] extracted from the earthquake PSA and strong-wind PSA to analyze extreme snowfall. The framework typically includes the following several elements: 1) the use of specific criteria for disaster screening to eliminate extremely unlikely hazards or combinations thereof, 2) using the collected data, selecting appropriate hazard intensity measures, and conducting disaster risk analyses to obtain the frequency of the initiating events (IEs), and 3) establishing a quantitative model of the impact of a hazard, typically an event tree (ET) or fault tree (FT) model.

Researchers have studied both light water reactors (LWRs) and non-LWRs within this framework. The screening of hazards is based on a series of standards, including the ASME/ANS Standards [10, 11], IAEA NS-R-3 [12], and IAEA SSG-3 [13], which are summarized in technical reports [14]. Narumiya et al. [15] proposed a method for selecting combined hazards by calculating risk factors (product of the frequency and consequences). Choi et al. [16] discussed the classification, combination, and impact of external hazards on nuclear power plants (NPPs) and provided risk calculations (multidimensional integrals) for specific combinations. Kubo et al. [17] established a method to quantify the risks caused by multiple combinations of hazards. Considering the correlation between earthquakes and flood failures, they conducted a dynamic probabilistic risk assessment (PRA) of earthquake-induced flood events. In addition, they were coupled with a thermal hydraulics code and risk assessment using a plant interactive dynamics (RAPID) framework. Yamano et al. [18] developed a PRA method for the combined hazards of strong winds and heavy rain. The combined analysis of the risk probability evaluates the risk curve based on the maximum instantaneous wind speed, hourly rainfall, and duration. Kantarzhi et al. [19] developed an ice dynamics model for the Russian FNPP deployment environment. Based on meteorological data and site conditions, they determined the ice loads on the structure of the FNPP.

Considering the PSA of extreme snowfalls, scholars typically use the depth of snow [9],maximum load of the frost and icing [9], snow rate [20], low-temperature duration [21], minimum temperature [22], blockage [23], or a combination of the hazard intensities. Juraj [24] utilized ANSYS to study the load effects of extreme snowfall with a return period of 10⁴ years on structures. Scholars typically use extreme value distributions (including the Gumbel and Weibull distributions) to describe the distribution of hazard quantities for disaster risk analyses.

The PSA models for snow are typically developed based on a Level 1 PSA. By analyzing the impact of extreme snowfall on the SSCs, the PSA model of an internal event can be added to the snow PSA. The Japan Atomic Energy Agency (JAEA) developed sodium fast reactors (SFRs) and conducted a PSA under a combination of extreme snowfall and low-temperatures. Yamano et al. [21, 25] converted 50-year weather data from a typical SFR plant site into hazard intensities (annual maximum snow depth and annual maximum snow depth) and obtained the relevant hazard curve. The results demonstrate that the vital action of humans is critical for improving the speed of snow removal and achieve the necessary snow removal. Assuming that the initiating event is a loss of offsite power, Nishino et al. [20] also considered recovery measures to prevent the loss of DHRS functionality (snow removal and filter replacement), and installed electric heaters around the inlet and outlet as an additional countermeasure.

Because the deployment area of an FNPP can be offshore or in the open sea, both mobile and moored deployments pose a challenge in collecting meteorological data for snow hazards. The FNPP investigated in this study is expected to be deployed offshore of Yantai and is not intended to move widely [3]. Therefore, utilizing the meteorological data of nearby land to characterize the deployment site is acceptable.

As indicated in the aforementioned, the scope of the PSA in this study will be limited to Level 1. Similar to the analysis framework of land-based nuclear power plants [26, 27], the Level 1 PSA of FNPP usually includes initiating events, event sequences, success criteria, and human factor analysis, etc. Considering the difference between the external and internal PSAs for an FNPP in the event of an extreme snowfall, the external initiating events were mainly focused on. The entire analysis ultimately estimates the core damage frequency (CDF) and helps understand the advantages and disadvantages of existing or envisaged safety-related systems and procedures for preventing core damage.

Extreme Snowfall Hazard Analysis

2.2

Case Study in the Bohai Sea

2.2.1

Collection of historical records

The FNPP off Yantai was considered as the research object and a case study for the risk analysis of extreme snowfall was provided. Owing to the lack of data regarding the snow thickness in Yantai, we obtained the daily temperatures (maximum, minimum, and average) and precipitation data over the past 39 years from the National Greenhouse Data System [31] and the National Centers for Environmental Information (NCEI) [32]. The two meteorological stations(Yantai and Yantai North) that were nearest to the FNPP were adopted.

According to the definitions provided by the China Meteorological Administration, the formation of snow occurs by the direct sublimation of water vapor in the atmosphere or the direct solidification of water droplets. Specifically, the conditions for the formation of snowfall are as follows: 1) presence of ice crystals in the atmosphere, 2) sufficient water vapor, and 3) an air temperature below 3 ℃ (freezing point). Based on the aforementioned conditions, an average temperature of less than 3 ℃ along with the occurrence of precipitation on a particular day is considered snowfall. Because the staff of a nuclear power plant can usually clear snow within 24 h, the snowfall was analyzed for a limited duration of one day. The snow-to-liquid ratio (SLR) refers to the ratio of the depth of snow to the equivalent depth of the liquid after the snow melts, which can be used to calculate the snow depth. $SLR=\frac{SD}{SL}$ (14) Here, SLR indicates the snow-to-liquid ratio (cm/mm), SD denotes the new accumulated snow depth (cm) between the current and following day, and SL indicates the accumulated precipitation (mm) within the same period as that of the new snow depth.

Yang et al. [33] demonstrated that the multiyear average SLR in the northern coastal area of the Shandong Peninsula (in the Bohai Sea), which is known for ocean-effect snowstorms, was 1.3 cm/mm. The distribution of SLR in the northern Shandong Peninsula, including Yantai, is approximately a normal distribution, with a mean value of 1.30 and a variance of 0.65. Considering the significant uncertainties in the meteorological data, we also studied their impact on the hazard curve, as shown in Table 1. Based on the SLR, precipitation was converted into snow depth and sorted, as indicated in Table 2. Subsequently, the snowfall rate was calculated using Eq.15 based on the calculated snow depth SD and duration of snowfall Δ T; it was also sorted and included in Table 2. $SV=\frac{SD}{\text{Δ}T}$ (15)

Table 1Full-screen View

Uncertainty parameter of SLR, unit: cm/mm

Type	Value
Minimum	0.7
25th percentile value	1.2
Median	1.3
75th percentile value	1.6
Maximum	2.0

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Table 2Full-screen View

Extreme snowfall data of Yantai. SLR=1.3 cm/mm

No.	Cumulative distribution function	Snow depth (cm)	Snow speed (cm/day)
1	0.015306	2.60	1.72
2	0.040816	2.99	1.85
3	0.066327	4.42	1.91
4	0.091837	4.55	2.60
5	0.117347	4.55	2.77
6	0.142857	5.20	2.99
7	0.168367	5.72	3.02
8	0.193878	5.98	3.06
9	0.219388	6.89	3.42
10	0.244898	8.32	3.64
11	0.270408	9.23	3.66
12	0.295918	10.79	4.10
13	0.321429	11.31	4.42
14	0.346939	11.96	4.55
15	0.372449	12.09	4.55
16	0.397959	12.09	5.20
17	0.423469	12.22	5.33
18	0.448980	13.845	5.40
19	0.474490	14.56	5.66
20	0.500000	16.185	5.98
21	0.525510	16.38	6.05
22	0.551020	17.615	6.92
23	0.576531	17.94	7.93
24	0.602041	18.07	8.97
25	0.627551	18.72	9.04
26	0.653061	19.695	9.36
27	0.678571	20.54	9.36
28	0.704082	20.605	9.36
29	0.729592	21.06	10.30
30	0.755102	21.71	10.79
31	0.780612	23.79	10.86
32	0.806122	25.61	11.96
33	0.831633	27.495	13.75
34	0.857143	28.08	17.62
35	0.882653	31.98	19.70
36	0.908163	37.44	19.89
37	0.933673	52.39	21.06
38	0.959184	59.67	26.20
39	0.984694	84.24	84.24

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2.2.2

Annual exceedance probability evaluation

Using the analysis method described in Sect. 2.1, the Gumbel and Weibull distributions were used to fit the snow depth and speed of the extreme snowfall. The results are presented in Table 3, and a comparison between the fitted value of the cumulative probability and measured value is shown in Figs. 1 and 2. As shown in Fig. 2, the deviation between the Gumbel fitting value and the measured value was within 20% for snow thickness. The deviation between the fitted and measured values was significant for the small measured values, whereas it was within 20% for the significant measured values. For the snowfall rate, the deviation between the fitted values of the two distributions and the measured value was relatively large. The deviation between the measured values was within the range of 20%. These findings are consistent with those in other studies [21]. Based on the analysis results, it is recommended to use the Gumbel distribution to fit the annual exceedance probability of the snow thickness, and the Weibull distribution to fit the snow rate, for the hazard analysis of extreme snow of the Yantai plant site.

Table 3Full-screen View

Fitting results of the extreme snow hazard (SLR = 1.3 cm/mm), parameters: μ, θ or η, m. The confidence boundary for the parameter uncertainty is 95%.

Distribution	Parameters	Parameters Uncertainty	p-value
Snow depth
Gumbel	(11.85, 9.12)	(11.54, 12.15), (8.65, 9.59)	0.9926
Weibull	(19.05, 1.58)	(18.63, 19.47), (1.49, 1.67)	0.9843
Snow speed
Gumbel	(5.14, 4.27)	(4.90, 5.38), (3.87, 4.68)	0.7144
Weibull	(8.63, 1.42)	(8.28, 8.98), (1.31, 1.54)	0.8305

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Fig. 1Full-screen View

Distribution fitting of the snowfall extreme value data (SLR=1.3 cm/mm)

Fig. 2Full-screen View

Cumulative probability measurement and fitting values (SLR=1.3 cm/mm)

There are two primary sources of uncertainty regarding the snow speed and depth. The first source of uncertainty is the original meteorological data, which refers to the SLR uncertainty discussed in this study. We use the minimum (SLR = 0.7 cm/mm) and maximum values (SLR = 1.3 cm/mm) in the hazard curve to represent the uncertainty, as depicted in Figure 3. We provided the 5th (SLR = 0.786 cm/mm) and 95th (SLR = 1.914 cm/mm) percentile values of the SLR to quantify the uncertainty. Another source of uncertainty is the parameter uncertainty inherent in the fitting distribution process. Table 3 lists the uncertainties encountered during the fitting process for a given SLR. Table 4 presents the 95th percentile results for the two types of parameters under uncertainty.

Table 4Full-screen View

The uncertainty of the distribution of the fitting parameters, considering the SLR uncertainty and fitting uncertainty. The confidence boundary for the parameter uncertainty is 95%.

Snow speed parameter	η	m
Value	(5.2203, 12.7134)	(1.4207, 1.4209)
Snow depth parameter	μ	θ
Value	(7.1643, 17.4485)	(5.5178, 13.4383)

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Fig. 3Full-screen View

Hazard Curve of the Snowfall

2.2.3

Snow hazard curves and evaluation

Annual exceedance frequency refers to the probability of a specific event or phenomenon occurring within a given year. It represents the likelihood of an event surpassing a certain threshold or level within a single year. Typically, the annual exceedance frequency of external events is used as the frequency of initiating events. The annual exceedance probability (1-F(x)) curves of the snow depth and snowfall speed are shown in Fig. 3. The solid line represents the fitted hazard curve obtained by applying the corresponding distribution function to the data points. To consider the uncertainty of the SLR, we plotted the hazard curves under the conditions of the maximum, minimum, and median SLR, as shown in Fig. 3. This demonstrates that the uncertainty of the hazard analysis results caused by the uncertainty of the SLR can reach several orders of magnitude for significant hazard parameters (snow depth, snow speed).

Power Plant Response and the Impact of Extreme Snowfall on Safety-Related SSCs

The impacts of extreme snowfall on floating nuclear power plants include the following: direct damage of snow load on buildings, snow blockage of ventilation holes, and the indirect impact of long-term power plant isolation. The potential damage from extreme snowfall significantly varies owing to the characteristics of snow. The specific impacts of extreme snowfall on an FNPP are as follows:

• Damage of structure and exposed parts caused by snow load.

• The failure of systems and equipment that depend on air circulation owing to the blockage of snow at the vent, mainly the heating, ventilation and air Conditioning (HVAC) system and diesel generator equipment.

• Loss of off-site power (LOOP).

All buildings, regardless of the safety classification, are designed to withstand the impact of snow. In addition, the design of safety-grade buildings can prevent aircraft crashes, earthquakes, and external hazards, thereby providing sufficient safety margins against extreme snowfall. Juraj et al. [24] also confirmed this, demonstrating that structures have a failure load that is nearly twice the magnitude of extreme snow loads. Therefore, the main impact of extreme snowfall on floating nuclear power plants is possibly the failure of systems and equipment that depend on air circulation owing to the blockage of snow at the vent and loss of off-site power caused by extreme snowfall. Whether an FNPP requires off-site power depends on its design. Because the FNPP in our study is located offshore, off-site power can be supplied through submarine cables. Although the impact of extreme snowfall on submarine cables is lower than its impact on off-site power for onshore NPPs, considering that onshore power transmission and conversion equipment are located in the same area as the FNPP, this study assumes that a snowfall thickness exceeding 100 cm causes damage to the off-site power grid equipment, leading to LOOP.

In our study, the extreme snowfall led to a LOOP-initiating event. When a LOOP occurs in a land-based nuclear power plant, the dependency of the safety-related systems on the electrical power system can impact the accident sequence. In particular, equipment failures during a LOOP event, such as valves being unable to open or close, may result in the inability to perform the corresponding safety functions, leading to an inability to lower the reactor pressure and cool the core [34]. This situation is similar for an FNPP. The response of the safety-related system equipment of the plant resembles its response to an internal LOOP event, and an on-site emergency power supply must be considered. A combination of the successful or failed responses of the residual heat removal, pressure relief, and safety injection functions were utilized for the event sequence analysis. It is also possible to consider snow clearing at the vent in response to extreme snowfall events at a power plant. In this case, if the relevant personnel do not recognize the necessity of clearing snow, the snow at the vent will reach a threshold, and blockage of the vent may lead to the unavailability of the diesel generator. It is conservatively assumed that the unavailability of the diesel generators will lead to a loss of the emergency power supply of the plant, leading to a secondary station blackout (SBO) accident. Subsequently, the response process of the power plant must consider the loss of the relevant system that supports the power supply. The diesel generator is the main equipment affected by snow blockages at the vent. Although snow blockage at the vent may also lead to the failure of the HVAC systems, resulting in a gradual rise in the temperature within the plant, it may also lead to the failure of the diesel generator, which is a slow development process that can be included in the previous impact.

Extreme Snowfall PSA Model

The event tree (ET) analysis describes the response of a power plant to the initiating events through a series of events, linking the success or failure of several safety systems/functions to the final states of the plant (intact core: OK/core damage: CD). Based on previous assumptions, extreme snowfall events lead to the loss of the off-site power supply (LOOP) of floating nuclear power plants. Based on the Level 1 PSA model of an internal event [4] of an FNPP, an event tree model of extreme snowfall events for an FNPP was developed by referring to the event tree of the LOOP of an internal event and considering the unique snow removal response of extreme snowfall events. An event tree model of the core damage caused by extreme snowfall in an FNPP can be developed by combining the system model of a Level 1 PSA model of an internal event with personnel reliability modeling. The event trees in the PSA model are shown in Fig. 4 through Fig. 7. The abbreviations of the function events in the event trees are listed in Table 5 (Figs. 5, 6).

Fig. 4Full-screen View

FNPP event tree (initial event: extreme snowfall)

Fig. 5Full-screen View

FNPP event tree (secondary event: LOFW)

Fig. 6Full-screen View

FNPP event tree (secondary event: MLOCA)

Fig. 7Full-screen View

FNPP event tree (secondary event: SBO)

A fault tree (FT) analysis is a standard method for the reliability assessment in nuclear power plants, enabling the determination of the probabilities of the top events in event trees. It utilizes graphical and top-down approaches to decompose complex system failures from the system to the component level. Based on the design of various safety-related systems in ACP100 [35] and by referring to the fault tree of AP1000, we established fault trees for the safety systems of the FNPP. Figure 8 and 9 present the corresponding fault trees for the DGEN and PRS functional events. In the FNPP PSA model, the FT method is also employed for a system reliability analysis [36], considering factors such as random failures, common-cause failures (CCF) of equipment, human errors, unavailability owing to testing and maintenance, and failures in support systems. The multiple Greek etter (MGL) model was adopted for the CCF analysis in the PSA software called Risk Spectrum. Regarding human errors, the primary consideration is the impact of personnel unreliability on equipment during the initiation of events. The data is primarily obtained from NUREG/CR-1278 [37], and an example of the snow clearance by personnel affecting the on-site power is discussed in this section. The model parameters and logic for equipment testing and maintenance were set accordingly in Risk Spectrum, with data primarily sourced from AP1000, ACP100, and NUREG/CR-6928 [38].

Fig. 8Full-screen View

FNPP fault tree (function event: DGEN)

Fig. 9Full-screen View

FNPP fault tree (function event: PRS)

The data required to quantify the CDF caused by extreme snowfall in floating nuclear power plants include the relevant data used in the Level 1 PSA model of an internal event, the frequency of LOOP-initiating events caused by the extreme snowfall, and the probability of snow removal failure. The frequency of LOOP-initiating events caused by extreme snowfall can be estimated based on a site-specific risk analysis of extreme snowfall. As shown in Table 6, we analyzed the annual exceedance frequency corresponding to a snow depth of 100 cm and snowfall speed of 100 cm/day, and finally obtained the most conservative result (3.00E-03/plant year) as the frequency of the initial event.

According to Noroozi et al. [39], the impacting factors of extreme snowfall on the workers include low temperatures, freezing, comprehensive weather effects, ocean ice, low visibility, and work pressures. According to Islam et al. [40], the impact is mainly owing to the following several aspects: 1) Compared to land-based nuclear power plants, floating platform environments can generate ship motion, noise, and vibration under extreme snowfall, which increases the workload and pressure of snow-clearing personnel. 2) Low ambient temperatures may lower the body temperature, severely affecting the mental and sensory abilities and making it difficult to accurately determine the blockage locations. 3) Cold weather can significantly reduce physical performance and hinder the completion of snow-clearing tasks.

A simple reliability model considering the following two aspects can be adopted for snow-removal at the air vent: 1) reliability of the relevant personnel realizing the necessity of snow removal, P_AW; 2) reliability of the snow-removal operation, P_RM. The probabilities of failure of the two aforementioned types of events can be evaluated using an appropriate probability of human error, as expressed in Eq. 16. Based on the data above, the CDF caused by the extreme snowfall of a specific floating nuclear power plant can be estimated to assess the risk of floating nuclear power plants caused by extreme snowfall. $P_{\text{SW}-\text{RM}}=P_{\text{AW}}+P_{\text{RM}}=7.35\times {10}^{-3}$ (16) Here, the values indicated in the formula above can be found in NUREG/CR 1278 [37]. Although the values of NUREG/CR-1278 are typically used in land-based nuclear power plants, this result is acceptable considering the similarity between land-based nuclear power plants and FNPPs, as well as the conservatism of the probability of failure in NUREG/CR-1278.

The probability of failure of an individual receiving good skills training for 60 min to perform the step-by-step task under the average pressure level was used to estimate P_AW (8.5×10^-4). This result is similar to the value obtained by Islam et al. using a human error assessment and reduction technique (HEART) method. In their study, the probability of personnel error in cleaning the air filter for the maintenance of a sub-item of marine engine exhaust turbochargers was 1.16×10^-4, which was at task Level H. Considering the similarity between these two tasks and the increasing difficulty of the task under extreme snowfall conditions, if the task was assigned to Level G, the probability of personnel error obtained by using the HEART method during the snow-removal process was 5.8×10^-4.

The probability of failure of a person receiving good training to perform the step-by-step task under a high-pressure level was used to estimate P_RM (6.5×10^-3). This result is similar to that of Shufan Li [41] regarding the personnel unreliability during small LOCA of FNPPs(the probability of human failure is 5.8×10^-3).

For simplification, we used the values of NUREG/CR-1278 to consider the personnel errors during the snow removal process. The aforementioned parameter uncertainty was considered to obey a Lognormal distribution, and the error factor (EF) was conservatively considered as EF=30.

Result and Analysis

Conclusion

A methodological study for the probabilistic safety analysis of external events caused by extreme snowfall in floating nuclear power plants was presented. The primary conclusions of the analysis are as follows: (1) The intensity of the extreme snowfall specific to the plant site can be characterized by the snow depth and rate of snowfall. The use of the Gumbel and Weibull distributions to fit the annual exceedance probability of the snow thickness and snowfall rate demonstrates good applicability. (2) The significant impacts of extreme snowfall on floating nuclear power plants include the loss of off-site power and unavailability of diesel generators owing to snow blockage at the air vents; extreme snowfall presents challenges for the pneumatic and check valves in related safety systems. (3) The PSA of extreme snowfall for a specific floating nuclear power plant can be conducted based on a Level 1 PSA of an internal event. The results of the quantitative analysis demonstrate that the CDF of extreme snow is 1.13E-10.

In addition, note that the quantitative calculation of CDF is based on analyzing the extreme snow hazards. We adopted conservative assumptions and were aware of the uncertainties in meteorological data that can lead to uncertainties in the frequency of the initiating events that span several orders of magnitude, which can be compensated for by a more detailed meteorological data collection and hazard analysis.