RELKO Ltd.
PSA 2015, International Topical MeetingEngineering
on Probabilistic
Safety Assessment
and Analysis
& Consulting
Services
Sun Valley, ID, USA, April 26-30, 2015
USING OF EXTREME VALUE THEORY
IN EXTERNAL EVENT PSA OF
WWER440 REACTORS
Zoltan Kovacs, Jana Macsadiova and Filip Osusky
RELKO Ltd.
Engineering & Consulting Services
RELKO Ltd.
Engineering & Consulting Services
CONTENTS









Introduction
EEPSA – natural events other than seismic event
Construction of the hazard curves – Statistics of extreme values
IE initiated from external natural events
Fragility analysis
Accident sequence modeling
FT modeling
Results
Conclusions
2
RELKO Ltd.
Engineering & Consulting Services
INTRODUCTION
 The fundamental step in addressing the threats from external hazards is to
identify those that are of relevance to the plant.
 External hazards can be screened out from further consideration on two criteria,
either because they are incapable of posing a significant threat to nuclear safety
or because the frequency of occurrence is extremely low.
 A figure of 1 in 10 million years is quoted as a cut off frequency (1.0E-7 /year).
3
RELKO Ltd.
Engineering & Consulting Services
INTRODUCTION
 The following types of natural and man-made external events are as a minimum
taken into account in the design of the nuclear power plants with WWER440
type reactors according to site specific conditions:
1) extreme wind loading, tornado,
2) extreme outside temperatures,
3) extreme rainfall, snow conditions and site flooding,
4) icing and lightning,
5) earthquake,
6) airplane crash,
7) other nearby transportation, industrial activities and site area conditions which
reasonably can cause fires, explosions or other threats to the safety of the
nuclear power plant.
4
RELKO Ltd.
Engineering & Consulting Services
EEPSA – natural events other than
seismic event
 PSA is used to assess the overall risk from the plant, to demonstrate that a
balanced design has been achieved, and to provide confidence that there are no
"cliff-edge effects„.
 The external event PSA includes the following main steps:
 identification of potentially relevant external events (natural events other




than seismic event)
identification of PSA relevant buildings
screening analysis
detailed analysis
PSA modeling and quantification (hazard curves, fragility curves,
implementation into the internal event PSA)
5
RELKO Ltd.
Engineering & Consulting Services
EEPSA – natural events other than
seismic event
 After a screening process the following natural external events are considered
for the Slovak NPPs in the EEPSA:
1) extreme wind loading,
2) tornado
3) extremely low and extremely high outside temperatures,
4) extreme rainfall, snow conditions and site flooding,
5) icing and lightning,
 Credible combinations of individual events, including internal and external

hazards, that could lead to anticipated operational occurrences or design basis
accident conditions, must be also considered in the design. Engineering
judgment and probabilistic methods can be used for the selection of the event
combinations.
However, the combination of individual events are not involved in the EEPSA for
WWER plants at the present time.
6
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 Statistical theory of extreme values is used to analyze observed extremes and to
forecast further extremes. Let the values X1 , X2, ...Xn are the sequence of
independent and identically distributed variables, for example extreme
temperatures or extreme wind.
 The maximal temperature per year is Mn = max (X1 , X2, ...Xn ) and Mn is
available for 30 years.
 For distribution of extreme values three types of distributions are considered,
which are described by the distribution function G(z).
7
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
Gumbel distribution:
𝐺𝐺 𝑧𝑧 = exp − exp −
Fréchet distribution:
Weibull distribution:
𝑧𝑧 − 𝑏𝑏
𝑎𝑎
0,
𝑧𝑧 − 𝑏𝑏
𝐺𝐺 𝑧𝑧 = �
exp −
𝑎𝑎
,
−∞ < 𝑧𝑧 < ∞
−𝛼𝛼
𝑧𝑧 − 𝑏𝑏
exp − −
𝐺𝐺 𝑧𝑧 = �
𝑎𝑎
1,
𝛼𝛼
𝑧𝑧 ≤ 𝑏𝑏,
, 𝑧𝑧 > 𝑏𝑏;
,
𝑧𝑧 < 𝑏𝑏,
𝑧𝑧 ≥ 𝑏𝑏;
All three distributions are applicable for extreme values. The following
parameters are used:
(scale parameter), (location parameter),
(shape parameter).
8
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
The above mentioned three distributions can be
combined into a single distribution of generic extreme
values (GEV distribution) with the distribution
function:
This model has three parameters:
(location
parameter),
(scale parameter) and
(shape
parameter). The above mentioned distributions
correspond to cases
,
and
. The case
of
corresponds to Gumbel distribution with the
distribution function:
,
9
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 The first step of analysis is data collection about the parameters of extreme





meteorological events.
The data source for the Slovak nuclear power plants is the measurement by the
meteorological stations of Slovak Hydro-meteorological Institute (SHMU) on the
plant sites.
Station data is measured at a single point. These data usually have high quality.
For data collection it is important to consider the location of the station, and
whether it is representative of the site in question, for example the distance to it,
the height over sea level of the station, and if it is close to the water.
The objective is to collect enough data. We want as much data as possible, in
order to get a good picture of the analyzed process. For weather data, including
temperature, a common rule of thumb is to have at least 30 years of daily data.
It is very important that the data is quality checked, in particular for outliers (for
example if a temperature value of 10 has accidentally been entered as 100). So,
any such values would have a huge impact on the results.
This is less of a problem nowadays with automatic data reading, but is more
likely with old data that was typed by hand.
10
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 The next step is the identification of extreme values (maximal or minimal values)


from the collected data.
The most common approach is to extract the yearly maximum (or minimum)
values from the time series, and then build a mathematical model around these
values.
By modeling how the maximum values have looked like in the past, we can
draw conclusions on how the extreme values work in general.
11
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 A popular method for analyzing these maximum values is the study of return



periods.
The concept is the following: We have a list of annual maximum values that we
want to build a model around. We assume that these maximum values are
random in the sense that we cannot predict their exact value beforehand.
However, by having a list of historical maximum, we can draw conclusions on the
probability for the annual maximum to take a value within a certain range. This is
done by fitting a so called probability distribution to the maximum values.
The model gives answer also to the general question ”what is the probability that
the annual maximum will fall between a and b ?”.
For example, if we are studying extreme temperatures, this model could answer
the question ”what is the probability of getting an annual maximum temperature
of between 20 °C and 25 °C ?”.
12
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 The width of the interval depends on how much data we have. The more data we



build or model on, the smaller the confidence interval is, which reflects that we
have more information and thus a smaller uncertainty.
In addition to being able to give answers to the question ”what is the probability
that the annual maximum will fall between a and b ? ”, the probability distribution
can answer the inverse question: ”What is the annual maximum such that the
probability of exceeding this value is p ? ”
For example, we might want to know the temperature such that the probability
for an annual maximum temperature to exceed this value is 1%. The annual
maximum value that is exceeded with probability 1/p is called the p-year return
level.
Equivalentely, we say that the return period for that temperature is 100 years.
So, the annual maximum temperature that is exceeded with a 1% risk is called
the 100-year return level, or in the case of temperature simply the 100-year
temperature. This name comes from the fact that on average, this temperature is
only exceeded once every 100 years.
13
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 In case of obtaining maximal temperatures the calendar years are used for data


collection.
However, it is not possible to apply in case of minimal temperatures. It is
necessary to ensure that the collected values are independent (only independent
values can be used in the mathematical distributions).
If calendar years are used the minimal values of temperatures can be dependent
(given cold weather around December 31th). To solve this problem the calendar
year is defined with the beginning of July 1th and with the end of June 30th for
data collection.
14
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 The traditional method using only the highest (lowest) value from every


measurement year is known as the annual maximum method.
The method is relatively simple to apply, but has the obvious disadvantage of
giving dubious results for short measurement series.
However, some methods to derive estimates for long return periods from short
data series have been developed, e.g., the exceedance probability method.
15
RELKO Ltd.
Engineering & Consulting Services
CONSTRUCTION OF HAZARD CURVES –
Statistics of extreme values
 It is important to verify that the model fits the data.
 This is done by performing a goodness-of-fit test between the data and the


distribution.
This test will answer the question ”with what certainty can I say that my model
fits the data?”.
Because the annual maximum values are assumed to come from a random
process, this question can never be answered with absolute certainty, but is
rather answered with a certain confidence, for example 95%.
16
RELKO Ltd.
Engineering & Consulting Services
The observed minimal temperatures from the Bohunice site
Winter
Tmin
1983-1984 1984-1985 1985-1986
[°C]
Winter
Tmin
[°C]
[°C]
[°C]
[°C]
[°C]
[°C]
[°C]
-12.6
-19,0
-12.6
-17.6
-18.4
-20.7
-13.6
-14.1
-14.6
-10.1
-20.1
-16.1
-15.3
-16.2
-19.6
-8.8
2007-2008 2008-2009 2009-2010
[°C]
Winter
Tmax
-15.5
2004-2005 2005-2006 2006-2007
Winter
Tmax
-12.3
2001-2002 2002-2003 2003-2004
Winter
Tmin
-10.6
1998-1999 1999-2000 2000-2001
Winter
Tmin
-10.7
1995-1996 1996-1997 1997-1998
Winter
Tmin
-26.1
1992-1993 1993-1994 1994-1995
Winter
Tmin
-16.6
1989-1990 1990-1991 1991-1992
Winter
Tmin
-24.0
1986-1987 1987-1988 1988-1989
Winter
Tmin
-13.8
-11.7
-17.7
-17.5
2010-2011 2011-2012 2012-2013
[°C]
-18.1
-15.1
-13.3
17
RELKO Ltd.
Engineering & Consulting Services
The calculated values of the lowest temperatures are presented for the
confidence intervals of 5%, 50% and 95%.
Return period
(y)/confidence
interval
50%
5%
95 %
5.00E+00
-18.9207
-17.1055
-20.7359
1.00E+01
-21.4452
-19.1235
-23.7668
1.50E+01
-22.8695
-20.2481
-25.4908
2.00E+01
-23.8667
-21.0317
-26.7017
2.50E+01
-24.6349
-21.6337
-27.6361
5.00E+01
-27.0012
-23.4812
-30.5211
1.00E+02
-29.3500
-25.3081
-33.3919
2.00E+02
-31.6902
-27.1237
-36.2568
5.00E+02
-34.7778
-29.5143
-40.0412
1.00E+03
-37.1112
-31.3187
-42.9038
1.00E+04
-44.8588
-37.3001
-52.4174
1.00E+05
-52.6050
-43.2726
-61.9374
1.00E+06
-60.3510
-49.2408
-71.4613
1.00E+07
-68.0971
-55.2066
-80.9876
1.00E+08
-75.8431
-61.1708
-90.5155
1.00E+09
-83.5892
-67.1339
-100.044
18
RELKO Ltd.
Engineering & Consulting Services
Daily minimum temperatures
depending on the return period
10
-10
Daily minimum temperature [°C]
-30
5%
-50
95 %
50 %
-70
Observed
temperatures
-90
-110
1.0E+09
1.0E+08
1.0E+07
1.0E+06
1.0E+05
1.0E+04
1.0E+03
1.0E+02
1.0E+01
1.0E+00
Return period [year]
19
RELKO Ltd.
Engineering & Consulting Services
Daily maximum temperatures
depending on the return period
75
70
Daily maximum temperature [°C]
65
60
55
50
5%
45
95 %
40
50 %
35
Observed
temperatures
30
25
1.0E+09
1.0E+08
1.0E+07
1.0E+06
1.0E+05
1.0E+04
1.0E+03
1.0E+02
1.0E+01
1.0E+00
Return period [year]
20
RELKO Ltd.
Engineering & Consulting Services
IE initiated from external natural events
Extreme wind, tornado, extreme snow:






Loss of operational service water trains (1,2,3)
Opening of all steam dump stations to the atmosphere or all SG safety valves
Closing of all quick closing valves on the steam lines
Loss of offsite power (loss of all non-category 6 kV busbars),
Loss of circulating cooling water,
Loss of main feedwater
21
RELKO Ltd.
Engineering & Consulting Services
IE initiated from external natural events
Extremely high outside temperatures:
 Inadvertent reactor trip
Extremely low outside temperatures:
 Loss of operational service water trains (1,2,3)
Extreme rainfall:
 Loss of operational service water trains (1,2,3)
 Loss of circulating cooling water
Icing and lightning:
 Loss of offsite power
22
RELKO Ltd.
Engineering & Consulting Services
Fragility analysis – DG building
1
0.9
0.8
5%
0.7
Damage probability
95 %
0.6
15 %
85 %
0.5
16 %
84 %
0.4
25 %
75 %
0.3
35 %
65 %
0.2
50 %
0.1
0
0
10
20
30
40
50
60
70
80
90
100
Wind speed [m/s]
23
RELKO Ltd.
Engineering & Consulting Services
Fragility analysis – DG building
v HCLPF (m/s)
35.03
Betar
0.1
Betau
0.12
v m (m/s)
50.3
24
RELKO Ltd.
Engineering & Consulting Services
Accident sequence modeling
 The main objective of the accident sequence modeling is:
 to modify the event trees, developed within the internal event PSA study (if


they are applicable for the EEPSA),
to construct the event trees for the specific EE-induced initiating events that
reflect the plant response and
to construct the generic event trees that integrate these event trees to
EEPSA model and provides possible combination of single initiating events.
25
RELKO Ltd.
Engineering & Consulting Services
FT modeling
 The fault trees are constructed to adequately describe the logical combinations

of equipment failures and human errors leading to the failure of safety systems
to fulfill their intended functions. The system models of the internal initiator PSA
are a good starting point for developing fault trees for the EEPSA. These existing
system fault trees are extended and modified for the purposes of the seismic
analysis.
The following tasks are performed to develop system fault trees so that they
meet the requirements of the EEPSA:
 addition of EE induced causes for component failure modes that are
included in the PSA models for internal initiators
 addition of new EE-induced component failure modes that are not included
in the PSA models for internal initiators due to their low probability of
occurrence,
 modeling of dependent failures,
 modeling of EE caused failures of structures, and failures from spatial
system interactions,
26
RELKO Ltd.
Engineering & Consulting Services
RESULTS
External natural event
Extreme wind
Tornado
Extreme snow
Extreme rainfall
Extremely high
temperature
Extremely low
temperature
Icing
Lightening
Total
CDF (1/y)
4.95E-06
4.89E-05
9.78E-08
3.89E-10
2.80E-09
9.09E-10
3.39E-09
1.12E-10
5.40-05
27
RELKO Ltd.
Engineering & Consulting Services
Conclusions
 Finally, it can be concluded that the EE contribution to the overall CDF is
extremely high due to extreme wind and tornado. There are two reasons:
 The capacity of structures and components of the plant against natural EE is
underestimated by the applied deterministic methodology or
 The capacity of structures and components of the plant is really low and
safety upgrades are needed to be implemented in order to reduce the risk
from external natural events.
28