ML20133D980
| ML20133D980 | |
| Person / Time | |
|---|---|
| Site: | Saint Lucie  |
| Issue date: | 01/07/1997 |
| From: | FLORIDA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML17229A191 | List: |
| References | |
| NUDOCS 9701100159 | |
| Download: ML20133D980 (22) | |
Text
..
PSL PRA TASK 6.6 REVISION O PAGE 25 OF 64 i
APPENDIX B:
CALCULATION OF PSL LOSP INITIATOR EVENT FREQUENCY AND CONFIDENCE LIMITS t
(a) PLANT-CENTERED 1
n := 51 1 := 1089.6 f := 2 n + 1 f - 103 E(n,t) := 2 n E( n, t) - 0.04727 1
let Z1 = +1.645 for 95% CL Z2 = -1.645 for 5% CL x a= Chi-square value a - Confidence Limit Z u 1.645 f
3 x (f,z) := f.! 1 - 2,, 7, 2-(for f>40) a
(
Sf 3 9f The confidence limits are calculated by the equation:
I a(f,Z)
CL(Z) :=
2t therefore, for 95% CL:
Z1 := 1.645 x (f,Z1) - 127.68927 CL(21) - 0.05859 a
for 5% CL:
22 := -1.645
% a( f,Z2) - 80.58052 CL(Z2) = 0.03698 (b) GRID-RELATED n := 12 t := 1089.6 f:= 2 n + 1 f - 25 E( n, t) - 0.01147 from Table A.5 Reference (9),x^2 for 95% :
x i := 37.652 o
from Table A.5 Reference (9),x^2 for 5% :
% a2 := 14.611 "I
for 95% CL CL1 :=
CL1 - 0.01728 2t for 5% CL CL2:=
CL2 - 0.0067 2t 9701100159 970107 PDR ADOCK 05000335 P
PDR FAUSERSOMSLUCE\\ TASK 6-6.RVO
PSL PRA TASK 6.6 REVISION 0 PAGE 26 OF 64 l
',~
CALCULATION OF PSL LOSP INITIATOR EVENT FREQUENCY APPENDIX B:
AND CONFIDENCE LIMITS t
(c) WEATHER-INDUCED j
n := 10 f:= 2 n + 1 f-21 E( n, t ) - 0.00964 from Table A.5 Reference [9],x^2 for 95% :
Iat := 32.67 from Table A.5 Reference [9],x^2 for 5% :
I a2 := 11.59 for 95% CL cL1 :=
CL1 - 0.01499 2t for 5% CL CL2 :=
CL2 - 0.00532 2.t l
l F.WSERSOMM.UCE\\ TASK 64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 27 OF 64 i
APPENDIX C:
TIME. LINES FOR REPRESENTATIVE PSL LOSP SCENARIOS I
Definitions of parameters:
a
- Weibull parameter.
b
- Weibull parameter.
A
- DG D1 failure rate.
1
- DG D2 failure rate.
2 1
- DG Dl/DG D2 common cause failure rate.
3(
- TD AFW pump failure rate.
1
l i
5
}
(
- HPSI Pump run failure rate.
T,
- Mission time for sequence.
T,i
- Mission time for Diesels.
T,3
- Mission time for HPSI pump (Injection).
1 T,
- Mission time for HPSI pump (Recirc).
T,m
- Battery depletion time.
Tco
- Time to Core Damage following loss of core cooling.
i i
Definitions of events:
t i
DlS
- DG D1 fails to start.
D2S
- DG D2 fails to start.
D1R
- DG D1 fails to run.
D2R
- DG D2 fails to run.
DCCS : DG D1 & DG D2 common cause failure to start.
DCCR : DG D1 & DG D2 common cause failure to run.
5 ABS
- TD AFW pump fails to start.
ABR : TD AFW pump fails to run.
ACR : MD AFW pump fails to run.
i HPIR : HPSI pump fails to run (Injection).
HPRR : HPSI pump fails to run (Recirc).
BTD : Battery depletion.
CD
- Core damage.
i e
FMJsERSOMstUCIE\\rAsK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 28 OF 64 i
Functions definitions:
E(A,t) = A e-A' 8
1't-v'3 I
5 G(v,t) =
0 3 W(t) = a b t*-la "
M(t) = a *
D1S Case 1-
= Aft r
()
(_/
LOSP 1
0 Trro ts Teo Figure (3): Case 1 Scenario.
R = [,I"'#"M(t +T y.G(Tgi)dt (29) 3 i
c D1S D2R Case 2*.
- ft r
()
(_,,,/
=
0 ti Toro t
Teo l
Figure (4): Case 2 Scenario.
( 2 t)d k
( )
M~I )
k"1 d
2 C
I i
0 0
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PSL PRA TASK 6.6 REVISION O PAGE 29 OF 64 i
l D2S D1R ft r Case 3A:
()
()
=
=
0 ti Tom tz Teo Figure (5): Case 3A Scenario.
I
~~I" WI(t,+T ).G(Tm,tp E(1,t,)dt dt:
(31)
R
=
w 3
i y
A T, a
a i
D2S D1R V
A'"
\\7 A
2n7r
()
()
=
=
=
0 Taro ti t
Teo Figure (6): Case 3B Scenario.
VI(f +T ).E(A,,t -'i).G(Tm 's)dl d'2 (32)
~~
Ru " A, T, a
2 co 2
i a
R=R
+ R, (33) 3 y
F.WSER$hDMStUQE\\ TASK 64JtVO
PSL PRA TASK 6.6 REVISION O PAGE 30 OP 64
\\
i I
D1R D2R ft r Case 4A:
()
()
LOSP 0
ts t
TsTo t:
Teo j
5 Figure (7): Case 4A Scenario.
I
~ ~ "
~6
~6 am '3 '2)ECA 2 's).E(1,t )dt,dt dt (34)
R, =
Wl(t +T ).G(T 3 i z 3 3 c3 2
A,\\ Ti 4
D2R D1R Case 4B:
()
()
=
=
0 ts t:
Toro t
Teo Figure (8): Case 4B Scenario.
I R,, =
~ ~ " f6~6W/(t +T ).G(T,,,t -t ).E(A,,t:-t,).E(1,t )dt,d'2dt (35)
~
3 cy 3 i 2 i 3
A, A T1 -)
-3 P.MJ5ER90MStUC!lhTASK64.RYO
PSL PRA TASK 6.6 REVISION O PAGE 31 OF 64 r
i 1
D2R D1R Case 4C:
ft
=
()
()
=
=
=
=
0 ti Two la to Teo Figure (9): Case 4C Scenario.
1 v.-r as s
a Re=
WI(t,+T ).G(Tm2-t,).E(\\,t,)dt dt dt (36) co iz 3 (37)
R, = Ru+R,+Re DCCS ft r Case 5'
=
()
( /
=
0 TsTo ti Tco Figure (10): Case 5 Scenario.
1 R=
~~#"W/(t, +T ).G(T
,r,) dt, (38) i 3
co
.3 l
l I
l FNJSER9DMStUCE\\ TASK 64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 32 OF 64 i
t DCCR Case 6:
ft r
(/
()
=
0 ti Two ta Tm Figure (11): Case 6 Scenario.
I
~ #"
~
W/(t,+T ).G(Tm '2-t ).E(1,t ) dt,dt:
(39)
R=
co i
3 i
\\ / D1S Ti m ABS Om
= After Case 7:
()
=
=
0 Teo Figure (12): Case 7 Scenario.
R, = WI(T )
(@)
co FM1SDtSOMStUCENTAOK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 33 OF 64 4
t ABS D1R nr Case 8:
=
()
=
=
0 ti Teo Figure (13): Case 8 Scenario.
R, =
" "W/(t,+T )E(A,t,) dt, (41)
I w
i A,Tua X7DecS ass n
2n7r e
s.
()
=
0 Teo Figure (14): Case 9 Scenario.
R, = MTco)
FMISERSOMStUCIE\\ TASK 64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 34 OF 64 i
4 1
l l
ABS DCCR Case 10:
nr
=
()
LOSP 0
ti Tco Figure (15): Case 10 Scenario.
I R,, =
v.-r"WI(t, +T ).E(\\,t,) dt, (43) w NTao I
D1S ABR ner Case 11:
=
()
=
=
0 ti Teo i
Figure (16): Case 11 Scenario.
I R,, =
~~#"WI(t,+T ).E(A,,r,) dt, (44) w A,T, a
1 FAUSER50MFLUC1hTASK64RVO
PSL PRA TASK 6.6 REVISION O PAGE 35 OF 64 i
a i
ABR D1R f
Case 12A:
=
()
=
=
O ti tz Tm Figure (17): Case 12A Scenario.
1 v.-r. ** W/(t +T ).E(A,t,-t,).E(1,,t,) dt dt (45)
Riu " A, A,T,,T, -)
a cy 3
i o
i D1R ABR
\\/
O At7: r Case 12B:
(j
- LOSP
=
0 ts t
Tm Figure (18): Case 12B Scenario.
'Wl('2+Ty.E(1,,t -t,).E(1,t,) dt dt:
(46)
~~
Ri2s " A, A,T,T, a
3 i
a i
(47) i2 " R, + Rig R
iz FNJSERSOMSLUCETASK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 36 OF 64 s
t DCCS ABR Time g
paTo O co After Case 13:
N]
N)
LOSP O
Tom t1 Teo Figure (19): Case 13 Scenario.
1 r"W/(t, +T ).E(1,t,) dt, (48)
R,3
=
w ABR DCCR Case 14A:
- fler
()
=
0 ts tz Tm Figure (20): Case 14A Scenario.
1 v.-r g
R,y =
W/(t,+Ty.E((,t -f ).E(1,,t,) dt dt, (49) 2 i i
A 7_7 FMJSERSOMStUCm\\ TASK 64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 37 OF 64 4
i i
DCCR ABR V
O O"
ft r
% )
%)
~
Tm
~
j
=
0 ti ta=
Tm Figure (21): Case 14B Scenario.
I R,, = A A,T,,T,-)~#"'#"
~'WI(t +T ).E(A,t,-t,).E(1,t,) dt,dt (50) 2 w 3
3
-o 3
R,=Riu + R,,
(51) 3 HPIR D1R Time co
= Aner Case 15A*
()
=
0 ti t
Tm Figure (22): Case 15A Scenario.
W/(t:+T ).E(A,,t -f ).E(1,t,) dt,dt:
(52)
R,y =
co 2 t A,%T Taao o
F.AUSERSOMSLUCIhTASK64RVO
PSL PRA TASK 6.6 REVISION O PAGE 38 OF 64 t
\\
D1R HPIR V
O
= Aft r Case 15B:
LOSP O
ti t
Tm Figure (23): Case 15B Scenario.
1 R,, = A, A.T,T,, ov.-r
'Wl(t,+T )E(1.,t -l ).E(A,t ) dt,dt:
(53) co a i ii
-)
R
= R,3, + R,
(54) is is HPRR D1R 7
O Case 16A:
- ft r (y
=
0 ti ta Tm Figure (24): Case 16A Scenario.
I R,y =
Wl(t +T ).E(1,,'2-f ).E(A,t ) dt,dt (55) 2 co i
i A, A T T,
o
-)
o F.MJSERSOMStUCECASK64RVO
1 PSL PRA TASK 6.6 REVISION O PAGE 39 OF 64 i
D1R HPRR Att r Case 16B:
( /
=
0 ti t
Ta Figure (25): Case 16B Scenario.
i l
I
~6WI(t,+T )E(1,t,-t,).E(1,,t,) dt,dt (56)
R,, = k, k,T Twwo co 2
R,, = R,,, + R,,,
(57)
ACR D1R f
Case 17A:
=
(_./
=
0 ti tz Tm Figure (26): Case 17A Scenario.
1
~ ~ "
~6W/(t +T ).E(A,,'2-f ).E(1 i) dt dt (58)
R
=
2 c3 i
5 i z iu k, k,T,T
-)
~o w
FMISER90MStUCIhTASK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 40 OF 64 9
i i
D1R ACR r
Case 17B:
=
( /
=
1 0
ti in Tm Figure (27): Case 17B Scenario.
I R,, =
~#" r.
,'WI(t +T ) E(A t -l ) E(A t ) dt dt (59) a.
3, a i i,,
3 A, A T,Tg -)
o S
R,, = R,,, + R,,,
(60)
I FNJSERSDMSLUCE\\ TASK 64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 41 OF 64 APPENDIX D:
TWO-PARAMETER WEIBULL DISTRIBUTION FOR PLANT-i CENTERED OSP NON RECOVERY DATA n := $1
$ *: 0.88 b
b i := 1 26 i
i := 27 n i
1 0.003 27 0.433 2
0.003 3
0.483 3
0.004 5
0.500 TOL := 0.000001 4
0.017 30 0.500 5
0.017 31 0.500 6
0.033 32 0.500 7
0.067 3
0.633 8
0.067 34 0.667 9
0.083 35 0.667 10 0.083 36 0.767 11 0.133 37 0.900 12 0.150 38 0.900 13 0.150 39 0.933 3
0.167 5
1.033 3
0.183 E
1.483 16 0200 42 1.500 17 0.250 43 1.667 H
0250 E
1.750 19 0.250 45 1.967 20 0.267 46 2.167 21 0.283 47 2.333 22 0.300 48 2.750 23 0.333 49 4.617 24 0.333 50 5.917 3
0.333 5
7.433 3
0.400 (if in(t)
$ := root 11-in(t,)\\,$
[(t)"
0 "Ii i
/
S - 1.094955 Y
-[(t';'
A = 1.074904 A :=
i a := 0 a.1.082302 b = 1.094955 F.WSERSOMStUCHhTASK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 42 OF 64 APPENDIX D:
TWO. PARAMETER WEIBULL DISTRIBUTION FOR PLANT-CENTERED OSP NON. RECOVERY DATA t
PLOT OF CUMULA11VE LOSP NONRECOVERY PROBABILITY APPROXIMATED AS A WElBULL DISTRIBUTION (PLANT-CENTERED )
J := 1.18 x(j) := 0.2-(j - 1)
P(j) := e'*("(ll) x(j) P(l}
j := 19 36 x(]) P(j) 0 1
3.6 0.012 0.2 0.83 3.8 0.009 0.4 0.672 4
0.007 0.6 0.539 4.2 0.005 0.8 0.428 4.4 0.004 1
0.339 4.6 0.003 1.2 0.267 4.8 0.002 1.4 0.209 5
0.002 1.6 0.164 5.2 0.001 1.8 0.127 5.4 0.001 T
0.099 5.6 7.943 10
2.2 0.077 5.8 6.005 10
2.4 0.059 6
4.536 10" i
2.6 0.046 6.2 2.8 0.035 6.4 3.424 10-'
I 0.027 U
2.582 10
3.2 0.021 6.8 1.945 10
3.4 0.016 7
1.102 10
I 1 38 Nonrecovery Probability vs.
Time 1
l N<
0 a(j) 7 r.WSERSOMSLUCETASK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 43 OF 64 APPENDIX E:
TWO. PARAMETER WEIBULL DISTRIBUTION FOR GRID.RELAT.
n := 12
$ := 0.88 1 :: 1.. n l
8 1
0.133 TOL := 0.000001 0
7 0.300 5
0.333 6
0.550 7
0.917 8
1.033 g
2.000 Io 2.083 E
2.833 3
6.467 (t)E :(t) ir I
In(t)
,S S = 0.884114
$ := root E(i)
(i s
1 I.[(t)I A = 0.752431 A :=
i b := S
- p a - 0.777647 b - 0.884114 FMJSEk&DMSitJCENTASK64.RVO
PSL PRA TASK 6.6 REVISION O PAGE 44 OF 64 APPENDIX E:
TWO-PARAMETER WEIBULL DISTRIBUTION FOR GRID RELAT.
4 PLOT OF CUMULATIVE LOSP NONRECOVERY PROBABILITY APPROXIMATED AS A WElBULL DISTRIBUTION (GRID-RELATED)
)
..(9 6
j :: 1. 36 x := 0.2-() - 1 )
P := e j
3 P,
x l
Nonrecovery Probability vs.
g, 0.4 0.707579
~
1 g
0.609545 OJ 0.528129
}
1 0.459486 g
0.401051 y
0.350964 y
0.307808 y
0.27047 2
0.238056 2.2 0.209835 U
0.185205 2
2J 0.163663 2J 0.144785 3
0.128214 p
3.2 0.113646 1
3J 0.100821 4
y 0.089516 3.8 0.07954 4
4 0.070726 4.2 0.062932
\\
U 0.056032 4J 0.04992 g
4.8 0.0445 i
1 0.03969 5.2 0.035419 5
0.031624
\\
1 U
0.028249 U
0.025246 a
7
[
0.022572
'l 6}
0.020191 6.4 0.018068 U
0.016174 i
U 0.014485 T
0.012977 FAUSERSOMStUCIF.\\ TASK 6 6.RVO
PSL PRA TASK 64 REVISION O PAGE 45 OF 64 i
APPENDIX F:
TWO-PARAMETER WEIBULL DISTRIBUTION FOR WEATHER.
INDUCED OSP NON RECOVERY DATA t
n := 10
$ := 0.88 o
t :=
I:s 1 n g
i T
0.033 TOL := 0.000001 T
0.233 T
0.400 7
1.750 5
1.817 6
2.667 7
4.000
~
8_ 8.900
.[(t)0 In(t) 9_ 11.000 10 18.967 in(t)
,S
$-0.695364
~
0 ;* #
~ -
- p 1
l (t[.
A = 0.250485
)
A :=
i a := A' a - 0.381886 b - 0.695364 FNJSER9DMSLUCIlhTASK64RVO
PSL PRA TASK 6.6 REVISION O PAGE 46 OF 64 i
APPENDIX F:
TWO. PARAMETER WEIBULL DISTRIBUTION FOR WEATHER.
INDUCED OSP NON. RECOVERY DATA 1
PLOT OF CUMULATIVE LOSP NONRECOVERY PROBABILITY APPROXIMATED AS A WElBULL DISTRIBUTION (WEATHER-INDUCED)
.. (9 =
j :s 1 36 x := 0.2-( j - 1 )
P := e 3
3 x
P, 0
1 E
0.882754 Nonrecovery Probability vs.
U 0.817145 Time 5
0.765128
~.8 0.721085 0
1 0.682573 E2 0.648233 5
0.617205 g
0.588895 g
0.562874 2
0.538814 2.2 0.51646 5
0.495608 2.6 0.476089
\\
5 0.457766 3
0.440521
(
p 32 0.424252
_L 34 0.408875 3.6 0.394314 5
0.380503
\\
[
0.367384 42 0.354906 3
4.4 0.343022 4.6 0.331692 E
0.320877 T
0.310545 E
0.300665 I
5 0.291209 E
0.292152 5
0.27347 0
1 0.265141 "I
6.2 0.257147 i
5 0.249468 6.6 0.242088 l
B 0.234991 I
l T
0.228163
\\
F.*USERSOMSLUCHATASK6-6.RVO