ENGLISH 7_Q4_LESSON 2_ Employing a Variety of Strategies for Effective Interp...
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1. University of Technology Education HCMC
Faculty of Electrical & Electronics Engineering
ASSETMENT RELIABILITY OF POWER SYSTEM
SECTION
PROABILITY THEORY
NGUYEN ANH TOAN
ID: 10025250028
2. Objective
Objects
. Reliability theory applied to power systems
4. THEORY
define
P)A(=lim )nA)/n
Roughly,probability is how frequently we expect
different outcomes to occur if we repeat the
experiment over and over )”frequentist“ ) view
5. THEORY
Addition rule
A method of finding a probability of
.union of two events
) P)E1
E1 E2 E1 E2
6. THEORY
Multiplication rule
A method of finding probability of
.intersection of two events
) P)E1∩E2(
If E1 and E2 are independent, then
P)E1.) ∩E2( = P)E
7. THEORY
Conditional probability rule
If an event E depends on a number of
mutually exclusive events Bj, then
P)E( =Σj ]P)E | Bj( ])×P)Bj
B2
B1 B3
E
B5 B4
8. THEORY
Complementation rule
Probability of the set of outcomes that
.are not included in an event
)P)Ē( = 1 –P)E
9. THEORY
Counting methods for computing probabilities
Permutations Combinations
n! n!
P (n, r ) = C(n, r ) =
(n − r )! (n − r )! r !
n n!
=
r )n − r (!r!
n ! = n ⋅ (n − 1) ⋅ (n − 2) ⋅ (n − 3) ⋅ ... ⋅ 3 ⋅ 2 ⋅ 1
10. THEORY
Series reliability model
If any of the subsystem or component
fails, the series system experiences an
.overall system failure
)R)X1 )R)X2 )R)X3 )R)X4
RS =Π) R)Xi
11. THEORY
Parallel reliability model
The system will fail if all the units in
.the system fail
)R)X1
)R)X2
)R)X3
RS =1-Π]) ]1-R)Xi
)R)X4
12. Application
Power system
A
3 GENERATOR
B Each 50MW
Probability of failure 0.01
C Failure independently
Find probability distribution of generator capacity ?
13. Application
State space
A A A A
B B B B
C C C C
A A A A
B B B B
C C C C
