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University of Technology Education HCMC University of Technology Education HCMC Faculty of Electrical & Electronics Engineering Faculty of Electrical & Electronics Engineering SECTION PROABILITY THEORY ASSETMENT RELIABILITY OF POWER SYSTEM NGUYEN ANH TOAN ID: 10025250028
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University of Technology Education HCMCUniversity of Technology Education HCMCFaculty of Electrical & Electronics EngineeringFaculty of Electrical & Electronics Engineering
SECTION
PROABILITY THEORY
ASSETMENT RELIABILITY OF POWER SYSTEM
NGUYEN ANH TOANID: 10025250028
Objective
ObjectsObjects
Reliability theory applied to power systems..
Agenda
● Theory●Application● Conclusions
THEORY
P)A(=lim )nP)A(=lim )nAA)/n)/n
definedefine
Roughly,probability is how frequently we expect different outcomes to occur if we repeat theexperiment over and over )”frequentist“ ) view
THEORY
Addition ruleAddition rule
A method of finding a probability of .union of two events
) P)E1UE2( = P)E1( + P)E2( –P)E1 E2∩
E1 E2 E1 E2
THEORY
Multiplication ruleMultiplication rule
A method of finding probability of.intersection of two events
) P)E1 E2( = P)E1(×P)E2 |E1∩
If E1 and E2 are independent, then
P)E1.) E2( = P)E1(×P)E2∩
THEORY
Conditional probability ruleConditional probability rule
If an event E depends on a number ofmutually exclusive events Bj, then
P)E( =Σj ]P)E | Bj( ])×P)Bj
B1
B2
B3
B4B5
E
THEORY
Complementation ruleComplementation rule
Probability of the set of outcomes that .are not included in an event
)P)Ē( = 1 –P)E
THEORY
Counting methods for computing probabilities
Permutations Combinations
!( , )
( )!
nP n r
n r=
−!
( , )( )! !
nC n r
n r r=
−
!(!)
!
rrn
nn
r −=
! ( 1) ( 2) ( 3) ... 3 2 1n n n n n= ⋅ − ⋅ − ⋅ − ⋅ ⋅ ⋅ ⋅
THEORY
Series reliability modelSeries 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
THEORY
Parallel reliability modelParallel reliability model
The system will fail if all the units in.the system fail
)R)X1
)R)X2
)R)X3
)R)X4
RS =1-Π]) ]1-R)Xi
Application
Power systemPower system
A
B
C
3 GENERATOR Each 50MW Probability of failure 0.01 Failure independently
Find probability distribution of generator capacity ?
Application
State spaceState space
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
Application
LevelLevel
A
B
C
A
B
C
A
B
C
A
B
C
Application
CAPACITY(MW) PROBABILITY
0 0.000001
50 0.000297
100 0.029403
150 0.970299
Generating probability distributionGenerating probability distribution
λλ=0.01=0.01!(!)
!
rrn
nn
r −=
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Conclution
Probability rules We know a bit about power system reliability.
?
THE ENDTHE END
