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
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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 −=
Page 28Page 28
Conclution
Probability rules We know a bit about power system reliability.