Opt imum Operasi dan Keandalan
Sist em Tenaga List rik
Oleh :
Prof. Ontoseno Penangsang, Ph.D Dr. Eng. Rony Seto W ibow o
Laborat orium Simulasi Sist em Tenaga List rik
Cont ent s
•
Basic Probabilit y Theory•
Applicat ion of Binomial Dist ribut ion•
Generat ion Syst em Reliabilit y Analysis•
Transmission Syst em Reliabilit y AnalysisDAFTAR PUSTAKA
•
Roy Billint on, Ronald N Allan, “ Reliabilit yEvaluat ion of Engineering Syst ems” Plenum Press : New York, 1992
•
Roy Billint on, Ronald N Allan, “ Reliabilit yEvaluat ion of Pow er Syst ems” Plenum Press : New York, 1996
Basic Probabilit y Theory
Oleh :
Dr. Eng. Rony Seto W ibow o
Probabilit y Concept
• Mathematically, it is a numerical index that can vary between zero to unity
Example
•
Anggap kit a melempar dua buah daduPermut at ions and Combinat ions
• The number of permutations of n different items is the number of ways these items can be arranged
Example
•
Anggap kit a mempunyai 3 buah buku dengan nama A, B dan C. Berapa kemungkinan kit a menyusun ket iga buku t ersebut ?Rules for Combining Probabilit ies
•
Rule 1 – Independent event s•
Rule 2 – M ut ually exclusive event s•
Rule 3 – Complement ary event s•
Rule 4 – Condit ional event s•
Rule 5 – Simult aneous occurrence of event s•
Rule 6 – Occurrence of at least one if t w o event sExample
Probabilit y Densit y Funct ion
• The summat ion of
probabilit ies should equal unit y
• Probabilit y densit y Funct ion (a) Separat e dat a
Probabilit y Dist ribut ions Funct ion
• PDF is obt ained by
summat ing t he densit y funct ion (numerically, int egrat ing)
• Discret e random variable : (a) Separat e dat a
Probabilit y Dist ribut ions
• Cont inuous random variable :
(a) Probabilit y
M at hemat ical Expect at ion
•
M oment s of dist ribut ion, also know n asExample
•
The data of copper lengt h measurement are as follow s :5,97 5,97 5,98 5,98 5,98 5,99
5,99 5,99 5,99 5,99 6 6
6 6 6 6,01 6,01 6,02
6,02 6,02
Variance and St andard Deviat ion
•
A measure of dispersion of a dist ribut ion is defined as Variance V(x)Example
•
The data of copper lengt h measurement are as follow s :5,97 5,97 5,98 5,98 5,98 5,99
5,99 5,99 5,99 5,99 6 6
6 6 6 6,01 6,01 6,02
6,02 6,02
Applicat ion of t he Binomial
Dist ribut ion
Oleh :
Dr. Eng. Rony Seto W ibow o
General Charact erist ic
•
Binomial dist ribut ion can be represent ed by general expression :(p+q)2
•
Required condit ions are :– Fixed number of t rial
– Tw o possible out comes : success ad failure
– Probabilit ies of success and failure are remain const ant
Binomial Coefficient s
•
One essent ial aspect of t he binomial dist ribut ion is t o evaluat e nCr1
1 1
1 2 1
1 3 3 1
Expect ed value
•
Expect ed value of binomial dist ribut ion can be expressed as follow s:•
Finally,Example
Generat ion Syst em Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibow o
Int roduct ion
•
Generat ion syst em planning is one of t he crucial st eps in modern elect ric ut ilit y.•
Generat ion expansion plan must sat isfycust omer needs for reasonably price, reliable and qualit y.
•
The elect ricit y indust ry is a very capit al int ensive indust ryExpansion Plan Considerat ion
•
Uncert aint y of load in t he fut ure•
Unit reliabilit y and maint enance schedules•
Fuel Cost s•
Environment Issues•
Const ruct ion Cost s•
Const ruct ion TimesReliabilit y Indices
Reliabilit y indices most ly used in generat ion syst em expansion are :
•
Loss of Load Probabilit y (LOLP)•
Expect ed Value of Demand not served
(DNS)Pract ical Generat ion Planning
In Pract ical, t he considerat ions are :
•
Load Grow t h•
Const ruct ion Time•
Availabilit y of Sit es•
Availabilit y of FuelProbabilist ic Generat ing Unit M odels
M ainly, generat ion syst ems consist of many t ype of generat ors. They can be cat egorized as t he follow ing :
•
Based Load unit s. Capacit y fact or : 90 – 95 %. Nuclear, Coal St eam Turbine unit s•
M idrange unit s. Capacit y fact or : 30 – 75 %. Combine Cycle unit s, St eam Turbine Unit sTransmission Syst em Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibow o
Dist ribut ion Syst em Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibow o
