Optimum Operasi dan Keandalan Sistem Ten
Opt imum Operasi dan Keandalan
Sistem Tenaga List rik
Oleh :
Prof. Ontoseno Penangsang, Ph.D
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Content s
•
•
•
•
•
Basic Probabilit y Theory
Applicat ion of Binomial Dist ribut ion
Generat ion Syst em Reliabilit y Analysis
Transmission Syst em Reliabilit y Analysis
Dist ribut ion Syst em Reliabilit y Analysis
DAFTAR PUSTAKA
• Roy Billint on, Ronald N Allan, “ Reliabilit y
Evaluat ion of Engineering Syst ems” Plenum
Press : New York, 1992
• Roy Billint on, Ronald N Allan, “ Reliabilit y
Evaluat ion of Power Syst ems” Plenum Press :
New York, 1996
• Robert L. Sullivan, “ Power Syst em Planning”,
M cGraw -Hill, 1977
Basic Probabilit y Theory
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Probabilit y Concept
• Mathematically, it is a numerical index that can vary
between zero to unity
• Probability of success and failure can formulated as
follows:
Example
• Anggap kita melempar dua buah dadu
sekaligus, berapa peluang kita mendapat kan
angka t otal dadu 9?
Permutat ions and Combinat ions
• The number of permutations of n different items is the
number of ways these items can be arranged
• The number of combinations of n different items is the
number of different selections of r items, each without
regard to the order or arrangement of the items in the
groups
Example
• Anggap kita mempunyai 3 buah buku dengan
nama A, B dan C. Berapa kemungkinan kita
menyusun ket iga buku t ersebut ?
• Berapa kemungkinan komposisi panit ia yang
t erdiri dari 3 orang, dimana jumlah orang yang
akan kita pilih adalah 4 orang?
Rules for Combining Probabilit ies
•
•
•
•
•
•
Rule 1 – Independent event s
Rule 2 – M ut ually exclusive event s
Rule 3 – Complementary event s
Rule 4 – Condit ional event s
Rule 5 – Simultaneous occurrence of event s
Rule 6 – Occurrence of at least one if t wo
event s
• Rule 7 – Applicat ion of condit ional probabilit y
Example
• Suat u pabrik mempunyai 2 plant . Plant 1
membuat 70% barang yang dibut uhkan dan
plant lainnya menghasilkan 30%. Jika 90 %
produk plant 1 memenuhi standard dan 80%
produk plant 2 memenuhi standard. Berapa
peluang pabrik t ersebut menghasilkan produk
yang memenuhi standard?
Probabilit y Densit y Funct ion
• The summat ion of
probabilit ies should equal
unit y
• Probabilit y densit y Funct ion
(a) Separate data
(b) Grouped data
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
(b) Grouped dat a
Probabilit y Dist ribut ions
• Cont inuous random
variable :
(a) Probabilit y
dist ribut ion funct ion f(x)
(b) Probabilit y densit y
funct ion F(x)
M at hemat ical Expectat ion
• M oment s of dist ribut ion, also know n as
expect ed value, is referred t o as t he average
value or populat ion mean
Example
• The data of copper lengt h measurement are as
follows :
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
• Det ermine t he average lengt h of t he copper?
Variance and Standard Deviat ion
• A measure of dispersion of a dist ribut ion is
defined as Variance V(x)
• Standard deviat ion
Example
• The data of copper lengt h measurement are as
follows :
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
• Det ermine t he variance and standard deviat ion?
Applicat ion of t he Binomial
Dist ribut ion
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
General Characterist ic
• Binomial dist ribut ion can be represent ed by
general expression :
(p+q)2
• Required condit ions are :
– Fixed number of t rial
– Two possible outcomes : success ad failure
– Probabilit ies of success and failure are remain
constant
– All t rial must be independent
Example
Binomial Coefficient s
• One essent ial aspect of t he binomial
dist ribut ion is t o evaluat e nCr
1
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Expected value
• Expect ed value of binomial dist ribut ion can be
expressed as follows:
• Finally,
E(x) = np
Example
• A small generat ing plant is t o be designed t o
sat isfy a constant 10 M W load. Four alt ernat ives
are being considered:
1.
2.
3.
4.
1 x 10 M W unit
2 x 10 M W unit
3 x 5 M W unit
4 x 3 1/ 3 M W unit
Unavailable probabilit y of each unit is equal t o
0.02 and t herefore, t he probabilit y of available is
0.98. Please develop capacit y outage probabilit y
tables.
Capacit y Outage Probabilit y
Expected Load Losses
Invest ment Cost s of Plant
Expected Load Curtailment
Effect of Unavailabilit y
System Risk w it h One Unit in Reserve
Generat ion System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
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 isfy
cust omer needs for reasonably price, reliable
and qualit y.
• The elect ricit y indust ry is a very capital
int ensive indust ry
• Expansion plan should att ract new invest ors
Expansion Plan Considerat ion
•
•
•
•
•
•
•
Uncertaint 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 Times
Financial Support
Reliabilit 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)
• Frequency and Durat ion (FD)
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 Fuel
t hen, detailed reliabilit y analysis is required t o
ensure t hat all sat isfying t he desired reliabilit y
level
Probabilist 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 s
• Peakers. Capacit y fact or : 5 – 10 %. Gas
t urbines and Hydro unit s
Transmission System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Dist ribut ion System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Sistem Tenaga List rik
Oleh :
Prof. Ontoseno Penangsang, Ph.D
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Content s
•
•
•
•
•
Basic Probabilit y Theory
Applicat ion of Binomial Dist ribut ion
Generat ion Syst em Reliabilit y Analysis
Transmission Syst em Reliabilit y Analysis
Dist ribut ion Syst em Reliabilit y Analysis
DAFTAR PUSTAKA
• Roy Billint on, Ronald N Allan, “ Reliabilit y
Evaluat ion of Engineering Syst ems” Plenum
Press : New York, 1992
• Roy Billint on, Ronald N Allan, “ Reliabilit y
Evaluat ion of Power Syst ems” Plenum Press :
New York, 1996
• Robert L. Sullivan, “ Power Syst em Planning”,
M cGraw -Hill, 1977
Basic Probabilit y Theory
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Probabilit y Concept
• Mathematically, it is a numerical index that can vary
between zero to unity
• Probability of success and failure can formulated as
follows:
Example
• Anggap kita melempar dua buah dadu
sekaligus, berapa peluang kita mendapat kan
angka t otal dadu 9?
Permutat ions and Combinat ions
• The number of permutations of n different items is the
number of ways these items can be arranged
• The number of combinations of n different items is the
number of different selections of r items, each without
regard to the order or arrangement of the items in the
groups
Example
• Anggap kita mempunyai 3 buah buku dengan
nama A, B dan C. Berapa kemungkinan kita
menyusun ket iga buku t ersebut ?
• Berapa kemungkinan komposisi panit ia yang
t erdiri dari 3 orang, dimana jumlah orang yang
akan kita pilih adalah 4 orang?
Rules for Combining Probabilit ies
•
•
•
•
•
•
Rule 1 – Independent event s
Rule 2 – M ut ually exclusive event s
Rule 3 – Complementary event s
Rule 4 – Condit ional event s
Rule 5 – Simultaneous occurrence of event s
Rule 6 – Occurrence of at least one if t wo
event s
• Rule 7 – Applicat ion of condit ional probabilit y
Example
• Suat u pabrik mempunyai 2 plant . Plant 1
membuat 70% barang yang dibut uhkan dan
plant lainnya menghasilkan 30%. Jika 90 %
produk plant 1 memenuhi standard dan 80%
produk plant 2 memenuhi standard. Berapa
peluang pabrik t ersebut menghasilkan produk
yang memenuhi standard?
Probabilit y Densit y Funct ion
• The summat ion of
probabilit ies should equal
unit y
• Probabilit y densit y Funct ion
(a) Separate data
(b) Grouped data
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
(b) Grouped dat a
Probabilit y Dist ribut ions
• Cont inuous random
variable :
(a) Probabilit y
dist ribut ion funct ion f(x)
(b) Probabilit y densit y
funct ion F(x)
M at hemat ical Expectat ion
• M oment s of dist ribut ion, also know n as
expect ed value, is referred t o as t he average
value or populat ion mean
Example
• The data of copper lengt h measurement are as
follows :
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
• Det ermine t he average lengt h of t he copper?
Variance and Standard Deviat ion
• A measure of dispersion of a dist ribut ion is
defined as Variance V(x)
• Standard deviat ion
Example
• The data of copper lengt h measurement are as
follows :
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
• Det ermine t he variance and standard deviat ion?
Applicat ion of t he Binomial
Dist ribut ion
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
General Characterist ic
• Binomial dist ribut ion can be represent ed by
general expression :
(p+q)2
• Required condit ions are :
– Fixed number of t rial
– Two possible outcomes : success ad failure
– Probabilit ies of success and failure are remain
constant
– All t rial must be independent
Example
Binomial Coefficient s
• One essent ial aspect of t he binomial
dist ribut ion is t o evaluat e nCr
1
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Expected value
• Expect ed value of binomial dist ribut ion can be
expressed as follows:
• Finally,
E(x) = np
Example
• A small generat ing plant is t o be designed t o
sat isfy a constant 10 M W load. Four alt ernat ives
are being considered:
1.
2.
3.
4.
1 x 10 M W unit
2 x 10 M W unit
3 x 5 M W unit
4 x 3 1/ 3 M W unit
Unavailable probabilit y of each unit is equal t o
0.02 and t herefore, t he probabilit y of available is
0.98. Please develop capacit y outage probabilit y
tables.
Capacit y Outage Probabilit y
Expected Load Losses
Invest ment Cost s of Plant
Expected Load Curtailment
Effect of Unavailabilit y
System Risk w it h One Unit in Reserve
Generat ion System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
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 isfy
cust omer needs for reasonably price, reliable
and qualit y.
• The elect ricit y indust ry is a very capital
int ensive indust ry
• Expansion plan should att ract new invest ors
Expansion Plan Considerat ion
•
•
•
•
•
•
•
Uncertaint 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 Times
Financial Support
Reliabilit 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)
• Frequency and Durat ion (FD)
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 Fuel
t hen, detailed reliabilit y analysis is required t o
ensure t hat all sat isfying t he desired reliabilit y
level
Probabilist 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 s
• Peakers. Capacit y fact or : 5 – 10 %. Gas
t urbines and Hydro unit s
Transmission System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya
Dist ribut ion System Reliabilit y
Analysis
Oleh :
Dr. Eng. Rony Seto W ibowo
Laboratorium Simulasi Sistem Tenaga List rik
Teknik Elekt ro – ITS Surabaya