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PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing the Surge Arresters Optimizing the Surge Arresters Location for Improving Lightning Location for Improving Lightning Induced Voltage Performance of Induced Voltage Performance of Distribution Network Distribution Network Ernesto Perez, Ernesto Perez, member, IEEE member, IEEE Andres Andres Delgadillo Delgadillo , , student member, IEEE, student member, IEEE, Diego Diego Urrutia Urrutia , , member, IEEE, member, IEEE, Horacio Horacio Torres, Torres, senior member, IEEE senior member, IEEE NATIONAL UNIVERSITY OF COLOMBIA NATIONAL UNIVERSITY OF COLOMBIA June 2007 June 2007

Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

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Page 1: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

PhD ThesisERNESTO PEREZ GONZALEZ

Optimizing the Surge Arresters Optimizing the Surge Arresters Location for Improving Lightning Location for Improving Lightning Induced Voltage Performance of Induced Voltage Performance of Distribution NetworkDistribution Network

Ernesto Perez, Ernesto Perez, member, IEEEmember, IEEE

Andres Andres DelgadilloDelgadillo, , student member, IEEE,student member, IEEE,

Diego Diego UrrutiaUrrutia, , member, IEEE,member, IEEE,

HoracioHoracio Torres, Torres, senior member, IEEEsenior member, IEEE

NATIONAL UNIVERSITY OF COLOMBIANATIONAL UNIVERSITY OF COLOMBIA

June 2007June 2007

Page 2: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Presentation OutlinePresentation Outline

1.1. IntroductionIntroduction

2.2. ModellingModelling Lightning Induced VoltageLightning Induced Voltage

3.3. Improving Lightning performanceImproving Lightning performance

4.4. Optimizing ToolOptimizing Tool

5.5. Conclusions and Future WorkConclusions and Future Work

Page 3: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Introduction Introduction -- MotivationMotivation

Power quality has become one of the main Power quality has become one of the main area of interest around the world for mains, area of interest around the world for mains, utilities, industries and consumers.utilities, industries and consumers.

Lightning causes around 50% of the network Lightning causes around 50% of the network electromagnetic disturbances (short electromagnetic disturbances (short interruptions and voltage sags)interruptions and voltage sags)

Page 4: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Introduction Introduction -- MotivationMotivation

Millions of USD for losses caused by Millions of USD for losses caused by lightning in distribution networklightning in distribution network

Is important to look forward techniques Is important to look forward techniques for reducing lightning impact on for reducing lightning impact on distribution networks.distribution networks.

Shielding wire groundingsShielding wire groundings, , surge surge arrestersarresters and and enhacementenhacement of Line BIL of Line BIL are a very useful techniqueare a very useful technique

Page 5: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Lightning Induced Voltage Lightning Induced Voltage ModellingModelling

Correct definition of number and location of protective devices Correct definition of number and location of protective devices ((shielding shielding wire groundingswire groundings and and surge arresterssurge arresters))

By means of accurate calculation of lightningBy means of accurate calculation of lightning--induced overvoltages on induced overvoltages on real distribution networks real distribution networks

Optimized design of distribution networks against Optimized design of distribution networks against external overvoltagesexternal overvoltages

Page 6: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Link with Transient Analysis SoftwareLink with Transient Analysis Software

- LIOV-EMTP/MATLAB (Methodology A)EMTP96EMTP96 –– using using TACSTACS on a on a DLL DLL andand MATLAB MATLAB –– usingusing SS--functionfunction

- YALUK-ATP (Methodology A)ATPATP –– Using Using Foreign ModelsForeign Models on a on a DLLDLL

- LIV-ATP (Methodology B)ATPATP programmed in programmed in MODELSMODELS

0 Finite Difference Method

+ Characteristic

YALUK R=Zc

kmax

V 0

+_ + _

V kmax

R=Zc

ZL ZLUr0 Ukmax

source Type60 –ATP Load Impedance

Foreign MODELS ATP ATP

Induced Voltage

Software

Transient Prgram Transient Prgram

Page 7: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Diminishing Number of FailuresDiminishing Number of Failures

Surge Arrester (SA) helps to Diminish Surge Arrester (SA) helps to Diminish the fault rate due to induced Voltagesthe fault rate due to induced Voltages

The best solution for a straight line is The best solution for a straight line is locate a SA locate a SA Every PoleEvery Pole

Page 8: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Diminishing Number of FailuresDiminishing Number of Failures

Which is the best SA Which is the best SA location?location?

oo If the number of SA is If the number of SA is fixed and limited?fixed and limited?

oo If it is used a Complex If it is used a Complex distribution Network with distribution Network with nonnon--homogeneous pole homogeneous pole distribution?distribution?

S/E

30 6km

A

BC

Measurement Point

Page 9: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Software Tool Software Tool –– StructureStructure

It was developed a It was developed a OptimizigOptimizig Software Tool for Software Tool for SA location.SA location.

Object function is diminish number of failures Object function is diminish number of failures for a fixed number of SAfor a fixed number of SA

Based on Genetic Algorithm (GA) TechniqueBased on Genetic Algorithm (GA) Technique

Each Each ‘‘individualindividual’’ (possible solution) is (possible solution) is characterized with an unique SA locationcharacterized with an unique SA location

For each individual it should be calculated the For each individual it should be calculated the lightninglightning--induced voltage performance of the induced voltage performance of the lineline..

It is used a certain number of strokes for this It is used a certain number of strokes for this tasktask

Page 10: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

What is What is Genetic Algorithm?Genetic Algorithm?

Initial individual generation

C1 C2 C3 C4 C5 C6

Page 11: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

C8

Individuals Mating

Crossing

C1 C6 C2 C4 C5 C3

C7 C9

What is What is Genetic Algorithm?Genetic Algorithm?

Page 12: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

What is What is Genetic Algorithm?Genetic Algorithm?

C1 C2 C4 C5C7

C8

C9

Crossing

New Generation

C7 C9

Comparison

F(C1) F(C2) F(C7)

Comparison

F(C3) F(C4) F(C8)

Comparison

F(C5) F(C6) F(C9)

Mating C1 C6 C2 C4 C5 C3

Evaluation of Objective Function

Page 13: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

What is What is Genetic Algorithm?Genetic Algorithm?

C2 C3 C4 C5C7

C8

C9

Initial generation

CrossingC7 C9

Comparison

F(C1) F(C2) F(C7)

Evaluation of Objective Function

Comparison

F(C3) F(C4) F(C8)

Comparison

F(C5) F(C6) F(C9)

C1 C6 C2 C4 C5 C3

New Generation

Page 14: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 15: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 16: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 17: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 18: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 19: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 20: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 21: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 22: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 23: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

GeneticGenetic AlgorithmAlgorithm SchemeScheme

Evaluating Objective Function

Evaluating Objective Function

Random generation of first individuals

Selecting ‘parents’

Execution YALUK-ATP Population

Reading Data Output Files

Assigning Probability

Crossover and Mutation

ModifyingData cases

Chromosomes Population

Comparison between ‘parents’ and ‘sons’

Execution YALUK-ATP

Output Files

Chromosomes new individuals

Fitness Values

Reading Data Fitness Values

Modifying Data cases

Rep

lace

men

t with

new

Gen

erat

ion

Page 24: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Example of Genetic Algorithm ToolExample of Genetic Algorithm Tool

20 Nodes Network (three phase)20 Nodes Network (three phase)

Location of 4 three phase Surge ArrestersLocation of 4 three phase Surge Arresters

4845 possible SA locations4845 possible SA locations

Lightning performance calculated withLightning performance calculated with

oo 40 Strokes40 Strokes

oo 100 Strokes100 Strokes

It is chosen a base case with a SA located It is chosen a base case with a SA located randomlyrandomly

Page 25: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Effect of Power System ComponentsEffect of Power System Components

1.3 m 1.3 m

10 m

CBABranch 1

Branch 3

Branch 2

Main Feeder

N01

N02

N03

N04N05

N06N07

N16

N15

N08

N10N11

N09

N19

N18

N17

N20

N12

N13

N14

1 km500 m0 m

1413

1011

12

20

17

18

19

9

16

15

8

7

6

5

4

3

2

1

Part of Real Network with a main feeder and three Part of Real Network with a main feeder and three branches with different length. branches with different length.

Total length 7km Total length 7km aproxaprox..

Page 26: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Branch 1

Branch 3

Branch 2

Main Feeder

N01

N02

N03

N04N05

N06N07

N16

N15

N08

N10N11

N09

N19

N18

N17

N20

N12

N13

N14

1 km500 m0 m

1413

1011

12

20

17

18

19

9

16

15

8

7

6

5

4

3

2

1

EngineeringEngineering ApplicationApplication

- Random case diminish the number of outages for 200kV from 35 to 20

SA – Location - Random

0,1

1

10

100

1000

50 100 150 200 250 300 350

Voltage [kV]

Num

ber o

f Ind

uced

Vol

atge

exc

eedi

ng th

e ab

scis

sa/1

00 k

m y

ear

Open Circuit

Random Case

Page 27: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

Branch 1

Branch 3

Branch 2

Main Feeder

N01

N02

N03

N04N05

N06N07

N16

N15

N08

N10N11

N09

N19

N18

N17

N20

N12

N13

N14

1 km500 m0 m

1413

1011

12

20

17

18

19

9

16

15

8

7

6

5

4

3

2

1

EngineeringEngineering ApplicationApplication

SA – Location – Genetic Alg

- Random case diminish the number of outages for 200kV from 35 to 20

- Running Genetic Algorithm Tool the number of failures for 200kV is 10

0,1

1

10

100

1000

50 100 150 200 250 300 350

Voltage [kV]

Num

ber o

f Ind

uced

Vol

atge

exc

eedi

ng th

e ab

scis

sa/1

00 k

m y

ear

Open Circuit

Random Case

percentile 60 (100 strokes)

Page 28: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

ConclusionsConclusions

Here is described a new methodology based on Here is described a new methodology based on genetic algorithms intended to find an optimal genetic algorithms intended to find an optimal solution for the location of a set of surge solution for the location of a set of surge arresters.arresters.

This methodology could bring better results This methodology could bring better results when a reasonably probability curve is possible when a reasonably probability curve is possible to be obtained for each individual. to be obtained for each individual.

Greater number of strokes should be used for Greater number of strokes should be used for each solution, implying that big efforts should each solution, implying that big efforts should be done in order to reduce induced voltage be done in order to reduce induced voltage computation timecomputation time..

Page 29: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

ConclusionsConclusions

This tool allows to find a This tool allows to find a ““goodgood”” solution but not always solution but not always this is the best one.this is the best one.

This proposed methodology contributes on the This proposed methodology contributes on the researching focused on the using of artificial intelligence researching focused on the using of artificial intelligence techniques, such as, genetic algorithms for designing and techniques, such as, genetic algorithms for designing and planning the distribution network systems optimally.planning the distribution network systems optimally.

Further work should be done in Further work should be done in incrasingincrasing the number of the number of parameters to simulate meanwhile it is improve the parameters to simulate meanwhile it is improve the computation time.computation time.

Page 30: Optimizing the Surge Arresters Location for Improving Lightning …ewh.ieee.org/soc/pes/lpdl/archive/2007_GM_PES... · 2007. 7. 17. · PhD Thesis ERNESTO PEREZ GONZALEZ Optimizing

IEEE – PES General Meeting –Tampa June 25th 2007

THANK YOU THANK YOU

FOR YOUR ATTENTIONFOR YOUR ATTENTION