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Paper Title

Optimization of Electrical System for a Large DC Offshore Wind Farm by Genetic Algorithm

M. Zhao, Z. Chen, F. Blaabjerg

Institute of Energy Technology, Aalborg University

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Contents

∙ Introduction∙ Optimization Model∙ Genetic Optimization∙ Application Example∙ Summary

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Background

∙ Going to sea∙ Large investment∙ High cost in

Electrical system∙ Challenge in

optimization of Electrical System

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Optimization Model

Minimize Cost

Subject to

Objective Obj_Value = Cost - α(Rsys - Rmin)

Function∙ α is the penalty coefficient

minsysR R

Cost:

isystem

Cost price System Reliability Rsys

Reliability Threshold Rmin

Combined

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Reliability Calculation Introduction∙ Reliability Calculation Modeling

▫ Viewed as a graph▫ Stochastic network▫ Component in two states▫ Multiple terminals

∙ Component Reliability λ: Failure rate

r: Repair duration

∙ Reliability Definition:

1. >= 1 Operative paths

2. N Operative paths (√) N = Number of WT

3. >=M Operative paths (+) M < N

1(1 )jR r

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Reliability Calculation

∙ Step 1: Find an operative path L_i from all the wind turbines to PCC

∙ Step 2: Repeat Step 1 to Find all the possible operative paths

_ __

L i pq jj L i

R R

_ 1j

pq jj

R j operativeR

R j fail

_ __

sys L i pq ji i j L i

R R R

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Genetic Algorithm

ParentsSelected

goodindividuals

Evaluateusing fitness

function

Selection Operator

Newgeneration(Children)

Crossoveroperator

Mutation Operator

InitialPopulation

Convergent

Stop

No

Yes

• Deal with complex, multi-variables optimization problems

• Capable to find global optimum solution

• Flow chart of GA

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Optimization Structure

Data of componentsData of wind and grid

system

Possibleconfiguration

Predefineassumption and

rules

Knowledgedatabase

Costcalculation

ReliabilityEvaluation

Generateinitial N

configurations

Competitionand

reproduction

Final optimumconfiguration

Generic Algorithm

I nputI nput

Output

Not satisfied

satisfied

Evaluation

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Optimization Variables and Coding

∙ Encoding▫ The design of system is represent by some variables, which are

encoded into binary string.

∙ Decoding

1 0 0 1 1 0 0 0 1 0 1 0

X7X6

X5X4X3

X2

X11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 0

X8 X9

Bi t i ndexBi t val ue

Opti mi zati onVari abl es

Binary String

Network ModelN=<V, F>

Parameter Database<Data_V, Data_F>

Decoding

NetworkSimplify

GeneticAlgorithm

Cost, ReliabilityCalculation

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Variable examples

∙ Local grid topology – X1

∙ DC-DC converter location – X2

Star

DC

WT

WT

Rectifier

DC/DC

Cluster

Rectifier

DC/DC

Cluster

DC/DC

Star

DC

WT

WT

Rectifier

DC/DC

Cluster

Rectifier

Star

DC

WT

WT

Rectifier DC/DC

DC/DC

Cluster

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GA Implementation

∙ Selection: Rank-based selection▫ Chromosomes are ranked according to fitness values▫ Selection operator:▫

◦ Less fitness value -> higher probability to be selected

∙ Crossover: Single-Point crossover.

∙ Mutation: Full bits mutation with variable probability ∙ Pm=Pm-ΔPm

∙ Feasibility Check

2 4( 1)( )

2( 1)

bias bias bias RandIndex N

bias

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Generation Updating

∙ Adaptive Generation Gap

▫ G=0.4+C((FAVG(t-1)-FAVG(t))/FAVG(t)) FAVG(t-1)>FAVG(t)

▫ G=0.4 FAVG(t-1)<FAVG(t)

C is a constant which determines how the improvement of fitness will influence G

Parent 1 Parent 2 Parent i Parent N

Fi tnessGood Bad

Chi l d 1 Chi l d N-1Chi l d j Chi l d N

Repl ace Repl ace

G * N

Generati on K

GA Operator

Generati on K+1 Parent 1 Parent 2 Chi l d 1 Chi l d j

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Application Example

∙ 2 MW wind turbines∙ 200 MW offshore wind farm∙ 150 km DC transmission

N Population size 20MAX_G Maximum generation 70Pc Probability of crossover 0.6Pm,init Initial probability of mutation 0.1Pm,step Step value of Pm. 0.0018Rmin Reliability threshold 0.5α Penalty coefficient 40C Replacement Ratio 5Bias Bias coefficient in selection 2.0

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Optimization Results

0 10 20 30 40 50 60 70500

520

540

560

580

600

620

640

660

680

700

ITERATION

FIT

NE

SS

VA

LUE

OR

CO

ST

Average FitnessMinumum FitnessAverage Cost

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Best 5 solutions

Chromosome Cost (MDDK)

Reliability

0x0A09 511.558 0.6473

0x0A29 512.058 0.6473

0x74A8 514.898 0.6663

0x0B28 517.788 0.663

0x0B6A 519.956 0.6872 WT Rectifier

Other Clusters

DC/DC INVERTERPCC

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Summary

∙ Electrical system of an offshore wind farm can be modeled as:

‘Network Data’ and ‘Component Parameters’

∙ Via defining variables to present a system design, Genetic Algorithm can be applied to optimize the electrical system.

∙ Objective: Minimum cost with required reliability .

∙ More factors shall be considered in the future.

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Thank You For Your Attention!