1 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

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

3 Background ∙Going to sea ∙Large investment ∙High cost in Electrical system ∙Challenge in optimization of Electrical System

4 Optimization Model Minimize Cost Subject to Objective Obj_Value = Cost - α(R sys - R min ) Function ∙ α is the penalty coefficient Cost:System Reliability R sys Reliability Threshold R min Combined

5 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

6 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

7 Genetic Algorithm Deal with complex, multi-variables optimization problems Capable to find global optimum solution Flow chart of GA

8 Optimization Structure

9 Optimization Variables and Coding ∙Encoding ▫The design of system is represent by some variables, which are encoded into binary string. ∙Decoding

10 Variable examples ∙Local grid topology – X1 ∙DC-DC converter location – X2

11 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

12 Generation Updating ∙Adaptive Generation Gap ▫ G=0.4+C((F AVG (t-1)-F AVG (t))/F AVG (t))F AVG (t-1)>F AVG (t) ▫ G=0.4F AVG (t-1)<F AVG (t) Cis a constant which determines how the improvement of fitness will influence G

13 Application Example ∙2 MW wind turbines ∙200 MW offshore wind farm ∙150 km DC transmission NPopulation size20 MAX_GMaximum generation70 P c Probability of crossover0.6 P m,init Initial probability of mutation0.1 P m,step Step value of P m R min Reliability threshold0.5 αPenalty coefficient40 CReplacement Ratio5 BiasBias coefficient in selection2.0

14 Optimization Results

15 Best 5 solutions ChromosomeCost (MDDK)Reliability 0x0A x0A x74A x0B x0B6A

16 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.

17 Thank You For Your Attention!