![Page 1: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/1.jpg)
FACTS Placement Optimization For Multi-Line Contignecies
Josh WilkersonNovember 30, 2005
![Page 2: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/2.jpg)
What’s the Problem?
Line goes down in the power grid Load is redistributed sub-optimally Another line is overloaded due to new
distribution Wash, rinse, repeat Continues on until islanding occurs or load
reaches steady state Rolling black out occurs (a.k.a. Cascading
Failure) Similar what happened in August, 2003
![Page 3: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/3.jpg)
What’s the Problem?
Why does the grid behave this way?Not intended for this kind of useClash between physics and economics
Cascading failure => great physical and economical damage
Need something to hold us over until the much needed expansion is done
![Page 4: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/4.jpg)
A Means to an Answer
Flexible AC Transmission System (FACTS)
Enhances controllability and power transfer capability
More control is given to the way load is distributed
![Page 5: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/5.jpg)
A Means to an Answer
So why not just put FACTS devices on every line?
A single FACTS device is very expensive New Problem: How to place a minimum number
of FACTS devices while still providing a certain level security to the grid
Solution can be attained by analyzing how the grid behaves after one or more lines go down
![Page 6: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/6.jpg)
What’s Been Done?
A number of the scenarios involving one line going down (single line contingency)
Using brute force Using evolutionary computation Next step: scenarios involving multi-line
contingencies
![Page 7: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/7.jpg)
What’s Been Done?
Not much work (if any) done involving MLC’s and FACTS placement It would be more fitting to analyze a
placement in the face of MLC’s rather than SLC’s.
![Page 8: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/8.jpg)
My Plan
Brute force?Way too many scenarios to considerOn the order of 2*1013 scenarios to consider
for 2 line MLC’s and 5 FACTS devices on the IEEE 118-Bus
Leaves only evolutionary computation
![Page 9: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/9.jpg)
Why an EA?
Problem space is huge Problem space is generally unknown The potential time saved vs. deterministic
algorithm This is the type of problem EA’s were
made for
![Page 10: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/10.jpg)
EA Details
Modify the ‘blackbox’ code from assignment 2 to allow for MLC’s
In an attempt to stay par with the SLC version, run 180 MLC scenarios
6 Parameter sets3 base sets which vary on contingency mode
used: SLC mode, 2 Line MLC, 3 Line MLC
![Page 11: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/11.jpg)
EA Details
RepresentationUse fixed length arrays to represent the lines
which FACTS devices are placed on Fitness Evaluation
Select random lines to be involved in each MLC scenario using Monte Carlo sampling
Take the average PI Metric across MLC scenarios considered for each placement
![Page 12: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/12.jpg)
EA Details
PopulationSize: 75Number of Parent Pairs: 20Number of Offspring per Parent Pair: 2
![Page 13: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/13.jpg)
EA Details
Selection MethodBoltzmann scheme
Varying selective pressure based off of population diversity (simulated annealing)
![Page 14: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/14.jpg)
EA Details
Selective Chance vs. Population Diversity
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
Diversity Value
Pro
babili
ty o
f S
ele
ction'''
'''''
More Fit
Less Fit
Modified More Fit
Modified Less Fit
![Page 15: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/15.jpg)
EA Details
Selection MethodHow diversity is gauged
Percentage of solutions within half a standard deviation of the average
Should result in the population bouncing from optima to optima until it gets stuck on global optima
![Page 16: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/16.jpg)
EA Details
RecombinationUniform recombination
Mutation Individual Mutation (80%)Gene Mutation (20% or 40%)
No genetic clones allowed!
![Page 17: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/17.jpg)
EA Details
Parameter Set 1: SLC 20% gene mutation chance
Parameter Set 2: SLC 40% gene mutation chance
Parameter Set 3: 2 Line MLC 20% gene mutation chance
Parameter Set 4: 2 Line MLC 40% gene mutation chance
Parameter Set 5: 3 Line MLC 20% gene mutation chance
Parameter Set 6: 3 Line MLC 40% gene mutation chance
![Page 18: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/18.jpg)
EA Details
The Goal: Two Objectives:
1. Initial mapping of problem space
2. See how highly fit MLC placements perform in SLC scenarios
![Page 19: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/19.jpg)
Results
Some surprising, some not so surprising
![Page 20: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/20.jpg)
ResultsAverage Best Individual
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 25 50 75 100 125 150 175 200 225 250 275 300
Generation
PI M
etr
ic'' 1 Line, 0.2 Mut.
1 Line, 0.4 Mut.
2 Lines, 0.2 Mut.
2 Lines, 0.4 Mut.
3 Lines, 0.2 Mut.
3 Lines, 0.4 Mut.
![Page 21: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/21.jpg)
ResultsAverage Standard Deviation
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 25 50 75 100 125 150 175 200 225 250 275 300
Generation
Sta
ndard
Devia
tion`̀
'̀''
1 Line, 0.2 Mut.
1 Line, 0.4 Mut.
2 Lines, 0.2 Mut.
2 Lines, 0.4 Mut.
3 Lines, 0.2 Mut.
3 Lines, 0.4 Mut.
![Page 22: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/22.jpg)
Results
Test of highly fit placements from MLC scenarios in SLC scenariosWere not even competitive with results from
SLC EASome even performed worse in SLC
scenarios than they did in MLC scenarios
![Page 23: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/23.jpg)
Results
Summary: As the number of lines involved in the contingency
increases, so does the PI Standard deviation also seems to rise as the number
of lines in contingency rises Boltzmann scheme seems to be working as intended Need better way to pick lines for MLC scenarios,
placements getting ‘lucky’ with random lines.
![Page 24: FACTS Placement Optimization For Multi-Line Contignecies](https://reader035.vdocument.in/reader035/viewer/2022081504/56813af2550346895da36f02/html5/thumbnails/24.jpg)
Questions?