FACTS Placement Optimization For Multi-Line Contignecies

Josh WilkersonNovember 30, 2005

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

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

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

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

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

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.

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

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

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

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

EA Details

PopulationSize: 75Number of Parent Pairs: 20Number of Offspring per Parent Pair: 2

EA Details

Selection MethodBoltzmann scheme

Varying selective pressure based off of population diversity (simulated annealing)

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

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

EA Details

RecombinationUniform recombination

Mutation Individual Mutation (80%)Gene Mutation (20% or 40%)

No genetic clones allowed!

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

EA Details

The Goal: Two Objectives:

1. Initial mapping of problem space

2. See how highly fit MLC placements perform in SLC scenarios

Results

Some surprising, some not so surprising

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.

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.

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

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.

Questions?