FACTS Placement Optimization For Multi-Line Contignecies Josh Wilkerson November 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 use  Clash 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 consider  On the order of 2*10 13 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 sets  3 base sets which vary on contingency mode used: SLC mode, 2 Line MLC, 3 Line MLC

EA Details Representation  Use 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 Population  Size: 75  Number of Parent Pairs: 20  Number of Offspring per Parent Pair: 2

EA Details Selection Method  Boltzmann scheme Varying selective pressure based off of population diversity (simulated annealing)

EA Details

Selection Method  How 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 Recombination  Uniform 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

Results

Test of highly fit placements from MLC scenarios in SLC scenarios  Were not even competitive with results from SLC EA  Some 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?