The Regional Power Grid TeamPower Grid Agenda ItemsAdjacency Matrix for GridDegree Distribution HistogramDegree Distribution on log-linHomogenized Network ImageNotes on Zones 1 - 3Notes on Zones 5 - 7Notes on Zone 4 and Zone 8Comments on ComparisonsExistence of Hubs & RobustnessOverall Grid ResilienceMore on Network MetricsThe Regional Power Grid TeamPresentation # 3: Network ResultsKaren Tapia-AhumadaJehanzeb NoorKatherine SteelMay 09, 2006Power Grid Team, 2006 2Power Grid Agenda Items Building Network Matrix and Images Network Level Results Zone Level Results Comparisons and Insights Comments, Questions and AnswersPower Grid Team, 2006 3Groups 1 Æ Red (zones 1 – 3)Groups 2 Æ Blue (zones 4 – 5) Groups 3 Æ Green (zones 6 – 8) Building Adjacency Matrix: 8 zones to 3 groupsPower Grid Team, 2006 4Adjacency Matrix for GridHierarchy is evident from the structure of this adjacency matrixTools Used: UCINET, Pajek, Matlab, MSExcel More than 1600 nodes and more than 2500 links Each block (below diagonal) pertains to a zone in this power pool Off-diagonal entries (far off) show inter-zonal and high voltage linksPower Grid Team, 2006 5Nodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersLinks:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersOverall Power GridPower Grid Team, 2006 6Degree Distribution HistogramNMm/n<k>Max kLlogn/log<k> AlphaC<k>/nROverall 1658 2589 1.562 3.117 2514.356.521 No 0.149 0.002 0.10 Most nodes (more than 90%) only have two other connections Very few (only 27) nodes have a degree above 10 Most nodes are localized, with few central ones (critical to network)Power Grid Team, 2006 7Degree Distribution on log-linCumulative degree distribution - Overall Grid1101001000100000 5 10 15 20 25Ordered degreeCumulative degree distribution Exponential degree distribution (looking at whole curve) Distribution depends on the scale chosen for degrees Small world effect - high clustering coefficient and similar path length as compared to a random networkPower Grid Team, 2006 8Homogenized Network Image Two congested zones in the grid (in yellow) namely zone 4 and zone 8 345 kV lines are “backbone” for grid level, 115 kV lines for zonal level Less congested zones have smaller lines and sparsely distributed nodesPower Grid Team, 2006 9Zonal Analysis – Zone 1Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersDegree distribution - Zone 10204060801001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25DegreeFrequencyCumulative degree distribution - Zone 11101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionNMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 1 210 314 1.495 2.952 9 9.514 4.939 No 0.155 0.014 -.094Power Grid Team, 2006 10Degree distribution - Zone 2025507510012345678910111213141516171819202122232425DegreeFrequencyCumulative degree distribution - Zone 21101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionZonal Analysis – Zone 2NMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 2 139 175 1.259 2.504 10 9.174 5.376 No 0.073 0.018 .001Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersPower Grid Team, 2006 11Degree distribution - Zone 302040608010012345678910111213141516171819202122232425DegreeFrequencyZonal Analysis – Zone 3Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 3 92 115 1.250 2.421 7 7.809 5.114 No 0.179 0.026 .208Nodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersCumulative degree distribution - Zone 31101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionPower Grid Team, 2006 12Notes on Zones 1 - 3 These three zones are the most sparse in terms of nodes and links, and relatively small Lots of localized generation – zone 3 has some large units (export power to rest of grid) Degree correlations of zone 1, zone 2 are ~0, zone 3 is ~0.2 (highly connected generators) Average path length is smaller than overall Edge to node ratio is lowPower Grid Team, 2006 13Zonal Analysis – Zone 5 NMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 5 88 113 1.284 2.568 9 6.287 4.747 No 0.160 0.029 -0.16Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersDegree distribution - Zone 5025507510012345678910111213141516171819202122232425DegreeFrequencyCumulative degree distribution - Zone 51101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionPower Grid Team, 2006 14Zonal Analysis – Zone 6NMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 6 137 288 2.102 2.851 11 9.500 4.696 No 0.231 0.021 -0.09Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersDegree distribution - Zone 6025507510012345678910111213141516171819202122232425DegreeFrequencyCumulative degree distribution - Zone 61101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionPower Grid Team, 2006 15Degree distribution - Zone 7025507510012515012345678910111213141516171819202122232425DegreeFrequencyZonal Analysis – Zone 7Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersN M m/n <k> Max k L logn/log<k> Alpha C <k>/n RZone 7 301 441 1.465 2.93 13 7.902 5.309 No 0.121 0.010 -.086Nodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersCumulative degree distribution - Zone 71101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionPower Grid Team, 2006 16Notes on Zones 5 - 7 These zones are intermediate in terms of nodal (and also population) density, load vs. generation balances out High voltage lines in these zones are also grid’s backbone The degree correlation is negative for all three, which is different from other zones Removing these interconnecting lines to other zones leaves one zone (5) highly disconnectedPower Grid Team, 2006 17Zonal Analysis – Zone 4NMm/n<k>Max kLlogn/log<k>Alpha C <k>/n RZone 4 393 667 1.697 3.394 25 7.853 4.889 No 0.111 0.009 0.34Links:< 115 Æ Black115 Æ Red230 Æ Green345 Æ BlueOthersNodes:GenÆ RedLoad Æ BlueBus Æ YellowTr Æ BlackOthersDegree distribution - Zone 4025507510012515017520012345678910111213141516171819202122232425DegreeFrequencyCumulative degree distribution - Zone 41101001000100000 5 10 15 20 25Ordered degreeCumulative degree distributionPower Grid
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