The Regional Power Grid Team
Presentation # 2: Status report
Karen Tapia-Ahumada
Katherine Steel
Jehanzeb Noor
April 25, 2006
1
Agenda Items
„
Revised method of matrix generation
„
System representation
„
Analyses on Power Grid
„
Histograms, Degree Distributions & Metrics
„
Next steps
„
Expected Outputs & Conclusions
Noor, Steel, Tapia-Ahumada
2
Revised Method
T1
A
B
A
B
B
A
C
T2
d
T1
A
B
T2
A
C
B
A
t
„
I. For transformers add a new node in matrix for each one
„
II. Use “dummy” node to represent all parallel paths
„
III. For taps add a “dummy” node to show paths
Noor, Steel, Tapia-Ahumada
B
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Revised Method
Using this method our system representation changed from:
„
The order of 103 nodes and 103 paths
To:
„
More than 1600 nodes
generators
286
loads
700
transformers
333
taps
115
buses
128
dummy nodes
103
others
„
10
About 2400 paths (estimated)
Noor, Steel, Tapia-Ahumada
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System Representation
Nodes:
Red Æ Generator
Green Æ Load
Gray Æ Others
Links:
Red Æ < 115kV
Blue Æ 115kV
Black Æ 230kV
GreyÆ 345kV
PurpleÆ HVDC
Representing the
system at zonal level is
easier to visualize
Æ Grid shown next
Noor, Steel, Tapia-Ahumada
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The Overall Power Grid
• Impossible to visualize and
difficult to analyze in UCINET
• MATLAB more suitable
• Clustering Coeff. = 0.06
• Edge/node ration ~ 1.5
• For sub-sets of network,
edge/node ratio varies:
• ratio (low population
density) = 1.37
• ratio (high population
density) = ~ 3
• About 40 inter-connections
with other zones and grids
Noor, Steel, Tapia-Ahumada
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Zonal Degree Histogram and
Cumulative Distribution Plots
Cumulative degree distribution for some zones
Degree distribution for some zones
1000
Cumulative degree distribution
350
300
Frequency
250
200
150
100
50
100
10
1
0
0
1
2
3
4
5
6
7
8
9
2
4
10 11 12 13 14 15 16 17 18 19 20
6
8
10
12
14
16
18
20
Ordered degree
Degree
• Most of the nodes are connected to few edges – is this scale-free?
•As we will see, sub-set (i.e. zonal) distributions look similar to overall grid
• This specific “subset” is one of two congested ones among three “subsets”
• Not a simple graph: has double edges and self-loops as expected in a grid
• A lot of redundant paths for network reliability and unseen contingencies
Noor, Steel, Tapia-Ahumada
7
# of nodes
Overall Degree Histogram and
Cumulative Distribution Plots
Number of Edges
• Pearson coefficient 0.04 (almost zero); metrics comparable to western grid
• West grid: edge/node = 2.6; degree correl. = 0.03; clustering coeff. = 0.08
• Cumulative degree distribution similar to western grid (Newman’s paper)
• Kmax = 36 Æ i.e. at node in a very congested zone (also high LMP $/MWh)
Noor, Steel, Tapia-Ahumada
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Next Steps
„
„
Validate all Data and Interconnections!
Identify clusters and sub-sets of network
„
„
Identify existing clusters (using algorithms like
Newman-Girvan in UCINETtm) and filtering
Study the reasons for existence of clusters
„
„
„
Geographical
Sociological (industrial zones, high populations)
Contingency-based (addition of nodes & links)
Noor, Steel, Tapia-Ahumada
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More Next steps
„
Compare with other grids
„
„
„
Study degree distributions
„
„
„
See if network topology can be mapped across
Find potential similarities in clustering
Find if network follows a power or other law
Compare other known degree distributions
Define “critical” nodes & identify examples
Noor, Steel, Tapia-Ahumada
10
Expected Output & Conclusion
„
„
„
This grid seems to follow trends similar to
the western power grid (from what we know
and can compare so far). More to follow…
The edge to node ratio (zonal and overall),
clustering and Pearson coefficients have low
values typical to large technological networks
We expect to get insights to grid topology,
empirical structural models and metrics…
Noor, Steel, Tapia-Ahumada
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Questions and Comments?
Contact information
Karen
JZ
Kate
Noor, Steel, Tapia-Ahumada
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