Zooming-in and Zooming-out Computer
Methods for Contingency Screening in
Large Scale Power Networks
Sanja Cvijid,
Marija Ilid
and
Carnegie Mellon University
sanja13@andrew.cmu.edu, milic@ece.cmu.edu
March 13th, 2012
Peter Feldmann
IBM
feldmann@us.ibm.com
Motivation
 Contingency Analysis:
 Each contingency very similar to the original network
 Why re-compute the whole DF matrix?
 Efficient distributed algorithm for solving ”DC” power
flow
 Enable re-use of power flow data in normal operation
and contingencies
 Repeat computations in the area with a contingency only
 Minimize exchange of information in multi-area
environments
2
Outline
Distributed coordinated “DC” Power Flow
Algorithm
 Internal Line Outage
algorithm
exchange of information
 Tie-Line Outage
algorithm
exchange of information
AC Contingency Screening
 using continuation homotopy methods
Conclusion and Future Work
3
10-bus example: ZOOM-IN tree transf.[1-3]
ZOOM-IN
1
1A
2A
S
3A
1A
2B
1B
2
2A
S
S
3
S
S
3A
1C
2C
3B
S
4B
2B
1B
S
S
S
S
S
3C
3B
ZOOM-IN (area k)
tree
trans.
1C
S
flow
comp.
4B
2C
3C
4
10-bus example: ZOOM-OUT tree transf.
3
4
B
A
S
S
S
S
S
S
C
ZOOM-OUT
ZOOM-OUT
tree
trans.
4
A
B
5
6
flow
comp.
C
5
Network Transformations and Exchange of
Information
Bidirectional transformations[2]
 “down”: topological transformations into a spanning tree
𝑇
𝑋22 = 𝐶12
∙ 𝑋11 ∙ 𝐶12
 “up”: computes line flows
𝐹1 = 𝐶12 ∙ 𝐹 2
ZOOM-IN (area 1)
tree
trans.
ZOOM-IN (area k)
flow
comp.
𝐹
𝑋(1)
(1)
tree
trans.
𝑋(𝑘)
flow
comp.
𝐹 (𝑘)
ZOOM-IN (area n)
...
tree
trans.
flow
comp.
𝐹 (𝑛)
ZOOM-OUT
tree
trans.
𝑋(𝑛)
flow
comp.
6
Internal Contingency
NORMAL OPERATION
4
5
6
7
ZOOM-IN (area 1)
tree
trans.
TREE REPRESENTATION
5
4
OUTAGE OF LINE 6-7
4
6
ZOOM-IN (area k)
flow
comp.
𝐹 (1)
7
7
6
tree
trans.
flow
comp.
𝑋(𝑘) 𝑛𝑒𝑤
𝐹 (𝑘)
ZOOM-IN (area n)
...
tree
trans.
flow
comp.
𝐹 (𝑛)
ZOOM-OUT
tree
trans.
flow
comp.
7
Tie-line Contingency
OUTAGE OF LINE 3-8
TREE REPRESENTATION
A
B
C
ZOOM-IN (area 1)
tree
trans.
ZOOM-IN (area k)
flow
comp.
tree
trans.
flow
comp.
𝐹 (𝑘)
𝐹 (1)
ZOOM-IN (area n)
...
tree
trans.
flow
“up”
comp.
𝐹 (𝑛)
ZOOM-OUT
tree
trans.
flow
comp.
8
New approach to AC Contingency Screening
 Improves chances for global convergence
 Used for solving systems of nonlinear equations: f(x)=0
 Constructs a sequence of problems that lead to the
problem of the interest
easy
Base Case
ACPF(x)=0
hard
homotopy
y(λ)=(1-λ)*y
Contingency k
ACPF_ck(x)=0
λ
9
0
Source: http://en.wikipedia.org/wiki/Homotopy
1
9
Homotopy for Ill-Conditioned Systems [4]
 Converges in cases when Newton-Raphson fails to converge
 Example: 11-bus system[5]
DCPF
homotopy
ACPF
1.024∠0
1.024∠0
1.072∠0.05
1.103∠0.04
1.064∠0.072
1.119∠0.061
1.089∠0.083
1.124∠0.067
1.042∠0.070
1.095∠0.060
1.089∠0.102
1.129∠0.089
0.578∠0.380
1.086∠0.301
0.778∠0.567
1.723∠0.363
0.583∠0.525
1.300∠0.354
0.426∠0.974
1.326∠0.453
0.589∠1.149
1.790∠0.473
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Conclusions & Future Work
Algorithm for Contingency Screening
 more efficient distributed algorithm than the existing
methods
 given fixed clustering into areas was assumed
What is the optimal clustering for
 maximum computational efficiency
 minimum the amount of information exchange
AC contingency screening based on homotopy
 examine different homotopy functions
11
References
 [1] H. H. Happ ,“Diakoptics and Piecewise Methods“, IEEE Transactions on Power
Apparatus and Systems, 1970
 [2] Sanja Cvijid, Marija Ilid, “Contingency Screening in a Multi-Control Area System Using
Coordinated DC Power Flow”, ISGT Europe 2011, Manchester, December 2011
 [3] Sanja Cvijic, Marija Ilic “Contingency Screening in a Multi-Control Area System Using
Coordinated DC Power Flow”, Carnegie Mellon University provisional patent filing, August
5, 2011
 [4] Peter Feldmann, Sanja Cvijic, “ Power Flow and Optimal Power Flow analysis using
Homotopy methods”, IBM provisional patent filing: YOR8-2011-0847, August 22, 2011
 [5] S. Iwamoto, Y. Nakanishi and Y. Tamura, “A Load Flow Calculation for lcl-Conditioned
Power Systems”, Electrical Engineering in Japan
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