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Zooming-in and Zooming-out Computer Methods for Contingency
Screening in
Large Scale Power Networks
Sanja Cvijid, Marija Ilid and Peter Feldmann
Carnegie Mellon University IBM [email protected],
[email protected] [email protected]
March 13th, 2012
mailto:[email protected]:[email protected]:[email protected]
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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
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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
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10-bus example: ZOOM-IN tree transf.[1-3]
4
S S
S
1A 2A
3A
1B 2B
3B 4B 1C 2C
3C
S
S
S
S
S
S
1A 2A
3A
1B 2B
3B 4B
1C 2C
3C
ZOOM-IN
S
S
S
1 2 3
ZOOM-IN (area k)
tree
trans. flow
comp.
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10-bus example: ZOOM-OUT tree transf.
5
S S
S
S S
S
A B
C
3 4
ZOOM-OUT
A B
C
4 5 6 ZOOM-OUT
tree
trans. flow
comp.
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Network Transformations and Exchange of Information
Bidirectional transformations[2]
“down”: topological transformations into a spanning tree 𝑋22 =
𝐶12
𝑇 ∙ 𝑋11 ∙ 𝐶12
“up”: computes line flows 𝐹1 = 𝐶12 ∙ 𝐹
2
6
. . .
𝑋(1) 𝑋(𝑛)
𝐹(1) 𝐹(𝑛)
ZOOM-IN (area 1)
tree
trans. flow
comp.
ZOOM-IN (area k)
tree
trans. flow
comp.
ZOOM-IN (area n)
tree
trans. flow
comp.
ZOOM-OUT
tree
trans. flow
comp.
𝑋(𝑘) 𝐹(𝑘)
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Internal Contingency
7
4
6
4 5
6 7
5
7
4
6
NORMAL OPERATION OUTAGE OF LINE 6-7
7
TREE REPRESENTATION
. . .
𝐹(1) 𝐹(𝑛)
ZOOM-IN (area 1)
tree
trans. flow
comp.
ZOOM-IN (area k)
tree
trans. flow
comp.
ZOOM-IN (area n)
tree
trans. flow
comp.
ZOOM-OUT
tree
trans. flow
comp.
𝑋(𝑘)𝑛𝑒𝑤 𝐹
(𝑘)
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Tie-line Contingency
8
A B
C
TREE REPRESENTATION OUTAGE OF LINE 3-8
“up”
. . .
𝐹(1) 𝐹(𝑛)
ZOOM-IN (area 1)
tree
trans. flow
comp.
ZOOM-IN (area k)
tree
trans. flow
comp.
ZOOM-IN (area n)
tree
trans. flow
comp.
ZOOM-OUT
tree
trans. flow
comp.
𝐹(𝑘)
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New approach to AC Contingency Screening
9
Base Case
ACPF(x)=0
Contingency k
ACPF_ck(x)=0 y(λ)=(1-λ)*y
homotopy
easy hard
λ 1 Source: http://en.wikipedia.org/wiki/Homotopy
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0
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
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Homotopy for Ill-Conditioned Systems [4]
Converges in cases when Newton-Raphson fails to converge
Example: 11-bus system[5]
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1.024∠0 1.103∠0.04 1.124∠0.067
1.119∠0.061
1.723∠0.363
1.790∠0.473
1.326∠0.453
1.095∠0.060
1.129∠0.089
1.086∠0.301
1.300∠0.354
0.578∠0.380
0.583∠0.525
1.089∠0.102
1.024∠0 1.072∠0.05 1.089∠0.083
1.064∠0.072 1.042∠0.070
0.778∠0.567
0.426∠0.974
0.589∠1.149
DCPF ACPF homotopy
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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
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References
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[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
