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Cascading dynamics of power grid networks

R. Pfitzner1,2

, K. Turitsyn3,2

, M. Chertkov2

1 ETH Zurich, 2 LANL, 3 MIT

May 24, 2011

Konstantin Turitsyn Cascading failure dynamics

http://find/

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Outline

Motivation: basic facts about cascading failures

Dynamical model

Results: effect of load fluctuations (arXiv:1012.0815)

Results: mitigation techniques (arXiv:1104.4558)

Path forward

Konstantin Turitsyn Cascading failure dynamics

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Cascading failures

Cascades in power grids:About 20 large blackouts (>300MW ) happen every year.

Annual damage to US economy around $100 billions.

Power-law probability distribution, i.e. enhanced probability of

large cascades.Will get only worse: more demand, intermittent generation.

Unlike epidemic cascades

Non-local response (failure of one component affect all the

network).Hierarchical (i.e. not scale-free) networks.

Konstantin Turitsyn Cascading failure dynamics

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Model

Potential flow on the graphs:pij- flow over the edge (ij):

xijpij=i j

gi - generator nodes (sources)di - load nodes (sinks)

Kirchchoff Law:

ji

pij= gi, i Gg

di, i Gd0, i G0\ (Gg Gd)

G 1

G 2

3

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G 13 14

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G 22

G 23

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G 27

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9 21

Konstantin Turitsyn Cascading failure dynamics

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Tripping events

Each line and generator have limited capacities:

|pij|

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Algorithm: load fluctuations

Loads are assumed to be random and increase in linear fashion:

di =d0i + dit.

with d0i chosen from optimal power flow solution anddibeing an

i.i.d random variable with variance d0i .

At each step the moment of next overloading event is calculated:

t = min(1, tgen, tline)

tgen= min

iG

ggmaxi g

0i

gi

tline= min(i,j)

pmaxij p

0ij

pij

Konstantin Turitsyn Cascading failure dynamics

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Optimal Power Flow: d0, g0

choose d

Identify islands

t = min(1, tl, tp)

dt =d0 +td

Droop Control Identify islands

Power Flow cut one overloaded line

Line Check

Finish

no violation and t = 1

violation

no

violation

and

t