Cascade Failures from Distributed Generation in Power Grids

Transcription

1 Cascade Failures from Distributed Generation in Power Grids Antonio Scala Univ. di Roma La Sapienza, IMT Alti Studi Lucca, LIMS London AIIC Italian Experts on Critical Infrastructures Sakshi Pahwa and Caterina Scoglio, KSU September 18, 2012 Antonio Scala Cascade Failures from Distributed Generation in Power Grids 1/20

2 Summary Introduction (over?)simplied model for cascades Mean eld solution of the model Analysis of realistic networks Analysis of synthetic networks Conclusions Antonio Scala Cascade Failures from Distributed Generation in Power Grids 2/20

3 Toward Smart Grids 1 st paradigm shift: Liberalization of the Energy Markets 2 nd paradigm shift: the Smart Grid challenge decentralization distributed sources renewable energy uctuations Antonio Scala Cascade Failures from Distributed Generation in Power Grids 3/20

4 DC power ow Linearization of the AC power ow equations for small phase-angle dierences along branches leads to the DC power ow system Lθ = P P i total power (generation load) on the i th bus θ i phase angle on the i th bus L Laplacian associated with the admittance matrix Y we also consider the maximum capacities C of the branches Antonio Scala Cascade Failures from Distributed Generation in Power Grids 4/20

5 Grids & Networks Antonio Scala Cascade Failures from Distributed Generation in Power Grids 5/20

6 AC vs DC Antonio Scala Cascade Failures from Distributed Generation in Power Grids 6/20

7 AC vs DC Antonio Scala Cascade Failures from Distributed Generation in Power Grids 7/20

8 Metrics Standard blackout indices to measure blackout size load shed energy unserved duration number of blackouts number of customers aected we use the fraction of failed links Antonio Scala Cascade Failures from Distributed Generation in Power Grids 8/20

9 Some assumptions If after an initial failure some other lines exceed their thermal limits, these overheated lines are not tripped instantaneously, but almost will be trip within few minutes all external characteristics (load congurations and renewable generation) remain unchanged in this relatively short time span no operator action is taken in this relatively short time span reaction time (typical between 15 minutes to an hour) not available for fast adjustments Antonio Scala Cascade Failures from Distributed Generation in Power Grids 9/20

10 DC cascades Model - Not considering transients - Not considering phase sync - Not considering voltage instabilities - Just a sequence of load sheddings Fix initial conditions Solve power ow & cut branches with ows above capacity until all branches are OK Report nal conguration Antonio Scala Cascade Failures from Distributed Generation in Power Grids 10/20

11 WESTERN INTERCONNECTION (WSCC) July 2, 1996 Sequence of system separations

12 Mean Field Long range = model can be solved mean eld Antonio Scala Cascade Failures from Distributed Generation in Power Grids 12/20

13 Correlated Loads f fraction of failed links α relative increase of the loads L i (α) = L 0 i (1 + α) All the loads have a maximally correlated increase Antonio Scala Cascade Failures from Distributed Generation in Power Grids 13/20

14 Correlated Loads: Random Grids N=50 N=100 N=200 N=400 Antonio Scala Cascade Failures from Distributed Generation in Power Grids 14/20

15 Renewable Sources distributed generation can be highly uncorrelated ows can reverse Antonio Scala Cascade Failures from Distributed Generation in Power Grids 15/20

16 Fluctuations Customer Related Renewable related We make the loads L stochastic L i = L 0 (1 + σξ i i ) where ξ i are independent random variables uniformily distributed between [ 1, 1] σ parametrises the strenght of the uctuations Antonio Scala Cascade Failures from Distributed Generation in Power Grids 16/20

17 Correlated Loads f fraction of failed links σ relative strenght of the uctuations L i (σ) = L 0 i (1 + σξ i ) All the loads have an uncorrelated increases Antonio Scala Cascade Failures from Distributed Generation in Power Grids 17/20

18 Fluctuations: Random Graphs N=50 N=100 N=100 N=200 Antonio Scala Cascade Failures from Distributed Generation in Power Grids 18/20

19 Summary We have investigated an (over?)simplied cascade overload model subject to correlated/uncorrelated noise Correlated noise (uniform load increase) induces an abrupt breakdown of the system Uncorrelated noise (distributed renewable sources) also induce an abrupt breakdown of the system, but only for large grids Antonio Scala Cascade Failures from Distributed Generation in Power Grids 19/20

20 THANKS TO: US grant HDTRA Self Healing Networks CNR-PNR National Project Crisis-Lab UPCOMING: FP7 IP MULTIPLEX - Foundational Research on MULTIlevel complex networks and systems antonio.scala@phys.uniroma1.it