Revealing Temporal Features of Attacks againstSmart Grid

Jun Yan, Yihai Zhu, Haibo He, Yan SunDepartment of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881

Email: {jyan, yhzhu, he, yansun}@ele.uri.edu

Abstract—Protecting smart grid against malicious attacks is amajor task for the power and energy community. While differentinitial failures could trigger cascading effects resulting in same orclose final impact, the pattern of intermediate cascading processvaries significantly. In this paper we propose an approach toanalyze temporal features and predict critical intermediate stagesto help prevent a massive cascading failure. Initial victims frommost vulnerable set of nodes are tested in a topological cascadingmodel under different fault tolerances, and the results revealthat they are usually followed by a dramatic increase of failedcomponents at some critical point. By analyzing the processes offailure propagation, we identify important temporal features ofcascading failure and predict critical moments to allow quick andproper response at an early stage. This work provides informativedecision support for defense against large blackouts caused eitherby random contingencies or attack schemes.

I. INTRODUCTION

The traditional power transmission networks, which used

to be monitored and operated manually, is now evolving to-

wards computer-based automatic power systems of generation,

distribution and protection with the integration of computer

communication networks. This new generation of power grid,

referred to as the smart grid, brings significant benefits of

efficiency, reliability, flexibility and adaptability with facilities

like distributed generation, advanced metering infrastructure

(AMI) and renewable resources, among others. However, due

to the growing interconnection of power grids and commu-

nication networks, the smart grid also faces increasing cyber

security issues, since attackers also have more power to access

information of power grids, manipulate data transmission,

and blacks out the power grid either by injecting false data

or modify the operation status of critical substations and

transmission lines [1]–[3].

For smart grid attackers, a general goal is to maximize

the effect of their attacks with lower cost and risk, which

usually means their attacks will aim at triggering cascading

failures by just taking down a few components whose failure

can lead to blackouts in power grids. According to the reports

on the 2003 North America blackout [4] and the recent 2012

North India blackout [5], blackouts are highly associated the

structural vulnerability of power grids as well as delayed or

ineffective response to the early failure propagation. As the

complex dynamics of the procedure of power system cascading

This work was supported by National Science Foundation (NSF) undergrant 1117314.

failure are often difficult to be disintegrated for comprehensive

analysis, these cascading based attacks pose major challenges

to the power and energy community.To address these challenges, many power grid models for

cascading analysis have been developed [6]–[8]. Among them,

ac power flow model have their strength in accuracy as

they carry the reactive power in calculation, which better

approximate power grid in reality at the cost of greater

computational complexity [6] [9]. Dc power flow models are

very popular with a tradeoff between the precision of power

grids approximation and the computational cost of simulation

[10], but they require detailed physical parameters of the power

grid that are hard to obtain in reality. High-level statistic

approaches use historic data to analyze the power grid failure

from a general perspective [11] [12]. Topological models are

also frequently used in the security analysis of power system

as they provide powerful tools from complex system and

computer science fields [13] [14] and work with most GIS

databases of electric utilities in industry.In addition, many researches also work on the modeling and

analysis of cascading failure [6] [15]. Contingency analyses

focus on the study of how different initial victims can influ-

ence the cascading consequence [9] [16]. Studies on system

dynamics and operation status also plays a important role in

cascading analysis [17]–[19]. Finally, detection, prediction and

prevention of both anomaly and attacks like false data injection

can provide helpful decision support from the security and

defense perspective [20]–[22].Besides the smart grid security researches above, there is

one less-developed topic on cascading failure, i.e. the assess-

ment of temporal features or patterns for the intermediate

stages of cascading failure, which can add a new perspective

to the cascading analysis. In reality, a cascading failure rarely

propagates across the whole power transmission network and

blacks out large scale areas without being detected, mitigated

or stopped by self-protective mechanism or rescue effort. In

order to reduce the risk and impact of major blackouts, the

knowledge of temporal features and patterns is critical for

responding to cascading failures with timely and sufficient

defense strength at an early stage. To be specific, there are

three major reasons to further investigate the cascading failure

from the time domain:

1) While various selections of victims can lead to similar

scale of cascading failures in a power grid, the procedure

978-1-4673-4896-6/13/$31.00 ©2013 IEEE

of each varies from one another by features like the

scale, rate, duration of failure propagation at certain

critical moments.

2) The resources available to defend cascading failure are

usually limited and require different amount of time

to activate, so timing is critical to properly deploy the

defense power to optimize the effect of rescuing efforts.

3) Though well-design power systems with larger fault

tolerance can be more resilient to cascading failures and

smart grid attacks, the required cost of hardware and

maintenance can be intimidating. Thus comprehensive

studies on temporal features which add a “temporal”

factor to the power system tolerance can maximize the

effectiveness and efficiency of defense with relatively

lower system tolerance, which is critical for smaller,

distributed infrastructures and facilities.

The complex process of power grid cascading failure pro-

vides many temporal features available for cascading analysis.

In this paper, we are particularly interested in the critical

moments during the cascading failure process, which reveal

key information like how the failure propagates, when the

optimal period to react to these cascading effects is and

how the fault tolerance of different power systems affects

these temporal characteristics. The goal of temporal feature

analysis is to add another dimension of power grid security

analysis other than traditional electrical properties, structural

vulnerability and operation dynamics and to contribute to a

comprehensive understanding of smart grid security.The rest of this paper is organized as follows: In Section

II we will first describe the modelling of power grid and

cascading failure in this paper, and then define several typical

temporal features which highlight critical information in cas-

cading failure. In Section III simulation results on a test power

grid will be presented analyzed to reveal how to identify these

features of cascading failure and what factors will affect them.

The conclusion and future work is in Section IV.

II. MODELING POWER GRID CASCADING FAILURE AND

ITS TEMPORAL FEATURES

A. Topological Model of Cascading FailureAs mentioned above, there are various available approaches

that model the power grids based on different aspects. Gen-

erally speaking, the topological models are more scalable and

computationally efficient, and they can approximate power

systems well with proper definition of grid structure and

cascading model. In addition, they can be directly applied to

the latest geospatial data which are widely used in industry.

Since we are mostly interested in the revelation of temporal

features and patterns of power grid cascading failure, a simple

topological model of node cascading failure [23] is chosen for

the work presented in this paper, and all the temporal feature

analyses can be extended to real dc or ac power flow models.

The details of power system and cascading failure modeling

are discussed below.First, in what follows a substation is referred to as a node v

and a transmission line as a branch l, and the load L(v) of a

node v is defined as the sum of the degree of all its neighbors

in the power grid, as shown in equation (1).

L(v) =∑

u∈N(v)

deg(u) (1)

where deg(u) is the degree, or the sum of number of branches

connecting to node u, and N(v) is the set of immediate

neighboring nodes directly linked to node v.

In our cascading failure model(CFM), we assume that a

power grid is originally in normal operation with initial load

L0(v) for each node v. A cascading failure is triggered by

the attack on a selected initial victim node v0, whose status is

instantly set to“failed” and load redistributed to its neighboring

nodes in N(v0). The load of these immediate neighbors that

are not failed will be updated according to a redistribution

function described in equation (2). An overloading happens on

node v if L(v) > L0(v) is satisfied at a certain moment during

the cascading; a failure occurs if the overloading status of a

node lasts long enough with its overloading ratio above a given

threshold, which is a positive value representing the designed

fault tolerance of a power system. This threshold, assigned

to a power grid as a universal constant T , determines if an

overloaded node is still safe within an acceptable range, or it

has reached a certain state that will be considered in danger

and needs to be isolated from the transmission network. A

failed node v will have all its load proportionally redistributed

to its immediate neighbors,

ΔL(w) =L(w)∑

u∈N(v)

L(u)(2)

where ΔL(w) is the extra load redistributed to node w ∈N(v). According to (2), if two neighboring nodes A and B

both carry a load of 100, and the total load of all of Node

A’s neighbors is 1000, then when Node A first fails during

the cascading failure, Node B will carry an extra load of

10 since its original load contributes to 10% of the total

neighboring load of Node A. The redistribution will cause

overloading to all surviving neighbors of v in the grid and

can lead to subsequent cascading failures. Once a node fails,

it will be disconnected from the power grid, which means

it will be removed from the neighborhood sets of all nodes

in current power grid topology, and any branches connecting

to this failed node will be tripped as no more power could

be delivered through it. Note that an isolated node is also

regarded as failed since all branches connecting to it have been

tripped. If no failure occurs after a certain amount of time,

the power grid is considered as stabilized, which marks the

end of cascading failure. In a general topological model, the

temporal intervals are not associated with a physical time unit;

so to avoid ambiguous use of time, for the rest of the paper

we use “round” as the conceptual unit length of time in our

model, which could be related to a specific time period, e.g.

seconds or milliseconds, according to real world application

needs.

Update Overloading Timer

Initiates an attack on selected victims

Load Redistribution

Overloaded Node Identified?

Node Failure Identified?

Power Grid Topology Updated

Cascading Failure EndsN

Y

N

Y

Fig. 1. The flowchart of cascading failure model. A cascading failure endswhen no failure emerges for 3D rounds.

In reality, each overloading node will still be able to carry

a certain amount of extra load for a period of time. From the

defensive view, this period represents a transitional window

embedded in the power system that allows proper reactions

before the overloading situation worsens. Therefore we apply

a time-delay overcurrent relay in our model which monitors

and modifies the status of overloading nodes. To be specific, a

timer will be triggered whenever a node starts to overload,

and its output is defined as an accumulative function of

both overloading ratio and time. In each round we test the

overloading status of nodes, increase the value of the timer

and update cascading node failures accordingly. It may take

several rounds for a node turns from overloading to failure, and

once it fails the corresponding load redistribution and topology

updating will be executed before the next round.

With the assumptions above, the accumulative time-delay

function is defined as

d(n) =n∑

k=0

L− TL0 (3)

where n is the number of rounds that a node has been in

overloading status, T is the tolerance of a given system, and

L is the current load of a given node. Similar to [9], the timer

is triggered when L is larger than its capacity TL0, and an

empirical threshold of d(n) is set up so that any node carrying

an extra load of 50% of its capacity for D rounds will be

regarded as failed, and the relay will instantly disconnect all

failed nodes from the power grid. In other words, D is the

maximal time-delay before the relay considers the overloading

of a given node is fatal enough to be cut off from the power

grid.

According to equation (3), the overloading timer launches

only when a node’s load exceeds its capacity, otherwise it will

be reset to zero thus will not affect the status of a node if it has

already failed or recovered from a dangerous state. Equation

(3) also shows that nodes with lower overloading ratio or less

overloading rounds will remain alive for longer period.

In summary, the overall procedure of cascading failure is

illustrated in Fig.1, and this builds up the platform for our

temporal feature analysis.

B. Temporal Features of Cascading Failure

To reveal the temporal features in the intermediate stages of

cascading failures initiated by attacks, in this paper we choose

a simple measurement, i.e. the percentage of failed nodes at

a given moment, denoted as PoF , to evaluate the cascading

process. It is defined as the ratio of the number of failed

nodes to the current round over the total number of nodes in a

power grid. For each cascading failure initiated from different

victims, we find three useful aspects to look into the temporal

feature based on PoF :

1) Leaps: A “leap” is the sudden boost the number of

failure within a small number of rounds during the nonlinear

increase of PoF over time, which means an acceleration of

cascading failure during this period. Its duration and mag-

nitude differentiate various process of cascading failure from

each other and provides key information on the optimal timing

for response action. With similar final PoF , the duration of a

cascading failure can tell how quick a leap shocks the power

grid and the magnitude can illustrate how strong the impact is.

Specifically, a leap of the failure percentage occurs between

round n and n+Δn if the following criterion is satisfied

PoF (n+Δn)− PoF (n) ≥ P1 (4)

for all rounds between n and n + Δn. In this paper we set

P1 = 0.025, thus we will consider an continuous increase of

PoF as a leap if its magnitude is no less than 2.5% for at

least one round, and its duration is the max Δn that satisfies

the condition in 4). Note that P1 is related to the strength of

the initial attack, and for some large power grids P1 should

be decreased accordingly as the powerful attacks in smaller

grids is not likely to lead to the same magnitude of leaps for

large areas.

2) First response moment: In the early stage of failure

propagation, the period before the first leap occurs or the

overall failure percentage reaches a certain level is often

the golden time to take actions to minimize the impact of

cascading failure. The first response moment n0 is defined as

n0 = min{n1, n2} (5)

where

n1 =argminn

{PoF (n+ 1)− PoF (n) ≥ P1} (6)

n2 =argminn

{PoF (n) ≥ P2} (7)

In the equations above, we choose P1 = 0.025 as in previous

case, and choose P2 = 0.1 as the threshold for a significant

damage to the power grid. Hence equation (5) identifies the

very first round n0 in which either a leap appears, or the failure

percentage reaches 10%.

3) Number of leaps and buffer period: In each cascading

procedure, there could be multiple leaps, and the number of

leaps in a single cascading procedure reflects how radical the

increase of PoF is. Given a fixed final failure percentage

PoF , a number of leaps indicate that the cascading failure will

go through several stages, between which the rate propagation

will slow down for certain amount of time, then accelerate

again when some more critical components fail due to the fatal

overloading. Hence these intervals between leaps of a PoF

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Fig. 2. The power grid of Bay Area with 510 nodes, displayed in ArcMap10.0. Substations are marked in green and transmission lines in blue

curve, if exists, can provide useful information on the buffer

periods during which actions should be taken to effectively

mitigate the cascading failure before the next dramatic rise of

failure percentage.

The knowledge of this feature reveals more importance

when the defense strength of power grids are limited to cope

with small scale cascading failures. There can be many small

leaps and buffer periods in some cases, and each of them

requires power grid managers to reallocate power demands,

activate backup resources that can be put into effect during

transitional window to restore normal power delivery; whereas

in other cases, fast cascading failure with consecutive large

leaps merely allows very limited time to response immediately

at an early stage.

For all temporal features discussed above, one fact to notice

in our model is that the system parameters such as maximal

time-delay D, system tolerance T as well as the spatial

connection can substantially affect the cascading procedure

in different power grids. Therefore in the simulation we will

also test how these factors can impact the cascading failure.

III. SIMULATION RESULT

A. Benchmark System and Parameter Setup

In the following simulations, we will reveal temporal fea-

tures of cascading failure by testing various maximal delays

D, victim sets v0 and system tolerances T . The test power

grid in our simulation is the Bay Area grid which is extracted

from the POWERmap GIS dataset provided by PLATTS and

whose topology and geometry are described in Fig.2. It is a

typical regional power grid of a metropolitan area which will

easily draw the attention of potential attackers.

We consider the power grid has a possible system tolerance

T ranging from 1.0 to 2.0 in our simulation. Assuming that

attackers can only obtain limited information of the power grid

such as the topology and the top loaded nodes, but they have

no further knowledge of the status of power grid generation,

operation or management, intuitively they are likely to choose

the nodes with the greatest load, if no other cost of attack

considered. So we perform the simulation of a single victim

attack on the nodes with the greatest initial load to explore

the temporal features in cascading failure and how they are

affected by different system parameters.

B. Temporal Feature Revealed

First, by setting system tolerance T = 1.1, we select the top

9 nodes with the largest load as the candidate set of victims,

and then simulate the cascading process for various values of

D that yield a cascading failure under the given tolerance.

The PoF curves obtained from simulations with respect to

the number of rounds are illustrated in Fig.3. Some general

information is shown in Table I, where OL0 is the number of

overloaded nodes at Round 1 when the corresponding node is

attacked, and PoFf is the final failure percentage after each

attack under the condition that T = 1.1 and D = 0. As we

can see from Fig.3 and TableI, the final percentage of failure

is very close and therefore exploring the temporal feature can

be the practical way to compare the vulnerability of different

nodes in terms of cascading failure.

TABLE IGENERAL INFORMATION ON THE NODES UNDER ATTACK

Rank Load Node ID F0 PoFf

1 15 2496 26 92.94%

2 14 2112 24 92.94%

3 38 1380 20 92.75%

4 53 1131 13 92.94%

5 29 825 11 92.75%

6 77 781 11 92.75%

7 76 741 13 92.94%

8 57 702 13 92.94%

9 55 689 13 92.94%

Take the cascading failure of attacking Node 55 as an

example and assume we have the prior knowledge that D = 4.

Note that a leap in this power grid involves the failure of at

least 12 nodes within one round, which can be a serious failure

in the power system. From Fig.4, we can identify three leaps

during the cascading failure: a minor leap takes place at Round

8, two major ones from Round 10 to Round 12 and Round 26

to Round 35, respectively. Hence the first response time n0 in

this specific case is 8, and there is one short buffer period

at Round 9, another longer one from Round 16 to Round

25. These temporal features highlight the critical moments

for responding to the cascading failure caused by attacking

Node 55: To avoid a cascading failure in the gird, actions

must be made within 8 rounds to deal with the 13 overloaded

nodes after the failure of Node 55, by either calling up backup

resources or cutting off demands. If this critical period is

missed, the failure propagation will accelerate and it would

be difficult to limit the cascading effect until Round 13, after

which the cascading speed slows down to less than 2.5% per

round for 13 rounds. And this will be the last chance to curb

the cascading failure at a failure percentage of about 22%.

However, it is observed that during this period, although there

are 4 rounds with only one or no node failure, there are already

over 15% nodes failed and between 8 to 34 nodes overloaded,

so it requires much more effort to stop the cascading failure

compared to the first response period. After this period, the

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 15, L0 = 2496

D = 0D = 1D = 2D = 3D = 4D = 5

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 14, L0 = 2112

D = 0D = 1D = 2D = 3D = 4D = 5

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 38, L0 = 1380

D = 0D = 1D = 2D = 3

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 53, L0 = 1131

D = 0

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 29, L0 = 825

D = 0

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 77, L0 = 781

D = 0D = 1

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 76, L0 = 741

D = 0D = 1D = 2D = 3

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 57, L0 = 702

D = 0D = 1D = 2D = 3

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1Node 55, L0 = 689

D = 0D = 1D = 2D = 3D = 4D = 5

Fig. 3. The cascading failure caused by attacks when T = 1.1. The X-axis is the round of cascading failure while the Y-axis is the failure percentage PoF .Each cascading failure starts from different attack victims that have the greatest load in Bay Area.

0 5 10 15 20 25 30 35 40 45 500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Rounds of cascading failure

Δ Po

F

Fig. 4. The change of failure percentage PoF compared to previous roundafter attacking node 57, given T = 1.1 and D = 4

failure percentage exhibits another fast rise before it finalizes

at about 92%.

C. Factors that affect temporal features

As shown in Fig.3, the maximal time-delay D plays an

important role in the cascading procedure. Many nodes only

have one major leap because of the heavy initial load they

carried, especially when D is low and allows little time before

an overloading turns to a failure. In Fig.3, the cascading

procedure for all these 9 nodes are quite similar when D = 0and so it is hard to discover important information from the

corresponding PoF curves.

However, when the value of D is increased, some nodes like

Node 14, 38, 76 57 and 55 will yield some leaps during the

cascading, and buffer periods emerge when D is increased

large enough. In reality, if D is large enough, the power

system will have enough time to restore normal operation

automatically or manually, hence eliminating the chance of

cascading failure. For instance, for Node 53 and 29, by

increasing D to any integers larger than 0, no cascading failure

will occur in Bay Area even if the nodes being attacked have

the 4th and 5th largest load in the power grid. As shown in

the figures, a leap can also be delayed by increased D as a

nonlinear function of D, and the total number of rounds of

cascading failure before it stabilizes, the first response time

n0 is also increased by D accordingly.

Also, from the PoF curves, we can see that the spatial

location and connection can affect temporal features as well.

First, when two nodes are spatially close to each other, their

PoF curves exhibit similar patterns given the same system

parameters, as shown in cases of attacks on Node 15 and

14, and Node 55 and 57. Besides, while the buffer periods

can start at various rounds with different lengths if D is

changed, they always correspond to a certain value of failure

percentage PoF , which is associated with a given geographic

area affected by the cascading failure and therefore the buffer

period is also related to the cluster of failed nodes.

Finally, choose the single victim attack on node 57 as an

example, the effect of system tolerance T on the interme-

diate stages of cascading failure are shown in Fig.5, which

exhibits similar pattern to the effect of maximal time-delay D.

Increasing T from 1.0 to 1.3 can break down a large leap into

smaller ones, thus generates a buffer period and increases the

length of it. Also when T reaches a threshold, it can essentially

prevent the cascading failure; for instance, when T is equal

or larger than 1.3, there will be not cascading effect if the

attacker chooses to initiate the cascading failure from Node

57. However, in reality the cost to construct and maintain such

a high tolerance can be prohibitive, which means the temporal

feature is still important in providing critical information for

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Rounds of cascading failure

Per

cent

age

of fa

ilure

T=1.0T=1.1T=1.2T=1.3

Fig. 5. The influence of system tolerance when D = 1. Each cascadingfailure starts from Node 57 in Bay Area.

the timing of defense response.

IV. CONCLUSIONS AND FUTURE WORK

In this paper we reveal several critical temporal features in

the cascading analysis of power system. While for the most

loaded nodes in the power grid the cascading procedure leads

to similar final failure percentage, the intermediate process

vary significantly. Therefore, temporal features such as the

temporal location, magnitude, duration, number of occurrence

of leaps as well as the buffer period that allows a second

chance to response provides key information on the defense

against smart grids attacks. This study on the temporal fea-

tures of cascading procedure caused by malicious attacks can

provide a critical dimension to a comprehensive understanding

of smart grid security, including operation, protection as well

as planning of the smart grid.

There are several interesting future research directions along

this topic. For instance, in our current study we focus on the

topological structure of the grid. It would be important to

consider power flow analysis models and use branch tripping

instead of substation failure, such as the models presented in

[9] and [24], to understand the grid behavior under attack.

From a defense perspective, it is also useful to simulate

different defense strategies and observe the grid reactions to

different types and stages of grid failures, either through cyber-

attacks or physical failures of the grid.

REFERENCES

[1] X. Li, X. Liang, R. Lu, X. Shen, X. Lin, and H. Zhu, “Securing smartgrid: cyber attacks, countermeasures, and challenges,” CommunicationsMagazine, IEEE, vol. 50, no. 8, pp. 38 –45, Aug. 2012.

[2] P.-Y. Chen, S.-M. Cheng, and K.-C. Chen, “Smart attacks in smart gridcommunication networks,” Communications Magazine, IEEE, vol. 50,no. 8, pp. 24 –29, Aug. 2012.

[3] D. Kundur, X. Feng, S. Liu, T. Zourntos, and K. Butler-Purry, “Towardsa framework for cyber attack impact analysis of the electric smart grid,”in Smart Grid Communications (SmartGridComm), 2010 First IEEEInternational Conference on, Oct. 2010, pp. 244 –249.

[4] “Final report on the august 14, 2003 blackout in the united statesand canada: Causes and recommendations,” U.S.-Canada Power SystemOutage Task Force, Tech. Rep., Apr. 2004.

[5] “Report of the enquiry committee on grid disturbance in northern regionon 30th july 2012 and in northern, eastern & north-eastern region on 31stjuly 2012,” The Enquiry Committee, Ministry of Power, Government ofIndia, Tech. Rep., Aug. 2012.

[6] M. Vaiman, K. Bell, Y. Chen, B. Chowdhury, I. Dobson, P. Hines, M. Pa-pic, S. Miller, and P. Zhang, “Risk assessment of cascading outages:Methodologies and challenges,” Power Systems, IEEE Transactions on,vol. 27, no. 2, pp. 631–641, May 2012.

[7] M. Vaiman, K. Bell, Y. Chen, B. Chowdhury, I. Dobson, P. Hines,M. Papic, S. Miller, and P. Zhang, “Risk assessment of cascadingoutages: Part 1 - overview of methodologies,” in Power and EnergySociety General Meeting, 2011 IEEE, Jul. 2011, pp. 1 –10.

[8] M. Papic, K. Bell, Y. Chen, I. Dobson, L. Fonte, E. Haq, P. Hines,D. Kirschen, X. Luo, S. Miller, N. Samaan, M. Vaiman, M. Varghese,and P. Zhang, “Survey of tools for risk assessment of cascading outages,”in Power and Energy Society General Meeting, 2011 IEEE, Jul. 2011,pp. 1–9.

[9] M. Eppstein and P. Hines, “A “random chemistry” algorithm for identify-ing collections of multiple contingencies that initiate cascading failure,”Power Systems, IEEE Transactions on, vol. 27, no. 3, pp. 1698–1705,Aug. 2012.

[10] B. Stott, J. Jardim, and O. Alsac, “Dc power flow revisited,” PowerSystems, IEEE Transactions on, vol. 24, no. 3, pp. 1290 –1300, aug.2009.

[11] H. Ren and I. Dobson, “Using transmission line outage data to estimatecascading failure propagation in an electric power system,” Circuits andSystems II: Express Briefs, IEEE Transactions on, vol. 55, no. 9, pp.927–931, Sep. 2008.

[12] A. Holmgren and S. Molin, “Using disturbance data to assess vulner-ability of electric power delivery systems,” Journal of InfrastructureSystems, vol. 12, no. 4, pp. 243–251, 2006.

[13] E. Cotilla-Sanchez, P. Hines, C. Barrows, and S. Blumsack, “Comparingthe topological and electrical structure of the north american electricpower infrastructure,” Systems Journal, IEEE, vol. PP, no. 99, p. 1, May2012.

[14] S. Jonnavithula and R. Billinton, “Topological analysis in bulk powersystem reliability evaluation,” Power Systems, IEEE Transactions on,vol. 12, no. 1, pp. 456–463, Feb. 1997.

[15] R. Baldick, B. Chowdhury, I. Dobson, Z. Dong, B. Gou, D. Hawkins,H. Huang, M. Joung, D. Kirschen, F. Li, J. Li, Z. Li, C.-C. Liu, L. Mili,S. Miller, R. Podmore, K. Schneider, K. Sun, D. Wang, Z. Wu, P. Zhang,W. Zhang, and X. Zhang, “Initial review of methods for cascading failureanalysis in electric power transmission systems,” in Power and EnergySociety General Meeting - Conversion and Delivery of Electrical Energyin the 21st Century, 2008 IEEE, Jul. 2008, pp. 1 –8.

[16] N. Bhatt, S. Sarawgi, R. O’Keefe, P. Duggan, M. Koenig, M. Leschuk,S. Lee, K. Sun, V. Kolluri, S. Mandal, M. Peterson, D. Brotzman,S. Hedden, E. Litvinov, S. Maslennikov, X. Luo, E. Uzunovic, B. Far-danesh, L. Hopkins, A. Mander, K. Carman, M. Vaiman, M. Vaiman,and M. Povolotskiy, “Assessing vulnerability to cascading outages,” inPower Systems Conference and Exposition, 2009. PSCE ’09. IEEE/PES,Mar. 2009, pp. 1 –9.

[17] B. A. Carreras, V. E. Lynch, I. Dobson, and D. E. Newman, “Complexdynamics of blackouts in power transmission systems,” Chaos: AnInterdisciplinary Journal of Nonlinear Science, vol. 14, no. 3, pp. 643–652, 2004.

[18] I. Dobson, B. A. Carreras, V. E. Lynch, and D. E. Newman, “Complexsystems analysis of series of blackouts: Cascading failure, critical points,and self-organization,” Chaos: An Interdisciplinary Journal of NonlinearScience, vol. 17, no. 2, p. 026103, 2007.

[19] D. Newman, B. Carreras, V. Lynch, and I. Dobson, “Exploring complexsystems aspects of blackout risk and mitigation,” Reliability, IEEETransactions on, vol. 60, no. 1, pp. 134–143, Mar. 2011.

[20] G. Hug and J. Giampapa, “Vulnerability assessment of ac state estima-tion with respect to false data injection cyber-attacks,” Smart Grid, IEEETransactions on, vol. 3, no. 3, pp. 1362 –1370, Sep. 2012.

[21] Y. Yuan, Z. Li, and K. Ren, “Modeling load redistribution attacks inpower systems,” Smart Grid, IEEE Transactions on, vol. 2, no. 2, pp.382 –390, Jun. 2011.

[22] J. Lin, W. Yu, X. Yang, G. Xu, and W. Zhao, “On false data injection at-tacks against distributed energy routing in smart grid,” in Cyber-PhysicalSystems (ICCPS), 2012 IEEE/ACM Third International Conference on,Apr. 2012, pp. 183 –192.

[23] W. Wang, Q. Cai, Y. Sun, and H. He, “Risk-aware attacks and catas-trophic cascading failures in u.s. power grid,” in Global Telecommuni-cations Conference (GLOBECOM 2011), 2011 IEEE, Dec. 2011, pp.1–6.

[24] E. Bompard, E. Pons, and D. Wu, “Extended topological metrics forthe analysis of power grid vulnerability,” Systems Journal, IEEE, vol. 6,no. 3, pp. 481–487, Sep. 2012.