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Electric Power Systems Research 143 (2017) 329–338

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Electric Power Systems Research

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e p s r

risk optimization model for enhanced power grid resilience against hysical attacks

asim Nezamoddini a, Seyedamirabbas Mousavian b,∗, Melike Erol-Kantarci c

The Department of Industrial and Systems Engineering, State University of New York, Binghamton, NY, USA The School of Business, Clarkson University, Potsdam, NY, USA The School of Electrical Engineering and Computer Science, University of Ottawa, ON, Canada

r t i c l e i n f o

rticle history: eceived 14 February 2016 eceived in revised form 17 August 2016 ccepted 18 August 2016 vailable online 25 October 2016

eywords: ransmission system security hysical attacks

a b s t r a c t

Secure operation of the power systems is a major concern of the power system operators, consumers and governments. Besides inevitable malfunction of the power grid components, deliberate disruptions caused by malicious attacks put the security of the power systems at high risk. Transmission systems have been targeted by attackers to interdict the supply of power to consumers. In this paper, we address the problem of the transmission system security and develop an optimization model to determine the optimal investment decision for the resilient design of the transmission systems against physical attacks. We measure the damage of the physical attacks in terms of the load curtailment. We model the optimal protection decision problem as a mixed integer linear programming (MILP) problem to minimize the

oad curtailment/shed ixed integer linear programming

investment costs such that the risk of the load curtailment exceeding a certain threshold value, after an attack to the power grid, be less than the risk tolerance value, defined by power system operators. We use the small 6-bus test system to describe the problem and our methodology. We run our experiments on the IEEE 24-bus and IEEE 57-bus systems to test the performance of our model. Experimental results show that the developed model is a promising enhancement to ensure secure and safe operation of the transmission systems.

. Introduction

Power grids are indispensable components of modern life. The afe and secure operation of the power grid is of the highest prior- ty for power grid operators, consumers and government. However, isruptions in power supply are sometimes inevitable due to the alfunction of the power grid components and environmental

ssues [1]. As a case in point, weather related power outages in the nited States cost $18–$33 billion in annual average between 2003 nd 2012 [2]. Deliberate disruptions, caused by malicious attacks to he power grids, are major concerns for the power grid stakeholders s well. Malicious attacks to power grids not only cause disruption

n power supply but also lead to substantial economic burdens for he utility companies. For example, the recent attack to the substa- ion in California on April 16, 2013 resulted in damaging 17 giant ransformers and 27 days of repair time [3]. A report from Wall

∗ Corresponding author. E-mail addresses: [email protected] (N. Nezamoddini),

[email protected] (S. Mousavian), [email protected] M. Erol-Kantarci).

Street Journal showed that 274 instances of deliberate damages to the power grid were reported over the last three years, which put more emphasis on necessity of enhanced protection and resilience of the power grid [4]. However, substantial protection costs pre- clude the full protection of all grid components and encourage power system investors to investigate critical components of the system for enhanced security [5]. Damages to the critical power grid components may entail cascading outages and cause blackouts [6]. Hence, a risk assessment model is necessary to determine potential vulnerabilities of the power grid and provide the system operators with enhanced protection plans within the budgetary restrictions.

Due to the statistics mentioned above, the problem of power grid resilience against physical attacks has attracted the interests of the research community as well. The main objective is to determine the best investment policy for protecting the power grid compo- nents against physical attacks where the attacker’s resources are limited [7]. The interdiction attacks cause topological changes to

the power grid which impact is measured in terms of the load shed [8]. Authors in [9] developed a multi-level optimization problem in the form of defender-attacker-defender to identify the critical components necessary to be hardened for minimizing the potential damages of the terrorist attacks. Multi-level optimization problems

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Nomenclature

Sets and indices K set of buses G set of generators L set of transmission lines I set of protection levels

̊ set of attack scenarios k index of buses g index of generators l index of transmission lines i index of protection levels � index of attack scenarios

Constants Ci cost of the protection level i Ri reliability of the protection level i Lk load of bus k (MW) Sl susceptance of transmission line l (siemens) ı�l binary parameter which equals 1 if transmission line

l is interdicted in scenario �, and 0 otherwise Hlk incidence matrix coefficient (−1, 0 or 1) at bus k of

transmission line l pmaxg maximum generation of generator g (MW) pming minimum generation of generator g (MW) f max l

maximum capacity of transmission line l (MVA) threshold of the load curtailment (MW) � risk tolerance value of the threshold load curtail-

ment N attacker’s budget in terms of the number of trans-

mission lines interdicted

Decision variables xil binary decision variable which equals 1 if transmis-

sion line l is equipped with protection level i, and 0 otherwise

w� binary decision variable which equals 1 if the load curtailment exceeds the threshold in scenario �, and 0 otherwise

p�g energy dispatched by generator g in scenario �. (MW)

f�l power flow at transmission line l in scenario � (MVA)

��k load curtailment of bus k in scenario �. (MW) ��˛(l) voltage angle at the from-bus end of the transmis-

sion line l in scenario � (◦) ��ˇ(l) voltage angle at the to-bus end of the transmission

a t o t p s s w t m i s [ l

line l in scenario � (◦) P� probability of the attack success in scenario �

re complicated. A bilevel optimization problem can be converted o a single level optimization problem using Karush–Kuhn–Tucker ptimality conditions [10]. Authors in [11] showed that decomposi- ion methods can be applied effectively to solve large scale bilevel rotection models. Iterative heuristics are also proposed to solve uch complex optimization problems [12]. Computational time in uch problems is of the interests of the research community as ell [13,14]. Game theory models are introduced in [15] to tackle

he defender-attacker problems. The application of game theory

odels in defender-attacker problems have been further studied

n [16] as static games and in [17] as leader-follower games. zero- um Markov games in [18] and graph theory based methods in 19–21] are introduced to solve the power grid interdiction prob- em. Furthermore, transmission switching has been suggested as

ems Research 143 (2017) 329–338

a corrective action when the power grid is attacked [22]. Authors in [23] applied meta-heuristic methods to solve the interdiction model with the possibility of transmission switching. The men- tioned defender-attacker models aim at hardening the power grid against the worst potential attack scenarios. Besides, the underlying assumption of the interdiction models is that the protected com- ponents will no longer be at risk and completely secure. However, it is not a realistic assumption. To alleviate this problem, we define a protection reliability index which represents the probability that the protection mechanism can keep the transmission line active even after malicious attacks. In other words, protection reliability index represents the likelihood of the attacker’s failure in harming the transmission line due to the protection mechanisms placed in service. Besides, there are situations where decision makers pre- fer to equip some grid components with partial protections due to the substantial protection costs. After a comprehensive review, the author in [24] concluded that it has been difficult in power sys- tems studies to relate reliability and resiliency to market efficiency and economic losses. Hence, we propose a new model for power grid protection, which provides power system operators with more flexibility in terms of the resiliency scales against the risk of mali- cious attacks. Various line protection techniques are introduced in [25] that incur different costs for utility companies. For example, intrusion detection devices, access controls, lighting, fencing, cam- eras, sensors, and buffer zone security are suggested as protection mechanisms [26] with lower reliability and small to medium cost investments. Moreover, more reliable protection mechanisms such as undergrounding or double circuiting of the transmission lines can be used at higher costs to enhance physical security against physical disruptions [27]. A communication mechanism can also be devised to alarm guards/police to accelerate the response time to intrusions [28]. Hence, we consider the possibility of different protection levels and study risk in our model formulation as a deci- sion parameter where the protected components are less likely to be tampered by attackers.

2. Protection optimization model

This paper aims at developing a protection model to equip crit- ical components of the transmission systems with more reliable protections. Attackers may target the physical structure of the power grid such as transmission lines, transmission towers or insu- lators [28]. These attacks incapacitate the entire transmission line and cause insufficient available transmission capacity that even- tually interrupt the balance between power supply and demand. Therefore, control actions such as load curtailment/shedding need to be taken after an attack in order to stabilize the system [29]. Load curtailment reduces lower-priority loads with the permission of the customers; in case curtailment is not sufficient to prevent power imbalance or there is not enough time to implement the load curtailment, load will be shed [30]. The goal of this paper is to minimize the investment costs of protection such that the risk of load curtailment/shedding exceeding a certain threshold value would be controlled. The assumptions of our proposed model are as follows.

• There are potential protection mechanism which provide trans-

mission lines with different reliability levels at different costs.

• Attackers have limited budgets to tamper with the system. • Attackers do not have complete information about the protec-

tions plans. • The risks are calculated in terms of total load curtailment.

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The objective function of our mathematical model, given in Eq. 1), is to minimize the investment costs of equipping the transmis- ion lines with more reliable protections:

= min x

L∑ l=1

I∑ i=1 Cixli (1)

here Ci is the cost of the protection level i and xil is the binary ecision variable which equals 1 if transmission line l is equipped ith protection level i, and 0 otherwise.

We consider that attackers have limited budget to tamper with he transmission lines. The attackers’ budget is represented in Eq. 2):

l=1 ı�l = N ∀� ∈ ̊ (2)

here ı�l is a binary input parameter that equals to one if the ransmission line is interdicted and 0 otherwise. The attacker’s total udget is represented by parameter N.

The goal is to find the optimal investment plan such that the load urtailment would be controlled under all potential attack scenar- os. We use the linearized optimal power flow constraints, known s DC-OPF constraints [31,32], and modify them as follows such hat the attack scenarios and load curtailment are integrated in the

odel. Notice that Lk represents the peak load to ensure that the odel considers worst cases when the slightest attacks may result

n load curtailment:

l=1 Hlkf�l(1 − ı�l) + p�k + ��k = Lk ∀k ∈ K; ∀� ∈ ̊ (3)

q. (3) is the load balance constraint where Hlk is the incidence atrix coefficient (−1, 0 or 1) at bus k of transmission line l, p�g

epresents energy dispatched by generator g in scenario � and �l determines the power flow at transmission line l in scenario . In Eq. (3), interdicted lines by the attacker are excluded from

he list of connected transmission lines when ı�l = 1. Moreover, the oad curtailment stem from the attack is obtained by ��k at bus k. qs. (4) and (5) represent the voltage angles and the power flows onstraints in the modified DC-OPF. Notice that ��˛(l) and ��ˇ(l) epresent voltage angle at the from-bus end and the to-bus end f the transmission line l in scenario �, respectively, and Sl is the usceptance of transmission line l.

�l − Sl(��˛(l) − ��ˇ(l)) ≥ −Mı�l ∀l ∈ L; ∀� ∈ ̊ (4)

�l − Sl(��˛(l) − ��ˇ(l)) ≤ Mı�l ∀l ∈ L; ∀� ∈ ̊ (5) e used the big-M parameter, M, to exclude the voltage angles and

ower flow constraint from the model for the transmission line that s interdicted, ı�l = 1. Eqs. (6) and (7) represent the constraints on he capacities of the transmission lines and generators:

f max l

(1 − ı�l) ≤ f�l ≤ f maxl (1 − ı�l) ∀l ∈ L; ∀� ∈ ̊ (6) min g ≤ p�g ≤ pmaxg ∀g ∈ G; ∀� ∈ ̊ (7)

Eq. (8) is provided to ensure that the load curtailment at each us does not exceed the load of the bus.

≤ ��k ≤ Lk ∀� ∈ ˚; ∀k ∈ K (8)

There are potential levels of protection which provide transmis-

ion lines with different protection reliability at different costs. A ransmission line will be protected by only one of the protection

echanisms or will be left unprotected as given in Eq. (9). In Eq.

ems Research 143 (2017) 329–338 331

(9), xli is a binary variable that determines line l is protected by pro- tection type i. Notice that xl0 = 1 means that line l is not protected and C0 = 0 accordingly:

I∑ i=1 xli = 1 ∀l ∈ L (9)

The goal of the proposed model is to ensure that the obtained protection plan guarantees that the risk of the load curtailment exceeding a certain threshold would be less than a predetermined acceptable risk tolerance value, e.g. the risk of the load curtailment exceeding 10 MW would be less than 1% considering all potential attack scenarios. The risk constraint is given in Eq. (10):

( K∑ k=1 ��k ≥

) ≤ � ∀� ∈ ̊ (10)

where is the load curtailment threshold after the attack from the power system operators’ standpoint and � is the acceptable risk tolerance value. To represent Eq. (10) in a linear fashion, we use the binary variable w� with the definition given in Eq. (11):

w� =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎩

1 K∑ k=1 ��k ≥

0 K∑ k=1 ��k <

∀� ∈ ̊ (11)

Furthermore, Eq. (12) is considered to ensure that the risk of the load curtailment exceeding a certain threshold value is less than the predetermined acceptable risk value, �:

P�w� ≤ � ∀� ∈ ̊ (12) where P� is the probability of the successful attack in scenario �. Eq. (13) shows how the scenario probabilities are calculated where Ri is the reliability index of the protection type i. The protection reli- ability index represents the probability that the transmission line remains functional after a malicious attack due to the protection mechanisms placed in service:

P� = L∏ l=1

I∑ i=1 xli(1 − Ri)ı�l ∀� ∈ ̊ (13)

Eq. (13) is nonlinear which makes Eq. (12) nonlinear as well. To represent Eq. (13) in a linear fashion, we use variable u� = lnP�. Hence, we obtain Eq. (14) which is still nonlinear:

u� = L∑ l=1

( I∑ i=1 xli(1 − Ri)ı�l

) ∀� ∈ ̊ (14)

Considering variable xli being binary, we can obtain the equiva- lent linear Eq. (15):

u� = L∑ l=1

I∑ i=1 xliı�l ln((1 − Ri)) ∀� ∈ ̊ (15)

Now, we are able to represent Eq. (12) linearly by using Eqs.

(16)–(18):

.w� − M(1 − w�) ≤ K∑ k=1 ��k ∀� ∈ ̊ (16)

332 N. Nezamoddini et al. / Electric Power Systems Research 143 (2017) 329–338

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d p l e s

e p i r t t l a s

T L

T R

Table 3 Load curtailments of the single-line and two-line attack scenarios.

Scenario # Attacked lines Load curtailment (MW)

1 Single line 0 2 2, 3 6.25 3 2, 5 50.00 4 2, 6 1.81 5 2, 8 8.09 6 2, 9 2.97 7 2, 10 10.00 8 2, 11 1.03 9 3, 8 3.00 10 5, 8 0.57

anisms. Moreover, the scenario probabilities under the two given protection decisions are compared in Table 9. The results confirm that the protection costs may change the protection decisions sig- nificantly while satisfying the risk constraints.

Table 4

Fig. 1. The 6-bus test system.

k=1 ��k < (1 − w�) + Mw� ∀� ∈ ̊ (17)

� ≤ ln(�) + M(1 − w�) ∀� ∈ ̊ (18) Finally, Eq. (19) shows that the decision variables xli are binary:

li ∈ {0, 1} ∀l ∈ L; ∀i ∈ I (19)

. Case study and scenario reduction strategy

In this section, we use the 6-bus test system introduced in [31] to escribe the problem and our methodology on a small and simple ower system. Next, we explain our scenario reduction strategy for

arger power systems. We test the efficacy of our approach in the xperimental results section using a middle size and a larger power ystems.

.1. Case study

The 6-bus test system includes six buses, three generators and leven transmission lines. Fig. 1 shows the 6-bus test system. Load rofile is given in Table 1. Table 2 shows the reliability levels and

nvestment costs of the four assumed protection mechanisms. The eliability level of Mechanism 0, no enhanced protection of the ransmission lines, is assumed to be 0.50. Besides, it is assumed that

he attacker’s budget is limited and may target two transmission ines at most. Hence, all single-line and two-line attack scenarios re enumerated and resulting load curtailments are calculated and ummarized in Table 3.

able 1 oad in the 6-bus test system (MW).

Bus 1 2 3 4 5 6 Load 0 0 0 70 70 70

able 2 eliability levels and costs of the protection mechanisms.

Protection level 0 1 2 3 Protection reliability 0.5 0.8 0.9 0.99 Cost (p.u.) 0 1 2 3

11 5, 10 10.00 12 7, 9 30.00 13 Other 2-lines combinations 0

First, we explore how the 6-bus test system should be protected considering different risk tolerance values if the threshold of the load curtailment is 40 MW, = 40. Therefore, the model is supposed to protect the system against Scenario 3, introduced in Table 3, such that the probability of that scenario be less than or equal to the risk tolerance value. In this experiment, we analyze the impact of risk tolerance values ranging from 0.001 to 0.500 on protection plans. The results are summarized in Table 4 and show that risk averse protection plans increase investment costs substantially and require more number of higher-reliability protection mechanisms to be installed.

Next, we run an experiment to study the impact of the load curtailment threshold value on the resultant protection plans. The results, summarized in Table 5, show that lower threshold val- ues necessitate protection of more number of transmission lines. The reason is that more attack scenarios are effective when the threshold is set to lower values. To test the validity of our obtained solutions, we calculated the probabilities of the attack scenarios after the protection plan, given in Table 5, is implemented for = 0 and � = 0.01. We summarized the results in Table 6 which confirms that the probability of load curtailment under any attack scenario is equal to or less than the risk tolerance value.

To study the impact of costs, we compare the protection plans under the two cost profiles, provided in Table 7. The protection decisions for the two mentioned cost profiles are given in Table 8 when = 0 and � = 0.01. The results show that the protection plans are very sensitive to the relative cost ratio of the protection mech-

Impact of risk tolerance value on protection plans.

Risk (�) (l: protected line, i: protection level) Total cost (p.u.)

0.500 – 0 0.100 (2,1) 1 0.050 (2,2) 2 0.010 (2,3) 3 0.001 (2,3),(5,2) 5

Table 5 Protection plans for different load curtailment threshold values at � = 0.01.

(l: protected line, i: protection level) Total cost

0 (2,3),(5,3),(8,3),(9,3) 12 10 (2,3),(7,3),(10,3) 9 30 (2,3),(7,3) 6 50 (2,3) 3 >50 – 0

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Table 6 Scenario probabilities.

Scenario attacked lines Load curtailment (MW) Probability after protection

2, 3 6.25 0.0100 2, 5 50.00 0.0001 2, 6 1.81 0.0100 2, 8 8.09 0.0001 2, 9 2.97 0.0001 2, 10 10.00 0.0100 2, 11 1.03 0.0100 3, 8 3.00 0.0100 5, 8 0.57 0.0001 5, 10 10.00 0.0100 7, 9 30.00 0.0100

Table 7 Protection costs.

Protection level 0 1 2 3 Protection reliability 0.5 0.8 0.9 0.99 Cost plan #1 (p.u.) 0 1 2 3 Cost plan #2 (p.u.) 0 1 1.25 3

Table 8 Cost impact on protection decisions at = 0 and � = 0.01.

Cost plan (l: protected line, i: protection level)

#1 (2,3),(5,3),(8,3),(9,3) #2 (2,3),(3,2),(5,2),(7,2),(8,2),(9,2),(10,2)

Table 9 Scenario probabilities of the two cost profiles.

Scenario attacked lines

Load curtailment (MW)

Probability cost #1

Probability cost #2

2, 3 6.25 0.0100 0.0010 2, 5 50.00 0.0001 0.0010 2, 6 1.81 0.0100 0.0100 2, 8 8.09 0.0001 0.0010 2, 9 2.97 0.0001 0.0010 2, 10 10.00 0.0100 0.0010 2, 11 1.03 0.0100 0.0100 3, 8 3.00 0.0100 0.0100

t w l m i b t m s

T I

Table 11 Load profile of the IEEE 24-bus system.

Bus Load (MW) Bus Load (MW)

1 108 13 265 2 97 14 194 3 180 15 317 4 74 16 100 5 71 17 0 6 136 18 333 7 125 19 181 8 171 20 128

5, 8 0.57 0.0001 0.0100 5, 10 10.00 0.0100 0.0100 7, 9 30.00 0.0100 0.0100

Finally, we study the impact of the attacker’s budget on pro- ection plans. In this experiment, we assume � = 0.001 and = 40 hereas the attacker’s budget varies between 1 and 3 transmission

ines. The results, summarized in Table 10, show that the invest- ent cost increases as the attacker’s budget increases. As a case

n point, the investment cost increases by 80% when the attacker’s udget is increased from two lines to three lines. The reason is that he attacks are more severe and the system investors need to equip

ore number of transmission lines with enhanced protections to ecure the safe operations of the power grid.

.2. Scenario reduction strategy

In the case study, we enumerated all attack scenarios and btained the load curtailments to describe the problem and our

able 10 mpact of attacker’s budget on protection plans.

Attacker’s budget (l: protected line, i: protection level) Total cost (p.u.)

1 – 0 2 (2,3),(5,2) 5 3 (2,3),(5,2),(7,1),(9,3) 9

9 175 21 0 10 195 22 0 11 0 23 0 12 0 24 0

methodology. Our model included all potential attack scenarios for the 6-bus test system to obtain the optimal protection deci- sions. We were able to include all scenarios since the test system was small. However, it is not possible to enumerate and include all potential scenarios for large systems since it is known that MILP solvers suffer from the curse of dimensionality. Therefore, we need to reduce the number of potential scenarios to handle larger power systems.

Our strategy to reduce the number of potential scenarios is based on two principals. First, it is more likely that the attack damages are more severe if the attackers target the transmission lines in the same neighborhood. Therefore, we consider the incident transmis- sion lines of a bus and those of its adjacent buses a neighborhood. Secondly, it is likely that the attacker attempts to form an island by attacking N transmission lines assuming that the attacker has the knowledge of the structure of the system. Islands could happen when a series of buses are connected and those buses are adjacent to less than N buses. Thus, we consider the incident transmission lines to these connected buses a special neighborhood as well. Next, we find all combinations of 1, 2, .. ., N transmission lines in each neighborhood to form the list of the potential scenarios and remove the repeated scenarios from the list.

4. Experimental results

To show the efficacy of our model in larger power systems and the importance of the scenario reduction strategy, we test the per- formance of our proposed protection optimization model on the IEEE 24-bus and IEEE 57-bus test systems introduced in [33].

4.1. 24-Bus test system

The IEEE 24-bus test system consists of 38 transmission lines, 24 buses and 33 generators. The IEEE 24-bus test system is shown in Fig. 2. The load profile is given in Table 11 and the protection levels are as provided in Table 2. We refer the readers to [33,32] for additional systems data.

We set the threshold value to 50 MW and the risk tolerance value to 0.01. We assume that the attacker may target three trans- mission lines at most simultaneously. Therefore, the total number of potential attack scenarios is 9177 scenarios including attacks to 1, 2 and 3 transmission lines. The number of attack scenarios is reduced to 2513 by applying the proposed scenario reduction strategy, which accounts for 73% reduction in total number of sce- narios. The optimal protection decision is obtained and provided in Table 12.

To show the efficacy of our model, we enumerated all attack scenarios and obtained the load curtailments, which took more than 12 h CPU time. The attack scenarios that result in load curtail- ment, their load curtailments and corresponding probabilities after implementing the protection plan, given in Table 12, are listed in

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Fig. 2. The IEEE 24-b

Table 12 Protection decision at = 50 MW and � = 0.01.

(l: protected line, i: protection level) Total cost

T u h

no-protection level on the optimal decision. Assuming = 0 MW and � = 0.01, we find the optimal protection cost where R1 varies

(2,3),(4,3),(9,3),(10,3),(11,1),(12,1) (13,1),(23,3),(28,3),(29,3)

able 13. Notice that attack scenarios in which load curtailment is nder the threshold value are marked with an asterisk and could ave a probability greater than the risk tolerance value.

Next, we show the protection decision when the power system perators are more conservative and set the threshold value to zero,

= 0. The results are provided in Table 14.

us test system.

Next, we study the effect of threshold value on protection plans in the IEEE 24-bus test system. The risk tolerance value is set to 0.01, � = 0.01, in the experiment whereas the threshold value, , varies between 0 and 250 MW. The protection plans are summa- rized in Table 15. The results show that lower threshold values necessitate protection of more number of transmission lines as well as more utilizing more number of higher-reliability protection mechanisms.

Furthermore, we analyze the impact of the reliability level of the

between 0.05, . . ., 0.79. The results are summarized in Fig. 3. Notice that the optimal decision is not sensitive to the reliability of the no-protection level, R1, when it is less than 0.68.

N. Nezamoddini et al. / Electric Power Systems Research 143 (2017) 329–338 335

Table 13 Load curtailment under the attack scenarios for the IEEE 24-bus test system.

Scenario # Attacked lines Load curtailment (MW) Probability

1 3, 9 71 0.00500 2 4, 8 74 0.00500 3 5, 10 136 0.00500 4 19, 23 194 0.00500 5* 1, 4, 10 41 0.00005 6 1, 8, 10 115 0.00250 7 2, 6, 7 180 0.00250 8 2, 6, 27 180 0.00250 9 7, 23, 29 165 0.00005 10 7, 24, 28 110 0.00250 11 11, 12, 13 171 0.00800 12* 11, 16, 17 18.1 0.05000 13* 12, 16, 17 11.5 0.05000 14* 13, 16, 17 14.5 0.05000 15* 21, 22, 23 24 0.00250 16 23, 27, 29 165 0.00005 17 24, 27, 28 110 0.00250 18 25, 26, 28 212 0.00250 19 29, 34, 35 181 0.00250 20 29, 36, 37 309 0.00250

Table 14 Protection decision at = 0 MW.

� (l: protected line, i: protection level) Total cost

0.001 (2,1),(3,3),(4,3),(5,2),(6,3),(8,2),(9,2) (10,3),(12,1)(13,3),(16,1),(17,3) (19,2),(21,1),(23,3),(24,1),(25,1) (28,3),(29,3),(35,1),(37,1),

0.01 (2,3),(8,3),(9,3),(10,3),(11,1),(12,1),(13,1) (16,1),(17,1)(23,3),(28,3),(29,3)

0.05 (3,1),(4,1),(5,1),(6,1),(8,1),(9,1),(10,1) (13,1),(17,1)(19,1),(23,1),(28,1),(29,1)

0.10 (2,1),(3,1),(4,1),(10,1),(13,1) (16,1),(23,1),(28,1),(29,1)

Table 15 Protection decision at � = 0.01.

(l: protected line, i: protection level) Total cost

0 (2,3),(8,3),(9,3),(10,3),(11,1),(12,1),(13,1) (16,1),(17,1)(23,3),(28,3),(29,3)

50 (2,3),(4,3),(9,3),(10,3),(11,1),(12,1) (13,1),(23,3),(28,3),(29,3)

100 (2,3),(10,3),(11,1),(12,1),(13,1) (23,3),(28,3),(29,3)

150 (2,3),(11,1),(12,1),(13,1),(23,3) (25,1),(26,1),(28,1),(29,3)

200 (26,2),(28,1),(29,3) 6 250 (36,3) 3

Fig. 3. The effect of the reliability of the no-protection level on optimal protection decision.

Table 16 Load profile of the IEEE 57-bus system.

Bus Load (MW) Bus Load (MW) Bus Load (MW)

1 55 20 2.3 39 0 2 3 21 0 40 0 3 41 22 0 41 6.3 4 0 23 6.3 42 7.1 5 13 24 0 43 2 6 75 25 6.3 44 12 7 0 26 0 45 0 8 150 27 9.3 46 0 9 121 28 4.6 47 29.7 10 5 29 17 48 0 11 0 30 3.6 49 18 12 377 31 5.8 50 21 13 18 32 1.6 51 18 14 10.5 33 0 52 4.9 15 22 34 0 53 20 16 43 35 6 54 4.1

17 42 36 0 55 6.8 18 27.2 37 0 56 7.6 19 3.3 38 14 57 6.7

4.2. 57-Bus test system

The IEEE 57-bus test system consists of 80 transmission lines, 57 buses and 7 generators. Fig. 4 shows the IEEE 57-bus test systems. The load profile is given in Table 16 and the protection levels are as provided in Table 2. We refer the readers to [33,32] for additional systems data.

We set the risk tolerance value to 0.01 and assume that the attacker may target three transmission lines at most simulta- neously. Therefore, the total number of potential attack scenarios is 85, 400 scenarios including attacks to 1, 2 and 3 transmission lines. The number of attack scenarios is reduced to 8612 by applying the proposed scenario reduction strategy, which accounts for 90% reduction in the total number of scenarios. The optimal protection decision considering the scenario reduction strategy is provided in Table 17.

Furthermore, we show the protection decision when the power

system operators conservatively set the threshold value to zero, = 0. The results are summarized in Table 18. The results confirm that conservative designs necessitate higher reliability protections

Table 17 Protection decision at � = 0.01.

(l: protected line, i: protection level) Total cost

70 – 0 60 (80,3) 3 50 (41,3) 3 40 (13,1),(16,3),(17,3),(28,1),(33,1)

(40,2),(41,3),(48,2),(61,1),(63,3) 20

30 (13,1),(16,3),(17,3),(19,3),(28,1),(33,3) (34,3),(41,3),(45,3),(61,1),(63,3),(80,3)

20 (16,3),(17,3),(20,3),(33,3),(34,3),(35,2) (36,1),(41,3),(42,3),(60,1),(61,3),(62,1), (63,3),(64,3),(67,3),(68,3),(79,1)

10 (4,3),(16,3),(17,3),(19,1),(20,2),(28,1) (29,1),(33,1),(34,1),(36,1),(40,3),(41,1) (42,2),(43,2),(44,2),(45,3),(46,2),(47,2) (48,2),(49,1),(53,1), (57,3),(59,2),(60,2) (61,2),(62,1),(63,3),(64,3),(67,2),(68,2) (69,2),(70,2),(80,2)

0 (4,3),(16,3),(17,3),(19,1),(23,1),(28,1) (29,2),(30,2),(31,2),(32,2),(34,3),(35,1) (37,2),(38,2),(39,2),(40,2),(42,2),(43,2) (44,2),(46,2),(47,2),(48,2),(49,2),(55,3) (56,3),(57,3),(59,2),(60,2),(61,2),(63,2) (64,2),(65,2),(67,2),(68,2),(69,2),(70,2) (77,3),(80,2)

336 N. Nezamoddini et al. / Electric Power Systems Research 143 (2017) 329–338

Fig. 4. The IEEE 57-bus test system.

Table 18 Protection decision at = 0 MW.

� (l: protected line, i: protection level) Total cost

0.001 (4,2),(13,2),(16,2),(17,2),(20,3),(21,3),(23,1) (26,3),(27,3),(29,3),(30,3),(31,2),(32,2),(33,2) (34,3),(35,2),(37,2),(38,2),(39,3),(40,3),(42,3) (43,3),(44,3),(46,3),(47,3),(48,3),(49,1),(51,2) (55,2),(56,2),(57,3),(58,2),(59,3),(60,3),(61,3) (62,1),(63,3),(64,3),(65,3),(67,3),(68,3),(69,3) (70,3),(71,3),(72,2),(75,3),(76,2),(77,3),(80,3)

123

0.01 (4,3),(16,3),(17,3),(19,1),(23,1),(28,1) (29,2),(30,2),(31,2),(32,2),(34,3),(35,1) (37,2),(38,2),(39,2),(40,2),(42,2),(43,2) (44,2),(46,2),(47,2),(48,2),(49,2),(55,3) (56,3),(57,3),(59,2),(60,2),(61,2),(63,2) (64,2),(65,2),(67,2),(68,2),(69,2),(70,2) (77,3),(80,2)

0.05 (4,1),(16,1),(17,1),(21,1),(26,1),(27,1) (29,1),(30,1),(31,1),(32,1),(33,1),(34,1) (37,1),(38,1),(39,1),(40,1),(42,1),(43,1) (44,1),(46,1),(47,1),(48,1),(55,1),(56,1) (57,2),(59,1),(60,1),(61,1),(63,1),(64,1) (65,1),(67,1),(68,1),(69,1),(70,1),(71,1) (75,1),(77,2),(80,1)

0.10 (4,1),(9,1),(16,1),(17,1),(19,1),(29,1),(30,1) (34,1),(39,1),(40,1),(42,1),(43,1),(44,1) (46,1),(47,1),(48,1),(55,1),(56,1),(57,1) (59,1),(60,1),(61,1),(64,1),(65,1),(67,1) (68,1),(69,1),(70,1),(77,1),(80,1)

Table 19 Effect of protection costs on optimal decisions at = 0 and � = 0.01.

Cost plan (l: protected line, i: protection level)

#2 (4,2),(16,2),(17,2),(19,1),(23,1),(26,2),(27,2) (28,1),(29,2),(30,2),(31,2),(32,2),(33,2),(34,2) (35,1),(37,2),(38,2),(39,2),(40,2),(42,2),(43,2)

(44,2),(46,2),(47,2),(48,2),(49,1),(55,2),(56,2) (57,3),(59,2),(60,2),(61,2),(62,1),(63,2),(64,2) (65,2),(67,2),(68,2),(69,2),(70,2),(71,2),(75,2) (77,3),(80,2)

as well as more number of transmission lines with enhanced pro- tections.

To study the effect of protection costs in larger systems, we compare the protection decisions under the cost profiles, given in Table 7, and summarized the results in Table 19. The model favors to replace expensive high-reliability protection schemes with more number of the relatively cheaper schemes.

5. Discussion and future research

In this paper, the necessity of the power grid resilience against physical attacks is discussed. However, modern power grids are heavily relied on information and communication technologies that could be maliciously targeted by cyber-attackers to tamper with the grid. Simultaneous cyber-physical attacks could put the

er Systems Research 143 (2017) 329–338 337

s f c a

e c r T t l m n c d

o t m a l s a e s o w t o c t c s s r l s t p o t p 2 r r s r I c o n o i

s g a

Table 20 Computational times.

Test system Computational time

N. Nezamoddini et al. / Electric Pow

afe and secure operations of the power systems at high risks. To urther extend power grid resiliency, it is necessary to develop omprehensive protection models that address cyber and physical ttacks together and determine a more inclusive protection plan.

Furthermore, we proposed an effective scenario reduction strat- gy that significantly reduces the number of scenarios and the omputational time accordingly. However, we believe that more esearch needs to be done to improve the computational efficiency. here are two general approaches to reduce the computational ime in this problem, reducing the number of scenarios and paral- el computations. The former can be implemented by developing

ore efficient scenario reduction strategies whereas the latter ecessitates reformulating the proposed model such that parallel omputing techniques and decomposition methods such as Ben- ers decomposition and scenario decomposition can be utilized.

. Conclusions

The transmission system security is of the highest priorities f the power system stakeholders. To enhance the resiliency of he transmission system against physical attacks, the MILP opti-

ization model was developed. The model determines the optimal llocation of the enhanced protection schemes to transmission ines. The goal of the model is to minimize the investment costs uch that the risk of the load curtailment, caused by a malicious ttack, exceeding a certain threshold value be less than the risk tol- rance value. Considering the risk in protecting the transmission ystems against physical attacks is one of the main contributions f the paper. This contribution provides power system investors ith more flexibility comparing to the other models, which pro-

ect the system only against worst attack scenarios and are based n the unrealistic assumption that the protected transmission lines an no longer be attacked. The load curtailment is obtained using he modified DC-OPF constraints integrated to our model without onsidering the generation costs in the objective function. The rea- on is that the generation cost is not the priority when the power ystem security is compromised and the supply of power is dis- upted temporarily. In fact, any feasible solution that keeps the oad curtailment/shedding under the threshold value would be atisfactory in emergency situations. The only obstacle for using he proposed model on a much larger power system is the com- uter processing time, which is highly depending on the number f attack scenarios. To alleviate the problem, we proposed an effec- ive scenario reduction strategy. The performance of the proposed rotection optimization model was tested on the IEEE 6-bus, IEEE 4-bus and IEEE 57-bus test systems. We utilized the scenario eduction strategy and showed the efficacy of the strategy on both educing the number of scenarios and obtaining the global optimal olutions. The proposed scenario reduction strategy successfully educed the number of scenarios by 73% and 90% in IEEE 24-bus and EEE 57-bus test systems, respectively. The experimental results onfirmed that conservative protection plans, in which higher risk f unsatisfied demand is not tolerated, necessitate protecting more umber of transmission lines as well as utilizing more number f the higher-reliability protection mechanisms, which together ncrease the investment costs substantially.

ppendix A. Attacks to generators

In this paper, we studied the resiliency of the transmission ystems against physical attacks. However, attackers may target eneration assets as well to endanger the sources of power gener- tion directly. Our proposed optimization model can be extended

[

IEEE 6-bus 3 s IEEE 24-bus 235 s IEEE 57-bus 4.2 h

to accommodate these attacks too. Eqs. (1), (7) and Eq. (15) need to be modified as follows and Eqs. (23) and (24) be added:

Z = min x,y

L∑ l=1

I∑ i=1 Cixli +

G∑ g=1

I∑ i=1 C′ i ygi (20)

pming (1 − ϑ�g) ≤ p�g ≤ pmaxg (1 − ϑ�g) ∀g ∈ G; ∀� ∈ ̊ (21)

u� = L∑ l=1

I∑ i=1

xliı�l ln((1 − Ri)) + G∑ g=1

I∑ i=1

ygiϑ�g ln((1 − R′i)) ∀� ∈ ̊ (22)

I∑ i=1 ygi = 1 ∀g ∈ G (23)

ygi ∈ {0, 1} ∀g ∈ G; ∀i ∈ I (24) where C′

i is the cost of the generation protection level i; ygi is the

binary decision variable which equals 1 if generator g is equipped with protection level i and 0 otherwise; ϑ�g is a binary input param- eter which equals to one if the generator g is interdicted in the attack scenario � and 0 otherwise and R′

i is the reliability index of

the generator protection type i.

Appendix B. Computational time analysis

All experiments were performed on a 64-bit laptop with an Intel Core i5 2.4 GHz processor and 8 GB RAM. We used IBM ILOG CPLEX Optimization Studio 12.6 as the optimization solver in our exper- iments. The attack scenarios are obtained using MATLAB R2012a and MatPower [32]. The computation times in MATLAB are trivial.

Table 20 summarizes the computational time for obtaining the optimal protection decisions for the studied test systems. The com- putation time increases for the larger power systems since the number of potential attack scenarios increase significantly.

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