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Integration of Preventive and Emergency Responsesfor Power Grid Resilience Enhancement

Gang Huang, Student Member, IEEE, Jianhui Wang, Senior Member, IEEE, Chen Chen, Member, IEEE,Junjian Qi, Member, IEEE, and Chuangxin Guo, Senior Member, IEEE

Abstract—Boosting the resilience of power systems is one ofthe core requirements of smart grid. In this paper, an integratedresilience response framework is proposed, which not only linksthe situational awareness with resilience enhancement, but alsoprovides effective and efficient responses in both preventiveand emergency states. The core of the proposed frameworkis a two-stage robust mixed-integer optimization model, whosemathematical formulation is presented in this paper as well.To solve the above model, an algorithm based on the nestedcolumn-and-constraint generation decomposition is provided, andcomputational efficiency improvement techniques are proposed.Preventive response in this paper considers generator re-dispatchand topology switching, while emergency response includes gen-erator re-dispatch, topology switching and load shedding. Severalnumerical simulations validate the effectiveness of the proposedframework and the efficiency of the solution methodology. Keyfindings include: 1) in terms of enhancing power grid resilience,the integrated resilience response is preferable to both indepen-dent preventive response and independent emergency response;2) the power grid resilience could be further enhanced by utilizingtopology switching in the integrated resilience response.

Index Terms—Blackouts, emergency response, generator re-dispatch, integrated resilience response, load shedding, naturaldisasters, optimization, preventive response, resilience, resiliencedefinition, resilience enhancement, resiliency, robust optimization,situational awareness, topology switching.

I. INTRODUCTION

AS a direct impact of climate change, the frequency andintensity of natural disasters have largely increased over

the past decades and are expected to continuously increasein the future [1]. Natural disasters can cause power outages;in fact, they are the leading cause of blackouts (e.g., 80% ofall major power outages between 2003-2012 were caused bynatural disasters [2]), which affect millions of people and costthe U.S. economy alone billions of dollars each year [3]. Withother infrastructures and our society as a whole increasinglydepending on electricity [4], it is vitally important to providecontinuous electric power, especially against natural disasters.

This work is supported in part by the Key Program of National Natural Sci-ence Foundation of China (51537010), the National Basic Research Program(973 Program, 2013CB228206), the China Scholarship Council, and the U.S.Department of Energy Office of Electricity Delivery and Energy Reliability.

G. Huang and C. Guo are with the College of Electrical Engineer-ing, Zhejiang University, Hangzhou, Zhejiang 310027, China (e-mail:huanggang@zju.edu.cn; guochuangxin@zju.edu.cn).

J. Wang is with the Department of Electrical Engineering, SouthernMethodist University, Dallas, TX 75205, USA and the Energy SystemsDivision, Argonne National Laboratory, Argonne, IL 60439, USA (email:jianhui.wang@ieee.org).

C. Chen, and J. Qi are with the Energy Systems Division, Argonne Na-tional Laboratory, Argonne, IL 60439, USA (e-mail: morningchen@anl.gov;jqi@anl.gov).

Adaptation

Planning Operation

Recovery

Resilience

Planning

Preventive

Response

Emergency

Response

Resilience

Restoration

Resilience Response

Fig. 1. The milestones of resilience enhancement strategies. Here, the scopeof this paper is outlined in the red arrow shape, and the blue storm imageindicates natural disasters.

To make the power grid stronger and smarter against naturaldisasters, the concept of resilience was recently introduced[3]–[7]. It is different from the concept of reliability; the focusof reliability is on high-probability events, while the focus ofresilience is on high-impact events. However, although thereis wide agreement in both academia and industry that powergrid resilience enhancement is of key importance [3], [5]–[7], there is no agreement yet on the resilience definition. Inthe literature, over 70 definitions for resilience can be foundin different disciplines [8], and some of them are completelydifferent from others. But, as [8] pointed out, these definitionsvary between two features: adaptation and recovery. Here, by“adaptation” we mean the process of changing in oder to makethe system suitable for a new situation, and “recovery” meansthe process of returning to a normal condition after a periodof disturbance. In the context of power systems, these twofeatures could also be found among all the different definitions[4]–[7]. Thus, in this paper, we propose defining the powergrid resilience as the ability of power grids to adapt to disasterscenarios and recover to pre-disaster states.

Based on the above definition of resilience, resilience en-hancement strategies could be categorized into two groups:enhancing the adaptation ability and enhancing the recoveryability. On the other hand, following the traditional classifi-cation of power system practices, these strategies can also becategorized from the perspective of planning and from theperspective of operation, while the operation strategies canbe further divided by the three operating states—preventivestate, emergency state, and restorative state [9]—that powergrids will go through. As a result, we have in total fourtypes of power grid resilience enhancement strategies (i.e.,resilience planning, preventive response, emergency response,and resilience restoration), as depicted in Fig. 1.

Generally, resilience planning includes hardening [3], veg-etation management [10], distributed generation resource al-

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location [11], and so forth. These are important to enhancepower grid resilience, but this paper will focus on the operationstrategies, because they as the “smarter” measures could pro-vide more specific and therefore more cost-effective strategiesthan resilience planning [6]. Resilience restoration will alsonot be discussed here, as the focus of this paper is on theadaptation ability of power grids. There are many interestingworks on the resilience restoration, and readers interested in itare referred to [7], [12], [13]. To conclude, this paper aimsto enhance the resilience adaptation ability of power gridsfrom the perspective of operation. Therefore only preventiveresponse and emergency response, which can be collectivelycalled resilience response, will be included. The red arrowshape in Fig. 1 shows the scope of this paper.

In general, preventive response is comprised of the actionsavailable before disaster scenarios unfold, and emergencyresponse comprises the actions taken in the aftermath of adisaster. For simplicity, only the indispensable components ofpower grids (i.e., generators, transmission lines, and loads)will be taken into account in this paper, and other facilities, forexample, the emerging energy storage [14], are not considered.Accordingly, the specific strategies we will consider includegenerator re-dispatch, topology switching, and load shedding.As power grids in the preventive state are being operated tosatisfy all the demands without violating any operating con-straints [9], load shedding is considered only in the emergencystate. Generator re-dispatch and topology switching can beutilized in both preventive and emergency states, but evidentlythe emergency state will have fewer resources than the pre-ventive state. Nevertheless, although preventive response andemergency response both have resources to enhance powergrid resilience, they are traditionally deployed independently.

To further enhance the power grid resilience, this paperproposes integrating the preventive response and emergencyresponse. Other models that boost the power grid resiliencefrom the perspective of operation can also be found in theliterature [15]–[20], but they mainly utilize only independentemergency response. Independent preventive response is oftennot adequate to keep the generation-demand balance afternatural disasters unfold, and this will be verified in Section V.On the other hand, the topology switching we will investigateis also distinguished from that in the literature. The widelydiscussed topology switching in the literature is in fact thein-service lines (ISLs) switch off [21]–[26], but with thedevelopment of new facilities against natural disasters, theout-of-service lines (OSLs) switch on (e.g., the backup trans-mission lines [27]) has emerged, and this will be consideredalong with the ISLs switch off in this paper. Other possibleimplementations of OSLs switch on in the preventive stateinclude: 1) restoring the outage-scheduled transmission lines[28], 2) rescheduling or canceling the outage schedules [29].

The main contributions of this paper are as follows:

1) An integrated resilience response (IRR) framework isproposed to integrate the preventive response and emer-gency response. With the proposed IRR framework,situational awareness and resilience enhancement aredirectly linked.

2) The mathematical formulation of the core of the pro-posed IRR framework, which is a two-stage robustmixed-integer optimization (RoMIO) model, is pro-posed to support the decision-making process. With theRoMIO model, both the preventive response strategy andthe emergency response strategy can be derived.

3) To solve the RoMIO model, a solution methodologybased on the nested column-and-constraint generationdecomposition is presented, and computational effi-ciency improvement techniques are also provided.

Through the research conducted in this paper, two keyfindings can be made:

1) In terms of enhancing power grid resilience, the inte-grated resilience response is preferable to both inde-pendent preventive response and independent emergencyresponse.

2) The power grid resilience could be further enhanced byutilizing topology switching in the integrated resilienceresponse.

The remainder of this paper is organized as follows. SectionII describes the IRR framework. Section III presents the math-ematical formulation of the RoMIO model. Section IV givesthe solution methodology for the RoMIO model. Section Vprovides case studies along with analysis. Section VI containsa brief discussion of practical implications. The conclusion isdrawn in Section VII.

II. CONCEPTUAL FRAMEWORK

The IRR framework is based on the situational awareness,which will be discussed in Section II-A. Then, conceptualframework of the IRR will be given in Section II-B.

A. Situational Awareness

Situational awareness provides critical information aboutpower grids and natural disasters, which is the foundationfor resilience response decision making. In the situationalawareness, power outage prediction is of vital importancebecause it connects power grids to natural disasters.

Power outage prediction is a multidisciplinary researchfield. It is often accomplished through the development ofpower outage prediction models based on parameters of naturaldisasters. For example, to predict storm-related power outages,storm data including wind, rainfall, and storm surge are usedas inputs to a regression model in [30]. Since this paper aimsto investigate the resilience response strategies based on theresults of power outage prediction, we here do not specify theparticular prediction model or disaster data that are used topredict power outages; instead, we focus on the damage fromnatural disasters in this paper. The storm will be used as anexample, as it is one of the most severe natural disasters [7].

While there is an underlying assumption in this paper thatthe situational awareness is sufficient, insufficient situationalawareness could also impact the power grid resilience. Gener-ally, delayed, incorrect or deficient resilience response may bederived with insufficient situational awareness. This is anotherinteresting topic for research, and readers that are interestedin it are referred to [31]–[33].

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Activate

DeactivateObtain

outage prediction

Y

N

Perform

emergency

response

Perform

preventive

response

Scenario

retained?

Update

disaster information

Update

network topology

Update

system parameters

Emergency

Response

Preventive

Response

Situational

Awareness

Retain

possible worst

scenario(s)

with

emergency

response

Run the

RoMIO model

Run the

RoMIO-E model

Fig. 2. The integrated resilience response framework.

B. The Integrated Resilience Response Framework

Based on the situational awareness, here we propose theIRR framework to enhance power grid resilience. The flowchart of the framework is depicted in Fig. 2, and the responseprocess is summarized as follows:• Situational awareness: Activate the IRR framework when

the disaster is brewing. Update the disaster forecast in-formation from national meteorological services or localweather forecast offices, and obtain the power outageprediction based on it. Gather the obtained power outageprediction results and the latest information of powergrids (including the network topology and system param-eters), and they will serve as inputs to the next stage.

• Preventive response: Run the RoMIO model, whosemathematical formulation will be presented in SectionIII, to derive effective preventive and emergency responsestrategies. Speedily perform the derived preventive re-sponse when it is available, and retain the emergencyresponse strategies in accord with possible worst disasterscenario(s) for the next stage.

• Emergency response: Check whether the realized disas-ter scenario is retained during the preventive responsestage. If retained, the corresponding emergency responsestrategy previously derived from the RoMIO model willbe immediately performed; otherwise, run the RoMIO-E model, which is the emergency response module ofthe RoMIO model and will be presented in Section IIIas well, then perform the derived emergency response.When the emergency response has been performed, de-activate the framework for future use.

Considering the provided data from SCADA and WAMS,in this paper we will take into account the following sys-tem parameters: loads at each bus, initial generator outputs,generator capacities, generator ramp-up limits, transmissionline capacities, and transmission line parameters. The networktopology data that we will take into account include the buslocations and the transmission line status.

Some natural disasters can sweep across a large area fora relatively long period of time. To capture this spatial andtemporal dynamics of natural disasters, time horizon should

be considered in the IRR framework, and the above responseprocess could then work in a rolling manner. But here wewill focus on the integration of preventive and emergencyresponses without introducing the rolling mode, thus no timehorizon will be considered in this paper.

III. MATHEMATICAL FORMULATION

The mathematical formulation of the RoMIO model ispresented in this section. Sections III-A, III-B, and III-Cpertain to the modeling of preventive response, damage fromnatural disasters, and emergency response, respectively. Theentire RoMIO model and its abstract mathematical formulationare given in Section III-D.

A. Preventive Response

As previously mentioned, power grids in the preventive stateare being operated to satisfy all the demands without violatingany operating constraints. From an economic point of view, theminimum-cost operating point of the system is optimal. Butto enhance the power grid resilience, the load shedding costin the emergency state should also be considered during thepreventive state. Hence the objective of the preventive responsein the RoMIO model is:

min∑g∈G

cgpag +

∑d∈D

cdpcd,s, (1)

where cg is the offer price of generator g, cd is the sheddingprice of load d, pag is the power output of generator g in thepreventive state, and pcd,s is the power shed of load d in theemergency state.

Based on the traditional DC power flow model, the powerbalance within power grids is described as follows:∑g∈Gi

pag −∑

(i,j)∈Li

paij =∑d∈Di

Pd, i ∈ B (2)

(saij − 1)Mij ≤ paij +Bijθaij ≤ (1− saij)Mij , (i, j) ∈ L, (3)

where (2) represents power balance constraints for each bus,and (3) represents power balance constraints for each trans-mission line. Note that the modeling of topology switchinghas already been included in (3). Here, generator output pagand transmission line status saij are independent variables, lineflow paij and voltage angle θai are dependent variables. Pdis the power demand of load d, Bij = −1/Xij , where Xij

is the reactance of transmission line (i, j), and Mij is a bigM constant for transmission line (i, j), which can be easilychosen, for example, by Mij = Pmax

ij −Bij(Θmaxi −Θmin

j ).Following the convention in [23], [24], [34], each generator

capacity is limited as follows:

pag ≤ Pmaxg , g ∈ G. (4)

In addition, the generators are subject to ramp-up constraints:

pag − p0g ≤ P a,maxg , g ∈ G. (5)

Here, Pmaxg is the generator capacity, p0g is the initial generator

output, and P a,maxg is the generator ramp-up capacity in the

preventive state. The ramp-down constraints are ignored, as the

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focus of this paper is on power grid damage induced by naturaldisasters, which cause capacity deficiencies, not surpluses [34].

Each transmission line is limited as follows:

− Pmaxij saij ≤ paij ≤ Pmax

ij saij , (i, j) ∈ L, (6)

and each bus should meet the voltage angle limits:

Θmini ≤ θai ≤ Θmax

i , i ∈ B. (7)

Furthermore, although the resources are usually less limitedin the preventive state than that in the emergency state, thenumber of ISLs that we can switch off and the number ofOSLs that we can switch on are still limited against naturaldisasters. As a result, we have:∑

(i,j)∈L

s0ij(1− saij) ≤ KaI (8)

∑(i,j)∈L

(1− s0ij)saij ≤ KaO, (9)

where s0ij represents the initial state of transmission line (i, j),KaI and Ka

O are the quantity limits for the ISLs switch offand OSLs switch on respectively. After the employment ofpreventive response, transmission line (i, j) is in service ifsaij = 1 and out of service if saij = 0.

B. Damage From Natural Disasters

Damage from natural disasters can cause load shedding, andthe worst disaster scenario satisfies the following function:

max∑d∈D

pcd,s. (10)

Based on the natural disaster information, statistical modelsand simulation models can be utilized to predict power out-ages. This process corresponds to the situational awareness,which we previously discussed in Section II. As the focus ofthis paper is on investigating the resilience response strategiesbased on the results of power outage prediction, we do notspecify the particular prediction model or disaster data thatare used to predict power outages. Instead, we focus on thedamage from natural disasters in this paper. For brevity, thedamage from storms will be modeled here.

As the strength of storms could be reflected by the numberof damaged transmission lines [11], and many existing works(e.g., [30]) that aim to assess the impact of storms on powergrids using statistical methods also estimate the aggregatednumber of damage within a given area, we here assume thestrength of storms is predictable and the estimated maximumnumber of damaged transmission lines is known. Accordingly,the damage from storms can be modeled by an uncertaintyset based on the estimated maximum number of damagedtransmission lines as follows:∑

(i,j)∈L

(1− sbij) ≤ Kb, (11)

where Kb is the estimated maximum number of damagedtransmission lines, sbij = 0 indicates that line (i, j) will bedamaged and sbij = 1 indicates it will not be damaged.

The uncertainty set based on Kb is used because it isa tractable method given that the statistical information ofdamaged transmission lines is difficult to obtain. We heremodel the transmission lines because they are the most com-monly damaged electricity infrastructures against storms [35].The damage from other natural disasters could be similarlymodeled. Specifically, for those natural disasters that havesimilar effects of storms and will damage transmission lines(e.g., icing), a similar uncertainty set based on the estimatedmaximum number of damaged transmission lines could be for-mulated to model the damage; for other natural disasters thatwill affect other components (e.g., flooding mainly affects thegenerators rather than the transmission lines), an uncertaintyset based on the estimated maximum number of other damagedcomponents could then be utilized to model the damage. Inthe latter case, we mention that the status of other componentsmay be introduced, and the RoMIO model should be relevantlymodified to adapt to this change.

This paper assumes the situational awareness is sufficientand the estimated maximum number of damaged transmissionlines is known. Considering Kb with uncertainty and modelingthe damage from natural disasters in a different way are otherissues that will be interesting to research.

C. Emergency ResponseAfter natural disasters unfold, power grids enter the emer-

gency state and should be operated to satisfy as many demandsas possible. Thus, the objective becomes:

min∑d∈D

pcd,s. (12)

The power balance constraints of the system are similar tothat in the preventive state:∑g∈Gi

pcg −∑

(i,j)∈Li

pcij +∑d∈Di

pcd,s =∑d∈Di

Pd, i ∈ B (13)

(scij − 1)Mij ≤ pcij +Bijθcij ≤ (1− scij)Mij , (i, j) ∈ L (14)

where generator output pcg , transmission line status scij , andpower shed pcd,s are independent variables, line flow pcij andvoltage angle θci are dependent variables; the rest of thesymbols are consistent with that in the preventive state.

Similar to the preventive state, each generator capacity islimited as follows:

pcg ≤ Pmaxg , g ∈ G, (15)

and the generators are subject to emergency state ramp-upconstraints:

pcg − pag ≤ P c,maxg , g ∈ G. (16)

Note that the ramp-up constraints for emergency state are notthe same as that for preventive state, because generators inthe emergency state will usually have shorter time to rampup. Generally, we have P c,max

g ≤ P a,maxg .

Each transmission line and each bus are limited similarly tothat in the preventive state:

− Pmaxij scij ≤ pcij ≤ Pmax

ij scij , (i, j) ∈ L (17)

Θmini ≤ θci ≤ Θmax

i , i ∈ B. (18)

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In addition, the following constraints are involved when theload shedding is performed:

0 ≤ pcd,s ≤ Pd, d ∈ D. (19)

The constraints for ISLs switch off and OSLs switch on inthe emergency state are given as follows:∑

(i,j)∈L

saijsbij(1− scij) ≤ Kc

I (20)

∑(i,j)∈L

(1− saij)sbijscij ≤ KcO (21)

scij ≤ sbij , (i, j) ∈ L, (22)

where KcI and Kc

O are the quantity limits for ISLs switchoff and OSLs switch on in the emergency state. After theemployment of emergency response, transmission line (i, j)is in service if scij = 1 and out of service if scij = 0.

Furthermore, as the emergency state has fewer resilienceresources than the preventive state, the emergency state mayhave not only tighter ramp-up capacities for generators (i.e.,P c,maxg ≤ P a,max

g ), but also tighter switching limits for trans-mission lines. To reflect this difference in topology switchinglimits, we assume that the OSLs in the preventive state areunavailable to the emergency state, and emergency responsecould only switch on the lines that are previously switchedoff by the preventive response. Another reason behind thisassumption is that some sources of OSLs in the preventivestate, for example, restoring the outage-scheduled transmissionlines [28], need a relatively long time that the emergency statecannot afford. Thus, we have:

scij ≤ s0ij + saij , (i, j) ∈ L. (23)

D. Integration of Preventive and Emergency Responses

Based on Sections III-A–III-C, the entire RoMIO model canbe given as follows:

min (1)

s.t. (2)− (9)max (10)

s.t. (11)min (12)

s.t. (13)− (23).

(24)

However, it is difficult to directly solve the above model,because there are quadratic terms and cubic terms in (20)–(21). To deal with this issue, we introduce binary variablessij,1 = saijs

bij , sij,2 = sbijs

cij , and sij,3 = saijs

bijs

cij , then (20)–

(21) become: ∑(i,j)∈L

(sij,1 − sij,3) ≤ KcI (25)

∑(i,j)∈L

(sij,2 − sij,3) ≤ KcO, (26)

where sij,1, sij,2, and sij,3 are all products of multiple binaryvariables, and they can be linearized by:

s =∏k∈N

sk ⇐⇒

s ≤ sk, k ∈ Ns ≥∑k∈N

sk − card(N ) + 1, (27)

where card(·) is the number of elements in a set, and sk (k ∈N ) and s are binary variables.

Due to the above relaxation, the objective functions andconstraint functions of the RoMIO model become eitherlinear or mixed-integer linear now. Its abstract mathematicalformulation can be given as follows:

mins1,x1

cT1 x1 + cT3 x3

s.t. A1

[sT1 x

T1

]T ≤ b1maxs2

cT3 x3

s.t. A2s2 ≤ b2mins3,x3

cT3 x3

s.t. A3

[sT1 x

T1 s

T2 s

T3 x

T3

]T ≤ b3,

(28)

where s1, x1, s2, s3, and x3 are made up of saij , {pag , paij , θai },sbij , {scij , sij,1, sij,2, sij,3}, and {pcg, pcd,s, pcij , θci }, respectively.

When natural disasters unfold, the first two levels of the tri-level problem (28) are determined, and only s3 and x3 remainundecided. This corresponds to the emergency response mod-ule of the RoMIO model, and we refer to it as the RoMIO-Emodel. Note that the RoMIO-E model is a single-level mixed-integer linear optimization model, which can be efficientlysolved using the state-of-the-art MIP (i.e., mixed-integer linearprogramming) solvers. But the entire RoMIO model is muchharder to solve because it is a tri-level problem with binarydecision variables in each level. In the next section, we willpropose a solution methodology to solve it efficiently.

IV. SOLUTION METHODOLOGY

The RoMIO model is a tri-level mixed-integer linear opti-mization problem, and the nested column-and-constraint gen-eration (NC&CG) decomposition framework proposed in [36]is able to solve this kind of problem. However, a generalalgorithm based on the NC&CG decomposition can be verytime-consuming, and this will impose practical limitations onthe application of the IRR framework against natural disasters.In this section, we will present our solution methodology andthe techniques we use to efficiently solve the RoMIO model.

A. NC&CG Decomposition-Based AlgorithmThe tri-level problem (28) can be decomposed into a single-

level min problem as the master problem and a bi-level max-min problem as the subproblem:

mins1,x1,si3,x

i3,η

cT1 x1 + η

s.t. cT3 xi3 ≤ η

A1

[sT1 x

T1

]T ≤ b1A3

[sT1 x

T1 s∗iT2 siT3 xiT3

]T ≤ b3∀i ∈ {1, · · · , k}

(MP-I)

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maxs2

mins3,x3

cT1 x∗1 + cT3 x3

s.t. A2s2 ≤ b2A3

[s∗T1 x∗T1 sT2 s

T3 x

T3

]T ≤ b3,(SP-I)

where (MP-I) and (SP-I) will be iteratively solved to providethe lower bound and upper bound for (28), respectively. Here,η is a newly introduced variable, k is the iteration number,and variables denoted by an asterisk (∗) in (MP-I) or (SP-I)represent the optimal values derived from each other. Aftereach iteration, k is updated by adding 1, and new variablesand constraints will be generated and added to (MP-I).

It has been proved that the above iteration will terminatein finite steps and the optimal value can be achieved [36].Here, (MP-I) is a classical mixed-integer linear programmingproblem and can be directly solved with the state-of-the-artMIP solvers, but (SP-I) is a bi-level problem with integers ineither level and cannot be straightforwardly solved. Thus, werewrite (SP-I) in a tri-level form as follows:

maxs2

mins3

minx3

cT1 x∗1 + cT3 x3

s.t. A2s2 ≤ b2A3

[s∗T1 x∗T1 sT2 s

T3 x

T3

]T ≤ b3.(29)

Then it can be decomposed into the following master prob-lem and subproblem, which will also be iteratively solved toprovide upper bound and lower bound for (SP-I), respectively:

maxs2,x

j3,λ

j ,τcT1 x

∗1 + τ

s.t. τ ≤ cT3 xj3

A2s2 ≤ b2A3

[s∗T1 x∗T1 sT2 s

∗jT3 xjT3

]T ≤ b3AT

3,5λj = −c3 (MP-II)

cT3 xj3 = (A3,1−4

[s∗T1 x∗T1 sT2 s

∗jT3

]T − b3)Tλj

λj ≥ 0

∀j ∈ {1, · · · , k′}

mins3,x3

cT1 x∗1 + cT3 x3

s.t. A3

[s∗T1 x∗T1 s∗T2 sT3 x

T3

]T ≤ b3, (SP-II)

where λj represents the dual variables of the constraintA3

[s∗T1 x∗T1 sT2 s

∗jT3 xjT3

]T ≤ b3 in the (SP-II) problem, τis a newly introduced variable, k′ is the iteration number, andnew variables and constraints will be generated and added to(MP-II) after each iteration. Note that

[A3,1−4 A3,5

]= A3.

B. Computational Efficiency Improvement Techniques

Theoretically, both Karush-Kuhn-Tucker conditions (KKT)and strong duality theory (SDT) can be used in the NC&CGdecomposition. But they will both introduce bilinear terms,and it is fundamentally more difficult to deal with bilinearterms than with linear ones. As a result, the algorithm can beeffective, but not efficient, especially when a large number ofbilinear terms are introduced.

When applying the KKT, bilinear terms are introduced dueto the following constraint:

(b3 −A3

[s∗T1 x∗T1 sT2 s

∗jT3 xjT3

]T) ◦ λj = 0, (30)

where “◦” denotes the component-wise multiplication.When the SDT is applied, the constraint that introduces

bilinear terms becomes:

cT3 xj3 = (A3,1−4

[s∗T1 x∗T1 sT2 s

∗jT3

]T − b3)Tλj . (31)

We already have A3 =[A3,1−4 A3,5

], and A3,1−4 can

be further referred to as[A3,1 A3,2 A3,3 A3,4

]. Note that

A3,1, A3,2, A3,3, A3,4, and A3,5 here represent the blockmatrices of A3, corresponding to s1, x1, s2, s3, and x3,respectively. In (30) and (31), s2, xj3, and λj are the variables.Thus, the number of bilinear terms in (30) will be determinedby the amount of nonzero terms in A3,3 and A3,5, while thenumber of bilinear terms in (31) will be determined by theamount of nonzero terms in A3,3 only.A3,3 is a relatively sparse matrix, and according to (13)–

(19), (22)–(23), and (25)–(27), the number of nonzero termsin A3,3 and A3,5 can be derived as follows:

NA3,3= 4card(L) (32)

NA3,5= 12card(L) + 5card(G) + 6card(B), (33)

where card(L), card(G), and card(B) represent the number oftransmission lines, generators, and buses, respectively.

The number of bilinear terms in (30) is NA3,3 + NA3,5 ,while the number in (31) is NA3,3

, which means that muchfewer bilinear terms will be introduced if the SDT is appliedto the RoMIO model. Furthermore, the above difference isonly for one calculation of (MP-II), and this calculation willbe repeated several times for one calculation of (SP-I), whileseveral calculations of (SP-I) will be required to solve thewhole problem. Due to this cumulative effect, the differencein the number of bilinear terms will be greatly enlarged.

Thus, from an efficiency point of view, we propose usingthe SDT in our solution methodology because it could providebetter computational efficiency for the RoMIO model, and thiswill be validated in Section V.

A linearization technique to deal with the bilinear termsinduced by the SDT is provided as follows:

y = λs

λ ∈ R≥0s ∈ {0, 1}

⇐⇒

y ≥ 0

y ≤ λy ≤Ms

y ≥ λ−M(1− s)λ ∈ R≥0s ∈ {0, 1}

(34)

where y is a newly introduced variable, M is a large number,λ ∈ R≥0 and s ∈ {0, 1} represent the elements of decisionvariables λj and s2 respectively.

V. ILLUSTRATED CASES

We apply case studies on three different systems here,including a modified version of the PJM five-bus system,the IEEE one-area RTS-96 system, and the IEEE three-area

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RTS-96 system. The effectiveness of the proposed integratedresilience response will be verified, and the efficiency of theproposed SDT-based solution methodology will be investi-gated. We note that the emergency state decision making (i.e.,the RoMIO-E model), as we previously stated in Section III-D,is a classical mixed-integer linear programming problem, andit can be directly and efficiently solved using the state-of-the-art MIP solvers. Thus we will focus on verifying theefficiency of the proposed solution methodology to solve theentire RoMIO model for the preventive state decision making.All the tests here are carried out on a 2.90-GHz Intel(R)Core(TM) i7-4600M based laptop, and Gurobi 6.5 [37] is usedas the MIP solver with optimality tolerance set to be 1×10−3.The maximum time limit for preventive state decision makingis set as 1 hour, and “NA” indicates the methodology fails tosolve the problem within the maximum time limit.

A. PJM Five-Bus System

The PJM five-bus system [38], depicted in Fig. 3, has fourgenerators, three loads, and seven transmission lines (includingone OSL in the preventive state). The system data we use aregiven in Appendix A. The ramp-up capacity in the emergencystate is set to be 25% of that in the preventive state. Thequantity limits for both ISLs switch off and OSLs switch onin preventive and emergency states are set to be the numberof OSLs in the preventive state.

1 2

3

45

Fig. 3. The PJM five-bus system. Note that the dashed line in the figurerepresent the OSL in the preventive state.

As previously stated, independent preventive response (re-ferred to as “PR”) includes generator re-dispatch in the pre-ventive state, and independent emergency response (referredto as “ER”) includes generator re-dispatch and load sheddingin the emergency state; we will use them as benchmarks forour case studies. Based on the PR and ER, we will investigatethe benefits of the integrated resilience response (referred to as“IRR”), which includes generator re-dispatch in the preventivestate, and generator re-dispatch and load shedding in theemergency state. Furthermore, we will also investigate thebenefits of the IRR with topology switching in both preventiveand emergency states (referred to as “IRR-TS”).

Table I gives the load shed with the PR, ER, IRR, andIRR-TS when the estimated maximum number of damagedtransmission lines (i.e., Kb) varies. Here, “5” indicates thatthe response strategy cannot keep the generation-demandbalance after disasters unfold.

From Table I, it can be seen that the PR fails to keep thepower balance in all of the seven cases. This is because inde-pendent preventive response aims to withstand contingencieswith only pre-disturbance strategies, and this will not work

TABLE ILOAD SHED OF THE PJM FIVE-BUS SYSTEM UNDER DIFFERENT Kb

Kb Load shed (MW)PR ER IRR IRR-TS

1 5 189 39 02 5 429 300 3003 5 639 489 3004 5 639 489 4895 5 688 638 4896 5 688 638 6387 5 688 638 638

under severe disturbances like natural disasters. This confirmsthe necessity of emergency response to keep the power balanceagainst natural disasters.

It can also been observed that while the ER could keepthe power balance against natural disasters, much more loadwill have to be shed, compared to the IRR or IRR-TS. Forexample, when Kb = 1, the ER has to shed 189 MW tokeep the power balance, but the IRR has to shed only 39MW, and the IRR-TS does not have to shed any load. Thisshows that integrated resilience response is preferable to bothindependent preventive response and independent emergencyresponse in terms of enhancing power grid resilience, and thepower grid resilience could be further enhanced by utilizingtopology switching in the integrated resilience response.

The total cost of the ER, IRR, and IRR-TS under differentKb and the corresponding operating cost in the preventivestate are given in Table II. We can see that the total costcould be greatly reduced if we utilize the IRR or IRR-TSrather than the ER. For example, the total cost of the ERis $206,520 when Kb = 1, but the total cost of the IRR is$59,945 while the total cost of the IRR-TS is $16,463. Onthe other hand, the operating cost of the IRR or IRR-TS doesnot increase a lot compared to the ER. In fact, we can seethat the operating cost could even decrease if the IRR-TSis applied. For example, when Kb = 2, the operating costis reduced from $17,520 to $16,163 by utilizing the IRR-TSrather than the ER. This confirms the cost-effectiveness of theintegrated resilience response. We note that while the IRR andIRR-TS in some cases have the same load shed (please seeTable I), the IRR-TS could have lower operating cost becausethe topology switching provides more flexibility to the systemand the system could therefore be operated with lower cost.The operating cost of the ER keeps the same because thegenerator re-dispatch in the emergency state will not influencethe operating cost in the preventive state.

We also investigate the influence of generator ramp-upcapacity on power grid resilience here. The emergency stateramp-up capacity (i.e., P c,max

g ) is investigated because itwill depend on the disaster severity. The base values of thecapacities are kept the same as that in Appendix A, and TableIII gives the simulation results of the system with the ER,IRR, and IRR-TS when the emergency state ramp-up capacityvaries from 20% to 180%. Here, Kb is assumed to be 3.

From Table III, it can be seen that larger ramp-up capacities

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TABLE IITOTAL COST AND OPERATING COST OF THE PJM FIVE-BUS SYSTEM

UNDER DIFFERENT Kb

Kb Total cost ($) Operating cost ($)ER IRR IRR-TS ER IRR IRR-TS

1 206,520 59,945 16,463 17,520 20,945 16,4632 446,520 320,315 316,163 17,520 20,315 16,1633 656,520 509,077 320,315 17,520 20,077 20,3154 656,520 509,637 508,970 17,520 20,637 19,9705 705,520 655,675 509,637 17,520 17,675 20,6376 705,520 655,675 655,375 17,520 17,675 17,3757 705,520 655,675 655,375 17,520 17,675 17,375

TABLE IIILOAD SHED OF THE PJM FIVE-BUS SYSTEM UNDER DIFFERENT P c,max

g

P c,maxg Load shed (MW)

ER IRR IRR-TS

20% 669 519 30940% 662 512 30260% 654 504 30080% 647 497 300

100% 639 489 300120% 632 482 300140% 624 474 300160% 617 467 300180% 609 459 300

can cause less load to be shed in order to keep the powerbalance. Note that when the IRR-TS is applied, load shed isno longer reduced when the P c,max

g is larger than 60% of thebase value. This is because the load at Bus-2 is 300 MW, andwhen Kb = 3, this load cannot be served as long as Line 1-2and Line 2-3 are damaged. In other words, the IRR-TS is notable to alleviate this situation with larger P c,max

g here becausethe load shed is not caused by the output limit of generators.

Table IV gives the computational time to solve the IRRproblem and IRR-TS problem with the KKT-based solutionmethodology and the SDT-based solution methodology. Wecan see that the proposed SDT-based methodology is alwaysfaster to solve either problem. But a big difference cannotbe observed here because the PJM five-bus system is small.To further compare these two methodologies, we will conductresearch on larger systems in the next subsections.

B. IEEE One-Area RTS-96 System

The IEEE one-area RTS-96 system is the first versionof the IEEE Reliability Test System, which was developedto be a reference system to test and compare results fromdifferent power grid operation strategies. An updated versionof the system can be found in [39], and we apply a slightmodification to the transmission line data, which could befound in Appendix B. The modified system has 12 generators,36 transmission lines (including 34 ISLs and 2 OSLs in thepreventive state), and 17 loads.

TABLE IVCOMPUTATIONAL TIME FOR IRR AND IRR-TS OF THE PJM FIVE-BUS

SYSTEM UNDER DIFFERENT Kb

Kb Solving IRR (s) Solving IRR-TS (s)KKT SDT KKT SDT

1 0.576 0.514 2.470 1.1192 1.281 1.016 1.837 1.4053 0.691 0.516 1.936 1.3404 1.172 1.034 0.936 0.7215 0.892 0.827 1.588 1.3626 0.451 0.421 0.957 0.5467 0.452 0.420 0.482 0.407

When Kb varies from 1 to 10, Table V gives the corre-sponding load shed of the system with the PR, ER, IRR, andIRR-TS.

TABLE VLOAD SHED OF THE IEEE ONE-AREA RTS-96 SYSTEM UNDER

DIFFERENT Kb

Kb Load shed (MW)PR ER IRR IRR-TS

1 5 739 64 02 5 1,139 356 2893 5 1,242 590 3564 5 1,522 766 5905 5 1,772 1,016 7666 5 1,772 1,250 1,0167 5 1,834 1,303 1,2508 5 1,834 1,312 1,3039 5 1,834 1,366 1,303

10 5 1,850 1,366 1,312

From Table V, we can again see that independent preventiveresponse is not able to keep the power balance even whenKb = 1. This emphasizes the necessity of applying emergencyresponse against natural disasters. On the other hand, althoughindependent emergency response could always keep the powerbalance with load shedding, a large portion of the load shed bythe emergency response could be saved if we apply integratedresilience response, and the load shed could be further reducedif topology switching is utilized in the integrated resilienceresponse. For example, when Kb = 2, the ER has to shed1,139 MW to keep the power balance, but the IRR and IRR-TS have to shed only 356 MW and 289 MW respectively.

The total cost and operating cost of the ER, IRR, and IRR-TS here follow the same trend as that in Table II, thus theyare not presented for simplicity. For the same reason, the loadshed under different P c,max

g is also not presented here.The computational time to solve the IRR and IRR-TS under

different Kb is provided in Table VI. From this table, it can beseen that the KKT-based solution methodology fails to solveany of the problems within the maximum time limit, but theproposed SDT-based methodology could efficiently solve allthe cases for the IRR problem and IRR-TS problem. Thisconfirms the efficiency of the proposed solution methodology.

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In addition, we can see that the computational time willapproximately increase with the growth of Kb, and althoughthe topology switching in the integrated resilience responsefurther enhances the power grid resilience, it also increasesthe computational time. But, for the IEEE one-area RTS-96 system, both the IRR problem and IRR-TS problem canbe efficiently solved by the proposed methodology, as themaximum time needed is 62.47 seconds.

TABLE VICOMPUTATIONAL TIME FOR IRR AND IRR-TS OF THE IEEE ONE-AREA

RTS-96 SYSTEM UNDER DIFFERENT Kb

Kb Solving IRR (s) Solving IRR-TS (s)KKT SDT KKT SDT

1 NA 1.12 NA 3.072 NA 1.78 NA 2.953 NA 4.30 NA 8.514 NA 9.34 NA 29.655 NA 8.82 NA 35.976 NA 8.18 NA 30.947 NA 19.87 NA 32.728 NA 19.12 NA 44.599 NA 22.88 NA 62.47

10 NA 40.56 NA 56.01

C. IEEE Three-Area RTS-96 System

The IEEE three-area RTS-96 system is the latest versionand largest one of the IEEE Reliability Test System. To in-vestigate the computational efficiency of the proposed solutionmethodology on larger systems, here we perform a third casestudy on the IEEE three-area RTS-96 system. Each area ofthe system shares the same parameters as that in Section V-B,where we assume there are two OSLs in the preventive statein Area-A. The data for the interconnections between areascould be found in [40]. The modified system has in total 36generators, 110 transmission lines, and 51 loads.

Table VII gives the load shed of the system with the PR,ER, IRR, and IRR-TS when Kb varies from 1 to 10. Notethat “NA” in the table indicates that we fail to get the optimalsolution within the maximum time limit.

The observations we made in previous case studies couldalso be seen in this system:

• The independent preventive response cannot keep thepower balance in any of the ten cases.

• The independent emergency response could keep thepower balance with load shedding.

• Compared with the independent preventive response andindependent emergency response, the integrated resilienceresponse could greatly enhance the power grid resilience.And with topology switching in the integrated resilienceresponse, the load shed could be further reduced. Forexample, when Kb = 3, we need to shed 2,006 MWload to keep the power balance with the ER, but we onlyneed to shed 308 MW if the IRR is applied and 289 MWif the IRR-TS is applied.

TABLE VIILOAD SHED OF THE IEEE THREE-AREA RTS-96 SYSTEM UNDER

DIFFERENT Kb

Kb Load shed (MW)PR ER IRR IRR-TS

1 5 1,648 0 02 5 1,941 289 2893 5 2,006 308 2894 5 2,275 603 NA5 5 2,376 866 NA6 5 2,437 1,042 NA7 5 2,470 1,303 NA8 5 2,499 1,303 1,3039 5 2,532 1,366 1,303

10 5 2,532 1,366 1,303

But we note that the resilience benefit of topology switching issmaller than that in the IEEE one-area RTS-96 system, becausewe have the same number of OSLs in the preventive state butthe system is bigger now. This indicates that the benefits oftopology switching could be limited when applying to largesystems, as the number of OSLs in the preventive state willnot increase with the growth of system scale in reality due toconsiderations such as financial constraints.

We also note that while we could get all the optimalsolutions for the IRR problem, we fail to derive optimalsolutions for the IRR-TS problem in four of the ten cases.This indicates that topology switching introduces too muchcomputational burden to the RoMIO model. To better analyzethis problem, we provide the computational time to solve theIRR and IRR-TS in Table VIII.

TABLE VIIICOMPUTATIONAL TIME FOR IRR AND IRR-TS OF THE IEEE

THREE-AREA RTS-96 SYSTEM UNDER DIFFERENT Kb

Kb Solving IRR (s) Solving IRR-TS (s)KKT SDT KKT SDT

1 NA 3.87 NA 32.012 NA 5.70 NA 44.303 NA 20.51 NA 2,657.274 NA 22.93 NA NA5 NA 27.44 NA NA6 NA 25.32 NA NA7 NA 17.14 NA NA8 NA 33.10 NA 131.669 NA 41.53 NA 466.1710 NA 55.77 NA 1,849.56

From Table VIII, the computational efficiency of the pro-posed SDT-based methodology over the KKT-based methodol-ogy could again be proved. In addition, it is seen that althoughthe proposed solution methodology could quite efficientlysolve the IRR problem (with no more than 1 minute), itneeds much longer time to solve the IRR-TS problem. In fact,the proposed solution methodology cannot always derive theoptimal solution for the IRR-TS problem within the maximum

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time limit. This indicates that with topology switching consid-ered, the integrated resilience response problem will be muchharder to solve.

VI. PRACTICAL IMPLICATIONS

Before implementing the integrated resilience response, avariety of practical implications should be taken into account.

The first issue is on the feasibility of the proposed resilienceresponse in practice. While current practice in many areasindicates that preventive response and emergency response arenot only possible but also being done, some may argue thatemploying emergency response, especially topology switch-ing, after the damage of natural disasters is impractical becauseof potential threats to the power grid. This concern mainlylies on the dynamic process of power grids, as the focus ofthis paper is in fact on the system adequacy against naturaldisasters, and the analysis in this paper is from the steady statepoint of view. In other words, to reach a solid conclusion inpractice, the presented model would need to be modified toinclude constraints ensuring dynamic feasibility, or the derivedresults need to be further validated via dynamic simulation.

Although detailed procedures for ensuring the feasibilitybased on dynamic simulation studies is beyond the scope ofthis paper, we in this section provide the dynamic simulationusing PSS/E as an example of checking whether the systemcan settle down after the employment of emergency response.The IEEE one-area RTS-96 system in this paper is chosento be checked due to the availability of dynamic parameters.The data required to run the time-domain simulation could befound in [41], and the worst disaster scenario of the systemwith Kb = 1 is chosen as the representative case becauseother disaster scenarios require no topology switching in theemergency response. Following the convention in [42], weassume the damage occurs at t = 2s, then we performtopology switching 10 seconds later and generator re-dispatchafter another 10 seconds (10 seconds is chosen in [42] to allowenough time for the breaker to operate and transients to dampdown). Fig. 4 and Fig. 5 show the generator relative rotorangles and bus frequencies, respectively. It can be confirmedfrom Fig. 4 that the system could keep the transient stabilityduring the dynamic process of emergency response, and Fig.5 confirms that the system frequency could be recovered intime. In summary, the emergency response is not necessarilyantithetical to maintaining dynamic security.

In addition, although voltage problems can be associatedwith the process of rotor angles going out of step, voltageinstability can occur where angle stability is not an issue [43].Thus, the AC feasibility should also be studied and ensuredbefore the results can be implemented.

Another issue is the solution time. This paper has proventhat the integrated resilience response could greatly enhancethe power grid resilience, but it should be noted that computa-tional burden is therefore introduced. Though the problem ofintegrated resilience response without topology switching canbe efficiently solved by the proposed solution methodology,when topology switching is included, how to solve the modelefficiently in large systems is still an open question.

Fig. 4. Generator relative rotor angles of the representative case. Note thatrotor angles here are relative to the slack generator (i.e., Unit 4 in [39]).

Fig. 5. Bus frequencies of the representative case.

We also want to mention that several technologies arerequired to implement the integrated resilience response. Forexample, the transmission lines should be opened and closedquickly with sufficient situational awareness, and this requiresfurther investment in communication and switching technol-ogy. Other technologies that could enhance the performancesof generators or loads during either preventive state or emer-gency state [44]–[55] will also be beneficial to power grids, butwe note that a full cost-benefit analysis should be conducted tosupport the decision making. With the development of these“smart grid” technologies, the power grids would be muchsmarter and stronger against natural disasters.

VII. CONCLUSION

This paper proposes an integrated resilience response (IRR)framework to enhance the power grid resilience against naturaldisasters. The core of the proposed IRR framework is atwo-stage robust mixed-integer optimization (RoMIO) model,whose mathematical formulation and solution methodologyare both provided. Through the research undertaken in thispaper, we validate that the integrated resilience response is

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preferable to both independent preventive response and inde-pendent emergency response. In addition, we also prove thatpower grid resilience could be further enhanced by utilizingtopology switching in the integrated resilience response.

The proposed IRR framework could incorporate other re-sponse strategies that are not investigated in this paper, aslong as they can be modeled in the similar way to generatorre-dispatch, load shedding, or topology switching. The IRRframework in this paper is proposed to enhance the power gridresilience against natural disasters, but they can also be easilymodified to deal with other uncertainties that power grids face,for example, the cyber security and the massive integration ofrenewable energy resources.

APPENDIX A

The data of the PJM five-bus system are listed in TablesIX–XI. Among the transmission lines, Line 4-5B is the OSLin the preventive state.

TABLE IXGENERATOR DATA OF THE PJM FIVE-BUS SYSTEM

Bus P 0g (MW) Pmax

g (MW) Pa,maxg (MW) cg ($/MW)

1 210 210 60 153 323.49 520 100 304 0 200 50 405 466.51 600 150 10

TABLE XLOAD DATA OF THE PJM FIVE-BUS SYSTEM

Bus Pd (MW) cd ($/MW)

2 300 10003 300 10004 400 1000

TABLE XITRANSMISSION LINE DATA OF THE PJM FIVE-BUS SYSTEM

Line Xij Pmaxij Line Xij Pmax

ij

(p.u.) (MW) (p.u.) (MW)

1-2 0.0281 400 3-4 0.0297 3001-4 0.0304 300 4-5A 0.0297 2401-5 0.0064 300 4-5B 0.0297 2402-3 0.0108 300

APPENDIX B

The transmission line data of the IEEE one-area RTS-96system are given in XII. Here, Line 14-16B and Line 15-21Bare the OSLs in the preventive state.

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Gang Huang (S’15) is currently pursuing the Ph.D.degree in electrical engineering at Zhejiang Univer-sity, Hangzhou, Zhejiang, China. During 2015–2016,he was a visiting Ph.D. student with the EnergySystems Division, Argonne National Laboratory, Ar-gonne, IL, USA.

He is a recipient of the Chinese GovernmentScholarship in 2015. His research interests includepower grid operation and control, system resilience,and mathematical optimization with applications tophysical systems.

0885-8950 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2017.2685640, IEEETransactions on Power Systems

13

Jianhui Wang (M’07–SM’12) received the Ph.D.degree in electrical engineering from Illinois Insti-tute of Technology, Chicago, IL, USA, in 2007.

Presently, he is an Associate Professor with theDepartment of Electrical Engineering at SouthernMethodist University, Dallas, TX, USA. He alsoholds a joint appointment as the Section Leadfor Advanced Power Grid Modeling in the EnergySystems Division at Argonne National Laboratory,Argonne, IL, USA.

Dr. Wang is the secretary of the IEEE Power &Energy Society (PES) Power System Operations, Planning & EconomicsCommittee. He is an associate editor of Journal of Energy Engineering and aneditorial board member of Applied Energy. He has held visiting positions inEurope, Australia and Hong Kong including a VELUX Visiting Professorshipat the Technical University of Denmark (DTU). Dr. Wang is the Editor-in-Chief of the IEEE Transactions on Smart Grid and an IEEE PES DistinguishedLecturer. He is also the recipient of the IEEE PES Power System OperationCommittee Prize Paper Award in 2015.

Chen Chen (M’13) received the Ph.D. degree inelectrical engineering from Lehigh University, Beth-lehem, PA, USA, in 2013.

During 2013–2015, he worked as a PostdoctoralResearcher at the Energy Systems Division, ArgonneNational Laboratory, Argonne, IL, USA. Dr. Chen iscurrently a Computational Engineer with the EnergySystems Division at Argonne National Laboratory.His primary research is in optimization, communica-tions and signal processing for smart electric powersystems, cyber-physical system modeling for smart

grids, and power system resilience. He is an editor of IEEE Transactions onSmart Grid and IEEE Power Engineering Letters.

Junjian Qi (S’12–M’13) received the Ph.D. degreein electrical engineering from Tsinghua University,Beijing, China, in 2013.

Dr. Qi is currently a Postdoctoral Appointee atthe Energy Systems Division, Argonne NationalLaboratory, Argonne, IL, USA and a joint appointedArgonne Staff at the Computation Institute, Univer-sity of Chicago, Chicago, IL, USA. He was a visitingscholar at Iowa State University, Ames, IA, USA inFebruary–August 2012, and a Research Associate atthe Department of Electrical Engineering and Com-

puter Science, University of Tennessee, Knoxville, TN, USA in September2013–January 2015. Dr. Qi is the Secretary of the IEEE Task Force on“Voltage Control for Smart Grids”. His research interests include cascadingblackouts, power system dynamics, state estimation, synchrophasors, voltagecontrol, and cybersecurity.

Chuangxin Guo (M’10–SM’14) received the Ph.D.degree in electrical engineering from Huazhong Uni-versity of Science and Technology, Wuhan, Hubei,China, in 1997.

He is currently a Professor and the Vice Dean withthe College of Electrical Engineering, Zhejiang Uni-versity, Hangzhou, Zhejiang, China. Prior to joiningZhejiang University, he worked as the Director ofBeijing Dongfang Electronics Research Institute andthe Deputy Chief Engineer of Dongfang ElectronicsCo., Ltd. During August–October 2012, he was a

Senior Visiting Scholar at University of Washington, Seattle, WA, USA.