ieee transactions on smart grid, vol. 9, no. 2, march …dkundur/pub_pdfs/farhamkuntsg18.pdf ·...

IEEE TRANSACTIONS ON SMART GRID, VOL. 9, NO. 2, MARCH 2018 1205

A Cyber-Physical Control Framework forTransient Stability in Smart Grids

Abdallah Farraj, Member, IEEE, Eman Hammad, Student Member, IEEE, and Deepa Kundur, Fellow, IEEE

Abstract—Denial of service attacks and communication latencypose challenges for the operation of control systems within powersystems. Specifically, excessive delay between sensors and con-trollers can substantially worsen the performance of distributedcontrol schemes. In this paper, we propose a framework fordelay-resilient cyber-physical control of smart grid systems fortransient stability applications. The proposed control schemeadapts its structure depending on the value of the latency. As anexample, we consider a parametric feedback linearization (PFL)control paradigm and make it “cyber-aware.” A delay-adaptivedesign that capitalizes on the features of PFL control is pre-sented to enhance the time-delay tolerance of the power system.Depending on the information latency present in the smart grid,the parameters and the structure of the PFL controller areadapted accordingly to optimize performance. The improvedresilience is demonstrated by applying the PFL controller to theNew England 39-bus and WECC 9-bus test power systems follow-ing the occurrence of physical and cyber disturbances. Numericalresults show that the proposed cyber-physical controller cantolerate substantial delays without noticeable performancedegradation.

Index Terms—Cyber-physical systems, distributed control, dis-tributed energy resources, smart grid, system resilience, time-delay tolerance, transient stability.

I. INTRODUCTION

MODERN power grids employ control, communications,and sensor technologies to improve resilience and

efficiency. Such smart grid technologies can allow bidirec-tional information flow. In addition, the integration of morerenewable energy sources into the power grid can enablenontraditional control schemes. However, reliability of thecyber and physical assets of the smart grid is a paramountpriority.

Cyber and physical disturbances can affect the perfor-mance of smart grids. Events that lead to disruption includedenial of service attacks, false data injection attacks, cyber-physical switching attacks, and physical faults. Resilienceagainst attacks and faults must be addressed through a

Manuscript received September 24, 2015; revised March 5, 2016 andMay 17, 2016; accepted June 12, 2016. Date of publication June 20, 2016;date of current version February 16, 2018. This work was supported in partby the U.S. National Science Foundation under Grant ECCS-1028246, andin part by the Natural Sciences and Engineering Research Council of Canadaunder Grant RGPIN 227722. Paper no. TSG-01190-2015.

The authors are with the Department of Electrical and ComputerEngineering, University of Toronto, Toronto, ON M5S 3G4,Canada (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSG.2016.2581588

defense-in-depth paradigm whereby prevention, detection, andreaction approaches for protection are employed at variouslevels.

Preventative defence approaches employ mechanisms thatobstruct the execution of an attack in order to limit its impacton power systems. Examples of preventative strategies includeencryption and secure communication protocols that representan initial level of defense against cyber intrusions [1], [2];relays and circuit breakers are also a form of initial defenseto prevent the propagation of a severe fault [3], [4]. Detectionstrategies are employed when preventive defense approachesare unsuccessful in thwarting a disturbance; these strategiesuse models of abnormal behavior as well as system measure-ments to identify anomalies. Detection techniques can be usedto detect the occurrence of an unwanted system state [5],successful cyber attack [6], or a combination of both [7].Furthermore, reaction approaches involve using strategies torecover from a disturbance and include techniques to controlsystem operation [8]. In this work we focus on this last strat-egy, specifically to enhance power grid resilience through theuse of distributed controllers.

Parametric feedback linearization (PFL) distributed con-trollers are recently proposed in [9] and [10] to addresstransient stability of power systems following the occurrenceof a physical disturbance. The PFL controller utilizes an exter-nal energy storage system (ESS) to inject and absorb powerfrom the system in order to stabilize rotor speed and achievephase cohesiveness among the system generators.

For this work, we adopt a general multi-agent frameworkthat enables system level studies and cyber-physical interactionmodeling. We focus on the transient stability problem whichis ideal for investigating cyber-physical dependencies withina tractable paradigm. Other relevant issues including voltageand small-signal stability and wide-area control are beyondthe scope of this work. In addition, we specifically analyzeand apply the PFL controller in this study. Further, the frame-work incorporates the effects of denial of service (DoS) andswitching attacks. Specifically, we focus on control strategiesto provide greater resilience to these attacks.

In this article a framework for cyber-physical control insmart grid systems is proposed where the controller adaptsits structure and parameters based on communication latencyand the state of the cyber component of the grid. Further,a delay-adaptive design is presented for the PFL controller.Moreover, the delay-adaptive characteristic function of thePFL controller is evaluated for the New England 39-bus andWECC 9-bus test power systems. Also the performance of the

1949-3053 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.

mailto:[email protected]



http://ieeexplore.ieee.org

http://www.ieee.org/publications_standards/publications/rights/index.html

1206 IEEE TRANSACTIONS ON SMART GRID, VOL. 9, NO. 2, MARCH 2018

proposed cyber-physical control is numerically evaluated whenthe power system undergoes cyber and physical disturbances.

The rest of this paper is organized as follows. The prob-lem setting and the proposed framework are presented inSections II and III. A cyber-enabled PFL control is detailedin Section IV. Sections V and VI investigate the performanceof the controller under the proposed design. Conclusions andfinal remarks are shown in Section VII.

II. CONTROL FOR RESILIENT SMART GRIDS

The concept of resilience refers to the ability of a givensystem to bounce back from an external or internal disruption.Power system resilience is linked to the traditional concept ofpower system security that refers to the ability of a power gridto remain intact despite a physical contingency.

According to [11], power system control can be classifiedinto mechanical and electrical. Mechanical control subsystemsinclude fuel supply, boiler pressure, and turbine speed controls.Electrical control includes generator voltage, network, andload controls. Both categories of control are coupled throughan energy control center. The associated system dynamics canbe classified according to the time scale of a phenomena [11].For example, transient stability and governor control have timescale ranges from around a fraction of a second to tens ofseconds, respectively.

Transient stability describes the ability of the power systemto remain in synchronism when subjected to large distur-bances. Transient stability during the presence of a physicalfault can be achieved by maintaining both rotor speed synchro-nization and phase angle cohesiveness. Speed synchronizationrequires the rotor speeds of all the generators to agree asymp-totically with a common value typically set to 60 Hz andnormalized in this paper to 0. Phase angle cohesiveness meansthat the difference between the phase angle of the differentgenerators in the power system should be below a predefinedthreshold typically chosen to be 100◦.

Circuit breakers are used as a first line of defense toclear the faults within a power system. In transient stabil-ity studies, it is of interest to compute the critical clearingtime of these circuit breakers. The critical clearing time isrelated to the maximum power transfer in the pre-fault stateof the power system [11]. A traditional way of assessing apower system’s transient stability is to study transient energyfunctions based on Lyapunov’s method. For multi-machinepower systems, potential energy boundary surface (PEBS) andboundary controlling unstable equilibrium points (BCU) arewidely used. More information about traditional analysis ofthe angle stability problem in power systems can be foundin [11, Ch. 9].

The movement to a smarter grid involves the marriageof information technology with power delivery components.Smart grid cyber assets include the communications networkinfrastructure, information technology systems, computing ele-ments, data storage, and distributed controllers. Cyber datais collected over the power grid using sensors; for example,phasor measurements units (PMUs) can be used to report time-stamped voltage and current readings from different locations

around the power grid. This data is then transferred to dis-tributed or centralized controllers via communication links.The timely availability of high-granularity system data facili-ties new control schemes to better stabilize the power systemafter the occurrence of a disturbance.

Wide-area monitoring Systems (WAMS) improve overallsystem reliability through situational awareness and advanceddecision-making and control. PMUs are used to read currentand voltage phasors at the substation bus on the transmis-sion power network and send the readings at a specific rateto phasor data concentrators (PDCs). PMUs use global posi-tion system (GPS) clocks to synchronize and time-stamp thereadings in order to enable a direct access to the state of thepower grid. Further, a PDC receives 30-200 synchrophasorreports from PMUs per second, and it aligns the data fromthe multiple PMUs to provide a view of the overall powergrid. PMU-based wide-area control and monitoring applica-tions are of interest to the smart grid community as successfuloperation of such applications requires careful treatment ofdelays in the communication network. Examples of recentwork include [12]–[17].

Cyber security issues of smart grid systems have recentlysurfaced due to the increased implementation of smart gridapplications. It is observed that the shift to a cyber-enabledpower grid also introduces new system vulnerabilities thatexploit information systems which can lead to growing poten-tial for cyber and physical attacks on the power grid. Commonclasses of cyber and physical attacks on smart grid systemsinclude:

• False data injection attacks against state estimation: anadversary exploits the configuration of the power systemto introduce an arbitrary error into certain state variableswhile bypassing existing techniques for bad measurementdetection [18];

• Denial of service attacks: an adversary interrupts theoperation of the cyber component of the power grid byjamming the communication channels, attacking network-ing protocols, and flooding the network traffic. This attackleads to causing communication link failure and excessivedelays and consequently results in preventing the timelyexchange of information between the sensors, actuators,and control systems [19];

• Switching attacks: an adversary causes physical distur-bance in the power system by switching on and offone or more elements of the grid to cause instabil-ity within the power system. Effective switching attackscould be, for example, based on understanding the struc-ture of the power system and accessing system stateinformation [20]–[22].

Such types of attacks can lead to system instability. Given thehigh degree of recent research activity in false data injectionattacks, we focus in this work on the lesser investigated DoSand switching attacks.

Both cyber and physical disturbances can affect the per-formance of smart grid systems. Distributed control schemesthat rely on the availability of a cyber network presentopportunities to enhance the stability and resilience ofthe power grid by mitigating certain types of cyber and

FARRAJ et al.: CYBER-PHYSICAL CONTROL FRAMEWORK FOR TRANSIENT STABILITY IN SMART GRIDS 1207

Fig. 1. Multi-agent smart grid system. (a) New England test power system(b) Cyber-physical agent.

physical disturbances. Recent research activity in this areaincludes [9], [10], [23]–[26]. However, the impact of cyberattacks and communication latency on the performance of suchcontrol schemes must be carefully studied in order to fullyunderstand best practices for resilience.

We assert in this paper that resilience to cyber and physicalattacks must be more carefully addressed given the intentionaland targeting nature of the disturbance. Further, we believethat a distributed control paradigm is an appropriate responsestrategy to cyber attack. Essentially the process of control liesat the cyber-physical interface of the smart grid whereby itmakes use of sensor information to make decisions and actu-ate change on the physical system. Thus the control processhas the ability to inhibit the propagation of a cyber attack tothe (physical) power delivery network placing it at an effec-tive location within the overall smart grid. Consequently, wepropose in this work a cyber-physical control framework tomitigate intentional disturbances (DoS and switching attacks)and achieve transient stability in the face of naturally-occurringfaults.

III. A FRAMEWORK FOR CYBER-PHYSICAL CONTROL

In this section we adopt a general multi-agent frameworkto model the smart power grid. This framework enables sys-tem level studies and cyber-physical interaction modeling.We focus on control strategies that provide greater resilienceagainst faults, DoS attacks, and switching attacks.

A. System Model

We assume that the smart grid is comprised of N cyber-physical agents where each agent contains a synchronous

Fig. 2. WECC test power system.

generator, an associated sensor that provides information ongenerator rotor angle and speed, a distributed controller thatprocesses sensor data from local and neighboring agents, anda fast-acting ESS that can inject or absorb real power in thesystem depending on the value of the control signal. Further,a communication network connects the sensors, ESSs, anddistributed controllers of the smart grid system. The over-all multi-agent system is considered to be cyber-physical innature. The physical dynamics of each agent can depend onits own state (specifically, the state of its generator) as well asthe states of other agents in the system. As an example, weconsider the New England 10-generator 39-bus (physical) testpower system with associated cyber-physical agents as shownin Fig. 1 and the 9-bus WECC test system as shown in Fig. 2.

Traditionally, a centralized physical controller refers to ascheme where the states of all agents need to be collectedfor processing and decision making; this control approachmay require a significant communication overhead whichleads to potential cyber attacks. On the other hand, a decen-tralized controller would only require the state of its ownagent; this control scheme eliminates the need for signifi-cant communication infrastructure. However, a decentralizedapproach may experience long convergence times for the con-troller tasks. Furthermore, the controller makes use of itsown local state and those of its neighbors in a distributedcontrol paradigm; such scheme balances the communica-tion requirements with convergence speed. Fig. 3 depicts thecentralized, distributed, and decentralized control schemes.Mathematically, distinctions between these control approachescan be represented as [27]

ui =⎧⎨

⎩

fi(x) centralized controlfi(xi, x∗

i

)distributed control

fi(xi) decentralized control(1)

where ui is the output of the controller at agent i, xi is thephysical state of agent i, x = [x1, . . . , xN]T is the physicalstate of all agents in the system, and x∗

i is the state of theneighbor agents of agent i.


Fig. 3. Centralized vs. decentralized vs. distributed control.

B. Transient Stability

Using the previously-described multi-agent framework ofthe smart system, let N denote the number of generators inthe power system. Also, for Generator i, where i ∈ {1, . . . , N},let Pe,i, Pm,i, ωi, X′

di, δi, Mi, and Di denote its electricalpower (in pu), mechanical power (in pu), relative normalizedrotor speed (in pu), direct-axis transient reactance (in pu),rotor angle (in radians), inertia (in seconds), and dampingcoefficient (in seconds), respectively. The relative normal-ized rotor speed of Generator i is calculated here as ωi =(ωact

i − ωnom)/ωnom, where ωnom is the nominal angular rotorspeed of the power system and ωact

i is the actual angular rotorspeed of Generator i.

We employ the swing equation model to describe thedynamics of coupled synchronous generators in the powersystem. The swing equation links the rotor acceleration of asynchronous generator to the difference between the mechan-ical torque supplied by the prime mover and electromagnetictorque output of that generator. As such, this model is usedto describe the effects of any imbalance between mechani-cal input and electrical output powers during disturbances.Further, the Kron reduction technique [28] can be usedto eliminate bus nodes in a power system and reduce thepower network into nodes of dynamic generators; conse-quently, Kron reduction is used in this work to scale down theorder of the interconnections and determine effective mutualcouplings between synchronous generator pairs. The combi-nation of these models has recently been shown to effectivelycharacterize transient stability within power systems [9].

Let δi and ωi denote the derivatives of δi and ωi with respectto time, respectively. The swing equation model of Generator iis expressed as [29], [30]

δi = ωi

ωi = 1

Mi

(−Di ωi + Pa,i)

(2)

where Pa,i = Pm,i − Pe,i denotes the accelerating power ofGenerator i.

A Synchronous generator is typically equipped with powercontrol schemes to help adjust its internal settings in responseto changes and faults in the power grid. However, these localpower controls have slow reaction to rapid changes. As such,without external power control, synchronous generators cannot

alone achieve transient stability in the presence of a switchingattack or during a severe fault. Thus, through possible appli-cation of control strategies, transient stability can be achievedand/or the stability time can be enhanced. Consequently, exter-nal distributed controllers can represent a critical asset for theprotection and stability of smart grid systems. Applying a con-trolled fast-acting stabilizing ESS at Generator i’s bus modifiesthe swing equation to

δi = ωi

ωi = 1

Mi

(−Di ωi + Pa,i + ui)

(3)

where ui is the output of the ESS at Generator i’s bus. Thecontrolled ESS affects the dynamics of the synchronous gener-ator by injecting and/or absorbing real power at the associatedgenerator’s bus.

C. Cyber-Aware Control Scheme

Communication latency is an aggregate result of process-ing and propagation delays in the communication network.Delay also depends on the communication medium, topology,and protocols. Generally, sensor sampling and quantizationdelay, possible cryptographic delay if security processing isemployed, channel propagation delay, and queueing delay con-tribute to the overall latency. Furthermore, DoS attacks cancripple communications links to cause excessive delays. Inaddition, delay can be affected by intermediate nodes betweenthe source and destination (such as data and traffic concentra-tors and other controllers). We emphasize that the delay thatwe study in this work is the total delay between the sensorsand the controllers.

Communication delay poses a challenge for wide-areadamping controllers in power systems as shown in [31]–[33].Several works consider the development of a delay-adaptivecontrol; for example, [34]–[37] demonstrate that communi-cation latency complicates the design of real-time controlsystems. To damp inter-area oscillations, [33] explores a two-level control system that implements a second order Padéapproximation of communication delay. A similar approachusing a predictor-based H∞ control with a fourth order Padéapproximation of communication delay is investigated in [32].Because the measurements of the power system take cer-tain time before they affect the input of the controller, theclosed-loop control system is termed a dead-time system [32].


Furthermore, [21] and [38] demonstrate how communica-tion latency impacts the performance of recently-developedtransient stability control schemes in smart grid systems. Forexample, it is demonstrated in [38] that the performance of theflocking-based controllers deteriorates with increasing latencybetween sensors and controllers.

In contrast to (1) where the output of the controller isfunction of the physical state of the system (i.e., x), a “cyber-aware” controller of Generator i takes into consideration thecyber state of the network as demonstrated by

ui = fi(x, y) (4)

where in this case y represents the cyber state of the smart gridsystem. Further, time-delay tolerance is defined as the longestlag that a closed-loop control system can tolerate to keep thesystem stable [31]. One goal of the cyber-aware controlleris to enhance the time-delay tolerance of the power systemespecially during DoS attacks.

Variable-structure systems are nonlinear control systemscharacterized by ordinary differential equations with dis-continuous state functions [39], [40]. Such systems can beuseful in modeling and analyzing the behavior of smartgrids. We take a simple, yet effective, approach to designa cyber-aware controller that mitigates the effects of longcommunication delays and lost cyber connectivity betweensystem agents. Specifically, building on the variable-structureconcept, latency is categorized into discrete ranges, basedon which the controller switches between predefined corre-sponding configurations depending on the delay range of themeasurements.

Let the communication latency between the sensors and thecontroller be termed τ . Then, a cyber-aware controller forGenerator i can take the following form

ui =

⎧⎪⎨

⎪⎩

f1(x, y) τ ≤ τ1f2(x, y) τ1 < τ ≤ τ2...

...

(5)

where f1, f2, . . . are predefined configurations of the controller.

IV. PARAMETRIC FEEDBACK LINEARIZATION CONTROL

A PFL controller is a tunable distributed controller thateasily integrates with generator governors. When a power sys-tem undergoes transient instability due to faults or switchingattacks, the PFL controller utilizes the physical state informa-tion of the power system to execute a feedback linearizationaction that synchronizes the generators more aggressively.

The utilization of PFL control for power systems (fullyor partially) decouples the dynamics of the physical systemresulting in an interesting system response against communi-cation delays. Specifically, a piecewise linear delay-adaptivecharacteristic function can be used to describe the behaviorof the power system under PFL control. Utilizing this charac-teristic function, a parameter of the PFL control is adjustedto account for the degree of information lag in the cybercomponents of the smart grid system.

A. “Physical” PFL Control

Centralized and decentralized PFL schemes are recentlyproposed in [9] and [10], respectively. A distributed flavorof this controller is also proposed in [23]. A centralizedPFL (CPFL) controller relies on collecting the power systemdata before taking a stabilizing action. On the other hand, adecentralized PFL (DPFL) controller only requires local mea-surements to compute the control signal. Further, a distributedPFL (DiPFL) control scheme utilizes the sensor readings of acluster of agents.

The CPFL controller requires receiving timely measure-ments of the rotor speed and phase angle of all synchronousgenerators in the power system in order to calculate the controlsignal. Mathematically, the CPFL control signal is expressedas [9]

uci = −(Pa,i + αi ωi

)(6)

where αi > 0 is called the frequency stability parameterof Generator i. The αiωi term will asymptotically drive thenormalized rotor speed of Generator i to 0. The CPFL con-troller fully cancels the nonlinear terms in the swing equationof Generator i provided that all system measurements areobtained. Consequently, the swing equation of the intercon-nected power system reduces into decoupled linear equationsafter implementing the CPFL controller.

Since the communication channels relaying the system mea-surements from the sensors to the controllers are vulnerableto cyber attacks and long communication delays, the DPFLcontroller only utilizes the measurements from the sensors sit-uated near the local generator bus. As a result, the acceleratingpower term (i.e., Pa,i) cannot be estimated and consequentlycannot be cancelled, resulting in a partially linearized controlsystem. Mathematically, the DPFL control signal is expressedas [10]

udi = −αiωi. (7)

Consider a power system that has been partitioned intonon-overlapping areas Sj ⊆ N, where j = 1, 2, 3, . . .. Thepower system can be partitioned into clusters depending onthe mutual physical coupling between generator pairs of thesystem. Thus, generators within an area have higher mutualcoupling. Then, following [41], a DiPFL control can be for-mulated for each area as a two-level control scheme. Inthe first control level, a feedback linearization controller isused to affect the rotor speed against a dynamic referencespeed, termed as ω. The first-level DiPFL control signal forGenerator i in area Sj is formulated as [23]

uDii = −αi(ωi − ω) . (8)

To eliminate static errors due to noise, false data injections,and equipment bias errors, ω is controlled with a proportionalcontroller at the second control level as

˙ω = − γi

Nj

∑

k∈Sj

ωk (9)

where γi > 0 is called the control update ratio and Nj is thenumber of generators in area Sj.


B. Robustness Analysis

We investigate the robustness of the PFL controller in thepresence of measurement uncertainty or unavailability. Someof the causes of measurement unreliability include:

• Excessive communication latency between the sensorsand the controllers during DoS attacks;

• Noisy measurements due to interference and noise incommunication channels;

• Sensor equipment bias and saturation;• False data injections;• Missing measurements due to unavailable sensors.

Here, the measurements must be estimated at the controllerside resulting in a possible difference between the actual andestimated values.

Let the estimated measurements of the relative normalizedrotor speed (ωi) and rotor angle (δi) be denoted as ωi andδi, respectively. We also model the uncertainty in the nonlin-ear component of the swing equation using Pa,i. The overallrelationships between the actual and estimated quantities arerepresented as

δi = (1 + eδi

)δi

ωi = (1 + eωi

)ωi

Pa,i = (1 + ePi

)Pa,i (10)

where the parameters eδi , eωi , and ePi capture the degreeof uncertainty in the rotor phase angle, rotor speed, andaccelerating power of Generator i, respectively.

The value of the feedback control signal for Generator i inthe presence of measurement uncertainty is then given by

uci = −(

Pa,i + αi ωi

)(11)

which leads to closed-system dynamics of the form

xi = Ai xi + fNL(xi) (12)

where

Ai =⎡

⎣0 1

0 − 1

Mi

[Di + αi

(1 + eωi

)]

⎤

⎦ (13)

and

fNL(xi) = [0,−ePi Pa,i

]T. (14)

We focus on the effects of measurement error by neglectingmodel uncertainty, and so we assume ePi 1. Thus, thesystem dynamics can be approximated as

xi = Ai xi. (15)

It can be shown that the eigenvalues of Ai are given by0 and −1

Mi

[Di + αi(1 + eωi)

]. A sufficient condition to ensure

that the nonzero eigenvalue lies in the left-hand plane is

eωi > −Di + αi

αi(16)

where we assume αi > 0 which is necessary for a stabilizingcontroller. Reformulating (16), we observe that

1 + eωi = ωi

ωi> −Di

αi. (17)

This implies that as long as the rotor speed estimate, ωi, has thecorrect sign as ωi, stabilization will occur. In fact, even if thesign of ωi is reversed, stabilization is possible as long as |ωi|is bounded to be less than |ωi|Di/αi. The reader is remindedthat both ωi and ωi represent incremental rotor speeds where0 corresponds to the utility frequency of 50 or 60 Hz.

The result in (17) indicates that the margin of stability isaffected by the inverse of αi. As such, when the communi-cation delay is substantial, the estimation of the system statevariables becomes less accurate, then decreasing the value ofα can enhance the system stability. Accordingly, varying thevalue of α can extend the time-delay tolerance of the systemespecially when the communication links between the sensorsand the controller experience excessive delays or during DoSattacks.

C. “Cyber-Physical” PFL Control

Under PFL control, we anticipate that the decoupling of thepower system dynamics would result in a direct piecewise lin-ear relationship between communication delay and the optimalfrequency stability parameter, where the parameters of this lin-ear relationship are characteristic of the power system understudy. It is to be noted that if δ is delayed, then the acceleratingpower term cannot be estimated correctly and so it may notcancel out perfectly. However, even though there is an incom-plete cancellation of Pa,i because of the communication delay,we can assume that if the delay is bounded, there is a bound onthis error. So if we neglect this error, the dominant dynamicsof the closed-control system are linear and decoupled.

A gain-scheduling control design is an approach to designnon-linear control systems. In this approach, rather than seek-ing a single robust controller for the entire operating rangeof a specific input parameter, the design parameters of thecontroller are made dependent on the specific value of thatinput parameter. Building on this concept, the “cyber-physical”PFL controller is proposed to have a gain-scheduling design.Consequently, the PFL controller for Generator i is proposedto be adaptive to a delay value of τ at time t as

uci(t) = −Pa,i(t − τ) − αi(τ )ωi(t − τ). (18)

In other words, the frequency stability parameter of the PFLcontroller is made adaptive to latency rather than being a fixed-value parameter.

Let α∗i (τ ) denote the values of the frequency stability

parameter that optimize the performance of the PFL controllerfor the various values of delay. Given the values of the com-munication latency are known to the controller for each sensormeasurement, then once a measurement is received by the PFLcontroller, the controller can apply the corresponding optimalvalue of the frequency stability parameter.

A cyber-physical PFL control that is robust to delays andextends the time-delay tolerance is proposed in this work tocombine the philosophies of variable-structure systems andgain-scheduling control design. The gain-scheduling approachis utilized where the frequency stability parameter is madeadaptive to the value of delay between the sensors and thecontrollers. Further, the variable-structure design means that


the cyber-physical PFL controller switches between predefinedcontrol schemes depending on the value of delay.

In this case we specify the control signal of the cyber-physical PFL controller as

ui =⎧⎨

⎩

uci(x, α∗

c

)τ ≤ τopt

uci(x, α∗(τ )) τopt < τ ≤ τmax

udi(xi, α

∗d

)τmax < τ

(19)

where α∗d is the optimum value of the DPFL controller’s fre-

quency stability parameter, and α∗c is the optimum value of

CPFL controller’s parameter when the latency is not greaterthan τopt; further, the frequency stability parameter is madeadaptive to the communication latency when the delay is upto τmax. As obvious from (19) the cyber-physical controllerutilizes the centralized form for τ ≤ τmax. However, when thedelay exceeds τmax, the controller switches to the decentralizedmode. Consequently, the proposed cyber-physical controlleremploys the variable-structure and gain-scheduling designconcepts. It is to be noted that τopt, τmax, and the optimalvalues of α are dependent on the power system.

The work in [24] proposes a two-tier smart grid controlbased on flocking concepts. To minimize communication over-head amongst the generators, different generators are groupedinto homogeneous clusters. Further, full communication con-nectivity amongst the generators of a cluster is assumed;however, inter-cluster connectivity is assumed in [24] to occurbetween the head generators in each cluster.

Our work is similar to that of [24] in that both contributionsconsider the problem transient stability of the power system.However, the proposed work is different in several ways; forexample, our controller changes its structure and parametersdepending on the value of the communication latency. In addi-tion, we employ feedback-linearization control instead of theflocking-based control. Moreover, our model adapts to the sit-uation of complete communication network loss by switchingto a decentralized mode of control. Finally, we assert thatour framework is general and thus does not solely apply toa specific power system.

D. Unavailable Sensors Case

Further, we propose a modified DiPFL controller to addressthe case when some cyber-physical agents do not possess theirown local sensors. Consequently, such agents do not have mea-surements of their local rotor angle and speed. Thus, to controlthe output of the local ESS we employ available readingsfrom other agents within the cluster. Given that the physi-cal coupling is strong within each area, the different agentsare expected to share close dynamics. As such, the state of anagent without a local sensor can be inferred from the otheragents in the cluster.

Specifically, consider the case when agent i in area Sj doesnot have an associated sensor; consequently, the values of δiand ωi are unknown. However other agents in Sj have sensorsand so the values of their rotor speed and angle are known andshared with all agents of Sj. Define the set Sj to be the set of allagents in Sj except agent i; i.e., Sj has Nj−1 agents. Followingthe results of (8) and (9), we propose that the control signal

TABLE INEW ENGLAND SYSTEM FAULT DETAILS

of the different agents in area Sj be calculated as

ui ={

−αi

(ωj − ω

)i = i

−αi(ωi − ω) i �= i(20)

where

ωj = 1

Nj − 1

∑

k∈Sj

ωk

˙ω = −γiωj . (21)

In this case the available readings from the agents of the areadetermine the control signal for each agent.

V. LATENCY CHARACTERISTIC FUNCTION

Here we try to find the latency characteristic function ofthe CPFL controller (i.e., the optimal values of α for the cor-responding values of τ ). The results of this study will beused in building the cyber-physical PFL controller of (19).We consider both the New England and WECC test powersystems.

For the following results, stability time of a generator ismeasured by finding the difference between the time afterwhich the relative normalized rotor speed of the generatoris restricted to a 0.8333% threshold (i.e., the time when theactual rotor speed of the generator is limited to ± 0.5 Hz) andthe time when the stabilizing controller is activated. Further,for the New England test power system, the average stabil-ity time and control power values do not take into accountGenerator 10’s results because it represents an equivalentgenerator cluster.

A. New England Power System

The New England 10-generator 39-bus test power system(shown in Fig. 1) is considered. The values of Mi’s and X′

di’sare found from [42] and [43] and the damping coefficients areset to 20 ms. Four case studies are considered in this work asshown in Table I. The power system is assumed to be runningin normal state from t = 0 to t = 0.5 s. A three-phase faultoccurs at the faulted bus at t = 0.5 s, then the tripped lineis removed to clear the fault at t = 0.6 s. Finally, the CPFLcontroller is activated on all generators at t = 0.7 s.

We evaluate the latency characteristic function for theNew England power system for communication latencies up to225 ms. Fig. 4 displays the relation between the communica-tion latency and the optimum values of the frequency stabilityparameter, stability time, and control power for this test sys-tem. For the results in this figure, the optimum values of α

refer to the set of frequency stability parameters that yield


Fig. 4. Optimal performance versus latency in the New England test power system.

Fig. 5. Optimal performance versus latency in the WECC test power system.

the lowest mean stability time for a certain communicationlatency.

It is noted from Fig. 4 that a high value of α makes the sta-bility time lowest for latency values up to 115 ms. However,for higher values of latency, a better strategy is to let the valueof α decline with increasing the value of latency. This obser-vation aligns with the results of (17) where it is observed thatdecreasing the value of α can enhance the system stabilitywhen there is a substantial communication latency.

Considering the four case studies mentioned in Table I, acurve fitting approach is used to find the optimal values ofα as a function of τ . Interestingly, it is found that the CPFLcontroller can adapt its frequency stability parameter using apiecewise linear characteristic function as

α∗(τ ) ={

1 τ ≤ 115 ms−8.86 τ + 2.02 115 ms < τ ≤ 225 ms.

(22)

As a result of (6), (19), and (22), the cyber-physical PFL con-troller is proposed for the New England test power system as

ui =⎧⎨

⎩

−Pa,i − ωi τ ≤ 115 ms−Pa,i + (8.86τ − 2.02)ωi 115 ms < τ ≤ 225 ms−α∗

dωi 225 ms < τ.

(23)

B. WECC Power System

Extending the above approach to the WECC 9-bus3-generator test power system (shown in Fig. 2), five casestudies are considered as shown in Table II. For simulating

TABLE IIWECC SYSTEM FAULT DETAILS

this power system, D1 = 5 ms, D2 = 1 ms, D3 = 2 ms,X′

d1 = 0.08 pu, X′d2 = 0.18 pu, X′

d3 = 0.12 pu, M1 = 50 ms,M2 = 15 ms, and M3 = 35 ms. A three-phase fault occurs atthe faulted bus at t = 0.5 s, then the tripped line is removedto clear the fault at t = 0.6 s, and the CPFL controller is acti-vated on all generators at t = 0.7 s. Fig. 5 displays the relationbetween τ and the optimum values of α, stability time, andcontrol power for the five test cases.

Considering the results of Fig. 5, and similar to the approachtaken in (22), curve fitting is employed to find the latencycharacteristic function for the CPFL controller as

α∗(τ ) ={

1 τ ≤ 15 ms−12.8 τ + 0.92 15 ms < τ ≤ 62.5 ms.

(24)

Consequently, the cyber-physical PFL controller is proposedfor the WECC test power system as

ui =⎧⎨

⎩

−Pa,i − ωi τ ≤ 15 ms−Pa,i + (12.8τ − 0.92)ωi 15 ms < τ ≤ 62.5 ms−α∗

dωi 62.5 ms < τ.

(25)


Fig. 6. Stability time of the PFL controller.

Fig. 7. Control power of the PFL controller.

VI. NUMERICAL RESULTS

In this section we numerically evaluate the performance ofthe proposed controller and compare the results with the tradi-tional “physical” PFL controller. For this study we apply bothcontrollers to the New England test power system; however,it is to be noted that similar results can be obtained for theWECC test power system.

A. New England Power System

The four test cases of Table I are considered for theNew England test power system. Stability time of the systemgenerators and the average control power are the measuresthat are used to evaluate the performance of the proposedcyber-physical PFL controller. The strategy of (23) is used,and α∗

d = 30 is applied when the controller is in the decen-tralized mode. Further, the performance is compared to thatof the delay-inadaptive traditional PFL controller where α isset to 1 regardless of delay values.

Fig. 6 illustrates the average stability time of the PFLcontroller. It is observed that when the frequency stabilityparameter is constant regardless of the value of latency, thePFL controller can stabilize the New England power sys-tem as long as the communication latency is below about150 ms. However, when α is varied to accommodate the com-munication latency as shown in (22), the cyber-physical PFLcontroller can stabilize the power system’s generators providedthat the latency is less than 225 ms. Further, for higher val-ues of latency, the cyber-physical PFL controller can switch tothe decentralized mode and still be able to stabilize the powersystem.

Further, Fig. 7 displays the average external power usedby the PFL controller. It is observed that the proposed cyber-physical PFL controller has a substantial power gain over the

Fig. 8. Response to concurrent physical and cyber disturbances.

Fig. 9. Performance when Generators 3 and 8 do not have associated sensors.

delay-inadaptive controller especially for high values of com-munication latency. Consequently, the proposed cyber-physicalcontrol scheme increases the robustness of the PFL con-troller to communication delays and increases the time-delaytolerance.

B. Numerical Example

Consider the New England test power system with an esti-mated average latency of 50 ms during normal operations.Assume that a three-phase fault occurs at Bus 17, Line 17-18is removed, and the PFL controller is activated at t = 0.5 s,0.6 s, and 0.7 s, respectively. Further, assume a DoS attack tar-gets the communication network at t = 0.8 s; consequently, thecommunication latency starts to increase. At t = 1.4 s, the DoSattack is stopped and the latency quickly starts to drop to nor-mal values. As a result of the DoS attack, the communicationlatency changes as shown in Fig. 8(a).

The cyber-physical PFL controller responds to the varyingnature of latency by adapting its α parameter as describedin (23) and shown in Fig. 8(b). When τ > 225 ms (for1.2 ≤ t < 1.5 s in this example), the controller switches tothe decentralized mode and α∗

d = 1.5 is used.

C. Unavailable Sensors Case

Consider the case when Generators 3 and 8 do not havetheir own local sensors. Consequently, the proposed cyber-physical controller utilizes the structure of (20) and (21). Thepower system generators are clustered in three separate areasas {1, 8, 10}, {2, 3, 9, 4, 5}, and {6, 7}. Assume that a three-phase fault occurs at Bus 11, Line 11-10 is removed, andthe PFL controller is activated at t = 0.5 s, 0.6 s, and 0.7 s,respectively. Fig. 9 displays the relative normalized rotor speedfor selected generators in the system. Results of this figureshow that the different generators stabilize quickly; however,


as expected, the generators that do not have local sensors takerelatively longer time to achieve stability.

VII. CONCLUSION

This article proposes a framework for cyber-physical con-trol to improve system resilience in smart grids. Specifically,the proposed control scheme adapts its structure and parame-ters depending on communication latency values between thesensors and the controllers in the power grid. A delay-adaptivedesign that capitalizes on the features of parametric feedbacklinearization (PFL) control is presented in this work in orderto enhance the time-delay tolerance of the power system andto react to cyber and physical attacks.

The performance of the proposed cyber-physical controlscheme is demonstrated when the PFL controller is appliedto the New England 39-bus and WECC 9-bus test powersystems following the occurrence of a physical disturbance.Numerical results also show that the proposed controller cantolerate substantial delays without noticeable degradation inperformance and is able to stabilize the power system effec-tively. Future directions of this work include investigatingother types of control schemes, incorporating other types ofcyber attacks, and investigating cyber-aware wide-area controlschemes.

REFERENCES

[1] T. Flick and J. Morehouse, Securing the Smart Grid: Next GenerationPower Grid Security. Amsterdam, The Netherlands: Syngress, 2011.

[2] W. Stallings, Network Security Essentials: Applications and Standards,5th ed. Harlow, U.K.: Pearson, 2013.

[3] S. H. Horowitz and A. G. Phadke, Power System Relaying, 4th ed.Chichester, U.K.: Wiley, 2014.

[4] B. Ravindranath and M. Chander, Power System Protection andSwitchgear. New Delhi, India: New Age Int., 2011.

[5] A. Abur and A. G. Expósito, Power System State Estimation: Theoryand Implementation. Boca Raton, FL, USA: CRC Press, 2004.

[6] R. Berthier, W. H. Sanders, and H. Khurana, “Intrusion detectionfor advanced metering infrastructures: Requirements and architec-tural directions,” in Proc. IEEE Int. Conf. Smart Grid Commun.(SmartGridComm), Gaithersburg, MD, USA, Oct. 2010, pp. 350–355.

[7] S. Zonouz et al., “SCPSE: Security-oriented cyber-physical state esti-mation for power grid critical infrastructures,” IEEE Trans. Smart Grid,vol. 3, no. 4, pp. 1790–1799, Dec. 2012.

[8] P. Kundur, Power System Stability and Control (EPRI Power SystemEngineering Series). New York, NY, USA: McGraw-Hill, 1994.

[9] A. K. Farraj, E. M. Hammad, and D. Kundur, “A cyber-enabled stabiliz-ing controller for resilient smart grid systems,” in Proc. IEEE PES Conf.Innov. Smart Grid Technol. (ISGT), Washington, DC, USA, Feb. 2015,pp. 1–5.

[10] E. M. Hammad, A. K. Farraj, and D. Kundur, “A resilient feedbacklinearization control scheme for smart grids under cyber-physical dis-turbances,” in Proc. IEEE PES Conf. Innov. Smart Grid Technol. (ISGT),Washington, DC, USA, Feb. 2015, pp. 1–5.

[11] P. W. Sauer and M. A. Pai, Power System Dynamics and Stability.Upper Saddle River, NJ, USA: Prentice-Hall, 1998.

[12] K. Zhu, M. Chenine, and L. Nordström, “ICT architecture impact onwide area monitoring and control systems’ reliability,” IEEE Trans.Power Del., vol. 26, no. 4, pp. 2801–2808, Oct. 2011.

[13] R. Liu, C. Vellaithurai, S. S. Biswas, T. T. Gamage, and A. K. Srivastava,“Analyzing the cyber-physical impact of cyber events on the powergrid,” IEEE Trans. Smart Grid, vol. 6, no. 5, pp. 2444–2453,Sep. 2015.

[14] J. W. Stahlhut, T. J. Browne, G. T. Heydt, and V. Vittal, “Latencyviewed as a stochastic process and its impact on wide area power sys-tem control signals,” IEEE Trans. Power Syst., vol. 23, no. 1, pp. 84–91,Feb. 2008.

[15] M. Mokhtari, F. Aminifar, D. Nazarpour, and S. Golshannavaz, “Wide-area power oscillation damping with a fuzzy controller compensating thecontinuous communication delays,” IEEE Trans. Power Syst., vol. 28,no. 2, pp. 1997–2005, May 2013.

[16] G. N. Ericsson, “Information security for electric power utili-ties (EPUs)—CIGRÉ developments on frameworks, risk assessment, andtechnology,” IEEE Trans. Power Del., vol. 24, no. 3, pp. 1174–1181,Jul. 2009.

[17] M. Chenine, J. Ullberg, L. Nordström, Y. Wu, and G. N. Ericsson,“A framework for wide-area monitoring and control systems interop-erability and cybersecurity analysis,” IEEE Trans. Power Del., vol. 29,no. 2, pp. 633–641, Apr. 2014.

[18] Y. Liu, P. Ning, and M. K. Reiter, “False data injection attacks againststate estimation in electric power grids,” ACM Trans. Inf. Syst. Security,vol. 14, no. 1, pp. 13–33, Jun. 2011.

[19] S. Liu, X. P. Liu, and A. El Saddik, “Denial-of-service (DoS) attackson load frequency control in smart grids,” in Proc. IEEE PESInnov. Smart Grid Technol. (ISGT), Washington, DC, USA, 2013,pp. 1–6.

[20] E. Hammad, A. M. Khalil, A. Farraj, D. Kundur, and R. Iravani,“Tuning out of phase: Resonance attacks,” in Proc. IEEE Int. Conf.Smart Grid Commun. (SmartGridComm), Miami, FL, USA, Nov. 2015,pp. 491–496.

[21] A. K. Farraj, E. M. Hammad, D. Kundur, and K. L. Butler-Purry,“Practical limitations of sliding-mode switching attacks on smart gridsystems,” in Proc. IEEE Power Energy Soc. Gen. Meeting (PESGM),Jul. 2014, pp. 1–5.

[22] S. Liu, S. Mashayekh, D. Kundur, T. Zourntos, and K. L. Butler-Purry,“A smart grid vulnerability analysis framework for coordinated vari-able structure switching attacks,” in Proc. IEEE Power EnergySoc. Gen. Meeting (PESGM), San Diego, CA, USA, Jul. 2012,pp. 1–6.

[23] E. Hammad, A. Farraj, and D. Kundur, “Paradigms and performance ofdistributed cyber-enabled control schemes for the smart grid,” in Proc.IEEE Power Energy Soc. Gen. Meeting (PESGM), Denver, CO, USA,2015, pp. 1–5.

[24] J. Wei and D. Kundur, “Two-tier hierarchical cyber-physical secu-rity analysis framework for smart grid,” in Proc. IEEE PowerEnergy Soc. Gen. Meeting (PESGM), San Diego, CA, USA, 2012,pp. 1–5.

[25] J. Wei and D. Kundur, “A flocking-based model for DoS-resilientcommunication routing in smart grid,” in Proc. IEEE Glob. Commun.Conf. (GLOBECOM), Anaheim, CA, USA, Dec. 2012, pp. 3519–3524.

[26] J. Wei, D. Kundur, T. Zourntos, and K. L. Butler-Purry, “A flocking-based dynamical systems paradigm for smart power system analysis,”in Proc. IEEE Power Energy Soc. Gen. Meeting (PESGM), San Diego,CA, USA, Jul. 2012, pp. 1–8.

[27] M. Andreasson, “Control of multi-agent systems with applications todistributed frequency control of power systems,” Licentiate thesis, KTHSchool Elect. Eng., Stockholm, Sweden, Mar. 2013.

[28] F. Dörfler and F. Bullo, “Kron reduction of graphs with applications toelectrical networks,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 60,no. 1, pp. 150–163, Jan. 2013.

[29] P. M. Anderson and A. A. Fouad, Power System Control and Stability(IEEE Power Systems Engineering Series). New York, NY, USA:IEEE Press, 1994.

[30] F. Dörfler and F. Bullo, “Synchronization and transient stability inpower networks and non-uniform Kuramoto oscillators,” in Proc.Amer. Control Conf. (ACC), Baltimore, MD, USA, Jun./Jul. 2010,pp. 930–937.

[31] H. Wu, K. S. Tsakalis, and G. T. Heydt, “Evaluation of time delay effectsto wide-area power system stabilizer design,” IEEE Trans. Power Syst.,vol. 19, no. 4, pp. 1935–1941, Nov. 2004.

[32] B. Chaudhuri, R. Majumder, and B. C. Pal, “Wide-area measurement-based stabilizing control of power system considering signal transmis-sion delay,” IEEE Trans. Power Syst., vol. 19, no. 4, pp. 1971–1979,Nov. 2004.

[33] S. Zhang and V. Vittal, “Design of wide-area power system damp-ing controllers resilient to communication failures,” IEEE Trans. PowerSyst., vol. 28, no. 4, pp. 4292–4300, Nov. 2013.

[34] B. Wittenmark, J. Nilsson, and M. Törngren, “Timing problems in real-time control systems,” in Proc. Amer. Control Conf. (ACC), vol. 3.Seattle, WA, USA, Jun. 1995, pp. 2000–2004.

[35] J. Nilsson and B. Bernhardsson, “Analysis of real-time control systemswith time delays,” in Proc. IEEE Conf. Decis. Control (CDC), vol. 3.Kobe, Japan, Dec. 1996, pp. 3173–3178.


[36] J. Nilsson and B. Bernhardsson, “LQG control over a Markov commu-nication network,” in Proc. IEEE Conf. Decis. Control (CDC), vol. 5.San Diego, CA, USA, Dec. 1997, pp. 4586–4591.

[37] J. Nilsson, B. Bernhardsson, and B. Wittenmark, “Stochastic analysisand control of real-time systems with random time delays,” Automatica,vol. 34, no. 1, pp. 57–64, Jan. 1998.

[38] A. K. Farraj, E. M. Hammad, J. Wei, D. Kundur, and K. L. Butler-Purry,“Performance evaluation of flocking-based distributed cyber-physicalcontrol for smart grid,” in Proc. IEEE Int. Conf. Smart Grid Commun.(SmartGridComm), Venice, Italy, Nov. 2014, pp. 964–969.

[39] D. Liberzon, Switching in Systems and Control (Systems and Control:Foundations and Applications). Boston, MA, USA: Birkhauser, 2003.

[40] A. Sabanovic, L. Fridman, and S. K. Spurgeon, Variable StructureSystems: From Principles to Implementation (IET Control EngineeringSeries). London, U.K.: Inst. Eng. Technol., 2004.

[41] M. Andreasson, D. V. Dimarogonas, H. Sandberg, and K. H. Johansson,“Distributed control of networked dynamical systems: Static feedback,integral action and consensus,” IEEE Trans. Autom. Control, vol. 59,no. 7, pp. 1750–1764, Jul. 2014.

[42] T. Athay, R. Podmore, and S. Virmani, “A practical method for thedirect analysis of transient stability,” IEEE Trans. Power App. Syst.,vol. PAS-98, no. 2, pp. 573–584, Mar. 1979.

[43] B. Pal and B. Chaudhuri, Robust Control in Power Systems (PowerElectronics and Power Systems Series). New York, NY, USA: Springer,2006.

Abdallah Farraj (S11–M’12) received the B.Sc.and M.Sc. degrees in electrical engineering from theUniversity of Jordan, Amman, Jordan, in 2000 and2005, respectively, and the Ph.D. degree in electricalengineering from Texas A&M University, CollegeStation, TX, USA, in 2012. He is currently a Post-Doctoral Fellow with the University of Toronto,Toronto, ON, Canada.

He is a Fulbright Scholar. His current researchinterests include cognitive communications, cyber-security of smart grids, downhole telemetry systems,

wireless communications, and signal processing applications. He was a recip-ient of the Best Paper Award at the IEEE SmartGridComm 2015, the BestPoster Award from the Institute for Sustainable Energy 2014 Symposium,and the Teaching Award from the Computer Science Student Union at theUniversity of Toronto.

Eman Hammad (S’14) received the B.Sc. degreefrom the University of Jordan, Amman, Jordan,and the M.Sc. degree from Texas A&M University,College Station, TX, USA, in 2000 and 2011,respectively, both in electrical engineering. Sheis currently pursuing the Ph.D. degree with theDepartment of Electrical and Computer Engineering,University of Toronto, Toronto, ON, Canada.

She had a long professional experience in the ITindustry in Jordan and U.S. Her current researchinterests include cyber-physical systems with partic-

ular interest in cyber-security, resilient control, and cooperative game theory inthe context of smart grids. She was a recipient of the IEEE SmartGridComm2015 Best Paper Award, the Hatch Graduate Scholarship for SustainableEnergy Research, and the Best Poster Award from the Institute for SustainableEnergy 2014 Symposium. She served as a Technical Program Committee andan Organizing Committee Member for several conferences and workshops.She is currently serving as the IEEE Toronto Communication Society ChapterChair.

Deepa Kundur (S’91–M’99–SM’03–F’15) receivedthe B.A.Sc., M.A.Sc., and Ph.D. degrees from theUniversity of Toronto, in 1993, 1995, and 1999,respectively, all in electrical and computer engi-neering. She is a Professor and the Director of theCentre for Power & Information with the EdwardS. Rogers Sr. Department of Electrical & ComputerEngineering, University of Toronto.

She has authored over 150 journal and confer-ence papers. She is also a recognized authority oncyber security issues and has appeared as an expert

in popular television, radio, and print media. Her research interests lie at theinterface of cyber security, signal processing and complex dynamical net-works. She has participated on several editorial boards and currently serveson the Advisory Board of the IEEE Spectrum. She also currently serves asthe General Chair for the Workshop on Communications, Computation, andControl for Resilient Smart Energy Systems at ACM e-Energy 2016 andCyber-Physical Smart Grid Security and Resilience at Globecom 2016, theGeneral Chair for the Symposium on Signal and Information Processing forSmart Grid Infrastructures at GlobalSIP 2016, and the Symposium Co-Chairfor the Communications for the Smart Grid Track of ICC 2017.

Prof. Kundur was a recipient of best paper recognitions at numerous venuesincluding the 2015 IEEE Smart Grid Communications Conference, the 2015IEEE Electrical Power and Energy Conference, the 2012 IEEE CanadianConference on Electrical & Computer Engineering, the 2011 Cyber Securityand Information Intelligence Research Workshop, the 2008 IEEE INFOCOMWorkshop on Mission Critical Networks, and teaching awards at both theUniversity of Toronto and Texas A&M University. She is a fellow of theCanadian Academy of Engineering.

ieee transactions on smart grid, vol. 9, no. 2, march …dkundur/pub_pdfs/farhamkuntsg18.pdf ·...

Documents