junbo zhao , life fellow, ieee ieee proof

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IEEE TRANSACTIONS ON POWER SYSTEMS 1

Power System Robust Decentralized Dynamic StateEstimation Based on Multiple Hypothesis Testing

1

2

Junbo Zhao, Student Member, IEEE, and Lamine Mili, Life Fellow, IEEE3

Abstract—This paper proposes a fast and robust unscented4Kalman filter based decentralized dynamic state estimator (DSE)5for power system online monitoring and control. The proposed ro-6bust DSE is able to detect, identify, and suppress three types of7outliers, namely the observation, innovation, and structural out-8liers. Observation outliers refer to the received PMU measure-9ments providing unreliable metered values due to gross errors or10cyber attacks; innovation outliers are typically caused by impul-11sive system process noise, whereas structural outliers are induced12by incorrect parameters of the generators or its associated con-13trollers, such as exciters and speed governors. To enable the fast14estimation of generator states of large-scale power systems in a15decentralized manner, two model decoupling approaches are pre-16sented and compared. It is shown that the generator decoupling17approach presented in this paper achieves higher statistical effi-18ciency than the ones proposed in the literature in the presence of19both small and large measurement noise. To detect and distinguish20three types of outliers, projection statistics based multiple hypoth-21esis testing approach is proposed. Specifically, three hypotheses22corresponding to the occurrence of three types of outliers are as-23sumed by constructing three innovation matrices; these matrices24are made up by time-correlated innovation vectors, and/or pre-25dicted states, and/or measurements; then projection statistics are26applied to each of the innovation matrix and its calculated pro-27jection values are checked by a statistical test to validate the as-28sumed hypothesis. The identified outliers are further suppressed29by a generalized maximum-likelihood-type estimator. Numerical30results carried out on the IEEE 39-bus system demonstrate the31effectiveness and robustness of the proposed method.32

Index Terms—Dynamic state estimation, robust statistics, decen-33tralized estimation, outliers, parameter errors, unscented Kalman34filter, hypothesis testing, projection statistics.35

I. INTRODUCTION36

THE wide-area deployment of phasor measurement units37

(PMUs) on power transmission grids has made possible38

the real-time monitoring and control of power system dynamics.39

However, these functions may not be reliably achieved without40

the development of a fast and robust dynamic state estimator41

(DSE). Indeed, the benefits of using a DSE are an improved42

Manuscript received July 12, 2017; revised November 13, 2017; acceptedDecember 15, 2017. This work was supported by the U.S. National ScienceFoundation under Grant ECCS-1711191. Paper no. TPWRS-01039-2017. (Cor-responding author: Junbo Zhao.)

The authors are with the Bradley Department of Electrical and ComputerEngineering, Virginia Polytechnic Institute and State University, Falls Church,VA 22043 USA (e-mail: [email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TPWRS.2017.2785344

dynamic security assessment scheme and an enhanced local 43

and global system control, to cite a few. 44

To enable the implementation of a power system DSE, several 45

types of Kalman filters are advocated, including the extended 46

Kalman filter (EKF), the unscented Kalman filter (UKF), the 47

ensemble Kalman filter (EnKF) [1]–[8]. In [1]–[3], centralized 48

DSEs using EKF, UKF and EnKF have been proposed. They all 49

require accurate knowledge of the status of each system compo- 50

nent as well as the real-time wide-area PMU measurements. Al- 51

though a global dynamic state estimation may be implemented 52

to achieve global control applications, they may require large 53

computing times that are incompatible for applications in large- 54

scale interconnected power systems. This motivates the devel- 55

opment of decentralized DSE that is implemented at each local 56

synchronous generator, and therefore, is fast to execute [4]– 57

[8]. In [4]–[6], EKF-based DSEs are proposed to estimate the 58

state variables of classical and fourth-order synchronous gen- 59

erators. Since the power system can have strong nonlinearities 60

when operating under stressed conditions or subject to severe 61

disturbances, the first-order Taylor series expansion-based EKF 62

may induce large estimation errors. To circumvent this diffi- 63

culty, UKF-based DSEs are advocated [7], [8]. Note that the 64

model decoupling approach of [4]–[8] to enable the decentral- 65

ized implementation of a DSE is achieved by treating metered 66

generator terminal voltage phasors as inputs and real and re- 67

active power injections or current phasors as outputs. On the 68

other hand, although decentralized DSE is faster to execute 69

compared with the centralized approaches, its global measure- 70

ment redundancy decreases significantly, and as a result, they 71

are more vulnerable to outliers. For a general cyber-physical 72

system that involves dynamic model and measurements, three 73

types of outliers, namely the observation, innovation and struc- 74

tural outliers, are defined in [9]. In power system DSE problem, 75

they are defined specifically as follows: observation outliers 76

refer to the received PMU measurements providing unreliable 77

metered values due to gross errors, cyber attacks, and measure- 78

ment losses; innovation outliers are typically caused by impul- 79

sive system process noise due to unknown disturbances and 80

sudden changes of the model inputs while structural outliers 81

are induced by incorrect parameters of the generators or its as- 82

sociated controllers, such as exciters, speed governors. In the 83

literature [4]–[8], only observation outliers are considered [8], 84

where the normalized innovation vector-based statistical test is 85

advocated to detect them. However, the detection threshold of 86

this approach is system-dependent and sensitive to the change 87

of process and measurement noises, which limits its practical 88

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

value. In addition, this approach may fail to work in presence of89

innovation or structural outliers.90

In this paper, a fast and robust unscented Kalman filter-based91

decentralized DSE is proposed. Our robust DSE is able to de-92

tect, identify, and suppress observation, innovation and struc-93

tural outliers. To enable the fast and decentralized estimation94

of generator states of large-scale power systems, two model95

decoupling approaches are presented and compared. The first96

one is achieved by treating the metered generator terminal volt-97

age phasors as inputs and the current phasors and frequency98

as outputs. By contrast, the second one takes measured current99

phasors as inputs while treating voltage phasors and frequency100

as outputs. It is shown that the latter one has higher statistical101

efficiency than the former one in the presence of both small and102

large measurement noise. To detect and distinguish the three103

types of outliers, projection statistics-based multiple hypothe-104

sis testing approach is proposed. Specifically, three hypotheses105

corresponding to the occurrence of three types of outliers are106

tested using three different innovation matrices; these matrices107

are made up of time-correlated innovation vectors and/or pre-108

dicted states and/or measurements; then projection statistics are109

applied to each of the innovation matrix and its calculated pro-110

jection values are checked via a statistical test to validate the111

assumed hypothesis. Then, a generalized maximum-likelihood112

type (GM)-estimator that uses the convex Huber score function113

is advocated to suppress the identified outliers, yielding robust114

state estimates. Finally, the estimation error covariance matrix115

is updated through the total influence function-based approach.116

The remainder of the paper is organized as follows.117

Section II presents the problem formulation. Section III de-118

scribes the proposed robust DSE and Section IV shows and119

analyzes the simulation results. Finally, Section V concludes120

the paper.121

II. PROBLEM FORMULATION122

Decentralized DSE is implemented at each synchronous gen-123

erator using local PMU measurements. Consequently, syn-124

chronous generator model and measurement functions are125

derived first. In this paper, the two-axis model with IEEE-DC1A126

exciter and TGOV1 turbine-governor is considered. It is rep-127

resented by the following differential and algebraic equations128

[10],129

Differential equations of generator:130

T ′do

dE ′q

dt= − E ′

q − (Xd −X ′d) Id + Efd, (1)

T ′qo

dE ′d

dt= − E ′

d −(Xq −X ′

q

)Iq , (2)

dδ

dt= ω − ωs, (3)

2Hωs

dω

dt= TM − Pe −D (ω − ωs) , (4)

Differential equations of IEEE-DC1A exciter:131

TEdEfd

dt= − (KE + SE (Efd))Efd + VR, (5)

132TFdVFdt

= − VF +KF

TEVR − KF

TE(KE + SE (Efd))Efd,

(6)

TAdVRdt

= − VR +KA (Vref − VF − V ) , (7)

Differential equations of TGOV1 turbine-governor: 133

TCHdTMdt

= − TM + PSV , (8)

TSVdPSVdt

= − PSV + PC − 1RD

(ω

ωs− 1

), (9)

Algebraic equations: 134

Vd = V sin (δ − θ) , Vq = V cos (δ − θ) , (10)

Id =E ′q − Vq

X ′d

, Iq =Vd − E ′

d

X ′q

, (11)

Pe = VdId + VqIq ,Qe = −VdIq + VqId, (12)

where T ′do , T ′

qo , TE , TF , TA , TCH and TSV are time constants, 135

in seconds; KE , KF and KA are controller gains; Vref and PC 136

are known control inputs; E ′q , E′

d , Efd , VF , VR , TM and PSV 137

are the q-axis and d-axis transient voltages, field voltage, scaled 138

output of the stabilizing transformer and scaled output of the 139

amplifier, synchronous machine mechanical torque and steam 140

valve position, respectively; Xd , X ′d , Xq and X ′

q are generator 141

parameters; V and θ are the terminal bus voltage magnitude and 142

phase angle, respectively; Pe and Qe are the active and reactive 143

electrical power outputs; Id and Iq are the d and q axis currents, 144

respectively. 145

The above differential and algebraic equations can be put into 146

the following discrete-time state space form: 147

xk = f (xk−1 ,uk ) + wk , (13)

zk = h (xk ) + vk , (14)

where (13) and (14) correspond to (1)–(9) and (10)–(12), re- 148

spectively; xk is the state vector that includes state variables of 149

the synchronous generator, the exciter and the governor; zk is 150

the measurement vector that contains a collection of generator 151

terminal voltage phasors, current phasors and frequency; the 152

noises wk and vk are assumed to be white and with covariance 153

matrices Qk and Rk , respectively; uk represents the input vec- 154

tor; f(·) and h(·) are the vector-valued functions. It is worth 155

pointing out that Vref and PC are the voltage and power ref- 156

erences of the exciter and speed governor, respectively, whose 157

values are adjusted by the local generator operator. Hence, it 158

is reasonable to consider them as the known generator param- 159

eters. Therefore, only local PMU measurements and generator 160

parameters are needed to perform decentralized DSE. 161

Problem statement: the decentralized DSEs proposed in [4]– 162

[8] are vulnerable to outliers and do not achieve high statistical 163

efficiency in presence of thick tailed-probability distribution 164

of the measurement noise. This paper will develop a robust 165

DSE to address these problems while satisfying the follow- 166

ing constraints: given a limited number of PMUs installed at 167

the terminal bus of each generator, i) decouple the generator 168

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ZHAO AND MILI: POWER SYSTEM ROBUST DECENTRALIZED DYNAMIC STATE ESTIMATION BASED ON MULTIPLE HYPOTHESIS TESTING 3

from each other to enable the decentralized state estimation169

and thus make the algorithm suitable for large-scale power170

system applications; ii) detect, distinguish and suppress three171

types of outliers; iii) if generator parameter errors occur, lo-172

cate them in order to perform appropriate model calibration and173

validation.174

III. THE PROPOSED ROBUST DECENTRALIZED DSE175

We first present two generator decoupling approaches to en-176

able the decentralized implementation of a DSE. Then, we derive177

the proposed robust decentralized DSE using multiple hypoth-178

esis testing to detect, identify, and suppress the three types of179

outliers.180

A. Generator Model Decoupling Approaches181

Once a disturbance takes place at one point of the power sys-182

tem, synchronous generators will response to it. These responses183

reveal themselves in their terminal voltage or current phasors184

[8]. In other words, a generator is coupled with the power system185

at the point of connection, and its interactions with the rest of the186

system are through the terminal voltage and current phasors. If187

the generator terminal voltage or current phasors are measured188

by PMUs, its responses to the disturbance are captured com-189

pletely and no other system information is required. By doing190

so, a generator model can be decoupled from the rest of the191

system from a DSE prospective and its dynamic states can be192

estimated using only local measurements [8]. Based on the way193

of treating these measurement pairs, two decoupling approaches194

can be achieved: A1) taking the metered terminal voltage pha-195

sors as inputs and the current phasors and frequency as outputs;196

A2) taking the metered terminal current phasors as inputs and197

the voltage phasors and frequency as outputs. It should be noted198

that at the model decoupling stage the generator terminal real199

and reactive powers are not taken as model outputs as advocated200

by several references [4]–[6]. This is due to the fact that gross201

error on single voltage or current phasor will propagate to both202

real and reactive powers, causing a smearing effect. On the other203

hand, as shown by [11], the terminal real and reactive powers,204

when measured, enable a better observability of the generator205

states than either the voltage phasors or the current phasors.206

Therefore, in this paper if both the voltage phasors and current207

phasors are not detected as outliers by the proposed multiple208

hypothesis testing shown in the next section, the terminal real209

and reactive power will be taken as outputs. Otherwise, if any210

voltage phasors and current phasors are flagged as outliers, the211

outputs in the two model decoupling approaches will be pre-212

ferred. We illustrate the two decoupling approaches A1) and213

A2) on an interconnected power system with m synchronous214

generators shown in Fig. 1, and the ith generator is taken as an215

example.216

A1: Taking the current phasor Ii∠φi as known inputs and the217

voltage phasor Vi∠θi and frequency fi as outputs, we have ui =218

[Ii φi ]T , Idi = real[Iiej (φi−δi +π2 ) ], Iqi = Imag[Iiej (φi−δi +

π2 ) ],219

Vdi = E ′di + IqiX

′qi and Vqi = E ′

qi − IdiX′di . Define zi =220

Fig. 1. Interconnected system with m synchronous generators.

[z1 z2 z3 ]T , the measurement function can be expressed as 221

z1 = Vi =√V 2di + V 2

qi + vV i, (15)

z2 = θi = δi − arctan

(VdiVqi

)+ vθi, (16)

z3 = fi = f0(Δωi + 1) + vf i, (17)

where vi = [vV i vθi vf i ]T is the measurement noise vector. 222

A2: Taking the voltage phasor Vi∠θi as known inputs 223

and the current phasor Ii∠φi and frequency fi as outputs, 224

we have ui = [Vi θi ]T , Vdi = Visin(δi − θi), Vqi = Vicos(δi − 225

θi), Idi = (E ′qi − Vqi)/X ′

di and Iqi = (−E′di + Vdi)/X ′

qi . De- 226

fine zi = [z1 z2 z3 ]T , the measurement function can be ex- 227

pressed as 228

z1 = Ii =√I2di + I2

qi + vI i , (18)

z2 = φi = arg(Iqi − jIdi) + δi + vφi, (19)

z3 = fi = f0(Δωi + 1) + vf i, (20)

where vi = [vI i vφi vf i ]T is the measurement noise vector. 229

Note that if our proposed multiple hypothesis testing method 230

does not flag any voltage phasors and current phasors as outliers, 231

we advocate the use of the terminal real and reactive power as 232

outputs. As a result, z1 and z2 of the two decoupling approaches 233

A1) and A2) are rewritten as 234

Pei = VdiIdi + VqiIqi + vP i, (21)

Qei = − VdiIqi + VqiIdi + vQi, (22)

where vi = [vP i vQi vf i ]T is the measurement noise vector. 235

Therefore, the dynamical system model of the ith generator at 236

the time sample k can be expressed as 237

xik = f i

(xik−1 ,u

ik

)+ wi

k , (23)

zik = hi

(xik

)+ vik , (24)

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where wik is the system process noise that includes the noise238

associated with the input vector ui and the model approximation239

error.240

Remark: In a multi-machine power system, a common refer-241

ence is required to define the voltage and rotor angles. Usually,242

the angle of the synchronous machine that has the largest in-243

stalled capacity is used as the reference [10]. Interestingly, North244

American Electric Reliability Corporation (NERC) has a reg-245

ulation rule of installing PMUs to monitor and calibrate the246

machine with the largest generation capacity [12]. Therefore, it247

is not difficult to obtain the reference angle. On the other hand,248

although [7], [13] presented an approach to avoid the defini-249

tion of the reference angle for decentralized DSE by redefining250

the i-th rotor angle with αi = δi − θi , it may suffer from the251

following two drawbacks:252� After the dynamic state estimation, the estimated αi of the253

ith local generator can be used to estimate its internal rotor254

angle through δi = αi + θi . However, θi is always subject255

to noise or even gross errors. As a result, the estimate256

of δi is biased, which may subsequently deteriorate the257

performance of the control actions;258� To damp out inter-area oscillations, the knowledge of just259

a few local generator dynamic state variables may not be260

sufficient. Coordinated controls are usually required and261

in this case, the reference angle can be easily defined at the262

coordination level. Interestingly, this has been implicitly263

shown in [8], [14]. Note that inappropriate local controls264

of inter-area oscillations can produce adverse effects.265

Based on the above discussions, we conclude that the choice266

of a reference angle depends on specific applications.267

B. The Proposed Robust DSE268

The model decoupling approach enables a generator to be269

decoupled from the rest of the system model, which in turn al-270

lows us to rely only on local measurements to estimate the state271

variables of a generator through (23) and (24). To this end, this272

paper presents a robust decentralized UKF-based DSE, termed273

the RDUKFI. Our choice of the UKF as the basic filter is moti-274

vated by the fact that it achieves a more balanced performance275

between computational efficiency and ability to cope with strong276

system nonlinearities than other filters [15]. The RDUKFI con-277

sists of four major steps, namely a batch-mode regression form278

step, an outlier detection and processing step using multiple hy-279

pothesis testing, a robust state estimation step, and a robust error280

covariance matrix updating step. In the following subsections,281

we will discuss them in detail. Note that the index i associated282

with the generator is neglected for simplicity but without loss283

of generality.284

1) Batch-Mode Regression Form: The main idea of the UKF285

is to use a set of chosen deterministic sigma points for statis-286

tical information propagation. For instance, if a state estimate287

with mean xk−1|k−1 ∈ Rn×1 and covariance matrix Σxxk−1|k−1288

is given at time step k-1, its statistics can be captured by 2n289

weighted sigma points defined as [15]290

χjk −1 |k −1

= xk−1|k−1 ±(√

nΣxxk−1|k−1

)

j, (25)

with weights wj = 1/2n, j = 1, ..., 2n. Then, each sigma point 291

is propagated through the nonlinear system process model (23), 292

yielding the following transformed samples 293

χjk |k −1

= f(χj

k −1 |k −1

). (26)

Then, the predicted state xk |k−1 and its covariance matrix 294

Σxxk |k−1 are calculated by the weighted sample mean and sample 295

covariance matrix of the transformed sigma points. Formally, 296

we have 297

xk |k−1 =2n∑

j=1

wjχjk |k −1

,

Σxxk |k−1 =

2n∑

j=1

wj (χjk |k −1

− xk |k−1)(χjk |k −1

− xk |k−1)T + Qk .

To derive the regression model, we will apply statistical 298

linerization [16], [17] to the nonlinear measurement function 299

around xk |k−1 . The main idea of statistical linerization is to 300

approximate the nonlinear function η = g(x) around x sta- 301

tistically with η = Gx + b + ζ, where G = (P xη )T (P xx)−1 ; 302

P xη and P xx are the cross-covariance matrix between x and η, 303

and self-covariance matrix of x, respectively; b = η − Gx and 304

η = g(x); ζ is the statistical linerization error. Following these 305

procedures, the statistical linerization of the nonlinear measure- 306

ment function h(·) around xk |k−1 yields 307

zk = Hk

(xk − xk |k−1

)+ h

(xk |k−1

)+ vk + εk , (27)

where Hk = (Σxzk |k −1

)T (Σxxk |k −1

)−1 ; εk is the statistical lin- 308

earization error term with zero mean and covariance matrix 309

Lk = Σzzk |k −1

− (Σxzk |k −1

)T Σxxk |k−1 Σxz

k |k −1, where 310

Σxxk |k−1 =

2n∑

j=1

wj (χjk |k −1

− xk |k−1)(χjk |k −1

− xk |k−1)T + Qk .

Σzzk |k −1

=2n∑

j=1

wj (zjk |k −1− zk |k−1)(zjk |k −1

− zk |k−1)T + Rk ,

Σxzk |k −1

=2n∑

i=1

wj (χjk |k −1

− xk |k−1)(zjk |k −1− zk |k−1)T ,

and zk |k−1 =∑2n

j=1 wjzjk |k −1

is the predicted measurement vec- 311

tor; zjk |k −1

= h(χjk |k −1

). 312

Define xk |k−1 = xk + Δk , where xk is the true state vector; 313

Δk is the prediction error and E[ΔkΔT

k

]= Σxx

k |k−1 . Then, the 314

equations associated with the state predictions and measurement 315

functions can be reorganized into the following batch-mode 316

regression form: 317

[zk + Hk xk |k−1 − h(xk |k−1)

xk |k−1

]=

[Hk

I

]xk +

[vk + εk

Δk

]

where I is an identity matrix. It can be further rewritten in a 318

compact form as 319

zk = Hkxk + ek , (28)

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and the error covariance matrix of ek is given by320

W k =

[Lk + Rk 0

0 Σxxk |k−1

]

= SkSTk , (29)

where Sk is calculated by the Cholesky decomposition321

technique.322

Note that the state prediction errors of the batch-mode regres-323

sion form should be uncorrelated before the state estimation.324

This can be done by pre-multiplying S−1k on both sides of (28),325

yielding326

S−1k zk = S−1

k Hkxk + S−1k ek , (30)

which is further organized to the compact form given by327

yk = Akxk + ξk , (31)

where E[ξkξk T ] = I .328

2) Outlier Detection and Processing Using Multiple Hy-329

pothesis Testing: As mentioned before, there are three types330

of outliers, i.e., observation, innovation and structural outliers.331

Specifically, observation outliers affect the measurements in332

zk ; innovation outliers are usually caused by unknown sys-333

tem disturbances reflected in the process noise wk or the in-334

correct inputs uk ; structural outliers are induced by param-335

eter errors of the generator, exciter, governor, etc. It should336

be noted that structural outliers will affect all the predicted337

states in this decentralized scheme-based state estimation due338

to the strong dependence among each predicted state. On the339

other hand, if the voltage phasor is taken as input vector and340

has gross errors, it will trigger the following cascading chain:341

V ∠θ → VR → VF → Efd → E ′q → E ′

d , which makes all the342

the predicted states incorrect, yielding innovation outliers. If343

the current phasor is taken as input vector and has gross errors,344

the cascading chain is as follows: I∠φ→ Id → Iq → E ′q →345

E ′d → Efd → VF → VR → Pe → ω → TM , which makes all346

the other predicted states incorrect, yielding innovation outliers.347

Based on the above analysis, it is clear that there are three hy-348

potheses corresponding to each outlier scenario plus one addi-349

tional hypothesis to determine whether there are outliers or not.350

Therefore, we need to validate each hypothesis and determine351

which type of outliers occurs.352

First of all, we need to check the following hypothesis:353

Hypothesis 1 :{H0 : no outliers

H1 : occurrence of outliers. (32)

To this end, we propose to apply the projection statistics (PS)354

at each measurement sample to a 2-dimensional matrix Z1 that355

contains time-correlated samples of the innovations and of the356

predicted state variables. Specifically, we have357

Z1 =[

zk−1 − h(xk−1|k−2) zk − h(xk |k−1)xk−1|k−2 xk |k−1

], (33)

where zk−1 − h(xk−1|k−2) and zk − h(xk |k−1) are the inno-358

vation vectors while xk−1|k−2 and xk |k−1 are the predicted state359

vectors at time instants k-1 and k, respectively. The choice of360

Z1 is motivated by the fact that the innovation vector and the361

predicted state vector are time series samples of power sys- 362

tem responses and have strong temporal correlations. If out- 363

liers occur, this relationship is violated. Thus, by checking this 364

statistical property of the matrix Z1 , we are able to detect 365

outliers. The PS is defined as [9], [17]: 366

PSj = max‖�‖=1

∣∣lTj � −medi

(lTi �

)∣∣

1.4826medκ∣∣lTκ � −medi

(lTi �

)∣∣ , (34)

for i, j, κ = 1, 2, ...,m+ n, where n and m are the number of 367

state variables and measurements taken as outputs, respectively; 368

lTj , lTi and lTκ are the j th, ith and κth row vector of Z1 , respec- 369

tively. The PS values of the predictions and of the innovations 370

are separately calculated. Extensive Monte Carlo simulations 371

revealed that the PS values follow a chi-square distribution 372

with degree of freedom 2. Thus, if we define the set Π1 = 373

{PSi > τ = χ22,0.975 , i = 1, ...,m+ n}, then Hypothesis 1 374

can be rewritten as 375

Hypothesis 1 :{H0 : |Π1 | = 0H1 : 1 ≤ |Π1 | ≤ m+ n

, (35)

where |Π1 | represents the cardinality of the set Π1 ; H1 and H0 376

correspond to occurrence of outliers and no outliers, respec- 377

tively; PSi denotes the ith PS value; τ is determined according 378

to the chi-square distribution at a significance level 97.5%. If 379

H0 is accepted, the robust regression shown in the next sub- 380

section is performed; otherwise, the outlier detection rule is 381

applied and additional procedures are executed to distinguish 382

between them. It is worth pointing out that we can apply the PS 383

to higher dimensional samples, but we found that applying them 384

to 2-dimensional time series data is sufficient to check if the sta- 385

tistical correlations of the innovation vector and the predicted 386

state vector are broken up by outliers. Note that an unnecessary 387

higher dimensional samples will induce more computing burden 388

of the PS algorithm. 389

For any generator with n state variables and m outputs, it 390

is noticed that if the number of bad measurements flagged by 391

the PS is less than m, only observation outliers occur. This is 392

because both innovation and structural outliers will affect all n 393

predicted states, and as a result, all m measurements will be 394

flagged as outliers by the PS. The latter is due to the fact that the 395

predicted states dominate the data of the matrix Z1 ∈ R(m+n)×2 396

and if they are wrong, the PS method breaks down, that is, it 397

identifies all the good measurements that are associated with 398

the innovation vectors as outliers. However in the case where 399

all the mmeasurements are outliers, then all bad measurements 400

will be flagged as outliers as well. Therefore, extra test should 401

be performed to differentiate observation outliers that are in 402

extreme scenario with innovation and structural outliers. To this 403

end, we propose to apply the PS to the matrix Z2 ∈ Rm×3 that 404

includes 3 dimensional consecutive samples, that is, 405

Z2 =[zk−2 zk−1 zk

], (36)

where the received measurements zk−2 and zk−1 must be re- 406

placed by their corresponding estimated values if they have 407

outliers. Our choice of matrix Z2 is motivated by two facts: 408

i) when all m measurements are outliers at time instant k, two- 409

dimensional consecutive samples are not sufficient to detect 410

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outliers due to the lack of redundancy; to address this issue,411

we propose to include one more dimensional sample, which412

increases the global redundancy, and thus, the detectabil-413

ity of the outliers; ii) time-correlated measurements are414

independent from the predicted states and consequently415

innovation/structural outliers do not affect the detection of ob-416

servation outliers. Extensive Monte Carlo simulations showed417

that the PS values calculated from Z2 follow a chi-square dis-418

tribution with degree of freedom 3. Let us now define the set419

Π2 = {PSi > χ23,0.975 , i = 1, ...,m}. The hypothesis 2 used to420

distinguish observation outliers with innovation and structural421

outliers is thus expressed as422

Hypothesis 2 :{H0 : |Π1 | − |Π2 | ≥ 0H1 : |Π2 | = m

, (37)

where hypothesis H1 corresponds to the scenario that all m423

measurements are outliers while H0 corresponds to the occur-424

rence of innovation and/or structural outliers. If the hypothesis425

H1 is confirmed, we propose to replace all m measurements426

with their previous estimated values at time instant k − 1. Then,427

Hypothesis 1 in (35) is tested again and if all newly replaced m428

measurements are flagged as outliers, the occurrence of inno-429

vation and/or structural outliers is double confirmed (note that430

this indicates the possibility of the occurrence of three types431

of outliers simultaneously); otherwise, only the extreme outlier432

scenario associated with the observations presents. To further433

distinguish innovation and structural outliers, we propose to434

replace the system inputs u by its estimated values at the previ-435

ous time instant and obtain new predicted state vector xnewk |k−1 ,436

yielding a new matrix Z3 for outlier detection given by437

Z3 =

[zk−1 − h(xk−1|k−2) zk − h(xnew

k |k−1)xk−1|k−2 xnew

k |k−1

]

, (38)

where zk−1 and zk must be replaced by their estimated values if438

they were detected as outliers in the former steps. Next, define set439

Π3 = {PSi > χ22,0.975 , i = 1, ...,m+ n}, the hypothesis 3 used440

to differentiate innovation and structural outliers is expressed as441

Hypothesis 3 :

{H0 : |Π3 | = 0H1 : |Π3 | = m

. (39)

If the hypothesis H1 is validated, structural outliers exist; oth-442

erwise innovation outliers has occurred.443

After the detection and differentiation of outliers, we propose444

to process them using the following rules:445� Rule 1: if only observation outliers occur, they are down-446

weighted via the weights given by447

�i = min(1, d2/PS2

i

), (40)

where the parameter d is set as 1.5 to yield good statistical448

efficiency at Gaussian distribution and other thick-tailed449

non-Gaussian distributions [2], [17];450� Rule 2: if only innovation outliers occur, the inputs are451

replaced by their estimated values at the last time instant452

and new predicted states are obtained;453� Rule 3: if only structural outliers occur, predicted states are454

replaced by filtered state variables at the last time instant;455

� Rule 4: if both observation and innovation outliers occur, 456

the inputs are replaced by their estimated values at the last 457

time instant and new predicted states are obtained, while 458

observations are processed according to rule 1; if both 459

observation and structural outliers occur, rules 1 and 3 are 460

applied; 461� Rule 5: If three types of outliers occur simultaneously, 462

predicted states are replaced by filtered state variables at 463

the last time instant; bad observations are replaced by their 464

estimated values at the last time instant. 465

Remark 1: By using our multiple hypothesis testing ap- 466

proach, we are able to distinguish between three types of out- 467

liers. If structural outliers occur, additional actions are needed 468

to locate incorrect parameters of the generator, requiring that a 469

model calibration need to be executed. This will be proposed as 470

our future work. 471

Remark 2: The more types of outliers are present, the more 472

time is required for executing the multiple hypothesis testing 473

rules. However, the computing time is not prohibitively large 474

for our robust DSE as the decentralized scheme enables the 475

outlier detection and processing to be quickly executed at each 476

local generator. This will be shown in the simulation results 477

section. 478

3) Robust Regression: After the outlier detection and pro- 479

cessing, corresponding weights �i, i = 1, ...,m+ n are as- 480

signed to the measurements and the predicted states via (40); 481

then the robust regression is performed by using a robust GM- 482

estimator that minimizes the following objective function: 483

J (xk ) =m+n∑

i=1

�2i ρ (rSi ) , (41)

where rSi = ri/s�i is the standardized residual; ri = yi − 484

aTi x is the residual, where aTi is the ith row vector of the 485

matrix Ak ; s = 1.4826 · bm · mediani |ri | is the robust scale es- 486

timate; bm is a correction factor; ρ(·) is the convex Huber-ρ 487

function [2]. 488

To minimize (41), the following necessary condition must be 489

satisfied 490

∂J (xk )∂xk

=l∑

i=1

−�iais

ψ (rSi ) = 0, (42)

where ψ (rSi ) = ∂ρ (rSi )/∂rSi . By dividing and multiplying 491

the standardized residual rSi to both sides of (42) and putting it 492

in a matrix form, we get 493

ATk Λ (yk − Akxk ) = 0, (43)

where Λ = diag(q (rSi )) and q (rSi ) = ψ (rSi )/rSi . By using 494

the IRLS algorithm [9], the state estimates at the j iteration can 495

be calculated 496

Δx(j+1)k |k =

(ATk Λ(j )Ak

)−1ATk Λ(j )yk , (44)

where Δx(j+1)k |k = x

(j+1)k |k − x

(j )k |k . The algorithm converges 497

when∥∥∥Δx

(j+1)k |k

∥∥∥∞

≤ 10−2 . 498

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4) Update the Error Covariance Matrix: Following our pre-499

vious work, the estimation error covariance matrix Σxxk |k is500

updated using the total influence function-based approach [2].501

Formally, we have502

Σxxk |k =

EF [ψ 2 (rS i )]{EF [ψ ′(rS i )]}2

(ATk Ak

)−1(ATk Q�Ak

)(ATk Ak

)−1

(45)

where Q� = diag(�2i

).503

IV. NUMERICAL RESULTS504

Extensive simulation results of several scenarios are carried505

out on the IEEE 39-bus system to test the effectiveness and ro-506

bustness of the proposed robust DSE. In the case studies, Line507

15–16 is tripped at t = 0.5 s to simulate system disturbance.508

The time-domain simulation results are taken as the true values.509

The collections of simulated voltage phasor, current phasor and510

frequency at each generator’s terminal bus are treated as PMU511

measurements. A random Gaussian variable with zero mean and512

covariance matrix equal to 10−6I is assumed for system process513

noise. The generator model assumed for transient simulation is514

the detailed two-axis generator model, whose parameter values515

are taken from [18]. The maximum iteration of the IRLS algo-516

rithm is 20. The break point of the Huber cost function is set to 2.517

The root-mean-squared error (RMSE) of all estimated generator518

state variables is used as the overall performance index while the519

estimated rotor angle, rotor speed, d- and q-axis voltages of Gen-520

erator 5 are taken for illustration due to the limitation of space.521

When the metered generator terminal voltage phasor is used as522

model input while the current phasor and frequency are treated523

as outputs/measurements, the decentralized DSE approach will524

be called the DUKFV. By contrast, when the metered generator525

terminal current phasor is used as model input while the voltage526

phasor and frequency are treated as outputs/measurements, the527

decentralized DSE approach will be called the DUKFI. Its ro-528

bust version, which is our proposed robust DSE, will be termed529

the RDUKFI. The choice of developing a robust version of the530

DUKFI instead of the DUKFV is motivated by the fact that the531

former achieves much higher statistical efficiency than the latter532

in the absence of outliers regardless of the level of measurement533

noise. This is confirmed by the results shown in Figs. 2 and534

3. In other words, if the DUKFI is made robust against out-535

liers, it will outperform the robust DUKFV in presence of both536

measurement noise and outliers.537

A. Case 1: Sensitivity to Measurement Noise538

Measurement noise with different variances is implemented539

to test the sensitivity of each method. Specifically, normal and540

large noises are considered; they are assumed to be distributed541

with zero means and covariance matrices 10−6I and 10−4I , re-542

spectively. The test results are displayed in Figs. 2 and 3. It can543

be concluded from these two figures that our RDUKFI outper-544

forms the DUKFV and the DUKFI in presence of both normal545

and large measurement noises; the DUKFI that uses our model546

decoupling approach achieves much higher statistical efficiency547

than the DUKFV. In addition, it is observed that with the in-548

creased noise level, all three methods have increased estimation549

Fig. 2. Root-mean-squared error of the DUKFV, the DUKFI and the RDUKFIin the presence of normal measurement noise.

Fig. 3. Root-mean-squared error of the DUKFV, the DUKFI and the RDUKFIin the presence of large measurement noise.

error, which is expected. This is because given certain level 550

of measurement redundancy, any estimator will have increased 551

estimation error with the increase of measurement noise; the 552

higher measurement redundancy, the better capability of an es- 553

timator to filter out noise. Nevertheless, our RDUKFI is least 554

sensitive to the increase of noise level among three methods. 555

B. Case 2: Robustness to Observation Outliers 556

Due to imperfect phasor synchronization, the saturation of 557

metering current transformers or by metering coupling capacitor 558

voltage transformers (CCVTs), to name a few, gross errors can 559

occur in the PMU measurements [2], [19]. To test the robustness 560

of three methods to observation outliers, the measured voltage 561

magnitude and angle of Generator 5 is contaminated with 20% 562

error from t= 4 s to t= 6 s. The results are shown in Fig. 4 and 563

its zoomed in version is displayed in Fig. 5. 564

We can find that the estimated generator state variables pro- 565

vided by the DUKFV and the DUKFI are significantly biased 566

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Fig. 4. Estimated rotor angle, rotor speed, d- and q-axis voltages ofGenerator 5 by the DUKFV, the DUKFI and the RDUKFI in the presenceof observation outlier, where the measured voltage magnitude and angle ofGenerator 5 is contaminated with 20% error from t = 4 s to t = 6 s.

Fig. 5. Zooming in the Fig. 4 for better illustration of the proposed RDUKFIfrom t = 0 to t = 10 s.

in the presence of observation outliers due to their lack of ro-567

bustness. However, our RDUKFI that uses multiple hypothesis568

testing is able to detect these two observation outliers and bound569

their influence, yielding excellent tracking performance. Note570

that during the multiple hypothesis testing process, the test re-571

sults on hypothesis 1 indicate that 2 observations are flagged as572

outliers, and consequently the occurrence of only observations573

outliers is declared. Then, the observation outliers are down-574

weighted and suppressed by the GM-estimator.575

C. Case 3: Robustness to Innovation Outliers576

The system inputs u can be incorrect due to unknown distur-577

bances or erroneous metered values by PMUs, yielding innova-578

tion outliers. To test the robustness of the proposed method to579

this type of outliers, the system inputs are contaminated with580

20% error from t = 2 s to t = 4 s. Comparison results of the581

Fig. 6. Estimated rotor angle, rotor speed, d- and q-axis voltages ofGenerator 5 by the DUKFV, the DUKFI and the RDUKFI in the presenceof innovation outlier, where the model inputs are contaminated with 20% errorfrom t = 2 s to t = 4 s.


DUKFV, the DUKFI and the RDUKFI are displayed in Fig. 6. 582

This figure is further zoomed in and is shown in Fig. 7 for better 583

illustration. It can be concluded that the DUKFV and the DUKFI 584

are not robust to innovation outliers as they have very large es- 585

timation errors. By contrast, in the multiple hypothesis testing 586

process, Hypothesis 1 indicates that all outputs/measurements 587

are flagged by PS as outliers; then Hypothesis 2 is tested and its 588

result indicates the occurrence of innovation and/or structural 589

outliers. After replacing the model inputs by its estimated value 590

at the previous time instant, new predicted state variables are 591

obtained and Hypothesis 3 is then tested. The result confirms 592

the occurrence of innovation outliers. As a result, the newly pre- 593

dicted state variables associated with the measurements are used 594

for robust estimation by the GM-estimator, yielding negligible 595

biased state estimates. 596

D. Case 4: Robustness to Structural Outliers 597

Due to aging processes, variations of the machine tempera- 598

ture during its operation, the effect of saturation on generator 599

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Fig. 8. Estimated rotor angle, rotor speed, d- and q-axis voltages ofGenerator 5 by the DUKFV, the DUKFI and the RDUKFI in the presence ofstructural outlier, where the d- and q-axis transient reactance of Generator 5 arecontaminated with 20% Gaussian random errors due to the effect of saturationon generator inductances from t = 0.6 s to t = 2.6 s.


inductances, etc., the parameters of synchronous generator can600

change significantly while remaining unknown to the operator601

of the power plant. In this paper, we consider the case where602

following a system disturbance, there exist saturations on the603

inductances of Generator 5 from t = 0.6 s to t = 2.6 s, yield-604

ing structural outliers. Note that the saturation level of a syn-605

chronous machine does not change instantaneously; in fact, it606

has an oscillatory behavior for post-disturbances. Thus, to sim-607

ulate the oscillatory behavior during the saturation period, 20%608

random errors simulated by Gaussian distribution are added to609

the d- and q-axis transient reactance. Estimated rotor angle, ro-610

tor speed, d- and q-axis voltages of Generator 5 by the DUKFV,611

the DUKFI and the RDUKFI are displayed in Fig. 8 associated612

with its zoomed in version shown in Fig. 9. We observe from613

this figure that both the DUKFV and the DUKFI yield large bi-614

ases on the state estimates in the presence of structural outliers.615

TABLE IAVERAGE COMPUTING TIMES OF THE THREE METHODS AT EACH PMU SCAN

Cases DUKFV DUKFI RDUKFI

Case 1 0.282 ms 0.296 ms 0.85 msCase 2 0.396 ms 0.286 ms 1.07 msCase 3 0.473 ms 0.295 ms 1.31 msCase 4 0.275 ms 0.264 ms 1.35 ms

The DUKFV is less sensitive to this type of outliers than the 616

DUKFI and spends less time re-tracking the system true states. 617

By contrast, thanks to the multiple hypothesis testing and the 618

robust GM-estimator, our RDUKFI can bound the influence of 619

the structural outliers, yielding very small biases on the state 620

estimates when outliers occur. 621

E. Computational Efficiency 622

The average computing times of the DUKFV, the DUKFI and 623

the RDUKFI for Cases 1–4 in each PMU scan are tabulated in 624

Table. I. All the tests are performed on a PC with Intel Core 625

i5, 2.50 GHz, 8 GB of RAM. It is observed from Table. I that 626

all three methods have comparative computational efficiency 627

and their computing times are much lower than the PMU scan 628

rate, which is 16.7 ms for 60 sample/s. The DUKFI is the most 629

computational efficient approach, followed by the DUKFV. The 630

proposed RDUKFI is the most time consuming approach among 631

them, which is expected as it needs additional multiple hypothe- 632

sis testing and robust regression procedures. However, these two 633

procedures just impose slight computing burden to the proposed 634

method since the RDUKFI is implemented at each local genera- 635

tor and very fast to execute. A closer look at the computing time 636

of the proposed method under different conditions reveals that it 637

requires more time in Cases 2–4 than in Case 1. This is because 638

more time is required to test multiple hypotheses when outliers 639

occur. In addition, it should be noted that we need to check all 640

the three hypotheses so that innovation and structural outliers 641

can be distinguished while only two hypothesis are required for 642

the detection of observation outliers. Therefore, the computing 643

times of Cases 3 and 4 are larger than that of Case 2. Finally, the 644

proposed RDUKFI is implemented locally and independent of 645

other generators and other system wide-area measurements, it is 646

thus suitable for large-scale power system online applications. 647

F. Discussion of Practical Industry Application 648

The proposed robust DSE is implemented at each genera- 649

tor substation using generator dynamic models as well as local 650

PMU measurements. Since generator model and parameters, 651

measurement devices and local computer have been there al- 652

ready, no hardware modification has to be carried out. The only 653

requirement is to add an additional software block at the local 654

computers that performs the dynamic simulation using mea- 655

sured current phasors as inputs and combine their simulation 656

outputs with the measured voltage phasors and frequency for 657

dynamic state estimation. It should be noted that the results of 658

the robust DSE can be used for power system online monitor- 659

ing, control and protection [13], [20], [21]. For example, a recent 660

patent by the vendor ABB demonstrated the value of the DSE for 661

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online monitoring [20]. The effectiveness of the DSE assisted662

adaptive protection scheme has been tested in real system [21].663

Thus, although some costs are needed to change the existing664

code for the DSE implementation, its benefits for system online665

monitoring, control, and protection are promising.666

V. CONCLUSION AND FUTURE WORK667

In this paper, a fast RDUKFI-based decentralized DSE is668

proposed. It is implemented at each local generator and inde-669

pendent of the other generators, system parameters, and thus670

suitable for large-scale power system online applications. Fur-671

thermore, our RDUKFI is able to detect, distinguish and sup-672

press the observation, innovation and structural outliers while673

achieving high statistical efficiency in presence of both normal674

and large measurement noise. We propose projection statistics-675

based multiple hypothesis testing approach for outlier detection676

and processing. The identified outliers are suppressed by a gen-677

eralized maximum-likelihood type (GM)-estimator. Numerical678

results carried out on the IEEE 39-bus system demonstrate the679

effectiveness and robustness of the proposed method.680

It should be noted that the proposed robust DSE is general681

in that it can be easily extended to estimate the dynamic states682

of other power system components, such as dynamic loads,683

wind generators and various types of higher order exciters. In684

addition, the 9th-order two-axis model with DC1A exciter is685

one of the recommended models by IEEE for transient stability686

analysis [22]. Thus, we believe that our results have practical687

meanings. The test of the proposed DSE for more detailed gener-688

ator models will be carried out as future work. Furthermore, the689

proposed multiple hypothesis testing approach will be extended690

to locate the specific erroneous parameter values for parameter691

calibration.692

REFERENCES693

[1] Z. Huang, K. Schneider, and J. Nieplocha, “Feasibility studies of applying694Kalman filter techniques to power system dynamic state estimation,” in695Proc. 8th Int. Power Eng. Conf., Singapore, Dec. 2007, pp. 376–382.696

[2] J. B. Zhao, M. Netto, and L. Mili, “A robust iterated extended Kalman697filter for power system dynamic state estimation,” IEEE Trans. Power698Syst., vol. 32, no. 4, pp. 3205–3216, Jul. 2017.699

[3] N. Zhou, D. Meng, Z. Huang, and G. Welch, “Dynamic state estimation700of a synchronous machine using PMU data: A comparative study,” IEEE701Trans. Smart Grid., vol. 6, no. 1, pp. 450–460, Jan. 2015.702

[4] Z. Huang, P. Du, D. Losterev, and B. Yang, “Application of extended703Kalman filter techniques for dynamic model parameter calibration,” Proc.704IEEE Power Energy Gen. Meeting, 2009, pp. 1–6.705

[5] L. Fan and Y. Wehbe, “Extended Kalman filtering based real-time dynamic706state and parameter estimation using PMU data,” Elect. Power Syst. Res.,707vol. 103, pp. 168–177, Oct. 2013.708

[6] E. Ghahremani and I. Kamwa, “Local and wide-area PMU-based decen-709tralized dynamic state estimation in multi-machine power systems,” IEEE710Trans. Power Syst., vol. 31, no. 1, pp. 547–562, Jan. 2016.711

[7] G. Anagnostou and B. C. Pal, “Derivative-free Kalman filtering based712approaches to dynamic state estimation for power systems with unknown713inputs,” IEEE Trans. Power Syst., vol. 33, no, 1, pp. 116–130, Jan. 2018.714

[8] A. K. Singh and B. C. Pal, “Decentralized dynamic state estimation in715power systems using unscented transformation,” IEEE Trans. Power Syst.,716vol. 29, no. 2, pp. 794–804, Mar. 2014.717

[9] M. Gandhi and L. Mili, “Robust Kalman filter based on a general-718ized maximum-likelihood-type estimator,” IEEE Trans. Signal Process.,719vol. 58, no. 5, pp. 2509–2520, May 2010.720

[10] P. Sauer and M. A. Pai. Power System Dynamics and Stability. Englewood721Cliffs, NJ, USA: Prentice-Hall, 1997.Q1 722

[11] A. Rouhani and A. Abur, “Observability analysis for dynamic state esti- 723mation of synchronous machines,” IEEE Trans. Power Syst., vol. 32, no. 4, 724pp. 3168–3175, Jul. 2017. 725

[12] NERC Reliability Guideline, “PMU placement and installation,” NERC, 726Atlanta, GA, USA, 2016. 727

[13] A. K. Singh and B. C. Pal, “Decentralized control of oscillatory dynamics 728in power systems using an extended LQR,” IEEE Trans. Power Syst., 729vol. 31, no. 3, pp. 1715–1728, May 2016. 730

[14] J. B. Zhao, L. Mili, and F. Milano, “Robust frequency divider for power 731system online monitoring and controls,” IEEE Trans. Power Syst., to be 732published. Q2733

[15] S. Julier and J. K. Uhlmann, “Unscented filtering and nonlinear estima- 734tion,” Proc. IEEE, vol. 92, no. 3, pp. 401–422, Mar. 2004. 735

[16] T. Lefebvre, H. Bruyninckx, and J. De Schutter, “Comment on “a new 736method for the nonlinear transformation of means and covariances in 737filters and estimators,” IEEE Trans. Automat. Control, vol. 47, no. 8, 738pp. 1406–1408, Aug. 2002. 739

[17] J. B. Zhao and L. Mili, “Robust unscented Kalman filter for power system 740dynamic state estimation with unknown noise statistics,” IEEE Trans. 741Smart Grid, to be published. 742

[18] IEEE PES TF on Benchmark System for Stability Controls, “Benchmark 743systems for small-signal stability analysis and control,” IEEE Power En- 744ergy Soc., Piscataway, NJ, USA, Tech. Rep. PES-TR18, Aug. 2015. 745

[19] A. Rouhani and A. Abur, “Linear phasor estimator assisted dynamic state 746estimation,” IEEE Trans. Smart Grid, vol. 9, no. 1, pp. 211–219, Jan. 2018. 747

[20] E. Scholtz, V. D. Donde, and J. C. Tournier, “Parallel computation of 748dynamic state estimation for power system,” U.S. Patent Appl. 13 832 670, 749Mar. 15, 2013. 750

[21] “Setting-less protection: Laboratory testing-final report,” Power Syst. Eng. 751Res. Center, Arizona State Univ., Tempe, AZ, USA, 2014. Q3752

[22] IEEE Guide for Synchronous Generator Modeling Practices and Appli- 753cations in Power System Stability Analyses, IEEE Std 1110-2002, 2003. 754

Junbo Zhao (S’13) received the Bachelor’s degree in 755electrical engineering from Southwest Jiaotong Uni- 756versity, Leshan, China, in 2012. He is currently work- 757ing toward the Ph.D. degree at the Bradley Depart- 758ment of Electrical and Computer Engineering, Vir- 759ginia Polytechnic Institute and State University (Vir- 760ginia Tech), Falls Church, VA, USA. 761

He did a summer internship at Pacific Northwest 762National Laboratory from May 2017 to August 2017. 763He has authored two book chapters, and authored or 764coauthored more than 30 peer-reviewed journal and 765

conference papers and nine Chinese patents. His research interests lie in power 766system real-time monitoring, operations and cyber security that include power 767system state estimation, power system dynamics and stability, static and dy- 768namic load modeling, power system cyber attacks and countermeasures, big 769data analytics, and robust statistics with applications in the smart grid. 770

Dr. Zhao is currently the Chair for the IEEE Task Force on Power Sys- 771tem Dynamic State and Parameter Estimation, and the Secretary of the IEEE 772Working Group on State Estimation Algorithms and the IEEE Task Force on 773Synchrophasor Applications in Power System Operation and Control. 774

775Lamine Mili (LF’17) received the Electrical Engi- 776neering Diploma from the Swiss Federal Institute of 777Technology, Lausanne, Switzerland, in 1976, and the 778Ph.D. degree from the University of Liege, Liege, 779Belgium, in 1987. 780

He is a Professor in electrical and computer en- 781gineering, Virginia Tech, Falls Church, VA, USA. Q4782He has five years of industrial experience with the 783Tunisian electric utility, STEG. At STEG, he worked 784in the planning department from 1976 to 1979 and 785then at the Test and Meter Laboratory from 1979 to 786

1981. He was a Visiting Professor with the Swiss Federal Institute of Technol- 787ogy, Lausanne, Switzerland, the Grenoble Institute of Technology, Grenoble, 788France, the Ecole Superieure D’electricit, Gif-sur-Yvette, France, and the Ecole 789Polytechnique de Tunisie, La Marsa, Tunisia, and did consulting work for the 790French Power Transmission company, RTE. His research has focused on power 791system planning for enhanced resiliency and sustainability, risk management of 792complex systems to catastrophic failures, robust estimation and control, non- 793linear dynamics, and bifurcation theory. He is a co-founder and co-editor for 794the International Journal of Critical Infrastructure. He is the chairman for the 795IEEE Working Group on State Estimation Algorithms. He was a recipient of 796several awards including the U.S. National Science Foundation (NSF) Research 797Initiation Award and the NSF Young Investigation Award. 798

799

junbo zhao , life fellow, ieee ieee proof

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