seismic-resilient bulk power grids: hazard ... · the monte carlo simulation is ... seismic hazard...

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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 1

Seismic-Resilient Bulk Power Grids HazardCharacterization Modeling and Mitigation

Mostafa Nazemi Student Member IEEE and Payman Dehghanian Member IEEE

AbstractmdashThe operation of the electricity delivery infrastruc-ture is environmentally driven and vulnerable to a wide rangeof high-impact low-probability (HILP) hazards Among differentclasses of HILP disasters earthquakes are one of the most un-predictable hazards which may lead to widespread disruptionsof mission-critical services and infrastructures This article intro-duces a comprehensive framework for modeling and characteriza-tion of seismic hazards vulnerability assessment of electric systemsto the earthquake and corrective actions and mitigation strategiesensuring operational resilience The Monte Carlo simulation isemployed to produce a realistically large set of possible earthquakescenarios to capture the stochastic nature of seismic hazards Aninclusive approach is then introduced based on the fundamentalprinciples of fragility curves to assess the vulnerability of powergeneration facilities in the face of HILP earthquakes A new seismicrisk metric is suggested that takes into account both hazard andvulnerability probabilities as well as the financial consequencesdue to postquake disruptions in power generation stations Alongwith the generation redispatch strategy as a conventional mitigationsolution following a nontrivial contingency a new mitigation strat-egy centered on corrective network topology control is formulatedto maximize the load outage recovery following HILP disruptionsThe proposed decision support tool enables a swift restoration andimproved resilience in dealing with the aftermath of the HILPearthquakes Efficacy of the proposed framework is numericallyanalyzed and verified on both the IEEE 57-bus and IEEE 118-bustest systems

Index TermsmdashCorrective topology control (CTC) decision-making earthquake high-impact low-probability (HILP)mitigation resilience risk vulnerability

I INTRODUCTION

A Problem Statement and Research Motivation

EXTREME natural disaster events such as floods wind-storms tsunamis and earthquakes have caused catas-

trophic damages on the power energy delivery infrastructure [1]According to [2] 58 of all the US grid outages in the 10-yeartime interval of 2003ndash2012 are driven by the weather-causedhigh-impact low-probability (HILP) events resulting in an es-timated $18ndash33 billion annual loss Among different HILP

Manuscript received February 28 2019 revised July 16 2019 and September21 2019 accepted October 28 2019 Review of this manuscript was arrangedby Department Editor A Solis (Corresponding author Payman Dehghanian)

The authors are with the Department of Electrical and Computer Engi-neering George Washington University Washington DC 20052 USA (e-mailmostafa_nazemigwuedu paymangwuedu)

Color versions of one or more of the figures in this article are available onlineat httpieeexploreieeeorg

Digital Object Identifier 101109TEM20192950669

disasters earthquakes are one of the most unpredictable anddisastrous hazards [3] which may lead to widespread disruptionsin electrical power grid and its critical infrastructure On January17 1994 the Northridge earthquake struck the city of LosAngeles and surrounding areas resulting in 25 million cus-tomers out of power [4] The Great Hanshin earthquake occurreda year later affecting the city of Kobe Japan Twenty fossil-fired power generation units six 275-kV substations and two154-kV substations were damaged resulting in approximately26 million customers affected by electricity outages [5] OnOctober 17 1989 the Loma Prieta earthquake in the greaterSan Francisco Bay Area in California caused 63 deaths 3757injuries and $6 billion in property damage [6] Nearly 2 millioncustomers were disconnected immediately from the Los Angelespower network following the 1994 Northridge earthquake theestimated economic loss due to the Northridge earthquake wasexceeding $49 billion [7] On May 18 2008 the Wenchuanearthquake caused extensive damage to the local power trans-mission and distribution systems in Sinchuan province Chinawhere approximately 900 substations and 270 transmission linesof the State Power Grid were damaged It has been estimated thatat least 90 of the damage could have been avoided by adoptingnew guidelines for seismic design planning and adaptation [8]Approximately 90 of Chileans did not have electricity immedi-ately following the 88 (MW ) earthquake on February 27 2010The event caused the largest power transmission company inChile to have direct losses of approximately $65 billion [9] Thedevastating Tohoku Chiho Taiheiyo-Oki earthquake on March11 2011 and its aftershocks damaged 14 power plants 70transformers and 42 transmission towers among other fail-ures The outage stemming from the event affected 46 millionresidents and the April 7 aftershock affected an additional 4million [10] Recently on November 30 2018 a magnitude 7earthquake rocked southern Alaska resulting in downed powerlines collapsed roads and fleeing population [11]

The power grid is a complex interconnected network oftechnologies in generation transmission distribution controland communications that are decentralized across a wide rangeof geographical regions and are therefore widely exposedto external threats Traditionally power systems planning andoperation paradigms were driven by known reliability metricsand evaluation strategies However it has become more appar-ent over the past years that further considerations beyond theclassical reliability view are required to keep the lights on atall times As the frequency of catastrophic HILP-caused powergrid outages has been significantly trending higher in recent

0018-9391 copy 2019 IEEE Personal use is permitted but republicationredistribution requires IEEE permissionSee httpwwwieeeorgpublications_standardspublicationsrightsindexhtml for more information


2 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT

years [12] planning solutions in preparation for decisions inadaptation to and mitigation ie swift response and recoveryin the face of seismic disasters has been sensed as an urgentneed [3]

B Literature Survey

There are several studies in the literature which have focusedon the impacts of seismic hazards on the electric power systemsDifferent upgrading strategies were introduced in [13] using anew quantitative index to decide on vulnerable nodes under dif-ferent seismic scenarios The criticality of electric componentswas evaluated in [14] using the resistance index of electric equip-ment during various earthquake conditions in Japan In [15] arisk-based seismic model is proposedmdasha suite of earthquakescenarios and a set of consequential scenarios for each earth-quake condition are defined to optimize the capacity expansionof transmission and generation sectors In [16] and [17] aseismic vulnerability assessment using the network hierarchicaldecomposition is employed and tested on the IEEE 118-bus testsystem which was stressed by uniformly and spatially distributedearthquake scenarios In [18] the authors study the vulnerabilityof the interdependent European gas and electricity transmissionnetworks using a GIS-based probabilistic reliability model inwhich the network fragility curves in terms of different perfor-mance measures are evaluated A framework for seismic risk as-sessment in electric power systems was proposed in [19] whereseismic hazard is modeled using a probabilistically weightedhazard scenario approach A set of earthquake scenarios withcorresponding occurrence probabilities is considered in orderto assess the accessibility of electric components following anearthquake A framework was proposed in [20] to assess thesystem resilience in terms of energy not supplied and energyindex of unreliability following an earthquake three adapta-tion measures (eg robustness redundancy responsiveness)are evaluated for the northern Chilean electric power systemSimilarly the authors in [21] generated multiple earthquakescenarios using Monte Carlo simulations (MCS) to sample theearthquake magnitude and locations A ground motion predic-tion is utilized to sample peak ground acceleration (PGA) atthe site of each component In [22] seismic electric powersystem models are developed by identifying the possibility ofsequential failures of substations The authors in [23] collecteda large damage dataset to develop fragility curves for a widerange of electric equipment In [24] the seismic performance ofelectric power systems in the city of Los Angeles is evaluatedby applying historic seismic events (eg 1971 San Fernandoand 1994 Northridge earthquakes) to electric components andassessing the loss of connectivity index using fragility curvesSimilarly [25] evaluated the degradation performance of the LosAngeles Department of Water and Powerrsquos (LADWPrsquos) electricpower system using 47 earthquake scenarios to develop the riskcurves for the LADWPrsquos power transmission system In [26]the sequential failures of transmission network under severeearthquakes are identified by considering multiple earthquakescenarios representing the Los Angeles area seismic hazardIn [27] and [28] the seismic performance and vulnerability of

the electrical power system in San Francisco Bay area followingthe 1989 Loma Prieta earthquake is evaluated by assessing thenetwork power imbalances due to postquake disconnection ofsubstations The loss of connectivity between substations thefailure probability of substations and transformers and system-wide power imbalances are evaluated in [29] considering asample earthquake scenario with moment magnitude equal to75 Seismic fragility curves of high-voltage transmission towersin South Korea were developed centered on the limit states thatare defined based on the assumption of linear elastic behaviorof power towers and a set of 20 recorded ground motions inSouth Korea [30] The authors in [31] presented an algorithm toevaluate the serviceability of water distribution systems follow-ing a scenario-based earthquake characterization considering thedependence of water availability on the serviceability of electricpower systems The seismic vulnerability of an interconnectedwater and power system was evaluated in [31] demonstratingthe importance of taking infrastructure interactions into ac-count Likewise a framework to capture the interdependenceamong different sectors such as electric power water distri-bution transportation and telecommunication infrastructureswas proposed utilizing the conditional probabilities of failuresfollowing a seismic hazard [32] In [33] an optimal mitigationstrategy to address seismic risks in the Central United Stateswas investigated considering a suite of earthquake scenariosthat nearly replicate the exceeding curves for PGA as measuredat 81 control locations across the New Madrid Seismic Zone(NMSZ) Similarly a computationally effective procedure fortransmission and generation expansion planning decisions wasproposed in [33] to optimize the seismic mitigation strategies inlarge-scale power systems

Despite a vast majority of research focusing on planningand operation strategies in response to seismic hazards therestill remain several challenging concerns neither solved noreffectively respondedmdashhow does earthquake energy propagatethrough the ways that seismic waves pass how is the earthquakeenergy attenuated and which parameters affect the earthquakeenergy attenuation how can the earthquake energy parameters(eg PGA) at the location of power equipment (eg powergenerating units) be assessed how can the earthquake energybe quantified in terms of fragility curves of the equipment andconsequently how can the impact of seismic shocks be assessedin terms of different probability damage states following anearthquake

C Research Contributions

The main contributions of this article are highlighted asfollows

1) Seismic Hazard Modeling and Impact Characterization onPower Generation Facilities We develop a model that system-atically captures the effects of earthquakes on power generationsystems by considering realistically large sets of scenarios gener-ated via MCS to include the stochastic nature of ground motionsWe then illustrate how the seismic forces can be quantified usingan analytical attenuation relationship (AR) Numerical modelscentered on the concept of fragility curves are developed to


NAZEMI AND DEHGHANIAN SEISMIC-RESILIENT BULK POWER GRIDS HAZARD CHARACTERIZATION MODELING AND MITIGATION 3

Fig 1 Proposed framework for seismic-resilient power gridsmdashoverallarchitecture

assess different damage state probabilities following an HILPearthquake hazard

2) Seismic Hazard Mitigation Through Corrective NetworkTopology Control Instead of positioning the grid operator ina reactive mode in response to seismic outages a decision-making support tool is suggested that provides the operatorswith different restoration strategies to mitigate the impacts ofseismic hazards across the network In this context the proposedoptimization engine suggests power network reconfigurationusing transmission line switching (TLS) actions ie removinglines out of service hence modifying the network topology andthe way electricity flows in the grid The suggested approach isa temporary corrective solution employing the network existinginfrastructure with minimum additional costs to swiftly recoverthe electricity outages

The rest of this article is structured as follows Section IIpresents an overview of the proposed three-stage frameworkSection III elaborates the extensive numerical analysis of theproposed framework applied to two different test case systems1) the IEEE 118-bus test system and 2) the IEEE 57-bus testsystem Section IV concludes this article

II PROPOSED FRAMEWORK BIG PICTURE

Fig 1 presents an overall structure of the proposed three-stageframework for realizing a seismic-resilient bulk power gridThe framework is centered on the HILP earthquake hazardcharacterization seismic vulnerability assessment models andseismic mitigation strategies details on which are provided inthe following

Fig 2 2018 MMI hazard map of USA showing estimate of earthquake shakingfor (a) 50 probability of exceedance (PE) in 50 years (likely) (b) 10 PE in50 years (infrequent) and (c) 2 PE in 50 years (rare) [34]

A Seismic Hazard Characterization

The first step to model an HILP seismic hazard is to identifythe geological risks in a vast area of interest seismic hazardmaps are developed to illuminate areas that are affected orvulnerable to a particular natural hazard such as earthquakeground motion landslides liquefaction etc Particularly theearthquake-mapped hazard refers to an estimate of the probabil-ity of exceeding a certain amount of ground shaking or groundmotion in 50 years For instance Fig 2 expresses the 2018modified Mercalli intensity (MMI) hazard map of the UnitedStates reflected through the estimates of earthquake hazardssurpassing different probability of exceeding (PE) levels in50 years [34] As one can see a seismic hazard depends onthe magnitudes and locations of likely earthquakes how oftenthey occur and the properties of the rocks and sediments that theearthquake waves travel through The most common criterion todetermine the range of a ground motion is the horizontal PGAwhich is defined as the largest absolute value of accelerationdetermined for a given component Horizontal acceleration istypically employed to define the ground motion properties dueto its inherent relationship with inertia forces In fact the largestdynamic forces occurring on a structure are closely related toPGA Since the earthquake energy propagation and attenuationare highly dependent on the properties of the soils that the earth-quake passes through the earthquake intensity parameters (egPGA) should be evaluated at the location of power generation



Fig 3 Illustration of seismic wave propagation the hypo-center of anearthquake and distance between the test case location and the earthquakersquosepicenter

facilities through an analytical AR quantified based on severalprobabilistic derivations According to Fig 3 the reduction inpeak ground motion (eg acceleration) with distance from theepicenter (R) for an earthquake with a given magnitude (M ) isillustrated and can be quantified based on a suitable analyticalAR Several factors affect the attenuation relationship which areas follows [35]

1) source specifications magnitude fault mechanism anddistance from the seismic source

2) the direction of wave propagation reflection refractionand energy absorption due to the properties of the materialthe seismic waves pass through

3) the geology and topography effects of the siteAccording to [36] a general formulation to quantify AR is

introduced as follows

ln(Ψ) = ν + f1(M) + f2(R) + f3(Z) + ε (1)

where Ψ is the strong ground motion parameter and is directlyrelated to the magnitude M and inversely related to the distanceR The coefficients corresponding to these relationships can beobtained empirically through statistical methods over accelero-grams ν is a constant ε is a random error with mean value ofzero and standard deviation of σ representing the presence ofuncertainty in Ψ Other parameters such as site conditions faultmechanism sediment thickness etc can be mathematicallymodeled in a general form of f3(Z)

The main challenge in seismic hazard mitigation is originatedfrom the fact that an HILP earthquake cannot be accuratelypredicted As demonstrated in Fig 4 the MCS technique isemployed in this article in order to capture the uncertain-ties regarding the stochastic occurrence of earthquakes TheMCS technique enables the generation of a huge database withmany possible earthquake scenarios Earthquake characteris-tics (eg magnitude epicenter distance soil type) are firstdefined through the analytical AR A huge set of earthquakescenarios is next generatedmdashincluding slight to severe hazardscenariosmdashto quantify the PGA values at the location of power

system generation facilities (eg conventional power generatingunits)

B Seismic Vulnerability Assessment Model

In order to evaluate the seismic vulnerability of power equip-ment a set of damage states are introduced highlighting the factthat different structures respond differently to earthquakes andas a result different damage states with different probabilitiesare defined based on the fundamental principles of the fragilitycurves Fragility curves are statistical tools representing theprobability of exceeding a given damage state (or performance)as a function of an engineering demand parameter that representsthe ground motion (preferably spectral displacement at a givenfrequency) Generally fragility curves are obtained throughdifferent methods [37] as follows

1) Expert judgmentmdashthe oldest and simplest approach tocompute the fragility curves based on the earthquakeengineersrsquo experience where the accuracy of the re-sults is highly dependent on the experience of the ex-perts and the number of expert consultants This methodis subject to a significant uncertainty and may be lessaccurate

2) Empirical methodmdashcentered on the earthquake historicalcatalogues A very dense network of ground motion datarecords is required to reduce the uncertainty in the empir-ical fragility curves

3) Analytical methodmdashthe most popular in developing seis-mic vulnerability curves of different structures This ap-proach is realized through analysis of simulations andhistorical data on the structural models and encapsulatesboth real andor synthetic ground motions [38]

4) Hybrid methodmdashfragility curves are derived by synergis-tically combining the features of both experimental andanalytical methods [39]

The damage functions for power system equipment are char-acterized in the form of log-normal fragility curves correlatingthe probability of being in or exceeding a damage state for agiven seismic parameter According to [40] each fragility curveis characterized by a median and log-normal standard deviation(σ) of the PGA parameter which corresponds to the damage statethresholds and associated variability The probability of residingin or exceeding a state of structural damage (ϑ) is described asfollows

P [ϑ|Sd] = Φ

[1

σϑln

(Sd

Sdϑ

)](2)

where Sd is the spectral displacement Sdϑ is its median valueσϑ is the standard deviation corresponding to the natural loga-rithm of the spectral displacement at which a structure reachesthe damage state threshold and Φ is the standard cumulativenormal distribution function

In order to quantitatively assess the impact of a seismic shockon power generation facilities with a given horizontal PGA(ρ) the probability associated with different states of structural



Fig 4 Flowchart of the employed MCS procedure

Fig 5 Different fragility curves for power generation facilities

damage should be quantified In this article fragility curves forconventional power generating units are defined correspondingto five states of damage which respectively are

1) no damage2) slight damage

3) moderate damage4) extensive damage5) complete damageDifferent fragility curves are demonstrated in Fig 5 The

probability corresponding to each state of damage following a



TABLE IOVERVIEW OF AN HILP EARTHQUAKErsquoS IMPACTS ON POWER GENERATION FACILITIES

seismic hazard is evaluated as follows

PC = P (C|ρ) (3)

PE = P [E|ρ]minus P [C|ρ] (4)

PM = P [M |ρ]minus P [E|ρ] (5)

PSl = P [Sl|ρ]minus P [M |ρ] (6)

PN = 1minus P [Sl|ρ] (7)

where NSlME and C respectively stand for none slightmoderate extensive and complete damage states of a grid ele-ment following an HILP earthquake The cumulative probabilityof each damage state is evaluated directly based on differentfragility curves [41] while the individual probability of eachstate of damage is assessed using (4)ndash(7) Different powergeneration facilities may be affected differently by an HILPearthquake depending on the geographical location and vicinityto the earthquakersquos epicenter Hence generating units may beon different operational availability modes following an HILPearthquake For instance according to Table I if the powergenerating unit undergoes an extensive and complete operationaldamage state it will be out of service following the hazardLikewise if the generating unit enters the moderate damagestate it is assumed that the power generating unit will lose50 of its operational functionality (capacity) ie a deratedoperating state The none and slight damage states may causeslight damages the impacts of which on the power generatingunit can be ignored [42]

C Seismic Mitigation Strategy

1) Seismic Hazard Risk Metric for Power Generation Sys-tems A general risk metric that encapsulates the hazardprobability vulnerability and consequences is proposed as fol-lows [43]

Rtsys =

sumkisinK

⎛⎝sum

qisinQ

(P tk[Γq|T ]Ct

k(Γq))⎞⎠ (8)

where Rtsys is the spatiotemporal state of risk for power gen-

eration equipment at time t P tk[Γq|T ] is the vulnerability ie

the probability of an abnormal condition Γq in the system orcomponent performance in the face of hazardous condition kwith the threat intensity T at time t and Ct

k(Γq) is the worthof loss ie an estimate of the consequential losses due to thehazardous condition k In this article wherever ldquordquo is usedin the equations it means multiplication The proposed riskmeasure can be defined as a stochastic process referenced in time

and space

Rtsys(x t) =

sumkisinK

⎛⎝sum

qisinQ

(P tk[Γq(x t)|T (x t)]Ct

k(Γq(x t)))⎞⎠

(9)where x represents the spatial parameter (longitude and latitude)and t reflects the temporal parameter obtained via timing sensors(eg GPS) K and Q in (8) and (9) represent respectively theset of extreme weather conditions k and the set of componentsq of the system which are subjected to the extreme weathercondition k

The vulnerability in the proposed risk model reflects the prob-ability that a seismic hazardous condition will cause an eventor undesirable state in the electricity grid Such disorders mayinclude the shortage in generation capacity (ie a compromisedgeneration adequacy) and efficiency of the electricity generationsystems

In the face of a severe seismic hazard the expected impacts onthe grid operation in terms of economic loss could be quantifiedas consequence The consequences can be different dependingon whether there is a load curtailment in the system due the HILPearthquake If the earthquake does not result in an electricityoutage (Θ= 0) the imposed cost includes the maintenance costsand the redispatch costs of the available power generating unitsIn case of a postquake electricity outage (Θ = 1) the imposedcost depends on the maintenance costs electricity outage costsand economic impact of operation adjustments (generation re-dispatch) in mitigation of the power grid violations all togetherare aggregated and quantified as the economic consequencesThe total imposed costs corresponding to the failure or partialloss of generation in generating unit q at time t represented asCt

k(Γq) is quantified as follows

Ctk(Γq) =

Ct

Mq +sum

ωisinΩ(CtLRq + Ct

ICq) if Θ = 1

CtMq + Ct

RDq if Θ = 0

(10)where the first term Ct

Mq is the fixed cost corresponding to thecorrective maintenance actions to fix the damaged equipmentThis cost includes the replacement cost of the equipment thecost of labor and the cost of maintenance tools and materialsWhen there is no load outage in the system Θ = 0 the secondterm (variable cost) includes the generation redispatch costsCt

RDq = Δsum

gisinG cgPg to meet the demanded loads Other-wise Θ = 1 and the second term (variable cost) includes thelost revenue costs Ct

LRq imposed to the electric utility and theinterruption costs Ct

ICq imposed to the interrupted customersThe former cost function highlights the utilityrsquos lost revenue dueto its inability to sell power during the replacement or corrective



maintenance interval and can be quantified as follows [44]

CtLRq =

sumωisinΩ

(χtωEENSt

ωq

)(11)

whereχtω is the electricity price ($MWh) at load point ω at time

t EENStωq is the expected energy not supplied (MWh) at load

point ω due to failure of equipment q at time t Here the EENSindex of reliability is calculated through the probabilistic stateenumeration method [44] by solving the following optimizationproblem (12) subject to a set of constraints in (13)ndash(28)

minhisinH

sumωisinΩ

(ILt

ωh = P tω minus P tsupplied

ωh

)(12)

Png minus

summ

VnVm(Gnm cos δnm +Bnm sin δnm)

minus Pnω = 0 foralln (13)

Qng minus

summ

VnVm(Gnm sin δnm minusBnm cos δnm)

minusQnω = 0 foralln (14)

Pjnm = VnVm(Gnm cos δnm +Bnm sin δnm)

minusGnmV 2n forallj (15)

Qjnm = VnVm(Gnm cos δnm minusBnm sin δnm)

+ V 2n (Bnm minus bshnm) forallj (16)

P 2jnm +Q2

jnm le (Smaxj )2 forallj (17)

δminn le δn le δmax

n foralln isin N (18)

V minn le Vn le V max


(P tg minus rdntg )ζtg le P t

g le (P tg + ruptg )ζtg forallg isin G (20)

Qming ζtg le Qt

g le Qmaxg ζtg forallg isin G (21)

0 le rtg le min(rmaxg Δg

) forallg isin G (22)

0 le rdntg le min(rdnmaxg Δdn

g

) forallg isin G

(23)

P tg + rtg le Pmax

g forallg isin G (24)

Pming le P t

g minus rdntg forallg isin G (25)sumgisinG

ruptg ge Ruptz forallz isin Z (26)

sumgisinG

rdntg ge Rdntz forallz isin Z (27)

0 le ILntωh le Pnt

ω foralln isin N forallh isin H (28)

where h and H are respectively the contingency state and theset of all contingency states ω and Ω are the load points and theset of all load points and t reflects the time Here up to the thirdorder of system contingencies are taken into account to evaluatethe system reliability performance following the HILP incidentAt each contingency state the optimization problem in (12) tries

to minimize the total curtailed load (ILtωh) As it can be seen

in (12) the load outage at each load point is assessed by takingthe difference between the actual demand (P t

ω) and the suppliedload (P tsupplied

ωh ) following the contingency event Equations (13)and (14) represent two sets sets of nonlinear nodal active andreactive power balance constraints where Pn

g and Qng are the net

active and reactive power injected (generated) at bus n Gnm

is the real part of the elements in the bus admittance matrixYBus corresponding to the nth row and mth column Bnm is theimaginary part of the elements in the bus admittance matrix YBus

corresponding to the nth row andmth column Vn and Vm are thevoltage at bus n and bus m δnm is the difference in the voltageangle between bus n and bus m and Pn

d and Qnd are the real and

reactive demanded load at bus n Pjnm and Qjnm in constraints(15) and (16) represent active and reactive power flow limitsat a branch from bus n in the direction toward bus m j is isthe branch which connects bus n to bus m and bshnm representsthe shunt susceptance of the line connecting bus n to bus m Theinequality constraints (17) limit the active and reactive powerflow corresponding to the from and to ends of each transmissionline j to the apparent power flow Smax

j Constraints (18) and(19) reflect the upper and lower bounds of bus voltage angleδn and bus voltage magnitude Vn for each node (bus) n in thesystem Supply constraints are presented in (20) and (21) whichenforce the output of generating unit g within the set of allgenerating units G to be zero if it gets disconnected from thenetwork at time t If a generating unit g is available the changein its active and reactive power output (P t

g Qtg) is limited to

the predetermined margins Disconnection of generating unitsis modeled through a vector of binary variables ζtg with 1denoting the availability of components and 0 otherwise rdntg

and ruptg reflect the downward and upward reserve rate of eachgenerating unit Constraints (22) reflect that the reserve rate (rtg)for each generating unit must be positive and limited above bya reserve offer quantity (rmax

g ) as well as the physical ramp rate(Δg) of the generating unit g Similarly constraint (23) statesthat the downward reserve rate must be positive and cappedwith a downward reserve offer quantity (rdnmax

g ) as well as thedownward physical ramp rate of the generating unit (Δdn

g ) Con-straints (24) and (25) enforce that the total amount of generatedpower in each generating unit g at time t (P t

g ) plus the reserverate of the generating unit (rtg) does not exceed its maximumcapacity (Pmax

g ) and likewise the total amount of generatedpower minus downward reserve of the generating unit (rdntg )is always higher than its minimum capacity (Pmin

g ) Constraints(26) and (27) ensure that enough upward and downward capacityat time t (Rupt

z Rdntz ) is procured by all system generating units

according to the reserve requirements in each region (z) Finallyconstraint (28) ensures that the interrupted load in bus n at timet following a contingency state h (ie ILnt

ωh) is less than thetotal demand at bus n (Pnt

ω )Probability and duration of each contingency state h are

evaluated in (29) and (30) by employing the availability ofonline components (y) and unavailability of the failed ones(x) [44] in particular πt

h is obtained in (29) by multiplyingthe availability of online components and unavailability of the



failed components in a contingency state h and τ th is calculatedin (30) using the failure rates of online equipment and repairrates of the failed equipment in a given contingency state In allthe abovementioned calculations the common two-state Markovmodel for each system component is considered [44] [45]

πth =

prodxisinΛx

ϑx

(ςx + ϑx)timesprodyisinΛy

ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)

where ϑ and ς are the failure rate and repair rate of equipmentThe EENS index of reliability is calculated as follows

EENStωq =

sumhisinH

πthτ

thIL

tωh forallω isin Ω (31)

where EENStωq is the expected energy not supplied at load point

ω due to failure of equipment q at time tThe third variable term in the cost function (10) highlights the

customer interruption costs due to an electricity outage event hat time t which is calculated as [45]

CtICq =

sumωisinΩ

EENStωqVOLLω (32)

where VOLL is the value of the lost load and represents the unitinterruption cost for various customer sectors at a given loadpoint VOLL is directly correlated to the outage duration and isdetermined through historical data and customer surveys [45]

2) Network Corrective Topology Control (CTC) As the elec-tric grid keeps being exposed and vulnerable to HILP hazardsresearch on enhancing its resilience in the face of highly uncer-tain difficult-to-manage disasters has been conducted over thepast few years [43] [46] [47] Enhancing the grid structuralresilience is primarily focused toward deployment of the ldquohard-eningrdquo plans through reinforcement preventive maintenanceof the critical assets vegetation management efficient alloca-tion of flexible energy resources (eg energy storage units)etc [41] The grid operational resilience is targeted through fastemergency response and remedial actions defensive islandingoperation and control of the microgrids etc While the strategiesabove can be individually or collectively approached we areutilizing the network corrective topology switching to mitigatethe HILP-engendered risks across the grid

Following a contingency that results in local or widespreadelectricity outages a general accepted strategy in the electric sec-tor is redispatching the system available generating units in orderto maximize the load outage recovery Although this strategycan help the power system operators to recover a considerableportion of the load outage there still may remain some loadsin the disconnected network which cannot be solely recoveredby redispatching the available power generating units We referto such events as ldquonontrivialrdquo contingencies Complementingthe redispatch strategy CTC is an efficient approach whichadds another layer of fast and efficient control and providespower system operators with a promising restoration solutionto recover load outages following a contingency Harnessing

the built-in flexibility of the network topology by temporarilyremoving lines from service [12] [43] [48] the CTC is practicedthrough TLS actions offering a greater control on the flow ofpower and the way electricity flows in the network By relyingon the existing infrastructure and available generation resourceswith minimum additional costs the proposed framework aimsat safeguarding the grid by quickly and iteratively recoveringfrom the consequences of HILP earthquakes (eg outagescongestions grid violations etc)

If an HILP seismic event hits the bulk power system andconsequently leading to some load outages the following CTCoptimization would be called in advance to mitigate the risks

max

(GcupK minus

sumforallnisinN

un

)(33)

subject to

θmin le θn minus θm le θmax forallk(mn) isin K (34)sumforallk(n)

Pk minussum

forallk(n)Pk +

sumforallg(n)

Pg = Pnω minus un foralln isin N

(35)

Pmink (1minus weierpk) le Pk le Pmax

k (1minus weierpk) forallk isin K (36)

Bk(θn minus θm)minus Pk + weierpkηk ge 0 forallk isin K (37)

Bk(θn minus θm)minus Pk minus weierpkηk le 0 forallk isin K (38)

Pmink weierpk le Pk le Pmax

k weierpk forallk isin K (39)

Bk(θn minus θm)minus Pk + (1minus weierpk)ηk ge 0 forallk isin K (40)

Bk(θn minus θm)minus Pk minus (1minus weierpk)ηk le 0 forallk isin K (41)

maxPming Pg minus τrg le Pg

le minPmaxg Pg + τrg forallg isin GG (42)

0 le un le Pnω foralln isin N (43)

Pk = 0 forallk isin K (44)

Pg = 0 forallg isin G (45)sumforallkisinKK

weierpk = γ (46)

weierpk isin 0 1 forallk isin KK (47)

The above optimization model is a mixed integer linear pro-gramming problem formulated based on the DC optimal powerflow (DCOPF) formulation The primary decision variables inthe above optimization formulation are weierpk and un where weierpk

determines the switching action on transmission line k (0 noswitch 1switch) and un denotes the unfulfilled demand at busn in case of a contingency The objective function (33) is tomaximize the load outage recovery () corresponding to theseismic event contingency set G cup K (which includes outage oftransmission lines and generating units) The algorithm followedto solve the optimization model is a binary switching tree (BST)that iteratively finds the best line to switch and the optimal



Fig 6 IEEE 118-bus test system studied including four seismic zones

time-constrained generator redispatch until either the entiresystem demand is satisfied or a prespecified stopping criterionis met As a result it provides multiple switching operations andcorresponding redispatch actions to iteratively improve the loadoutage recovery and enhance the system operational resilienceAdditional details on the BST algorithm employed to solve thisoptimization problem can be found in [12] Constraint (34) setsthe angle difference range of the adjacent buses where k(mn)indicates the transmission line k which connects node (bus) mto node n The node balance constraints with modifications toaccount for partial demand fulfillment at each bus are presentedin (35) where

sumforallk(n) Pk is the net power flow through trans-

mission line k which comes from nodensum

forallk(n) Pk indicatesthe net power flow through transmission line k which goes tonode n

sumforallg(n) Pg is the total generated power at node n Pn

ω isthe demand at bus n and un indicates the unfulfilled demand atbusn This constraint ensures a power balance at each node in thesystem at all times (ie the sum over all the incoming power to anode is equal to the sum of all outgoing power from that node)Constraints (36) and (39) set the capacity limits of in-service(k isin K) and out-of-service (k isin K) transmission lines whileconstraints (37) (38) (40) and (41) determine the power flowthrough the transmission lines Note that ηk is a big value for line

TABLE IICOEFFICIENTS OF THE APPLIED AR MODEL

k The redispatch constraints for the online generating units arecharacterized in (42) where Pg denotes the generator dispatchConstraints (43) set the bounds for unmet demand variable un ateach bus limited above by the total demanded electricity at thatsubstation The line and generating unit outages are reflected inconstraints (44) and (45) respectively Constraints (46) and (47)are devised in addition to several other considerations to be ableto generate several topology control solutions per event (outagescenario) that would further improve the objective function ifsubsequently implemented in the form of a sequence The benefit(the amount of load outage recovery) achieved via the developedoptimization model is attributed to both switching actions andthe 10-min generation redispatch [12] Note that γ in constraint



Fig 7 Evaluated PGA at the location of the largest power generating unit in each seismic zone in Test Case 1 considering earthquake scenarios generated byMCS (a) g1 in Zone 1 (b) g12 in Zone 2 (c) g13 in Zone 3 and (d) g17 in Zone 4

(46) denotes the maximum number of switchable transmissionlines

III SIMULATION RESULTS AND DISCUSSION

A Test Case I IEEE 118-Bus Test System

1) Test System Description The proposed framework is ap-plied on the IEEE 118-bus test system which contains 118buses (substations) 186 transmission lines 19 conventionalgenerating units with a total capacity of 58592 MW and 99 loadbuses with a total demand power of 4519 MW [49] [50] Allsimulations have been performed on a laptop with a 340-GHzIntel Core i7-2620 processor and 8 GB of RAM using CPLEX1261 optimization package [51]

2) Seismic Hazard Characterization The single-line dia-gram of the 118 test-case study considering four differentseismic zones is depicted in Fig 6 Each seismic zone is char-acterized based on the specific geological properties eg theproperties of soil and sediments that the seismic waves passthrough the potential intensity of geological faults faults shapeand mechanisms etc Motivated by [36] the specific AR usedin this article is described as follows

ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)

whereMW is the moment magnitude scale andR is the epicenterdistance of an HILP earthquake hazard The coefficients defined

in (48) for each seismic zone segmented in Fig 6 are detailed inTable II

3) Seismic Vulnerability Assessment of Power GenerationFacilities In order to assess the postquake vulnerability andaccessibility of each power generating unit the proposed MCSis employed to generate at least 100 000 earthquake scenariosat each defined seismic zone The proposed MCS procedure(see Fig 4) is followed and consequently the PGA valueat the location of power generating units across the networkis quantified through the applied AR model The number ofacceptable scenarios depends on the prescribed boundaries forepicenter and earthquake magnitude parameters in the MCSengine We here assume that the maximum epicenter distancevalue for power generating units located in Zone 1 Zone 2Zone 3 and Zone 4 are 250 200 100 and 300 km respectivelyLikewise the boundaries on the earthquake magnitude in allscenarios are set between 45 and 75 surface magnitude [36]Eventually the MCS engine generates a unique database ofearthquake scenarios at each seismic zone Fig 7 demonstratesthe evaluated PGA at the location of the largest generatingunit in each seismic zone According to Fig 5 and (3)ndash(7)different probability damage states for 19 power generatingunits across the test case are evaluated with the correspondingprobabilities tabulated in Table III Without loss of generalitywe assume that the PGA for each power generating unit ateach zone is the mean PGA value of all 100 000 earthquakescenarios



TABLE IIIPROBABILITY OF DIFFERENT DAMAGE STATES FOR ALL GENERATING UNITS IN TEST CASE 1

Fig 8 Illustration of the probability of three functional modes for system generating units in different zones of Test Case 1 following the HILP earthquakehazard (a) Zone 1 (b) Zone 2 (c) Zone 3 and (d) Zone 4

According to Table I the postquake accessibility of powergenerating units in none and slight damage states is 100 inmoderate damage state is 50 and in extensive and completedamage states is 0 The postquake accessibility of each powergenerating unit is demonstrated as a probability function inFig 8 which can be set differently depending on the zonalgeological characteristics The power generating units locatedin Zone 3 are found to be the most vulnerable when fac-ing an HILP earthquake since the probability of derated andnonfunctional (total failure) states for generating units in thiszone are higher than that for other generating units across the

network Additionally the most significant portion of the systemtotal power generation portfolio (ie 3197) is generated bythe three generating units located in Zone 3 Therefore wehereafter focus on Zone 3 to develop the mitigation strategieswhen subjected to a seismic hazard The approach is howevergeneric enough to be applied to other seismic zones in thesystem

4) Seismic Consequences and Risk Assessment Consideringthree different postquake functionalities (ie healthy deratedand fail) for each power generating unit in Zone 3 results ina total number of 27 different scenarios with corresponding



Fig 9 VOLL for zonal load points in the studied 118-bus test network

probabilities Each scenario will migrate the grid into a newoperating state with different levels of power generationadequacy and vulnerability The risk factor per scenario of anHILP earthquake in Zone 3 and the economic consequencescan be assessed through the proposed formulations (9) and(10) respectively The maintenance cost Ct

Mq is considered1000 $MWh generation outage Similarly the electricity priceχtω is assumed 109 $MWh The VOLL for different load points

are illustrated in Fig 9 reflecting a mixed portfolio of loadtypes and categories of electricity customers (eg industrialcommercial residential agricultural etc) at each load pointNumerical results on the risk assessment in different scenariosare tabulated in Table IV As one can see in this table thereare nine scenarios out of the total 27 in which there is no loadoutage recorded following the HILP earthquake

5) Seismic Mitigation Solution Through CTC Strategies Ac-cording to the presented results in Table V the system willexperience load outages following an HILP seismic hazard in 18different scenarios Therefore there are two strategies that sys-tem operators can employ to recover the load outages employingthe network existing infrastructure 1) the traditional generationredispatch solutions and 2) the proposed CTC strategies Theproposed CTC optimization framework is simulated in all 18scenarios and the results are tabulated in Table V It can beseen that by temporarily switching transmission lines out ofservice and changing the network topology the load outagerecovery percentage can be significantly increased compared

to the traditional redispatch-alone strategies For instance theinitial load outage caused by the g13 contingency is 8052 MWof which only 340549 MW (4229 of the system total loadoutage) can be recovered through the redispatch-alone strategyNonetheless transmission line 112 (connecting bus 65 to bus68) can be switched OFFthrough which 605906 MW (7525 )of the system total load outage can be recovered Additionaldetails corresponding to the load outage recovery in differentload points are provided in Table V where the performance ofthe two mitigation strategies can be compared The comparisonresults in scenario 11 are depicted in Fig 10 Likewise theexpected value of interruption costs across the system (ieconsidering all 99 load points) over all scenarios with loadoutages are demonstrated in Fig 11

The system-wide risk improvement in two different cases offollowing 1) the redispatch-only practices and 2) CTC strate-gies are evaluated associated with different scenarios and theresults are illustrated in Fig 12 The system operation risk in theface of a seismic HILP hazard is generally improved consideringthe redispatch or CTC mitigation strategies One may howeversee that comparing to the redispatch-alone practice the CTCstrategies appeared to be more effective in terms of load outagerecovery and system-wide risk mitigation The computation runtime of the proposed CTC strategy for different switching lineoptions is tabulated in Table VI From this table one can seethat the more switchable transmission lines found the highercomputation run time will be



TABLE IVRISK ASSESSMENT RESULTS FOR DIFFERENT POWER GENERATION SCENARIOS IN ZONE 3 SUBJECTED TO A MULTITUDE OF SEISMIC CONDITIONS IN TEST CASE 1

TABLE VPERFORMANCE COMPARISON OF THE REDISPATCH-ALONE VERSUS THE PROPOSED CTC MITIGATION STRATEGIES ON SYSTEM-WIDE LOAD OUTAGE RECOVERY

IN TEST CASE 1

6) Sensitivity Analyses on the Number of Switchable LinesThe proposed analytics are generic enough to accommodate apredefined number of switching actions (γ) to be selected inthe form of a sequence In order to demonstrate the applicationwe resimulated the proposed CTC solutions in some randomscenarios to account for a maximum of three TLS actions (note

switching more number of transmission lines out of service in theface of extreme HILP events when the power grid experiences anemergency operating condition is highly unlikely as it may leadto system operating conditions where the required operationalrobustness is compromised) The numerical results are tabulatedin Table VII The three optimal topology control solutions



Fig 10 Illustration of the system-wide load outage following the g13 contingency in Test Case 1

Fig 11 Expected value of interruption cost across the network in Test Case 1 across all studied scenarios

Fig 12 Risk factor improvement comparison against an HILP seismic hazard in Test Case 1mdashtraditional generation redispatch strategy versus the proposedCTC mitigation solutions

include a one-line a two-line as well as a three-line switchingactions all accompanied by a 10-min generation redispatch ateach level With the changes that the proposed CTC strategyimpose to the power flows across the grid a significant loadoutage recovery can be achieved which results in an enhancedpower system resilience following an HILP seismic event Insome scenarios eg scenarios 7 12 14 16 and 17 changingthe number of switching lines does not change the benefit (the

TABLE VICOMPUTATION TIME REQUIRED FOR DIFFERENT SWITCHING

SCENARIOS IN TEST CASE 1



TABLE VIIPERFORMANCE COMPARISON OF THE REDISPATCH-ALONE VERSUS THE PROPOSED CTC STRATEGIES WITH DIFFERENT SWITCHING

LINE ACTIONS ON SYSTEM-WIDE LOAD OUTAGE RECOVERY IN TEST CASE 1

TABLE VIIIPROBABILITY OF DIFFERENT DAMAGE STATES FOR THE TWO MOST

VULNERABLE GENERATING UNITS IN TEST CASE 2

amount of load outage recovery) and the optimization engineis not able to find any feasible solution because the networktopology is at the best optimal configuration and additionalbenefits cannot be realized In addition the benefit obtainedby the optimization engine is attributed to both the switchingaction and the 10-min generation redispatch Thus the powersystem operators are provided with several recovery solutionsand can make a final decision on which solution to implement atthe end

B Test Case 2 IEEE 57-Bus Test System

1) Test System Description and Seismic Hazard Characteri-zation The proposed framework is applied to the IEEE 57-bustest system which contains 57 buses (substations) 80 transmis-sion lines and seven conventional generation units [52] Herewithout loss of generality we assume that the most vulnerableseismic zone segment includes the generation units G1 and G2which are connected to bus 8 and bus 9 respectively

2) Seismic Vulnerability Assessment of Power GenerationFacilities The MCS technique is employed to generate 100 000probable earthquake scenarios and consequently the PGA atthe location of generation units is calculated using the proposedattenuation relationship in (48) The probability of differentdamage states for the two generation units is tabulated in Ta-ble VIII

3) Seismic Consequences and Risk Assessment Consideringthree different postquake functionalities (ie healthy deratedand fail) for the aforementioned generating units results in atotal number of nine different scenarios with the correspondingprobabilities Numerical risk factors in different scenarios aretabulated in Table IX

4) Seismic Mitigation Solution Through CTC StrategiesThe proposed CTC optimization framework is simulated in allscenarios in which there is load outage following the HILPearthquake and numerical results are tabulated in Table X It can

be seen that the proposed CTC strategies can help increase theload outage recovery more efficiently compared to the traditionalredispatch-alone solution For instance the initial load outagecaused by G1 and G2 contingency is 410 MW of which only100 MW (2439) can be recovered through the redispatch alonestrategy However transmission line 69 (connecting bus 53 tobus 54) can be switched OFFthrough which 132 MW (3220)of the system total load outage can be recovered

C Discussions

1) Implementation Time For each CTC strategy or a selectedsequence of switching actions the computation time wouldbe the number of switches in the sequence multiplied by theallowable generation redispatch time plus the actual time takenby the utilities for implementing one TLS action We consider inour article that the generation dispatch must be attainable (ieconsidering each generators ramping rate) by ramping updownthe generators at most in τ minutes (in this article τ is set to10 min) In our article we assumed that the line switches areinstantaneous That is a two-line TLS sequence needs 20 minto be implemented in practice However it actually depends onthe utility practices (various possible redispatch times betweenthe switching actions within a given sequence) and the imple-mentation procedures followed in different utilities

2) N-k Reliability Criterion Regarding the N-k contin-gency check after switching actions some recent litera-ture suggests that the system should be able to meet theN minus 1 criterion after switching implementations [12] ieeven the CTC suggests some transmission lines to be of-fline (thereby realizing a network topology change) the sys-tem is able to withstand any additional failure of singleelements Future research is needed to efficiently incorporatethe N minus 1 criterion into the proposed CTC methodology

3) Practical Considerations In addition the operation ofcircuit breakers (CBs) for frequent switching implementationis not cheap System CBs might need emergency maintenanceafter several switching actions which may cause some additionalcosts In this article we neglect marginal costs for switching aCB since the true marginal costs of switching a CB is difficultto quantify In addition the cost of switching a CB is negligiblecompared to the gained economic benefits by minimizing thecustomer outages in the case of contingencies when the pro-posed CTC strategy is implemented If the proposed method isgoing to be realized in day-to-day operations the impact of CB



TABLE IXRISK ASSESSMENT RESULTS FOR DIFFERENT POWER GENERATION SCENARIOS IN TEST CASE 2 SUBJECTED TO A MULTITUDE OF SEISMIC CONDITIONS

TABLE XPERFORMANCE COMPARISON OF THE REDISPATCH-ALONE STRATEGY VERSUS THE PROPOSED CTC STRATEGIES IN TEST CASE 2

maintenance and degradation over time due to an increase inswitching frequency should be considered in the cost functions

IV CONCLUSION

This article proposed a comprehensive analytical architectureto model characterize and mitigate the HILP hazards in generaland earthquakes in particular The proposed framework firstcharacterized the seismic hazards then suggested a novel modelto quantitatively assess the vulnerability of power generationfacilities in the face of severe earthquakes and eventuallypresented the corrective topology control mitigation strategiesfor improved resilience In the first stage MCS technique wasutilized to generate a realistically large set of possible earthquakescenarios taking into account the stochastic nature of seismicevents According to the seismic source specification groundmotion magnitude fault mechanism distance from the seismicsource the direction of seismic wave propagation and theproperties of the soils and sediment that the seismic waves passthrough an analytical attenuation relationship was employed tocharacterize the seismic hazard via the peak ground accelerationat the site of the case studies In the second stage an effective ap-plication of fragility curves was pursued to assess the vulnerabil-ity of power generation facilities in facing the earthquake hazardsand estimate the postquake accessibility of power generatingunits Finally in the third stage a risk-based mitigation supporttool based on corrective topology control actions was suggestedto maximize the load outage recovery following seismic eventsThe efficiency of the proposed mitigation strategies was verifiedas compared to the traditional generation redispatch mitigationsolutions Harnessing the network built-in flexibility throughthe existing network infrastructure with minimum additionalcosts it was concluded that the CTC strategies could add anotherlayer of agile control response and recovery offering significantadvantages in boosting the system operational resilience

REFERENCES

[1] R J Campbell ldquoWeather-related power outages and electric system re-siliencyrdquo Congr Res Service Library Congr Washington DC USARep R42696 2012

[2] National Research Council The Resilience of the Electric Power DeliverySystem in Response to Terrorism and Natural Disasters Summary of aWorkshop Washington DC USA National Academies Press 2013

[3] W Bakun et al ldquoImplications for prediction and hazard assessment fromthe 2004 Parkfield earthquakerdquo Nature vol 437 no 7061 pp 969ndash9742005

[4] X Dong M Shinozuka and S Chang ldquoUtility power network systemsrdquoin Proc 13th World Conf Earthq Eng 2004 pp 1ndash15

[5] M Noda ldquoDisaster and restoration of electricity supply system byHanshin-Awaji earthquakerdquo in Proc Seminar Earthq Disaster ManageEnergy Supply Syst Chin Taipei Earthq Response Cooperation ProgramEnergy Supply Syst 2001 pp 5ndash6

[6] Major California Earthquakes [Online] Available httpscnicocompgsearthquakeearth3aspx

[7] D R Todd N J Carino R M Chung H S Lew A W Taylor and W DWalton ldquo1994 Northridge earthquake Performance of structures lifelinesand fire protection systemsrdquo Nat Inst Standards Technol GaithersburgMD USA Tech Rep 5396 1994

[8] J Eidinger ldquoWenchuan earthquake impact to power systemsrdquo in ProcTCLEE Lifeline Earthq Eng Multihazard Environ 2009 pp 1ndash12

[9] G Long ldquoReconectando a Chile despueacutes del terremotordquo Revista BusChile 2010

[10] Y Shumuta ldquoTohoku Chiho-Taiheiyo-Oki earthquakemdashDamage of elec-tric power facilities in Tohoku Electric Power Co Incrdquo Central Res InstElect Power Ind Tokyo Japan 2011

[11] 2018 Alaska Earthquake Report [Online] Available httpswwwnationalgeographiccomscience201811powerful-alaska-earthquake-building-damage-fatalities

[12] P Dehghanian Y Wang G Gurrala E Moreno-Centeno and MKezunovic ldquoFlexible implementation of power system corrective topologycontrolrdquo Elect Power Syst Res vol 128 pp 79ndash89 2015

[13] I Vanzi ldquoStructural upgrading strategy for electric power networks underseismic actionrdquo Earthq Eng Struct Dyn vol 29 no 7 pp 1053ndash10732000

[14] Y Shumuta ldquoPractical seismic upgrade strategy for substation equipmentbased on performance indicesrdquo Earthq Eng Struct Dyn vol 36 no 2pp 209ndash226 2007

[15] N R Romero L K Nozick I D Dobson N Xu and D A JonesldquoTransmission and generation expansion to mitigate seismic riskrdquo IEEETrans Power Syst vol 28 no 4 pp 3692ndash3701 Nov 2013



[16] J Buritica S Tesfamariam and M Saacutenchez-Silva ldquoSeismic vulnerabilityassessment of power transmission networks using complex-systems basedmethodologiesrdquo in Proc 15th World Conf Earthq Eng Lisbon Portugal2012 pp 24ndash28

[17] J A B Corteacutes M Saacutenchez-Silva and S Tesfamariam ldquoA hierarchy-basedapproach to seismic vulnerability assessment of bulk power systemsrdquoStruct Infrastruct Eng vol 11 no 10 pp 1352ndash1368 2015

[18] K Poljanšek F Bono and E Gutieacuterrez ldquoSeismic risk assessment of in-terdependent critical infrastructure systems The case of European gas andelectricity networksrdquo Earthq Eng Struct Dyn vol 41 no 1 pp 61ndash792012

[19] A M Salman and Y Li ldquoA probabilistic framework for seismicrisk assessment of electric power systemsrdquo Procedia Eng vol 199pp 1187ndash1192 2017

[20] S Espinoza et al ldquoSeismic resilience assessment and adaptation ofthe Northern Chilean power systemrdquo in Proc IEEE Power Energy SocGeneral Meeting 2017 pp 1ndash5

[21] A Poulos S Espinoza J de la Llera and H Rudnick ldquoSeismic riskassessment of spatially distributed electric power systemsrdquo in Proc 16thWorld Conf Earthq Eng Santiago Chile 2017 pp 1949ndash3029

[22] J E Beavers Ed Advancing Mitigation Technologies and Disaster Re-sponse for Lifeline Systems Reston VA USA American Soc Civil Eng2003

[23] T Anagnos ldquoDevelopment of an electrical substation equipment perfor-mance database for evaluation of equipment fragilitiesrdquo Pacific Gas ElectSacramento CA USA Pacific Earthq Eng Center Richmond CA USA1999

[24] M Shinozuka T-C Cheng M Feng and S-T Mau ldquoSeismic perfor-mance analysis of electric power systemsrdquo Res Prog Accomplishments1997ndash1999 pp 61ndash69 1999

[25] M Shinozuka X Dong X Jin and T Cheng ldquoSeismic performanceanalysis for the LADWP power systemrdquo in Proc IEEEPES TransmissDistrib Conf Exhib Asia Pacific 2005 pp 1ndash6

[26] M Shinozuka X Dong T Chen and X Jin ldquoSeismic performance ofelectric transmission network under component failuresrdquo Earthq EngStruct Dyn vol 36 no 2 pp 227ndash244 2007

[27] T Adachi and B R Ellingwood ldquoComparative assessment of civil in-frastructure network performance under probabilistic and scenario earth-quakesrdquo J Infrastruct Syst vol 16 no 1 pp 1ndash10 2010

[28] A-S Ang J Pires and R Villaverde ldquoA model for the seismic reliabilityassessment of electric power transmission systemsrdquo Rel Eng Syst Safvol 51 no 1 pp 7ndash22 1996

[29] M Shinozuka A Rose and R Eguchi ldquoEngineering and socioeconomicimpact of earthquakes An analysis of electricity lifeline disruptions inthe New Madrid areamdashMonograph 2rdquo Multidiscip Center Earthq EngRes State Univ New York Buffalo Buffalo NY USA Tech Rep PB-99-130635XAB 1998

[30] H-S Park B H Choi J J Kim and T-H Lee ldquoSeismic performanceevaluation of high voltage transmission towers in South Koreardquo KSCE JCivil Eng vol 20 no 6 pp 2499ndash2505 2016

[31] T Adachi and B R Ellingwood ldquoServiceability of earthquake-damagedwater systems Effects of electrical power availability and power backupsystems on system vulnerabilityrdquo Rel Eng Syst Saf vol 93 no 1pp 78ndash88 2008

[32] L Duentildeas-Osorio J I Craig and B J Goodno ldquoSeismic response ofcritical interdependent networksrdquo Earthq Eng Struct Dyn vol 36 no 2pp 285ndash306 2007

[33] N Romero L K Nozick I Dobson N Xu and D A Jones ldquoSeismicretrofit for electric power systemsrdquo Earthq Spectra vol 31 no 2pp 1157ndash1176 2015

[34] US Earthquake Hazards Program [Online] Available httpsearthquakeusgsgov

[35] O W Nuttli ldquoSeismic wave attenuation and magnitude relations foreastern North Americardquo J Geophys Res vol 78 no 5 pp 876ndash8851973

[36] G G Amiri A Mahdavian and F M Dana ldquoAttenuation relationshipsfor Iranrdquo J Earthq Eng vol 11 no 4 pp 469ndash492 2007

[37] A M Billah and M S Alam ldquoSeismic fragility assessment of highwaybridges A state-of-the-art reviewrdquo Struct Infrastruct Eng vol 11 no 6pp 804ndash832 2015

[38] E N Farsangi F H Rezvani M Talebi and S Hashemi ldquoSeismic riskanalysis of steel-MRFs by means of fragility curves in high seismic zonesrdquoAdv Struct Eng vol 17 no 9 pp 1227ndash1240 2014

[39] A J Kappos G Panagopoulos C Panagiotopoulos and G PenelisldquoA hybrid method for the vulnerability assessment of RC and URMbuildingsrdquo Bull Earthq Eng vol 4 no 4 pp 391ndash413 2006

[40] Multi-Hazard Loss Estimation Methodology Earthquake Model DeptHomeland Secur Federal Emergency Manage Agency Washington DCUSA 2003

[41] M Nazemi M Moeini-Aghtaie M Fotuhi-Firuzabad andP Dehghanian ldquoEnergy storage planning for enhanced resilience ofpower distribution networks against earthquakesrdquo IEEE Trans SustainEnergy to be published doi 101109TSTE20192907613

[42] G M Karagiannis S Chondrogiannis E Krausmann and Z I TurksezerldquoPower grid recovery after natural hazard impactrdquo Eur CommissionLuxembourg UK Rep EUR 28844 EN 2017

[43] P Dehghanian B Zhang T Dokic and M Kezunovic ldquoPredictive riskanalytics for weather-resilient operation of electric power systemsrdquo IEEETrans Sustain Energy vol 10 no 1 pp 3ndash15 Jan 2019

[44] R Billinton and R N Allan Reliability Evaluation of Engineering Sys-tems Concepts and Techniques 2nd ed New York NY USA Plenum1992

[45] W Li Probabilistic Transmission System Planning vol 65 Hoboken NJUSA Wiley 2011

[46] M Panteli C Pickering S Wilkinson R Dawson and P MancarellaldquoPower system resilience to extreme weather Fragility modelling proba-bilistic impact assessment and adaptation measuresrdquo IEEE Trans PowerSyst vol 32 no 5 pp 3747ndash3757 Sep 2017

[47] M Panteli P Mancarella D N Trakas E Kyriakides and N D Hatziar-gyriou ldquoMetrics and quantification of operational and infrastructure re-silience in power systemsrdquo IEEE Trans Power Syst vol 32 no 6pp 4732ndash4742 Nov 2017

[48] M Nazemi P Dehghanian and M Lejeune ldquoA mixed-integer distribu-tionally robust chance-constrained model for optimal topology control inpower grids with uncertain renewablesrdquo in Proc IEEE Milan PowerTech2019 pp 1ndash6

[49] H B Puttgen ldquoComputational cycle time evaluation for steady state powerflow calculationsrdquo Thomson-CSF Division Simulateurs La DeacutefenseFrance Dec 1985 [Online] Available httpssmartechgatechedujspuibitstream1853355562e-21-675302129 frpdf

[50] ldquoPower system test case archiverdquo Dept Elect Eng Univ WashingtonSeattle WA USA 2007 [Online] Available httpwwweewashingtoneduresearchpstca

[51] CPLEX Optimization Studio [Online] Available httpwww-01ibmcomsoftwarecommerceoptimizationcplex-optimizer

[52] IEEE 57-Bus Data [Online] Available httpicsegitiillinoiseduieee-57-bus-system

Mostafa Nazemi (Srsquo18) received the BSc degree inelectrical engineering from the K N Toosi Universityof Technology Tehran Iran in 2015 and the MScdegree in energy systems engineering from the SharifUniversity of Technology Tehran Iran in 2017 Heis currently working toward the PhD degree in elec-trical engineering with the Department of Electricaland Computer Engineering George Washington Uni-versity Washington DC USA

His research interests include power system re-silience power system planning and operation en-

ergy optimizations and smart electricity grid applicationsMr Nazemi was the recipient of the 2018 Certificate of Excellence in Re-

viewing by the Editorial Board Committee of the Journal of Modern Power andClean Energy for his contributions to the journal

Payman Dehghanian (Srsquo11ndashMrsquo17) received theBSc degree from the University of Tehran TehranIran in 2009 the MSc degree from the Sharif Uni-versity of Technology Tehran Iran in 2011 andthe PhD degree from Texas AampM University Col-lege Station TX USA in 2017 all in electricalengineering

He is an Assistant Professor of Power SystemsEngineering with the Department of Electrical andComputer Engineering George Washington Univer-sity Washington DC USA His research interests

include power system protection and control power system reliability andresiliency asset management and smart electricity grid applications

Dr Dehghanian is the recipient of the 2013 IEEE Iran Section Best MScThesis Award in Electrical Engineering the 2014 and 2015 IEEE Region5 Outstanding Professional Achievement Awards and the 2015 IEEE-HKNOutstanding Young Professional Award



years [12] planning solutions in preparation for decisions inadaptation to and mitigation ie swift response and recoveryin the face of seismic disasters has been sensed as an urgentneed [3]

B Literature Survey

There are several studies in the literature which have focusedon the impacts of seismic hazards on the electric power systemsDifferent upgrading strategies were introduced in [13] using anew quantitative index to decide on vulnerable nodes under dif-ferent seismic scenarios The criticality of electric componentswas evaluated in [14] using the resistance index of electric equip-ment during various earthquake conditions in Japan In [15] arisk-based seismic model is proposedmdasha suite of earthquakescenarios and a set of consequential scenarios for each earth-quake condition are defined to optimize the capacity expansionof transmission and generation sectors In [16] and [17] aseismic vulnerability assessment using the network hierarchicaldecomposition is employed and tested on the IEEE 118-bus testsystem which was stressed by uniformly and spatially distributedearthquake scenarios In [18] the authors study the vulnerabilityof the interdependent European gas and electricity transmissionnetworks using a GIS-based probabilistic reliability model inwhich the network fragility curves in terms of different perfor-mance measures are evaluated A framework for seismic risk as-sessment in electric power systems was proposed in [19] whereseismic hazard is modeled using a probabilistically weightedhazard scenario approach A set of earthquake scenarios withcorresponding occurrence probabilities is considered in orderto assess the accessibility of electric components following anearthquake A framework was proposed in [20] to assess thesystem resilience in terms of energy not supplied and energyindex of unreliability following an earthquake three adapta-tion measures (eg robustness redundancy responsiveness)are evaluated for the northern Chilean electric power systemSimilarly the authors in [21] generated multiple earthquakescenarios using Monte Carlo simulations (MCS) to sample theearthquake magnitude and locations A ground motion predic-tion is utilized to sample peak ground acceleration (PGA) atthe site of each component In [22] seismic electric powersystem models are developed by identifying the possibility ofsequential failures of substations The authors in [23] collecteda large damage dataset to develop fragility curves for a widerange of electric equipment In [24] the seismic performance ofelectric power systems in the city of Los Angeles is evaluatedby applying historic seismic events (eg 1971 San Fernandoand 1994 Northridge earthquakes) to electric components andassessing the loss of connectivity index using fragility curvesSimilarly [25] evaluated the degradation performance of the LosAngeles Department of Water and Powerrsquos (LADWPrsquos) electricpower system using 47 earthquake scenarios to develop the riskcurves for the LADWPrsquos power transmission system In [26]the sequential failures of transmission network under severeearthquakes are identified by considering multiple earthquakescenarios representing the Los Angeles area seismic hazardIn [27] and [28] the seismic performance and vulnerability of

the electrical power system in San Francisco Bay area followingthe 1989 Loma Prieta earthquake is evaluated by assessing thenetwork power imbalances due to postquake disconnection ofsubstations The loss of connectivity between substations thefailure probability of substations and transformers and system-wide power imbalances are evaluated in [29] considering asample earthquake scenario with moment magnitude equal to75 Seismic fragility curves of high-voltage transmission towersin South Korea were developed centered on the limit states thatare defined based on the assumption of linear elastic behaviorof power towers and a set of 20 recorded ground motions inSouth Korea [30] The authors in [31] presented an algorithm toevaluate the serviceability of water distribution systems follow-ing a scenario-based earthquake characterization considering thedependence of water availability on the serviceability of electricpower systems The seismic vulnerability of an interconnectedwater and power system was evaluated in [31] demonstratingthe importance of taking infrastructure interactions into ac-count Likewise a framework to capture the interdependenceamong different sectors such as electric power water distri-bution transportation and telecommunication infrastructureswas proposed utilizing the conditional probabilities of failuresfollowing a seismic hazard [32] In [33] an optimal mitigationstrategy to address seismic risks in the Central United Stateswas investigated considering a suite of earthquake scenariosthat nearly replicate the exceeding curves for PGA as measuredat 81 control locations across the New Madrid Seismic Zone(NMSZ) Similarly a computationally effective procedure fortransmission and generation expansion planning decisions wasproposed in [33] to optimize the seismic mitigation strategies inlarge-scale power systems

Despite a vast majority of research focusing on planningand operation strategies in response to seismic hazards therestill remain several challenging concerns neither solved noreffectively respondedmdashhow does earthquake energy propagatethrough the ways that seismic waves pass how is the earthquakeenergy attenuated and which parameters affect the earthquakeenergy attenuation how can the earthquake energy parameters(eg PGA) at the location of power equipment (eg powergenerating units) be assessed how can the earthquake energybe quantified in terms of fragility curves of the equipment andconsequently how can the impact of seismic shocks be assessedin terms of different probability damage states following anearthquake

C Research Contributions

The main contributions of this article are highlighted asfollows

1) Seismic Hazard Modeling and Impact Characterization onPower Generation Facilities We develop a model that system-atically captures the effects of earthquakes on power generationsystems by considering realistically large sets of scenarios gener-ated via MCS to include the stochastic nature of ground motionsWe then illustrate how the seismic forces can be quantified usingan analytical attenuation relationship (AR) Numerical modelscentered on the concept of fragility curves are developed to




















ln(Ψ) = ν + f1(M) + f2(R) + f3(Z) + ε (1)











P [ϑ|Sd] = Φ

[1

σϑln

(Sd

Sdϑ

)](2)















PC = P (C|ρ) (3)








Rtsys =

sumkisinK

⎛⎝sum

qisinQ

(P tk[Γq|T ]Ct

k(Γq))⎞⎠ (8)





and space

Rtsys(x t) =

sumkisinK

⎛⎝sum

qisinQ


k(Γq(x t)))⎞⎠





Ctk(Γq) =

Ct

Mq +sum

ωisinΩ(CtLRq + Ct

ICq) if Θ = 1

CtMq + Ct

RDq if Θ = 0



RDq = Δsum







CtLRq =

sumωisinΩ

(χtωEENSt

ωq

)(11)




minhisinH

sumωisinΩ

(ILt


ωh

)(12)

Png minus

summ



Qng minus

summ







P 2jnm +Q2








Qming ζtg le Qt





g

) forallg isin G

(23)

P tg + rtg le Pmax


Pming le P t



sumgisinG


0 le ILntωh le Pnt
































πth =

prodxisinΛx

ϑx


ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)


EENStωq =

sumhisinH

πthτ

thIL





CtICq =

sumωisinΩ

EENStωqVOLLω (32)






max

(GcupK minus

sumforallnisinN

un

)(33)

subject to


Pk minussum

forallk(n)Pk +

sumforallg(n)


(35)














weierpk = γ (46)























ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES


















































































ln(Ψ) = ν + f1(M) + f2(R) + f3(Z) + ε (1)











P [ϑ|Sd] = Φ

[1

σϑln

(Sd

Sdϑ

)](2)















PC = P (C|ρ) (3)








Rtsys =

sumkisinK

⎛⎝sum

qisinQ

(P tk[Γq|T ]Ct

k(Γq))⎞⎠ (8)





and space

Rtsys(x t) =

sumkisinK

⎛⎝sum

qisinQ


k(Γq(x t)))⎞⎠





Ctk(Γq) =

Ct

Mq +sum

ωisinΩ(CtLRq + Ct

ICq) if Θ = 1

CtMq + Ct

RDq if Θ = 0



RDq = Δsum







CtLRq =

sumωisinΩ

(χtωEENSt

ωq

)(11)




minhisinH

sumωisinΩ

(ILt


ωh

)(12)

Png minus

summ



Qng minus

summ







P 2jnm +Q2








Qming ζtg le Qt





g

) forallg isin G

(23)

P tg + rtg le Pmax


Pming le P t



sumgisinG


0 le ILntωh le Pnt
































πth =

prodxisinΛx

ϑx


ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)


EENStωq =

sumhisinH

πthτ

thIL





CtICq =

sumωisinΩ

EENStωqVOLLω (32)






max

(GcupK minus

sumforallnisinN

un

)(33)

subject to


Pk minussum

forallk(n)Pk +

sumforallg(n)


(35)














weierpk = γ (46)























ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES











































































PC = P (C|ρ) (3)








Rtsys =

sumkisinK

⎛⎝sum

qisinQ

(P tk[Γq|T ]Ct

k(Γq))⎞⎠ (8)





and space

Rtsys(x t) =

sumkisinK

⎛⎝sum

qisinQ


k(Γq(x t)))⎞⎠





Ctk(Γq) =

Ct

Mq +sum

ωisinΩ(CtLRq + Ct

ICq) if Θ = 1

CtMq + Ct

RDq if Θ = 0



RDq = Δsum







CtLRq =

sumωisinΩ

(χtωEENSt

ωq

)(11)




minhisinH

sumωisinΩ

(ILt


ωh

)(12)

Png minus

summ



Qng minus

summ







P 2jnm +Q2








Qming ζtg le Qt





g

) forallg isin G

(23)

P tg + rtg le Pmax


Pming le P t



sumgisinG


0 le ILntωh le Pnt
































πth =

prodxisinΛx

ϑx


ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)


EENStωq =

sumhisinH

πthτ

thIL





CtICq =

sumωisinΩ

EENStωqVOLLω (32)






max

(GcupK minus

sumforallnisinN

un

)(33)

subject to


Pk minussum

forallk(n)Pk +

sumforallg(n)


(35)














weierpk = γ (46)























ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES


































































CtLRq =

sumωisinΩ

(χtωEENSt

ωq

)(11)




minhisinH

sumωisinΩ

(ILt


ωh

)(12)

Png minus

summ



Qng minus

summ







P 2jnm +Q2








Qming ζtg le Qt





g

) forallg isin G

(23)

P tg + rtg le Pmax


Pming le P t



sumgisinG


0 le ILntωh le Pnt
































πth =

prodxisinΛx

ϑx


ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)


EENStωq =

sumhisinH

πthτ

thIL





CtICq =

sumωisinΩ

EENStωqVOLLω (32)






max

(GcupK minus

sumforallnisinN

un

)(33)

subject to


Pk minussum

forallk(n)Pk +

sumforallg(n)


(35)














weierpk = γ (46)























ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES


































































πth =

prodxisinΛx

ϑx


ςy(ςy + ϑy)

(29)

τ th =

⎛⎝sum

xisinXςx +

sumyisinY

ϑy

⎞⎠

minus1

forallh isin H (30)


EENStωq =

sumhisinH

πthτ

thIL





CtICq =

sumωisinΩ

EENStωqVOLLω (32)






max

(GcupK minus

sumforallnisinN

un

)(33)

subject to


Pk minussum

forallk(n)Pk +

sumforallg(n)


(35)














weierpk = γ (46)























ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES


















































































ln(PGA) = C1 + C2

(MW + 038

106

)+ C3 ln (R) (48)
























IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES



















































































IN TEST CASE 1
























C Discussions









IV CONCLUSION


REFERENCES




















































































C Discussions









IV CONCLUSION


REFERENCES




































































IV CONCLUSION


REFERENCES































































seismic-resilient bulk power grids: hazard ... · the monte carlo simulation is ... seismic hazard...

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