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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2020.3007725, IEEETransactions on Industry Applications

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Resiliency Enhancement of Distribution PowerGrids Using Mobile Marine Power Source

Morteza Dabbaghjamanesh, Senior Member, IEEE, Amirhossein Moeini, Member, IEEE,Soroush Senemmar, Student Member, IEEE, and Jie Zhang, Senior Member, IEEE

Abstract—In this paper, a new configuration security frame-work is developed for reliability and resiliency improvementof distribution networks by the coordination of the security-constraint unit commitment (SCUC) and mobile marine powersources (MMPSs) under both post-disaster and normal restora-tion operations. It is assumed that a MMPS contains non-dispatchable distributed generators (DGs), e.g., photovoltaics(PV), as well as dispatchable DGs, e.g., gas turbines and dieselgenerators. A mixed-integer linear programming model is formu-lated for coordinating MMPSs and SCUC under both normal andextreme conditions (e.g., natural disasters, cyber and physicalattacks). To better characterize the uncertainties in renewablegeneration and electric load, a deep learning gated recurrent unitis adopted to forecast the PV power output. The proposed modelis tested on the IEEE 69-bus distribution network to validatethe effectiveness and merits of MMPSs. Results show that thereliability and resiliency could be enhanced by using MMPSswithin the network.

Index Terms—Configuration security, deep learning, resiliencyand reliability, mobile marine power sources, security drivenconfiguration management.

NOMENCLATURE

Sets/Indiceslm,mn Indices of distribution linesD/d Set/index of loadΩN/n,m, l Set/index of bus nodesΩS/s Set/index of MMPSΩT /t Set/index of timeΩDGM/k Set/index of DGs in MMPSsΩDG/i Set/index of DGsΩU/u Set/index of uncertain variableΩDL Set of distribution linesParameters and variablesCks Generation cost of the kth unit in the sth

MMPS.Ci Generation cost of the ith unit.CE

snt/CDsnt Entrance/departure cost of sth MMPS to node

n at time t.CM

st Sailing cost of sth MMPSs to node n at timet.

M. Dabbaghjamanesh and J. Zhang are with the Department of MechanicalEngineering, The University of Texas at Dallas, Richardson, TX 70850,USA (e-mail:mortezadabba;[email protected])(Corresponding author:JieZhang)

S. Senemmar is with the Department of Electrical and Computer Engineer-ing, The University of Texas at Dallas, Richardson, TX 70850, USA (e-mail:[email protected])

A. Moeini is with the Department of Electrical and Computer Engineering,Missouri University of Science and Technology, Rolla, MO 65409, USA(email: [email protected])

Fnmt Power flow in line nm at time t.Iit Status of unit i at time t. 1 if unit is on;

otherwise, it is 0.ILlm Current of line lm at time tLEsnt/L

Dsnt Entrance/departure status of the sth MMPS at

time t: 1 if MMPSs is connects to node n;otherwise, 0.

LMst Sailing status of the sth MMPS at time t: 1 if

MMPSs is connects to node n; otherwise, 0.Lshmt Load shedding of bus m at time t.

Lsnt Status of the sth MMPS in bus n at time t. 1if it is located at bus n; otherwise, it is 0.

Nh/NT Total number of customers interrupted/served.No Number of interruptionsOsnt The sth MMPS operating status at time t. 1 if

it is operating in bus n; otherwise, it is 0.PGit Power of the ith unit at time t.PGkst Power of the kth unit in the sth MMPS at time

t.PLlmt Transmitted active power from line lm at time

tPDn Load demand at bus nQL

lmt Transmitted reactive power from line lm attime t

RU,RD Ramp up/down rate of units.rt The percentage of load for spinning reserveSU, SD Startup and shutdown costsTnms Moving time of the sth MMPS from mode n

to node mTCLnt Service time of the load in post-disaster

restoration at time t.T onit , T

offit Number of successive on/off hours for unit i at

time tUT,DT Minimum up/down time of unitsVmt Voltage of node m at time tWn Load importance (weight) at bus nWsnt The sth MMPSs waiting status at time t. 1 if

it is waiting in bus n; otherwise, it is 0.Z,X,R Impedance, Reactance, Resistanceγ Energy to money conversion coefficientθnm Phase of impedance between bus n and mδ, δn Bus voltage angle, voltage angle of bus nδkst Status of the kth unit in the sth MMPS at time

t. 1 if unit is on; otherwise it is 0.Υh Restoration time (minutes)

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I. INTRODUCTION

GRID modernization and demand growth have been in-creasing the size and complexity of modern power grids.

In addition, power outages make the grid more vulnerable tothe disproportionately increasing generation units and loads[1]. On the other hand, natural disasters, cyber/physical at-tacks, and grid contingencies are costly, hardly preventable,and unpredictable, which increases the need of service restora-tion from reliable and fast energy resources [2].

Natural disasters can cause widespread and severe damagesto power grids. Thus, millions of people leave without powerfor weeks or months. For instance, approximately 2.2 millioncustomers were reported without power, when in 2012 hurri-cane Sandy hit the USA East Coast [3]. Weather-related poweroutages occur more frequently in recent years, especially inthe coastlines, which cause tremendous economic loss andsignificant life risks [4]. One of the key requirements for aresilient power grid is the rapid and effective response ofelectric service restoration, where reliable power supply isgreatly dependent on the most recovery activities [5].

Recently, a significant amount of research has been per-formed to enhance the power system resiliency by usingmobile generation units due to their strategical and technicalbenefits for the grid. For instance, in [6], mobile emergencygeneration units in the presence of natural disasters wereproposed to improve the resiliency of distribution lines. In [7],mobile truck-mounted energy storage systems, as well as elec-tric vehicles, were employed to improve the resiliency of a dis-tribution power grid. The resiliency of distribution power gridswas investigated in [8] and [5] by decomposing the powergrid into interconnected microgrids and using mobile energystorage systems. Dabbaghjamanesh et al. [9] investigated atechnique for mobile renewable energy plants and power gridintentional islanding to increase the power grid resiliency. Leiet al. [10] investigated a resilient scheme for disaster recoveryto develop a co-optimization framework for both repair crewsand mobile power sources. In [11], mobile distributed energyresources were considered to improve the distribution networkresiliency. Power grid resiliency enhancements by consider-ing dynamic line rating constraint and mobile storage wereinvestigated in [12]–[15]. Although different mobile energyplant types were introduced for enhancing the power gridresiliency after disasters, platforms with large capacity mobileenergy that can recover and move large loads have not beeninvestigated in the literature.

As one of the key benefits of mobile energy sources, mobilemarine power sources (MMPSs) can move quickly to theaffected area and connect to the local distribution/transmissionlines. In addition, a single MMPS can generate up to 500MW, which is sufficient to bring electricity for 250,000 people[16]. This large power source could lead to a significantbenefit to the grid, such as assisting operations of powergrid, enhancing the resiliency of power systems (by rapidlysupplying power to areas that are affected by natural disasters),and preventing investments on the infrastructure of powertransmission. The capital investment cost of MMPSs’ largeupfront has also motivated to be used for several purposes.

Moreover, countries with large islands often have difficulties todeliver power to island regions, because connecting differentislands with cables of sub-sea are complex and costly [17].Furthermore, power lines of islands are separated from grids ofthe mainland. Furthermore, serving a small size of populationis undesirable economically by building local power plants.

The benefits of using MMPSs in operation and planningof power systems are twofold: i) improve the power grid re-siliency in the presence of contingencies and natural disasters,and ii) improve the power grid reliability in normal operation.It should be noted that the model has been investigated forthe transmission network reliability and resiliency in [18].Also, a synergistic network approach is developed in [19],where each ships is modeled as a microgrid. It is important tonote that the coordination of MMPSs and security-constraintunit commitment (SCUC) is challenging [20]–[22]. This studyinvestigates the effects of MMPSs on power systems economicefficiency, reliability, and resiliency in the period of post-disaster. To better characterize the uncertainties (on MMPSs)in electric loads and renewable generation, an algorithm ofdeep learning gated recurrent unit (DLGRU) is adopted topredict the power generation of photovoltaic (PV) plants onMMPSs. The main contributions of this paper are summarizedas:• Develop a coordination framework of MMPSs and SCUC

in power system operations, by taking into account ofthe impacts on base station and the transportation cost ofMMPSs.

• Integrate MMPSs in power system operations to enhancethe power grid reliability and resiliency in the presenceof natural disaster or contingency.

The rest of the paper is organized as follows. The overallMMPSs and SCUC coordination framework is formulated inSection II. The adopted deep learning technique for renewableand load forecasting is described in Section III. Simulationresults on the IEEE 69-bus distribution network are discussedin Section IV, followed by the conclusion in Section V.

II. MODELS AND MATHEMATICAL FORMULATIONS

A. Objective function

In this study, MMPSs are adopted for (i) improving theresiliency of power grids, in the presence of natural disaster orother contingencies, and (ii) increasing the reliability and eco-nomic efficiency of power system operations. Hence, the coor-dination of MMPSs and SCUC is a multi-objective problem,which seeks to minimize the operation cost, while maximizingthe resiliency of the network, as F (x) = F2(x)− F1(x).

1) Minimizing the operation cost:

min F1(X) =∑

n,m∈ΩN

∑s∈ΩS

∑t∈ΩT

[CEsntL

Esnt + CD

sntLDsnt

+CMst L

Mst ] +

∑k∈ΩDGM

∑s∈ΩS

∑t∈ΩT

[CksPGkstδkst

+SUkst + SDkst] +∑

i∈ΩDG

∑t∈ΩT

[CiPGit Iit + SUit + SDit]

(1)




3

2) Maximizing the resiliency [5]:

max F2(X) = γ ×∑

n∈ΩN

WnPDn T

CLn,t

−∑t∈ΩT

∑s∈ΩS

∑i∈ΩDG,k∈ΩDGM

[PGit + PG

kst](2)

The first term of (2) is the system performance, which can beevaluated by the total electrical energy supplied to consumersbased on their weighting priority. Here, the variable TCL

n,t isdetermined based on the travel time of MMPSs to the loadcenter. The second term in (2) specifies the power generationcost of the network, which includes both DGs and MMPSs.It should be noted that the resiliency of the network can beincreased either by maximizing the system performance orminimizing generation cost [5]. Figure 1 shows a typical powergrid resilience curve during a natural disaster event. The powergrid performance includes five states as [5], [23]:• Natural disaster progress state, which is [te, tpe].• Post-event degraded state, which is [tpe, tr].• Restoring state, which is [tr, tpr].• Post-restoration state, which is [tpr, tir].• Infrastructure recovery state, which is [tir, tpi].

This paper investigates the power grid resiliency in the post-disaster period, where the main focusing time period is [tr, tir],i.e., the restoring and post-restoration stages, as highlightedin Fig. 1. Indeed, during this time period, MMPSs could beutilized and sailed to the affected area and compensate for theshortage of power.

Fig. 1. Power grid resilience curve during a natural disaster event [5].

B. Constraints

Two types of constraints should be considered in the coor-dination of SCUC and MMPSs.

1) SCUC operation constraints: Limitations (3)-(15) aredefined as day-ahead SCUC operation constraints.

Power generation constraints: The active and reactivepowers of the generation units should be within the limitsas [24], [25]

IitPGi ≤ PG

it ≤ IitPGi ∀t ∈ ΩT ,∀i ∈ ΩDG (3)

IitQGi ≤ QG

it ≤ IitQGi ∀t ∈ ΩT ,∀i ∈ ΩDG (4)

Ramp up and down constraints: Each generation unit isconstrained by the ramp-up and ramp-down rates limits as

PGit − PG

i(t−1) ≤ RUi ∀t ∈ ΩT ,∀i ∈ ΩDG (5)

PGi(t−1) − P

Git ≤ RDi ∀t ∈ ΩT ,∀i ∈ ΩDG (6)

Min up and down time constraints: The generation units areconstrained by the minimum up and down time limits givenby (7) and (8), respectively.

T onit ≥ UTi(Iit − Ii(t−1)) ∀t ∈ ΩT ,∀i ∈ ΩDG (7)

T offit ≥ DTi(Ii(t−1) − Iit) ∀t ∈ ΩT ,∀i ∈ ΩDG (8)

Spinning reserve constraint: Equation (9) represents thespinning reserve constraint, which is to supply the load de-mand in case of unexpected load rise or generation fall.∑

i∈ΩDG

IitPGi ≥ P

Dt (1 + rt%) ∀t ∈ ΩT

(9)

Network constraints: The grid operational network limita-tions are considered as follows.∑

lm∈ΩDL

[PLlmt −Rlm(ILlmt)

2

]−

∑mn∈ΩDL

PLmnt + PG

it

+PGkt = PD

t − P sht ∀t ∈ ΩT ,∀i ∈ ΩDG,∀k ∈ ΩDGM

(10)

∑lm∈ΩDL

[QL

lmt −Xlm(ILlmt)2

]−

∑mn∈ΩDL

QLmnt +QG

it

+QGkt = QD

t −Qsht ∀t ∈ ΩT ,∀i ∈ ΩDG,∀k ∈ ΩDGM

(11)(Vimt)

2 − (Vint)2 = 2(RmnP

Lmnt +XmnQ

Lmnt)

−(Zmn)2(ILmn)2 + ∆Vmnt ∀t ∈ ΩT ,∀mn ∈ ΩDL(12)

(Vmt)2(ILmn)2 = (PL

mn)2 + (QLmn)2

∀t ∈ ΩT ,∀mn ∈ ΩDL(13)

V ≤ Vmt ≤ V ∀t ∈ ΩT ,∀mn ∈ ΩDL (14)

|∆Vmnt| ≤ (V − V )(1− wLmnt)

∀t ∈ ΩT ,∀mn ∈ ΩDL(15)

0 ≤ ILmnt ≤ ILwLmnt ∀t ∈ ΩT ,∀mn ∈ ΩDL (16)

2) MMPSs constraints: Equations (17)-(30) formulate theMMPSs constraints.

MMPSs moving (sailing) constraints: Equations (17) and(18) ensure that the MMPSs are moving (sailing) or connectingto a node (operating) at any time.∑

Lsnt +∑

LMst = 1;∀s ∈ ΩS ,∀n ∈ ΩN ,∀t ∈ ΩT (17)

Wsnt +Osnt ≥ LMnms(t−1) − L

Mnmst

∀s ∈ ΩS ,∀nm ∈ ΩN ,∀t ∈ ΩT(18)

MMPSs entering/departing constraints: MMPSs enteringand departing constraints are defined in (19) and (20), respec-tively. Furthermore, Equation (21) ensures that the MMPSscan not enter and depart at the same time.

LDsnt ≥ Lsn(t−1) − Lsnt ∀s ∈ ΩS ,∀t ∈ ΩT (19)

LEsnt ≥ Lsnt − Lsn(t−1) ∀s ∈ ΩS ,∀t ∈ ΩT (20)

LEsnt + LD

snt ≤ 1 ∀s ∈ ΩS ,∀t ∈ ΩT (21)




4

MMPSs operational constraints: MMPSs can either operateor wait at a port at any time, as expressed in (22). Also, basedon Equation (23), MMPSs are restricted to operate and sailsimultaneously.

Lsnt = Wsnt +Osnt ∀s ∈ ΩS ,∀n ∈ ΩN ,∀t ∈ ΩT (22)

Osnt ≤ Lsn(t−1) ∀s ∈ ΩS ,∀n ∈ ΩN ,∀t ∈ ΩT (23)

MMPSs sailing time limitations: MMPSs moving timebetween two nodes are constrained by (24) and (25).∑

Lsnmt ≤ Tnms + (1− LD

snt)M

∀s ∈ ΩS ,∀nm ∈ ΩN ,∀t ∈ ΩT(24)

∑Lsnmt ≥ Tnm

s − (1− LDsnt)M

∀s ∈ ΩS ,∀nm ∈ ΩN ,∀t ∈ ΩT(25)

3) MMPSs operation constraints: MMPSs operation con-straints include power generation, ramp up and down, andminimum up and down times, as expressed in (26)-(30).

δkstPGk ≤ PG

kt ≤ δkstPGk ∀t ∈ ΩT ,∀k ∈ ΩDGM (26)

PGskt − PG

sk(t−1) ≤ RUsk ∀t ∈ ΩT ,∀k ∈ ΩDGM (27)

PGsk(t−1) − P

Gsk,t ≤ RDsk ∀t ∈ ΩT ,∀k ∈ ΩDGM (28)

T onskt ≥ UTsk(δskt − δsk(t−1)) ∀t ∈ ΩT ,∀k ∈ ΩDGM (29)

T offskt ≥ DTi(δsk(t−1) − δskt ∀t ∈ ΩT ,∀k ∈ ΩDGM (30)

C. Reliability Evaluation

The main reliability indices that are evaluated during thepost-disaster restoration are defined as follows [26], [27].

System Average Interruption Duration Index (SAIDI):SAIDI is the total duration of an interruption for the averagecustomer during the restoration, which is calculated as:

SAIDI =

∑ΥhNh

NT∀h ∈ [tr, tir] (31)

Customer Average Interruption Duration Index (CAIDI):CAIDI is the average time to restore service, which is calcu-lated as:

CAIDI =

∑ΥhNh∑Nh

∀h ∈ [tr, tir] (32)

Average Service Availability Index (ASAI): ASAI is theratio of the total number of customer hours that service wasavailable during the restoration to the total customer hoursdemanded, which is calculated as

ASAI = 100×[1−

∑ΥhNh

NT × T

]∀h ∈ [tr, tir] (33)

It should be noted that only one blackout is considered inthis study. Hence, other reliability indices, e.g., customer inter-rupted per interruption index and system average interruptionfrequency index, are not affected during the post-disaster. Theproposed optimization problem is solved by using a heuristicmethod, known as the collective decision based optimizationalgorithm (CDOA), which is adopted from [14].

III. DEEP LEARNING GRU TECHNIQUE

A number of solar power forecasting methods have beeninvestigated in the literature, and one of the most populartechniques is the recurrent neural network (RNN). The mainbenefit of RNN than other machine learning techniques is itsability to predict the future of the system based on the pastand present information of the system. However, the mainissue of the RNN technique is the vanishing or explodinggradient during the training of the network [28]. To solvethis issue, several different techniques have been proposed inthe literature [29]. Two of the most popular techniques arethe long short-term memory (LSTM) and the gated recurrentunits (GRU) [29]–[31]. These two techniques can prevent theexploding/vanishing gradient of the RNN by controlling theweights and biases between two cells. Between these twotechniques, GRU has shown better performance due to itslower complexity and higher speed of training [32], [33]. Tothis end, in this paper, we have adopted GRU to generatesolar power forecasts (for PV plants on MMPSs) to assist thescheduling of MMPSs.

A. Gated Recurrent Unit

GRU was proposed by Cho et al. in 2014 [32]. The data flowin GRU is controlled by several gates, and a block diagram ofGRU is presented in Fig. 2.

ht = (1− zt)ht−1 + ztht (34)

where zt is an update gate that stores the information ofupdates of each unit, which is given by,

zt = σ(Uzht−1 +Wzxt + bz) (35)

where σ is a differentiable and smooth activation function.Uz , bz and Wz are the previous activation constant, the bias,and input constants of the update gate (z), respectively. Thecandidate activation in (34) and Fig. 2 is updated as shownbelow.

ht = tanh(U(rt⊙

ht−1)Wxt (36)

where rt is the reset gate, and⊙

is an element-wise multipli-cation. Fig. 3 shows the block diagram of the proposed deeplearning model.

rt = σ(Urht−1 +Wrxt + br) (37)

Fig. 2. The block diagram of GRU.




5

Fig. 3. The block diagram of the proposed deep learning model.

The solution procedure of the coordination framework ofMMPSs and SCUC is explained in Algorithm 1.

Algorithm 1 Solution procedureData Definition: Define the number of MMPSs, number ofgenerators, generator characteristics, MMPSs features, andparameter settings for the optimization problem.for time=1:24 do

for t=1: Number GRU cells do1. Update gate Zt based on the weights and biases todecide the ratio of input data that can be passed.2. The reset gate rt is updated to forget some rangeof input data.3. A memory unit ht is obtained based on the amountof data that is forgotten.4. From the memory unit ht, update gate Zt, andprevious cell output ht−1, the next output ht is selectedand applied to the next GRU unit based on the derivedequations.

endSolve the MILP optimization problem (1)-(27).if there is a contingency, physical attacks, or naturaldisaster then

1. Calculate the total required power for the damagedarea2. Check the status of MMPSs and calculate thedistance to the damaged area3. Sail MMPSs that have available capacity tocompensate for the power shortage of the damagedarea4. Solve the optimization problem (1)-(27)5. Evaluate the index of (2)6. Go to next step

elseGo to next step

endCalculated the DGs output power, cost functions (1) and(2), and the energy not supplied

end

Fig. 4. Single line diagram of the modified IEEE 69-bus test system.

2 4 6 8 10 12 14 16 18 20 22 24

Time (h)

0

500

1000

1500

2000

2500

Po

wer

(kW

)

Total

Area1

Area2

Area3

Area4

Fig. 5. Hourly load of each area.

2 4 6 8 10 12 14 16 18 20 22 24

Time (h)

0

200

400

600

800

1000

Po

wer

(kW

)

Red Bus

Blue Bus

Green Bus

Pink Bus

Fig. 6. Hourly load of each affected bus.

IV. SIMULATION RESULTS

In this section, a modified IEEE 69-bus distributed testsystem is selected to evaluate the benefits of MMPSs. Fig. 4shows the single line diagram of the modified IEEE 69-bustest system, and it is assumed that four areas are affected by anatural disaster. For instance, Area 1 contains red bus, whileArea 4 contains red, blue, green, and pink buses. The totalload demand in each affected area is shown in Fig. 5. Fig. 6depicts the load demand at each affected bus individually(red, blue, green, and pink). Furthermore, the characteristicsof dispatchable generation (DG) units and MMPSs are sum-marized in Table I. Table II shows power forecasts of the PVsystem which is located on MMPS, by using the GRU model.The forecasting mean square error (MSE) is 0.0027 [p.u.],indicating the high-performance of the GRU technique.

It is assumed that the four areas are affected by a naturaldisaster, as small (Area 1), medium (Area 2), and large (Areas3 and 4) portions of the grid. Five different cases (i.e., normaloperation case and Areas 1-4 damaged cases) are investigatedand compared as follows.




6

TABLE ICHARACTERISTICS OF GENERATION UNITS

Ci PGi /PG

i UTi/DTi CE /CD CM

Type ($/kWh) (kW) (h) ($) ($/kWh)DG 3.2 200/300 3/3 - -

MMPS1 2.2 0/150 1/1 250/250 600MMPS2 2.72 0/250 1/1 350/350 800

TABLE IIHOURLY PV POWER FORECASTING

Time Actual Data Forecasted Data(hour) (kW) (kW)

1-8 0 09 20.7 20.5610 41.2 42.8711 54.4 56.4112 65.2 63.2113 67.7 68.1514 64.7 66.2815 55.8 58.6216 36.1 36.1317 3.6 10.38

18-24 0 0

Case 1 - Normal Operation Case: In this case, the networkoperates under the normal condition, i.e., the network is withinthe time interval [0, te] (refer to Fig. 1). Fig. 7 shows the outputpower of the DG and MMPSs under the normal condition ofthe grid. It is shown that the cheapest units (MMPSs 1 and 2)are committed with their maximum capacity; that means, theoutput power of the generation units is purely based on theeconomic consideration. The total operation cost of this caseis $124,684.15.

5 10 15 20 240

1000

2000

Pow

er

(kW

)

Unit1

5 10 15 20 24149

150

151

MMPS1

5 10 15 20 24

Time (h)

249

250

251

MMPS2

Fig. 7. Generation units output power in normal condition

Case 2 - Area 1 Damaged: In this case, only Area 1 of thegrid is affected and disconnected from the main grid due to thenatural disaster, which is shown in Fig. 4 as the red bus/area.In this case, MMPS 1, the closet MMPS to the affected area, issailed to compensate for the shortage of power. Fig. 8 showsthe output power of the generation units for this case. It isshown that the MMPS 1 is OFF for the first three hours, whenit is sailing to the affected area; and it is ON after sailing andentering the affected area. Moreover, MMPS 2 is committedwith its maximum capacity for the entire horizon. The totaloperation cost of the grid in Case 2 is $151,646.22, which isincreased in comparison to Case 1 due to sailing, entering, and

departing costs of the MMPS 1. It should be noted that all ofthe loads have been satisfied after 3 hours, and the resilienceof the grid has been enhanced by using MMPSs.

5 10 15 20 240

1000

2000

Pow

er

(kW

)

Unit1

5 10 15 20 240

50

100MMPS1

5 10 15 20 24

Time (h)

249

250

251MMPS2

Fig. 8. Generation units output power in Area 1

Case 3 - Area 2 Damaged: In this case, morebuses/branches of the grid are affected when Area 2 is dam-aged by the natural disaster as shown in Fig. 4. Accordingto Figs. 6 and 7, both MMPSs 1 and 2 should sail to Area2 to compensate for the shortage of power. Fig. 9 depictsthe generation units output power of this case. It is shownthat MMPSs 1 and 2 are connected to Area 2 after three andfour hours, respectively. It should be noted that MMPS 1 isconnected sooner than MMPS 2 due to its faster speed andshorter distance to the damaged grid. Though both MMPSs 1and 2 are connected to the area with their maximum capacityto help the service restoration, the two MMPSs’ total capacityis still not enough to compensate for the load demand of Area2. The total operational cost of Case 3 is $151,646.22.

5 10 15 20 241000

1500

2000

Pow

er

(kW

)

Unit1

5 10 15 20 240

100

200

MMPS1

5 10 15 20 24

Time (h)

0

200

400MMPS2


Case 4 - Area 3 Damaged: When Area 3 is damaged, theaffected area is not fully connected. Based on the load demandin Fig. 6, the load of the left part of the affected area (greenbus) is smaller than that of the right part (red plus blue buses).Hence, the larger capacity MMPS, i.e., MMPS 2, is sailed andconnected to the higher demand area to compensate for morepower shortage. Also, MMPS 1 is sailed and connected to thesmaller grid (green bus). Fig. 10 displays the optimal outputpower of the generation units. In comparison with the previousArea 2 case, the output power of the main DG has significantlybeen reduced, due to less demand in the main grid. Also,similar to the Area 2 case, MMPS 2 is committed withits maximum capacity once connected. However, unlike theprevious case, MMPS 1 is only committed with approximately




7

half of its capacity due to the lower demand. It should benoted that in this case, the total load demand of the left part(green buses) has been satisfied, while the total demand ofright part (red plus blue buses) has not been satisfied due tothe shortage of the power. The total operational cost of thiscase is $62,648.31.

5 10 15 20 240

500

1000

Pow

er

(kW

)

Unit1

5 10 15 20 240

50

100MMPS1

5 10 15 20 24

Time (h)

0200400

MMPS2


Case 5 - Area 4 Damaged: When Area 4 is damaged by thenatural disaster, the damaged area is also decomposed into twoparts that are not connected with each other. In this case, bothMMPSs are not able to satisfy the load demand of any parts.The total operational cost of this case is $62,650.35, whichis very close to the previous case when Area 3 is damaged.Indeed, here, the line ampacity of the right part (green and pinkbuses) allows MMPS 1 to commit with its maximum capacity.Fig. 11 displays the optimal output power of the generationunits for this case.

5 10 15 20 240

500

1000

Pow

er

(kw

)

Unit1

5 10 15 20 240

100

200

MMPS1

5 10 15 20 24

Time (h)

0

200

400MMPS2


TABLE IIIOPERATION COST

Damaged F1(x) F2(x) ENS TotalArea ($) ($) (kWh) Cost ($)

Normal Operation 124684.15 - - 124684.15Area 1 125124.71 4580.02 102.73 129704.73Area 2 124948.01 26698.21 2559.50 151646.22Area 3 39553.40 23094.91 5869.46 62648.31Area 4 39553.40 23094.91 21053.85 62650.35

Table III summarizes the post-disaster operation costs ofboth the main grid and the damaged grid. As can be seen, byincreasing the affected grid size, the operational cost (F1(x))has been decreased, while the resiliency cost (F2(x)) has beenincreased. However, the total cost has been decreased as less

load is satisfied. The loss of load is quantified by the energynot supplied (ENS) reliability index, which is presented inTable III. It is observed that by increasing the size of thedamaged area, the ENS value is increased. Also, accordingto the results of Table III, compared to the normal conditionand Area 1 damaged case, the Area 2 damaged case has ahigher generation cost, due to sailing both MMPSs 1 and 2to compensate for the shortage of power, which can increasethe total operation cost. Also, compared to Area 3 and Area4 damaged cases, the Area 2 damaged case has a higheroperation cost, as well as less load shedding; that means highergeneration units participate in the network.

Fig. 12 depicts the energy supplied percentage in the post-disaster period [tr, tir]. It is observed that the ENS of thesystem is increased, by expanding the damage. However, thesystem can still supply a significant portion of the loads byutilizing high-capacity MMPSs.

5 10 15 20 24

Time (h)

0

20

40

60

80

100

Ener

gy s

uppli

ed (

%)

Area1 Area2 Area3 Area4

Fig. 12. Energy supplied (%), in the post-disaster period

Table IV shows the daily reliability indices of the networkin the post-disaster restoration period with and without consid-ering MMPSs. Based on this table, by using the high-capacityMMPSs in the post-disaster period, the power grid reliabilityhas been significantly improved. For instance, in Area 1, byusing the proposed MMPS model, the SAIDI reliability indexhas been improved by 87%. However, by increasing the sizeof the affected area, this improvement has been decreased dueto the lack of efficient power sources.

TABLE IVRELIABILITY EVALUATION CONSIDERING MMPSS

Considering Area SAIDI CAIDI ASAIMMPSs No. (minutes) (# of customers) (%)

Yes Area 1 17.3 180 98.7No Area 1 138.8 1440 90.3Yes Area 2 51 268 96.4No Area 2 273.4 1440 81.01Yes Area 3 84.2 302 94.14No Area 3 400.5 1440 72.18Yes Area 4 122.3 281 91.50No Area 4 626.2 1440 56.51

One of the main objectives in the post-disaster networkresiliency is to increase the system performance in the intervalof [tr, tir] of the resiliency curve. Fig. 13 shows the systemperformance of all areas during the normal and post-disasterperiods. Based on the figure, the resiliency of the networkhas been increased significantly by considering MMPSs. For




8

(a)

(b)

(c)

(d)Fig. 13. Resiliency curve of each area with/without MMPSs, (a) Area 1, (b)Area 2, (c) Area 3, (d) Area 4.

instance, in the Area 1 damaged case, the system is returnedalmost to the normal operation after 3 hours.

V. CONCLUSION

This paper proposed a new approach for utilizing large ca-pacity mobile marine power sources to enhance the reliabilityand resiliency of distribution power grids in the occurrenceof incidents such as natural disasters, contingencies, andcyber/physical attacks. The proposed method was examinedon a modified IEEE 69-bus test system. Simulation resultsindicated that a close cooperation between MMPSs and thedistribution grid can significantly enhance the reliability of

the power system under both normal and extreme conditions.Utilizing the MMPSs in power grids could compensate fora large amount of loss of power and enhance the resiliencyof the network. Comparing with other mobile energy sourcessuch as mobile battery storage units, MMPSs have largercapacities and can be sailed and connected to the grid morequickly. This benefit can mitigate the energy not supplied.Also, using MMPSs in the post-disaster restoration wouldbe more interesting from the national level perspective, sinceoceans cover more than 70% of the Earths surface and areconnected. However, potential impacts of regulations andpublic policy on the development of the integrated MMPSsshould be investigated before formal adoption. Potential futurework will (i) consider MMPS as a microgrid instead of a singlegenerator, (ii) optimize the path schedule of MMPSs, and (iii)optimize the connection points of MMPSs to the affected grid.

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Morteza Dabbaghjamanesh (SM19) received theM.Sc. degree in electrical engineering from NorthernIllinois University, DeKalb, IL, USA, in 2014, andthe Ph.D. degree in electrical and computer engineer-ing form Louisiana State University, Baton Rouge,LA, USA in 2019. Currently, he is a ResearchAssociate in the Design and Optimization of EnergySystems (DOES) Laboratory at the University ofTexas at Dallas, Richardson, TX, USA. His currentresearch interests include power system operationand planning, reliability, resiliency, renewable en-

ergy sources, cybersecurity analysis, machine/deep learning, smart grids, andmicrogrids.

Amirhossein Moeini (S16-M19) received the Ph.D.degree in electrical engineering from the Universityof Florida, Florida, USA, in 2019. He is currentlya postdoctoral research fellow at the departmentof electrical and computer engineering at MissouriUniversity of Science and Technology. He publishedmore than 25 journal and conference papers andholds three USA patents. His current research inter-ests include Power Electronics, Multilevel Convert-ers, Deep/Machine Learning; Battery Management,EV Charging Stations.

Soroush Senemmar (S’20) received the B.Sc. andM.Sc. degrees from Shiraz University, Shiraz, Iran,in 2015 and 2019, respectively, all in electrical engi-neering. He is currently a Ph.D. student in electricalengineering with the Department of Electrical andcomputer Engineering, The University of Texas atDallas, Dallas, USA. His research interests includepower systems operation and planning, smart grids,operation and planning of multi-carrier energy sys-tems, and energy management.

Jie Zhang (M13-SM15) received the B.S. andM.S. degrees in mechanical engineering from theHuazhong University of Science and Technology,Wuhan, China, in 2006 and 2008, respectively, andthe Ph.D. degree in mechanical engineering fromRensselaer Polytechnic Institute, Troy, NY, USA,in 2012.He is currently an Assistant Professor ofthe Department of Mechanical Engineering at TheUniversity of Texas at Dallas. His research interestsinclude multidisciplinary design optimization, com-plex engineered systems, big data analytics, wind

and solar forecasting, renewable integration, and energy systems modelingand simulation.


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