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fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2737024, IEEE
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Resilience-Oriented Optimal Operation

of Networked Hybrid Microgrids
Akhtar Hussain, Student Member, IEEE, Van-Hai Bui, Student Member, IEEE,
and Hak-Man Kim, Senior Member, IEEE

Abstract—A resilience-oriented optimization strategy is pro-

posed in this paper by considering feasible islanding in normal CPen
n
Penalty cost for shedding load nth priority load.
operation and survivability of critical loads during emergency Pt ACL , PtDCL Total forecasted load of AC and DC sides.
period. A resilience index is proposed for assessing the capability Pgmin , Pgmax Min. and max. production limits of gth CDG.
LTS LTS
of each microgrid to feed local critical loads during sudden power Pm,max , Pm,max Upper and lower bounds for load to be shed.
disruptions. Based on the values of the proposed resilience index,  m , m ,  m Parameters for load curtailment penalty cost.
local optimization results are revised by changing the commit-  Constant for controlling stability/convergence.
ment status of dispatchable generators and energy storage ele-
Pt ARG , PtDRG Forecasted values of AC and DC side renewables.
ments. The uncertainties associated with renewable generations
and loads are realized via robust optimization method. The ad- Pt ,ACL
n , P DCL
t ,n Amount of nth priority load in AC and DC sides.
Buy Sell
justable power bounds, suggested by each microgrid for minimiz- PRt , PRt Electricity buying and selling prices.
ing the operation cost of the network, are also revised through the  ILC , PcapILC Efficiency and capacity of interlinking converter.
proposed resilience index. In emergency mode, decision between
feeding of lesser critical loads and battery charging along with a
Variables
strategy for minimization of load curtailment during switching of PgCDGac ,t
, PgCDGdc ,t
Production amount of gth AC and gth DC CDG.
scheduling windows is considered. These two considerations as- Pt Sho , Pt Sur Total shortage and surplus amount.
sure the survivability of critical loads during emergency period. Pt Ash , Pt Asu Shortage and surplus amount of AC side.
Finally, an incremental cost consensus algorithm is used for opti- Pt Dsh , Pt Dsu Shortage and surplus amount of DC side.
mal allocation of surplus power among the connected microgrids Pt xBC , Pt xBD Power charged to/discharged from x-side BESS.
having unserved loads. Three different network topologies are Pt EVC , Pt EVD Power charged to/discharged from EV.
considered in emergency mode for assessing the performance of
Pt FDC , PtTDC Power received from DC and transferred to DC.
the proposed approach.
Pt FAC , PtTAC Power received from AC and transferred to AC.
Index Terms— Adjustable power, consensus algorithm, hybrid Pˆt ,xLn , Pt ,xLn Bounded load and uncertainty bound for x-side.
microgrids, microgrid resilience, robust optimization. Pˆt ,xRG
n , Pt ,n
xRG
Bounded RDG and uncertainty bound for x-side.
Pt ,n , Pt ,xLn Lower and upper deviations for x-side load.
xL

NOMENCLATURE Pt ,xLn , Pt ,xLn Lower and upper bounds for x-side load.
Abbreviations Pt ,xRG n ,  P xRG
t , n Lower and upper deviations for x-side renewable.
BESS Battery energy storage system. Pt ,xRG
n , P xRG
t , n Lower and upper bounds for x-side renewable.
xL xL
CEMS Community EMS. zt , n , zt , n Scaled deviations for x-side load.
xRG xRG
CDG Controllable distributed generation. zt , n , zt , n Scaled deviations for x-side renewables.
DSO Distribution system operator. t ,  t Budget of uncertainty and dual variable.
EMS Energy management system. txl  , txl  Dual variables for x-side loads.
MG-EMS Microgrid energy management system. txr  , txr  Dual variables for x-side renewables.
RI t , RI t Actual and normalized values of resilience index.
Sets PgAdj Adjustable amount of gth CDG unit.
,t
Gac ,Gdc Set of AC and DC generators, respectively. RCL
Pt Amount of remaining critical load.
G Set of all AC and DC generators.
PteASH
, n
, PteDSH
, n Amount of nth load shed from AC and DC sides.
M Set of microgrids.
Pte , tSHED
Sur
Surplus power amount and consensus variable.
T Set of time intervals. e
PmLTS
,k
, PmMIS ,k Amount of load to shed and mismatch amount.
Constants pm, j , qm, j Entries of row and column stochastic matrices.
CgCDG
ac
,CgCDG
dc
Production cost of gth AC and gth DC CDG. ug,t , yg,t , zg,t Commitment status, startup indicator, and shut-
SU SU
Cgac , Cgdc Start-up cost of gth AC and gth DC CDG. down indicator for gth CDG.
SD SD
Cgac , Cgdc Shutdown cost of gth AC and DC CDG. x Microgrid type identifier (AC and DC sides).

I. INTRODUCTION
This work was supported by the Korea Institute of Energy Technol-
ogy Evaluation and Planning (KETEP) and the Ministry of Trade,
Industry & Energy (MOTIE) of the Republic of Korea (No.
20168530050030). (Corresponding author: Hak-Man Kim)
R ESILIENCE enhancement of power grids against natural
disasters has become a major consideration for electrical
engineers/researchers in the recent years. The frequency, in-
The authors are with the Department of Electrical Engineering, In-
cheon National University, Korea. (e-mail: hmkim@inu.ac.kr). tensity, and duration of weather-related events are increasing

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due to climate change [1]. According to U.S. Department of recovery, the resiliency-oriented problem formulation of mi-
Energy, 58% of grid outages are due to severe weather [2]. In crogrids is more challenging [5]. In [15], a model is suggested
the last decade, about 679 power outages occurred only in the for minimizing the load curtailment of microgrids by efficient-
U.S. due to weather events, each affecting at least 50000 cus- ly scheduling the available resources during extended islanded
tomers [3]. Hurricane Katrina in 2005, Japan Earthquake in periods. Different optimization problems are considered for
2011, and Hurricane Sandy in 2012 are among the recent natu- normal and emergency operations. An algorithm is proposed in
ral disasters, which resulted in major blackouts [1]. Due to the [16] to minimize load shedding in islanded mode followed by
absence of a universal accepted definition of resilience among a disturbance event. Uncertainties in loads and renewables are
the electric grid community, the authors in [4] have defined the quantified via stochastic optimization method. Battery opera-
resilience for electric grids after reviewing various key con- tion controller is used for controlling the operation mode and
cepts related to system resilience. In [4], the cyber-physical charging/discharging rate of batteries by [17]. A fuzzy system
resilience of a power system is defined as the ability of the is used for improving resilience of hybrid microgrids. The op-
system to maintain the continuous flow of electricity to the timization problem is divided into normal and emergency op-
customers with a given load prioritization scheme. eration modes by [5] for ensuring feasible islanding and sur-
Microgrids have the potential to improve the resilience of vivability of critical loads during the emergency period.
power systems by feeding local loads and thus lowering the As noted by [15], [16], the use of microgrid as a resiliency
possibility of load shedding [5]. Both single [6]-[9] and net- resource is well known and various studies are available in the
worked [10]-[14] microgrids are suggested for improving the literature [6]-[14]. However, mathematical modeling and algo-
resilience of power systems. The operational constraints for rithms for enhancing the resiliency of microgrids themselves
using microgrids as a resiliency resource are analyzed by [6]. are limited. In contrast to [5], [15], [16], a network of hybrid
It is demonstrated in [6] that microgrids have the potential to microgrids is considered in this study. Each microgrid analyz-
serve as a local resource, as a community resource, and as a es its ability to feed local critical loads upon sudden disruption
black start resource. In [7], thermal stress and reliability of by using the proposed resilience index. The possibility of fea-
neutral-point-clamped inverters are analyzed for resilient mi- sible islanding is also considered before proposing the adjust-
crogrids. A risk adjustable chance constrained programming able power bounds by each microgrid. The uncertainties asso-
approach is used by [8] for creating a tradeoff between risk ciated with renewable generations and loads are realized via
and cost for resilient microgrids. A double bus bar DC system robust optimization, and worst-case scenarios are considered.
is used in [9] for assessing the resilience of grid and to rebuild The conservatism of solution can be adjusted by controlling
more efficient partitions in run-time. An intelligent system is the budget of uncertainty. In emergency mode, each microgrid
developed for dynamically distributing load between the two considers the survivability of its critical loads and determines
buses to make self-sustainable microgrids. the amount of surplus/shortage power. In literature, consensus
Networked microgrids are more beneficial for enhancing the algorithms are mainly used for scheduling/dispatch of mi-
system resiliency due to their ability to support each other dur- crogrids [18]-[20]. However, in this study, consensus algo-
ing disturbance events. A transformative architecture is sug- rithm is utilized for optimal load shedding of microgrids. Load
gested by [10] where the on-emergency microgrids broadcast priority is considered and penalty cost of load curtailment is
requests for power support. The power support from normal used as a consensus variable.
operating microgrids is decided by a consensus algorithm. A
nested energy management system (EMS) is suggested by [11] II. RESILIENCE-ORIENTED OPERATION
for enhancing the resiliency of disconnected microgrids via
subgrouping. In order to overcome the resilience challenges of A. Terminologies and Definitions
communication after a disturbance event, a distributed EMS is 1) Feasible Islanding: The ability of the microgrid to switch
suggested by [12] for discovering global information by using from grid-connected mode to islanded mode without curtailing
only local information. A resilient outage management system at least its most critical loads (priority 1) is termed as feasible
is developed by [13] for reducing load shedding during dis- islanding. The commitment status of controllable distributed
turbance events. The unused capacities of individual mi- generators (CDGs) and energy storage elements are revised to
crogrids are used for feeding unserved loads by the community ensure service reliability to level 1 loads after a sudden disrup-
EMS. Distribution network operator and each microgrid are tion event [5].
considered as distinct entities by [14], with different objec- 2) Survivability: Survivability is defined as the ability of the
tives. Coordinated energy management is considered for the microgrid to feed maximum loads of the microgrid without
network of microgrids to support each other. compromising its most critical loads during the emergency
The major emphasis of the available literature [6]-[14] is period. Firstly, one interval of next scheduling window is in-
on use the microgrids as a resiliency resource. However, re- cluded while scheduling the previous interval. Secondly, the
cently algorithms for improving the resiliency of microgrid choice between feeding lesser priority loads at a given interval
itself have gained the attention of researchers [5], [15]-[17]. and battery energy storage system (BESS) charging for feeding
Due to the uncertain time of the incident and uncertain time of more critical loads in later intervals is considered to ensure
service reliability to critical loads [5].

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3) Adjustable Power: The amount of power by which a mi- Scheduling Scheduling horizon of CEMS in normal operation
crogrid can increase/decrease its generation in response to the time
Scheduling horizon of MG-EMSs in normal operation
command of the community EMS (CEMS) to reduce the oper-

Event occurrence time

t
ation cost of the entire network is termed as adjustable power. t+1 t+2 t+3 t+4 t+23 t+24
The CDGs having generation cost sandwiched between buying
and selling prices only have non-zero adjustable power. De- te te+1 te+2 te+3 te+4 te+5 te+6 te+7
tails about adjustable power can be found in [21]. Scheduling horizon of MG-EMS(s) in emergency operation

Scheduling of dispatchable generators and storage elements Horizon for resiliency analysis

is essential for the economic and efficient operation of mi- Fig. 2. Scheduling horizons of the proposed optimization scheme.
crogrids [22]. The optimization problem is decomposed into The configuration of the proposed hybrid AC/DC microgrid
normal and emergency operations in the proposed resilience- network is shown in Fig. 1. Each microgrid has an AC mi-
oriented optimization scheme. In normal mode, each microgrid crogrid and a DC microgrid, which are linked through an inter-
optimizes its local resources while considering feasible island- linking converter (ILC). Each AC microgrid contains a BESS
ing, by using the proposed resilience index. The commitment unit, wind turbine, CDGs, and prioritized AC loads. Similarly,
status of CDGs and BESS units is revised to assure feasible each DC microgrid contains a BESS unit, a fleet of electric
islanding. Similarly, during the computation of adjustable vehicles (EVs), photovoltaic cells, CDGs, and prioritized DC
bounds, feasible islanding is also considered by each mi- loads. Loads in each microgrid are prioritized from level 1 to
crogrid. These considerations will result in elevation of opera- N. Level 1 loads are considered as the most critical loads while
tion cost but will assure the survival of critical loads during level N loads are considered as the least critical loads.
emergencies. Each microgrid has a local EMS (MG-EMS), which is re-
In emergency mode, survivability of critical loads is consid- sponsible for the local operation. MG-EMS is also responsible
ered. The first interval of next scheduling window is consid- for evaluating the achievability of feasible islanding. CEMS
ered to avoid the curtailment of critical loads during switching increases/decreases the adjustable power of each MG within
of scheduling windows. In addition, BESS charging and feed- the suggested bounds by that MG and informs MG-EMSs.
ing of lesser critical loads is considered by each microgrid. CEMS uses the market price signals issued by distribution
After local optimization, surplus power of the network is system operator (DSO) to decide either to increase or decrease
shared between unserved loads in each microgrid. An incre- the power of CDGs (adjustable power). Each MG-EMS revis-
mental cost consensus algorithm is utilized to allocate the sur- es the commitment status of CDGs having adjustable power.
plus power among microgrids according to their load priority
level. The microgrids can achieve consensus by only com- C. Scheduling Horizons
municating with their adjacent neighboring microgrids. Different scheduling horizons are considered for normal and
emergency modes and scheduling horizons of MG-EMS and
B. System Configuration
CEMS are also different, as depicted in Fig. 2. Scheduling
Initially, AC microgrids were evolved, due to the dominance horizon for normal operation (T) is taken as 24-hours with a
of conventional power systems by the AC form [23]. Recently, time step of 1 hour. Scheduling horizon for emergency opera-
DC microgrids and distribution systems are also taken into tion (Te) is assumed as 2 hours with a time step of 15 minutes.
consideration due to the widespread of DC sources and loads The scheduling horizon for CEMS is assumed as 1 hour in
[24]. Therefore, future microgrids are predicted to be hybrid normal mode. During normal operation, CEMS can trade pow-
AC/DC microgrids [25], due to their capability to utilize bene- er with the utility grid while considering feasible islanding, as
fits of both AC and DC microgrids. Due to above-mentioned described in the previous section. If any disturbance is detect-
merits, a hybrid microgrid network is considered in this study. ed in the utility grid, each EMS switches its operation mode to
MG1- emergency mode. The connection status with the utility grid is
CEMS
EMS evaluated after each interval and operation mode is decided. It
is difficult to determine the clearance time of disturbance
PCC
DSO
Utility MG1 events precisely. Terefore, the scheduling horizon of the emer-
Grid
BC
..1 gency mode will be updated until the end of emergency or the
1
..
. AC CDGs
DC CDGs
. end of scheduling horizon.
BC N
N
RDG There are different levels of controls for microgrids due to
RDG
MG2- BC R
EMS
MG2 R
ILC BESS
the difference in the significance and time scale for each con-
BESS
BC trol level [26]. This paper is focused on energy management of
DC/
AC

EV
BC microgrids with emphasis on the resilience, which is consid-
.. 1

DC ..
1
ered as the uppermost level of microgrid control. Generally,
MGn- . AC Loads
Loads
.
EMS
MGn N
N voltage and frequency controls are considered as the lower-
AC Microgrid DC Microgrid
BC: Buck/Boost converter level controls of microgrids. Therefore, frequency control is
PCC: Point of common coupling Communication link Power link not considered in this paper, assumed to be fulfilled by lower
Fig. 1. Proposed hybrid AC/DC microgrid network. levels and is out of the scope for this article.

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III. PROBLEM FORMULATION: NORMAL MODE OPERATION z g ,t  max u g ,t 1  

 ug ,t , 0 , ug ,t  0,1 g  G, t  T (4)
A. Local EMS Pt ARG   PgCDG
ac ,t
 Pt ASh  Pt ASu  Pt ABD  Pt ABC  Pt ATr  Pt ACL
g ac Gac
In normal mode operation, initially, a deterministic model is
developed which is then transformed into a robust counterpart. where, Pt ATr   ILC . Pt FDC  PtTDC g ac  Gac , t  T (5)
Robust optimization has gained popularity due to its merits as Pt DRG
  PgCDG
dc ,t
 Pt DSh
 Pt DSu
 ILC
. Pt FAC
 Pt TAC
 Pt ES
 Pt DCL
mentioned in [27] and is used by several researchers [28]-[30]. g dc Gdc

Therefore, robust optimization is used in this study. where, Pt ES  Pt DBD  Pt DBC  Pt EVD  Pt EVC g dc  Gdc , t  T (6)
1). Deterministic Model: First two lines of the objective Pt ACL
= Pt ,ACL , Pt DCL
=  Pt ,DCL n  N , t  T (7)
n n
function (1) contain generation, startup, and shutdown costs of nN nN
AC side CDGs and DC side CDGs, respectively. The last line Pt FDC   ILC .PtTAC , Pt FAC   ILC .PtTDC , t  T (8)
contains the profit gained by trading power with the utility
grid. The amount of shortage and surplus power at local EMS Pt DSh
Pt Sho  Pt ASh  , Pt Sur  Pt ASu   ILC .Pt DSu , t  T (9)
is decided with reference to market price signals. If the genera-  ILC

tion cost of a CDG is higher than the market buying price, the
generation of that CDG is set to minimum and load is reflected 2). Robust Counterpart: The objective function of the robust
as shortage amount. Contrarily, if the generation cost of a counterpart is same with (1). The uncertainty bounds for load
CDG is lower than the market selling price, the generation of and renewable sources are given by equations (10) and (11).
that CDG is set to maximum and the extra power is reflected The bounded values of load ( Pˆt ,xLn ) and renewables ( Pˆt xRG ) at
as the surplus amount. In addition, the charging and discharg- time t can be obtained by using their nominal values and
ing decisions of energy storage elements are also made with bounded uncertainty values. The bounded value of uncertainty
reference to market signals. Charging in off-peak price inter-
for the load ( Pt ,xLn ) can take any value between upper ( Pt ,xLn )
vals and discharging in peak price intervals can increase the
benefit of microgrid. The constraints related to generations and lower ( Pt ,xLn ) deviation bounds, as given by (10). The
bounds, startup, and shutdown costs of CDGs are given by (2),
upper and lower deviation bounds can be computed by using
(3), and (4), respectively, with G =Gac+Gdc. u g ,t , y g ,t , and z g ,t
the nominal value of load along with upper ( Pt ,xLn ) and lower
are the indicators for commitment status, start-up, and
shutdown of gth CDG unit at time t. ( Pt ,xLn ) uncertainty bounds of the load. The Same process is
Load balancing of AC side is given by (5) and DC side by repeated for renewable power generators as shown in (11). The
(6). The AC microgrid can use AC-side RDGs, CDGs, and worst-case for the load balancing of the deterministic model
BESS units along with power transfer with the DC-side to would occur at the maximum increase in the load and maxi-
fulfill its demand, as shown in (5). Similarly, the DC microgrid mum decrease in the renewable power, as given by (12).
can use DC-side RDGs, CDGs, EVs, and BESS units along In order to cater for the worst-case, equation (12) will be
with power transfer with the AC-side to fulfill its demand, as added to right side of load balancing equations, i.e. (5) and
shown in (6). Both AC and DC side microgrids use energy (6).This inclusion transforms the deterministic model to a min-
storage elements as a source during their discharging mode max problem. Therefore, sub-problem is identified and its dual
and as a load during their charging mode. Total load in AC is computed. Equation (12) is the objective function of the
and DC microgrids can be obtained by summing all priority sub-problem with (13) and (14) as constraints. The dual of
loads as given by (7). Interlinking converter losses are encoun- sub-problem is given by equations (15)-(18). Finally, equation
tered for transferring power between AC and DC side mi- (19) can be added to the right side of equations (5) and (6) to
crogrids as given by (8). Similarly, power trading between the make a tractable robust counterpart. Where t is the budget of
DC-side microgrid and the utility grid is also subjected to in-
uncertainty and it controls the conservatism of the solution.
terlinking converter losses as given by (9). The models for
Robust optimization provides guaranteed immunity against the
BESS units and EVs are identical to those of [5].
worst-case realization if the uncertainties lie within the speci-
min   CgCDG
ac PgCDG
g ac Gac tT
ac ,t 
 y g ac ,t .CgSU
ac
 z g ac ,t .CgSD
ac  fied bounds.

Pˆt ,xLn =Pt ,xLn +Pt ,xLn , Pt ,xLn  Pt ,xLn  Pt ,xLn n  N , t  T (10)
   C
g dc Gdc tT
P   yCDG
g dc
CDG
g dc ,t
SU
g dc ,t .C g dc  z g dc ,t .CgSD
dc  (1) Where, Pt ,xLn  Pt ,xLn  Pt ,xLn and Pt ,xLn  Pt ,xLn  Pt ,xLn

+   PRtBuy .Pt Sho  RtSell .Pt Sur  Pˆt xRG =Pt xRG +Pt xRG , Pt xRG  Pt xRG  Pt xRG t  T (11)
tT Where, Pt xRG
 Pt xRG
 Pt xRG
and Pt xRG
 Pt xRG
 Pt xRG

Subject to
 
ug ,t  Pgmin  PgCDG
,t  ug ,t  Pgmax g  G, t  T (2) max  
  nN
 ,  n .Pt ,  n 
ztxL xL

nN
ztxL xL 


,  n .Pt ,  n   zt
xRG
.Pt xRG  ztxRG .Pt xRG  (12) 
yg ,t  max u g ,t  
 ug ,t 1 , 0 , ug ,t  0,1 g  G, t  T (3)

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Pt ,xLn  Pt ,xLn  Pt xRG  Pt xRG  t n  N , t  T (13) amount of a given CDG depends upon the amount of power
generated by that CDG at t and its maximum and minimum
0  ztxL xL
, n , zt , n , zt
xRG
, ztxRG  1 n  N , t  T (14) power generation limits. The amount of remaining critical load
  ( Pt RCL ) can be computed by using the worst-case values of
min   t .t   txl, n   txl, n  txr   txr   (15)
 nN nN 
1  Pt , 1 ) and the local power gener-
most critical loads ( Pt ,ACL DCL

t  txl, n  Pt ,xLn , t  txl, n  Pt ,xLn n  N , t  T (16)

ated by the microgrid. Similar to load, worst-case values of
t  txr   Pt xRG
, t  txr   Pt xRG
n  N , t  T (17) renewables ( Pt ARG , Pt DRG ) are considered to provide immunity
 , t t
xl 
, txl  , txr  , txr  0 t  T (18) against the generation uncertainties. The detailed process for
 t .t   txl, n   txl, n  txr   txr  n  N , t  T (19) resilience analysis by each microgrid is shown in Algorithm I.
nN nN Initially, the amount of remaining critical load is determined
3). Resilience Index: Each microgrid can compute its resili- by using (24), which indicates the ability of the microgrid to
ence index by using (20). The maximum and minimum possi- feed its critical loads locally. If the microgrid is not able to
ble values of the resilience index are given by (21). The ac- feed its most critical loads without the utility grid, the genera-
ceptable range of the proposed resilience index is given by tion amount of CDGs is revised. CDGs are initially sorted
(22). Equation (22) implies that in order to keep the resilience based on their operation cost and generation of CDGs is in-
index value within the acceptable range, at least the most criti- creased, starting from the cheapest CDG. If the amount of
cal loads need to be survived [5]. Each microgrid will evaluate Pt RCL is greater than the upper limit of selected CDG ( PgCDG
,max ),
this index and assure its value within the acceptable bounds
before proposing surplus/ shortage power to the CEMS. CDG is set to maximum. Then amount of Pt RCL is updated by
using (25) and adjustable bounds of the selected CDG by (23).

RIt   
 DCL 
n , r  Pt , n , r
Pt ,ACL
 N  n  N , t  T (20)
This process is repeated until Pt RCL  PgCDG
,max and then the gen-

 t , n 
 nN P ACL  P DCL 
t , n
  eration of selected CDG is set to Pt RCL . In this way, the ability
RI max   n N , RI t  0, RI max  n  N , t  T (21) of the microgrid to supply its local loads during sudden inter-
nN
ruption from the utility grid is assured.
RI t  RI t RI max , RIacc  1  N.RI max  ,1 n  N , t  T (22)
Pmin
g  PgCDG
,t 
 PgAdj
,t  Pg
max

 PgCDG
,t  g  G, t  T (23)
4). Adjustable Power Bounds: The constraints and bounds for  
the computation of adjustable power are given by equations 
Pt RCL  Pt ,ACL
1  Pt , 1
DCL

  Pt ARG   PgCDG
 ac ,t
 Pt
ABD
 Pt ABC  

(23)-(25). Equation (23) states that the adjustable power  g ac Gac 
 DRG 
 Pt   PgCDG  Pt ES  g  G, t  T (24)
Algorithm I Resilience analysis of microgrids. dc ,t 
 g dc Gdc 
1: Initial values
2: Run local optimization for each microgrid Pt RCL : Pt RCL  PgCDG
,t g  G, t  T (25)
3: while t < T do
4: Find surplus, shortage, and adjustable limits B. Community EMS
5: for all n < N do
RCL The objective of the CEMS is to increase/decrease the gen-
6: Determine Pt by equation (24)
eration of adjustable units and to decide the trading amount
RCL
7: if Pt ≤ 0 then with the utility grid. The objective function (26) contains the
8: Use surplus/shortage, and adjustable limits of step4 adjusted amount of AC side CDGs, DC side CDGs, and profit
9: else
10: for all g < G do
gained by trading power with the utility grid. Constraints (27)
11: Sort generators by price in array, g   and (28) shows the upper and lower limits of adjustable power.
12: end for Equation (29) shows the load balancing for CEMS. Due to the
13: for all g < G do consideration of adjustable power, CDGs with lower genera-
14: while Pt
RCL
≤ 0 do tion cost in the network are fully utilized. After adjusting the
15: Start from the cheapest generator of array adjustable power bounds, trading with the utility grid is decid-
16: Pg ,t
CDG

 min Pt RCL , PgCDG
,max  ed. CEMS monitors the trading amount of each microgrid with
RCL
the utility grid and due share is granted to each microgrid. The
17: Update Pt by (25) & adjustable bounds by (23) total adjustable amount in AC and DC microgrids can be com-
18: g puted by using (30) and (31), respectively.
19: end while
20: end for
21: end if
min   CgCDG
g ac Gac mM
ac , m 
ac

PgAdj,m,t    CgCDG
g dc Gdc mM
dc , mPgAdj,m,t
dc

22: end for
23: t++
24: end while
+   PRtBuy .PmBuy
,t  Rt
Sell
,t 
.PmSell (26)
mM

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PgAdj,m,min  PgAdj,m,t  PgAdj,m,max gac  Gac , m  M (27) The scheduling horizon for emergency operation (Te) is tak-
ac ac ac
en as 2-hours with a time step (te) of 15 minutes in this study.
PgAdj,m,min  PgAdj,m,t  PgAdj,m,max gdc  Gdc , m  M (28) It is difficult to exactly predict the event clearance time, there-
dc dc dc
fore, the scheduling window will be updated until the end of
 PmBuy
,t  Pg ac ,t  Pg dc ,t +  Pm,t =  Pm,t   Pm,t
Adj Adj Sur Sell Sho
the event. However, the developed model is valid for any
mM mM mM mM
g ac  Gac , gdc  Gdc , m  M (29) scheduling horizon with any uniform time step. After local
optimization, surplus amount or amount of load to be shed can
PgAdj,m,t    PgAdj g ac  Gac , m  M (30)
ac , m ,t
ac
mM g ac Gac be computed by using (35) and (36). PteMis is used for deter-
PgAdj,m,t    PgAdj g dc  Gdc , m  M (31) mining the shortage power in each microgrid, which uses the
dc dc , m ,t
mM g dc Gdc
worst-case realizations of loads ( PACL
n , te
, PDCL
n , te
) and renewables
IV. PROBLEM FORMULATION: EMERGENCY MODE OPERATION ( PteARG , PteDRG ), as shown in (35). Similarly, the surplus has
A. Local EMS also been determined by considering the same worst-case val-
In emergency mode operation, the objective is to minimize ues. Following two assumptions are made for each microgrid
the load shedding of microgrids. Therefore, penalty cost for in the emergency operation mode.
load shedding is assumed higher than the generation cost of  Microgrids can locally suffice at least their most critical
CDGs. In addition to generation and startup/shutdown costs of loads under the worst-case load-generation scenario.
CDGs, priority-wise penalty costs for load shedding are also  Only renewable power is not sufficient to suffice the critical
included in the objective function (32). Load balancing for AC loads even under the best-case scenario.
and DC side microgrids are given by (33) and (34). It can be The first assumption implies that each microgrid has the
observed from load balancing equations that all terms are iden- capability to serve its most critical loads ( 1 ) by using its lo-
tical to those of normal mode counterpart equations except the cal resources only, i.e. CDGs, RDGs, and energy storage ele-
power trading terms. Power trading terms (buying and selling) ments. Due to the second assumption, RDGs are not used for
are not included due to the absence of connection with the computing surplus power in (36).
utility grid. All other constraints of normal mode operation
B. Incremental Cost Consensus Algorithm
are valid after replacing t with te.
During emergencies, communication with CEMS may not
min 
g ac Gac te Te

 CgCDG
ac  PgCDG
ac ,te 
 y g ac ,te .CgSU
ac
 z g ac ,te .CgSD
ac  be reliable. However, some of the microgrids of the network
may still be interconnected. Microgrids having surplus power
   C
g dc Gdc te Te
P   y
CDG
g dc
CDG
g dc ,te
SU
g dc ,te .C g dc  z g dc ,te .CgSD
dc  (32) can assist microgrids with power shortage to increase the ser-
vice reliability. After local optimization, microgrids inform

.  PteASH
,  n  Pte ,  n 
their surplus/shortage power along with curtailment cost of
+   CPen
n
DSH
each load group to their neighboring connected microgrids(s).
nN te Te
Based on the curtailment cost of loads, their priority can be
ARG
Pte   Pgac ,te  Pte
CDG ABD
 PteABC  PteATr   Pn ,te  Pte
ASH ACL
determined and power allocation is based on load priority. An
g ac Gac nN
incremental cost consensus algorithm is used for achieving this
where, Pte
ATr
  ILC . PteFDC  PteTDC g ac  Gac , te  Te (33) objective for the interconnected microgrids.
Consensus algorithms have gained popularity in power dis-
DRG
Pte   CDG
Pgdc ,te 
ILC FAC
. Pte  Pte
TAC
 Pte 
ES
 DSH
Pn ,te  PteDCL
patch [18]-[20] due to their fast convergences and near to op-
g dc Gdc nN
timal solutions. Unlike central EMSs, distributed energy man-
where, Pte
ES
 PteDBD  PteDBC  PteEVD  PteEVC g dc  Gdc , te  Te (34) agement strategies (consensus algorithms) cannot guarantee a
  globally optimal solution but can provide a near to optimal
Mis
Pte   PteARG   PgCDG  PteABD  PteABC   PACL 
 ac ,te n , te  solutions. Distributed EMSs are more favorable in emergen-
 g ac Gac nN  cies where network communication is uncertain.
 DRG  ILC The cost of load shedding is approximated by a quadratic
 Pte   Pgdc ,te  Pte   Pn ,te  . g  G, n  N (35)
CDG ES DCL
curve as given by (37) and consensus variable is obtained by
 g dc Gdc nN 
using (38). The value of consensus variable is communicated
 Pmax
LTS
=Pte Mis
if Pte  0
Mis
among the interconnected microgrids after each iteration to

 g  G, te  Te (36) reach a near to optimal value. Matrix P and Q are associated
 Sur with the connections among the microgrids of the network.
 P =  ( PCDG  PCDG ) +P ABD  P ABC  else
 te g G gac ,max g ac ,te te te
Matrix P and Q have following two properties.
 ac ac
 P is a row-stochastic (summation of row entries is equal to
   ILC
   ( Pgdc ,max  Pgdc ,te )  Pte  Pte  Pte  Pte  . one) matrix and Q is a column-stochastic matrix.
CDG CDG DBD DBC EVD EVC

  gdc Gdc   If microgrid m is connected to microgrid j, pm, j  0 and

qm, j  0 , otherwise pm, j  qm, j  0 .

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The weights of entries of P and Q are free to choose if the

above-mentioned two conditions are satisfied. It has been
,k 1  m,k 1   m
PmLTS SHED
  2. m m  M (42)

proved by [30] that the convergence rate is not affected by the ,k 1   qm, j .Pj ,k  Pm,k 1  Pm,k
PmMIS MIS LTS

jM
LTS
   j  M ,m  M (43)
weights. In equations (44) and (45) 1/ d m and 1/ d m represent
 
1 d j  N m

the weights of the entries of P and Q, respectively. N m and pm, j   m , d m  N m j  M ,m  M (44)

0 otherwise
N mrepresent the neighbor sets for inward and outward direc-
1 d  j  N m

tions, respectively. The second property of P and Q matrices qm, j   m , dm  Nm j  M ,m  M (45)
can also be observed from these two equations. The detailed 
0 otherwise
process of consensus algorithm is shown in Algorithm II.
   
2
= m . PteSHED +m .PteSHED In Algorithm II, firstly, surplus/shortage power is deter-
CtSHED
e , n
PteSHED
, n , n , n   m te  Te ,n  N (37)
mined by each microgrid after local optimization using (35)

tSHED 
dCtSHED
,
e
SHED
Pt , 
n
 e n
  2. SHED
+ m te  Te ,n  N (38)
and (36). Then, P and Q matrices are determined by using (44)
e SHED m .Pte , n and (45) based on the connection information of microgrids.
dPt , 
e n Then, consensus variable is determined by microgrids having
 shortage power based on the priority of their loads. Then, con-
 SHED  any ferasible value sensus variable, load to be shed, and mismatch amount is ini-
 m,0
 LTS tialized by each microgrid by using (39). After each iteration,
 Pm,0  any ferasible value te  Te ,m  M (39)
Equation (40) assures that the value of consensus variable of
 Sur
 MIS Pte ,acc each microgrid lies within the acceptable limits. Finally, the

 m,0
P   PmLTS
,0 amount of load to be shed and power mismatch is updated by
N
using (42) and (43), respectively. This process is repeated until
mSHED
,k 1  m ,min when Pm , k < Pm,min
SHED LTS LTS
the mismatch is within the acceptable range, i.e. lesser than ɛ.

 SHED
m,k 1  m,max when Pm, k  Pm,max te  Te ,m  M (40) This condition assures the convergence of the algorithm. De-
SHED LTS LTS

 tails about the convergence of consensus algorithm under dif-

 Equation (41) when Pm,min  Pm, k  Pm,max
LTS LTS LTS
 ferent network topologies can be found in [28].
,k 1 
mSHED   pm, j . jSHED
,k ,k 
  .PmMIS j  M ,m  M (41)
V. NUMERICAL SIMULATIONS
jM

Algorithm II Consensus-based algorithm for load shedding. A. Normal Mode Operation

1: Initial values In normal mode, a network of three hybrid microgrids is
2: Run local optimization for each microgrid considered and the network can trade power with the utility
3: while te  Te do grid via CEMS. The time-of-use market price signals of DSO
4: LTS
Determine PteSur and Pmax by (35) & (36), define ɛ along with generation costs of CDGs are shown in Fig. 3. In
Sur
order to elaborate the effectiveness of the proposed optimiza-
5: Pte,acc  0, k  0 , determine P and Q matrices by (44) & (45)
tion scheme, in addition to the resilience-oriented scheme, a
6: for all m  M do conventional approach (without considering resilience) is also
7: Determine tSHED
e
by equation (38) simulated. Figures 4-6 show the optimization results of both
Sur Sur Sur
8: Pte,acc : 0, Pte,acc  Pte,m

9: Initialize m,0
SHED
, PmLTS , and PmMIS by equation (39)
Cost/Price (Won/kWh)

,0 ,0

10: while PmMIS

,k
> ɛ do

11: If PmLTS
,k
> PmLTS
,max
then
LTS LTS
12: Pm ,k 1 = Pm ,max

13: else if PmLTS

,k
< PmLTS
,min
then
LTS LTS
14: Pm ,k 1 = Pm ,min
Time (h)
15: else Determine m,SHED
k 1
by equation (41) Fig. 3. Time-of-use price signals and generation costs of CDGs.
16: end if
17: Determine PmLTS
,k 1
by equation (42)
a b
18: Determine PmMIS by equation (43)
Power (kW)

,k 1

19: k++
20: end while
21: end for
22: te ++
Time (h)
23: end while Fig. 4. Power balancing in MG1: a) conventional; b) resilience-oriented.

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TABLE II
ADJUSTED POWER AND AMOUNT OF POWER TRADING
a b
Ti Conventional (kW) Resilience-Oriented (kW)
Power (kW)

me Increase/Decrease Buy/ Increase/Decrease Buy/

(t) MG1 MG2 MG3 Sell MG1 MG2 MG3 Sell
8 96 0 0 469 14 0 0 471
9 111 0 0 434 111 0 0 426
Time (h) 10 9 0 0 577 90 0 0 449
Fig. 5. Power balancing in MG2: a) conventional; b) resilience-oriented. 11 89 0 0 496 89 0 0 298
19 192 0 0 28 192 -64 0 0
20 248 -31 -110 0 205 -117 0 0
a b
21 241 8 -110 0 198 -90 0 0
22 255 -37 -110 0 205 -105 0 0
Power (kW)

cannot be reduced further. This consideration has increased the

adjustment cost by 0.055% per MW of critical load. However,
Time (h) if any sudden event occurs, critical loads will be survived.
Fig. 6. Power balancing in MG3: a) conventional; b) resilience-oriented. It can be observed that during normal operation, operation
cost of the network has increased by 0.0024% per MW of crit-
conventional and resilience-oriented optimization schemes for ical in the local optimization phase and by 0.055% per MW of
each microgrid. It can be observed from the results of the critical load in the community optimization phase. This in-
conventional scheme that during off-peak intervals (shaded crease is not significant due to consideration of adjustable
regions), generation of CDGs is set to minimum and shortage power in each microgrid. In addition, during system disrup-
is proposed to the CEMS. During these intervals, buying from tions, the proposed solution can assure several benefits to the
the utility grid is more economical if only operation cost is microgrids that are explained in the next section.
considered. However, in the case of resilience-oriented opti-
mization scheme, generation of CDGs is equal to the amount B. Emergency Mode Operation
of most critical loads. Due to this consideration, operation cost In emergency case, the initial step is local optimization by
of the network has increased from 2.76 million KRW to 2.81 respective MG-EMSs. Local optimization results of all the
million KRW, which is an increase of 0.0024% per MW of three microgrids for both conventional and resilience-oriented
critical load. Since the increase in operation cost depends on schemes are shown in Figures 7-9. An event has been simulat-
the amount of critical load, therefore, increase in cost is ex- ed at the beginning of the second interval and the end time is
plained in terms of critical load amount. However, this not known. Therefore, scheduling window will be updated
consideration will assure the survivability of critical loads dur-
ing sudden disruption of grid.
a b
The adjustable power bounds suggested by each microgrid
Amount (kW)

for both conventional and resilience-oriented cases are tabulat-

ed in Table I. Intervals having non-zero upper/lower bounds
are tabulated in Table I. In case of conventional approach,
microgrids allow the CEMS to reduce the generation of expen- Time (15 minutes)
sive units to their minimum level. However, in the case of re- Fig. 7. Local results of MG1: a) conventional; b) resilience-oriented.
silience-oriented optimization, survivability of critical loads is
considered and limits are revised, especially lower limits. Fi-
a b
nally, the decided amounts of adjusted power in each micro-
Amount (kW)

grid and amount of electricity traded with the utility grid are
tabulated in Table II. In conventional case, generation of MG3
has been reduced to minimum level and then MG2 is reduced
due to higher generation cost of MG3. However, due to con- Time (15 minutes)
sideration of resilience, the lower bound of MG3 is zero, i.e. Fig. 8. . Local results of MG2: a) conventional; b) resilience-oriented.
TABLE I
ADJUSTABLE POWER BOUNDS ALONG WITH SHORTAGE/SURPLUS IN EACH MICROGRID
Conventional Approach (kW) Resilience-Oriented Approach (kW)
Time
Upper Bound Lower Bound Shortage/Surplus Upper Bound Lower Bound Shortage/Surplus
(t)
MG1 MG2 MG3 MG1 MG2 MG3 MG1 MG2 MG3 MG1 MG2 MG3 MG1 MG2 MG3 MG1 MG2 MG3
8 96 0 0 184 230 110 0 -239 -326 14 0 0 266 165 0 0 -202 -283
9 111 0 0 169 230 110 0 -225 -320 111 0 0 169 164 5 0 -206 -331
10 9 0 0 271 230 110 0 -253 -333 90 0 0 190 144 5 0 -197 -342
11 89 0 0 191 230 110 0 -165 -420 89 0 0 191 129 0 0 -99 -288
19 192 0 0 89 230 110 0 -43 -176 192 0 0 88 149 0 0 -41 -86
20 248 12 0 32 218 110 0 0 -107 248 12 0 32 117 0 0 0 -87
21 241 38 0 39 192 110 0 0 -139 241 38 0 39 90 0 0 0 -109
22 255 40 0 25 190 110 0 0 -108 255 40 0 25 105 0 0 0 -100

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surplus and unserved loads of all the three microgrids are tabu-
a b lated in Table III. Where, positive values indicate the surplus
Amount (kW)

amount and negative values indicate the unserved load

amount. Interval 2 of the resilience-oriented scheme (high-
lighted) is selected for evaluating the convergence of consen-
Time (15 minutes)
sus algorithm and sharing of surplus power among unserved
Fig. 9. . Local results of MG3: a) conventional; b) resilience-oriented. loads. Three different cases are considered in the emergency
mode to evaluate the effectiveness of the proposed resilience-
TABLE III oriented optimization scheme.
SURPLUS AND UNSERVED LOAD AMOUNT IN EACH 1). Case a: The network topology for case a along with row-
MICROGRID.
Time Time Conventional (kW) Resilience-Oriented (kW)
stochastic matrix (P) and column-stochastic matrix (Q) for the
(t) (te) MG1 MG2 MG3 MG1 MG2 MG3 given topology are shown in Fig. 10. The entries of P and Q
1 -313 -299 -190 -64 -82 -89 are determined in accordance with the properties mentioned in
2 -132 -202 -46 -36 26 -10 Section IV-B. If the microgrids are fully connected (two-way
2
3 155 0 1 166 18 0 communication is possible), then, Q is equal to the transpose
4 140 -2 32 114 0 12
of P, i.e.P=QT. The incremental cost of load shedding has con-
5 169 0 0 158 4 0
6 145 1 0 170 8 0 verged to an optimal value of 8.11 as shown in Fig. 11(a). Cor-
3 responding served loads of microgrid 1 and 3 are 16kW and
7 166 5 0 141 48 0
8 159 7 0 159 7 0 10kW, respectively. The surplus mismatch has converged to
zero as shown in Fig. 10(b).
until the end of the event or the end of the day (scheduling 2). Case b: The network topology for case b along with
horizon). The time step for emergency operation is 15minutes; corresponding matrices for the given topology is shown in Fig.
therefore, ramp rates of CDGs and charging/discharging rates 12. The incremental cost of load shedding has converged to
of energy storage units will play an important role. It can be the same optimal value (8.11) and mismatch has reduced to
observed that during the initial interval (highlighted), a lot of zero as shown in Fig. 11. Reduction of mismatch to zero in
load shedding is carried out by all the microgrids in the con- case a and case b implies that all the available surplus power is
ventional approach. However, due to readiness for feasible allocated to the microgrids having shortage power. Similarly,
islanding, most critical loads (level 1) are not shed in the pro- power allocation to microgrid1 and microgrid3 is also identi-
posed scheme by all the microgrids. Load shedding has been cal for case a and case b. Due to higher priority of unserved
reduced from 1185kWh to 281kWh, which is a reduction by loads in microgrid3, all required power (10kW) is allocated
76.25%. first and remaining power (16kW) is allocated to microgrid1.
It has been assumed that microgrids are not able to com- Therefore, no load shedding is carried out in microgrid3 and
municate with CEMS in emergency mode. However, some of 10kW of unavoidable load shedding is carried out in mi-
the microgrids may still be interconnected during emergencies. crogrid1 for both cases (case a and b). However, more itera-
In order to increase the service reliability of the interconnected tions have been taken to converge due to the absence of direct
microgrids, a distributed energy management strategy (incre- communication between microgrid1 and microgrid3 in case b
mental cost consensus) is used in the emergency operation. as compared to case a.
After local optimization, each microgrid EMS computes its 3). Case c: In case c, it is assumed that all the microgrids
surplus amount or unserved load amount along with its cur- cannot communicate with each other. Therefore, after local
tailment cost and informs its neighboring EMSs. Interval-wise optimization, further power sharing is not possible and un-
served loads mentioned in Table III will be curtailed to bal-
𝜆1𝑆𝐻𝐸𝐷
MG1 MG2 1 1 1 ance supply and demand.
𝜆𝑆𝐻𝐸𝐷
2
3 3 3
  1 2 12 0 
𝜆𝑆𝐻𝐸𝐷
3 𝜆𝑆𝐻𝐸𝐷
3 P  QT   1 1 1 𝜆1𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷
2  
𝜆1𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷 3 3 3 P  QT  1 3 1 3
2   MG1 MG2 MG3 13
1 1 1  
MG3  3 3 3  𝜆𝑆𝐻𝐸𝐷
2 𝜆𝑆𝐻𝐸𝐷
3  0 12 1 2 

Fig. 10. Network topology for case a along with corresponding matrices. Fig. 12. Network topology for case c along with corresponding matrices.

∆𝑃2𝑀𝐼𝑆 ∆𝑃3𝑀𝐼𝑆 ∆𝑃1𝑀𝐼𝑆 ∆𝑃2𝑀𝐼𝑆 ∆𝑃3𝑀𝐼𝑆

𝜆1𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷 ∆𝑃1𝑀𝐼𝑆 𝜆1𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷 𝜆𝑆𝐻𝐸𝐷
Mismatch (kW)
Incremental cost

2 3 2 3
Mismatch (kW)
Incremental cost

Amount (kW)
Amount (kW)

a a b
b

Iteration number Iteration number

Fig. 11. a) Incremental cost & surplus balancing; b) Surplus mismatch. Fig. 13. a) Incremental cost & surplus balancing; b) Surplus mismatch.

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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/TSG.2017.2737024, IEEE
Transactions on Smart Grid
10

TABLE IV load shedding amount by 78.36% for case a and case b. How-
AMOUNT OF LOAD SHED IN DIFFERENT CASES. ever, due to the absence of networking, load shedding amount
Conventional (kW) Resilience-Oriented (kW)
Time Time is reduced by 76.25% for case c. This reduction in load shed-
Case Case Case Case Case Case
(t) (te) ding amount implies that at least the most critical loads are
a b c a b c
1 802 802 802 235 235 235 survived during emergency operation. The reduction in load
2
2 381 381 381 21 21 46 shedding increases the service reliability on one hand and it
3 0 0 0 0 0 0 saves the penalty cost on the other hand. It can be concluded
4 0 0 -2 0 0 0 that the proposed resilience-oriented optimization strategy has
the capability to reduce load shedding considerably at the cost
The amount of load shed by both conventional and the pro- of a minute increase in the operation cost.
posed resilience-oriented optimization schemes in all the three
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1949-3053 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2017.2737024, IEEE
Transactions on Smart Grid
11

[18] Z. Zhang, and M. Y. Chow, "Convergence analysis of the incremental Akhtar Hussain received his B.E degree in Telecommu-
cost consensus algorithm under different communication network topol- nications from the National University of Sciences and
ogies in a smart grid," IEEE Trans. Power Syst., Vol. 27, no. 4, pp. Technology (NUST) Pakistan in 2011 and his M.S in
1761-1768, Nov. 2016. Electrical Engineering from Myongji University, Yongin,
[19] U. Kumar, A. Trivedi, D. Srinivasan, and T. Reindl, "A consensus- South Korea, in 2014. He worked as an associate engi-
based distributed computational intelligence technique for real-time op- neer in SANION; IEDs development company, in Korea
timal control in smart distribution grids,"IEEE Trans. Emer. Topics from January 2014 to May 2015. Currently, he is a Ph.D.
Compu. Intel., vol. 1, no. 1, pp. 51-60, Feb. 2017. student at the Incheon National University, Korea. His
[20] J. Cao, "Consensus-based distributed control for economic dispatch research interests are power system automation and protection, smart grids,
problem with comprehensive constraints in a smart grid," Ph.D. disser- and microgrid optimization.
tation, The Florida State University, 2014.
[21] V.H. Bui, A. Hussain, and H.M. Kim,"A Multiagent-based hierarchical Van-Hai Bui received B.S. degree in Electrical Engi-
energy management strategy for multi-microgrids considering adjustable neering from Hanoi University of Science and Technolo-
power and demand response," IEEE Trans. Smart Grid, (Accepted) gy, Vietnam in 2013. Currently, he is a combined Master
2016. and Ph.D. student in the Department of Electrical Engi-
[22] Y. Zhang, N. R. Asr, J. Duan, and M.Y. Chow, "Day-ahead smart grid neering, Incheon National University, Korea. His re-
cooperative distributed energy scheduling with renewable and storage search interests include microgrid operation and energy
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1748, Jun. 2016.
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Miao, and Z. Salameh, "A review of hybrid renewable/alternative energy mation Sciences from Tohoku University, Japan, in
systems for electric power generation: Configurations, control, and ap- 2011, respectively. He worked for Korea Electrotechnol-
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403, Oct. 2011. Feb. 2008. Currently, he is a professor in the Department
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"Stochastic centralized dispatch scheme for ac/dc hybrid smart distribu- Korea. His research interests include microgrid operation & control and DC
tion systems," IEEE Trans. Sustainable Energy, vol. 7, no. 3, pp. 1046- power systems.
1059, Jul. 2016.
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