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Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 11042-11050 11042  
 

www.etasr.com Albaker: Reliability-Constrained Optimal Scheduling of Interconnected Microgrids 

 

Reliability-Constrained Optimal Scheduling of 
Interconnected Microgrids 

 

Abdullah Albaker 

Department of Electrical Engineering, College of Engineering, University of Ha’il, Saudi Arabia 
af.albaker@uoh.edu.sa (corresponding author) 

Received: 18 April 2023 | Revised: 7 May 2023 | Accepted: 10 May 2023 

Licensed under a CC-BY 4.0 license | Copyright (c) by the author | DOI: https://doi.org/10.48084/etasr.5970 

ABSTRACT 

This paper proposes a Mixed-Integer Linear Programming (MILP) optimization model for the scheduling 
problem of the interconnected microgrid system. The proposed model is capable of efficiently minimizing 
the microgrids' total operating costs and improving the entire system's reliability, as it is constrained based 
on enhancing the interconnected microgrids' reliability. The Expected Energy Not Supplied (EENS) is 
considered in order to ensure minimizing the interconnected microgrids' power deficiency. Furthermore, 
the proposed model has the capability to solve the optimization problem considering the islanded operation 
of the interconnected microgrids, i.e. when disturbances occur on the upstream grid. Numerical 
simulations on a test system containing three interconnected microgrids are performed to evaluate the 
effectiveness of the model and the results demonstrate the merits and features of the reliability-constrained 
optimal scheduling model in minimizing the interconnected microgrids' total operating costs and 
enhancing the interconnected system reliability. 

Keywords-distributed energy resources; Expected Energy Not Supplied (EENS); interconnected microgrids; 

islanded operation; optimization; optimal scheduling   

I. INTRODUCTION  

The reliability of power systems is one of the most 
important factors of human quality of life, as power outages for 
a few minutes may cause serious problems [1-4]. Therefore, it 
is significant to constantly develop and improve the reliability 
of power systems in order to maintain their quality and 
sustainability [5-8]. Enhancing and evaluating the power 
systems’ reliability has been extensively researched and 
analyzed. Authors in [9] investigated the reliability analysis of 
the IEEE40-bus system coupled with enormous PV and wind 
systems. By dividing the power system layout into various 
parts, the zone branch approach was used to evaluate the 
reliability parameters of the distribution systems. In [10], a 
cost-reliability bi-objective optimization model was developed 
for microgrids to acquire the optimal sizing and sitting of 
energy storage systems. The developed model included 
minimizing the microgrid’s total cost and Loss Of Load 
Expectation (LOLE) and the ε-constraint method and fuzzy 
satisfying technique were utilized to solve the proposed 
problem. The uncertainty related to the availability of capacity 
and the load level was taken into consideration in [11] using a 
generic and coherent approach. In addition, applications were 
illustrated and a new method for the determination of the 
probabilistic assessment of reliability indices and performance 
quality metrics was described. In [12], a comprehensive 
methodological framework was proposed, based on 
quantitative and Latin hypercube sampling methods, to study 
the prospective impact of vehicle-to-grid with utility-connected 
battery swapping station for enhancing the supply 
dependability in future distribution networks. The study in [13] 

utilizes the fmincon optimization tool to inspect the impact of 
integrating renewable energy resources into microgrids in 
terms of measuring and evaluating the enhancement of the 
system’s reliability. The obtained results indicated the 
improvement of measuring the system’s reliability. Authors in 
[14] proposed an optimization model based on enhancing the 
reliability to solve the optimal scheduling problem of the 
integrated microgrids and evaluated some of the reliability 
indices of the system including CAIDI, SAIDI, and SAIFI. 
Microgrids as an intelligent technique are partially intended to 
support power systems’ reliability [15-18].  

Microgrids are typically designed to facilitate integrating 
Distributed Energy Resources (DERs) into power systems to 
support the local load demand and expand the predicted 
economic benefits [19-21]. DERs may involve non-
dispatchable renewable units, Battery Energy Storage Systems 
(BESSs), and dispatchable Distributed Generators (DGs) [22-
24]. Once the microgrids are developed, achieving optimal 
scheduling is a crucial factor in realizing the desired objectives. 
Several research studies have been extensively conducted in 
this field [25-31]. In [25], an optimization resiliency-oriented 
scheduling model was proposed to enhance the resiliency of the 
microgrid by reducing local load curtailment. Authors in [26], 
proposed an optimization model to solve the scheduling 
problem of several integrated microgrids using the Lagrangian 
relaxation method to preserve the microgrids’ privacy. In [27], 
a discretized step transformation scheme based on chance-
constrained programming was proposed considering the 
spinning reserve uncertainty to solve the scheduling problem 
for isolated microgrids. Authors in [28] proposed an optimal 



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scheduling strategy to regulate the microgrid operation and 
support its resiliency based on developed constraints that 
enable the islanding operation. Authors in [29] proposed a 
multi-objective optimization approach to determine the optimal 
scheduling of unbalanced microgrids considering energy 
saving, improvement of power quality, and cost minimization. 
In [30], an automated reinforcement learning-based 
optimization scheme was proposed considering multi-period 
forecasting associated with load and renewable generation to 
solve the optimal scheduling problem of isolated microgrids. 
Authors in [31] proposed a scheduling model considering 
radiation changes of photovoltaic systems and uncertainties 
associated with grid bid changes and load demand forecasting 
to solve the optimization problem. In addition, they utilized a 
modified bat algorithm to solve the proposed problem 
considering a variety of uncertainties. Nonetheless, the 
microgrids can be interconnected to each other to maximize the 
anticipated goals. The optimal interconnected operation of the 
microgrids can maximize the reliability and resiliency of local 
power systems, boost the economic advantages of individual 
microgrids, and foster the use of renewable energy resources. 

The current paper proposes a generic optimization model to 
solve the optimal scheduling problem of interconnected 
microgrids considering enhancing the interconnected system’s 
reliability. Based on the developed operational constraints, the 
proposed model minimizes each microgrid’s Expected Energy 
Not Supplied (EENS), hence, maximizing the reliability of each 
microgrid involved in the system. In addition, it minimizes the 
entire interconnected system’s total operation cost. 
Furthermore, it is featured with the capability to solve the 
scheduling optimization problem during the islanded operation. 
The proposed optimization problem is developed based on a 
Mixed Integer Linear Programming (MILP) and solved over a 
completed 24-hour scheduling horizon. 

II. MODEL OUTLINE 

The proposed reliability-constrained optimal scheduling 
model of interconnected microgrids aims to minimize each 
microgrid's "involved in the integrated system" total operation 
cost and minimize the microgrid's EENS. In addition, it 
considers the optimal scheduling of the interconnected 
microgrids during both grid-connected and islanded operations, 
i.e. during outages and disturbances. 

The microgrids will exchange the power (export and 
import) with the utility grid during the grid-connected mode to 
maximize their economic benefits, while they exchange power 
locally, i.e. among the interconnected microgrids, during the 
islanded mode to boost and maximize their reliability and own 
economic benefits. To clarify this significant point, there will 
be no local power exchange among the interconnected 
microgrids during the grid-connected mode since it will be 
more economical for the seller microgrid to sell its excess 
generation to the utility rather than the other interconnected 
microgrids. On the other side, the microgrid that experiences a 
power deficiency would prefer to buy the power from the 
utility, as they have the option to buy their further needs of 
power at cheaper prices at the hourly market prices. 
Accordingly, there is no power exchange among the 
interconnected microgrids during the grid-connected mode, 

while they will observably exchange power during the islanded 
operation for mutual benefits, i.e. to increase the seller 
microgrids’ economic benefits and minimize the buyer 
microgrids’ energy deficiency.  

The proposed interconnected microgrid system is 
demonstrated in Figure 1. It is worth mentioning that the 
developed model would significantly improve the individual 
microgrid’s reliability in addition to the overall reliability of the 
interconnected system as it pointedly encourages the 
microgrids to exploit all available DERs of the interconnected 
system as much as possible. In other words, the proposed 
model inspires the microgrids to exploit all installed DERs to 
supply the other microgrids that experience power deficiencies 
for mutual benefit. 

 

 
Fig. 1.  Interconnected microgrid system. 

III. PROBLEM FORMULATION 

The objective function of the proposed reliability-
constrained optimal scheduling problem of the interconnected 
microgrid system aims to minimize each microgrid's total 
operating costs and to minimize the probability of power 
deficiency occurrences within the microgrids, as follows: 

 (1)

 

The developed objective function involves four main 
expressions. The first expression represents the generated 
power from the installed dispatchable DERs, which is further 
multiplied by a commitment binary indicator to specify the 
commitment state. The second expression represents 
exchanging the power with the utility grid. Nonetheless, this 
expression could mean either cost or revenue depending on the 
power flow direction. The third expression represents the 
power exchange between the interconnected microgrids. 
However, this expression will bring cost for buyer microgrids 
and revenue for seller microgrids. The last expression is added 
to add value to the percentage of the power deficiency within 
the microgrids. The minus sign is added as the percentage of 
the power deficiency will be displayed in the negative. 
Nonetheless, it is multiplied by an auxiliary cost value, which 
is supposed to be higher than the other costs to prioritize the 
reliability of the interconnected system. It should be indicated 



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that the proposed optimization model is developed to be 
compatible with both, islanded and grid-connected, modes 
using the islanded operating indicator s. 

 (2) 

 (3) 

 (4) 

The total generated and imported power must be balanced 
with the total power demand, which is satisfied by (2). 
However, it is worth mentioning that the EENS is included in 
the power balance equation to achieve a feasible solution 
during outages or disturbances, i.e. during the islanded 
operation. The power exchange between the microgrids and the 
utility grid must be within the maximum line capacity limits, 
which is satisfied by (3). Nonetheless, the line capacity limits 
are multiplied by the islanding binary variable to regulate the 
microgrids’ operating modes among the islanded and grid-
connected operation. On the other side, the power exchange 
among the interconnected microgrids is also subjected to line 
capacity limits, which is satisfied by (4). However, it should be 
mentioned that this operational constraint is also multiplied by 
the islanding binary variable to force the power exchange 
between the interconnected microgrids to zero during the grid-
connected operation. 

 (5) 

 (6) 

 (7) 

 (8) 

 (9) 

The installed dispatchable units are subject to respective 
operational constraints to regulate their operation. Each 
dispatchable unit can generate power only between the 
maximum and minimum capacity limits, which are satisfied by 
(5). In addition, they are multiplied by a commitment binary 
variable I to state whether the dispatchable unit is committed or 
not during the specified optimal scheduling hour. Moreover, 
each dispatchable unit is restricted by the ramping up and down 
rate limits, as in (6) and (7), respectively. Furthermore, once 
the dispatchable unit is switched ON or OFF, it is restricted by 
the minimum up and down time limits, of (8) and (9), 
respectively. 

 (10) 

 (11) 

 (12) 

The adjustable loads are regulated by constraints (10)-(12). 
Each adjustable load in the microgrids is restricted by the 

minimum and maximum rated power, as in (10). However, 
some of the adjustable loads that are switched ON might be 
subject to a minimum required energy to accomplish the 
operating cycle, which is regulated by (11). On the other hand, 
some adjustable loads must operate continuously for a certain 
amount of time after being turned ON, which is satisfied by 
(12). 

 (13) 

 (14) 

 (15) 

 (16) 

 (17) 

 (18) 

 (19) 

The connected BESSs are subject to several operational 
constraints to acquire their optimal scheduling. Maximum and 
minimum charging and discharging restrictions apply to 
BESSs, as in (13) and (14). In accordance with the charging 
and discharging operations over the defined scheduling 
horizon, and taking into account the BESS efficiency, the 
stored energy in the BESS is calculated by (15). The minimum 
and maximum capacity restrictions impose additional limits on 
the BESSs, as in (16). Each BESS is restricted by time limits 
once it starts charging or discharging, as in (17) and (18), 
respectively. Furthermore, the binary variables u and v are 
added to the BESS operational constraints (19) to regulate their 
operation mode to either charge or discharge during the 
specified optimal scheduling time. 

 (20) 

  (21) 

The microgrids’ power deficiency is a significant factor in 
indicating the interconnected microgrids’ reliability; thus, it is 
restricted by the developed constraints (20) and (21). The 
probability of EENS is calculated by (20). The percentage of 
the microgrids’ power deficiency is regulated and measured by 
(21). 

IV. NUMERICAL SIMULATIONS  

Three independent microgrids were utilized to study and 
investigate the proposed reliability-constrained optimal 
scheduling model of the interconnected microgrids, which are 
named MG A, MG B, and MG C. The microgrids' local 
installed dispatchable generators are specified in Table I. The 
microgrids’ BESS characteristics are demonstrated in Table II. 
The efficiency of all BESS is supposed to be 90% [26]. Each of 
the microgrids is accompanied with its own renewable, i.e. 
nondispatchable, generators, and their forecasted power 
generation is shown in Figures 2 and 3, for solar PVs and wind 



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turbines power, respectively. Table III shows the characteristics 
of the adjustable loads that are installed in the microgrids. 

TABLE I.  CHARACTERISTICS OF INSTALLED 
DISPATCHABLE GENERATORS 

DG 
MG A MG B MG C 

Price ($/MWh) 
G 1 28.1 30.9 38.7 

G 2 38.9 45.7 46.9 

G 3 62.2 73.5 75.4 

G 4 66.3 78.4 – 

– Minimum up and down time (h) 
G 1 3 4 5 

G 2 3 4 4 

G 3 1 2 2 

G 4 1 3 – 

– Minimum and maximum capacity (MW) 
G 1 1 – 5 1 – 2 0.5 – 2 

G 2 1 – 5 0.5 – 2 0.8 – 2.5 

G 3 0.8 – 3 0.5 – 1 0.5 – 3.5 

G 4 0.8 – 3 1 – 3 – 

– Ramp up and down rate (MW/h) 
G 1 2.5 1 1.5 

G 2 2.5 2 1.5 

G 3 3 1 2.5 

G 4 3 1.5 – 

TABLE II.  MICROGRIDS’ BESS CHARACTERISTICS 

Microgrid 

BESS characteristics 
Charging and discharging 
minimum and maximum 

power (MW) 

Charging and 
discharging minimum 

operating time (h) 

Capacity 
(MWh) 

MG A BESS 0.4 – 2 5 10 

MG B BESS 0.2 – 1 4 5 

MG C BESS 0.8 – 2 4 6 
 

 
Fig. 2.  Solar PVs power in MG A, MG B, and MG C. 

The microgrids’ hourly fixed load data are shown in Figure 
4. All the microgrids are electrically connected to the utility 
grid as an infinite bus. The market price of the power exchange 
between the utility grid and the microgrids is demonstrated in 
Figure 5. Figure 5 also shows the price of the local power 
exchange among the interconnected microgrids, which is set to 
be 10% higher than the market hourly prices arbitrary to create 
incentive to local power exchanges. In addition, a marginal 
value of the power deficiency, i.e. , of $10/kWh is assumed 
[32]. The lines between each microgrid and the utility grid and 
the lines among the interconnected microgrids are subject to 
line capacity limits, which are restricted to 10MW and 2MW, 
respectively. A 24-hour scheduling horizon is considered to 
solve the proposed problem. In addition, 25-islanded-scenarios 

are considered to solve the optimization problem, where one 
scenario indicates the grid-connected operation and the rest 
indicate islanded operation in each specific hour. The 
optimization problem is programmed and solved using CPLEX 
11.0 in GAMS [33]. Five case studies were carried out to 
demonstrate the features and effectiveness of the proposed 
model. The summary of the microgrids’ total operation costs is 
shown in Table IX for all cases. 

 

 
Fig. 3.  Wind turbines power in MG A, MG B, and MG C. 

 
Fig. 4.  Hourly fixed load in MG A, MG B, and MG C. 

 
Fig. 5.  Hourly forecasted market prices and local power exchange prices. 

A. Case 0-Base Case: Individual Microgrid Optimal 
Scheduling 

In this case, each microgrid in the system is optimized 
individually, i.e. there is no interconnection among the 
microgrids, to ensure the lowest potential operational cost and 
maximum reliability. The total operational costs of MG A, MG 
B, and MG C, considering the islanded operation scenarios, are 
computed as $14,699.19, $9,387.56, and $10,001.18, 
respectively.  

TABLE III.  ADJUSTABLE LOAD 



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Microgrid 

Adjustable load characteristics 

Load 
type 

Required 
energy 
(MWh) 

Minimum and 
maximum 

capacity (MW) 

Start and 
end time 

(h) 

Minimum 
up time (h) 

MG A 

Shiftable 1 1.6 0 – 0.4 11 – 15 1 
Shiftable 2 1.6 0 – 0.4 15 – 19 1 
Shiftable 3 2.4 0.02 – 0.8 16 – 18 1 
Shiftable 4 2.4 0.02 – 0.8 14 – 22 1 

Cuirtailable 5 47 1.8 – 2 1 – 24 24 

MG B 

Shiftable 1 1.6 0 – 0.4 12 – 16 1 

Shiftable 2 2.4 0.02 – 0.8 15 – 23 1 

Cuirtailable 3 47 1.8 – 2 1 – 24 24 

MG C 

Shiftable 1 2 0 – 0.5 9 – 13 1 
Shiftable 2 2.4 0.2 – 0.8 11 – 17 1 

Cuirtailable 3 36 0.8 – 1.6 1 – 24 24 
 

 

 

 
Fig. 6.  Microgrids’ power deficiency in Case 0. 

In this case, each of the microgrids in the system 
experiences some power deficiency during the optimal islanded 
operation, which is illustrated in Figure 6. The percentage of 
the power deficiency in the microgrids is calculated as 1.61%, 
2.33%, and 7.67% for MG A, MG B, and MG C, respectively 
(see Table VIII). The hourly optimal scheduling of the installed 
BESSs in the microgrids is demonstrated in Figure 7. This case 
study demonstrates that although optimal solutions for 
microgrids are identified, the lack of complementary power 
supplies may result in failure to reach maximum reliability. 

B. Case 1: Optimal Scheduling when the Interconnection is 
only between MG A and MG B 

In this case, the impact of integrating MG A and MG B on 
the optimization outcomes is investigated. MG A's total 
operation cost is slightly reduced by 0.34% to $14,648.59, 

while the total operation cost of MG B is slightly increased by 
0.43% as it is computed to $9,428.60. It should be mentioned 
that the optimization outcomes of MG C are not impacted in 
this case study as its optimal scheduling results remained 
exactly the same as in the base case.  

 

 
Fig. 7.  Optimal scheduling of the BESS in Case 0. 

TABLE IV.  LOCAL POWER EXCHANGE BETWEEN MG A 
AND MG B IN CASE 1 

Scenario no. 1 2 3 4 5 6 7 8 

P
C(A-B) (MW) –0.26 –0.47 –0.36 –0.28 0.56 0 0.57 0.69 

Scenario no. 9 10 11 12 13 14 15 16 

P
C(A-B)

 (MW) 0.70 0.78 0.54 0.46 0.46 0 –0.32 –0.47 

Scenario no. 17 18 19 20 21 22 23 24 

P
C(A-B) (MW) –0.45 –0.12 –0.80 0 0 0 0 0 

 

 

 
Fig. 8.  Power deficiency differences in Case 1 for MG A and MG B. 

The hourly power deficiency is reduced by 81.98% and 
56.65% for MG A and MG B, respectively, as shown in Figure 
8. In this case, MG A and MG B experience power deficiency 
of 0.29% and 1.01%, respectively. The percentage of power 
deficiency is summarized in Table VIII for all cases. 
Obviously, enabling the integration among these two 
microgrids would result in permitting local power exchange 
among them. The results of the optimal hourly power exchange 
among the interconnected microgrids are shown in Table IV. It 
should be noted that the minus sign signifies that the power is 
transferred from MG A to MG B, and vice versa. Observably, 
allowing the integration among certain microgrids 



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demonstrates slight improvements in terms of interconnected 
microgrids’ economic benefits and improves their reliability as 
it authorizes further paths to optimize the microgrid scheduling. 

C. Case 2: Optimal Scheduling when the Interconnection is 
only between MG A and MG C 

In this case study, the interconnection among the 
interconnected microgrids is only enabled between MG A and 
MG C. The microgrids’ total operation cost is computed as 
$14,201.05 and $10,569.53 for MG A and MG C, respectively, 
while the total operating cost of MG B remained unchanged as 
in case 0. Even though the total operation cost of MG C is 
increased by 5.68%, the power deficiency of MG C is 
obviously reduced by 87.39%. The percentage of the power 
deficiency is computed as 0.22% and 0.97% for MG A and 
MG C, respectively, while it remained unchanged for MG B, as 
shown in Table VIII.  

TABLE V.  LOCAL POWER EXCHANGE BETWEEN MG A 
AND MG C IN CASE 2 

Scenario no. 1 2 3 4 5 6 7 8 

P
C(A-C)

 (MW) –2 –2 –2 –1.52 0.56 0 0.57 0.69 

Scenario no. 9 10 11 12 13 14 15 16 

P
C(A-C) (MW) 0.70 0.60 0.54 0.42 0.68 0.29 0 0 

Scenario no. 17 18 19 20 21 22 23 24 

P
C(A-C) (MW) 0 0 –1.06 –0.25 –1.66 –2 –1.94 –1.89 

 

 

 
Fig. 9.  Power deficiency differences in Case 2 for MG A and MG C. 

The hourly power exchange between MG A and MG C is 
illustrated in Table V. The minus sign indicates that the power 
is transferred from MG A to MG C, and vice versa. The 
improvements in the microgrids’ power deficiency are 
graphically illustrated in Figure 9, which also shows the hourly 
load curtailment in MG A and MG C. 

D. Case 3: Optimal Scheduling when the Interconnection is 
only between MG B and MG C 

In this case, the interconnection among MG B and MG C is 
activated, hence, the power can be locally exchanged among 
these interconnected microgrids. The optimization results of the 

hourly local power exchange are illustrated in Table VI, where 
the minus sign indicates that the power is exported from MG B 
to MG C and vice versa. The total operating costs of these two 
interconnected microgrids are slightly changed, as it is 
indicated in Table IX. MG B’s total operating cost is reduced 
by 0.61% (computed as $9,329.68), while MG C’s total 
operating cost is slightly increased by 1.19% (computed as 
$10,120.02). However, the power deficiency of these two 
microgrids is noticeably decreased, by 65.23% and 58.15% for 
MG B and MG C, respectively. The changes in the power 
deficiency are graphically demonstrated in Figure 10. The 
reduction percentage of total power deficiency is calculated as 
0.81% and 3.21% for MG B and MG C, respectively, as it is 
shown in Table VIII. On the other side, the optimization results 
of MG A have not been changed compared with the base case, 
as it is excluded in this case study from the interconnection. 

TABLE VI.  LOCAL POWER EXCHANGE BETWEEN MG B 
AND MG C IN CASE 3 

Scenario no. 1 2 3 4 5 6 7 8 

P
C(B-C) (MW) –0.74 –0.73 –0.84 –0.92 –0.90 –1.19 –0.84 –0.28 

Scenario no. 9 10 11 12 13 14 15 16 

P
C(B-C)

 (MW) –1.19 0 0 0 0 0 0.66 0.38 

Scenario no. 17 18 19 20 21 22 23 24 

P
C(B-C) (MW) 0.18 0.51 0.82 –0.21 –1.58 –1.22 –0.59 –0.73 

 

 

  
Fig. 10.  Power deficiency differences in Case 3 for MG B and MG C. 

E. Case 4: Optimal Ιnterconnected Microgrids Scheduling 

In this case, all microgrids are electrically interconnected in 
the studied system. This case study inspects and explores the 
potential impacts of interconnecting the microgrids on their 
total operating costs and reliability. The optimal local power 
exchange scheduling among the interconnected microgrids, 
over the scheduling horizon, is demonstrated in Table VII. The 
optimization results of the optimal scheduling of the BESS are 
slightly changed in this case study, which is demonstrated in 
Figure 11. These slight changes are caused by the local power 
exchange among the microgrids. The total operating costs of 
the interconnected microgrids are computed as $14,379.87, 
$9,328.19, and $10,308.36 for MG A, MG B, and MG C, 



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respectively. Even though the total operating costs are slightly 
increased in some of the microgrids (by 3.07% in MG C), the 
encountered power deficiency in all the microgrids is 
dramatically minimized to zero, which emphasizes a significant 
improvement in the interconnected system reliability. 

TABLE VII.  LOCAL POWER EXCHANGE BETWEEN ALL THE 
MICROGRIDS IN CASE 4 

Scenario no. 1 2 3 4 5 6 7 8 

P
C(A-B)

 (MW) –1.18 –1.42 –0.38 0 0.56 0 0.57 0.37 

P
C(A-C) (MW) –2 –2 –2 –1.13 0 0 0 0.32 

P
C(B-C) (MW) –0.72 –0.95 –0.02 –0.72 –0.90 –1.19 –0.84 0 

Scenario no. 9 10 11 12 13 14 15 16 

P
C(A-B) (MW) 0.70 0 0 0.17 0.46 0 –0.22 –0.47 

P
C(A-C) (MW) 0 0.78 0.54 0.42 0.68 0.27 0 0 

P
C(B-C)

 (MW) –0.39 0 0 0 0 0.48 0.44 0.38 

Scenario no. 17 18 19 20 21 22 23 24 

P
C(A-B) (MW) –0.45 –0.01 –0.80 0 0 0 0 0 

P
C(A-C) (MW) 0 0 –0.26 –0.04 –0.10 –0.91 –1.85 –1.66 

P
C(B-C) (MW) 0.10 0.48 0 –0.21 –1.56 –1.20 –0.90 –0.23 

TABLE VIII.  PERCENTAGE OF MICROGRIDS’ POWER 
DEFICIENCY IN ALL CASE STUDIES 

Case no. MG A MG B MG C 
Case 0 1.61% 2.33% 7.67% 

Case 1 0.29% 1.01% 7.67% 

Case 2 0.22% 2.33% 0.97% 

Case 3 1.61% 0.81% 3.21% 

Case 4 0% 0% 0% 

TABLE IX.  SUMMARY OF MICROGRIDS’ TOTAL 
OPERATION COST 

Case no. MG A MG B MG C 
Case 0 $14,699.19 $9,387.56 $10,001.18 

Case 1 $14,648.59 $9,428.60 $10,001.18 

Case 2 $14,201.05 $9,387.56 $10,569.53 

Case 3 $14,699.19 $9,329.68 $10,120.02 

Case 4 $14,379.87 $9,328.19 $10,308.36 
 

 
Fig. 11.  Optimal scheduling of the BESS in Case 4. 

V. CONCLUSION  

This paper highlighted the potential benefits and features of 
enabling the interconnection among adjacent microgrids and 
proposed a reliability-constrained optimal scheduling model for 
interconnected microgrids. The proposed model was capable of 
economically minimizing the interconnected microgrids’ total 
operating costs and was capable of efficiently maximizing the 
interconnected system's reliability. The key features of the 
proposed optimization model can be summarized as follows: (i) 
it ensures the minimization of the microgrids' total operating 
costs and supports the optimization of the battery energy 
storage systems scheduling, (ii) it is capable of efficiently 

maximizing the interconnected system reliability by 
minimizing the expected energy not supplied in the microgrids, 
(iii) it takes the potentiality of islanded operation scenarios into 
account (i.e. in the event of disturbances and outages), and (iv) 
it is developed based on mixed-integer linear programming to 
facilitate reaching fast and efficient optimal solutions. 

The proposed model exploited all the distributed energy 
resources installed in the microgrids, including the battery 
energy storage systems, to support the reliability and economic 
benefits of the microgrids by enabling local power exchange 
among the interconnected system. The proposed optimization 
scheme was investigated in several case studies, including the 
optimal individual scheduling of the microgrids as a base case, 
to explore and validate its performance and feasibility. The 
obtained optimization results indicated its superior performance 
in minimizing the microgrids’ total operating costs and the 
expected energy not supplied in the microgrids. Nevertheless, 
the proposed optimization model is generic, and various test 
systems could be applied to investigate its feasibility and 
performance without loss of generality. 

NOMENCLATURE 

Indices: 
ch Superscript for BESS charging operation mode. 
d Index for loads. 
dch Superscript for BESS discharging operation mode. 
i Index for DERs. 
s Index for scenarios. 
m,n Index for microgrids. 
t Index for time. 

Sets: 
DA Set of adjustable loads. 
G Set of dispatchable generators. 
M Set of microgrids. 
K Set of islanded scenarios. 
S Set of BESSs. 
T Set of time periods. 

Parameters: 
DR Ramping down rate. 
D Aggregated load demand. 
DT Minimum down time. 
Dmax Adjustable load maximum rated power. 
Dmin Adjustable load minimum rated power. 
E Total required energy of adjustable load. 
F(.) Generation cost of DERs. 
MC Minimum charging time of BESS. 
MD Minimum discharging time of BESS. 
MU Minimum operation time of adjustable load. 
PR Aggregated forecasted renewable generation. 
UR Ramping up rate. 
UT Minimum up time. 
 Forecasted hourly market prices. 

 Value of power deficiency. 

 Local power exchange prices. 

, Adjustable loads’ defined start and end times. 
 BESS efficiency. 

Variables: 
C Total stored energy in BESS. 
EENS Expected energy not supplied. 
I Binary variable for commitment status of dispatchable units. 
P DERs generated power. 
PC Local power exchange. 
PD Power deficiency. 
PM Power exchange with the utility. 
Tch BESS’s number of successive charging hours. 



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Tdch BESS’s number of successive discharging hours. 
Ton Total number of successive ON hours. 
Toff Total number of successive OFF hours. 
U Binary variable for islanding operation status. 
 Time period. 
u Discharging state of BESS. 
v Charging state of BESS. 
 Probability of expected energy not supplied. 
z Adjustable load status. 

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AUTHORS PROFILE 

 
Abdullah Albaker received his M.S. and Ph.D. degrees in 
electrical engineering, specializing in electric power 
engineering, from the University of Denver, Denver, CO, 
USA, in 2014 and 2018, respectively. He is currently an 
Assistant Professor of Electrical Engineering at the 
University of Ha’il, Ha’il, Saudi Arabia. His research 
interests include microgrid planning and operation, renewable 

energy and distributed generation, power system economics and reliability, 
smart electricity grids optimization, and machine learning.