INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue IV, April 2025
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Energy Management of Islanded Micro-Grid with Uncertainties
Using Nash Bargaining Solution
Ismaheel Oyeyemi Oladejo, Michael Olorunfemi Ayeni, Kolawole Michael Ajala,
Sunday Oluwagbenga Oni, Sunday
Samuel Ogundipe
Department of Electrical Engineering, The Polytechnic, Ibadan, Ibadan, Nigeria.
DOI : https://doi.org/10.51583/IJLTEMAS.2025.140400036
Received: 19 April 2025; Accepted: 23 April 2025; Published: 06 May 2025
Abstract: With the increasing integration of solar PV and wind energy in island micro-grids (MGs), the intermittent nature of
non-dispatchable sources and the unpredictability of load demands are unavoidable. As a result, maintaining high reliability and
system stability becomes a significant challenge. Additionally, demand-side management technologies and energy storage are
commonly implemented in island MGs to mitigate the negative effects of RESs. However, these solutions also introduce
uncertainties. Moreover, RESs in MGs are highly susceptible to external environmental factors such as solar radiation,
temperature fluctuations, and wind speed variations, making it difficult to ensure system stability, particularly in islanded mode.
To address these uncertainties, this paper considers six participant sites and proposes a Cooperative Game Theory (CGT) based
on Nash Bargaining Solution (NBC) for collaboration among the participants of MG under the condition of uncertainties
introduced by each participant. First energy transaction among the MG participants is modeled. Secondly, CGT using NBS is
applied to model the uncertainties in dispatchable and non-dispatchable energy resources of the participants. Moreover, using
NBS, a cooperative operation model among MG participants is established, which is transformed into profit maximization in
cooperation, ensuring fair profit distribution and improves economic outcomes. The simulation results show that cooperation
among all participants leads to an increase in their benefit values. Additionally, the findings suggest that the proposed model
demonstrates strong economic performance.
Keywords: Uncertainties, Nash Bargaining Solution, Micro-grid participants, Energy management system, Cooperative game
theory, etc.
I. Introduction
MGs have emerged in response to the growing adoption of dispatchable, non-dispatchable, and energy storage technologies. They
offer several advantages over traditional power systems, including reduced carbon emissions, increased operational flexibility,
cost savings, and improved efficiency. A typical MG is made up of distributed energy generation sources, RESs, energy storage
units, and various types of loads [1], [2]. MG functions include either while making connection to the upstream network or in
standalone (islanded) mode.
Globally, studies have shown that the implementation of islanded MGs for power generation remains relatively limited [3], with a
heavy reliance on diesel generators. This study introduces a model of a representative MG made up of six participants. Each site
is equipped with a solar PV array, a diesel generator, storage energy system (as illustrated in Fig. 1), and the capacity to share
excess energy with other participants based on demand at different times of the day. The MG model is characterized by three core
components: solar PV integration, battery storage, and an energy scheduling system. However, the design and operation of MGs
come with significant challenges, particularly in developing effective scheduling strategies. Addressing these challenges under
uncertainty is essential for efficient MG operation. In CGT, a major focus is placed on the fair distribution of profits among MG
participants. CGT provides a powerful framework for analyzing collaborative decision-making among multiple stakeholders [4],
[5]. In power systems, game theory (GT) is typically divided into cooperative and non-cooperative models [4], and both have
been widely studied for optimizing collaboration in multi-micro-grid and multi-stakeholder environments.
There many related reviews in this EMS of MG. Fuzzy optimization techniques [6] and Model Predictive Control (MPC)-based
optimization approaches [7] have been proposed for scheduling of MGs incorporating renewable energy sources to reduce
emissions and operational costs. However, both approaches rely on deterministic forecast data, which is not well-suited for
islanded MG operations, as small-scale demand is difficult to predict, and RES generation is highly variable [8]. In [9], a chance-
constrained stochastic optimization method was proposed to minimize the operational costs of MGs. However, this technique
involves high computational complexity and large problem sizes, which makes it difficult to guarantee solution accuracy [10].
Reference [11] provides an overview of various strategies for modeling uncertainty, defining objective functions, and identifying
possible constraints. Although simulations and experimental results using an Energy Management System (EMS) are presented,
the treatment of uncertainty is not sufficiently addressed. In [12], recent developments in uncertainty modeling are reviewed,
focusing on novel methods for capturing uncertainties in MGs caused by renewable energy variability and load fluctuations.
Reference [13] discusses approaches for managing uncertainties, the use of simulation tools, parameter modeling, and unit
commitment in power systems. In [14], different uncertainty management techniques are classified, and the strengths and
limitations of these methods are evaluated and compared.
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In the cooperative operation of MGs, ensuring a fair distribution of benefits among participants is a critical concern. Both
domestic and international researchers have thoroughly investigated how different game theory approaches can be applied to
optimize MG systems collaboratively. In [15], a robust scheduling method based on non-cooperative game theory is proposed to
achieve equitable profit distribution among microgrids. Reference [16] addresses the energy management challenges among
multiple MGs and introduces a non-cooperative game model that utilizes shared energy storage and flexible control strategies to
enhance the economic efficiency of each system. Nonetheless, since non-cooperative game theory prioritizes individual gains, it
may result in suboptimal outcomes for the entire system and fall short in achieving overall fairness.
Unlike non-cooperative games, cooperative game theory focuses on collective interests, allowing for stable solutions and
achieving Pareto optimal outcomes [17]. For example, Reference [18] introduces a cross-regional cooperation model between a
large power grid and smaller microgrids, leading to increased profits for all parties involved. Reference [19] presents a
cooperative model for multiple microgrids based on the Nash Bargaining Solution (NBS), which ensures fair profit distribution
and enhances the system's economic performance. In Reference [20], game theory utilizing NBS is applied to minimize costs and
distribute expenses fairly among MG participants. These studies demonstrate that cooperative game theory supports mutual
economic benefits. However, they do not adequately consider the uncertainties associated with energy transfer, particularly those
arising from renewable energy variability and fluctuating load demands. Effectively addressing these uncertainties can
significantly boost the profitability of each participant and improve overall system performance [21]. Therefore, further research
is essential to better understand and manage the uncertainties related to renewable energy generation and energy trading among
MG participants.
This paper proposes an uncertainty-aware EMS based on the NBS to promote distribution of profits with fairness. The system
encourages equitable cooperation, allowing participants to benefit reasonably from collaboration while also enabling energy
sharing. This reduces dependence on expensive grid electricity. Furthermore, the paper introduces a CGT-based framework
utilizing the NBS, specifically designed for islanded MGs where uncertainties stem from fluctuating renewable energy output and
varying load demands. These uncertain parameters can be estimated for each time interval using historical data. This paper has
the following key contributions:
A comprehensive energy management framework for isolated islanded MGs is developed, considering energy transfer between
participants, renewable energy scheduling, battery storage charging and discharging, and diesel generator utilization.
A CGT approach based on NBS is proposed, allowing participants with varying peak energy demands to efficiently transfer
excess energy between sites, thereby reducing overall operational costs.
It also ensures profits that are fairly distribution among the MG players.
The structure of this paper is as follows: Section 2 presents the optimization problem formulation. Section 3 explores uncertainty
modeling for MG participants and forecast generation scheduling is presented in Section 4. Section 5 details the simulations and
results and discussion, and Section 6 concludes with key insights into managing uncertainty in MGs.
Figure 1: A Typical Islanded MG Considered in Optimization Formulation
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Optimization Problem Formulation
This section discusses the challenge of uncertainty in scheduling within modern power systems. One notable example that has
attracted significant interest in recent years is the MG, which comprises various elements such as distributed generation units
(including both energy production and storage systems) and different types of loads (both controllable and uncontrollable). The
complexity of scheduling operations in such systems is mainly due to the extensive integration of renewable energy sources like
solar PV, which exhibit unpredictable behavior. The primary goal is to optimize the participants’ profit, calculated as the revenue
generated minus the annual operational costs.
(1)
where
is the profit in lower bound of the players/participants in the site and
is the lower profit (i.e status quo profit) of
the participants in the site.
(2)
where
the MGs income,
is the annualized cost of MG.
Maximizing individual profits
as shown in equation (2) can results to an unequal distribution of earnings among participants,
which may ultimately weaken the microgrid concept by making participation less appealing to some members. This method treats
each participant independently (independent approach), allowing them to pursue their own maximum profit and negotiate based
on self-interest. However, to enhance the overall performance of the microgrid while ensuring fair compensation for all
participants, equation (1) is employed. This equation promotes equitable profit distribution without compromising collective
efficiency. Game theory supports this idea by offering a framework for fair profit sharing. Under this model, individual profts
may be minimized to some extent to maximize the objective in equation (1), thereby achieving both fairness in rewards and
optimal system-wide performance.
The total income of the participant is calculated as follows [4], [22]
(3)
where
is the transfer selling price
(4)
where
is the transfer price of electricity between sites s and
and
represents electricity transfer at certain day and time.
The total annual MG cost
includes annualized Captial Cost (ACCs), cost of operation and maintenance cost (OMC),
annualized cost of replacement (ARC), transfer cost of buying energy (TBC) and annualized cost of fuel (AFC).
(5)
where
is calculated as follows
, where Ccap is the cost of capital (US $) and CRF (i, y) is the capital recovery factor (i represents 12%
interest rate and y is the annualized project lifetime). The calculation aspect of CRF is as follows [22]
(6)
The second and third terms of (5) indicates annualized cost of operation and maintenance (OMC) and annualized cost of
replacement calculated in (7) and (8) respectively
(7)
where, is the component reliability.
(8)
where Crep is the cost of replacement of battery (in US $), yrep is the battery lifetime, SFF is the sinking fund factor, which is
calculated as follows [12]
(9)
The fourth term of (5) is the MG transfer buying cost. This is given in [20] as follows.
(10)
where,
represents electricity price transfer between sites s’ and s and
is the quantity of electricity transferred.
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The fifth term of (5) represent annualized cost of fuel (AFC), in which is associated with both the generated and rated power. In
this scenario, the diesel generator is expected to operate at its rated power. Therefore, the annual cost of the diesel generator is
equivalent to the annual fuel cost and is represented in [20] as follows
(11)
in which is the cost of fuel.
represents the diesel generator’s hourly fuel consumption, which can be expressed in [22] given as
(12)
where represents the actual power output of the diesel generator in kilowatts (kW), and
denotes the generator's rated
power.
3.1 Constraints
.a) Constraints of Energy demand:
The consumption of primary energy resources is determined based on the efficiency of local electricity generation.
The total primary energy consumption includes both the energy used locally at a site and the energy imported from or exported to
other sites.
At each time step, the energy demand is met by the combined output of the solar PV, diesel generator, battery storage, and the
energy imported from other sites.
(13)
where represents the energy imported from other sites, represents energy imported to other sites, represents
energy supplied from diesel generator, represents energy stored in the battery and represents solar power, all at
time t.
b) Constraints of Power Balanced: The power balance represents the quantity of power that must be supplied or absorbed within
the system to maintain equilibrium in islanded mode. In this study, solar PV, diesel generator and a battery storage are utilized.
The equation for this power balance defines the relationship between the generated power and the required power at any given
moment.
(t) (14)
where is the load power, represents the power of solar PV, represents power of the battery and (t)
represents the power of diesel generator all at time t for the site s.
c) Battery Power Output: The use of upper and lower limits is equivalent to charge/discharge of battery storage units
(15)
where,
and
indicate the minimum power discharged and maximum power charged by the battery units
respectively.
d) Constraints of price level Transfer
In general, there are k discrete levels of transfer pricing. Accordingly, for the electricity price
, between two sites, the decision
variable
and the parameter
, correspond to each price level and can be aggregated across these discrete pricing levels.
(16)
By using one transfer price at a certain time
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(17)
For every pair of sites and in both directions of energy transfer, the transfer prices remain identical.
(18)
Electricity from a given site must first satisfy its own demand before it can be sold to another site. Additionally, a site cannot
simultaneously purchase electricity from others and sell it to participants.
Modelling Uncertainties for Micro-Grid Participants
In modeling MG, uncertainties in scheduling and operation are primarily influenced by the level of RE integration, especially
from solar sources. Within power distribution networks—and particularly in MGs—solar PV systems are the most widely
adopted type of RES. Since PV output relies on solar irradiation, the variability and unpredictability of sunlight introduce
significant uncertainties into power generation [14]. Another major source of uncertainty is the fluctuation in daily electricity
demand. Consequently, when developing models aimed at profit maximization, it's necessary to account for numerous uncertain
variables. In such scenarios, probabilistic analysis becomes a vital method for managing these uncertainties in power system
scheduling and operation. This section outlines a framework based on Cooperative Game Theory (CGT) to address problems
involving these uncertain parameters.
a) Solar PV
The generation of power from solar PV systems depends on solar radiation and ambient air temperature. In modeling these
uncertainties, both irradiation and air temperature are commonly expressed by a normal distribution [23].. The probability
distribution of the forecasted solar irradiation, characterized by its mean (μ) and standard deviation (σ), is provided in [12], [23]:
(20)
The solar PV output power generated is calculated as
(21)
where,
is the output PV power generated,
represents irradiation in hour (hr),
denotes standard irradiation,
and
are the temperature for air and cell respectively.
and K are respectively power of solar PV rated power an temperature
coefficient at maximum [23], [24].
b) Load Modelling
Due to the wide variety of electrical appliances—such as air conditioners, heaters, and refrigerators—accurately modeling
electrical load becomes a complex task. Load behavior is influenced by several factors, including time of day and prevailing
weather conditions [25]. Load models are generally classified into two categories: static and dynamic [13]. Static models reflect
the magnitude and frequency of the electrical load at a specific time, while dynamic models capture how load changes over time,
considering its time-dependent characteristics. This study employs a dynamic load model, which better represents the real-time
behavior of electrical demand, as shown in Table 1. Load modeling is essential for several applications, including long-term
system stability, equipment aging analysis, and inter-area oscillation assessments [22], [25]. According to Table 1 (adapted from
[22]), residential buildings show the highest peak and annual electricity demand, whereas fire stations have the lowest demand in
both categories
Table 1: Annual demand profile of each participant [22].
School
Hotel
Restaurant
Fire
station
Residential
building
Hospital
Total
Annualized energy
demand (kW)
49859
66028.5
90082
37631.5
68036
75004.5
456641.5
Energy peak demand
(kw)
10.7
11.6
17.7
6.8
18.6
7.2
0
Case study
The Table 2 and Table 3 proposed that the MG has six participant’s sites having the characteristics of solar PV units and battery
storage sources respectively in each site.
Table 2: Characteristics of Solar PV in each site
Technology
K
PV
20kW
0.001
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Table 3: Characteristics of battery storage units in each site
Battery storage unit
Min/max
charge/discharge power
(kW)
Minimum charge/discharge
time (hr)
Capacity (kWh)
-10/+10
2
20
Considering the uncertainty in modelling solar PV and load demand, the value of these parameters is forecast as shown in Figure
2 and Table 4
Figure 2: Solar Power for each Participant’s site (a) Summer (b) winter
Scheduling of Generation Uncertainty with Respect to The Load
In islanded mode, the energy demand needs to be entirely supplied by power generated locally. Any mismatch between
generation and consumption can lead to system instability and degraded power quality. Table 5 illustrates the energy scheduling
under this mode. Since the main grid is unavailable, the microgrid (MG) relies entirely on local energy sources to meet demand.
In this setup, the diesel generator serves as the only dispatchable source, providing backup to the non-dispatchable solar PV
system. Based on the load profiles in Table 4 and the generation schedules in Table 5 (column 1 for each participant), it’s evident
that diesel generator operation varies with changes in demand. Batteries stored excess solar energy during periods when sun
radiation is high and discharge low solar inputs, helping stabilize power availability from the solar PV system.
This combination of dispatchable and non-dispatchable sources with battery as a storage source is used to manage fluctuations in
power demand. For instance, between 1 a.m. and 6 a.m., when solar generation is inactive, the power generation using diesel and
batteries are used to meet the load. During this period, some participants experience low demand while others have high needs.
As a result, certain diesel generators are turned off, and their power shortfalls are covered by surplus energy from other
participants. For example, during early morning hours, the hospital, residential building and restaurant keep running of their
diesel generators to meet their own needs and supply power to others whose generators are off. Between 7 a.m. and 5 p.m. solar
generation is sufficient in meeting the entire load demand. During this period, all generations from diesel generators remain off,
batteries are being charged, and energy exchange among the MG participants is possible. If there's a sudden drop in solar PV
output, the system activates both diesel generators and batteries to maintain a balance between energy supply and demand.
For instance, from 6 p.m. to 9 p.m., most MG participants experience a surge in electricity demand. To compensate for this, diesel
generators and batteries are utilized to bridge the power shortfall. Later, between 10 p.m. and midnight, some participants show
lower energy usage while others maintain high demand, as shown in the load profile. In this scenario, each participant's battery
storage discharges equal amounts of power to satisfy their load requirements. Facilities like an hotel, a restaurant, and a
residential building continue to consume significant electricity, prompting the diesel generator to be activated to supply an hotel,
school and a residential building. Meanwhile, generators for other participants are turned off to conserve fuel and prolong
equipment lifespan. The battery performance during the mode of charging and discharging is shown Figure 3.
As indicated in the last column of Table 5, energy transfers between sites are tracked hourly. During early morning hours (1 a.m.
to 6 a.m.), energy transfer is minimal due to generally low consumption, with the exception of high energy demand of about 8.9
kWh from the restaurant. In the afternoon, most participants generate enough solar power to meet their needs, resulting in little to
no energy transfer during certain hours—such as from 1 p.m. to 4 p.m., when no energy exchange takes place within the MG.
From 6 p.m. to 9 p.m., energy transfer significantly increases due to high demand at some locations where local generation falls
short. To optimize energy usage, power is redistributed from participants with surplus to those in need. Between 10 p.m. and
midnight, aside from the restaurant, electricity demand remains low, leading to reduced energy exchange among MG participants.
Figures 4 and 5 show the total excess electricity after local consumption and total electricity transferred to other participants
respectively.
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Table 4: Energy consumption during the winter (Day 1) and summer (Day 2) seasons. [22]
Day
Period
(hr)
School (kW)
Hotel (kW)
Restaurant (kW)
Fire Station
(kW)
Residential
Building (kW)
Hospital (kW)
Daytime1
2.11
2.31
8.91
2.11
3.71
2.19
Daytime1
2.11
9.29
3.51
3.29
5.61
4.49
Daytime1
10.7
11.61
8.91
6.79
7.51
7.31
Daytime1
10.69
11.61
17.71
6.79
7.51
7.30
Daytime1
10.7
11.61
8.89
6.81
7.51
7.3
Daytime1
4.30
9.31
17.69
4.11
18.60
5.41
Daytime1
2.11
2.29
8.90
2.11
3.71
3.01
Daytime2
2.11
2.29
8.91
2.10
3.71
3.01
Daytime2
2.10
9.31
3.49
3.31
5.60
4.50
Daytime2
10.71
11.61
8.89
6.81
7.49
7.31
Daytime2
10.7
11.6
17.7
6.8
7.5
7.3
Daytime2
10.7
11.6
8.9
6.8
7.5
7.3
Daytime2
4.3
9.3
17.7
4.1
18.6
5.4
Daytime2
2.1
2.3
8.9
2.1
3.7
3.0
Given that: Pers. gen= Participant’s personal generation, Sf/Sl =Shortfall/Surplus, Dem = demand, Negative sign written under
Sf/Sl column represents shortfall.
Table 5: Scheduling of Generation Uncertainties with Respect to the Load
Time
(Hrs)
School (kW)
Hotel (kW)
Restaurant
(kW)
Fire Station
(kW)
Residential
Building (kW)
Hospital (kW)
Total
excess
Energy
(kW)
Total
energy
transf.
(kW)
Pers
Gen
Sf /Sl
Pers
Gen
Sf /Sl
Pers
Gen
Sf /Sl
Pers
Gen
Sf
/Sl
Pers
Gen
Sf /Sl
Pers
Gen
Sf /Sl
1
2.09
0
2.09
-0.21
5.41
-3.51
2.09
-0.1
5.51
1.81
5.1
2.09
3.81
3.81
2
2.09
0
2.09
-0.21
5.41
-3.51
2.09
-0.1
5.51
1.81
5.1
2.09
3.81
3.81
3
2.09
0
2.09
-0.21
5.41
-3.51
2.09
-0.1
5.51
1.81
5.1
2.09
3.81
3.81
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4
2.09
0
2.09
-0.21
5.41
-3.51
2.09
-0.1
5.51
1.81
5.1
2.09
3.81
3.81
5
2.09
0
2.29
0
5.59
-3.31
2.31
0.2
5.6
1.91
5.31
2.31
4.42
3.32
6
2.69
0.59
2.51
0.21
5.79
-3.09
2.41
0.3
5.79
2.1
5.89
2.91
5.51
3.11
7
5.31
3.19
5.31
-3.9
5.61
2.09
5.31
2
5.51
-0.1
5.39
0.92
8.2
4.1
8
7.71
5.61
7.21
-2.1
7.81
4.29
6.49
3.2
7.31
1.71
6.31
1.8
16.61
2.1
9
10.21
-0.51
9.01
-2.59
9.51
0.61
7.91
1.1
10.51
3.1
7.81
0.5
5.19
3.09
10
11.71
1.01
10.59
-0.71
11.39
2.51
8.4
1.6
11.51
4.09
8.52
1.21
10.3
0.71
11
12.81
2.1
12.11
0.49
12.61
3.69
9.51
2.7
12.61
5.09
9.63
2.32
16.4
0
12
13.01
2.31
12.81
1.21
13.11
-4.61
10.09
3.2
13.09
5.5
10
2.71
14.9
4.61
13
15.01
4.29
14.81
3.21
15.01
6.11
10.09
3.2
15.08
7.5
10
2.72
26.79
0
14
14.81
4.09
14.81
3.21
15.01
6.11
9.81
3
14.61
7.1
9.71
2.41
25.89
0
15
14.31
3.59
13.89
2.29
14.51
5.61
9.29
2.5
14.2
6.7
9.11
1.81
22.49
0
16
12.91
2.21
12.39
0.81
13.11
4.2
8.5
1.7
12.8
5.3
8.7
1.4
15.61
0
17
10.71
0
10.21
-1.41
10.81
1.91
7.09
0.32
10.61
3.11
7.21
-0.11
5.32
1.5
18
11.72
7.41
11.69
2.42
11.82
-5.89
9.91
5.81
11.52
17.09
10
4.59
20.22
13.1
19
11.11
6.81
11.21
1.89
11.21
-6.5
9.61
5.51
10.61
-8.1
9.82
4.41
18.61
14.5
20
10.89
6.59
10.79
1.5
10.9
-6.8
9.52
5.41
10.39
-8.2
9.5
4.1
17.6
15
21
10.5
6.71
10.61
1.3
10.69
-7
9..2
5.09
10.1
-8.52
9.33
3.9
16.5
15.5
22
2.09
0
2.09
-0.21
5.41
-3.51
2
-0.1
5.51
1.8
5.1
2.9
3.81
3.81
23
2.09
0
2.09
-0.21
5.41
-3.51
2
-0.1
5.51
1.8
5.1
2.09
3.81
3.81
24
2.09
2.1
2.3
2.12
8.9
5.41
2.11
2.09
3.7
5.51
3.1
2.09
3.81
3.81
Figure 3: Daily battery Power Output.
-6
-4
-2
0
2
4
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power Output (kW)
Time (hrs)
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Figure 4: Total Excess Electricity after Local site Consumption
Figure 5: Total Energy Transferred to the Participants.
II. Simulation Results and Discussion
Profit Allocated to each Participant in Micro-grid
The study presents simulations involving MG participants. The optimization problem is addressed using MATLAB software and
carried out on an HP laptop equipped with 4GB RAM and an Intel Pentium processor. Figure 4 illustrates the profit outcomes for
individual participants under two scenarios: cooperative operation and independent profit maximization within an islanded MG.
In this scenario, the fire station earns the least profit, while the restaurant achieves the highest. When comparing profit levels, the
fire station sees a 2.8% increase and the restaurant experiences a 2.1% rise as a result of participant cooperation, as depicted in
Figure 4.
Figure 4: Profits of the MG in both independent and Cooperative operation.
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Total excess Energy(kW)
Time (hrs)
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30
Total Energy Transferred (kW)
Time (hrs)
24925
25683
26827
24244
26551
24544
25440
26210
27377
24925
27096
25048
22000
23000
24000
25000
26000
27000
28000
School Hotel Restaurant Fire Station Residential Building Hospital
Independent Cooperative
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Electricity transfer between sites
Electricity can be exchanged among microgrid (MG) participants at a mutually agreed rate. In this scenario, a fixed transfer price
of 0.039 kWh is used, as referenced in [20] and [22]. Table 6 outlines the optimal hourly electricity transfers between sites. No
transfers occur between 1:00 AM and 4:00 AM, as well as from 8:00 PM to midnight, due to the absence of solar generation and
insufficient battery reserves to produce surplus energy. However, significant energy transfers take place between 7:00 AM and
10:00 AM, at noon, and from 5:00 PM to 6:00 PM.
Table 7 presents the total optimal electricity transferred over the course of one year among the participants. These transfers are
facilitated by variations in peak electricity demand profiles across the different sites. When one participant has excess energy
during a certain period, it is shared with others experiencing higher demand. For instance, over the span of a year, the school
supplies a total of 328.5 kW of electricity to the residential building, while the fire station contributes 720 kW to the same
building, among other examples. It also presents the yearly electricity exchange among the sites. A total of 37,590.5 kW of
electricity was transferred over the year, accounting for approximately 8percent of the total electricity demand annually.
Meanwhile, consumption with the local sites amounted to approximately 420,000 kW, representing about 92% of the total
demand of energy annually. Figure 6 illustrates the contribution of each site to the microgrid's energy demand in islanded mode.
The findings suggest that inter-site electricity transfers play a significant role in addressing uncertainties among microgrid
participants.
Table 6: Hourly Electricity Transfer between Sites in islanded mode
Time (hr)
Site
Amount of Electricity transferred (kW)
From
To
1
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
2
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
3
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
4
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
5
Hospital
Restaurant
2.3
Residential Building
Restaurant
1
6
Hospital
Restaurant
2.9
Residential Building
Restaurant
0.2
7
Nil
Nil
0
8
School
Hotel
2.1
9
Residential Building
Hotel
3.1
10
School
Hotel
0.7
11
Nil
Nil
0
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12
Residential Building
Restaurant
4.6
13
Nil
Nil
0
14
Nil
Nil
0
15
Nil
Nil
0
16
Nil
Nil
0
17
Restaurant
Hotel
1.4
Restaurant
Hospital
0.1
18
School
Residential Building
7.1
Fire Station
Restaurant
5.5
Hotel
Restaurant
0.4
19
School
Residential Building
6.8
Fire Station
Restaurant
5.5
Hotel
Residential Building
1.2
Hospital
Restaurant
1
20
School
Restaurant
6.5
Hotel
Restaurant
0.3
Fire Station
Residential Building
5.4
Hospital
Residential Building
2.8
21
School
Restaurant
6.2
Hotel
Restaurant
0.8
Fire Station
Residential Building
5.1
Hospital
Residential Building
3.4
22
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
23
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
24
Hospital
Restaurant
2
Residential Building
Restaurant
1.5
Residential Building
Fire Station
0.1
Residential Building
Hotel
0.2
Table 7: The energy exchanged between sites operating in islanded mode.
Site
Annual energy transferred (kW)
School
Hotel
1021
School
Restaurant
4636
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School
Residential Building
5001
Hotel
Restaurant
548
Hotel
Residential Building
438.5
Restaurant
Hotel
511.5
Fire Station
Restaurant
4015
Fire Station
Residential building
3833
Residential Building
Fire Station
256
Residential Building
Restaurant
5945
Residential Building
Hotel
1642
Hospital
Restaurant
77045
Hospital
Residential Building
2263.5
Figure 6: MG Electricity demand Contribution
III. Conclusions
The study investigates how uncertainties are managed in the islanded operation mode of a MG. These uncertainties mainly stem
from fluctuating load demands and non-dispatchable source integration. To address this, the study employs CGT for uncertainty
modeling, involving six participating sites, each outfitted with a dispatchable energy unit and solar photovoltaic (PV) system. The
focus is on optimizing generation scheduling to maximize individual participant profits under uncertain conditions, specifically
considering variations in load demand and renewable energy generation. The CGT approach, based on the NBS, is utilized to
tackle this optimization challenge.
Energy is distributed among participants as needed throughout the day. Findings reveal that the CGT-based uncertainty
management approach yields higher profits compared to when participants operate independently. The effectiveness of CGT over
the independent strategy is validated through empirical analysis. Simulation results indicate that while total expenses are higher
under the independent approach, cooperative management through CGT leads to increased income. Additionally, cooperation
among participants led to an 8% increase in energy transfers between sites. Overall, the study demonstrates that collaborative
resource sharing and energy transfers among MG participants result in more favorable economic outcomes.
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