Improving Energy Outcomes in Dynamically Formed Micro-grid Coalitions

Abstract

The energy micro-grid, which is a local energy network that generates and consumes its own electricity, has become an effective method for the rural electrification. Typically a micro-grid is also connected to the nearby external utility grid to sell and buy power. Any failures of the utility grid usually have negative implications on the micro-grid. Whenever there is a deficit of generation, a micro-grid is not able to meet its local demand, and as a result, the community that it serves suffers from the discomfort (“pain”) of not meeting its demand. To address this problem, we present in this paper the idea of forming coalitions among micro-grids in order to reduce the pain level of the communities in the coalition. We describe how sharing among the communities in the coalition works and how membership in such communities can be changed dynamically. Based on our simulation experiments, we observe that a dynamic coalition formation approach can provide improved energy outcomes in a straightforward manner.

Full text

Dynamic Coalition Formation in Energy
Micro-grids
Muhammad Yasir, Martin Purvis, Maryam Purvis,
Bastin Tony Roy Savarimuthu
Department of Information Science
University of Otago
Dunedin, New Zealand
{muhammad.yasir, martin.purvis, maryam.purvis, tony.savarimuthu}@otago.ac.nz
Abstract. In recent years the notion of electrical energy micro-grids, in
which communities share their locally-generated power, has gained in-
creasing interest. Typically the energy generated comes from renewable
resources, which means that its availability is variable-sometimes there
may be energy surpluses and at other times energy deficits. This energy
variability can be ameliorated by trading energy with a connected main
electricity utility grid. But since main electricity grids are subject to
faults or other outages, it can be advantageous for energy micro-grids to
form coalitions and share their energy among themselves. In this work
we present our model for the dynamic formation of such micro-grid coali-
tions. Our agent-based model, which is scalable and affords autonomy
among the micro-grids participating in the coalition (agents can join and
depart from coalitions at any time), features methods to reduce overall
discomfort, so that even when all participating micro-grids in a coalition
experience deficits; they can share energy so that overall discomfort is
minimized. We demonstrate the efficacy of our model by showing em-
pirical studies conducted with real energy production and consumption
data.
Keywords: Renewable Energy, Multi-agent Systems, Coalition Formation, Micro-
grids.
1 Introduction
A micro-grid (MG) is a local energy system that provides for the generation,
storage, and consumption of electrical power within a community [8]. The func-
tion of a micro-grid is to utilize the distributed local renewable energy resources
(such as wind and sun) and to satisfy power needs locally, thus minimizing the
reliance on nearby utility grids. As a result, the power losses during transmission
are reduced. Typically, a MG is connected to the nearby utility grid, so it can
sell during surplus generation (generation is more than demand) or buy dur-
ing deficient generation (generation is less than demand) power from an energy
utility company. However, renewable energy sources are intermittent in nature
and vary from hour to hour, and even from minute to minute, depending upon

local conditions [8]. This means that at any time, a MG may have an excess or
shortage of power generation. Different energy management strategies are used
to mitigate the impact of supply variations, such as storage devices (batteries,
fly wheels, capacitors, etc.), forecasting techniques, demand load management,
and backup generators. One of the approaches to address this issue is the inter-
connection of nearby micro-grids which, by trading among the communities , can
reduce the impact of irregularity with respect to renewable energy sources [8].
An agent-based architecture for local energy distribution among micro-grids has
been presented in Yasir et al. [22], where each micro-grid represents a community
which has its own power generation based on renewable energy sources and also
has its own electric energy demand which varies hourly. Every community has
a coordinator agent which, when it has a power surplus or deficit, is responsible
for power trading with other interconnected communities or to the utility grid.
We use that architecture as a basis on top of which we build our energy trading
model.
Due to the centralized nature of existing electric generation and distribution
systems, any technical fault or natural disaster can cause a wide-area blackout.
Such power outages from the utility grid will also affect communities having
MGs (hereafter interchangeably referred to simply as “communities”). Ordinar-
ily MGs are not able to fulfill all their power needs by themselves all the time.
So when a MG does not meet its demand, then the community will suffer hard-
ship from having to cope with an insufficient energy supply. For brevity, we will
refer to this hardship as “discomfort”, and we note that the discomfort level (as
discussed further below) is a nonlinear function of the energy deficit. So if the
energy deficit is doubled, then the discomfort level is more than doubled. In or-
der to address this problem, we believe that a useful approach is the formation of
coalitions among the communities. A coalition here is considered to be a group
of MGs that can distribute their electric power among each other. By operating
in coalitions, communities can reduce their overall discomfort level, even when
there is no additional external supply of energy.
In multi-agent systems, a coalition can be defined as a group of agents who de-
cide to cooperate in order to achieve joint goals [14]. According to [19], coalition
formation includes three activities: coalition structure generation, solving the op-
timization problem of each coalition, and dividing the obtained value among the
agents. In this paper, our work is focused on the first activity of the coalition for-
mation. We introduce a cooperation mechanism for dynamic coalition formation
to reduce the overall discomfort level of the communities present in the system
over time. The goal of our mechanism is not to find the optimal solution, but
to find a satisfactory coalition match for the community in a non-deterministic
environment (where community demand and generation vary hourly without ad-
vance knowledge) by relying on recent power and generation data.
The major contributions of this paper are twofold: 1) We have developed an
algorithm for dynamic coalition formation to reduce discomfort at two levels:
individual community level and at the system level (i.e. aggregation of commu-
nities). 2) We have investigated different power sharing mechanisms within the

coalition and their impact on the discomfort level of the community and the
system.
The rest of the paper is organized as follows. Related work on coalition forma-
tion in smart grids is discussed in Section 2. In Section 3 we present the problem
scheme addressed in this work. Section 4 presents our approach to addressing
that problem. Experiments and discussion are covered in Section 5. Section 6
presents conclusions and future work.
2 Related Work
Coalition formation in smart grids has been widely studied in the multi-agent
system community (see for example [18] [16] [11] [6]), and much of this work
has centered around two objectives: 1) reducing power losses and loads over the
utility grids by forming local coalitions among MGs and customers. 2) optimizing
monetary outcomes by trading power locally among MG participants.
Work in the first of these two areas has been conducted by studying coalitions
among MGs, between MGs and consumers, or between MGs and the utility grid
[17][3][6][13]. For example Chakraborty et al. [3] seek to reduce transmission
losses by encouraging power-trading among MGs based on locality. Wei et al. [6]
employ a game-theoretic coalition formation strategy to minimize power losses.
However, although these approaches seek to reduce transmission losses, they do
not address the coalition-formation process itself, as there are no mechanisms
for how distantly located MGs can form efficient coalitions. Also these studies
assume that the main utility grid is always available, so they have not considered
circumstances when the coalitions may be cut off from such grids.
Other MG coalition studies have focused on optimizing monetary outcomes
(the 2nd objective presented above) [4][5][13]. Some work has examined coali-
tions of plug-in hydroelectric vehicles (PHEV), which can form coalitions in
order to have sufficient aggregate power to qualify for power trading markets
[4][5]. In such approaches there is a broker that represents the coalition, and the
individual PHEVs have little autonomy. Mondal et al. [13] describe a model for
MGs competing with each other to attract consumer customers. In their work
there is no cooperation between the MGs, and hence no coalitions are formed.
In contrast, the goal of our coalition formation mechanism is to form coalitions
among the MGs in such a way that the members of a coalition complement their
weather and demand patterns. As a result, the coalition becomes more resilient
even during calamitous conditions and tries to reduce the aggregate discomfort
of the members. In our model, each community also has the autonomy to join
or leave the coalition by considering its demands, generation, and discomfort.
3 Problem Model
The scenario presented in our work concerns situations where communities hav-
ing MGs must rely on their production to meet their demand. In cases of their
own energy surpluses or deficits, they cannot get energy supplements from or
sell excesses back to the grid, which is now cut off from them. When a com-
munity encounters an energy deficit, it will suffer “discomfort” because of the

power shortage. We know from previous studies [1] [2] [20] that people or com-
munities are willing to pay more than 100% of the original electric tariff if the
power outage lasted for more than 24 hours. So we have assumed that there is
a continuous polynomial function that can represent the discomfort of the com-
munity. So when a deficit increases, the discomfort level increases non-linearly.
Supposing that dmdiis the demand of the community at a given time i, where
iis any hour of the day. geniis the generation of the community at given time
i,defiis the deficit of the community at time i, then we can calculate it as:
defi=Max[dmdi−geni
dmdi
,0] ∗maxRange (1)
For simplicity we normalize the value of defibetween 0 and 10, where 0 means
no deficit (i.e. generation is more than or equal to the demand) and 10 means
extreme deficit (i.e. no generation is produced locally). In Equation 1, maxRange
represents the maximum range of normalization i.e. 10.
The function for calculating the discomfort level is presented in Equation 2.
The value of discomfort is assumed to lie between 0 and 10 (where 0 means no
discomfort and 10 means extreme discomfort). This function takes defias an
input and gives the discomfort level for time i. Mathematically this function can
be expressed as:
f(defi) = a∗defi+b∗(defi)2+c∗(defi)3(2)
where a = 0.1, b = -0.01 and c = 0.01. A plot of this function is given in Figure
1.
Fig. 1: Discomfort be-
cause of deficit
For example, at a particular hour of the day, say
at 10 am, a community generates the electric power
of 200 kWh, and its demand for that hour is 350
kWh. So, by using Equation 1, we calculate the nor-
malized deficit value to be 4.28. By inserting this
value into Equation 2, the value of discomfort for
this hour becomes 1.02. The specific values used in
this function are not important and have been cho-
sen for illustration. We do believe, however, that the
non-linear shape of this function is generally represen-
tative of how discomfort is related to power consump-
tion deficits.
Communities are assumed to be dispersed across
a varied geography such that some communities may
sometimes have surplus power generation(have more available power than their
consumer demand levels require) due to good wind or sun, while at the same
time others may face deficits and thereby suffer discomfort. The idea of coali-
tion formation among the communities is to help communities that suffer from
extreme discomfort by receiving support from those who have a much smaller
level of discomfort. A community in a coalition that offers assistance at one time
would expect to receive reciprocal assistance when it encounters energy deficit
at a later point in time. To illustrate why this would be beneficial, let us consider
a simplified example of just two communities, C1 and C2. Suppose that during
a certain hour of the day C1 has enough energy generation that exactly matches

its demand (and hence has a discomfort level of 0), while C2 has no energy gen-
eration at all (and so has a discomfort level of 10). During another hour of the
same day, both communities C1 and C2 each have a power deficit level of 5 and
so have discomfort levels of 1.5. This means that during the first hour period
the aggregate discomfort of C1 and C2 is 10, and during the second hour period
the aggregate discomfort level of the two is 3 (computed using Equation 2, also
shown in Figure 1). So over the two hour period, the aggregate discomfort level
is 13.0.
If C1 and C2 were to form a coalition for mutual assistance, then during the
first hour C1 might offer 10% of its power to C2. This would result in a discom-
fort level of 0.1 for C1 and a discomfort level of 7.48 for C2. During the other
mentioned hour of the day, C2 would reciprocate by giving 10% of its power
back to C1, meaning that C2’s power deficit will be 6 and C1’s deficit will be
4. Their corresponding discomfort values for this period would then be 2.4 for
C2 and 0.88 for C1, making their aggregate discomfort level is 7.48 + 0.1 + 2.4
+ 0.88 = 10.86. So even though C2 would give up some power when it is in a
deficit, it benefits from being in the coalition. Note that the new comfort level
is smaller than the discomfort level of 13 when no coalition is formed.
So operating within a coalition is likely to have beneficial results for all parties.
The most effective coalitions will be those for which the excesses and deficits
of community members complement each other. The worst periods for some
coalition members match up with better periods for others, who may even have
energy excesses during those periods.
Of course, energy generation conditions may change over time, and so the most
effective coalition combinations over a geographic area may thereby change, too.
It would be best if we would allow MG communities to have the autonomy
of moving to a new coalition if it so desires. So in the following we present
our examination of communities that operate in four different configurations: 1)
Standalone - there are no coalitions and no energy sharing. 2) Fixed coalitions
- there is a single, unchanging coalition arrangement. 3) Dynamic coalitions -
communities have the option of joining a different coalition at the beginning of
every day. 4) Centralized system - all communities are members of one single
coalition.
For all coalition configurations (thus not the standalone configuration), a com-
munity may share its power with others when it has relatively low discomfort.
Similarly, a community can receive power from the coalition if it has a rela-
tively high discomfort level. The details of energy sharing within coalitions are
described in the next section. The dynamic coalition arrangement allows commu-
nities to change coalitions, and this coalition formation mechanism is described
in the next section. The centralized system considers a single large coalition
that is managed centrally. This system affords optimal energy swapping, but
offers less autonomy and has the vulnerability of a single point of failure and
high transmission losses. Since MGs are located at dispersed geographical lo-
cations, there will always be transmission losses associated with energy transfer.
These transmission losses are determined by the following formula:
PLoss
i= (Q2
i∗R/U2) + θ∗Qi(3)

where: PLoss
iis the transmission power loss during one hour (i) in watts (W)
from one community to another, Qiis the total amount of power transmitted
during hour iin kWh, Ris the resistance of the distribution line between two
MGs, Uis the optimal voltage of the line, and θis the fraction of power lost in
the transformer during step up and step down process. The power lost during
transmission is taken into account by the receiving MG.
4 System Model
In this section, we present the dynamic coalition formation mechanism. As with
any coalition formation, the goal is to reduce the overall discomfort level of com-
munities present in the coalition. The value of a coalition (v(cj)) is represented
by:
v(cj) =
s
X
i=1
discomfort of communityi(4)
where jis the coalition number, sis the number of communities present in the
coalition j. The goal of coalition formation is to minimize the value of v(cj).
At the start of every day, two processes run in a coalition. In the first pro-
cess, communities in the coalition calculate the amount they can give and take
to/from the coalition for the next 24 hours by using their predicted demand
and forecasted generation categorized into the best and worst hours. We assume
that the forecasted wind pattern for the next 24 hours is up to 93% accurate
[9]. Typically a community has twelve best and worst hours in a day. However,
sometimes the best and worst hours may not be equal in number. Best hours are
the hours in which a community has no discomfort or less discomfort. During
those hours, the community can help other members of the coalition by sharing
some proportion of its generation. Worst hours are the hours in which a commu-
nity has less generation or no generation and it suffers from extreme discomfort.
In other words, the community suffers more discomfort and seeks some power
from the other members of the coalition to get some relief from its discomfort.
Hence as a result, its overall discomfort of the day will be reduced.
In the second process, a community is selected to be the coordinator agent
for the coalition. In this work, the coordinator agent is selected by lexicographic
order. The responsibility of the coordinator agent is to broadcast an invitation
message to other communities outside its coalition, identify the potential mem-
bers of the coalition for joining the coalition, and manage the power-sharing
distribution within the coalition.
There are two main phases of our coalition mechanism. The operational phase
deals with the power distribution within the coalition, and the recruitment phase
deals with recruiting other communities to join the coalition. First we discuss
the operational phase. At the beginning of every hour, the coordinator agent
calculates the total amount of electric power from coalition members who commit
to give to the coalition and distributes the amount proportionally among the
members of the coalition who are expecting the power from the coalition for the
particular hour. We assume that communities do not cheat and reveal correct
information about their give and take commitment.
A community can make a commitment about the amount of power to be

given or taken from the coalition by using two approaches: dynamic offer and
fixed offer. In a dynamic offer a community curtails a calculated at-the-time
percentage of its generation from its 12 best hours and gives to its coalition. In
return, the community expects the same amount back from the coalition during
its 12 worst hours. However, in fixed offer, a community has a certain fixed value
(in percentage) to curtail its generation from its best hours and then expect the
same amount to return back during its worst hours.
Algorithm 1: Algorithms for fixed and dynamic offer of a community
input : Generation & demand of next 24 hours
output: Give & take amount for exisitng coalition
1Calculate best and worst hours slot
2Total discomfort in best hours = Pdiscomf ort in best hour discomfort
3Total discomfort in worst hours = Pdiscomf ort in worst hour discomfort
4Total actual discomfort = Total discomfort in best hours +
Total discomfort in worst hours
5Algorithm for fixed offer
6set certain value of α// value in percentage of generation
curtailment
7Total new discomfort = Compatibility Check(Best & worst hours, α)
8if Total new discomfort <Total actual discomfort then
9Make Offer(α)// amount to be given and taken from the
coalition
10 else
11 No offer
12 end
13 Algorithm for dynamic offer
14 set i = 1% // cutail of generation in percentage
15 while i≤100 do
16 Total new discomfort = Compatibility Check(Best & worst hours,i)
17 if Total new discomfort <Total actual discomfort then
18 Store order-pair (i, Total new discomfort) into discomfort-track-list
19 else
20 break
21 end
22 increment in i by 1
23 end
24 if discomfort-track-list then
25 Sort discomfort-track-list in ascending order w.r.t Total new discomfort
26 Pick the first order pair from discomfort-track-list & set the value of α
27 Make Offer(α)// amount to be given and taken from the
coalition
28 else
29 No offer
30 end

Algorithm 1 gives the pseudo-code of the fixed and dynamic offer of a commu-
nity to a coalition. At the beginning of each day, all communities in the system
calculate their best and worst hours of the next 24 hours by using predicted
demand and forecasted wind and sun information (line 1 of Algorithm 1). After
identifying the best and the worst hours of the next 24 hours, a community ag-
gregates the discomfort of the best and worst hours (line 4). For a fixed offer,
the community selects the fixed arbitrary value of percentage for curtailing its
generation from best hours (line 6 of Algorithm 1). If the selected value helps
in reducing the aggregate discomfort of the day, then the community makes the
offer otherwise the community does not participate in the coalition(lines 7-12
of Algorithm 1). However, for a dynamic offer (lines 13 to 30 of Algorithm 1),
the community looks at all the possibilities of curtailing its generation (from 1%
to 100%) from the best hours and observes its potential impact on the worst
hours (lines 14 to 23 of Algorithm 1). After assessing all the possibilities, the
community picks the best possible proportion (in percentage) for curtailing its
generation among all the possibilities (line 26) and then calculates the amount
of electricity to be given and taken to/from the coalition for the next 24 hours
(line 27 of Algorithm 1).
We now discuss, the recruitment phase. From a recruitment perspective, we
assume that the coalition is always looking for new communities to join the
coalition in order to reduce a coalition’s discomfort level. The coordinator agent
collects the best and worst hours information from all the members of the coali-
tion and categorizes the hours of the day into best hours and worst hours of the
coalition. For recruiting the new community in the coalition, the coalition follows
the following steps: at the start of every day, the coordinator agent of each coali-
tion calculates the average discomfort of each hour of the next day by collecting
best and worst hours information from the members of the coalition. The twelve
hours with the lowest discomfort are ranked as the “best hours”, while the re-
maining twelve hours are marked as the “worst hours”. The “best hours” imply
hours of the day during which the coalition can commit to sharing some of its
power with newcomer communities. The “worst hours” signify hours when the
coalition seeks to gain power assistance from a potential newcomer community.
After calculating best and worst hour information, the coordinator agent broad-
casts the invitation message to join its coalition along with the information of its
average discomfort for the worst and best hours. A new community must remain
with the coalition it joins for at least one day. In addition to what each coalition
coordinator agent does, all communities also calculate their own discomfort level
at the end of each day (see Algorithm 2). If the existing discomfort level of the
community is less than its rolling average discomfort, then the community is not
interested in leaving its present coalition and will reject all invitation messages
(line 10 of Algorithm 2). Otherwise, the community analyzes which coalition’s
invitation suits it best. The community identifies the matched and non-matched
hours. Matched hours are those hours in which the invitation-receiving commu-
nity’s best and worst hours match the inviting coalition’s worst and best hours.
While the remaining hours of the invitation-receiving community are declared as
non-matched hours (line 2 of Algorithm 2). An invitation-receiving community

can only make offers to the inviting coalition if the matched hours are present
(line 3 of Algorithm 2).
The offer mentions how much electric power it can expect from coalition during
the community’s worst hours and how much power a community can give to the
coalition during the coalition’s worst hours. The offer could be either a dynamic
offer or a fixed offer. The community then makes offer for matched (by using
Algorithm 1) and non-matched hours (by using Algorithm 3). For non-matched
hours offer, a community calculates its average discomfort level over the next 24
hours (line 1 of Algorithm 3). If the community employs a dynamic offer mecha-
nism, then the community offers a certain percentage of its generation (line 5 of
Algorithm 3) to the coalition if the non-matched hour’s discomfort is lower than
the average discomfort of the next 24 hours. For example, if average discomfort
of the day is 5 and the discomfort of the non-matched hour 4 is 3, then the value
of ψis 20% ((5-3)/10). However, if the non-matched hour’s discomfort is higher
than the average discomfort of the next day, then community expects certain
percentage of its deficit from the coalition (line 7 of Algorithm 3). In contrast
to dynamic offers, for a fixed offer of non-matched hours, a community always
uses fixed proportions for making offers for give and take to/from the coalition.
The offer made in non-matched hours either by using the dynamic or fixed offer
mechanism is always less than the offer made in matched hours. Once a coali-
tion receives an offer from a community, it calculates how much the coalition’s
average discomfort level would be decreased by inducting this community. This
calculation is done by adding and subtracting the power (the amount offered by
the prospective newcomer community) from the next day’s data of the coalition
and recalculating what the discomfort level would be. As part of this calcula-
tion, the coalition also takes into consideration the location of the prospective
new member by calculating the expected transmission losses associated with this
community during power trading. These losses result in deficits that affect the
coalition’s discomfort level. The coalition then ranks the offers in descending
order in terms of how much they would reduce its discomfort level, and then
it selects the top community from the list and sends its willingness to recruit
the community. After receiving the willingness signal from the coalition, the
prospective community also performs the same calculations done by the coali-
tion and selects the best coalition that helps in reducing its own discomfort level.
The community then sends a joining message to that coalition, while sending a
refusal message to any other coalition.
Once the community joins the coalition, the community and coalition must
fulfill their commitments. We assume that there is no cheating in fulfilling these
commitments. However, sometimes the community or the coalition is unable to
comply with their commitments because they were not able to generate the re-
quired power due to the intermittent nature of renewable sources such as wind
and sun.
5 Simulation Results
In our experiments, we investigated two questions: 1) What would be the impact
on discomfort level of a community present in a coalition as compared to a

Algorithm 2: A community’s analysis of invitation
1if current’s day discomfort value ≥rolling average discomfort + βvalue then
// where βis the threshold value;
2find matched and non-matched hours between community and invited
coalition;
3if matched hours are found then
4if community’s best hours = coalition’s worst hour & Vice versa then
// matched hours;
5Make offer ;
6Send offer to coalition;
7else
8Make offer for non-matched hours // Algorithm 3
9else
10 Reject coalition’s invitation
11 else
12 Reject coalition’s invitation
Algorithm 3: Algorithm for making offers during non-matched hours by
a community
1Calculate the average discomfort of the day;
2if offer mechanism is dynamic then
3foreach non-matched hours do
4if average discomfort of the day ≥discomfort of non-matched hour then
5ψ= (average discomfort of the day) - (discomfort of non-matched
hour);
// ψis the proportion of generation a community is
willing to give to coalition for the hour
6else
7η= (discomfort of the non-matched hour) - (average discomfort of
the day);
// ηis the proportion of its deficit a community is
expecting to take from coalition
8else
// offer mechanism is fixed;
9αis the certain fixed value (in percentage);
10 if average discomfort of the day ≥discomfort of non-matched hour then
11 community can give αof its generation to coalition
12 else
13 community expects αof its deficit from the coalition
community in no coalition? 2) What is the impact of different power-sharing
mechanisms on the discomfort level (of a community and the system) in dynamic
coalition formation.

5.1 Experimental Setup
Our experiments involved forty communities (C1 to C40). Each community has
an average hourly consumption of 1150 kWh and a wind turbine or array of
solar photovoltaic (PV) of 2000 kW generation capacity. However, the power
generation values for an individual community will vary, due to the dispersed
geography involving different wind speeds and solar radiations.
It could be possible that a community having renewable energy generation
(either wind or solar PV) always or most of the time has surplus. Similarly, it
is possible that a community has no surplus or most of the time it faces deficit
of generation. For our model, we have chosen a general configuration such that
most of the communities are in deficit most of the time. However, our mechanism
is also applicable to situations where communities have a surplus most of the
time. In our system, 13 communities have arrays of solar PV and the rest of
them have wind turbines. The power generated by a wind turbine is calculated
by using the formula [12]:
P= 1/2ρAV 3Cp(5)
where Pis the power in watts (W), ρis the air density in kilograms per cubic
meter (kg/m3), Ais the swept rotor area in square meters (m2), Vis the wind
speed in meters per second (m/s), and Cpis the power co-efficient.
We obtained the wind speed (V) data of forty different New Zealand areas
from the National Institute of Water and Atmospheric (NIWA) database [21]. We
also obtained hourly power consumption data of forty different places from the
Property Services office of the University of Otago [15]. The assumptions made
while running our experiments are as follows. All communities are situated at
sea level, so the air density value of is 1.23 kg/m3. The blade length of the wind
turbines is 45 meters (m). The cut-in and cut-out wind speeds of the turbines
are 3 and 25 meters per second (m/s), respectively. Theoretically the maximum
value of Cp is 59%, which is known as the Betz limit [12]. However, in practice
the value of Cp is in between 25%-45% [12], depending upon the height and
size of the turbine. The value of the power co-efficient (Cp) is 0.4 (i.e. 40%).
Similarly, the power generated by a solar PV is calculated by using the formula
[7]: E=A∗r∗H∗P R (6)
where Eis the power in kilowatt-hour (KWh), Ais the total solar panel area
(m2), ris the yield of solar panel (%). The value of rfor PV module of 4kWp
is 15%, His the solar radiation in kilo-Watt per meter square (kW/m2), PR
is performance ratio, which ranges between 0.5 and 0.9, with a default value of
0.75. We obtained the solar radiation (H) data of 13 different New Zealand areas
from the National Renewable Energy Laboratory [10].
The simulation runs for 4 years (i.e. 48 months). At the start of the simulation,
there are four coalitions present in the environment. Communities are initially
assigned to each coalition on the basis of proximity, i.e. communities located in
the same region of the grid belong to one coalition (see Figure 2). In Figure
2, house symbols represent a community. The arrow points to the centroid of
the coalition. The communities within a coalition can transfer power among

each other by using nearest point in the transmission line. The transmission
lines are the black horizontal and vertical lines intersecting at the center of the
figure. Transmission loss is calculated by using Equation 3. The initial value of
R (resistance in Equation 3 ) in our experimental setup is 0.2 ohms per km. The
value of θis 0.02. The value of U is 33 kV. We setup the distribution network
within a square region of 500 km x 500 km.
Fig. 3: C1: Standalone vs. Coalition Fig. 4: C2: Standalone vs. Coalition
5.2 Results
Fig. 2: Proximity based coalition
All communities in the environment
used our dynamic coalition formation
mechanism. As stated above, we ex-
amined two areas: a) the effect of
coalition sharing and b) the effect of
dynamic versus fixed offer.
Coalition vs no coalition
In order to measure the effects of
our dynamic coalition mechanism, we
conducted comparative experiments
by using three other approaches: stan-
dalone, fixed coalition, and the cen-
tralized system (discussed in Section
3). We show the effectiveness of our
coalition mechanism at two levels: at
the individual community level and at
the system level (the aggregate result
of all communities). Due to space con-
straints, we are not able to show the
results of all the communities present in the environment. So at the community
level, we have chosen two representative communities (C1 and C2). The total

power generation for C1 during the simulated four years period was more than
its demand, while the overall generation of C2 was less than its demand during
that period.
Fig. 5: System level: Standalone vs.
Coalition
Figures 3 and 4 show the discom-
fort level of community C1 and C2
over the simulated time period of four
years respectively. The results show
that the community employing the
standalone (no coalition) approach
suffers much more discomfort, as no
other community is able to help the
standalone community. The commu-
nity staying in a fixed coalition does
better compared to the community in
standalone mode, because, it gets help
from other members of the coalition
when it has severe discomfort levels.
However, when the community em-
ploys our dynamic coalition approach,
it experiences lower discomfort levels
compared to using the alternative ap-
proaches. This is because, communi-
ties present in a coalition that com-
plement each other for one day may not complement on the next day, as the
wind or solar pattern changes from minute to minute and the prediction of wind
pattern for more than 24 hours is not very accurate [9]. So our approach lets
the communities leave their original coalition (created on the basis of proximity)
and join the coalition that has a contrasting wind pattern or solar radiation.
Similarly, Figure 4 illustrates the discomfort level of community C2 for the sim-
ulated time period of four years. Again, when the community operates under the
dynamic coalition formation suffers less discomfort compared to the community
configurations using the fixed coalition and the standalone approach. Figure 5
shows the average discomfort of all 40 communities (i.e. the system level result)
in three configurations. It highlights that the dynamic coalition is the best in
reducing the discomfort of all the communities. The results (Figure 3-5) clearly
show that the dynamic coalition formation mechanism not only helps in reduc-
ing the discomfort in the individual community, but it is also helpful in reducing
discomfort at the societal level. By employing our dynamic coalition formation
approach, communities find the coalitions that complement the best and worst
hours of each other. As a result, there is an overall reduction in the discomfort
at the system level.
Dynamic coalition: Fixed vs dynamic offers
In Section 4, we described two methods (fixed and dynamic) of making offering
in the dynamic coalition formation mechanism. We compared these two meth-
ods with the centralized system at the community and at the system level. In

Fig. 6: Comparison of C1’s discomfort in
different approaches
Fig. 7: Comparison of C2’s discomfort in
different approaches
the fixed offer mechanism, we ran the experiments by varying the value of α
(Algorithm 1) i.e. 10%, 40% , and 80%.
Figure 6 depicts the result when C1 employed the two approaches for dynamic
coalition formation. The result shows that the fixed offer approach does not give
the optimal reduction in discomfort unless the community knows the best value
of α. However, in dynamic offers, C1 does not need to know the value of α
which gives the least possible discomfort. In our experiments, after trial and
error we found that the optimal value of αin fixed offers is 40%. Any increase
or decrease in the optimal value of α(i.e. 10% or 80%) results in the increase
of discomfort level. 40% is the optimal value of αfor the configuration we had
in our experiments. However, this is likely to change based on the underlying
data (e.g. sun and wind), whereas dynamic offers always finds the best possible
value to offer, which results in reducing its discomfort without any trial and error
method on any data set. We also found that the dynamic coalition formation
by using dynamic offers is also significantly closer to the centralized system
which is considered to be the optimally arranged power sharing mechanism.
However, because of the centralized system’s single-point-of-failure nature, it is
not resilient. Similarly, Figure 7 shows the result of C2, where a similar trend of
result was observed. The dynamic offer mechanism gives the highest reduction
in discomfort and is closer to the centralized system approach.
At the system level, it was also evident that the dynamic coalition with dy-
namic offers performs better than others. We ran our dynamic coalition forma-
tion mechanism using fixed and dynamic offers on low-loss transmission systems.
Results are shown in Figure 8. We found the dynamic coalition formation mech-
anism using dynamic offer performs better and closer to the centralized system.
Hence by employing our dynamic coalition formation using dynamic offer, not

only was the discomfort reduced significantly, but it also overcomes the issue of
single-point-of-failure present in the centralized system. We also conducted the
same set of experiments on high transmission loss systems and found the same
trends also exist.
6 Conclusion & Future work
Fig. 8: System’s discomfort level in low
losses configuration
In this paper, we have presented our
dynamic coalition-formation mecha-
nism for micro-grids when they oper-
ate in a situation where there is no
available support from a main util-
ity grid. The goal of the coalition for-
mation is to reduce the discomfort of
communities because of deficit power
generation.
Experiments show that our mech-
anism of dynamic coalition forma-
tion using dynamic offers is effective
in reducing discomfort level (i.e. dis-
comfort) of a communities. We have
also shown that, compared to the
standalone, fixed coalition, and dy-
namic coalition formation using fixed
offer approaches, the dynamic coali-
tion with dynamic offers outperforms
and reduces the discomfort level at community and at the system level by con-
siderable amounts. We believe the mechanism presented in this paper can be
used by remote (rural) communities to reduce their discomfort by improving the
availability of power required through local power sharing, while avoiding the
reliance of the main utility grid.
For future work, we intend to introduce a split and merge algorithm for the
coalition, so that coalitions could merge with other coalitions in order to more
optimally reduce transmission losses.
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