Citizens Collaboration to Minimize Power Costs in Smart Grids
A Game Theoretic Approach
Tarek AlSkaif
1
, Manel Guerrero Zapata
1
and Boris Bellalta
2
1
Dept. of Computer Architecture (DAC),
Universitat Politecnica de Catalunya (UPC), 08034 Barcelona, Spain
2
Dept. of Information and Communication Technologies,
Universitat Pompeu Fabra (UPF), 08018 Barcelona, Spain
Keywords:
Smart Cities, Smart Grids, Renewable Energy, Game Theory.
Abstract:
Generating the power necessary to run our future cities is one of the major concerns for scientists and policy
makers alike. The increasing global energy demands with simultaneously decreasing fossil energy sources
will drastically affect future energy prices. Strategies are already being implemented to develop solutions for
the generation and efficient usage of energy at different levels. Involving citizens in the efficient planning and
usage of power is a key. In this paper, we propose a game theory based power sharing mechanism between
end-users in smart grids. We consider that citizens can produce some amount of electric power obtained from
on-site renewable sources rather than just purchasing their whole demands from the grid. Simulation results
show that consumers can achieve considerable cost savings if they adopt the proposed scheme. It is also
noticed that the more the consumers cooperate, the higher the percentage of cost savings is.
1 INTRODUCTION
Smart grids are intelligently integrated operational
and technological systems for optimizing power gen-
eration, distribution, and consumption across a city.
They are the most dominant components of smart
cities. Unlike existing grids, where electricity flows
one-way from generators to consumers, smart grids
will ensure a two-way flow of electricity and infor-
mation between power plants and appliances, and all
points in between.
Demand-side management (DMS) (Gellings and
Chamberlin, 1987) refers to an efficient power con-
sumption planning at electric utilities and consumers.
In smart cities, power demands of consumers have
to be determined so that the allocation of power
supply and distribution can be performed optimally.
For additional power supply the power generator
may charge a higher price than the price in a peri-
odic contract due to the instantaneous need, which
is random and difficult to predict (Jirutitijaroen and
Singh, 2008). Moreover, generators and city govern-
ments will take into account the limitations on energy
sources in the city, which will also affect electricity
prices drastically. Generally, consumers have con-
flicting interests. They need to increase their power
consumption in some occasions, but at the same time
they want to reduce their monetary expenses and col-
laborate in the sustainability of their cities.
To achieve these conflicting goals, cooperation be-
tween consumers themselves is a key. Power con-
sumers (e.g., home, buildings, industry, among oth-
ers) can cooperate and share their electricity sources
in an intelligent and harmonized manner. For ex-
ample, suppose there are two neighboring consumers
who may have different power consumption sched-
ules. The first consumer may need additional power
in the morning, or in certain days while the other
is at work, or does not need it. If both consumers
share their power sources, they may allow each other
to borrow some predetermined amount of their un-
used power. This way cities will allow inhabitants to
share responsibilities while offering maximum con-
trol at the lowest level.
Game theory (Nisan et al., 2007) has been used re-
cently in a remarkable amount of research in this area
since it provides efficient analytical tools to model
interactions among entities with conflicting interests
in a distributed manner. Many games have been ap-
plied to address different challenges in smart grids
which will be summarized in Section 2. In this pa-
per, we propose a power sharing framework and use
game theory to model the interaction between ratio-
nal consumers in smart grids. Consumers may bor-
300
AlSkaif T., Guerrero Zapata M. and Bellalta B..
Citizens Collaboration to Minimize Power Costs in Smart Grids - A Game Theoretic Approach.
DOI: 10.5220/0005490103000305
In Proceedings of the 4th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS-2015), pages 300-305
ISBN: 978-989-758-105-2
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
row/lend each other some amount of power instead
of usually purchasing it from the provider at a higher
cost. The consumers cooperate and at the end of each
predetermined stage, they calculate their payoff (e.g.,
power costs) and decide to keep cooperating or not.
We prove and illustrate through simulation that coop-
eration is always preferable (i.e., rational consumers
always achieve cost savings by sharing their power).
To the best of our knowledge, this is the first work that
investigates the usability of game theory formulations
to design a local power sharing scheme between con-
sumers in smart grids.
The rest of the paper is organized as follows. Sec-
tion 2 surveys the related work. The system model is
illustrated in Section 3. The proposed game model is
described and analyzed in Section 4. Numerical re-
sults are discussed in Section 5. Finally, we conclude
the paper and give pointers for possible future direc-
tions in Section 6.
2 RELATED WORK
Many surveys can be found in the recent literature
that focus to a great extent on smart grids architec-
tures, challenges, potential applications, and commu-
nications requirements like (Niyato et al., 2011; Fang
et al., 2012; Siano, 2014). A survey of game theory
methods for smart grids is provided in (Saad et al.,
2012).
There are several studies that apply game theory
models in the smart grid context. A distributed load
management scheme based on a congestion game
is proposed in (Ibars et al., 2010). The goal is to
control the power demand at peak hours, and avoid
overloading both the generation and distribution ca-
pacity of the grid. To reduce electricity costs and
peak loads, a Real-Time Pricing (RTP)-based power
scheduling scheme for residential power usage is
proposed in (Chen et al., 2011) using a Stackel-
berg game model. In (Agarwal and Cui, 2012), a
non-cooperative load balancing game among power
demanding consumers and a retailer is formulated
with two pricing schemes: an average-cost and an
increasing-block pricing schemes. A Stackelberg
game between utility companies and end-users is pre-
sented in (Maharjan et al., 2013). The goal is to
maximize the revenue of each utility company and
the payoff of each user. In (Atzeni et al., 2013),
demand-side users are interested in minimizing their
power costs by owning some kind of distributed en-
ergy source and/or energy storage device. A non-
cooperative game is introduced to optimize their pro-
duction/storage strategy. Two models of dynamic
Figure 1: The proposed smart grid architecture.
pricing are presented in (Cui et al., 2013) to solve the
profit maximization problem of non-cooperative util-
ity companies in an oligopolistic market. In (Chen
et al., 2014), a game theory based real-time load
billing scheme is proposed to effectively convince
the selfish consumers to shift their peak-time con-
sumption and to fairly charge the consumers for their
energy consumption. A game theory based match-
making solution that harmonizes load demands with
the instantaneously available power, as well as the
amount of stored renewable energy in smart grids is
proposed in (Spata et al., 2014). A coalition game is
presented in (Luan et al., 2014) to allow consumers
not only to maximize their payment savings (i.e., by
scheduling their power consumption), but also to con-
sider the social welfare in the network as well.
3 SYSTEM MODEL
In this work we consider a generic smart grid which
consists of an electricity provider and a set of con-
sumers in a neighborhood (e.g., home, buildings,
among others) N = {n
1
, n
2
, . . . , n
N
}, as illustrated
in Fig. 1, where N = |N |. The consumers buy en-
ergy from the provider and can use renewable energy
sources as well. We assume that users’ power de-
mands may be variable both in quantity and time, and
that users can approximately predetermine their de-
mands for future time periods. Such variability could
be exploited by consumers to minimize the need of
buying additional power demands from the provider.
This is achieved by allowing consumers to cooperate
CitizensCollaborationtoMinimizePowerCostsinSmartGrids-AGameTheoreticApproach
301
through a borrow/lend power sharing scheme.
The consumers have demand management capa-
bilities. That is, each consumer is equipped with a
smart energy meter, which controls and organizes the
power consumption intelligently. Smart meters are
responsible of communications between consumers.
They exchange information about consumers’ addi-
tional demands and their available power that could
be shared with others.
A power demand of a consumer i depends on a
time period t ∈ T , where T is the set of all time
periods. At every time period t, each consumer has
three power values: i) an amount of power received
from the provider, ii) an amount of green power gen-
erated by on-site renewable energy sources, and iii) a
power demand value. From these value a consumer
can determine at every t if an additional power de-
mand is required or if there is a redundant amount of
power. After a series of time periods the consumer
i will have a power vector P
i
that indicates the addi-
tional demands, as well as the available power, at dif-
ferent time periods T . This power vector is defined as
P
i
= [P
1
i
, P
2
i
, . . . , P
T
i
], where P
i
∈ R. A negative value
of P
i
indicates a required additional demand, while a
positive one represents the available power that could
be shared with other consumers. Each time period can
represent different timing horizons such as an hour of
a day, a day in a month, a month in a year, among
others. We can easily calculate P
i
as follows:
P
i
= (P
ren,i
+ P
cont,i
) − P
dem,i
(1)
where P
ren,i
represents the power received from re-
newable sources, P
cont,i
represents the contracted
power received from the electricity company, and
P
dem,i
is the power demands of a user i. Let P
(+)
i
denote a vector contains the positive values of the
power vector P
i
(i.e., offers), and P
(−)
i
denote a vec-
tor contains the negative values of P
i
(i.e., additional
demands). We have:
P
i
= P
(−)
i
+ P
(+)
i
(2)
This power vector will determine the benefit and
costs of each consumer in the system, as we will see
in Section 4. By sharing power, it is possible that a
consumer can increase his/her power consumption at
a certain time period without the need of buying an
additional amount of power from the provider. How-
ever, consumers who borrow some amount of power
from their neighbors should also lend them an amount
of power at different schedules (i.e., when the other
consumer has some additional demands).
4 GAME FORMULATION AND
ANALYSIS
We formulate the interaction between consumers us-
ing a non-cooperative game similar to the repeated
Forwarder’s Dilemma game that has been used to ad-
dress several problems in the wireless communication
field (Felegyhazi and Hubaux, 2006). In this game
users cooperate in order to obtain mutual advantage.
The game can be defined as follows:
• Players. The set of players in this game are end-
users (i.e., power consumers) in a smart grid, N =
{n
1
, . . . , n
N
}.
• Strategies: The set of strategies, S, for each
player i:
– Cooperate (C). A consumer shares an amount
of power with another consumer in the grid. A
consumer who cooperates keeps cooperating as
long as his/her opponent cooperates.
– Defect (D). The consumer decides to stop shar-
ing power and leaves the game if the cost of ad-
ditional demands after sharing power (C
00
) are
not reduced, or if the other player defects.
• Payoff or Utility. The satisfaction of a player i in
a game is determined through the payoff function.
The benefits obtained (i.e., the indirect cost sav-
ings achieved by borrowing an amount of power),
as well as the payments (i.e., remaining power de-
mands that have to be purchased from the provider
(P
0t
i
), and the reduced amount of available power
that has been lent to an opponent (P
00t
i
)) are the
major factors that determine the payoff function
of this game at a time period t. We define the pay-
off function of a consumer i as follows:
π
i
= −C
1
P
0t
i
−C
2
P
00t
i
(3)
P
0t
i
+ P
00t
i
= P
(−),t
i
(4)
where C
1
is the cost of buying each additional
kWh from the provider (i.e., outside the contract),
and C
2
(C
2
< C
1
) is the cost of each kWh in the
fixed contract. It is worth mentioning that in case
of cooperation, the cost of additional demands is
reduced (i.e. an implicit benefit is achieved).
In this game, we assume that consumers are ra-
tional users who want to maximize their own wel-
fare by minimizing their power monetary costs. A
player’s strategy specifies the action he/she will take
at each stage for each possible strategy played by the
other player. We assume that the interaction among
players is reciprocal (i.e., consumers may be offer-
ing/demanding for a certain amount of power at dif-
ferent time periods, and need to borrow/lend some
SMARTGREENS2015-4thInternationalConferenceonSmartCitiesandGreenICTSystems
302
Table 1: The payoff matrix.
Player 2
Cooperate (C) Defect (D)
Player 1
Cooperate (C) a
1
, a
2
c
1
, b
2
Defect (D) b
1
, c
2
d
1
, d
2
amount of power from each other). Thus, we can iso-
late any pair of consumers and study the interaction
between them as a two-player game.
Definition 1. Nash equilibrium is a strategy profile,
from which no single player can individually improve
his welfare by deviating.
Formally, a strategy profile is said to be a NE if
for any player i, and for all of its strategies s
0
i
∈ S , we
have that:
u
i
(s
i
, s
−i
) ≥ u
i
(s
0
i
, s
−i
) (5)
The stage payoffs matrix is given in Table I, where
b
1
> a
1
> d
1
> c
1
(b
2
> a
2
> d
2
> c
2
) are the payoffs
of player 1 (player 2) in the different strategy profiles.
This game is known to be a symmetric nonzero-sum
game in which the strategy profile (D,D) is a strictly
dominated strategy, and a pure strategy Nash equilib-
rium (Felegyhazi and Hubaux, 2006). However, If
both consumers plays D, they have to buy their en-
tire additional power demands from the provider. If
the game is repeated, consumers can mutually mini-
mize their power costs by playing Cooperate (C) (i.e.,
by borrowing/lending some amount of power to each
other). The costs could be minimized from d
1
(d
2
)
to a
1
(a
2
) in this case. In other word, by cooperat-
ing, they can achieve an outcome that is better for
both players than mutual defecting. A player i would
play C as long as its opponent plays C. If one player
changes and chooses D, then the other will play D
forever. Switching to D could be interpreted as a pun-
ishment of the opponent. This may convince players
to cooperate instead of exploiting short advantages.
However, neither player would prefer defecting since
they know the end of the game. Cooperating in ev-
ery stage is also proved to be a Nash equilibrium in
such a repeated game. We will ensure via simulation
in Section 5 that players who have power to share can
not achieve better payoff by defecting.
It is assumed that players calculate their payoff in
each time period (e.g., weekdays). At the end of a pre-
defined number of time periods (e.g., one week), each
player measures the total payoff and compares it with
the expected payoff received when buying the entire
additional demands from the provider (i.e., when de-
fecting). Then, a decision whether to continue coop-
erating or not is made. This power sharing game is
illustrated in Fig. 2.
The reason of d
1
(d
2
) being greater than c
1
(c
2
) is
because if one consumer cooperates and the other de-
fects, the first has not only to buy the total additional
demands from the provider, but also his/her avail-
able power will decrease. As we mentioned before,
the cost of available power obtained from renewables
and/or in a regular contract is assumed to be cheaper
than the cost of additional demands (C
2
< C
1
).
Start
choose a random
pair of consumers
P
ren
, P
cont
, and P
dem
calculate P, P
(−)
, and
P
(+)
for each consumer
play Cooperate (C)
calculate the payoff
of each stage for each
player after and before
cooperation (C
00
and C
0
)
C
00
> C
0
?
cooperate
with
different
consumer?
continue cooperation
end
yes
nono
yes
Figure 2: The flow chart of the proposed power sharing
game.
5 NUMERICAL RESULTS
In our simulation, we consider a residential scenario
consisting of N consumers. First we will take a ran-
dom pair of consumers and study the interaction be-
tween them as a two-player game. Then, we will show
via simulations that the payoff of a consumer could
be increased by cooperating with more players. Each
time period t is set as one day. The interaction is held
onetime a day. Both players calculate their utility us-
ing the payoff function. After one week of interaction
(i.e., playing C), each player measures the total util-
ity, and compares it with the expected payoff received
without cooperation. Then, the consumer decides to
continue cooperation or not.
In our scheme we assume that citizens have
on-site renewable energy sources and they choose
the cheapest possible offer given by the electricity
company. Let us consider that the consumers buy
each kWh in the regular contract with a cost C
2
=
$0.09/kWh, and the cost of each additional required
kWh is C
1
= $0.20/kWh (these values are according to
CitizensCollaborationtoMinimizePowerCostsinSmartGrids-AGameTheoreticApproach
303
the payment of residential customers in the U.S (En-
ergy Information Administration, 2014)). Demands
in a regular contract can differ from one day to the
other, as demands on weekends, for example, could
be higher than in normal working days. Consumers
can share redundant power (i.e., obtained from renew-
able energy sources and/or received from the utility
company but not needed). However, if they do not
use or share this power, they can not return it to the
provider. We assume that values in power vectors are
uniformly distributed inside the range [x
1
, x
2
], where
x
1
, x
2
∈ R, negative values indicates the additional de-
mands, and positive ones represents the offers (i.e.,
the available power).
In our simulation, power demands, as well
as power offers, are generated through a uniform
pseudo-random number generator. We suppose that
consumers can share between 0 and 0.5 kWh of power
obtained from renewable sources per day. It is also
assumed that values in power vectors are between -2
and 2 kWh/day (i.e., x
1
= −2, x
2
= 2). In order to
investigate the strength of the proposed scheme, we
define three different simulation sets. In the first set,
additional power demands are set to be higher than
offers (i.e., demands are between -2 and -1 kWh/day,
and offers are between 0.5 and 1 kWh/day). In the
second one, power demands are set to be between -2
and -1, and offers are between 1 and 2. In the third
set, demands are between -1.5 and -1, but offers are
between 1.5 and 2. The proposed model is imple-
mented in MATLAB. Each value represents an av-
erage of 100 runs. Fig. 3 and Table II compare the
costs of additional power demands before (C
0
) and
after (C
00
) adopting the power sharing scheme in the
case of the 2-players game. It is observed that power
expenses are can be reduced if consumers mutually
keep playing Cooperate (C).
Due to the randomness in power consumption of
different end-users, the demands of a player may not
be satisfied by cooperating with only one player. In
addition, offers may not be totally borrowed -or even
not borrowed at all. Since obtaining the required
demand is limited by the offer availability of other
players, when the number of cooperating players in-
creases, the probability that the required demand is
satisfied by one or more players is higher. In Fig. 4
and Fig. 5, we show how a consumer can reduce
power costs if he/she cooperates with more players. It
is also observed that cost savings are achieved in the
three different simulation sets. Therefore, we believe
that cooperation and power sharing will be preferable
even for high power demanding users, which makes
the proposed scheme eligible to be a solution for the
proposed problem.
Table 2: The payoffs of players in one month for the three
different simulation sets.
Player 2
C D
Simulation set 1 Player 1 C -3.165, -3.090 -3.801, -2.804
D -2.896, -3.687 -3.532, -3.401
C D
Simulation set 2 Player 1 C -1.801, -1.863 -2.539, -1.531
D -1.459, -2.622 -2.197, -2.289
C D
Simulation set 3 Player 1 C -1.242, -1.287 -2.077, -0.911
D -0.860, -2.137 -1.694, -1.761
Simulation set 1 Simulation set 2 Simulation set 3
0
0.5
1
1.5
2
2.5
3
3.5
4
3.17
1.8
1.24
3.53
2.2
1.69
3.09
1.86
1.29
3.4
2.29
1.76
U.S Dollar/Month
After Cooperation Before Cooperation (Player 1)
After Cooperation Before Cooperation (Player 2)
Figure 3: The average monthly payoff of each player in the
power sharing game in case of playing (C,C) and (D,D).
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3 4
Average Monthly Costs of Additional Demands
Number of Players the Consumer Cooperates with
Simulation Set 1
2.962
2.687
2.568
2.366
2.127
Simulation Set 2
2.294
1.871
1.297
1.214
0.984
Simulation Set 3
1.438
0.906
0.684
0.497
0.406
Figure 4: The average monthly payoff of a consumer as a
function to the number of players he/she cooperates with.
6 CONCLUSION AND FUTURE
WORK
Future directions in smart cities are to involve people
and society in being part of the intelligence and suc-
cess of the city, helping their environment, and reduc-
ing their costs as well. In this paper we have presented
a game theory based power sharing scheme between
end-users in smart grids. We have proved via simula-
tions, and for different classes of consumers, that citi-
zens can noticeably minimize their power costs if they
SMARTGREENS2015-4thInternationalConferenceonSmartCitiesandGreenICTSystems
304
Simulation set 1 Simulation set 2 Simulation set 3
0
20
40
60
80
100
9.28
18.44
37.02
13.31
44.78
51.21
23.47
47.8
62.93
30.89
57.8
71.1
Percentage of Cost Savings (%)
1 Player 2 Players 3 Players 4 Players
Figure 5: The percentage of average cost savings of a con-
sumer when cooperating with one or more consumers.
share their power and cooperate. This scheme opens
the door to some interesting extensions. In the future,
we will propose a reputation/punishment scheme to
address two different points: i) the effect of selfish
and miss-behaving consumers, and ii) the reputation
and incentives received from the city (e.g., for being
green, for reducing the peak demands, or even for be-
ing positive in combating the climate change, among
others). The distribution of power consumption dur-
ing time periods, as well as power borrowing/lending
policies will be given more attention.
ACKNOWLEDGEMENTS
This work was partially supported by projects
TIN2013-47272-C2-2 and SGR-2014-881.
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