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Game-Theoretical Energy Management
for Residential User and Micro Grid
for Optimum Sizing of Photo Voltaic
Battery Systems and Energy Prices
Aqdas Naz1, Nadeem Javaid1(B
), Abdul Basit Majeed Khan2,
Muhammad Mudassar Iqbal3, Muhammad Aqeel ur Rehman Hashmi4,
and Raheel Ahmad Abbasi5
1COMSATS University, Islamabad 44000, Pakistan
nadeemjavaidqau@gmail.com
2Abasyn University Islamabad Campus, Islamabad 44000, Pakistan
3Riphah International University, Islamabad 44000, Pakistan
4University of Engineering and Technology, Taxila 47050, Pakistan
5Sardar Bahadur Khan Women University, Quetta 87300, Pakistan
http://www.njavaid.com
Abstract. There is emerging trend in power system, i.e., energy inter-
net that provides energy production, transmission, storage and utiliza-
tion. Which is used to manage and control energy centrally by using
information and communication technologies. In this paper, coordinated
management of renewable and traditional energy is focused. In proposed
work, storage system is embedded with renewable resources in microgrid,
so that after satisfying users energy requirement, surplus energy can be
stored in battery. Energy management is performed with storage capac-
ity includes cost of renewable resources, depreciation cost of battery and
bidirectional energy transmission. User and microgrid are two players
that are involved in non cooperative game theory. In order to maximize
the payoff of user as well as microgrid, the two stage non cooperative
game theoretic method optimizes battery capacity and prices. Which
are charged by micro grid from user and optimize user energy consump-
tion. The distributed algorithm is proposed to explain nash equilibrium
which ensures Pareto optimality in terms of increasing pay off of both
stakeholder. Furthermore, forecasting algorithm back propagation (BP),
Support Vector Machine (SVM) and Stacked Auto Encoder (SAE) are
used for forecasting historical data related to solar power generation.
Predicted data is, thus used by microgrid in defining energy prices and
battery storage capacity.
Keywords: Game theory ·Renewable energy resources ·Microgrid ·
User ·Nash equilibrium
c
Springer Nature Switzerland AG 2019
L. Barolli et al. (Eds.): WAINA 2019, AISC 927, pp. 1097–1106, 2019.
https://doi.org/10.1007/978-3-030-15035-8_106
1098 A. Naz et al.
1 Introduction
In order to achieve quality, traditional grid is transforming into smart grid.
Smart grid is considered as cyber physical system that contain different phys-
ical system such as energy production, energy distribution and energy usage.
Smart grid also contain several advanced techniques such as advanced metering
infrastructure (AMI), energy management system as well as electrical vehicle
[1]. Smart grid is different from traditional grid in terms of functionality and
it works centrally in bidirectional manner. Customer actively involves in distri-
bution of energy by announcing total energy requirement. Large electrical grid
is divided into small scale grid in smaller geographical areas [2,3,19,20]. Small
scale grids are also known as microgrid. Microgrid generates energy with the
help of renewable resources such as wind energy, hydro power and solar power.
That is the reason that microgrid total amount of energy is not defined as it
depends on the weather and climatic conditions. There can be the case when
microgrid does not produce sufficient energy and it purchase energy from utility
in order to full fill requirement of the users [4]. At the same time, if microgrid
is having surplus energy it will sale it to utility. In return, utility will award it
with certain subsidy. In real world energy management system contain different
kind of errors include, implementation, estimation errors. Such kind of errors
make system completely meaningless. Therefore, it is very important to bring
forecasting of energy generation in account along with its expected error. It helps
in performing contingency planning for better energy management [5,21,22]. In
our proposed work, game theoretic energy management system is proposed. It
contains two level players that includes user and micro grid. Back Propagation
(BP), Support Vector Machine (SVM) and Stacked Auto Encoder (SAE) fore-
casting techniques are used to forecast future solar power generation.
2 Contribution
This paper has following contribution: 1. It considers two stage stackelberg game
in which microgrid is leader and user is follower. Besides, MG may purchase
electricity from utility. If load demand of user exceeds its generation capacity as
shown in Figs. 1and 2. Two scenarios are considered in which energy manage-
ment with and without GT are discussed. In addition energy storage mechanism
is employed to reduce energy cost of MG. Game theory optimize payoff of both
player by the help of predicted energy generated by Photo voltaic (PV) cell.
3 Proposed System Model
Here, proposed system model has been discussed with two stage stackelberg
game theory in smart grid. Single microgrid with multiple residential user N=
{1,2, ....n}. Microgrid is regarded as supplier of power to user to ensure stability
of user [14–16]. Microgrid is equipped with smart meter to make residential users
schedule, consumption of energy. It also contains PV storage system. PV offers
Game-Theoretical Energy Management for Residential User 1099
power for residential user and charging the battery. It also send surplus energy
to the utility. After receiving utility price policy from information network, user
sends demand to micro grid and eventually that demand will be sent to utility.
In proposed system model. User in this scenario have shiftable and unshiftable
loads [17,18]. One day, as a period is taken for scheduling energy consumption
at user end. Kdenotes each time slots in a period. Here, the utility accepts
electricity demand from user for each time slots and real time price are sent to
user against each time slot. {Pk=pk
1, ...pk
j, ....pk
m}. Microgrid set its prices to
maximize the pay off as per demand of each user in real time.
3.1 User Energy Consumption and Cost Model
Let us assume N number of user is taken in the scenario with a set of N=
{1,2, ....N }. Complete day is split into Ktime slots. ln(k) represent total energy
consumption of user includes shiftable and unshiftable load. Daily energy usage
of load of user is represented by equation in [6] representing scheduling of on
peak hours to off peak hours.
3.2 Microgrid Cost Model
For trading purpose, microgrid and user exchange messages between each other.
Energy parameters between user and microgrid are agreed by both stack holders.
Amount of energy required by each user is xk
nand the price that is being charged
by microgrid mis pk
m. Total demand of electricity from user must be less or equal
than electricity generated by microgrid as shown under:
Xk
n≤Gk
m∀k∈K(1)
However, energy xmdemanded by user from microgrid mmust satisfy following
constraint:
en≤
K
k=1
xk
n,and
K
k=1
Gk
m+Δm≥
N
n=1
K
k=1
xk
m(2)
where, Δmshows amount of energy that is required by utility in case production
of renewable resources is not enough for usage of Nuser. Furthermore, price per
unit energy pk
mis finalized by microgrid. Here, Pk
mis price that is charged by
microgrid, therefore, energy that is required by user must fulfill constraint Eqs. 1
and 2.
3.2.1 Solar Power Generation
Mostly, hybrid system where generation plant and renewable resources are source
of energy in order to fulfill energy demand of user are difficult to manage. Specif-
ically if solar panels are placed with each user and consequently surplus energy
is sold back to utility. Centralized mechanism needs to be devised to store
energy and distribute among user and utility on requirement and generation
basis [23,24]. Assumption in proposed model is that generation of solar power
1100 A. Naz et al.
is cheaper than the power that is supplied by utility company. Priorities for
providing solar power at any working time in day light to residential users N
by microgrid is: Foremost priority is to be given to fulfill demand of Nusers
and to charge the batteries, at second priority, surplus energy is to be sold to
utility for generating revenue by trading. For microgrid, lets assume solar power
generation is en(k)≥0 in time slot k. Solar power generation provides energy
en(k)−el
n(k)−eb
n(k) = 0 means microgrid does not have surplus energy to
be sold to utility. In case en(k)−el
n(k)−eb
n(k)≥0 means microgrid is having
surplus power that is generated by solar panel is to be sold. Profit of microgrid
that it generates while selling surplus power to utility is:
Un=
K
k=1
λsen(k)−el
n(k)−eb
n(k)) (3)
CSP
n=am(ˆ
L+Δ)+bmg(ˆ
L+Δ)2+cm+F|Δ|(4)
3.2.2 Solar Power Storage System
Solar power requires storage system in order to store surplus energy after fulfill-
ing household load. Storage is considered as indispensable need for solar power
generation. Currently variety of batteries are available in markets [33]. Assump-
tion is that microgrid requires battery capacity y mWh and that may varies
within certain limits:
yε[yl,y
u] (5)
where ylrepresent lower limits of battery capacity whereas yurepresent upper
limits of battery. Daily depreciation cost function is represented as follows:
Cbat
m(y)=λbaty(6)
Solar Generated
Power
Solar Power
Generation
forcasting using
historical data
Residential
Users
Solar Panel for
Electricity
Generation
Battery Storage for
Solar generated
Power
D(x,k)
P(K)
Microgrid
Fig. 1. System model
Game-Theoretical Energy Management for Residential User 1101
where Cbat
m(y) cost of battery depreciation is represented in form of cents/kWh
and it is also correlated with the material and type of the battery. Battery
depreciation cost is linear increasing function according to the total capacity y
of battery. Apart of battery capacity parameter, there are certain parameters
that are required to be taken under consideration, i.e., charging and discharging
efficiency of battery. Let assume, 0 <η
ch <1 and 0 <η
disch <1 shows bat-
tery charging and discharging efficiency. s=[s1, ..., sk, ..., sK] represents state of
battery for whole day. Here, battery capacity is also defined therefore inequality
constraint regarding state of battery and capacity of battery is as shown:
0≤sk≤z(7)
hk
ch and hk
disch are binary variable that represents pattern of battery charging
and discharging in each time slot. Battery can either be charged or discharged
at the same time that is shown as:
hk
ch +hk
disch ≤1 (8)
Power state of battery at any time slot kis calculated as follows:
sk+1 =sk+ηcheb
k−1
ηdisch
˙
bl
k(9)
eb
h≤kb
k−1
ηdisch
˙
bl
k(10)
eb
n(k) represents energy that is required to charge the battery from solar gener-
ated power. Whereas, bl
n(k) represents total energy to discharge the battery to
fulfill requires to satisfy user requirement. Total energy that is require to charge
and discharge the battery must be under lower and upper limits of battery, thus,
value of eb(k)andbl
n(k) must satisfy Eqs. 11 and 12
eb
k≤hk
dischBch (11)
bl
n(k)≤hk
dischBdisch (12)
On the basis energy balance
lk=xk+el
k+bl
k(13)
Equation 13 shows that energy consumption of microgrid that is used by user,
charging the battery and surplus energy is transmitted to utility to generate
payoff.
Ck
m=xk
m+Cbat
m(y)+CSP
m+Δm(14)
Ck
mshows total cost of microgrid at time slot k.
1102 A. Naz et al.
3.3 Game Formulation and Analysis
In order to study, communication between microgrid and user, Multi leader and
single follower Stackelberg game has been purposed [5]. Primarily, it is multi
player game, where users being leader decides amount of energy to be demanded
from microgrid based on price of microgrid Pk
m. Whereas, microgrid as a fol-
lower decides prices and storage capacity of battery. In this paper, game theory
presented in [6] is extended.
3.4 Equilibrium Analysis
In multi level non cooperative game, the existence of pure equilibrium solution
is not promised always. Thus, it is required to determine the existence of NE
in proposed algorithm. As a matter of fact, variational equality is proven to
be more socially stable as compared to other NE as studied by [7]. Variational
equality is determine for all customers as discussed in [Demand].
Proposition 1: In case of user nN, every day cost function Unis persistently
differentiable in xnfor price pk
mand electricity consumption by user xn. There-
fore, strategy space of utility function of user Uis a non empty convex compact
convex subset of a Euclidean space.
Proof: Owing to persistent characteristics of the daily cost function
Fn(xn,x
−n,p
k). It is continuously differentiable in xn. The Hessian of
Fn(xn,x
−n,p
k) is calculated positive semi definite. Consequently, cost func-
tion of user nis convex in xn. Proposition 1depicts that daily cost function
Fn(xn,x
−n,p
k) is continuously differentiable. It is also convex in xn. Owing the
fact, energy cost Cn(xn,x
−n) has continuous quadratic form in context of xn.
Proposition 1is prerequisite of Proposition 2.
Proposition 2: For ∀nNand time slot kK, the NE of the non cooperative
game exist and it is also unique.
Proof: As per proof mentioned in [storage game theory, Th. 6], owing to the fact
that cost function Fn(xn,x
−n,p
k)isconvexinxn, the NE of the non cooperative
game exist and it is also unique.
As shown in Fig. 1, system model is shown in detail. Where micro grid
announces its prices on the basis of solar power generation forecasting. In this
paper, forecasting is performed using BP, SVM and SAE in order to deter-
mine forecasting error. It helps in efficiently forecasting energy generation. Thus
energy management will be more affective.
4 Simulation and Discussion
In proposed scenario, one year duration solar power data is taken form the NREL
site. In this section, game theoretic energy management effectiveness is verified.
In order to perform analysis on accuracy of solar power prediction. Figure 2
Game-Theoretical Energy Management for Residential User 1103
shows solar power generation in single day. It clearly shows the rise and fall
of the generation as per the solar radiations available in different time slots of
the day. Figure 3shows the trend of user energy consumption which helps in
deciding the peak hours, off peak hours and mid peak hours respectively. N
users are considered in the scenario which contain both shift able and fixed load
and power consumption of users are shown in Fig.3. Each day is divided into
24 h time slots k. Consumption of electricity usage at each slot varies depending
upon peak hours and off peak hours.
An analytical scenario is presented to verify the performance and effectiveness
of proposed game theory among user and micro grid. Where Nuser increases
its pay off by adjusting energy consumption. Besides, micro grid optimizes its
payoff by optimally finalizing energy rates pk
mand size of the battery y.
In this paper, TOU pricing scheme is adapted and single day is divided in 24
time slots k. Further, entire day is divided into 3 chunks. Single day is divided
into chunks on the basis of energy consumption, i.e., peak hours, off peak hours
and mid peak hours. Each chunk contain different pricing parameters.
DSM is not discussed in this paper on individual basis. Energy consumption
by user Nis catered collectively. However, energy management at micro grid
is discussed in detail that includes energy prices pk
mand size of the battery
y. Micro grid is equipped with renewable resources, i.e., photo voltaic cells. In
current scenario, it is assumed that micro grid consist of photo voltaic power
cell in terms of renewable resources.
Fig. 2. Solar power generation in 24 h
Fig. 3. Consumption of users in 24 h
1104 A. Naz et al.
Figure 4shows energy distribution by micro grid in Ktime slots without
game optimization. Energy is retrieved from utility in hours when solar energy
is not available for generation of solar energy whereas rest of hours, energy is
optimally used using solar power generation and battery. Figure 5shows energy
distribution by microgrid with game optimization.
Fig. 4. PV energy distribution without game
Fig. 5. PV energy distribution with game
Fig. 6. MAPE of different forecasting model with PV forecasting
Microgrid can take more benefit solar power when there are more day light
hours. It also affect battery capacity optimization once microgrid ensures energy
supply to user. However, day light timings and intensity will not be affect the pro-
posed game theoretic energy management. Microgrid employs 2 MW solar power
generation. Energy output by solar cells per day is shown in Fig.2. Solar power is
Game-Theoretical Energy Management for Residential User 1105
generated during 0600 to 1700 h. User cost relies only on discharging time and it
counts minimal except when battery discharges at peak demand hours. It shows
battery discharging time is from 17:00 to 22:00 h. Charging and discharging of
battery, in both cases in single hour is 1.5 kWh [9], whereas efficiency of battery
charging and discharging is taken as 7.2 cents/kWh [15]. Figure 6shows mape
values of 3 different forecasting algorithms including BP, SVM, SAE. Historical
data has been used for forecasting solar power that is called step 1, after retrieval
of foretasted data, it is added in historic data and used for prediction that is
termed as step 2 and so on. It is clearly shown in Fig. 6that mape increases
after each iteration. Simulation shows mape acquired as a result of forecasting
techniques implementation. SAE has performed best among all, therefore error
of SAE is taken as prediction error in objective function of microgrid. There
exist two scenario, that prediction error can be positive, i.e., Δ>0 and it can
be negative, i.e., Δ<0 respectively. Δ>0 shows that predicted output of solar
power is less than the actual. Which leads microgrid to purchase it from utility.
In the second scenario, Δ<0 is predicted value is greater than actual value.
Which shows microgrid will not procure electricity from utility [12].
5 Conclusion
In this paper, energy management system is focused mainly, which includes
single microgrid and multiple users. To use renewable resources generated energy
optimally, solar power generation forecasting is performed in which three existing
techniques are used and comparison among them is performed. The forecasting
error is, thus brought into account for analyzing the impact on pay off of both
stakeholders in game theory. Stackleberg game theory is utilized in this paper
to prove nash equilibrium among two player, i.e., user and microgrid. In future
work, cooperative energy management will be emphasized.
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