An Efficient Energy Management in Microgrid: A Game Theoretic Approach

Abstract

Presently, power systems have the capacities to accommodate different framework for incorporating economic dispatch, transmission, storage, and electricity consumption. This can provide an efficient energy management for controlling, coordinating, planning and operations. This paper focuses on coordinating the behaviors of a typical energy management of microgrid which is an issue on energy interconnections. A setup of microgrid, electricity users, storage and utility company is designed. Initially, optimal solution is formulated as a three stage Stackelberg game in which each player is allow to maximize its payoffs, while ensuring load stability and reliability. The method of backward induction is applied to examine the non cooperative game problem. We further proposed an efficient Jaya-based conditional restricted Boltzmann machine for microgrid power output forecasting which enable the microgrid make strategic decision. Simulation results validate the fact that accurate prediction of renewable energy can influence the choice of microgrid strategies.

Full text

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An Efficient Energy Management in Microgrid: A
Game Theoretic Approach
Omaji Samuel1, Zahoor Ali Khan2,∗, Sohail Iqbal3and Nadeem Javaid1
1COMSATS University Islamabad, Islamabad 44000, Pakistan
2Computer Information Science, Higher Colleges of Technology, Fujairah, United Arab
Emirates
3National University os Science and Technology, Islamabad 44000, Pakistan
∗Corresponding author: zkhan1@hct.ac.ae
Abstract—Presently, power systems have the capacities to
accommodate different framework for incorporating economic
dispatch, transmission, storage, and electricity consumption. This
can provide an efficient energy management for controlling,
coordinating, planning and operations. This paper focuses on
coordinating the behaviors of a typical energy management of
microgrid which is an issue on energy interconnections. A setup
of microgrid, electricity users, storage and utility company is
designed. Initially, optimal solution is formulated as a three stage
Stackelberg game in which each player is allow to maximize its
payoffs, while ensuring load stability and reliability. The method
of backward induction is applied to examine the non cooperative
game problem. We further proposed an efficient Jaya-based
conditional restricted Boltzmann machine for microgrid power
output forecasting which enable the microgrid make strategic
decision. Simulation results validate the fact that accurate pre-
diction of renewable energy can influence the choice of microgrid
strategies.
Index Terms—Energy management, Stackelberg game, Load
forecasting.
I. INTRODUCTION
Crises will continue to increase if environmental and world-
wide energy are not tackled with robust large scale energy
sources. These large scale energy resources are not solely
obtained from conventional power system but with microgrid
technology. Conventional power systems are described by
it centralized and unidirectional energy flow and generation
and is not adaptable for high-level distributed and diversified
renewable energy sources (RES) [1]. Microgrid on the other
hand, is in miniature of power system which consists of load
and distributed resources, and can function as stand-alone or
grid-connected mode [2]. Nowadays, several types of emerging
demand-side resources can be found in microgrid, including
thermostatic appliances and electric vehicles, which enhance
the operations of microgrid. The relevances of renewable
energy penetration on the distribution systems are multi fold:
firstly, the renewable energy used at the point of production
helps to support local energy demand, which enhances the
reliability and minimizes the pressure on power grid; secondly,
renewable energy ensures emission free environmental friend-
liness via utilizing renewable energy-fueled generators; finally,
microgrid supplies energy demand through local distributed
generators and also reduces the transmission power loses due
to long distances as well as procurement cost on transmission
lines and large scale transformers.
Presently, power industry is constantly witnessing high pen-
etration of renewable energy, which brings in mind the concept
of multi-microgrid to denote cluster of several microgrids
either by close electrical or spatial distance [2]. The objective
is to integrate large distributed energy resource penetration to
the power system. It also include high resilience and stability
through fast energy exchange which remove the monopoly of
energy distribution owned by state over sales of energy. Multi-
microgrid architecture like the conventional power system
operates based on time period of certain operation rules (i.e.,
planning and operation) [3], architecture of multi-microgrid
in terms of interface and layout based on cost are discussed
in [4]. In addition, architecture of multi-microgrid based on
system of systems is discussed in [5] to formulate bi-level
optimization problem which handled individual microgrid as
multiple stage robust optimization with uncertainty in RES.
Others includes hierarchical control strategies which involve
primary droop-control of power electronic device, secondary
control of active and real power; and finally, energy manage-
ment system formulated as economic dispatch (ED) problem
that minimizes economic profit.
ED deals with economic consideration of power system in
terms of generation units. Nowadays, several literature studies
the ED single and multi-objectives that solved optimal power
flow problem through meta-heuristic techniques [6], [7]. In
respect to multi-microgrid operations, numerous work focus on
two adoptable approaches that coordinate multi-microgrid ED
such as decentralized and centralized approach. The objective
of the later approach is to incorporate the entire entities into
the system as single entity with overall objectives. The cen-
tralize system organizes and coordinates the operations of all
distributed generators in respective of their distinct objectives.
Ref [8] proposes hybrid interactive communication optimiza-
tion solution to solve microgrids’ plug-in and plug-out opera-
tions. The hybrid consists of two layers; upper layer performs
distributed control between multi-microgrids with no central
control; whereas, lower layer performs centralized controlling
of individual microgrid. Optimal information exchange is
achieved via flexible communication links among microgrids.
Ref [9] proposes a model predictive control scheme for multi-

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microgrids energy management via coordination of individual
microgrids operations in an economic way through balancing
system-wide demand and supply. Chebyshev inequality and
delta method are applied to handle uncertainties of demand
and supply into quadratic and nonlinear programs. Ref [10]
presents a comprehensive evaluation of disparate microgrids
by applying mixed integer linear programming for yearly
simulations. They analyze short term daily operational cost
by using receding horizon model predictive control algorithm.
The aim of this scheme is to optimize flow of different energy
generators; to coordinate each microgrids entities and energy
exchange with the rest entity. In order to minimize the com-
plexities and computational efficiency, decentralized economic
dispatch of multi-microgrids is implemented in [11]–[14] to
reduce the operating cost, network complexity, improve effi-
ciency of storage usage. However, there exists limitations with
the above proposed models. The centralized technique requires
complete communication for all entities within the network.
However, it may not be scalable for plug and play distributed
energy resources, i.e., electric vehicle. Decentralized technique
is concerns about the individual goals of each entity which
does not guarantee global optimum. Thus, the conflict of
interests between the centralized and decentralized techniques
may push microgrids away from coordination. The focus of
this paper is to propose a non cooperative game approach that
capture the dynamic interconnections among utility company,
storage company, multi-microgrids and electricity users.
Cooperative and non cooperative game formed the fun-
damental building blocks of game theory. Each game is
concerned about reaching a balanced status in which no
player can make further adjustment of their strategies denoted
as Nash equilibrium for the later and core status for the
former [2]. In cooperative game, global optimum is achieved
vai coalition optimization model. Afterward, cost allocation
model is setup for fair distribution of profit to each individual
player. Hence, we can conclude that cooperative game is best
suitable for coordinated operation of multi-microgrids which
resolves conflicting interest among stakeholders (i.e, global
and local). Several work in the field of power system such as
transmission cost allocation, revenue sharing use the coopera-
tive game [15]–[20]. The cooperative game theory via nucleoli
concept is applied in [21], Shapely value concept is examined
in [23]. Whereas, a survey on smart grids’ game theoretic
methods are discussed in [22]. However, fewer application
of cooperative game in multi-microgrid coordinated operation
has not gained full exploration, in this regard, the authors
in [2] propose a cooperative game for coordinating multiple
microgrid operations using the bender decomposition (BD).
However, BD has not been extended to multiple objectives
which also requires several iterations to converge. On the
other hand, payoff of individual player in non cooperative
game depends on getting the maximum independent payoff.
However, global welfare is ignored. In retrospect, non coop-
erative game have not gain much exploration in field of smart
grid. Bingtuan et al. [30] propose a non cooperative game
theoretic method that optimizes storage capacity and energy
consumption. In addition, the method has a single photovoltaic
(PV) array which allows each user to own a PV-storage system
and can trade with grid where there is surplus; however, there
is no coalition among users which may compromise, cause
conflict and resentment. More so, a fair energy sharing is
not considered. Zhou et al. [29] demonstrates that the inner
variation of energy with the microgrids’ outer energy exchange
can be formulated using non cooperative game. However, the
principle of proportional sharing proposed to assign energy
trading among seller and buyers lack physical and economical
justification since the intermittent behaviors of microgrids
may indicate that the proposed strategies to maximize the
payoff may not be technically satisfactory as it does not
considered the correlation between microgrids behavior and its
generation. Zhenyu et al. [1] propose three-stage Stackelberg
game for energy management with big data-based renewable
power prediction. However, the genetic algorithm proposed
for wind load forecast is inefficient due to the following
reasons: computation complexity may occur if the sample
size increases; selecting wrong crossover probability value
can make the population change slowly, thus, it may not be
effective to explore all possibilities; choosing high mutation
value may produce individual that is totally different from the
main population; and finally it may lead in slow convergence
since only the fitted candidates are selected. In Liu et al. [26],
net power profile of the energy sharing network is enhanced
via a stochastic programming where the uncertainty of prices
, prosumer load and PV energy are considered. In order to
illustrate the energy consumption behavior of prosumer via
internal prices a Stackelberg game is used. However, this work
only considered the commercial and industrial prosumer while
ignoring the residential PV prosumer which we belief to have
the highest participant. Chen et al. [27] present a Nash equilib-
rium concept for the non cooperative game in order to examine
the strategic behavior of distributed microgrid. They consider
the economic factors, stability and efficiency of microgrid,
voltage angle regulations and power flow constraints. However,
the framework does not consider the generators as the leader
in Stackelberg game, storage dynamic and also to derive the
optimal power policies for scheduling players.
This paper focuses on the efficient and effective energy
usage of the RES. Due to the distribution energy management
problem which has multiple conflicting objective functions.
This paper aim at maximizes each objective function of the
active market player while ensuring power balancing and
reliability and also satisfying the electricity users demand.
Although, uncertainties exist in the RES that is uncontrollable,
we apply forecasting technique to obtain the short-term pre-
dictive value via deep learning approach. The contributions of
this paper are summarized as below:
1) A suitable framework is proposed using the three stage
Stackelberg to formulate uncertainty of microgrid’s deci-
sion making problems. It capture the dynamic interaction
and interconnection among power components. The first
stage is made up storage, utility company which act
as leaders of the microgrid, announces their electricity
prices to the microgrid. In the second stage, microgrid
acts as the leader of the electricity users and follower of
storage and utility company, adjust it strategies, energy

3
demand based of the electricity prices from the first
stage and announces it electricity prices to the electricity
users. Finally, the electricity users act as the follower of
microgrid, adjust their consumption based on electricity
prices received from the microgrid.
2) We resolve the uncertainty of RES by adopting a condi-
tional restricted Boltzmann machine (CRBM) to handle
the huge amount and high dimensional nonlinear data
by extracting multiple levels of distinct data abstraction.
Jaya algorithm is applied for parameter fitting of the
CRBM and the prediction error minimization. For com-
parative analyzes, The proposed model is compare with
other models in literature [1].
The organization of this paper is as follows: In Section I, we
present the introduction of the domain as well as review of
the related works on game theoretic approaches to energy
management in microgrid. Section II presents the system
model of energy management and problem formulation as
well as the objective functions. The algorithm of the RES
power forecasting and the optimization algorithm are discussed
in Section III. Simulations and analyzes are presented in
Section IV. Finally, Section V provides the conclusion and
expected future work.
WT PV
G
PV B
WT
WT PV
B
Utility
User 1 User 2 User N
...
Microgrid
1
...
WT G PV
B
Wind turbine
Biomass
Geothermal Photovoltaic
Microgrid
2
Microgrid
M
Bought energy
from microgrid
Sold energy to
microgrid
Bought energy
from utility
Sold energy to
utility
P1,g
E1,M
Pm,1 Pm,2 PM,m
E1,N E2,N EN,N
...
P2,g
E2,M PM,g
EM,M
...
Ps
Eg
Electric vehicle
Buffered sharing
Direct sharing Storage company
Fig. 1: Proposed system model.
II. SY ST EM M OD EL A ND P ROB LE M FO RM UL ATIO N
A. System model
Fig. 1 shows the architecture of the proposed energy man-
agement with electricity user, microgrid, storage company and
the utility. In this system, we assumed a single storage and
utility company; single microgrid with two generation sources,
i.e., wind and solar (photovoltaic) and Nnumber of electricity
users. To ensure stability of the system, microgrid requirement
are met by the utility and storage company. To get efficiency
of the proposed system model, microgrid is assigned to meet
the load demand of the electricity user. However, renewable
energy exhibits stochastic behavior for which microgrid may
not satisfy the load demand of electricity users at a certain
time and may need to procure more energy from the storage
company.
B. Objective function
The storage and utility company are the leaders of the game,
broadcast their unit electricity prices to the microgrid. With a
fair electricity prices, the utility and storage company intend
to maximize their payoff. The optimization of the utility and
storage company is given as:
Maximiz e
PgUg(Em,g, Pg),(1)
Maximiz e
PsUs(Em,s, Ps),(2)
The utility objective function is expressed as quadratic func-
tion of electricity demand Edem which is made of electricity
cost, Cutl(Edem )and Epul(Edem )is the pollutant emission
cost. Taking into account the line loss. We defined the utility’s
objective function as:
Ug(Em,g, Pg) = Revg(Em,g, Pg)−Cutl (gEm,g )
−Epul(gEm,g ),(3)
where,
Revg(Em,g , Pg) = Em,gPg,
Cutl(gEm,g ) = ag(gEm,g )2+bg(gEm,g )2+cg,
Epul(gEm,g ) = αg(gEm,g )2+βg(gEm,g ).
(4)
From Equation 3, first term represents the electricity revenue
and the second term and third term denote the power gener-
ation cost function and pollutant emission, respectively. Let
Em,g is microgrid’s quantity of electricity purchased from
utility, pgbe utility’s unit electricity prices. ag= 0.03, bg=
0.03, cg, αg= 0.08, βg= 0.08 be the cost parameters of
Cutl(gEm,g )and Epul (gEm,g),Ploss
gbe the transmission
power loss percentage (i.e., which is related to voltage , resis-
tance and efficiencies of transformer). Generated electricity
gEm,g is used to satisfy microgrids’ demand, Em,g and
g=1
1−Ploss
g.
C. Objective function of the storage company
The storage company objective function after considering
the power loss during charging and discharging is define as:
Us(Em,s, Ps) = Revs(Em,s , Ps)−Cs(sEm,s),(5)

4
where,
Revs(Em,s, Ps) = Em,s Ps,
Cs(Es, Ps) = cssEm,s
ηcηd
.(6)
From Equation 5, the first term represents the revenue of
the storage company and the second term represents storage
company cost function. Let Em,s is the microgrids’ quantity of
electricity purchased from the storage company, Psis the stor-
age company unit electricity prices, ηc= 0.5, ηd= 0.5are the
efficiencies of charging and discharging. cs= 1.5represents
the unit cost maintenance and operation and s=1
1−Ploss
s.
D. objective function of microgrid
Tn the three-stage Stackelberg game, microgrid performs
double roles such as follower of utility and storage, and leader
of users. The microgrid broadcast the electricity price to users,
and define the amount of power that is needed from the
utility and storage company. Microgrid maximizes its payoff
by adjusting its electricity prices and the quantity of electricity
demand. We assumed a single microgrid with two distributed
generators ( wind and solar) as source of power output, we also
consider the satisfaction function based on utility and storage
company quality of service of electricity. The optimization of
the microgrid is given as:
Maximiz e
Em,g,Em,s ,PmUm(Em,g , Pm),(7)
s.t. C1 : 0 ≤gEm,g ≤Eg ,max,
C2:0≤sEm,s ≤Es,max,
C3 : 0 ≤Pm≤Pm,max,
C4 : Em,s +Em,g =max
N
X
n=1
En,m −ˆ
Lwind,solar −∆,0,
C5 :
N
X
n=1
En,m −ˆ
Lwind,solar −∆>0.
(8)
Where Eg,max = 200kW, Es,max = 100kW, Pm,max =
50cents/kW h are the maximum amount of electricity utility
sold to microgrid, storage company and the maximum electric-
ity prices user can afford. If PN
n=1 En,m −ˆ
Lwind,solar −∆≤
0, then the microgrid is satisfied with it generated electricity.
The objective function of microgrid is defined as:
Um(Em,g, Pm) = Revm,g(Em,g ) + Revm,s (Em,s)
−Cm,g(Em,g , Pg)−Cm,s (Em,s, Ps)
+Revm(Ek,m, Pm)−Cm(ˆ
Lwind,∆)
−Cm(ˆ
Lsolar,∆) −Epul(ˆ
Lwind,∆) + F|∆|,
(9)
where,
Revm,g (Em,g) = Xm,g Em,g −dm,g
2(Em,g)2,
Revm,s(Em,s ) = Xm,sEm,s −dm,s
2(Em,s)2,
Cm,g(Em,g , Pg) = Em,g Pg,
Cm,s(Em,s , Ps) = Em,sPs,
Revm(En,m, Pm) =
N
X
n=1
En,mPm,
Cm(ˆ
Lwind + ∆) = am(ˆ
Lwind + ∆)2
+bm(ˆ
Lwind + ∆) + cm,
Cm(ˆ
Lsolar,∆) = csolar(ˆ
Lsolar + ∆)
Epul(ˆ
Lwind + ∆) = αm(ˆ
Lwind + ∆)2
+βm(ˆ
Lwind + ∆).
(10)
Let Revm,g (Em,g)be the satisfaction value and
Cm,g(Em,g , Pg)be utility company electricity sold to
microgrid , satisfaction parameter, Xm,g = 5 of utility
company is assume since it is hard to model satisfaction
parameter accurately. dm,g = 0.21 be the predefined
satisfaction parameter of microgrid, Revm,s(Em,s )
and Cm,s(Em,s , Ps)are same as Revm,g (Em,g)and
Cm,g(Em,g , Pg)previously defined. Let Revm(En,m , Pm)
be the revenue obtained from electricity users, En,m
is the nth users amount of electricity and Pmbe the
unit electricity price of microgrid, Cm(ˆ
Lwind,∆) and
Epul(ˆ
Lwind,∆) is the pollutant emission and wind power
generation cost function, with the constant parameters
am= 0.05, bm= 0.05, cm= 0.05, αm= 0.05, βg= 0.05.
Cm(ˆ
Lsolar,∆) is the cost function of the solar power
output, csolar be the operation and maintenance cost,
(ˆ
Lsolar + ∆) be the solar power output. Let ˆ
Lwind + ∆ and
ˆ
Lsolar + ∆ denote the wind and solar power prediction and
ˆ
Lwind,solar = 285kW be the actual capacity of the microgrid
power output, ∆is the prediction error such that F < 0, i.e.,
when prediction result is inaccurate, microgrid’s payoff will
decrease. Let F=−50 be the penalty factor.
E. Objective function of electricity users
The objective function of the nth electricity user is defined
with consideration of the satisfaction parameters. The electric-
ity user act as the follower of the microgrid and the amount
of power purchase by the electricity users depend on the Pm
to get maximize payoff. The nth electricity users is define as:
Maximiz e
En,m Un(En,m, Pm)s.t. En,m ≥En,b ,(11)
where En,b is the demand of nth electricity user and the
objective function is define as:
Un(En,m, Pm) = Revn,m (En,m)−Cn,m (En,m, Pm),(12)
where,
Revn,m(En,m ) = Xn,mEn,m −dn,b
2E2
n,m,
Cn,m(En,m , Pm) = En,mPm.
(13)

5
Let Revn,m(En,m )and Cn,m(En,m , Pm)be the satisfaction
value and payment that nth electricity user made from elec-
tricity bought from microgrid. Let Xn,m and dn,b be the
satisfaction parameter and predefined satisfaction parameter
of the microgrid
III. ALGORITHM OF THE MICROGRID POWER
FORECASTING
CRBM is the extension of the restricted Boltzmann ma-
chine, which is used to model time series and human ac-
tivities [28]. This paper addresses the parameter setting of
CRBM and train the network via an optimization algorithm.
Since wind and solar forecast is a time series problem, we
adopt the CRBM to handle the huge amount nonlinear data,
which is capable of extracting multiple levels of distinct data
abstraction. The concept of CRBM works where the higher
levels are derived from the lower level ones. In this section,
we describe CRBM based on mathematical details such as
energy function, probability reference and learning rules.
ξ(v, h, u;W) = −vTWvh −vTa−uTWuv v
−uTWuhh−hTb, (14)
where ξ(v, h, u;W)is the energy function with respect to
u,v,h and W,v= [v1, . . . , vn]collects all the real values
for the visible unit, and vnis the last visible neurons’ index.
u= [u1, . . . , un]is the real values for the history unit, and
h= [hi, . . . , hn]is the hidden unit with binary vectors.
Wvh ∈R,Wvu ∈Rand Wuh ∈Rdenote the weight
matrix connecting layers. b, a ∈Rdenote the biases for hidden
and visible neuron, respectively. Where Wvh is bidirectional;
while, Wuh and Wuv are non-bidirectional.
The stochastic or probability inference of CRBM is obtained
by deriving two conditional distributions. The first conditional
distribution is used for getting the probability of hidden layer
that is conditioned on the rest layers; i.e., p(h|v, u), while
the second is used to get the probability of the visible layer
conditioned on the rest layers, i.e., p(v|h, u). The inference is
carried out in parallel for individual unit type since there is
no connection between the neuron of the same layer [28].
p(h|u, v) = sig(uTWuh +vTWv h +b),(15)
p(v|h, u) = N(WuvTu+Wvh h+a, σ2),(16)
where for brevity, we choose σ= 1. The hidden layer
is activated by a sigmoid function that denotes the value
of probability. The term Ndenotes the Gaussian activation
function over the total input of individual visible layer, whose
value is used as the probability of visible layer.
In the learning rules step, parameters are adjusted by a
maximal likelihood function in which the gradients of energy
function with respect to the weight are being computed. Due
to the problem of deriving the gradient of the likelihood
function, a contrastive divergence is implemented to minimize
the Kullback-Leibler measure between the input data and the
forecast data. Update of various weights and biases is obtained
by finding the derivative of energy function with respect to
individual variables. The update is in two phases: using the
Gibbs sampling for each training, the hidden unit is updated
by initializing the visible unit with the training data, while
visible unit is updated using the values of hidden unit. The
equations for weights and biases are given in [28] and the
parameters of CRBM used in this paper are learning rate
(τ)=0.001, hidden layer=10; output layer=1, momentum=0.9
and weight decay=0.002; .
In this paper, the mean absolute percentage error (MAPE)
for the validation sample which is termed as the prediction
error ∆.
M AP E =1
N
N
X
n=1
|y−
n−yn
y−×100|,(17)
where y−
ndenotes the nth actual microgrid power output, and
ynrepresents the nth microgrid forecast power output. The
total time Ncan represent the hourly, daily, weekly, seasonal
or yearly time trends. Therefore, the final minimal value of
M AP E after a series of iterations is used as the validation
error (∆).
A. Forecast error minimization
The MAPE is further minimized using the Jaya optimization
algorithm and objective function, mathematically it is written
as:
minimize
NM AP E, τ ;∀n∈[1,2, . . . , N ],(18)
Jaya algorithm was developed by Rao in 2016 to solve the
constrained and non-constrained optimization problem [29].
Jaya algorithm is used as a tool for providing optimal solutions
in different domains like the microgrid [30], smart grid [31],
etc. We denote the optimization function as f(x)which is
require for minimization at any iteration r. Let var be the
number of decision variables (1,2, . . . , var)and the whole
candidate’s solution is represented as NS. Let f(x)good be the
candidates with a good solution and f(x)bad be the candidates
with a bad solution. The modified value is obtained using
equation (19).
Modβ
j,l,t =Modj,l,t
+r[0](Modj,good,t − |M odj,l,t |)
−r[1](Modj,bad,t − |Modj,l,t|),
(19)
where Modj,good,t is the value of variable lfor the good
candidate and Modj,bad,t is the value of variable lfor the bad
candidate; r[0] and r[1] are the two random numbers in range
of [0,1]. The term r[0](Modj,good,t −|M odj,l,t |)represents the
tendency of the solution to move close to the good solution;
whereas, the term r[1](Modj,bad,t − |Modj,l,t|)represents the
tendency of solution to avoid the bad solution. All accepted
function value at the each ris maintained, which serves
as input to subsequent iterations. The algorithm 1 illustrates
optimization process of the proposed Jaya-CRBM model. The
parameters of Jaya based optimization algorithm are popula-
tion size (POP)=30, number of decision variable=2, maximum
iteration (MaxGen)=1000, minimum population=0.1 and max-
imum population=0.9.

6
Algorithm 1 Proposed Jaya-CRBM
1: procedure JAYA ALGORITHM(∆)Get the minimized
forecast error
2: Intialized algorithm parameter
3: set gen = 0;
4: Train power output using CRBM,
5: Evaluate fitness of trained dataset,
6: while gen < maxGen do MaxGen is maximum
generation
7: for g∈POP do POP is the maximum
population
8: Calculate and store good and
9: bad individual solution,
10: Trim solution using Equation 19,
11: Evaluate fitness of trim
solution,
12: If previous fitness better
than later,
13: Replace population with the best,
14: Repeat until maximum iteration
reached,
15: gen=get+1;
16: return ∆
0
0
2
4
Pwind (kWh)
10-3
5
6
8
10
Day
15
20 7
6
Time (h)
5
4
3
2
25 1
Fig. 2: Wind power output [32].
0
0
0.5
Psolar (kWh)
5
1
1.5
10
Day
15
20 7
6
Time (h)
5
4
3
2
25 1
Fig. 3: Solar power output [32].
IV. SIMULATIONS AND DISCUSSIONS
This section discusses the proposed game theoretic energy
management with solar and wind power forecasting via sim-
ulation. To evaluate the forecasting model, hourly real data
of wind turbine and solar power which were collected from
National renewable energy laboratory (NREL) national wind
technology center are shown in Fig. 2 and Fig. 3, respectively.
The power received from utility company is assumed to be
lower than that of the microgrid. Similarly, utility company
pollutant emission cost is assumed to be higher than that
of microgrid. In addition, we also assumed microgrid is
preferred to use stored energy, i.e., the satisfaction parameter
of microgrid is higher than the storage company and the basic
load demand of each electricity users is also assumed to be
the same.
10 20 30 40 50 60 70 80 90 100
Basic Electricity Demand of Users E
n,b * 1 hour (kWh)
15
20
25
30
35
40
45
Price (cents/kWh)
the utility company pg
the energy storage company ps
the microgrid pm
Fig. 4: Showing the optimal prices of utility company, storage
company and microgrid.
Fig. 4, demonstrates the optimal prices of storage, utility
and microgrid in respect to user demand. The simulation
results report that there is monotonic increase of price for
storage, utility company and microgrid as the user demands
increases. It is also seen from simulation results that the
electricity prices of storage company is higher than the utility
company, it due to microgrids’ desire to get clean energy from
the storage company. More so, higher prices are reported for
microgrid than the utility and storage company, respectively.
This is because the microgrid desires to maximize its payoff
by announcing higher electricity prices to the electricity users
and the storage company.
Fig. 5 shows the procurement cost between t the storage
company and utility. From the simulation results, the amount
of microgrids’ power purchased from utility and storage com-
pany remains stable as the users electricity demand increases.
This is due to microgrid desire to pay get less power from
storage company and utility company as electricity demands
of users increases.
Fig. 6 presents the microgrids’ optimal payoff versus the
prediction error obtained from the power output forecasting by
Jaya-CRBM. If the forecast error is nonnegative, it means that
the predicted amount of power output is more than the actual
amount of power output; thus, microgrid may like pays more
to get electricity from storage and utility. From the simulation

7
10 20 30 40 50 60 70 80 90 100
Basic Electricity Demand of Users E
k,b * 1 hour (kWh)
0
2
4
6
8
10
12
14
16
18
Electricity procurement Quantity (kWh)
104
the utility company Em,g
the energy storage company Em,s
Fig. 5: Showing the electricity procurement cost from storage
and utility company.
1 2 3 4 5 6 7 8 9 10
The Prediction Error
137.5
138
138.5
139
139.5
140
140.5
141
141.5
142
Payoff of the Microgrid
En,b=40
En,b=60
En,b=80
Fig. 6: Showing microgrids’ optimal payoff versus prediction
error.
results, three different user load demand of 40, 60 and 80 kW
have been examined. the optimal payoff of microgrid decreases
monotonically due to the following reasons: the electricity
prices of microgrid is higher than both utility company and
storage company and microgrid is charged based on the power
output of the forecast wind and solar.
10 20 30 40 50 60 70 80 90 100
Basic Electricity Demand of Users E
k,b * 1 hour (kWh)
0
2000
4000
6000
8000
10000
12000
14000
Payoff
the utility company Ug
the energy storage company Us
the microgrid Um
Fig. 7: Showing the storage, utility company and microgrid
optimal payoffs.
Fig. 7 presents the optimal payoff of utility company, stor-
age company and microgrid versus the basic user electricity
demand. From the simulation results, the payoffs are shown
to monotonically increases as the electricity demand of users
increases. We also observed that the payoff of microgrid is
higher than both the payoffs of utility company and storage
company, respectively. Thus, microgrid may like buy from
storage company than from the utility, however, the payoff
of the storage company is higher than the utility company.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Step
6
8
10
12
14
16
18
20
22
24
MAPE (%)
Jaya-CRBM
BP
Genetic SAE
Fig. 8: Showing MAPE values for the three models versus
forecasting step.
Fig. 8 demonstrates the MAPE value of three algorithms,
i.e., the CRBM, back propagation (BP) and genetic stacked
encoder and decoder (Genetic SAE) versus the forecasting step
of the wind and solar energy. From the simulation results,
forecasting step increases along with MAPE values. Thus, an
inaccurate results will occur if the step continue to increases.
In addition, our proposed algorithms show better MAPE values
as compared to the other two algorithms.
V. CONCLUSION
This paper presents three-stage Stackelberg game for the
energy management which consists of the interconnections
between utility company, storage company, microgrid and
the electricity users. In order to provide efficient model for
microgrid operation, we perform power output forecast of
wind and solar which assists the microgrid to apply the energy
management strategies. We assume a single utility company,
storage company as leaders, whereas, microgrid leader of user
and follower of storage and utility company, while the users
as follower of microgrid to formulate three stage Stackelberg
game, where each player wishes to maximize its payoffs.
The closed form expression of the analysis via backward
induction for each stage and their respective optimal prices
are examined. Simulation is applied to validate the proposed
system that define the behavior of microgrid in respect to
the power output forecast error. In addition, a Jaya-CRBM
is applied to resolve the limitations of existing technique
in literature (Genetic SAE and BP), which demonstrates to
outperform the above mention technique. In our future work,
energy management regarding coordination between multi-
microgrid operations that is based on economic dispatch for

8
fuel cost minimization. This is achieve through scheduling of
generators which limits certain load demand at some specific
interval. The power loss of microgrids due to distance between
the multi-microgrid is also considered.
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