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1

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-

2

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) = cssEm,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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