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A multi-objective energy optimization in smart grid
with high penetration of renewable energy sources
Kalim Ullah1, Ghulam Hafeez∗1,2, Imran Khan1, Sadaqat Jan3, and Nadeem Javaid2
1Department of Electrical Engineering, University of Engineering and Technology, Mardan 23200, Pakistan
2Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad 44000,
Pakistan
3Department of Computer Software Engineeirng, University of Engineering and Technology, Mardan 23200,
Pakistan
∗Corresponding author: Ghulam Hafeez (ghulamhafeez393@gmail.com)
Abstract—Energy optimization plays a vital role in energy1
management, economic savings, effective planning, reliable and2
secure power grid operation. However, energy optimization is3
challenging due to the uncertain and intermittent nature of4
renewable energy sources (RES) and consumers’ behavior. A5
rigid energy optimization model with assertive intermittent,6
stochastic, and non-linear behavior capturing abilities is needed7
in this context. Thus, a novel energy optimization model is8
developed to optimize the smart microgrid’s performance by9
reducing the operating cost, pollution emission and maximizing10
availability using RES. To predict the behavior of RES like solar11
and wind probability density function (PDF) and cumulative12
density function (CDF), are proposed. Contrarily, to resolve13
uncertainty and non-linearity of RES, a hybrid scheme of14
demand response programs (DRPS) and incline block tariff15
(IBT) with the participation of industrial, commercial, and16
residential consumers is introduced. For the developed model,17
an energy optimization strategy based on multi-objective wind-18
driven optimization (MOWDO) algorithm and multi-objective19
genetic algorithm (MOGA) is utilized to optimize the operation20
cost, pollution emission, and availability with/without the involve-21
ment in hybrid DRPS and IBT. Simulation results are considered22
in two different cases: operating cost and pollution emission,23
and operating cost and availability with/without participating24
in the hybrid scheme of DRPS and IBT. Simulation results25
illustrate that the proposed energy optimization model optimizes26
the performance of smart microgrid in aspects of operation27
cost, pollution emission, and availability compared to the existing28
models with/without involvement in hybrid scheme of DRPS and29
IBT. Thus, results validate that the proposed energy optimization30
model’s performance is outstanding compared to the existing31
models.32
Index Terms—Smart grid; multi-objective energy optimization;33
solar; wind; demand response programs; incline block tariff34
I. INTRODUCTION35
Recent studies regarding energy optimization intended that36
energy consumption can be reduced to 25-35% without chang-37
ing existing system infrastructure by optimizing power usage38
and power generation. One of the approaches for reducing39
power loss, pollution emission, and economically meeting40
users’ needs is by renewable energy sources (RES) like wind41
and solar [1], [2], [3]. In recent years, a smart grid (SG) with42
high RES penetration has been introduced as a novel concept,43
and energy optimization has turned into an essential matter44
[4]. However, forecasting is indispensable prior to energy 1
optimization [5]. One of the major challenging issues in energy 2
optimization of RES, such as wind and solar, is uncertainty 3
in their behavior means real-time generation is different from 4
the forecasted one from these resources. Particularly due to 5
the presence of uncertainty in energy generation from these 6
RES, the SG operator’s responsibility to maintain a balance 7
between energy generation and consumption would confront 8
some problems. The SG operators keep a certain amount of 9
reserve as a backup to overcome uncertainty factors in energy 10
generation and maintain security level at the required level [6]. 11
The SG operators can overcome the problems described 12
above by purchasing more energy from independent power 13
producers or keeping fast-ramping fuel-based generators as a 14
backup resource. However, these solutions are accompanied 15
by some problems like increased operating cost and pollution 16
emission [7]. Another solution is intended to resolve this 17
problem and maintain a balance between energy generation 18
and consumption by decreasing energy consumption during 19
the shortage period caused by the prediction error of RES. 20
One approach that SG operators adopt energy storage systems 21
to manage energy shortages and maintain a balance between 22
generation and consumption [8]. A strategy to overcome 23
uncertainty in RES like wind and solar is demand response 24
programs (DRPS), which is discussed in [9], [10]. Federal 25
energy regulatory commission (FERC) defined DRPS in two 26
ways: (i) the program where consumers can change their 27
energy usage pattern in response to the pricing signal offered 28
by the SG operators, and (ii) the incentive payments intended 29
to induce lower energy usage at times of high energy demand 30
or when power system stability is endangered [11]. The former 31
one is called price-based DRPS, and the latter one is known 32
as incentive-based DRPS. For more in-depth understanding, 33
see [12]. Recently, significant research studies have been 34
conducted on implementing DRPS and modeling their role in 35
handling the stochastic behavior of RES in energy optimiza- 36
tion. DRPS are adopted in [13] to maintain a balance between 37
energy generation and smart microgrid consumption with 38
RES such as solar and wind. A particle swarm optimization 39
(PSO) algorithm is employed to optimize the intended model’s 40
operating cost. However, pollution function is not considered 41
2
Nomenclature.
AMI Advance metering infrastructure MT Micro turbine
BA Bat algorithm Rcon Residential consumers
CPP Critical peak pricing Ccon Commercial consumers
CDF Cumulative density function Icon Industrial consumers
CO2Carbon dioxide (Rconmax, t)Residential max reduced load
DSM Demand side management (Cconmax, t)Commercial max reduced load
DR Demand response (Iconmax, t)Industrial max reduced load
DST Decision support tool UOC(t)Uncertain operational cost
DGS Distributed generation COC(t)Certain operational cost
DRPS Demand response programs ciSolar irradiance
DERS Distributed energy resources PR Rated power
EMS Energy management system Eci Cutt-in speed
EV Electric vehicles ErRated speed
EENS Expected energy not served Eco Cut-off speed
FC Fuel cell Ewind Actual wind speed
GA Genetic algorithm P pE(ci)Output PV power
HWSPS Hybrid wind-solar power system Ac Solar arrays surface area
HEMS Home energy management system wi(T)Output power
LMF Linear mapping function oii(T)Offered price
MOGA Multi-objective genetic algorithm Si(T)DGS opening and closing period
MOWDO Multi-objective wind driven optimization ReciDG(T)Reserve cost of DGS
MOPSO Multi-objective particle swarm optimization RCjDR
j,s (T)Running cost of DGS
MINLP Mixed integer non-linear programming RecjDR (T)Reserve cost of DRPS
NOx Nitrogen oxide µ(Rk)Number of solutions in current rank
OLM Optimal load management NkTotal number of solutions
PDF Probability density function RkRank of solutions
PAR Peak to average ratio µkNumber of solutions of the rank Rk
PSO Particle swarm optimization ςco,t Amount of incentive payment to commercial consumer in each timeslot
RES Renewable energy sources ςin,t Incentive payment to industrial consumer in each timeslot
RTP Real time pricing ςre,t Incentive payment to residential consumer in each timesolt
SG Smart grid δand γPDF parameters
SO2Sulphur dioxide δγ Measurement parameters
SFL Shuffle frog leaping βγ Shape parameters
TLBO Teaching and learning based optimization ηPV efficiency
VOLL Value of lost load PVS Photovoltaic system
WES Wind energy system co Total number of commercial consumers
while modeling the microgrid energy optimization problem.1
The DRPS is implemented in [14] to control the SG frequency2
integrated with RES. A wind-thermal energy scheduling in3
SG is evaluated using DRPS and stochastic programming to4
optimize operation cost, and pollution emission [15], [16].5
The DRPS is investigated in operation management of the6
SG integrated with wind turbine and photovoltaic cells in7
[17], [18] using ε- constraint as a multi-objective optimization8
problem. The DRPS and spinning reserve are investigated9
in [19], [20], respectively to cover the wind power shortage10
problem in the power system.11
Alternatively, a mixed-integer linear programming (MILP)12
method is employed in [21] to solve the energy optimization13
problem. However, the authors focused only on forecasting14
and ignored uncertainty accompanied by RES. An energy15
optimization strategy in SG integrated with wind generation16
considering uncertainty is evaluated in [22]. The purpose17
of the authors is to maximize social welfare. However, the18
authors did not cater solar energy and incentive-based DRPS.19
A probabilistic model for energy optimization in SG with20
integrated wind and solar is evaluated in [23] to optimize21
operational cost and emission. They used beta probability22
density functions (PDF) and Rayleigh to model wind and23
solar behavior variation, respectively. A similar multi-objective24
energy management model integrated with RES is solved25
using a multi-objective particle swarm optimization (MOPSO)26
algorithm. The purpose of the authors is to optimize op- 1
erational cost and pollution emission [24], [25]. However, 2
the intended model is suitable for the said scenario, and 3
their performance is degraded with scalability. Similarly, in 4
[26], a scenario tree method is utilized to solve the energy 5
management problem. However, the modeling of solar irra- 6
diation is ignored in this study. Optimal energy management 7
and modeling of a microgrid integrated with RES are eval- 8
uated in [27], [28] by employing the mesh adaptive direct 9
search method. However, in this study, uncertainty caused 10
due to RES is not catered. A Monte Carlo technique based 11
stochastic planning approach is intended in [29] for stochastic 12
behavior modeling of wind energy. Furthermore, a DRPS 13
considering wind energy influence as an operational storage 14
in the electricity market is evaluated. In general, to overcome 15
uncertainties accompanied by RES such as solar and wind 16
energy, using reserve and ancillary services is as early as the 17
emergence of these resources. Recently, significant research 18
works on SG operation management have been conducted 19
[30], [31]. An expert energy optimization system is proposed 20
in [32], [33] for solar and wind connected with a microgrid to 21
cover accompanied uncertainties and minimize operation cost 22
and pollution emission. A smart energy optimization strategy 23
based on a heuristic algorithm is proposed for grid-interactive 24
microgrid [34] to optimize energy consumption and pollution 25
emission and obtain net-zero energy buildings. 26
3
Since there are three primary objectives in smart microgrid1
energy optimization, like operating cost, pollution emission,2
and availability, the above references have investigated this3
research area from different perspectives and provide a good4
study for understanding the theme. Some studies catered5
uncertainties caused by RES from the forecasting error of6
wind and solar energy in a system using mathematical meth-7
ods. On contrarily, some authors employed DRPS to tackle8
uncertainties accompanied by RES. Some studies catered9
to operating cost while others focused on pollution emis-10
sion. However, considering only one aspect (operating cost11
or pollution emission or availability) is insufficient. Every12
aspect (operating cost, pollution emission, and availability)13
is of prime importance and can be catered simultaneously.14
Besides, all models are valuable assets of literature and15
capable of performing energy optimization. However, there16
is no universal mechanism that is effective in all aspects,17
and some mechanisms are better for some specific scenarios,18
conditions, and objectives. Furthermore, the existing literature19
methods can tackle uncertainties caused by RES like wind and20
solar and the non-linear behavior of demand-side participants.21
However, their performance is not satisfactory and estimated22
results are not up to the mark. Therefore, an optimal energy23
optimization mechanism is needed, capable of performing24
energy optimization by catering all aspects simultaneously and25
finding a solution to overcome uncertainties accompanied by26
the RES and behavior of demand-side participants.27
With this study’s motivation, a novel model is developed28
based on a multi-objective genetic algorithm (MOGA) and29
multi-objective wind-driven optimization (MOWDO) algo-30
rithm to solve energy optimization problems and cater operat-31
ing cost, pollution emission, and availability simultaneously.32
The novelty and significant technical contributions of this work33
are outlined below:34
•A novel hybrid scheme of DRPS and IBT is introduced35
to overcome uncertainty caused by solar and wind RES36
which are integrated with smart grid using the concept37
of PCAO to obtain low cost, pollution emission and38
maximum availability of RES.39
•An energy optimization model is developed utilizing40
MOGA and MOWDO with Pareto fronts criterion using41
the non-linear sorting fuzzy mechanism to solve the42
multi-objective energy optimization problem.43
•PDF and CDF probabilistic models are employed through44
Monte-Carlo simulations to predict solar irradiation and45
wind speed to provide more explicit consent between46
planning and reality.47
•Results utilizing the proposed model have proven optimal48
compared to the benchmark models in aspects of operat-49
ing cost, pollution emission, and availability.50
The remaining sections of the paper are organized as fol-51
lows. The proposed energy optimization model is discussed in52
section II and proposed and benchmark techniques are demon-53
strated in section III. The simulation results and discussions54
are reported in section IV. Finally, the conclusion and future55
research directions are discussed in section V.56
II. PROPOSED ENERGY OPTIMIZATION MODEL 1
A novel energy optimization model is proposed to minimize 2
operating cost, pollution emission and maximize availability 3
with and without involvement in hybrid scheme of DRPS and 4
IBT using RES in the smart microgrid. The overall working 5
implementation diagram of the proposed model is shown in 6
Figure 1. The proposed energy optimization model consists of 7
subsystems, which are discussed in the following subsections. 8
A. Wind energy system 9
Energy demand is rapidly increasing to meet this rising en- 10
ergy demand without polluting the environment. Wind energy 11
is beneficial energy, which is converted into electrical energy 12
by employing wind turbines. Wind energy is based on the 13
availability of wind, speed of the wind, wind turbine power 14
curve, wind turbine shape, and turbine size. Wind energy is 15
stochastic and intermittent containing high variation. Speed 16
of wind is not the only variable that is affecting the power 17
captured by the wind turbine uses for power generation. The 18
correlation between speed of wind and direction of wind is 19
equally important as the speed of wind captured by the wind 20
turbine. Therefore, in this study, for wind speed prediction 21
and correlation between speed of wind and direction of wind, 22
probability density function (PDF) (Rayleigh) is used. In 23
this work, it is predicted by Rayleigh distribution employing 24
historical data [35], the PDF and CDF of Rayleigh distribution 25
are as follows: 26
Fv(vwind) = 1 −exp "−vwind
δ2γ2#(1)
27
fv(vwind) = 2
δ2γvwind ×exp "−vwind
δ2γ2#(2)
28
vn=δγλ(1 + 1
2) = 1
2δγλ(1
2) = √π
2δγ
αγ=2
√πδγ
(3)
where vnis the average wind speed of the particular area, the 29
scale parameter is shown in Equation 3. Therefore, in the case 30
of returning βγ to PDF and CDF, Rayleigh’s model of WES 31
will be achieved as a function of speed of wind according to 32
Equation (4) and (5). The PDF and CDF curves are shown in 33
Figure 2 and 3. 34
FE(Ewind) = π
2
Ewind
E2i
exp(−π
4)(Ewind
E2i
)2(4)
35
FE(Ewind)=1−exp(−(π
4)(Ewind
Ei
)2)(5)
For certain WES, the output power is defined below [36]: 36
pw(Ewind) =
0Ewind < Eci
P R Ewind−Eci
Er−Eci Eci ≤Ewind< Er
P R Er≤Ewind < Eco
0Ewind ≥Eco
(6)
where PR,Eci,Er,Eco ,Ewind denotes rated power, cut-in 37
speed, rated speed, cutoff speed and actual wind speed of wind 38
turbine respectively. AIR403 type wind turbine is used in this 39
study [37], where PR = 15kW, Eci= 3.8m/s, Eco= 18m/s, 40
4
1500 1550 1600 1650 1700 1750
Operating Cost (Ect)
2200
2250
2300
2350
2400
2450
2500
Emission (Kg)
MOWDO with (DRPS+IBT)
Pareto set solutions
MOGA with (DRPS+IBT)
MOPSO with (DRPS+IBT)
Min Emission
Min Operating Cost
Best Solution with (DRPS+IBT)
v wind 2
F (v ) = 1-exp
wind
v
2 2
1
( ) exp
wind
v wind wind
v
f v v
1 1
b i
( )
(1 )
( ) ( )
f (p ) = 1, 0; 0
0
i i i
c c dc
ci a b
Otherwise
PDF and CDF for Wind Energy
PDF and CDF for Solar Energy
Update position of each
particle
Checking Boundaries
Pareto rank 1 members of the
archieved population are fnal
siolution
END
Wind Energy Solar Energy
Storage Devices
Micro Turbine
Distributed
Generation
wind i
wind i
i wind r
w wind
r wind co
wind co
0 E < Ec
E -Ec
PR Ec E E
p (W )=
PR E E < E
0 E E
r i
E Ec
1 1
pE pE i
( )
( ) (1 )
( ) ( )
( ) if p [0, p (c )]
otherwise 0
c i c i
pE pE
A c A c
fp p ∈
Wind Energy Model
Photovoltaic Model
cos
1
1
1 1 1
minf (x) = ( )
= ( ) ( )
T
t
t
T T S
s
T T s
nF T
nCOC T n pr UOCs T
DG Grid
2
1
mi mi
1
minf (x) = ( )
= [E (T) + E (T)]
T
J
FEmission T
(1) Operating Cost Function
(2) Pollution Emission Function
(3) Availability
1AD
Optimization Results
Objective functions
0 10 20 30 40 50
Time (h)
0
40
80
120
Demand (%age of maximum)
Residentail
Industrial
Commercial
Figure 1: Overall implementation of the proposed energy optimization model with high penetration of renewable energy
sources engaging three service areas residential, commercial, and industrial in hybrid scheme of DRPS and IBT
5
Er= 17.5m/s. Output power of WES can be obtained using1
Equation 4 and 6 through transformation theorem [38].2
fpw(pw) =
1−[FE(v∞)−F E(Eci )], pw= 0
(Er−Eci
pR).(π
2E2i)×(Eci + (Er−Eci).pw
pR)..
×exp −(Eci+(Er−Eci ).pw
pR)2
2
√πEm,
0< pw< pR
Fv(pw)−Fv(vr), pw=PR
(7)
0 0.5 1 1.5 2
Normalized speed
0
0.5
1
1.5
Probability
PDF
Figure 2: PDF:Wind speed distribution model.
0 0.5 1 1.5 2 2.5
Observation
0
0.5
1
1.5
2
2.5
Cumulative Probability
CDF
Figure 3: CDF:Wind speed distribution model.
3
B. Solar energy system4
The solar energy system converts sunlight into electrical5
energy. Probabilistic models PDF and CDF are used to models6
the behavior of solar irradiance as illustrated in Equation 8 and7
9 taken from [39]-[40].8
fb(pi) =
Γ(δ+λ)
Γ(δ)Γ(λ)ciδ−1(1 −ci)λ−1dci
0≤ci≤1, a ≥0; b≥0
0otherwise
(8)
9
Fd(ci) =
ci
Z
0
Γ(δ+λ)
Γ(δ)Γ(λ)ciδ−1(1 −ci)λ−1dci(9)
where cishows solar energy in kw/m2.δand λare PDF 1
parameters that may find the mean value of the standard 2
deviation of solar energy data and are utilized as follows: 3
δ=η(σ(1 + σ)
δ2−1) (10)
4
λ= (1 −σ)( σ(1 + σ)
δ2−1) (11)
Equation 12 shows the amount of solar irradiance is converted 5
into solar energy in two days [41]. 6
ppE(ci) = Ac.η.ci(12)
where PpE(ci)shows the output power comes from solar 7
energy system in (kW), irradiance ci,Ac is the surface area of 8
solar arrays in m2and ηis solar energy system efficiency. 9
Equation 8 indicates, PDF fppEis output power of solar 10
energy system as follows: 11
fppE(ppE) =
Γ(δ+λ)
Γ(δ)Γ(λ)(Acηci)δ−1(1 −Acηci)λ−1
ifppE∈[0, ppE(ci)]
0otherwise
(13)
C. Hybrid wind-solar power system 12
The hybrid power system is a combination of wind and solar 13
energy systems. The power generated by the hybrid power 14
system is equal to the sum of power generated from solar 15
and wind energy system, which is mathematically modeled as 16
follows: 17
PH=pwind +psolar (14)
where Pwind and Psolar are independent variables according 18
to Equations 6 and 12. PHis hybrid power generated, which 19
is modeled as convolution between PDF of pwind and psolar 20
as follows [42]. 21
fh(PH) = fpwind(P pwind)∗f psolar (P psolar )(15)
It is non-trivial to use the continuous PDF mathematics. 22
Therefore, the Monte-Carlo simulation is employed here to get 23
distinct conditions; however, creating different contexts also 24
adds to the mathematical problem’s complexity. The proper 25
strategy to prevent math difficulty is to extract a continuous 26
PDF and execute it in different parts. In the proposed model, 27
we divided PDF into eight parts per time slot to provide the 28
desired power. 29
D. Proposed hybrid scheme of demand response programs and 30
incline block tariff 31
Electric utility companies initiate DRPS to encourage con- 32
sumers to participate in energy optimization to reduce cost. 33
Electric utility companies either give flexibility to consumers 34
to shift their load from on-peak hours to off-peak hours 35
or directly control their load through DRPS by providing 36
incentives. The DRPS has high flexibility, and all consumers 37
(residential, commercial, and industrial) concentrate all their 38
activities to relatively low price hours. Thus, there is a 39
6
possibility of building peaks during off-peak hours (rebound1
peaks), which overloads the entire power system that leads2
to instability or even blackout. In this regard, this work3
introduced a hybrid scheme by combining DRPS and IBT,4
where incentive payment could be different within the same5
hour based on the total energy consumption, which effectively6
reduced rebound peaks and enhanced the stability of the7
entire power system. Besides, the demand-side consumers8
like industrial, residential, and commercial are involved in9
our proposed hybrid scheme to overcome uncertainty and10
rebound peaks problems. The hybrid scheme of DRPS and11
IBT set two incentive payment levels, and energy consumption12
and their corresponding cost changes every hour. The hybrid13
scheme for residential, commercial, and industrial consumers14
is mathematically modelled in Equations 16, 17, and 18,15
respectively.16
RW(re,t)=
RCon(re,t).ςre1if 0 ≤RConT≤RConmax
RCon(re,t).ςre2if RConT>RConmax
0 otherwise
(16)17
CW(co,t) =
CCon(co,t).ςco1if 0 ≤CConT≤CConmax
CCon(co,t).ςco2if CConT>CConmax
0 otherwise
(17)18
IW(in,t)=
ICon(in,t).ςin1if 0 ≤IConT≤IConmax
ICon(in,t).ςin2if IConT>IConmax
0 otherwise
(18)
where re,co and in are residential, commercial and industrial19
consumers; RConT,CConT, and IConTdenote total energy20
consumption of residential, commercial, and industrial con-21
sumers, respectively; RCon (re, t),CCon (co, t) and ICon22
(in, t) shows reduced loads which are planned for each23
consumer in time slot t;RConmax,CConmax and I C onmax
24
are maximum energy consumption, represents threshold power25
consumption of IBT, respectively. ςre1,ςco1, and ςin1indicate26
overall incentive payment level that should be greater than27
ςre2,ςco2, and ςin2incentive payment level of residential,28
commercial, and industrial consumers, and RW (re, t),CW (co,29
t), and IW (in, t) shows costs due to the reduction of the load30
by each consumers during the proposed load reduction. The31
applications of hybrid scheme DRPS and IBT implementation32
involves to decrease electricity cost, avoid rebound peaks33
formation, avoid risk management, avoid uncertainty, and34
provide flexibility in energy optimization.35
E. Objective functions36
In this study, the proposed energy optimization model will37
cater three objectives: operational cost, pollution emission,38
and availability simultaneously in two cases. In case I, the39
proposed model’s main objectives are to minimize the opera-40
tion cost and pollution emission with and without involvement41
in the hybrid scheme of DRPS and IBT scheme. Similarly,42
in case II, operating cost and availability with and without43
involvement in the hybrid scheme of DRPS and IBT scheme44
is catered. The proposed model uses MOWDO and MOGA to45
optimize case I and case II’s desired objectives. The detailed 1
discussion is as follows. 2
1) Operating cost function: The operating cost is divided 3
into two categories: Certain operating cost and uncertain 4
operating cost. The uncertain operating cost includes start- 5
up and running costs of distributed generations (DGS). The 6
certain operating cost includes reserve cost provided by DGS, 7
DRPS, and power cost, which is purchased/sold, from/to the 8
utility and the probability of scenarios P rsare affected by 9
uncertainty in the wind and solar parameters in each case. The 10
uncertain operating cost includes running costs for the DGS 11
unit, reducing the load due to the DRPS+IBT implementation, 12
the costs related to the value of lost load (VOLL) and the 13
expected energy not served (EENS) cost for consumers. 14
minf1(x) =
T
P
T=1
nF cos t(T) =
T
P
T=1
nCOC(T)
+
T
P
T=1
n
S
P
s=1
prs×UOCs(T)
(19)
where P rsis the probability of scenarios. Certain and uncer- 15
tain operating cost functions are defined in Equation 20 and 16
21, respectively. 17
COC(T)
NDG
P
i=1
[wi(T)oi(T)si(T) + QUi(T)
.|si(T)−si(T−1)|+ReCiDG(T)]
+
J
P
j=1
ReCjDR (T).sbuy(T).WGrid−buy(T)
.oiGrid−buy (T)−ISell (T)WGrid−buy (T)
(20)
18
UOC(T) =
NDG
P
i=1
[RCiDGi,s (T) +
J
P
j=1
RCjDR j,s(T)
+EENs(T)×V OLL(T)
(21)
where wi(T)and oii(T)are output power and the given price 19
for the ith units in Tth time, si(T)represents ith DGS opening 20
and closing state during the Tth period, QUi(T) indicates the 21
operation and closing cost for the ith unit during the Tth 22
time, ReciDG(T),RecjD R(T)are reserved cost of ith DGS, 23
DRPS+IBT for the jth load during the Tth time, WGrid −24
buy(T) and WGrid−S ell(T) represents exchange power with 25
utility during time Tth time, wGrid−buy (T) and wGrid−sell(T) 26
indicates the offered-price for exchange power with utility 27
in electric markets in Tth time period. RCii,s DG (T)and 28
RCjDR
j,s (T)shows running costs of ith DGS units and the 29
costs because of reduced loads by jth DRPS during Tth time in 30
sth scenarios, EMNS(T) and VOLL(T) are expectation energies 31
not serve in sth scenarios in Tth time and value of lost load 32
in Tth time period, respectively. According to Equation 17, S33
is a state variable which contains the actual power generated 34
by DGS, charging and discharging of battery power and the 35
variable active power through the mounting grid. In terms 36
of operating costs in the proposed model, it is assumed that 37
DGS, as well as DRPS+IBT, are the spinning reserve suppliers 38
by suppressing uncertainties caused by wind and solar RE. 39
Therefore, the reserved cost is taken as a probability in every 40
start component of the objective functions. 41
7
Table I: Price and quantity offered packages for hybrid scheme of DRPS and IBT
Quantities in kW Quantities in kW Quantities in kW
Price in Ect/kWh Price in Ect/kWh Price in Ect/kWh
DRPS+IBT 1 0-10 10-20 20-50 50-70
0.19 0.23 0.29 0.40
DRPS+IBT 2 0-10 10-20 20-30 30-60
0.03 0.07 0.30 0.45
2) Pollution emission function: The emission function in-1
volves activities such as the amount of emission produced by2
DGS and the quantity of emission caused by the grid during3
purchase. Pollutants include CO2,S O2, and N O2, as well as4
a statistical model for the pollution function, can be obtained5
as follows.6
minf2(x) = P
T=1
FEmission (T)
=P
J=1
[EmiDG (T) + Emi Grid (T)] (22)
DGS pollution is calculated as follows:7
EmiDG(T) =
NDG
P
j=1
ECO2D G(j) + ESO2DG(j) + EN Ox DG (T)
×PjDG(T)
(23)
where ECO2D G(j),ESO2DG(j)and EN Ox DG (T)shows8
emissions generated due to CO2,S O2, and N O2,, by jth DGS9
respectively; is measured in K.g/Mwh. Similarly, the pollution10
caused by the grid during power purchase can be written as11
follows:12
EmiGrid(T)=(ECO2Gr id +ESO2Grid +EN Ox Grid )
×PGrid(T)
(24)
13
3) Availability function: Availability of the system deals14
with the capacity of the system to deliver power to consumers.15
The availability of the system in a specific duration is pre-16
sented by [43], which is given as follows.17
A= 1 −∆
D(25)
where A, D, ∆Drepresents the availability index, early18
demand and demand not met, respectively. ∆Dcan be defined19
as follows.20
∆D=
T
X
t=1
PbattMin (t)−PbattS OC (t)
−Psolar(t) + Pwind(t)
+Pnet(t)−PD(t)×U(t)
(26)
where ∆Dshows the demand not met, Pbatt(t),PSO C (t)21
represents minimum charge of proposed battery, status of22
charge of a battery in time slot t,PD(t),U(t) indicates the23
total demand in time tand step function, respectively. From24
Equation 26, if the supplied power is greater than or equal to25
demand, the above function will be equal to zero. However, if26
the power provided and power demanded are met, the function27
is equal to 1.28
F. Problem constraints29
The operation of the smart microgrid is ensured using30
following constraints.31
1) Power-network constraints: The total energy produced 1
by DGS and the power grid is equal to the overall demand 2
load. 3
NDG
X
l=1
PDG, i,s(T) + PGr id,s(T) =
Ns
X
i=1
PDemandl,s(T)−PDR,s (T)
(27)
PDemandl,s is Lth demands level in Tth time and sth scenar- 4
ios. In Equation 28, PDR(t) is an actual power involvement in 5
DRPS+IBT and given as: 6
PDR,x(T) = P
re
RCon(re, t, x) + P
co
CC on(co, t, x)
+P
in
ICon(in, t, x) (28)
7
2) Reserves and DGS power constraints: Energy produced 8
by DGS: 9
PminDG,x .I(x, t)≤PDG(x, t, s)≤Pmax DG,x .I(x, t)∀x, t, s
(29) 10
RDG(x, t)≥PD G(x, t, s)−PDG (x, t, 0) ∀x, t, s (30)
11
3) Battery ON-OFF constraints: Battery used in proposed 12
model are: 13
Ws(T) = Ws(T−1)1
+xcharge (T)qcharge (T)∆T.Icharge
−1
xdisch arg eqdischarge (T)∆T.IdischargeIdischarge(T)+
Icharge (T)
≤1Ws,minimum ≤Ws(T)≤Ws,maximumqcharg e(T)
≤qcharge ,maximum;qdischarg e(T)≤qdischarg e,maximum
(31)
where, Ws(T) and Ws(T-1) indicates power stored in battery at 14
time Tand (T-1) respectively, qcharge and qdischarg e are the 15
battery charge and discharge cycle during time ∆Trespec- 16
tively, xchar ge and xdischarge is charge and discharge allowed 17
by battery during the whole cycle, (Ws, minimum) and (Ws,18
maximum) indicates lower and higher power store by battery 19
and (qchrge , maximum),(qdischarge ,maximum) are maximum 20
charge and discharge of battery during ∆Tperiod [44]. 21
In this model, battery storage system involvement aims to 22
provide back-up power to the smart microgrid. If the source 23
power goes down, the battery offers services to the smart 24
microgrid and storing energy in off-peak hours. The battery 25
storage system’s applications balance the grid power, save the 26
smart microgrid’s cost, and assist the smart microgrid when 27
other sources of power go down. In this way, smart microgrid 28
efficiency increases. 29
8
G. Typical smart microgrid1
The smart microgrid system is shown in Figure 4 consisting2
of industrial, commercial, and residential consumers, with the3
participation of DGS, FC, MT, WES, PV, battery, and utility.4
The smart microgrid can be operated in stand-alone mode or5
conjunction with the main power grid [45], [46]. The devel-6
opment of smart microgrid is a part of SG concept, therefore,7
both have some common objectives in energy optimization8
such as DRPS and green technology implementation, reliable9
and secure energy provision [46]. The parameterized cognitive10
adaptive optimization and control approach is used to inte-11
grate predicted RESs with the smart microgrid that provides12
balance power to demand-side consumers. The inclusion of13
this technique in the model is due to its consistent, fastness14
and “plug-n-play” behavior, and it is suitable for any complex15
system, whether it is small or large. The PCAO is applied16
to the set of controllers shown in Figure 4. The signals are17
collected at point of common coupling (PCC) and deliver to18
PCAO based central controllers. The center controllers control19
signals in real-time according to the situation and operation20
inside the smart microgrid, as shown in Figure 4. There are21
different linear controllers (LC) which take control signals22
from central controller to reduce the complexity of system23
design and optimize the performance of the smart microgrid.24
The installation characteristics are listed in Table II, where25
DGS offered price in (Ect/kWh), start/shutting-down cost in26
(Ect), minimum power Pmin in (kW), maximum power Pmax
27
in (kW), CO2in (kg/MWh), SO2in (kg/MWh) and NOxin28
(kg/MWh) pollution produced by DGs and utilities, low and29
high energy generation [47].30
III. EXISTING AND PROPOSED MULTI-O BJ EC TI VE31
OPTIMIZATION METHODS32
In this work, two multi-objective algorithms like MOGA33
and MOWDO with Pareto fronts criterion using the non-34
linear sorting fuzzy mechanism compared to existing multi-35
objective particle swarm optimization (MOPSO) algorithm are36
employed for energy optimization. The detailed description of37
the adapted and existing algorithms are as follows.38
A. Multi-objective particle swarm optimization algorithm39
The multi-objective energy optimization problems include40
conflicting objectives under equality and inequality constraints,41
which must be solved simultaneously. In this work, three42
conflicting objectives like operating cost, pollution emission,43
and availability must be optimized simultaneously.44
minf(Y)=[F1(Y), F2(Y)...........FN(Y)]T(32)
subject to:45
ki(Y)<0i= 1,2,3....., Nueq
vi(Y)=0 i= 1,2,3...., Neq
(33)
where f(Y) contains an objectives function and Yconsist of46
variables of an optimization, Fi(Y) is objectives function, ki(Y)47
and vi(Y) are equalities and inequalities constraint and number48
of objective functions is denoted by N. For a multi-objective49
optimization problem, either xor ywill be one of two possible50
solutions. One will supersede the other. Therefore, when the 1
following two functions are matched, Ywill dominated Z.2
∀m∈ {1,2,3......., n}, fm(Y)≤fm(Z)
∃n∈ {1,2,3......., n}, fn(Y)< fn(Z)(34)
Hence, Pareto-fronts solution can be found with a non- 3
dominated solution (desired). Here, the Pareto-front opti- 4
mization concept is executed on particle swarm optimization 5
algorithm [48]. Optimization of operating cost and pollu- 6
tion emission, and operating cost and availability using RES 7
with/without DRPS+IBT through MOPSO [49]. 8
steps of MOPSO: 9
Step 1: Initialize and define inputs to algorithm. 10
Step 2: Calculate sources power from equations. 11
Step 3: Create populations from set XT=[X1, X2, . . . , XT].12
Step 4: Applying power dispatched technique for creating 13
populations and calculations of fitness function. 14
Step 5: Identifying non-dominated solutions. 15
Step 6: Separates non-dominate solution and store it in 16
archives. 17
Step 7: Selecting leader from non-dominated sort. Criterion 18
to select leader from non-dominate sort is: Divide the require 19
spaces in equal pieces and apply PDF to every single space. 20
Therefore, roulette wheel will select the leader onward. 21
Step 8: Update particles velocities and positions in right 22
direction. 23
Step 9: Regenerating an every particles optimal position. 24
Positions are compared with previous positions. 25
pbest,j (t+ 1) =
pbest,j (t)pbest,j (t)< Xj(t+ 1)
Xj(t+ 1) Xj(t+ 1) < pbest,j (t)
select randomly
(pbest,j (t)or Xj(t+ 1)) otherwise
(35)
Step 10: Non-dominated solutions are added. 26
Step 11: Dominated solution. 27
Step 12: Removing exceeded members if exceeded then given 28
numbers. 29
Step 13: Best possible solutions. 30
For choosing the best possible solution, Pareto fronts criterion 31
using non-linear sorting fuzzy mechanism is used that finds a 32
suitable location of variables in the archive. σk
iindicates an 33
optimal number of objective functions j, Pareto-fronts kand 34
is given as: 35
36
σjk=
1fj≤fjmin
fjmax−fj
fjmax−fjmin fjmax < fj< fjmin
0fj≥fjmax
(36)
The upper and lower bounds of objective function jare fjmax 37
and fjmin. These values are calculated using optimization 38
results for each objective function. σk
iranges in [0,1] where σk
i39
= 0 represent incomplete solutions in given functions, where 40
σk
i= 1 represent complete solutions. MOPSO flow chart is 41
shown in Figure 5. 42
B. Multi-objective wind-driven optimization algorithm 43
The multi-objective energy optimization problems include 44
conflicting objectives under equality and inequality constraints, 45
9
Distributed
Generation
LC
LC
LC
LC LC
Micro Turbine
Photovoltaics Storage Devices Fuel cell
Wind Energy
Feeder 1 Feeder 2 Feeder 3
T/F 2
T/F 1
T/F 3
PCC
Utility Grid
Micro Grid central controller
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
DRPS + IBT
Figure 4: Real-life practical schematic diagram of smart microgrid
10
Table II: Offer prices and pollution emission coefficients of distributed generation sources.
Units Types Offer price Start/Shutting-down CO2 SO2 NOx Pmin Pmax
(Ect/kWh) Cost(Ect) (kg/MWh) (kg/MWh) (kg/MWh) (kW) (kW)
1 Diesel 0.586 0.15 890 0.0045 0.23 30 300
2 MT 0.457 0.96 720 0.0036 0.1 6 30
3 FC 0.294 1.65 440 0.003 0.0075 3 30
4 PVS 2.584 0 0 0 0 0 25
5 WES 1.073 0 0 0 0 0 15
6 Battery 0.38 0 10 0.0002 0.001 -30 30
7 Utility - 0 950 0.5 2.1 -30 30
Obtaining the amount of wind and solar
power from proposed equations.
Uncertainty modeling of wind power and
solar power using eq 15
Initialize MOPSO particles
Calculated objectives
Update best position from
every particle eq 34
Select leader from every
particle
Separating and manage
non-dominated solutions
and repository
Add non-dominated solution
to the repository
Determine non-dominated
solutions
M repository
> M identified
Eliminate
excess member
of repository
Max no of
iteration?
Final solution=
RMain
START
END
Figure 5: Multi-objective particle swarm optimization
algorithm implementation flow chart
which must be solved simultaneously. In this work, three1
conflicting objectives like operating cost, pollution emission,2
and availability must be optimized simultaneously. MOWDO3
algorithm is based on position and velocity consisting of 54
main functions: Schaffer function, Kita function, Kursawe5
function, ZDT1 and ZDT4 functions. The proposed multi-6
objective algorithm aims to optimize operating cost, pollution7
emission, and availability. Moreover, the operating cost is a8
non-convex optimization problem. Therefore, to avoid local9
minima, we increase the probability of exploration (global10
minimization) more than the probability of exploitation (local11
minimization) in the search space. The particle converges to12
global minimization, and local minimization is avoided for13
operating cost optimization. The MOWDO algorithm flow14
chart is shown in Figure 6. MOWDO algorithm uses Pareto15
set ranks to find the best possible solution with and without16
NO
YES
Step1: Initializing size of population, Max no
of iteration, upper and lower limits, and give
pressure function values.
Step2: Initializing exact particles
position and velocity.
Step3: Calling non-dominating sort after
evaluating population members.
Step4: Taking pareto-front rank into external papulation.
Step5: Updating velocity of particles.
Step6: Using archived population as a global best
and using pareto-rank instead of population rank.
Step7: Updating position of each particle.
Step8: Checking boundaries.
Step9: Pareto rank1 members of the archived
population are the final solution.
Step9: No. of iterations
> Max no of iterations?
END
STAR
Figure 6: Multi-objective wind-driven optimization algorithm
implementation flow chart
involvement in hybrid scheme DRPS and IBT [50]. 1
1) Schaffer Function: In this function, limits of variables 2
are [−103,103], and optimized solution ranges [0,2]. Schaffer 3
functions are: 4
f1(k) = k2, f2(k) = (k−2)2(37)
2) Kita Function: Here, the limits of variables are [0,7]. 5
Kita multi-objective functions are: 6
f1(k1, k2) = −k12+k2(38)
and 7
f2(k1, k2) = k1
2+k2+1 (39)
11
Algorithm 1: Pseudo-code of the multi-objective wind-driven optimization algorithm for energy optimization
Desired results:
Optimized operating cost and pollution emission, operating cost and availability ;
Initialization:
Population size, maximum iteration, boundaries, pressure function, particles positions;
Max velocity for MOWDO (vold) = ±[0.5];
Implementation:
Evaluate pressure function for each member in population during each iteration;
Assign Pareto-front sets to every member of the population based on sorting using equation;
This Pareto-fronts information is in equation;
Uv= (1 −k)Ub−gXb+
j−1
j
RT (Xmax −Xb)×1
jk×ukotherd
Rank 1 are the archived population members with Pareto-fronts;
Equation
Uv= (1 −k)Ub−gXb+
j−1
j
RT (Xmax −Xb)×1
jk×ukotherd
Shows global best solutions so far with the non-dominated Pareto-fronts;
Update velocity;
Check boundaries with termination;
while iteration <Max iteration do
for j=1 do
Check Pareto fronts information;
if Iteration=250? then
Pareto rank1 members of the archived population are the final solution;
otherwise, back to step no 3 shown in MOWDO flow chart in Figure 6
end
if Iteration not equal to 250? then
Go to step 1 shown in Figure 6;
end
if fitness values >desired values then
Go to step 1 shown in Figure 6;
end
end
for k=1do
for j=1do
Calculate fitness coefficients;
Check Pareto fronts;
Calculate final best results;
end
end
end
subject to:1
k1
6+k2≤13
2,k1
2+15
2,5k1+k2≤30 (40)
This function is used to utilize pressure effect.2
3) Kursawe Function: Here, the limits of variables are [-3
5,5]. Kursawe multi-objective functions are:4
f1(k) =
N−1
X
j=1
(−10 exp(−0.2qk2i+k2j+1)) (41)
1
f2(k) =
N
X
j=1
|kj|0.8+ 5 sin(k3j)) (42)
2
4) ZDT1 Function: Here, variable limits are [0, 1]. ZDT1 3
multi-objective functions are: 4
f1(k) = k1
and
f2(k) = g(k[1 −qk1
g(k)])
where g(k) = 1 + 9(
N
P
j=2
ki
(N−1) )
(43)
12
Step3:
Solutions
having Rank=1
START
END
Step1: Assigning rank according to Ri.
Step2:Assigning linear mapping
function to find best and worst
solutions.
Step 4: Calculate the row
fitness value of these
solutions.
Step5: Assigning fitness
function to each rank.
Step6: Mutate
Step7: Testing to terminate
Figure 7: Multi-objective genetic algorithm implementation
flow chart
5) ZDT4 Function: Here, variable limits are k1 = [0, 1], and1
kj = [-5, 5] for j=2,3. . . ,n. ZDT4 multi-objective functions are:2
f1(k) = k1
and
f2(x) = g(k)1−rk1
g(k)
and,
g(k) = 1 + 10(N−1)
+
N
P
i=2
(k2j−10 cos(4πkj))
(44)
Following are the steps for proposed MOWDO algorithm.3
Step 1: Initializing population size (number of population),4
iterations (maximum number of iteration for an optimized5
results), limits (maximum and minimum bounds) and6
defining pressure function (initialize pressure function given7
to MOWDO according to the proposed conditions) to the8
algorithm.9
Step 2: Initializing particle’s position (the current particles10
position which will be used ahead in the process in such a11
way that it will be compared with the new position of the12
particles) and particle velocity (vold)(similarly the current13
velocity (vold)of particles which will be used ahead in the14
process in such a way that it will be compared with the new15
velocity (vnew)of the particles ) to MOWDO.16
Step 3: Evaluating population members and calling non-17
dominated sort.18
Step 4: Taking pareto-front members into external population.19
Step 5: Updating velocity (in this step the particles velocity20
are updated, meaning the particles have new velocity (vnew). 1
Step 6: Using archived population as global best. 2
Step 7: Taking pareto-front instead of population rank. 3
Step 8: Updating position. 4
Step 9: Checking boundaries (limits). 5
Step 10: Checking maximum iteration of the MOWDO. 6
Step 11: If reached to maximum iteration, then Pareto-rank 7
members of the archive population are the final solution. If 8
not reached to maximum iteration then algorithm back to step 9
3 as shown in the flow chart in Figure 6. 10
11
C. Proposed method: Multi-objective genetic algorithm 12
MOGA algorithm flow chart is shown in Figure 7. MOGA 13
use the non-dominated classification of the GA population and 14
at the same time maintain diversity in non-dominated solutions 15
[51]. The solutions which are near to Pareto optimal front are 16
ranked equal to 1 are proposed. These solutions are optimal 17
solutions. Similarly, all other solutions are ranked accordingly, 18
based on their location. To find the rank of a solution, the 19
following equation is used: 20
Rk= 1 + NK(45)
where Rkindicates the rank of solutions and NKrepresents 21
that how many solutions are there which can dominate the 22
solution k, if a large number of solutions dominates, it means 23
that the rank is higher. To combine more than one objective, 24
the equation as follows: 25
F(X) = m1·F1(X) + .... +mj·Fj(X) + ...... +mNfN(X)
(46)
where Xis string of the rank, F(X) is fitness function, Fj(X)26
is jth objective function and m1is a constant weight which 27
indicates objectives function. The operating cost is non-convex 28
optimization problem, therefore, to avoid local minima, in the 29
search space, we increase the probability of exploration (global 30
minimization) more than the probability of exploitation (local 31
minimization). The particle converges to global minimization 32
and local minimization avoided for operating cost optimiza- 33
tion. Flow chart of proposed method MOGA is shown in 34
Figure 7 and stepwise procedure of MOGA is as follows. 35
Step 1: Assigning rank according to Rk.36
Step 2: Using linear mapping function (LMF) to assign row 37
fitness to each solution. Linear mapping function will assign 38
the row fitness, also assign the row fitness function for the 39
worst solutions. 40
Step 3: Calculating the average of row fitness values for each 41
rank solutions. If the rank is 1 then checked the number of 42
solutions having rank 1, take the average of row fitness value 43
of these solutions. 44
Step 4: Applying crossover to each of assign values to produce 45
new string. 46
Step 5: Applying mutate. 47
Step 6: Algorithm returns to step number 1, if satisfying 48
conditions are not valid. 49
Now here we discussed that how to assign fitness values to 50
MOGA. 51
MOGA fitness assignment: Assign fitness values are calculated 52
13
Algorithm 2: Pseudo-code of multi-objective genetic algorithm for energy optimization
Inputs:
Population size, max iteration, Boundary conditions, crossover, mutation;
Output:
Optimization of operating cost and pollution emission, and operating cost and availability using RES;
Initialization:
Nk= No of solutions assigned;
Ri= Rank of solutions;
σshare= A constant which determines distance between two solutions;
Step1: Assigning Rank Rk=s, where s=1,2,3,.........................n;
Step2: Using LMF to assign row fitness to each solution to number of best and worst solutions;
Implementation:
Step3: Choose solutions having rank 1;
Step4: Calculate the average of row fitness value for each rank solutions;
Step5: Assigning fitness to each rank;
step6: Applying mutate;
Fitness assignment to MOGA Choose σshare;
Compute Rk and Nk using equation;
while iter <Maximum iterations do
for Rk=1 do
using equation Rk=1+Nk and check number of solutions having Rk=1;
Take average of row fitness value of obtained solutions;
if k∝N,K=K+1 then
back to step 1 as shown in MOGA flow chart in Figure 7;
otherwise, Go to step 4;
end
if Rk= other than 1 then
move to step 1;
Apply crossover to each assigned values to produce new string;
end
if conditions satisfied then
Pareto ranks are checked;
Apply mutate;
end
end
for Rk=1 do
for j=1do
Getting desired Pareto-fronts ranks;
Execution go back to step 1 if the following conditions are not satisfied;
end
end
end
as follows:1
Step 1: Choose σshare, which is a constant variable, denotes2
that how much distance is considered between two solutions.3
If σshare has a lower value then we say that the solutions are4
near.5
Step 2: Compute the number of solutions Nkand rank of6
solution Rkas shown in Equation 47.7
Step 3: If k∝N,k=k+1 then go to step 1. Otherwise, go to8
step 4 shown in MOGA flow chart 7.9
Step 4: Identify max rank Rk.10
The assign fitness value is called average fitness value, and11
given as follows: 1
Fk=Nk−
Rk+1
X
k=1
µ(k)−0.5[µ(Rk)−1] (47)
Equation 47 will give average fitness to each solution k. Where 2
Nkis total number of solutions, µkis number of solutions of 3
the rank Rk,µ(Rk)are the number of solutions in the current 4
rank. For every solution in the rank, we have to calculate the 5
niche count and as calculated as follows: 6
Nck=
µ(Rk)
X
j=1
sh(dkj)(48)
14
where kand jare two different solutions which must be in1
the same rank, (dkj) is a share fitness value. In this work, the2
computational time of the proposed and existing methods is3
evaluated in terms of convergence towards the best solution.4
The results of MOPSO, MOWDO and MOGA algorithms5
in terms of computational time and convergence rate are6
listed in Table III. It is obvious from the results that the7
number of iterations are set to 200 for the proposed and8
existing methods, the proposed method converged to the global9
best solution after 140 iterations while the existing methods10
(MOGA and MOPSO) converged after 160 and 180 iterations.11
Thus, the proposed method is faster in terms of convergence12
to the global best solution because it obtained the global best13
solution after 140 iterations, which is minimum compared to14
the existing methods. This faster convergence of the proposed15
method is due to the optimal section of control parameters like16
population size, upper and lower bounds, etc.
Table III: Proposed and existing algorithms convergence
assessment
Algorithms Iterations Convergence Computational time
MOPSO 200 180 40 sec
MOGA 200 160 34 sec
MOWDO 200 140 29 sec
17
IV. SIMULATION RESULTS,PERFORMANCE EVALUATIONS,18
AND DISCUSSIONS19
The smart microgrid is connected with a power gird serving20
three types of consumers residential, industrial and com-21
mercial, whose demand load curves are shown in Figure22
8 [52], [53]. The proposed optimization model consists of23
various participants like consumers (residential, commercials24
and industrials), sources (DGS, PVS, WES, Battery, Grid,25
MT, FC), and objective functions (operating cost and pollution26
emission, operating cost and availability) are shown in Figure27
4. The SG is connected with different types of consumers,28
units, substation and market operation, as shown in Figure29
4. From the weather forecast web site (Willy.Online.Ply.Ltd),30
the speed of the wind is shown in Figure 10 [54], which31
depicts data is collected for two days (48 hours). One day32
has the highest wind speed and the second day has the lowest33
wind speed. 25 kW SOLAREX MSX solar cells are proposed,34
containing arrays (10 ×2.5kW )with h=18.5% and s=10m35
[55]. Figure 11 indicates solar irradiance for 48 hours period36
[56]. Solar irradiance is taken for two days: sunny day and37
cloudy day. The sunny day has high solar irradiance. In38
contrast, day two, which is cloudy, having a lower intensity of39
solar irradiance. Both wind and solar energy systems have a40
power coefficient equal to 1. In contrast, other power sources41
and loads compensate for the required reactive power through42
capacitor banks installed on buses. The battery of 30 kWh43
capacity is considered in this work. The lower and upper limit44
is adjusted to 15% and 100% of the capacity for discharging45
and charging, respectively. The state of charge is controlled46
with efficiency of 95.5% [57]-[58]. The power consumed is47
assumed to be 4080kWh with a 1.33 V/kWh value of load48
lost. Offered price packages for implementation of the hybrid49
scheme of DRPS and IBT are listed in Table I and the actual 1
market price of APX is shown in Figure9. The demand- 2
side consumers, residential, commercial, and industrial, are 3
encouraged to participate in the hybrid scheme of DRPS and 4
IBT. 5
0 10 20 30 40 50
Time (h)
0
40
80
120
Demand (%age of maximum)
Residentail
Industrial
Commercial
Figure 8: Daily load curve end-users of residential,
commercial, and industrial sectors.
0 2 4 6 8 10 12 14 16 18 20 24 48
Time (h)
0
1.5
3
4.5
6
7.5
9
Real Time Market Price
Figure 9: The real-time market prices of APX.
0 10 20 30 40 50
time (h)
0
5
10
15
20
wind speed (m/s)
Figure 10: Wind speed forecasting with hour resolution.
To evaluate the effectiveness of the proposed model in 6
energy optimization, DRPS+IBT in operating cost, pollution 7
emission, and availability functions, to solve the uncertainty 8
issues caused by solar and wind RES by implementing DRPS 9
and IBT, the evaluation is considered in two different cases as 10
follows. 11
Case I: Optimization of operating cost and pollution 12
emission with and without involvement in the hybrid scheme 13
of DRPS and IBT. 14
Cas II: Optimization of operating cost and availability with 15
15
Table IV: Renewable energy sources like wind and solar power generation capacity comparison from the perspective of
operating cost and pollution emission with and without involvement in hybrid scheme of DRPS and IBT.
Cases Wind Power Solar Power Wind Power Solar Power Cover percentage Cover percentage
(kW) (kW) Factor (kW) Factor (kW) of wind power of solar power
Operating cost 9.11 5.22 57.15 91.47
without DRPS and IBT
Operating cost 7.07 3.03 57.15 91.47 8.2% 31.1%
with DRPS and IBT
Pollution emission 51.705 93.32 57.15 91.47
without DRPS and IBT
Pollution emission 45.81 87.05 57.15 91.47 6.8% 2.4%
with DRPS and IBT
Simultaneous optimization 25.33 92.11 57.15 91.47
without DRPS and IBT
Simultaneous optimization 20.93 75.13 57.15 91.47 5.1% 13.8%
with DRPS and IBT
0 10 20 30 40 50
Time (h)
0
0.5
1
1.5
2
2.5
3
Solar irradiance (kw/m2)
Figure 11: Solar irradiance forecasting with hour resolution.
and without involvement in the hybrid scheme of DRPS and1
IBT.2
3
In the cases mentioned above, all the power sources actively4
participate in the smart microgrid under their ecumenical and5
technical constraints to coordinate energy exchange with utility6
and consumers through a point of common coupling (PCC) to7
ensure economical, sustainable, secure and reliable operation.8
The proposed energy optimization model is developed in9
MATLAB 2017b to solve multi-objective energy optimization10
problems by catering operational cost and pollution emission,11
operating cost and availability, simultaneously, with and with-12
out involvement in the hybrid scheme of DRPS IBT.13
Case 1: Optimization of operating cost and pollution emis-14
sion with and without involvement in the hybrid scheme of15
DRPS and IBT.16
In this case, first operating cost and pollution emission are17
optimized without involvement in the hybrid scheme of DRPS18
and IBT. The optimal engagement of power sources in the19
smart microgrid to minimize operating cost and pollution20
emission are listed in Tables V and VI, respectively. It is21
obvious from Table V that in early hours where the price22
of energy is low, the battery must be charged on a priority23
basis. In contrast, during 9 to 16 hours where energy prices24
are high, the utility purchases energy from the smart microgrid25
DGs on a priority basis. In this manner, the operational cost is26
maintained optimized in the proposed model. Similarly, Table27
VI results represent that in most cases, the utility purchases28
energy from DGs of the smart microgrid to ensure minimum29
pollution emission. Since wind and solar most of the time 1
reach their maximum generation without causing any pollution 2
are considered in pollution emission function, which is shown 3
in Figure 18b. On the other hand, these resources offered 4
prices are higher compared to the power sources. Therefore, 5
they are ignored in the optimization of operation cost. 6
In the second part of case I, the optimization of operational 7
cost and pollution emission with the hybrid scheme of DRPS 8
and IBT is discussed. The power sources are optimally en- 9
gaged to minimize operation cost and pollution emission, and 10
results obtained are list in Tables VII and VIII, respectively. 11
From the results presented for case I, it is concluded that 12
the power sources are more optimized with involvement 13
in hybrid scheme DRPS and IBT compared to without 14
involvement case. Comparison results presented in Tables V 15
and VII illustrate that involvement in hybrid scheme DRPS 16
and IBT, production of wind energy reduced from 9.71 kW to 17
6.45 kW, and solar power generation reduced from 6.09 kW 18
to 3.20 kW. In contrast, the optimization of emission function 19
with and without involvement in the hybrid scheme of DRPS 20
and IBT shows that the use of hybrid scheme reduces the 21
production of wind from 52.11 kW to 44.48 kW, and from 22
93.32 kW to 87.13 kW. To visualize the energy produced by 23
solar and WES considering operation cost and emissions with 24
and without involvement in the hybrid scheme are depicted 25
in Figures 12a and 12b, respectively. Figure 13 indicates that, 26
in the case of emission function, a hybrid scheme lowers the 27
generation capacity of solar and WES and shifts the load from 28
on-peak to off-peak hours while ensuring the formation of 29
rebound peaks. In this case, the consumers participate in the 30
hybrid scheme of DRPS and IBT and agree that utility will 31
alleviate their energy consumption during specific scheduled 32
hours. It may also allow the utility operator to minimize the 33
scheduled power of power sources and avoid rebound peaks. 34
This behavior of consumers load demand before and after 35
involvement in DRPS and IBT are shown in Figure 13. 36
37
Case II: In case II, the operating cost reduction and 38
availability maximization with and without involvement in 39
the hybrid scheme of DRPS and IBT. The operational cost 40
reduction and availability of RES maximization are evaluated 41
on MOWDO and MOGA algorithms compared to the MOPSO 42
algorithm. The results obtained are graphically presented in 43
16
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
50
100
150
WT power (kw)
WT power for Emission cost with (DRPS+IBT)
WT power for Operation cost with (DRPS+IBT)
Forecast
(a) Wind turbine
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
30
60
90
120
150
PV power (kW)
PV Power for Emission Cost with (DRPS+IBT)
PV Powr for Operation Cost with (DRPS+IBT)
Forecast
(b) Solar cell
Figure 12: Output power of renewable energy sources integrated with SG considering operating cost and pollution with
involvement in hybrid of scheme of DRPS and IBT)
Table V: Energy resources optimization without involvement in hybrid DRPS and IBT for operating cost function. Optimized
resources like DGS, MT, FC, WES, PVS, battery, and utility are expressed in kW.
Hours DGS MT FC WES PVS Battery Utility
1 30.000 7.9514 7.283 0.178 0.000 11.587 30.000
2 32.287 12.912 27.010 0.178 0.000 -19.688 26.299
3 45.130 7.189 20.433 0.069 0.000 -19.786 21.963
4 38.075 6.000 24.565 0.000 0.000 -30.000 29.359
5 30.000 8.835 13.956 0.403 0.000 -14.207 26.011
6 37.393 8.068 23.610 0.091 0.000 -21.391 23.818
7 30.000 12.489 19.287 0.016 0.000 -0.705 22.912
8 33.650 9.813 26.953 0.066 0.075 26.505 22.939
9 104.78 28.71 21.210 0.178 0.112 30.000 -30.000
10 234.763 6.000 3.213 0.000 0.000 -15.975 -30.000
11 211.313 8.245 19.145 0.000 0.851 15.444 -30.000
12 283.868 6.000 5.132 0.000 0.000 -30.000 -30.000
13 272.073 6.000 8.400 0.054 1.695 -28.255 -29.966
14 218.992 13.747 24.529 0.473 0.342 21.758 -29.843
15 213.897 14.123 28.932 0.714 0.859 27.265 -29.791
16 226.268 13.190 6.804 0.300 0.338 24.099 -30.000
17 114.225 29.999 29.974 0.000 0.550 30.000 25.252
18 95.459 27.799 30.000 0.741 0.000 30.000 30.000
19 105.819 29.999 30.000 1.302 0.000 30.000 29.879
20 122.196 14.555 29.017 0.000 0.000 26.876 27.355
21 155.728 28.322 28.442 1.300 0.000 30.000 -23.792
22 79.629 28.946 26.685 0.555 0.000 29.860 29.323
23 272.073 6.000 8.400 0.054 1.695 -28.255 -29.966
24 218.992 13.747 24.529 0.473 0.342 21.758 -29.843
25 213.897 14.123 28.932 0.714 0.859 27.265 -29.791
26 226.268 13.190 6.804 0.300 0.338 24.099 -30.000
27 114.225 29.999 29.974 0.000 0.550 30.000 25.252
28 95.459 27.799 30.000 0.741 0.000 30.000 30.000
29 105.819 29.999 30.000 1.302 0.000 30.000 29.879
30 122.196 14.555 29.017 0.000 0.000 26.876 27.355
31 155.728 28.322 28.442 1.300 0.000 30.000 -23.792
32 79.629 28.946 26.685 0.555 0.000 29.860 29.323
33 104.789 28.719 21.210 0.178 0.112 30.000 -30.000
34 234.763 6.000 3.213 0.000 0.000 -15.975 -30.000
35 211.313 8.2457 19.145 0.000 0.851 15.444 -30.000
36 283.868 6.000 5.132 0.000 0.000 -30.000 -30.000
37 272.073 6.000 8.400 0.054 1.695 -28.255 -29.966
38 218.992 13.747 24.529 0.473 0.342 21.758 -29.843
39 213.897 14.123 28.932 0.714 0.859 27.265 -29.791
40 226.268 13.190 6.804 0.300 0.338 24.099 -30.000
41 114.225 29.999 29.974 0.000 0.550 30.000 25.252
42 95.459 27.799 30.000 0.741 0.000 30.000 30.000
43 105.819 29.999 30.000 1.302 0.000 30.000 29.879
44 122.196 14.555 29.017 0.000 0.000 26.876 27.355
45 155.728 28.322 28.442 1.300 0.000 30.000 -23.792
46 79.629 28.946 26.685 0.555 0.000 29.860 29.323
47 54.699 29.097 25.325 0.717 0.000 25.161 30.000
48 31.509 10.515 26.946 0.172 0.000 28.682 25.174
17
Table VI: Energy resources optimization without hybrid scheme of DRPS and IBT for pollution emission function. The
optimized resources like DGS, MT, FC, WES, PVS, battery, and utility are expressed in kW.
Hours DGS MT FC WES PVS Battery Utility
1 39.654 20.999 32.918 2.428 0.000 31.078 -30.000
2 35.000 26.862 30.000 1.428 0.000 29.518 -28.567
3 35.000 16.837 32.317 2.428 0.000 30.975 -28.547
4 35.105 8.678 28.565 0.781 0.000 30.576 -29.133
5 35.000 9.000 26.000 2.758 0.000 31.988 -32.981
6 35.000 19.279 27.000 0.9146 0.000 31.301 -29.288
7 36.727 29.000 31.678 2.501 0.000 30.735 -28.262
8 55.71 31.000 33.000 2.305 0.275 29.525 -12.000
9 64.526 32.726 29.456 2.630 4.112 30.000 -11.000
10 116.604 30.000 32.000 2.809 12.000 31.975 -20.000
11 129.775 30.000 30.999 11.775 13.851 31.444 -30.000
12 159.640 31.000 30.999 12.410 25.010 31.060 -30.000
13 148.210 28.000 29.988 4.915 21.695 29.245 -29.966
14 223.992 29.000 30.000 3.345 8.342 29.988 -24.843
15 168.908 28.987 30.000 1.980 4.819 32.205 -15.791
16 177.367 31.869 32.019 1.784 0.938 32.080 -19.000
17 165.097 31.999 32.953 1.993 0.550 31.060 -25.252
18 159.091 31.000 33.000 1.985 0.000 31.067 -30.000
19 157.215 27.000 28.812 1.310 0.000 32.340 29.879
20 119.726 29.540 29.986 1.310 0.000 26.886 29.355
21 111.116 29.322 30.000 1.320 0.000 30.800 23.792
22 76.699 31.000 33.000 1.555 0.000 32.810 29.323
23 148.210 28.000 29.988 4.915 21.695 29.245 -29.966
24 223.992 29.000 30.000 3.345 8.342 29.988 -24.843
25 168.908 28.987 30.000 1.980 4.819 32.205 -15.791
26 177.367 31.869 32.019 1.784 0.938 32.080 -19.000
27 165.097 31.999 32.953 1.993 0.550 31.060 -25.252
28 159.091 31.000 33.000 1.985 0.000 31.067 -30.000
29 157.215 27.000 28.812 1.310 0.000 32.340 29.879
30 119.726 29.540 29.986 1.310 0.000 26.886 29.355
31 111.116 29.322 30.000 1.320 0.000 30.800 23.792
32 76.699 31.000 33.000 1.555 0.000 32.810 29.323
33 64.526 32.726 29.456 2.630 4.112 30.000 -11.000
34 116.604 30.000 32.000 2.809 12.000 31.975 -20.000
35 129.775 30.000 30.999 11.775 13.851 31.444 -30.000
36 159.640 31.000 30.999 12.410 25.010 31.060 -30.000
37 148.210 28.000 29.988 4.915 21.695 29.245 -29.966
38 223.992 29.000 30.000 3.345 8.342 29.988 -24.843
39 168.908 28.987 30.000 1.980 4.819 32.205 -15.791
40 177.367 31.869 32.019 1.784 0.938 32.080 -19.000
41 165.097 31.999 32.953 1.993 0.550 31.060 -25.252
42 159.091 31.000 33.000 1.985 0.000 31.067 -30.000
43 157.215 27.000 28.812 1.310 0.000 32.340 29.879
44 119.726 29.540 29.986 1.310 0.000 26.886 29.355
45 111.116 29.322 30.000 1.320 0.000 30.800 23.792
46 76.699 31.000 33.000 1.555 0.000 32.810 29.323
47 48.515 31.573 32.999 0.917 0.000 29.121 31.456
48 41.253 33.227 34.000 0.619 0.000 32.632 -27.674
0 4 8 12 16 20 24 28 32 36 40 44 48
time (h)
0
50
100
150
200
250
300
Demand (KW)
After (DRPS+IBT)
Before (DRPS+IBT)
Figure 13: Consumers load demand with and without
implementation of hybrid scheme of DRPS and IBT
Figure 19, it is obvious that the operating cost is reduced by 1
7% with involvement in the hybrid scheme of DRPS and IBT 2
and 4% without involvement in the hybrid scheme of DRPS 3
and IBT and the availability of RES is maximized by 15% and 4
11%, as compared to MOPSO algorithm, respectively. Simi- 5
larly, the results of Figure 19 show the convergence character- 6
istics of the MOWDO algorithm to optimize operating cost and 7
maximize the availability of RES. Simulation results show that 8
the operating cost is reduced by 9% and 6% with and without 9
DRPS and IBT, at the same time, the availability of RES is 10
maximized by 20% and 17%, respectively. The convergence 11
characteristics of the MOGA algorithm is shown in Figure 19. 12
The results of Figure 19 shows the operating cost reduction 13
and availability maximization with and without involvement 14
in the hybrid scheme of DRPS and IBT. Simulation results 15
18
1550 1600 1650 1700 1750
Oprating cost(Ect)
2200
2250
2300
2350
2400
2450
2500
Emission(Kg)
Pareto set solutions
MOPSO without (DRPS+IBT)
MOWDO without (DRPS+IBT)
y=2498
x=1627
Min Cost
Min Emission
x=1980
y=2202
y=2370
x=1744
Best solution without (DRPS+IBT)
(a) Without hybrid scheme of DRPS and IBT
1400 1450 1500 1550 1600
Oprating cost(Ect)
1900
1950
2000
2050
2100
2150
2200
Emission(Kg)
Pareto set solutions
MOPSO with (DRPS+IBT)
MOWDO with (DRPS+IBT)
x=1595
y=2075
x=1840
y=1905
Min Emission
Min Cost
x=1477
y=2190
Best solution with (DRPS+IBT)
(b) With hybrid scheme of DRPS and IBT)
Figure 14: Pareto-fronts criterion using MOPSO and MOWDO algorithms for operating cost and pollution emission
with/without hybrid scheme of DRPS and IBT
1700 1750 1800 1850 1900 1950 2000
Oprating cost(Ect)
2200
2250
2300
2350
2400
2450
2500
Emission(Kg)
Pareto set solutions
MOPSO without (DRPS+IBT)
MOGA without (DRPS+IBT)
x=1775
y=2320
y=2250
Min Emission
x=1950
Min Cost
x=1700
y=2470 MOGA:Best solution without (DRPS+IBT)
(a) Without hybrid scheme of DRPS and IBT
1500 1550 1600 1650 1700 1750 1800
Oprating cost(Ect)
2000
2050
2100
2150
2200
2250
Emission(Kg)
Pareto set solutions
MOPSO with (DRPS+IBT)
MOGA with (DR+IBT)
x=1750
y=2095
Min Cost
x=1505
y=2225 MOGA: Best solution with (DRPS+IBT)
x=1590
y=2120
Min Emission
(b) With hybrid scheme of DRPS and IBT
Figure 15: Pareto-fronts criterion using MOPSO and MOGA algorithms for operating cost and pollution emission
with/without hybrid scheme of DRPS and IBT
1500 1550 1600 1650 1700 1750
Operating cost (Ect)
2200
2250
2300
2350
2400
2450
2500
Emission (Kg)
MOWDO without (DRPS+IBT)
Pareto set solutions
MOGA without (DRPS+IBT)
MOPSO without (DRPS+IBT)
Min Operating Cost
Min Emission
Best Solution without (DRPS+IBT)
(a) Without hybrid scheme of DRPS and IBT
1500 1550 1600 1650 1700 1750
Operating Cost (Ect)
2200
2250
2300
2350
2400
2450
2500
Emission (Kg)
MOWDO with (DRPS+IBT)
Pareto set solutions
MOGA with (DRPS+IBT)
MOPSO with (DRPS+IBT)
Min Emission
Best Solution with (DRPS+IBT)
Min Operating Cost
(b) With hybrid scheme of DRPS and IBT
Figure 16: Pareto-fronts criterion using MOPSO, MOGA, and MOWDO algorithms for operating cost and pollution emission
with/without hybrid scheme of DRPS and IBT
show that the operating cost is reduced by 12% and 6% with1
and without DRPS and IBT, at the same time, the availability2
of RES is maximized by 25% and 19%, respectively. The3
comparison of MOPSO, MOWDO and MOGA results are4
shown in Tables IX and X, respectively. From the proposed5
model, the operating cost reduction and availability of RES6
maximization are more with involvement in the hybrid scheme7
of DRPS and IBT compared to existing models and without8
participation in the hybrid scheme of DRPS and IBT.9
From the above-mentioned simulation results of cases I10
and II, the following discussion is concluded. The proposed11
energy optimization model optimally allocates power sources 1
in a smart microgrid for simultaneous catering operating cost 2
and pollution emission as two conflicting functions with and 3
without involvement in the hybrid scheme of DRPS and IBT. 4
According to Figures 14a, 14b, 15a, 15b, 16a and 16b, since 5
the operation cost and pollution emission objectives are con- 6
flicting, moving from the starting point of the curve towards 7
the endpoint, the Pareto fronts are equal to the change in 8
operating behavior from lowest costs and highest emissions, to 9
highest costs and lowest emissions, where a fuzzy mechanism 10
19
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
10
20
30
40
50
WT power (kW)
Multi objective optimization
Emission optimization
Cost optimization
(a) Wind turbine
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
15
30
45
60
75
PV Power (kW)
Multi objective optimization
Emission optimization
Cost optimization
(b) Solar cells
Figure 17: Renewable energy sources like wind and solar power generation for multi-objective optimization: operating cost
and pollution emission
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
10
20
30
40
50
WT power (kW)
WT Power for Emission Cost without (DRPS+IBT)
WT Powr for Operation Cost without (DRPS+IBT)
Forecast
(a) Wind turbine
0 4 8 12 16 20 24 28 32 36 40 44 48
Time (h)
0
30
60
90
120
150
PV power (kW)
PV Power for Emission Cost without (DRPS+IBT)
PV Powr for Operation Cost without (DRPS+IBT)
Forecast
(b) Solar cell
Figure 18: Output power of renewable energy sources integrated with smart microgrid considering operating cost and
pollution without hybrid scheme of DRPS and IBT
(a)
1 1.1 1.2 1.3 1.4 1.5
6
1
0.99
0.98
0.97
0.96
0.95
Availability
MOGA with DRPS+IBT
MOGA without DRPS+IBT
Max Operating Cost
Max Availability
Min Operating Cost
Min Availability
Best solution with and without (DRPS+IBT)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Oprating cost(Ect)*106
1
1.5
2
2.5
Availability
MOPSO with (DRPS+IBT)
MOPSO without (DRPS+IBT)
Min Operating cost
Min Availability
Max Operating cost
Max Availability
Best solution with and without (DRPS+IBT)
1 1.1 1.2 1.3 1.4 1.5 1.6
Operating cost (Ect)*106
Operating cost (Ect)*10
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
Availability
MOWDO without DRPS+IBT
MOWDO with DRPS+IBT
Min Operating Cost
Min Availability
Max Operating Cost
Max Availability
Best solution with and without (DRPS+IBT)
(b) (c)
Figure 19: Pareto-fronts criterion using MOPSO, MOGA, and MOWDO algorithms for operating cost and availability of
RES with/without involvement in hybrid scheme of DRPS and IBT
can compute the optimal operating point and best solutions.1
Figures 14a, 14b, 15a, 15b, 16a and 16b illustrate that using2
the hybrid scheme of DRPS and IBT helps to obtain optimal3
operation point such that where operation cost and pollution4
emission through MOGA are reduced by 24.5% and 19%5
and through MOWDO are minimized by 26 % and 13 %6
respectively, as compared to MOPSO algorithm.7
Figures 17a and 17b illustrates that the amount of solar and8
wind RES minimize operating cost and pollution emission9
functions, simultaneous minimization of both functions, and10
ensure avoidance of rebound peaks creation with involvement11
in the hybrid scheme of DRPS and IBT. Furthermore, it is 1
obvious from the results solar and wind power generation is 2
related to pollution emission function. Therefore, by simul- 3
taneous optimization, a balance is established between them. 4
Simulation results listed in Table IV are for better assessment 5
of output solar and power from the aspects of operating cost 6
and emission with and without involvement in the hybrid 7
scheme of DRPS and IBT. Results depict that in case I, the 8
state of catering operating cost is the optimal state that resolves 9
uncertainty caused by solar and wind power sources. Similarly, 10
for case II, results are listed in IX, which illustrates that the 11
20
Table VII: Energy resources optimization with involvement in hybrid scheme of DRPS and IBT for operating cost function.
The optimally engaged resources like DGS, MT, FC, WES, PVS, battery, and utility are expressed in kW.
Hours DGS MT FC WES PVS Battery Utility
1 39.654 10.999 10.918 0.428 0.000 0.768 30.000
2 37.000 11.862 13.00 0.428 0.000 -16.51 26.567
3 36.000 13.837 13.31 0.428 0.000 -19.97 29.547
4 32.105 11.678 21.5 0.781 0.000 -29.57 29.133
5 37.000 8.000 3.000 0.758 0.000 -29.99 3.981
6 39.000 7.279 7.000 0.914 0.000 -21.30 16.288
7 38.727 6.000 25.67 0.50 0.000 -29.73 28.262
8 58.717 10.000 29.000 0.305 0.275 -3.525 2.009
9 67.526 9.726 22.456 0.630 0.112 -20.00 -32.000
10 163.60 20.000 17.000 0.809 0.000 26.975 -32.000
11 229.7 4.000 5.999 0.775 0.851 28.444 -32.000
12 209.64 6.000 15.998 0.410 0.010 18.060 -30.000
13 247.21 5.000 27.988 0.915 0.695 -1.245 -30.966
14 223.99 5.000 5.000 0.345 0.342 -4.988 -34.843
15 268.90 28.987 27.000 0.980 0.819 -7.205 -32.791
16 219.36 15.869 25.019 0.78 0.938 -3.080 -32.000
17 121.09 31.999 29.953 1.99 0.550 11.060 7.252
18 45.091 31.000 29.000 0.98 0.000 5.067 29.000
19 51.215 33.00 30.812 1.31 0.000 30.34 31.879
20 87.726 33.54 28.986 1.31 0.000 27.88 31.355
21 91.116 29.32 24.000 0.32 0.000 25.80 -29.792
22 27.699 18.000 19.000 0.55 0.000 30.81 29.323
23 247.21 5.000 27.988 0.915 0.695 -1.24 -30.966
24 223.99 5.000 5.000 0.345 0.342 -4.98 -34.843
25 268.90 28.987 27.000 0.980 0.819 -7.20 -32.791
26 219.36 15.869 25.019 0.784 0.938 -3.08 -32.000
27 121.09 31.999 29.953 1.993 0.550 11.06 7.252
28 45.091 31.000 29.000 0.985 0.000 5.067 29.000
29 51.215 33.00 30.812 1.310 0.000 30.34 31.879
30 87.726 33.54 28.986 1.310 0.000 27.886 31.355
31 91.116 29.32 24.000 0.320 0.000 25.800 -29.792
32 27.699 18.000 19.000 0.535 0.000 30.810 29.323
33 67.526 9.726 22.456 0.630 0.112 -20.00 -32.000
34 163.60 20.000 17.000 0.809 0.000 26.975 -32.000
35 229.7 4.000 5.999 0.775 0.851 28.444 -32.000
36 209.64 6.000 15.999 0.410 0.010 18.060 -30.000
37 247.21 5.000 27.988 0.915 0.695 -1.245 -30.966
38 223.99 5.000 5.000 0.345 0.3428 -4.988 -34.843
39 268.90 28.987 27.000 0.980 0.8178 -7.205 -32.791
40 219.36 15.869 25.019 0.784 0.938 -3.080 -32.000
41 121.09 31.999 29.953 1.993 0.550 11.060 7.252
42 45.091 31.000 29.000 0.985 0.000 5.067 29.000
43 51.215 33.00 30.812 1.310 0.000 30.340 31.879
44 87.726 33.54 28.986 1.310 0.000 27.886 31.355
45 91.116 29.32 24.000 0.320 0.000 25.800 -29.792
46 27.699 18.000 19.000 0.555 0.00 30.810 29.323
47 4.515 15.573 27.999 0.917 0.000 23.121 31.456
48 29.253 16.22 30.000 0.619 0.000 -22.632 29.674
state of considering the availability of RES is the optimal state1
to resolve uncertainty caused by solar and wind power sources.2
Thus, from the above results and discussions, we come3
across to the conclusion that our developed energy optimiza-4
tion model based on MOWDO and MOGA has outstanding5
performance compared to the benchmark model in both cases6
with and without involvement in the hybrid scheme of DRPS7
and IBT.8
V. CONCLUSION9
An energy optimization model based on MOWDO and10
MOGA is developed for a smart microgrid by considering11
a novel hybrid scheme of DRPS and IBT as the program12
to cater to the uncertainty caused by solar and wind power13
sources of optimization function with conflicting objectives.14
The operating cost of smart microgrid, availability of RES, 1
and pollution emission caused by different power sources are 2
considered in two separate cases. The probabilistic method 3
is used to model and predict the non-linear and stochastic 4
behavior of solar and wind power generation. To ensure 5
optimal performance of smart microgrid power exchange co- 6
ordination with the electric utility company and consumers 7
is considered. Furthermore, to control energy consumption 8
and rebound peaks creation, consumers are encouraged to 9
participate in the hybrid scheme of DRPS and IBT via giving 10
incentives in the form of a price offer package. The energy 11
optimization model based on MOWDO and MOGA uses the 12
Pareto criterion and fuzzy mechanism to solve smart microgrid 13
energy optimization problems and obtain an optimal response. 14
Simulation results showed that when consumers participating 15
21
Table VIII: Energy resources optimization with involvement in hybrid scheme of DRPS+IBT for pollution emission function.
Optimally engaged resources like DGS, MT, FC, WES, PVS, battery, and utility are expressed in kW.
Hours DGS MT FC WES PVS Battery Utility
1 29.654 5.999 9.918 0.028 0.000 26.078 -30.000
2 29.000 6.862 23.000 0.328 0.000 28.518 -24.567
3 29.000 11.837 22.317 0.000 0.000 29.975 -27.547
4 29.105 5.678 22.565 0.000 0.000 19.576 -29.133
5 29.000 4.000 23.000 2.758 0.000 30.988 -31.981
6 29.000 6.279 27.000 0.918 0.000 5.301 -29.288
7 31.727 9.000 25.678 0.501 0.000 21.735 -28.262
8 29.717 9.000 33.000 0.305 0.000 29.525 29.000
9 34.526 27.726 29.456 0.630 3.112 29.000 -28.000
10 38.604 26.000 32.000 2.809 7.000 23.975 -20.000
11 76.775 30.000 30.999 10.775 9.851 26.444 20.000
12 100.640 28.000 30.999 16.410 11.010 21.060 15.000
13 148.210 28.000 29.988 2.915 21.695 29.245 29.966
14 42.992 25.000 25.000 1.345 23.342 27.988 1.843
15 129.908 28.987 27.000 2.980 7.819 23.205 15.791
16 126.367 31.869 23.019 1.784 5.938 29.080 19.000
17 165.097 26.999 21.953 1.993 0.550 28.060 30.252
18 77.091 29.000 19.000 1.985 0.000 30.067 5.000
19 57.215 25.000 26.812 1.310 0.000 30.340 23.879
20 59.726 26.540 25.986 1.310 0.000 26.886 18.755
21 67.116 28.322 27.000 1.320 0.000 27.800 29.792
22 41.699 28.000 25.000 1.555 0.000 26.810 17.323
23 148.210 28.000 29.988 2.915 21.695 29.245 29.966
24 42.992 25.000 25.000 1.345 23.342 27.988 1.843
25 129.908 28.987 27.000 2.980 7.819 23.205 15.791
26 126.367 31.869 23.019 1.784 5.938 29.080 19.000
27 165.097 26.999 21.953 1.993 0.550 28.060 30.252
28 77.091 29.000 19.000 1.985 0.000 30.067 5.000
29 57.215 25.000 26.812 1.310 0.000 30.340 23.879
30 59.726 26.540 25.986 1.310 0.000 26.886 18.755
31 67.116 28.322 27.000 1.320 0.000 27.800 29.792
32 41.699 28.000 25.000 1.555 0.000 26.810 17.323
33 75.726 26.540 25.986 1.310 0.000 26.886 18.755
34 70.116 28.322 27.000 1.320 0.000 27.800 29.792
35 71.699 28.000 25.000 1.555 0.000 26.810 17.323
36 83.515 26.573 26.999 0.917 0.000 29.121 18.456
37 61.253 28.227 27.000 0.619 0.000 28.632 -10.674
38 79.654 5.999 9.918 0.028 0.000 26.078 -30.000
39 78.992 25.000 25.000 1.345 23.342 27.988 1.843
40 77.367 31.869 23.019 1.784 5.938 29.080 19.000
41 75.097 26.999 21.953 1.993 0.550 28.060 30.252
42 77.091 29.000 19.000 1.985 0.000 30.067 5.000
43 57.215 25.000 26.812 1.310 0.000 30.340 23.879
44 59.726 26.540 25.986 1.310 0.000 26.886 18.755
45 67.116 28.322 27.000 1.320 0.000 27.800 29.792
46 41.699 28.000 25.000 1.555 0.000 26.810 17.323
47 33.515 26.573 26.999 0.917 0.000 29.121 18.456
48 31.253 28.227 27.000 0.619 0.000 28.632 -10.674
Table IX: Comparative evaluation of the proposed and existing models in aspects of operating cost and availability without
involvement in hybrid scheme of DRPS and IBT
Techniques Wind Turbine Solar surface Battery Availability index Operating cost
surface area (m2) area (m2) (kW) of wind power (Ect)
MOPSO 850 3000 365 98.47% 1.31*106
MOWDO 700 2870 358 98.17% 1.33*106
MOGA 690 2660 345 97.44% 1.2*106
Table X: Comparative evaluation of the proposed and existing models in aspects of operating cost and availability with
involvement in hybrid scheme of DRPS and IBT
Techniques Wind Turbine Solar surface Battery Availability index Operating cost
surface area (m2) area (m2) (kW) of wind power (Ect)
MOPSO 800 2800 340 98.57% 1.29*106
MOWDO 695 2760 328 98.37% 1.20*106
MOGA 650 2550 315 97.24% 1.19*106
22
in the hybrid scheme of DRPS and IBT, the operating cost,1
pollution emission would likely be minimized, and the avail-2
ability of RES would be maximized. Results show that in case3
I, the operating cost and pollution emission with and without4
DRPS and IBT is minimized by 24.5% and 19% with MOGA,5
and reduced to 26% and 13% with MOWDO as compared to6
MOPSO, respectively. Furthermore, in case II, operating cost7
is reduced by 12% and 6% with and without hybrid DRPS and8
IBT using MOGA, 13% and 8% using MOWDO compared9
to MOPSO, respectively. Similarly, the availability of RES is10
maximized by 20% and 17% using MOGA, 25% and 19%11
using MOWDO as compared to MOPSO, respectively.12
This work can be extending in the future by adopting intelli-13
gent rule-based techniques and compare them to parametrized14
cognitive adaptive optimization approach for energy optimiza-15
tion of the smart microgrid.16
REFERENCES17
[1] Ferreira, Willian M., Ivan R. Meneghini, Danilo I. Brandao, and Fred-18
erico G. Guimar˜
aes. “Preference cone based multi-objective evolutionary19
algorithm to optimal management of distribuited energy resources in20
microgrids.” Applied Energy 274 (2020): 115326.21
[2] Hakimi, Seyed Mehdi, Amin Hajizadeh, Miadreza Shafie-khah, and Jo˜
ao22
PS Catal˜
ao. “Demand Response and Flexible Management to Improve23
Microgrids Energy Efficiency with a High Share of Renewable Re-24
sources.” Sustainable Energy Technologies and Assessments 42 (2020):25
100848.26
[3] Hasankhani, Arezoo, and Seyed Mehdi Hakimi. “Stochastic Energy27
Management of Smart Microgrid with intermittent Renewable Energy28
Resources in Electricity Market.” Energy (2020): 119668.29
[4] Rayati, Mohammad, Sanaz Amirzadeh Goghari, Zahra Nasiri Gheidari,30
and AliMohammad Ranjbar. “An optimal and decentralized transactive31
energy system for electrical grids with high penetration of renewable32
energy sources.” International Journal of Electrical Power & Energy33
Systems 113 (2019): 850-860.34
[5] Hafeez, Ghulam, Khurram Saleem Alimgeer, and Imran Khan. “Electric35
load forecasting based on deep learning and optimized by heuristic36
algorithm in smart grid.” Applied Energy 269 (2020): 114915.37
[6] Pandit, Manjaree, Laxmi Srivastava, and Manisha Sharma. “Environmen-38
tal economic dispatch in multi-area power system employing improved39
differential evolution with fuzzy selection.” Applied Soft Computing 2840
(2015): 498-510.41
[7] Gazafroudi, Amin Shokri, Karim Afshar, and Nooshin Bigdeli. “Assess-42
ing the operating reserves and costs with considering customer choice43
and wind power uncertainty in pool-based power market.” International44
Journal of Electrical Power & Energy Systems 67 (2015): 202-215.45
[8] Vardakas, John S., Nizar Zorba, and Christos V. Verikoukis. “Performance46
evaluation of power demand scheduling scenarios in a smart grid envi-47
ronment.” Applied Energy 142 (2015): 164-178.48
[9] Patnam, Bala Sai Kiran, and Naran M. Pindoriya. “Demand response in49
consumer-centric electricity market: mathematical models and optimiza-50
tion problems.” Electric Power Systems Research (2020): 106923.51
[10] Bahmani, Ramin, Hamid Karimi, and Shahram Jadid. “Stochastic52
electricity market model in networked microgrids considering demand53
response programs and renewable energy sources.” International Journal54
of Electrical Power & Energy Systems 117 (2020): 105606.55
[11] US Department of Energy. Benefits of demand response in electricity56
markets and recommendations for achieving them. Report to the United57
States Congress; February 2006. http://eetd.lbl.gov.58
[12] Hafeez, Ghulam, Khurram Saleem Alimgeer, Zahid Wadud, Imran Khan,59
Muhammad Usman, Abdul Baseer Qazi, and Farrukh Aslam Khan.60
“An Innovative Optimization Strategy for Efficient Energy Management61
with Day-ahead Demand Response Signal and Energy Consumption62
Forecasting in Smart Grid using Artificial Neural Network.” IEEE Access63
8 (2020): 84415-84433.64
[13] Alavi, Seyed Arash, Ali Ahmadian, and Masoud Aliakbar-Golkar. “Op-65
timal probabilistic energy management in a typical micro-grid based-on66
robust optimization and point estimate method.” Energy Conversion and67
Management 95 (2015): 314-325.68
[14] Rezaei, Navid, and Mohsen Kalantar. “Smart microgrid hierarchical 1
frequency control ancillary service provision based on virtual inertia 2
concept: An integrated demand response and droop controlled distributed 3
generation framework.” Energy Conversion and Management 92 (2015): 4
287-301. 5
[15] Falsafi, Hananeh, Alireza Zakariazadeh, and Shahram Jadid. “The role of 6
demand response in single and multi-objective wind-thermal generation 7
scheduling: A stochastic programming.” Energy 64 (2014): 853-867. 8
[16] Zakariazadeh, Alireza, Shahram Jadid, and Pierluigi Siano. “Economic- 9
environmental energy and reserve scheduling of smart distribution sys- 10
tems: A multiobjective mathematical programming approach.” Energy 11
Conversion and Management 78 (2014): 151-164. 12
[17] Zakariazadeh, Alireza, Shahram Jadid, and Pierluigi Siano. “Stochastic 13
multi-objective operational planning of smart distribution systems con- 14
sidering demand response programs.” Electric Power Systems Research 15
111 (2014): 156-168. 16
[18] Al-Sumaiti, Ameena Saad, Mohammed Hassan Ahmed, Sergio Rivera, 17
Mohammed Shawky El Moursi, Mohamed MA Salama, and Tareefa Al- 18
sumaiti. “Stochastic PV model for power system planning applications.” 19
IET Renewable Power Generation 13, no. 16 (2019): 3168-3179. 20
[19] Mohammadnejad, Mehran, Amir Abdollahi, and Masoud Rashidinejad. 21
“Possibilistic-probabilistic self-scheduling of PEVAggregator for partici- 22
pation in spinning reserve market considering uncertain DRPs.” Energy 23
196 (2020): 117108. 24
[20] Parvania, Masood, and Mahmud Fotuhi-Firuzabad. “Integrating load 25
reduction into wholesale energy market with application to wind power 26
integration.” IEEE Systems Journal 6, no. 1 (2011): 35-45. 27
[21] Aslam, Sheraz, Adia Khalid, and Nadeem Javaid. “Towards efficient 28
energy management in smart grids considering microgrids with day- 29
ahead energy forecasting.” Electric Power Systems Research 182 (2020): 30
106232. 31
[22] Cicek, Nihan, and Hakan Delic. “Demand response management for 32
smart grids with wind power.” IEEE Transactions on Sustainable Energy 33
6, no. 2 (2015): 625-634. 34
[23] Aghajani, G. R., H. A. Shayanfar, and H. Shayeghi. “Demand side man- 35
agement in a smart micro-grid in the presence of renewable generation 36
and demand response.” Energy 126 (2017): 622-637. 37
[24] Aghajani, G. R., H. A. Shayanfar, and H. Shayeghi. “Presenting a multi- 38
objective generation scheduling model for pricing demand response rate 39
in micro-grid energy management.” Energy Conversion and Management 40
106 (2015): 308-321. 41
[25] Aghajani, Gholamreza, and Noradin Ghadimi. “Multi-objective energy 42
management in a micro-grid.” Energy Reports 4 (2018): 218-225. 43
[26] Ngoc, Phuc Diem Nguyen, Thi Thu Ha Pham, Seddik Bacha, and Daniel 44
Roye. “Optimal Management of Wind Intermittency in Constrained Elec- 45
trical Network.” Wind Farm: Impact in Power System and Alternatives 46
to Improve the Integration (2011): 109. 47
[27] Mohamed, Faisal A., and Heikki N. Koivo. “System modelling and 48
online optimal management of microgrid using mesh adaptive direct 49
search.” International Journal of Electrical Power & Energy Systems 32, 50
no. 5 (2010): 398-407. 51
[28] Mohamed, Faisal A., and Heikki N. Koivo. “Multiobjective optimization 52
using Mesh Adaptive Direct Search for power dispatch problem of 53
microgrid.” International Journal of Electrical Power & Energy Systems 54
42, no. 1 (2012): 728-735. 55
[29] Afshar, K., and A. Shokri Gazafroudi. “Application of Stochastic Pro- 56
gramming to Determine Operating Reserves with Considering Wind and 57
Load Uncertainties.” J Operation Automation Power Engg (2013): 23-30. 58
[30] Mohamed, Faisal A., and Heikki N. Koivo. “Online management genetic 59
algorithms of microgrid for residential application.” Energy Conversion 60
and Management 64 (2012): 562-568. 61
[31] Moghaddam, Amjad Anvari, Alireza Seifi, Taher Niknam, and Moham- 62
mad Reza Alizadeh Pahlavani. “Multi-objective operation management of 63
a renewable MG (micro-grid) with back-up micro-turbine/fuel cell/battery 64
hybrid power source.” Energy 36, no. 11 (2011): 6490-6507. 65
[32] Motevasel, Mehdi, and Ali Reza Seifi. “Expert energy management of a 66
micro-grid considering wind energy uncertainty.” Energy Conversion and 67
Management 83 (2014): 58-72. 68
[33] Alvarez, David L., Ameena S. Al-Sumaiti, and Sergio R. Rivera. 69
“Estimation of an optimal PV panel cleaning strategy based on both 70
annual radiation profile and module degradation.” IEEE Access 8 (2020): 71
63832-63839. 72
[34] Sun, Yongjun, Rui Ma, Jiayu Chen, and Tao Xu. “Heuristic optimization 73
for grid-interactive net-zero energy building design through the glowworm 74
swarm algorithm.” Energy and Buildings 208 (2020): 109644. 75
[35] Rahimi, Ehsan, Abdorreza Rabiee, Jamshid Aghaei, Kashem M. Mut- 76
taqi, and Ali Esmaeel Nezhad. “On the management of wind power 77
23
intermittency.” Renewable and Sustainable Energy Reviews 28 (2013):1
643-653.2
[36] Gen, Ba. “Reliability and cost/worth evaluation of generating systems3
utilizing wind and solar energy.” PhD diss., University of Saskatchewan,4
2005.5
[37] Mohamed, Faisal A., and Heikki N. Koivo. “System modelling and6
online optimal management of microgrid using mesh adaptive direct7
search.” International Journal of Electrical Power and Energy Systems8
32, no. 5 (2010): 398-407.9
[38] Abouzahr, Imad, and R. Ramakumar. “An approach to assess the10
performance of utility-interactive wind electric conversion systems.” IEEE11
Transactions on Energy Conversion 6, no. 4 (1991): 627-638.12
[39] Atwa, Y. M., E. F. El-Saadany, M. M. A. Salama, and R. Seethapathy.13
“Optimal renewable resources mix for distribution system energy loss14
minimization.” IEEE Transactions on Power Systems 25, no. 1 (2009):15
360-370.16
[40] Ettoumi, F. Youcef, A. Mefti, A. Adane, and M. Y. Bouroubi. “Statistical17
analysis of solar measurements in Algeria using beta distributions.”18
Renewable Energy 26, no. 1 (2002): 47-67.19
[41] Deshmukh, M. K., and S. S. Deshmukh. “Modeling of hybrid renewable20
energy systems.” Renewable and sustainable energy reviews 12, no. 121
(2008): 235-249.22
[42] Tina, G., S. Gagliano, and S. Raiti. “Hybrid solar/wind power system23
probabilistic modelling for long-term performance assessment.” Solar24
energy 80, no. 5 (2006): 578-588.25
[43] Shadmand, Mohammad B., and Robert S. Balog. “Multi-objective opti-26
mization and design of photovoltaic-wind hybrid system for community27
smart DC microgrid.” IEEE Transactions on Smart Grid 5, no. 5 (2014):28
2635-2643.29
[44] Mohandes, Baraa, Samrat Acharya, Mohamed Shawky El Moursi,30
Ameena Saad Al-Sumaiti, Haris Doukas, and Sgouris Sgouridis. “Optimal31
design of an islanded microgrid with load shifting mechanism between32
electrical and thermal energy storage systems.” IEEE Transactions on33
Power Systems 35, no. 4 (2020): 2642-2657.34
[45] Chowdhury, S. P., S. Chowdhury, and P. A. Crossley. “Islanding protec-35
tion of active distribution networks with renewable distributed generators:36
A comprehensive survey.” Electric Power Systems Research 79, no. 637
(2009): 984-992.38
[46] Mazzola, Simone, Marco Astolfi, and Ennio Macchi. “A detailed model39
for the optimal management of a multigood microgrid.” Applied Energy40
154 (2015): 862-873.41
[47] Kanchev, Hristiyan, Di Lu, Frederic Colas, Vladimir Lazarov, and Bruno42
Francois. “Energy management and operational planning of a microgrid43
with a PV-based active generator for smart grid applications.” IEEE44
Transactions on industrial electronics 58, no. 10 (2011): 4583-4592.45
[48] Kennedy, James. “Encyclopedia of machine learning.” Particle swarm46
optimization (2010): 760-766.47
[49] Coello, CA Coello, and M. Salazar Lechuga. “MOPSO: A proposal48
for multiple objective particle swarm optimization.” In Proceedings of49
the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No.50
02TH8600), vol. 2, pp. 1051-1056. IEEE, 2002.51
[50] Yang, Jie, Zhenping Ji, Shuai Liu, and Qiong Jia. “Multi-objective52
optimization based on pareto optimum in secondary cooling and EMS53
of continuous casting.” In 2016 International Conference on Advanced54
Robotics and Mechatronics (ICARM), pp. 283-287. IEEE, 2016.55
[51] Ishibuchi, Hisao, and Tadahiko Murata. “A multi-objective genetic local56
search algorithm and its application to flowshop scheduling.” IEEE57
transactions on systems, man, and cybernetics, part C (applications and58
reviews) 28, no. 3 (1998): 392-403.59
[52] Bouffard, Franc¸ois, Francisco D. Galiana, and Antonio J. Conejo.60
”Market-clearing with stochastic security-part I: formulation.” IEEE61
Transactions on Power Systems 20, no. 4 (2005): 1818-1826.62
[53] Bouffard, Francois, Francisco D. Galiana, and Antonio J. Conejo.63
”Market-clearing with stochastic security-part II: case studies.” IEEE64
Transactions on Power Systems 20, no. 4 (2005): 1827-1835.65
[54] Available online: https://wind.willyweather.com.au/66
[55] The Solar Power Group Company:67
https://www.enfsolar.com/directory/installer/67081/the-solar-power-group68
[56] Reconstruction and Short-term Forecast of the Solar Irradiance.69
taken from: https://www.lpc2e.cnrs.fr/en/scientific-activities/plasmas-70
spatiaux/projects/other-projects-anr-europe-etc/fp7-soteria/71
[57] Chen, Changsong, Shanxu Duan, Tong Cai, Bangyin Liu, and Gangwei72
Hu. “Smart energy management system for optimal microgrid economic73
operation.” IET renewable power generation 5, no. 3 (2011): 258-267.74
[58] Mirzaei, Mohammad Javad, Ahad Kazemi, and Omid Homaee. “RE-75
TRACTED: Real-world based approach for optimal management of76
electric vehicles in an intelligent parking lot considering simultaneous77
satisfaction of vehicle owners and parking operator.” Energy 76 (2014): 1
345-356. 2
