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1

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

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