MultiobjectiveSizingofanAutonomousHybridMicrogrid ...downloads.hindawi.com/journals/cin/2020/8894094.pdf · ResearchArticle MultiobjectiveSizingofanAutonomousHybridMicrogrid UsingaMultimodalDelayedPSOAlgorithm:ACaseStudyof

Research ArticleMultiobjective Sizing of an Autonomous Hybrid MicrogridUsing a Multimodal Delayed PSO Algorithm A Case Study ofa Fishing Village

Raja Mouachi 1 Mohammed Ali Jallal2 Fatima Gharnati1 and Mustapha Raoufi1

1Laboratory of Intelligent Energy Management and Information Systems Faculty of Sciences Semlalia Cadi Ayyad UniversityMarrakesh 40000 Morocco2I2SP Team Physics Department Faculty of Sciences Semlalia Cadi Ayyad University Marrakesh 40000 Morocco

Correspondence should be addressed to Raja Mouachi mouachirajagmailcom

Received 20 April 2020 Revised 5 July 2020 Accepted 13 July 2020 Published 7 August 2020

Academic Editor Rasit Koker

Copyright copy 2020 RajaMouachi et al)is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Renewable energy (RE) systems play a key role in producing electricity worldwide)e integration of RE systems is carried out in adistributed aspect via an autonomous hybrid microgrid (A-HMG) system)e A-HMG concept provides a series of technologicalsolutions that must be managed optimally As a solution this paper focuses on the application of a recent nature-inspiredmetaheuristic optimization algorithm named a multimodal delayed particle swarm optimization (MDPSO) )e proposed al-gorithm is applied to an A-HMG to find the minimum levelized cost of energy (LCOE) the lowest loss of power supply probability(LPSP) and the maximum renewable factor (REF) Firstly a smart energy management scheme (SEMS) is proposed to coordinatethe power flow among the various system components that formed the A-HMG)en theMDPSO is integrated with the SEMS toperform the optimal sizing for the A-HMG of a fishing village that is located in the coastal city of Essaouira Morocco )eproposed A-HMG comprises photovoltaic panels (PV) wind turbines (WTs) battery storage systems and diesel generators(DGs) )e results of the optimization in this location show that A-HMG system can be applied for this location with a highrenewable factor that is equal to 90Moreover the solution is very promising in terms of the LCOE and the LPSP indexes that areequal to 017$kWh and 012 respectively)erefore using renewable energy can be considered as a good alternative to enhanceenergy access in remote areas as the fishing village in the city of Essaouira Morocco Furthermore a sensitivity analysis is appliedto highlight the impact of varying each energy source in terms of the LCOE index

1 Introduction

Electricity has become one of the most essential parts ofmodern life Nowadays the electricity sector is facing seriouschallenges such as ensuring sufficient supply to keep up withthe ever-increasing demand of electrical energy reducing itscosts and limiting polluting emissions For these reasonsthe use of REs has become a global priority for most of theworldrsquos countries

In this regard the Moroccan government plans to de-crease the use of fossil fuel energy by producing more than40 of electrical energy using only clean and RE resourcesby 2020 [1] Besides they begin to take advantage of REresources by exploiting the high potential of solar and wind

resources through inaugurating several energy projects andimplementing several research projects to extend the use ofthe RE resources Currently with these projects and con-sidering the countryrsquos deployment of solar and wind en-ergies the national RE production will rise to 52 by 2030[2] Moreover Moroccan climate is favorable for the in-stallation of the medium and small scale A-HMG projects asa means to bring electricity production closer to con-sumption limit investment in transmission and reducelosses in distribution networks

RE in the form of an A-HMG system offers a reliable andoptimal cost-effective solution for centralized RE installa-tions A-HMG can operate in both off-grid and grid-con-nected configuration However A-HMG systems provide an

HindawiComputational Intelligence and NeuroscienceVolume 2020 Article ID 8894094 18 pageshttpsdoiorg10115520208894094

opportunity to use the advantages of RE resources incombination with conventional ones [3]

In the recent literature the primary goals are to for-mulate and implement energy production strategies withgreater flexibility higher efficiency and lower LCOEHowever reaching these goals cannot be accessible due tothe nonlinear behavior of RE production and storage sys-tems which are strongly dependent on weather changes Soto overcome these problems many optimization techniquesare employed in several scientific contributions in theliterature

)e optimization problem can result in a mono-objec-tive or multiobjective problem which can include theminimization of the LCOE LPSP and the pollutant emis-sions Two frequently used optimization techniques arestochastic dynamic programming methods for optimizingthe energy management problem with multidimensionalobjectives andmetaheuristic techniques to solve the problemof optimization with multiconstraints multidimensionaland highly nonlinear combinatorial problems

Based on the literature review we found several researchcontributions that are focused on the HMG systems opti-mization problems )e authors in [4] proposed a gener-alized formulation for intelligent energy management of aHMG in using multiobjective optimization to minimize theoperation cost and the environmental impact where theyapplied artificial neural network to predict RE generationand load demand )e problem formulation in this workincludes optimal battery scheduling taking into account theuncertainty of the HMG exogenous variables and forecastedentities However the proposed approach does not take intoconsideration the REF as an objective and the optimal sizingof battery storage is not taken into account

In the research presented in [5] a technical and eco-nomic method is proposed to optimize a HMG based onmixed integer linear programming In this paper the costfunction is solved via linear programming based on a generalalgebraic modelling system where the optimization phase ofthe HMG system was performed via HOMER software )eauthors have analyzed WT PV and biomass resource po-tential of a selected area in province Punjab Kallar Kahar)e cost of energy is calculated for different peak loadenergy demand profiles and grid availability However theproposed formulations do not introduce any storage solu-tion to solve the intermittence problem of RE and tominimize the emission of polluting gases by biomassresource

Taha and Yasser [6] presented a robust algorithm basedon a predictive control model for an isolated HMG in fourdifferent case studies to minimize the total operating cost tominimize the pollutant CO2 and to minimize the dumpenergy )e results showed that the optimal battery dailynumber of cycles minimum SOC and the initial SOC of thebattery storage depend the pool-price variation Moreoverthe number of scenarios required to achieve a good resultsmakes the problem very large and time-consuming to solve

A mixed method is proposed for microgrid energymanagement in [7] )is was achieved by using linear op-timization methods to obtain an optimal energy storage

system size)e grid-connectedmicrogrid system consists ofsolar PV two identical solid oxide fuel cells and a batterybank operated parallel with the load Moreover the pro-posed methodology neglected many important constraintson the LPSP and REF indexes

)e authors in [8] analyzed an energy managementsystem for a hybrid ACDC microgrid in an isolatedcommunity that employs a PV system for desalination inorder to minimize the daily operating costs by using themixed integer nonlinear programming )e aim of theproposed methodology is to manage all system assets toensure stable operation of the hybrid ACDC microgrid andsecured clean water supply for the customers )is contri-bution has neglected the REF and the availability objectives

Correa et al [9] proposed an energy management systembased on a virtual power plant )e studied microgrid has solarpanels and storage systems and works in an interconnectedmanner)ese elements aremodeled using linear programmingmethods to minimize the operating costs REs are incorporatedinto an energetic model and are mainly based on hydric re-sourcesMoreover the authors concluded that the battery sizingplays a crucial role in operational cost of the microgridHowever this contribution has considered a single objectiveoptimization problem since the statement of a number ofobjective optimization problems affects the convergence speedand the stability of the adopted algorithms

In the research presented in [10] an intelligent energymanagement system is proposed for HMG system in threestations in Iran )e objective for this study is to minimizethe operational costs and environmental impacts by using amultiobjective particle swarm optimization algorithm )eLCOE and the LPSP are defined as objective functions )eresult of optimization shows that HMG system can be ap-plied for one of the three proposed locations with a highREF However the optimal configuration and the LCOEindex are not a standard value which depends on location

)e authors in [11] presented an energy managementsystem for a PVWTDG stand-alone HMG which is op-timized using a particle swarm algorithm with Gaussianmutation )is paper minimizes both the capital and fuelcosts of the system However the authors mainly concen-trated on economic evaluation of hybrid energy systems butthey do not examine other aspects of sustainability of thesesystems

Katsigiannis et al [12] used multiobjective optimizationtechniques to size an A-HMG while simultaneously mini-mizing LCOE and CO2 emissions )e obtained results ofLCOE are not competitive

)e previous reviewed studies for A-HMG optimizationhave recorded the following gaps

(1) Few research contributions have considered morethan two objective optimization problems consid-ering the computational complexity that affects theconvergence speed and the stability of the adoptedalgorithms

(2) Many studies have dealt with the techno-economicanalysis of the A-HMG system while the optimalconfiguration and the LCOE index are not a standard

2 Computational Intelligence and Neuroscience

value which depends on several variables such aslocation weather and the applied optimizationtechnique

Based on the results presented by the studies mentionedabove the prime aim of the present work is adopting anefficient variant of PSO algorithm referred to as a MDPSOwhich is developed recently by Song et al [2])eMDPSO isapplied to design an optimal A-HMG with a high REF andminimal values of the LCOE and the LPSP indexes

)e elements of innovation of the present work are thefollowing

(1) A recent MDPSO metaheuristic algorithm wasadopted for an A-HMG system optimization

(2) )e stability and the convergence of the adoptedMDPSO algorithm were evaluated to build A-HMGwith a high REF and minimal values in terms of theLCOE and the LPSP indexes

(3) )e application of MDPSO improves the conver-gence speed of the traditional PSO algorithm anddecreases the probability of converging to localoptimum So the entire search space will be exploredefficiently

(4) )e applied optimizer demonstrates a high efficiencyto build an optimal A-HMG system for a fishingvillage that is located in the coastal city of EssaouiraMorocco

(5) )e developed A-HMG system present minimalvalues in terms of the LCOE and the LPSP with ahigh renewable factor compared to different A-HMGmodels developed in the literature

2 Autonomous Hybrid MicrogridSystem Description

)e proposed A-HMG system is composed of wind turbines(WTs) photovoltaic (PV) panels diesel generator (DGs)and battery storage bank as shown in Figure 1 which canvary greatly depending on specific parameters such as theavailability of renewable resources and desired services toprovide [13] )ese parameters have a high impact on de-cision-making and accordingly on the LCOE and reli-ability of the system In the following section a detailedmodelling of each component of A-HMG is introduced anddiscussed

21 Photovoltaic Energy System Model Morocco has a fa-vorable climate conditions for implementing large solarenergy projects Various models for calculating the outputpower of the PV system have been proposed in the liter-ature [2] In this work a simplified model that considersambient temperature and solar irradiance is used as shownin the following equation [10 14]

Ppv G times Pr times1 + K Tamb +[(TNOCT minus 20)800]G( 1113857 minus Tref( 11138571113858 1113859

Gref

(1)

where

(i) Ppv and Pr are the output power of the PV and therated power in watts (W) at the standard testcondition (STC) respectively

(ii) K is the temperature coefficient defined by(minus37times10minus3 (1degC))

(iii) Tref denotes the cell temperature (degC) at STC(iv) Tamb denotes the ambient temperature (degC)

(Tamb 25 degC )(v) G is solar radiation (Wm2)

(vii) Gref is solar radiation at STC (Gref 1000Wm2)(viii) TNOCT is the nominal operating cell temperature

22Wind Turbine Energy SystemModel Wind energy offersenormous benefits for Morocco where this energy isregarded as being abundant climate-friendly easy tooperate and cost-efficient Additionally the wind potentialin Morocco is highly important due to the ideal geographicalposition of the country

To determine the WT generator output power themeasured wind speed at reference height is first converted tocorresponding WT hub height )e power-law equation iscomputed by the following correlation [10]

V1

V2

h

href1113888 1113889

α

(2)

where

(i) h (m) is the WT hub height(ii) href (m) is WT reference height (h)(iii) V1 (ms) is the wind speed at WT hub height(iv) V2 (ms) is the speed at the reference height (href )(v) α is the power-law exponential (also known as

Hellmann exponent wind gradient or power-lawexponent)

)e WT output power can be expressed as [4 15 16]

PWT

0 if VltVcutminusin VgtVcutminusout

Pr

V3r minus V3

cutminusin( 1113857V

3minus V

3cutminusin1113960 1113961 if Vcutminusin leVltVr

Pr if Vr leVltVcutminusout

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where

(i) Pr (kW) is the rated power of the WT(ii) V (ms) is the wind speed(iii) Vcut-out (ms) is the cut-out speed of the WT(iv) Vr (ms) is the nominal speed of the WT(v) Vcut-in(ms) is the cut-in speed of the WT

Figure 2 portrays the power curve characteristics of atypical WT

Computational Intelligence and Neuroscience 3

Power lineCommunication lineCommunication line and control line

DC-BUS

AC-BUSPV PRE Load

Wind turbine

PBat

DCDC

ACDC

DCDC

Smart energy managementscheme (SEMS)

Battery

PWT

PPV

DCAC

Diesel generator

Figure 1 Schematic diagram of the A-HMG system

Firstperformance

region

Pow

er o

utpu

t

VCUT-IN VCUT-OUT

Rated power

Secondpeformance

region

VRated

Wind velocity

Figure 2 A typical WT power-wind speed characteristics [16]


23Battery StorageBankModel )e battery capacity of thesystem is designed to meet the energy demand duringperiods of non-availability of renewable energy (RE)sources In this regard the battery capacity is designed inaccordance with the desired autonomy day (AD) andwith the energy demand Pload using the followingequation

CB Pload times AD

ηBat times DOD times ηinv (4)

where

(i) DOD is the depth of discharge (80)(ii) ηinv (95) is the inverter efficiencies(iii) ηBat (85) is the battery efficiency

Moreover the state of charge of a battery at any giventime is SOC(t) and it is bounded by maximumSOC(SOCmax) and minimum SOC(SOCmin) )e WT andPV systems could produce a surplus or deficit energy Asurplusdeficit energy represent the power absorbeddeliv-ered by the battery storage system and it can be expressed asfollows

PBat(t) Ppv(t) + PWT(t)1113872 1113873 minusPload(t)

ηinv (5)

where

(i) PBat(t)lt 0 is an indication that the power generationhas deficit in energy demand

(ii) PBat(t)gt 0 indicates a surplus in power generation

)e battery storage bank charging occurs whenSOC(t)lt SOCmax and when (Ppv(t) + PWT(t)gt Pload(t)))erefore the SOC(t) can be expressed as follows [17]

SOC(t) SOC(t minus 1)(1 minus c) + PBat(t) times ηBat( 1113857 (6)

Furthermore when there is a deficiency in the powergeneration and SOC(t)gt SOCmin the battery storage bankthen discharges the energy stored into it to achieve theenergy demand according to

SOC(t) SOC(t minus 1)(1 minus c) + minusPBat(t) times ηBat( 1113857 (7)

where

(i) c denotes the self-discharge rate of the battery storagebank

24 DCAC Inverter Model )e inverter DCAC convertsthe electrical energy from DC to AC with the desired fre-quency of the load Its efficiency is defined by the followingequation

ηinv P

P + P0 + kP2 (8)

where P P0 and k are determined by using the followingequations [18ndash21]

K 1

η100minus P0 minus 1

P0 1 minus 991η10

minus1

η100minus 91113888 1113889

2

P Pout

Pn

(9)

where η10 and η100 are the efficiency of the inverter at 10and 100 of its nominal power respectively

25 Diesel GeneratorModel Diesel generator (DG) works asa secondary source of energy in the case of battery depletionduring peak energy demand

)e efficiency and the hourly fuel consumption of thediesel generator should be considered in designing a hybridenergy system and can be expressed by the following ex-pression [22 23]

F(t) aPDG(t) + bPr (10)

where

(i) PDG is the generated power (kW)(ii) F(t) is the fuel consumption (Lhour)(iii) Pr is the rated power (kW) of the DG(iv) a and b are constant parameters (LkW) which

represent the coefficients of fuel consumption andcan be approximated to 0246 and 008415 re-spectively [24]

Similarly the efficiency of the DG is calculated by thefollowing equation [25]

ηoverall ηbrakminusthermal times ηgenerator (11)

where

(i) ηoverall represents the overall efficiency of the DG(ii) ηbrakminusthermal is the brake thermal efficiency of the DG

3 Site of Implementation and A-HMGSystem Descriptions

Moroccan lands are blessed with abundant renewable energyresources predominantly those of solar and wind energiesIn the present study an A-HMG system was designed for asmall fishing village located in a coastal region in the middleof Morocco nearby the city of Essaouira at a latitude of3152degN and a longitude of 927degW

)is region is characterized by high irradiance levels and anaverage annual wind speed between 7 and 8ms [22 26] Itsexposure to the Atlantic Ocean moderates the temperatureamplitudes compared to inland regions )e economic andtechnical parameters of the A-HMG components are given inTable 1 )e hourly load profile is given in Figure 3 SimilarlyFigures 4ndash6 depict the hourly profiles of solar radiation windspeed and ambient temperature respectively


In general the efficiency of the resources (PV WT DGand battery) is reduced with time with a degradation factor)e energy generated by each resource is equal to the ratedenergy output multiplied by the degradation factor How-ever the impact of degradation on system performance istaken into account in this work where the PV and WTrsquosdegradation factor is considered as 05 per year and theDGrsquos degradation factor is considered as 07 per year

4 The Proposed Smart EnergyManagement Scheme

Having an efficient SEMS is one of the major criteria to beconsidered when designing the A-HMG system )e ob-jective of the proposed SEMS system is to coordinate thepower flow into the A-HMG system and tomaximize the useof renewable energy systems )e proposed SEMS system isbased on the following cases

Case 1 Sufficient energy is provided by PV and WTresources which will supply the load demand )enthe extra energy will be used to charge a battery storagebank if SOC(t)lt SOCmaxCase 2 )e energy that is provided by PV and WTresources exceeds the load demand and the batterystorage bank needs (SOC(t) SOCmax))erefore theextra energy will be consumed in a dump loadCase 3)e energy generated by PV andWTresourcesis not sufficient to supply the load demand andSOC(t) gt SOCmin )erefore the stored energy in thebattery storage bank will be used to satisfy the loaddemandCase 4 )e energy generated by the PV and WT re-sources is not sufficient to fulfill load demand and thebattery storage bank is also depleted (SOC(t)lt SOCmin) )erefore the DG is switched on to supplythe load demand and charge the battery storage bankMoreover when PV andWTresources start to generatepower the energy produced by DG will be stopped

)e main flowchart for the proposed SEMS is shown inFigure 7

5 Optimization Problem Formulation

)e objective of this section is to provide an optimal con-figuration of A-HMG system to satisfy the typical loaddemand presented in Figure 3 )e A-HMG system is op-timized based on a multiobjective problem which can begenerally defined as follows

MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where

(i) F(x) is a vector representing the objective functions(ii) f1(t) f2(t) fk(t) are the individual values of

the objective functions(iii) x is the vector of the design search space(iv) H(x) and G(x) denote the set of inequality and

equality constraints respectively

Table 1 Technoeconomic data of the considered power systems

System parameters ValuesA Pv unitLife time (years) 25Initial cost [$kW] 2150Rated power (W) 275DCDC converter efficiency () 95PV regulator cost [$] 1500B wind turbineLife time (years) 25Initial cost [$kW] 2000Blades diameter (m) 64Cut-in speed (ms) 25Cut-out speed (ms) 40Swept area (m2) 1286ACDC converter efficiency () 95Rated power (kW) 5Wind turbine regulator cost [$] 1000C Diesel generatorLife time (hours) 24000Initial cost [$kW] 1000Rated power (kW) 4D batteryLife time (years) 12Initial cost [$kWh] 280Rated power (kWh) 40Efficiency () 85E inverterLife time (years) 25Initial cost [$] 2500Efficiency () 92F economic parametersProject life time (years) 25Discount rate () 6OampM+ running cost () 20

25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)

Figure 3 Load profile


1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )

Figure 4 Hourly solar irradiance time series of the studied site

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0

Figure 5 Hourly wind speed time series of the studied site

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)

Figure 6 Hourly ambient temperature time series of the studied site


Start

Read input

Calculate PV and WT powerEstimation of load demand powerEstimation of energy and economic cost

Consideration of losses in converters and cables

IfPpv (t) + PWT (t) ge Pload (t)

Discharge battery

No Yes

IfSOC (t) le SOCmin

SOC (t) = SOC (t ndash 1)



Run diesel generator

No Yes

Run load with PV and WT

IfPpv (t) + PWT (t) gt Pload (t)

No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)

Figure 7 Main flowchart of the proposed SEMS


51 Objective Functions Descriptions )e A-HMG system isevaluated based on the LCOE the LPSP and REF)us theyare chosen as the objective functions where the goal ob-jective is to optimize the system so that it would guaranteereliable power supply at minimum cost and maximize thereliability of the A-HMG system in case of a blackoutavoiding power supply interruptions and their related costs

511 Levelized Cost of Energy )e LCOE is one of the mostused indicators of economic profitability of A-HMG systems[23] )e LCOE includes the hybrid system hardware initialcost and the operation andmaintenance costs It is defined asthe price per unit produced energy ($kWh) and expressedwith the following equation [27 28]

LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where

(i) TPV is the total present value of the whole systemcost and includes the capital replacement opera-tion and maintenance costs

(ii) Pload(t) is the hourly amount of energy consumed(iii) CRF is the capital recovery factor these can be

expressed as follows

CRF(β n) β(1 + β)n

(1 + β)n minus 1 (14)

where

(i) n is the life span typically equal to the life span of thePV panels [29]

(ii) β is the discount rate considered in the economicappraisal of the proposed system

)e discount rate is country-dependent and also subjectto the investment stability of the energy source )is pa-rameter may vary from 6 to 16 for renewable energysources in Morocco [30]

512 Reliability Analysis )e reliability of the A-HMGsystem is assessed based on the LPSP )e LPSP is a reli-ability index which indicates the probability of the powersupply failure to meet due to low renewable resources ortechnical failures to meet the energy demand It can bedescribed by the following equation [31 32]

LPSP 1113936

8760t1 Pload(t) minus PPV(t) minus PWT(t) + PDG(t) + PBatmin

1113872 1113873

11139368760t1 Pload(t)

(15)

where

(i) PWT(t) is the amount of power generated by thewind turbine at time t

(ii) Ppv(t) is the amount of power generated by the PVsystem at time t

(iii) PDG(t) is the amount of power generated by thediesel generator at time t

(iv) Pload(t) is the amount of power consumed at time t(v) PBatmin

is the minimum allowable storage capacity ofthe battery storage system

)e LPSP is a reliability index which indicates theprobability of the power supply failure to meet the energydemand )e LPSP value must be less than 5 based on theliterature

In this work the reliability evaluations are carried out inthe worst conditions when

Pload(t)gtPgenerate(t) (16)

52 Constraints REF is defined for MDPSO programmingas a boundary to determine the amount of energy comingfrom a DG as compared to the RE generators )e objectiveis to minimize the DG usage reducing the CO2 emissionsand reducing the cost of operation Hence the REF iscomputed as follows

REF() 1 minus1113936

8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)

)e REF is bounded by 0 and 1 where REF 0 meansthat the renewable energy is not used and REF 1 meansthat the energy is produced only by renewable energysources without using the DG

In addition the following constraints for the number ofrenewable energy generators (PV panels and WT) DG andthe autonomy days should also be satisfied

0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where

(i) Npv and NWT are the number of PVs and WTsrespectively

(ii) NAD and NDG are the number of DGs and au-tonomy days (AD) respectively

(iii) NPVmaxand NWTmax

are the maximum number ofPVs and WTs respectively

(iv) NADmaxand NDGmax

are the maximum number ofADs and DGs respectively

6 PSO Algorithm Evolution

61 PSOAlgorithm In the past few years a large number ofPSO-based approaches have been proposed for optimalsizing of the A-HMG system PSO algorithm was developedby Eberhart and Kennedy in 1995 for hard optimization


problems )e searching strategy of PSO algorithm is in-spired by the social behaviors of birds flocking or fishschooling where each particle of the swarm acts as a po-tential solution of certain optimization problem [3]

PSO algorithm is employed to intelligently select optimalparameters from N particles )e initialization matrixcontains N particles dispersed in a search space ofD-dimension

At the kth iteration in the searching process the ithparticle stores its historical best position Pbest as representedby (pbest(k) (pi1(k) pi2(k) piD(k)) and its global bestparticle Pgbest as denoted by (pgbest(k) (pgbest1(k)pgbest2(k) pgbestD(k)) )e process of displacement ofeach particle is managed by three rules [33 34]

(1) )e particle tends to take the direction of its currentvelocity

(2) )e particle tends to move toward its best position(3) )e particle tends to move to the best position

reached by its neighbors

In fact the position of the particle i will be updated toreach the global optimum based on the corresponding ve-locity vector Furthermore the velocity and the positionvectors of the particle i at the iteration k will be updated asfollows

Vi(k + 1) wVi(k) + c1r1 pbest(k) minus xi(k)( 1113857

+ c2r2 pgbest(k) minus xi(k)1113872 1113873

xi(k + 1) xi(k) + Vi(k + 1)

(19)

where

(i) k denotes the number of the current iteration(ii) w denotes the inertia weight(iii) c1 and c2 are called the acceleration coefficients

respectively cognitive and social parameters(iv) r1 and r2 are two uniformly distributed random

numbers in the interval [0 1] [2]

A variety of approaches has been proposed to improvethe capability of the traditional PSO algorithm [35]

Shi et al [36 37] introduced PSO with linearly de-creased inertia weight w on iteration generations theinertia weight of the current iteration w is given as fol-lowing equation

w win minus wfi( 1113857 timesitmax minus ititmax

+ wfi (20)

where

(i) win and wfi denote respectively the initial value andthe final value of the inertia weight

(ii) it is the number of current iteration(iii) itmax denotes the number of maximum iteration

Overall a larger inertia weight would make the PSO tendto the global exploration and otherwise a smaller one couldachieve the local exploitation

Hence the initial and final values w1 and w2 are gen-erally set as 09 and 04 respectively Additionally PSO withtime-varying acceleration coefficients have been introducedin [2 38] as calculated by the following equations

c1 c1i minus c1f( 1113857 timesitmax minus ititmax

+ c1f (21)


+ c2f (22)

where

(i) c1i and c2i are the initial values of the accelerationcoefficients c1 and c2

(ii) c1f and c2f are the final values of the accelerationcoefficients

)e improvement strategies of the traditional PSOmentioned above are principally concerning the parameterstudies

62 MDPSO Algorithm In 2017 Song et al developed aMDPSO algorithm for the global smooth path planning formobile robots [2]

)e principal novelty of the MDPSO algorithm as a newPSO algorithm is that it integrates two delayed terms in thetraditional velocity )e updating terms are the local andglobal delayed best particles selected from the correspondingvalues in the previous iterations stochastically and are addedinto the velocity updating model according to the evaluatedevolutionary state )e advantage of this method is to reducethe convergence speed of the traditional PSO algorithm andto decrease the probability of converging to local minimum[2]

)e following equations calculate the updating equationsfor the velocity and the position of the novel MDPSOalgorithm



+ Si(k)c3r3 pbest k minus τi(k)( 1113857 minus xi(k)( 1113857

+ Sg(k)c4r4 pgbest k minus τg(k)1113872 1113873 minus xi(k)1113872 1113873

xi(k + 1) xi(k) + Vi(k + 1)

(23)

where

(i) w is the inertia weight(ii) c1 and c2 are the coefficients for acceleration

updated and c3 and c4 are equal to c1 and c2 wherec1 c3 and c2 c4 respectively

(iii) r1 r2 r3 r4 are the random uniformly distributednumbers in [0 1]

(iv) τi(k) and τg(k) are the random delays uniformlydistributed in [0 k] for the local and the globaldelayed best particle respectively


(v) Si(k) and Sg(k) are the intensity factor of the newlyadded terms in the velocity updating modeldepending on the evolutionary factor

)e newly added terms in the velocity updating modelare closely related to the evolutionary factor (EF) defined in[39] to describe the swarm distribution propertiesAccording to the EF in the searching process the four statesare denoted as follows ξ(k) 1 is the exploration stateξ(k) 2 is the exploitation state ξ(k) 3 is the convergencestate and ξ(k) 4 the jumping out state respectively )emean distance between the particle i and the other particlesin the swarm denoted as di could be calculated by

di 1

S minus 11113944

S

j1jne 1

1113944

D

k1xik minus xjk1113872 1113873

2

11139741113972

(24)

where

(i) D is the particle dimension(ii) S is the swarm size

)erefore the evolutionary factor (EF) is given by thefollowing equation

EF digbest minus dimin

dimax minus dimin (25)

where

(i) digbest denotes the mean distance between the globalbest particle and the other particles in the swarm

(ii) dimin denotes the minimum and the maximum of di

in the swarm(iii) dimax denotes the maximum of di in the swarm

)e evolutionary state is classified confer to theevolutionary factor by a series of fuzzy functions in [40]Additionally in [35 41] equal division strategy is used forthe evolutionary state classification for the state pre-diction depending on a Markov chain )e formulation ofevolutionary used in this paper is expressed as follows[13]

ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)

Many strategies are used for the evolutionary states andthe main idea of these strategies is to adjust the velocityupdating model in an adaptive mode confer to the evaluated

evolutionary state In this work a novel strategy withmultimodal delayed information [2] is used to adaptivelyadjust the velocity updating model and expressed as follows

(i) State 1)e particles in the swarm are expected to flyinto the region around the global optimum as soonas possible )erefore only the normal terms in thevelocity updating model remained and the delayedinformation is ignored (mi(k) 0 and mg(k) 0))is state is the convergence state where ξ(k) 1

(ii) State 2 )e particles in the swarm are willing toexploit the region around the local best particles Sothe local delayed information is added into thevelocity updating model that is only the local bestparticles in the previous iterations are randomlyselected for the velocity updating with the intensityfactor mi(k)EF (k)) )is state is the exploitationstate where ξ(k) 2

(iii) State 3 In this state the global delayed informationis added to explore the whole search space in a morethorough way that is the global best particles in theprevious iterations are randomly selected for thevelocity updating with the intensity factormg(k) EF(k) because it is important to search theoptima as many as possible )is state is the ex-ploration state where ξ(k) 3

(iv) State 4)e local best particles are eager to jump outfrom the region around the local optima )us it isnecessary to provide more power for these particlesto escape from this region so that both of the localand global delayed information are used for thispurpose with the intensity factor mi(k)EF(k) andmg(k)EF(k) respectively )is state is the state ofjumping out where ξ(k) 4

)e above discussed states for multimodal delayed in-formation can be summarized in Table 2 as followswhere

(i) mi(k) and mg(k) denote the intensity factor deter-mined by the evolutionary state and evolutionaryfactor EF(k) in each iteration

)eMDPSO algorithm flowchart is depicted in Figure 8

7 Result Analysis and Discussion

71 MDPSO Parameters Configuration )e parametersconfiguration play a crucial role in manipulating the con-vergence speed of MDPSO algorithm )erefore there aremany scientific researchers [2 17 42ndash44] to improve thePSO algorithm performances because these parametersshould be selected carefully

Table 2 States for multimodal delayed information

State Mode mi(k) mg(k)Convergence state ξ(k) 1 0 0Exploitation state ξ(k) 2 EF(k) 0Exploration state ξ(k) 3 0 EF(k)Jumping out state ξ(k) 4 EF(k) EF(k)


Solar radiation WindSpeed Ambient

temperature

Economic data of theA-HMG system

components

Optimizationconstraints and design

variable

Fitness functiondefinition

SEMS

Start

Read the inputs of the MDPSO routine

Evaluate the fitness value of each particule

Update and save Pbest and Pgbest as historical information

Compute the mean distance di of each particle

Compute evolutionary factor EF

Classify the evolutionary state ξ (k)

Compute the inertia weight

Update the multimodal delayed information

Update the velocity and position

K = K + 1

Reached the maxiterations

End

Compute the acceleration coefficient

Yes

No

Figure 8 Flowchart of the proposed MDPSO algorithm


Table 3 Inertia weight and acceleration coefficients used in the present work

Parameters Reference Value

Acceleration coefficients [44]

c1i 25c1f 05c2i 05c2f 25

Inertia weight [17] win 09wfi 04

Table 4 Optimal results obtained

Location Parameters PVWTDGbattery

Essaouira (Morocco)

Number of iterations 200Number of particles 100Number PV panels 15Days of autonomy 5Number of WTs 1DG capacity (kW) 4

LPSP () 012LCOE ($kWh) 017

REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100

Figure 9 Convergence characteristic of MDPSO algorithm for the LCOE

0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()

Figure 10 Convergence characteristic of MDPSO algorithm for the LPSP


In Table 3 the parameters of the inertia weight and theacceleration coefficients are given by (20)ndash(22)

72 Results Analysis In this section the simulation resultsare presented )e SEMS for an A-HMG system is per-formed to fulfill the energy demand of a fishing village that islocated in the coastal city of Essaouira Morocco )eMDPSO method is applied to obtain the best configurationof A-HMG system and for sizing the components )eLCOE LPSP and REF are defined as objective functions)e studied system components are PV panels WTs batterystorage bank and DGs as illustrated in Figure 1 )e

simulation conditions of the A-HMG optimization processover one year consider a community of 15 houses and thelifetime of the A-HMG has been chosen as 25 years Table 4gives the best-found solution

)e obtained results in Table 4 show that we shouldinstall 15 units of PVs 1 unit of WT and 4 kW of DG )eminimum parameters come out to be 017 $kWh for LCOE012 for LPSP and 90 for REF However PVWTDGbattery as A-HMG system is the best configuration found forthe fishing village site that is located in the city of EssaouiraMorocco

)e advantages of our system have more reliability andcost-effectiveness compared to those that use only one

0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()

Figure 11 Convergence characteristic of MDPSO algorithm for the REF

PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55

Number of generators

Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG

15 20 25 30 35 40 45 50 55Number of PV panels

06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG

Figure 12 Sensitivity of LCOE to the variation of PV panels WTs and DGs numbers


source of energy )ese advantages are due to the combi-nation of the proposed SEMS with the robust MDPSOalgorithm

)e convergence characteristics of MDPSO for theA-HMG are depicted in Figures 9ndash11 for the LCOE theLPSP and the REF respectively As seen in Figure 9 thevalue of the LCOE decreases during the iteration process andthe same applies to the LPSP in Figure 10 Unlike the REFwhich increases as shown in Figure 11 we conclude that theMDPSO algorithm reduces the LCOE and the LPSP bymoving toward the best system size Moreover any declinein the objective function leads to having more informationabout the optimal size

)ese results will be confirmed through a sensitivityanalysis to reveal the robustness of the optimization results

73 Sensitivity Analysis )e sensitivity analysis is funda-mental because it gives a better understanding of the effectsof varying the input parameters of the A-HMG system )eanalysis has been extended to qualify and quantify the effectof parametric variation in the LCOE for the A-HMG systemwhich is computed by the MDPSO algorithm In addition

the LCOE values become more significant and more sen-sitive to lower numbers of PV panels WTs and DGs whichindicates that any change in the component size can changeLCOE Figure 12 shows the impact of component resizing onthe LCOE

)is shows that the LCOE savings of an A-HMG systemcan be enhanced with the integration of the additionalnumber of green technologies but it increases with the in-tegration of additional number of DGs It is also importantto note that the benefits of RE resources when comparedwith the brown technologies depend on the availability of thelocal RE resources the capacity of the battery and the levelof RE technologies penetration

In Figure 13 the effect of LCOE was analyzed due to thevariation of the number of houses in the village It can beobserved from the graph that the number of houses in thevillage has a nonlinear effect on LCOE

74 Comparison of LCOE Results with Similar HMGAnalysesin the Literature Table 5 shows the comparison of LCOEwith those available in literature )e achieved value of theLCOE index in this work is very interesting compared to

0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)

Figure 13 Sensitivity of LCOE to the variation of the houses number

Table 5 Comparison of LCOE with other studies available in the literature

Reference HMG components Location LCOE ($kWh) Optimization technique[45]-2016 PVWTDG Singapore (Singapore) 029 Distributed mutated particle swarm optimization

[39]-2016 PVWTFC

Nikouyeh (Iran) 056

Computer programGhadamgah (Iran) 0799Moaleman (Iran) 054Marvdasht (Iran) 062

[3]-2018 PVWTDGbattery Riyadh (Saudi Arabia) 033 Cuckoo Search algorithms[46]-2018 PVWTDGLB Chhattisgarh (India) 027 HOMER software[40]-2018 PVWTbattery Gokccedileada (Turkey) 190 HOMER software

[47]-2019 PVWTLBBDGFCH2

Dickinson (US) 037Genetic AlgorithmLubbock (US) 041

Tucson (US) 043

[48]-2020 PVWTDGbattery Baghdad (Iraq) 02330 PSO algorithmsRabat (Morocco) 03214)is study PVWTDGbattery Essaouira (Morocco) 017 MDPSOLB lead acid battery BDG biodiesel generators FC fuel cell and H2 hydrogen


those recently reported in the literature regarding theA-HMG system optimization )e LCOE can significantlydiffer from country to another However this comparison isvaluable as it can give an insight regarding the economicfeasibility of A-HMG system in the city of Essaouira Mo-rocco and for other sites across the coastal regions ofMorocco

)e developed A-HMG system presents minimal valuesin terms of the LCOE and the LPSP with a high REFcompared to different A-HMG models developed in theliterature [3 39 40 45ndash48] So few studies have consideredmore than two objective optimization problems consideringthe computational complexity that affects the convergencespeed and the stability of the adopted algorithms Howevermany research contributions have dealt with the tech-noeconomic analysis of the A-HMG system while the op-timal configuration and the LCOE index are not a standardvalue which depends on several variables such as locationweather and the applied optimization technique the case ofsome studies in literature [39]

Moreover the present work uses a MDPSO algorithmthat improves the traditional PSO algorithmrsquos researchstrategy and decreases the probability of converging to localoptimum )us the entire search space will be exploredefficiently contrary to other works in literature that used theconventional PSO algorithm for the optimization problem[48] )e MDPSO is a specific algorithm that gives to theuser the ability to modify and add more sophisticatedmathematical models for various RE technologies unlike thecommercial software tools that restrict the user [46] Finallythis paper does not used many numbers of scenarios that arerequired to achieve a good results where the high number ofscenarios makes the problem very large and time-consumingto solve [47]

8 Conclusions

In this paper a smart energy management scheme (SEMS)with a multimodal delayed particle swarm optimization(MDPSO) is developed for performing the optimal sizing forthe A-HMG system of a fishing village in the city ofEssaouira Morocco )e developed A-HMG system modelcontains PV panels WTs DGs and battery storage systems)e levelized cost of energy (LCOE) the lowest loss of powersupply probability (LPSP) and the maximum renewablefactor (REF) are defined as objective functions)e results ofthe optimization in this location show that A-HMG systemcan be applied for this location with a high renewable factorMoreover the solution is very promising in terms ofachieving values of the LCOE (017 $kWh) LPSP (012)and the REF (90) )erefore using renewable energy canbe considered as a good alternative to enhancing energyaccess in remote areas as the fishing village in the city ofEssaouira Morocco )e obtained results demonstrate ahigh efficiency of the successful application of the MDPSOfor the proposed SEMS compared to several research con-tributions in the literature )e utilization of the proposedmethod can help to overcome some of the technicalproblems that still limit the distribution of A-HMG system

projects in Morocco Finally sensitivity analysis is alsocarried out in order to verify the performance of the results

Data Availability

)e typical years of solar radiation wind speed and ambienttemperature time series are obtained using Meteonormsoftware

Conflicts of Interest

)e authors declare that they have no conflicts of interest

References

[1] M Enzili ldquoLrsquoenergie eolienne au maroc (Ressources Potentielet Projets)rdquo in Proceedings of the 6eme conference maroco-allemande sur lrsquoenergie eolienne-Casablanca November 2011

[2] B Song Z Wang and L Zou ldquoOn global smooth pathplanning for mobile robots using a novel multimodal delayedPSO algorithmrdquo Cognitive Computation vol 9 no 1pp 5ndash17 2017

[3] M A Mohamed A M Eltamaly A I Alolah andA Y Hatata ldquoA novel framework-based cuckoo search al-gorithm for sizing and optimization of grid-independenthybrid renewable energy systemsrdquo International Journal ofGreen Energy vol 16 no 1 pp 86ndash100 2019

[4] A Chaouachi R M Kamel R Andoulsi and K NagasakaldquoMultiobjective intelligent energy management for a micro-gridrdquo IEEE Transactions on Industrial Electronics vol 60no 4 pp 1688ndash1699 2012

[5] J Ahmad M Imran A Khalid et al ldquoTechno economicanalysis of a wind-photovoltaic-biomass hybrid renewableenergy system for rural electrification a case study of KallarKaharrdquo Energy vol 148 pp 208ndash234 2018

[6] M S Taha and A R M Yasser ldquoRobust MPC-based energymanagement system of a hybrid energy source for remotecommunitiesrdquo in Proceedings of the 2016 IEEE ElectricalPower and Energy Conference (EPEC) pp 1ndash6 IEEE OttawaCanada October 2016

[7] S Sukumar H Mokhlis S Mekhilef K Naidu andM Karimi ldquoMix-mode energy management strategy andbattery sizing for economic operation of grid-tied microgridrdquoEnergy vol 118 pp 1322ndash1333 2017

[8] S A Helal R J Najee M O Hanna M F ShaabanA H Osman and M S Hassan ldquoAn energy managementsystem for hybrid microgrids in remote communitiesrdquo inProceedings of the 2017 IEEE 30th Canadian Conference onElectrical and Computer Engineering (CCECE) pp 1ndash4 IEEEWindsor ON Canada April 2017

[9] C A Correa G Marulanda and A Garces ldquoOptimalmicrogrid management in the Colombian energy market withdemand response and energy storagerdquo in Proceedings of the2016 IEEE Power and Energy Society General Meeting(PESGM) IEEE July 2016 pp 1ndash5 Boston MA USA

[10] H Borhanazad S Mekhilef V Gounder GanapathyM Modiri-Delshad and A Mirtaheri ldquoOptimization ofmicro-grid system using MOPSOrdquo Renewable Energy vol 71pp 295ndash306 2014

[11] M Abedini M H Moradi and S M Hosseinian ldquoOptimalmanagement of microgrids including renewable energyscources using GPSO-GM algorithmrdquo Renewable Energyvol 90 pp 430ndash439 2016


[12] Y A Katsigiannis P S Georgilakis and E S KarapidakisldquoMultiobjective genetic algorithm solution to the optimumeconomic and environmental performance problem of smallautonomous hybrid power systems with renewablesrdquo IETRenewable Power Generation vol 4 no 5 pp 404ndash419 2010

[13] A M W Bhuiyan K S Islam M M HaqueM R R Mojumdar and M M Rahman ldquoCommunity-basedconvenient hybrid mini-grid implementation proposal andanalysis for Bangladeshrdquo International Journal of Innovationand Technology Management vol 2 pp 354ndash359 2011

[14] R Ayop and C W Tan ldquoA comprehensive review on pho-tovoltaic emulatorrdquo Renewable and Sustainable Energy Re-views vol 80 pp 430ndash452 2017

[15] L Wang and C Singh ldquoPSO-based multi-criteria optimumdesign of a grid-connected hybrid power system with multiplerenewable sources of energyrdquo in Proceedings of the 2007 IEEESwarm Intelligence Symposium IEEE Honolulu HI USApp 250ndash257 April 2007

[16] A L Bukar C W Tan and K Y Lau ldquoOptimal sizing of anautonomous photovoltaic wind battery diesel generatormicrogrid using grasshopper optimization algorithmrdquo SolarEnergy vol 188 pp 685ndash696 2019

[17] Y Shi and R C Eberhart ldquoParameter selection in particleswarm optimizationrdquo in Proceedings of the InternationalConference on Evolutionary Programming Springer BerlinHeidelberg pp 591ndash600 March 1998

[18] A Kaabeche and R Ibtiouen ldquoTechno-economic optimizationof hybrid photovoltaic wind diesel battery generation in astand-alone power systemrdquo Solar Energy vol 103 pp 171ndash1822014

[19] S Diaf D Diaf M Belhamel M Haddadi and A Louche ldquoAmethodology for optimal sizing of autonomous hybrid PVwind systemrdquo Energy Policy vol 35 no 11 pp 5708ndash57182007

[20] J Schmid ldquoDincklage RD von Power conditioning andcontrolrdquo Euroforum New Energies vol 3 pp 241ndash243 1988

[21] J S H Schimd and H Schimd ldquoInverter for photovoltaicsystemrdquo in Proceedings of the Fifth Contractorrsquos Meeting of theEuropean Community Photovoltaic Demonstration Projectsp 122 Lisbon Portugal 1991

[22] A El Fathi L Nkhaili A Bennouna and A OutzourhitldquoPerformance parameters of a standalone PV plantrdquo EnergyConversion and Management vol 86 pp 490ndash495 2014

[23] A Kaabeche M Belhamel and R Ibtiouen ldquoTechno-eco-nomic valuation and optimization of integrated photovoltaicwind energy conversion systemrdquo Solar Energy vol 85 no 10pp 2407ndash2420 2011

[24] Oslash Skarstein and K Uhlen ldquoDesign considerations with re-spect to long-term diesel saving in winddiesel plantsrdquo WindEngineering vol 13 no 2 pp 72ndash87 1989

[25] Y Azoumah D Yamegueu P Ginies Y Coulibaly andP Girard ldquoSustainable electricity generation for rural andperi-urban populations of sub-Saharan Africa the ldquoflexy-energyrdquo conceptrdquo Energy Policy vol 39 no 1 pp 131ndash1412011

[26] M K Deshmukh and S S Deshmukh ldquoModeling of hybridrenewable energy systemsrdquo Renewable and Sustainable EnergyReviews vol 12 no 1 pp 235ndash249 2008

[27] M Kolhe ldquoTechno-economic optimum sizing of a stand-alone solar photovoltaic systemrdquo IEEE Transactions on EnergyConversion vol 24 no 2 pp 511ndash519 2009

[28] V K Sharma A Colangelo and G Spagna ldquoPhotovoltaictechnology basic concepts sizing of a stand alone photo-voltaic system for domestic applications and preliminary

economic analysisrdquo Energy Conversion and Managementvol 36 no 3 pp 161ndash174 1995

[29] R Dufo-Lopez and J L Bernal-Agustın ldquoMulti-objectivedesign of PV-wind-diesel-hydrogen-battery systemsrdquo Re-newable Energy vol 33 no 12 pp 2559ndash2572 2008

[30] R K Rajkumar V K Ramachandaramurthy B L Yong andD B Chia ldquoTechno-economical optimization of hybrid pvwindbattery system using neuro-fuzzyrdquo Energy vol 36 no 8pp 5148ndash5153 2011

[31] R Luna-Rubio M Trejo-Perea D Vargas-Vazquez andG J Rıos-Moreno ldquoOptimal sizing of renewable hybridsenergy systems a review of methodologiesrdquo Solar Energyvol 86 no 4 pp 1077ndash1088 2012

[32] H Yang W Zhou L Lu and Z Fang ldquoOptimal sizingmethod for stand-alone hybrid solar-wind system with LPSPtechnology by using genetic algorithmrdquo Solar Energy vol 82no 4 pp 354ndash367 2008

[33] B C Mohan and R Baskaran ldquoA survey ant colony opti-mization based recent research and implementation on sev-eral engineering domainrdquo Expert Systems with Applicationsvol 39 no 4 pp 4618ndash4627 2012

[34] F Marini and B Walczak ldquoParticle swarm optimization(PSO) A tutorialrdquo Chemometrics and Intelligent LaboratorySystems vol 149 pp 153ndash165 2015

[35] Y Tang ZWang and J-a Fang ldquoParameters identification ofunknown delayed genetic regulatory networks by a switchingparticle swarm optimization algorithmrdquo Expert Systems withApplications vol 38 no 3 pp 2523ndash2535 2011

[36] Y Shi and R C Eberhart ldquoEmpirical study of particle swarmoptimizationrdquo in Proceedings of the 1999 congress on evolu-tionary computation-CEC99 (Cat No 99TH8406) vol 3IEEE Washington DC USA pp 1945ndash1950 July 1999

[37] Y Shi and R Eberhart ldquoA modified particle swarm opti-mizerrdquo in Proceedings of the 1998 IEEE International Con-ference on Evolutionary Computation Proceedings IEEEWorld Congress on Computational Intelligence (Cat No98TH8360) pp 69ndash73 May 1998

[38] M A Jallal S Chabaa and A Zeroual ldquoA novel deep neuralnetwork based on randomly occurring distributed delayedPSO algorithm for monitoring the energy produced by fourdual-axis solar trackersrdquo Renewable Energy vol 149pp 1182ndash1196 2020

[39] R Hosseinalizadeh H Shakouri G M S Amalnick andP Taghipour ldquoEconomic sizing of a hybrid (PV-WT-FC)renewable energy system (HRES) for stand-alone usages by anoptimization-simulation model case study of Iranrdquo Renew-able and Sustainable Energy Reviews vol 54 pp 139ndash1502016

[40] M Gokccedilek and C Kale ldquoOptimal design of a hydrogenrefuelling station (HRFS) powered by hybrid power systemrdquoEnergy Conversion and Management vol 161 pp 215ndash2242018

[41] N Zeng Z Wang H Zhang and F E Alsaadi ldquoA novelswitching delayed PSO algorithm for estimating unknownparameters of lateral flow immunoassayrdquo Cognitive Com-putation vol 8 no 2 pp 143ndash152 2016

[42] W Liu Z Wang X Liu N Zeng and D Bell ldquoA novelparticle swarm optimization approach for patient clusteringfrom emergency departmentsrdquo IEEE Transactions on Evo-lutionary Computation vol 23 no 4 pp 632ndash644 2018

[43] M Clerc and J Kennedy ldquo)e particle swarmmdashexplosionstability and convergence in a multidimensional complexspacerdquo IEEE Transactions on Evolutionary Computationvol 6 no 1 pp 58ndash73 2002


[44] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions onEvolutionary Computation vol 8 no 3 pp 240ndash255 2004

[45] C Shang D Srinivasan and T Reindl ldquoAn improved particleswarm optimisation algorithm applied to battery sizing forstand-alone hybrid power systemsrdquo International Journal ofElectrical Power amp Energy Systems vol 74 pp 104ndash117 2016

[46] C Phurailatpam B S Rajpurohit and L Wang ldquoPlanningand optimization of autonomous DCmicrogrids for rural andurban applications in Indiardquo Renewable and SustainableEnergy Reviews vol 82 pp 194ndash204 2018

[47] P Nagapurkar and J D Smith ldquoTechno-economic optimi-zation and environmental life cycle assessment (LCA) ofmicrogrids located in the US using genetic algorithmrdquo EnergyConversion and Management vol 181 pp 272ndash291 2019

[48] M Kharrich O Mohammed and M Akherraz ldquoDesign ofhybrid microgrid PVWindDieselBattery system case studyfor rabat and baghdadrdquo EAI Endorsed Transactions on EnergyWeb vol 7 no 26 2020


opportunity to use the advantages of RE resources incombination with conventional ones [3]

In the recent literature the primary goals are to for-mulate and implement energy production strategies withgreater flexibility higher efficiency and lower LCOEHowever reaching these goals cannot be accessible due tothe nonlinear behavior of RE production and storage sys-tems which are strongly dependent on weather changes Soto overcome these problems many optimization techniquesare employed in several scientific contributions in theliterature

)e optimization problem can result in a mono-objec-tive or multiobjective problem which can include theminimization of the LCOE LPSP and the pollutant emis-sions Two frequently used optimization techniques arestochastic dynamic programming methods for optimizingthe energy management problem with multidimensionalobjectives andmetaheuristic techniques to solve the problemof optimization with multiconstraints multidimensionaland highly nonlinear combinatorial problems

Based on the literature review we found several researchcontributions that are focused on the HMG systems opti-mization problems )e authors in [4] proposed a gener-alized formulation for intelligent energy management of aHMG in using multiobjective optimization to minimize theoperation cost and the environmental impact where theyapplied artificial neural network to predict RE generationand load demand )e problem formulation in this workincludes optimal battery scheduling taking into account theuncertainty of the HMG exogenous variables and forecastedentities However the proposed approach does not take intoconsideration the REF as an objective and the optimal sizingof battery storage is not taken into account

In the research presented in [5] a technical and eco-nomic method is proposed to optimize a HMG based onmixed integer linear programming In this paper the costfunction is solved via linear programming based on a generalalgebraic modelling system where the optimization phase ofthe HMG system was performed via HOMER software )eauthors have analyzed WT PV and biomass resource po-tential of a selected area in province Punjab Kallar Kahar)e cost of energy is calculated for different peak loadenergy demand profiles and grid availability However theproposed formulations do not introduce any storage solu-tion to solve the intermittence problem of RE and tominimize the emission of polluting gases by biomassresource

Taha and Yasser [6] presented a robust algorithm basedon a predictive control model for an isolated HMG in fourdifferent case studies to minimize the total operating cost tominimize the pollutant CO2 and to minimize the dumpenergy )e results showed that the optimal battery dailynumber of cycles minimum SOC and the initial SOC of thebattery storage depend the pool-price variation Moreoverthe number of scenarios required to achieve a good resultsmakes the problem very large and time-consuming to solve

A mixed method is proposed for microgrid energymanagement in [7] )is was achieved by using linear op-timization methods to obtain an optimal energy storage

system size)e grid-connectedmicrogrid system consists ofsolar PV two identical solid oxide fuel cells and a batterybank operated parallel with the load Moreover the pro-posed methodology neglected many important constraintson the LPSP and REF indexes

)e authors in [8] analyzed an energy managementsystem for a hybrid ACDC microgrid in an isolatedcommunity that employs a PV system for desalination inorder to minimize the daily operating costs by using themixed integer nonlinear programming )e aim of theproposed methodology is to manage all system assets toensure stable operation of the hybrid ACDC microgrid andsecured clean water supply for the customers )is contri-bution has neglected the REF and the availability objectives

Correa et al [9] proposed an energy management systembased on a virtual power plant )e studied microgrid has solarpanels and storage systems and works in an interconnectedmanner)ese elements aremodeled using linear programmingmethods to minimize the operating costs REs are incorporatedinto an energetic model and are mainly based on hydric re-sourcesMoreover the authors concluded that the battery sizingplays a crucial role in operational cost of the microgridHowever this contribution has considered a single objectiveoptimization problem since the statement of a number ofobjective optimization problems affects the convergence speedand the stability of the adopted algorithms

In the research presented in [10] an intelligent energymanagement system is proposed for HMG system in threestations in Iran )e objective for this study is to minimizethe operational costs and environmental impacts by using amultiobjective particle swarm optimization algorithm )eLCOE and the LPSP are defined as objective functions )eresult of optimization shows that HMG system can be ap-plied for one of the three proposed locations with a highREF However the optimal configuration and the LCOEindex are not a standard value which depends on location

)e authors in [11] presented an energy managementsystem for a PVWTDG stand-alone HMG which is op-timized using a particle swarm algorithm with Gaussianmutation )is paper minimizes both the capital and fuelcosts of the system However the authors mainly concen-trated on economic evaluation of hybrid energy systems butthey do not examine other aspects of sustainability of thesesystems

Katsigiannis et al [12] used multiobjective optimizationtechniques to size an A-HMG while simultaneously mini-mizing LCOE and CO2 emissions )e obtained results ofLCOE are not competitive

)e previous reviewed studies for A-HMG optimizationhave recorded the following gaps

(1) Few research contributions have considered morethan two objective optimization problems consid-ering the computational complexity that affects theconvergence speed and the stability of the adoptedalgorithms

(2) Many studies have dealt with the techno-economicanalysis of the A-HMG system while the optimalconfiguration and the LCOE index are not a standard














Gref

(1)

where








V1

V2

h

href1113888 1113889

α

(2)

where




PWT


Pr

V3r minus V3


3minus V



⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where





DC-BUS

AC-BUSPV PRE Load

Wind turbine

PBat

DCDC

ACDC

DCDC


Battery

PWT

PPV

DCAC

Diesel generator


Firstperformance

region

Pow

er o

utpu

t

VCUT-IN VCUT-OUT

Rated power

Secondpeformance

region

VRated

Wind velocity




CB Pload times AD


where




ηinv (5)

where







where



ηinv P

P + P0 + kP2 (8)


K 1


P0 1 minus 991η10

minus1

η100minus 91113888 1113889

2

P Pout

Pn

(9)





where





where













MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where






25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)



1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References

































































Gref

(1)

where








V1

V2

h

href1113888 1113889

α

(2)

where




PWT


Pr

V3r minus V3


3minus V



⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where





DC-BUS

AC-BUSPV PRE Load

Wind turbine

PBat

DCDC

ACDC

DCDC


Battery

PWT

PPV

DCAC

Diesel generator


Firstperformance

region

Pow

er o

utpu

t

VCUT-IN VCUT-OUT

Rated power

Secondpeformance

region

VRated

Wind velocity




CB Pload times AD


where




ηinv (5)

where







where



ηinv P

P + P0 + kP2 (8)


K 1


P0 1 minus 991η10

minus1

η100minus 91113888 1113889

2

P Pout

Pn

(9)





where





where













MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where






25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)



1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References






















































DC-BUS

AC-BUSPV PRE Load

Wind turbine

PBat

DCDC

ACDC

DCDC


Battery

PWT

PPV

DCAC

Diesel generator


Firstperformance

region

Pow

er o

utpu

t

VCUT-IN VCUT-OUT

Rated power

Secondpeformance

region

VRated

Wind velocity




CB Pload times AD


where




ηinv (5)

where







where



ηinv P

P + P0 + kP2 (8)


K 1


P0 1 minus 991η10

minus1

η100minus 91113888 1113889

2

P Pout

Pn

(9)





where





where













MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where






25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)



1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References






















































CB Pload times AD


where




ηinv (5)

where







where



ηinv P

P + P0 + kP2 (8)


K 1


P0 1 minus 991η10

minus1

η100minus 91113888 1113889

2

P Pout

Pn

(9)





where





where













MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where






25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)



1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References




























































MinF(x)

f1(x)

f2(x)

⋮

fk(x)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

Subject toH(x)le 0

G(x) 01113896

(12)

where






25

2

15

1

05

05 10 15 20

Time (hour)

Load

(kW

)



1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References





















































1200

1000

800

600

400

200

0

Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Irra

dian

ce (W

m2 )


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

Win

d sp

eed

(ms

)

12

10

8

6

4

2

0


Time (hours)0 1000 2000 3000 4000 5000 6000 7000 8000

45

40

35

30

25

20

15

10

5

0

Tem

pera

ture

(degC)



Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References





















































Start

Read input




Discharge battery

No Yes

IfSOC (t) le SOCmin





No Yes



No

Charge battery

IfSOC (t) ge SOCmax

SOC (t) = SOCmax

No Yes

Dump load

Return

Yes

(i)(ii)

(iii)

(i)





LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References























































LCOE$

kWh1113888 1113889

TPV1113936

8760t1 Pload(t)

times CRF (13)

where





(1 + β)n minus 1 (14)

where





LPSP 1113936


1113872 1113873

11139368760t1 Pload(t)

(15)

where











8760t1 PDG(t)

11139368760t1 PPV(t) + PWT(t)( 1113857

1113888 1113889 times 100 (17)



0leNPV leNPVmax

0leNWT leNWTmax

0leNAD leNADmax

0leNDG leNDGmax

(18)

where



















xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References






























































xi(k + 1) xi(k) + Vi(k + 1)

(19)

where







+ wfi (20)

where






+ c1f (21)


+ c2f (22)

where











xi(k + 1) xi(k) + Vi(k + 1)

(23)

where








di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References























































di 1

S minus 11113944

S

j1jne 1

1113944

D


2

11139741113972

(24)

where





where





ξ(k)

1 0leEFlt 025

2 025leEFlt 05

3 05leEFlt 075

4 075leEFle 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(26)
















temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References






















































temperature


components


variable


SEMS

Start










K = K + 1


End


Yes

No






c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References
























































c1i 25c1f 05c2i 05c2f 25




Essaouira (Morocco)



REF () 90

0 20 40 60 80 100 120 140 160 180 200Iteration

LCO

E ($

kW

h)

ndash100


0 20 40 60 80 100 120 140 160 180 200Iteration

ndash102

LPSP

()








0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References


























































0 20 40 60 80 100 120 140 160 180 200Iteration

ndash1032

ndash1034

ndash1036

ndash1038

REF

()


PV panels = 15

WT = 1

DG = 1

40

30

10

0

20

ndash10

ndash20

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

LCO

E ($

KW

h)

0 5 10 15 20 25 30 35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50 55


Number of WT0

05

5

10

10

15

15

20

20

25

25

30

30

35

35

40

40

45

45

50 55Number of DG


06506

05505

04504

03503

02502

027

026

025

024

023

022

021

02

019

018

WTPV panelsDG











0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References





























































0 20 40 60 80 100 120 140 160 180 200Number of houses

0

01

02

03

04

05

06

07

08

LCO

E ($

kW

h)




[39]-2016 PVWTFC

Nikouyeh (Iran) 056





Tucson (US) 043






8 Conclusions



Data Availability




References
























































8 Conclusions



Data Availability




References



































































































Documents

MultiobjectiveSizingofanAutonomousHybridMicrogrid ...downloads.hindawi.com/journals/cin/2020/8894094.pdf · ResearchArticle MultiobjectiveSizingofanAutonomousHybridMicrogrid UsingaMultimodalDelayedPSOAlgorithm:ACaseStudyof