amultiobjectiveoptimaloperationofastand-alonemicrogrid...

Research ArticleA Multiobjective Optimal Operation of a Stand-Alone MicrogridUsing SAPSO Algorithm

Guoping Zhang 1 Weijun Wang 1 Jie Du 2 and Hua Liu1

1Department of Military Installations Army Logistics University of PLA Chongqing 401331 China2Electric Power Research Institute Chongqing Electric Power Company Chongqing 401123 China

Correspondence should be addressed to Weijun Wang wjwang636126com

Received 19 September 2019 Revised 25 November 2019 Accepted 4 January 2020 Published 7 March 2020

Academic Editor Pietro Varilone

Copyright copy 2020 Guoping Zhang 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

Microgrid is an effective way to utilize renewable energy resources especially for satisfying the electricity requirements in remoteislands e operation optimization of an island microgrid is critical to ensure the effective performance of the whole microgridsystem and it is usually a multiconstrained and multiobjective optimization problem e main contribution of this study is anoperation optimization method for the stand-alone microgrid system in a remote island which includes wind PV battery anddiesel generator In this paper a novel operation optimization model for stand-alone microgrid is proposed in which the batterysystem is considered separately the multiobjective day-ahead optimization model considering economic cost battery depre-ciation cost and environmental protection cost is established In the optimization the output power of diesel generator andenergy storage system are chosen as the decision variables For this purpose an efficient search algorithm combining the particleswarm optimization (PSO) algorithm and the simulated annealing (SA) algorithm is developede hybrid algorithm is applied tosearch for the Pareto solution set of the optimization problem e search results are compared with those from traditional PSOalgorithm Also a grey target decision-making theory based on the entropy weight method is proposed to identify the best trade-off scheduling scheme among all the solutions and the results are compared with those from two other commonly used subjectiveand objective methods e results show that the proposed optimization method can be applied to the day-ahead operationoptimization of the microgrid system and help the user obtain the best compromise operation scheme for stand-alone microgrid

1 Introduction

Nowadays there are still many islands that have no access tothe public power grid these areas are highly dependent ontraditional diesel generators to supply their energy needs[1 2] e islands are usually rich in renewable energy re-sources such as solar and wind resources [3] Normally thevariation of renewable resources and the time distribution ofload demand may not match exactly [4] e main challengein developing renewable resources is their stochastic andintermittent natures In order to eliminate the impact of thisproblem the microgrid that integrates a variety of renewableenergy resources has been proposed [5] For remote areasprevious investigations have shown that this approach cansignificantly improve the reliability of the whole powersystem [6 7]

In the past years many studies have focused on theoptimal design and sizing of microgrid system to minimize

the life cycle cost while satisfying the power quality [8ndash11]Some powerful optimal design software tools such as HO-MER [12] and HYBRID2 [13] are developed With the in-creasing penetration rate of renewable energy generationthe uncertainty caused by the randomness and intermittencyof renewable energy resources has imposed a considerableimpact on the safe and reliable operation of the microgrid[14]

At present study of the optimal operation of microgridmainly considers its operation cost [15] environmental cost[16] power supply reliability [17] and so on Guo et al [18]proposed a multiobjective optimization model for isolatedmicrogrid system which aimed at the confliction of interestsbetween the distribution company and the distributedgeneration owners Azaza and Wallin [19] made a trade-offbetween three conflicting objectives namely the reliabilityof the system the cost of electricity production and theoperation environmental impact Zhang et al [20] used

HindawiJournal of Electrical and Computer EngineeringVolume 2020 Article ID 6042105 16 pageshttpsdoiorg10115520206042105

forecast load information instead of past information foroptimally designing a hybrid renewable energy scheme(WTPVBAT) to minimize TLCC of the scheme

However the microgrid optimal scheduling model is amulticonstrained multiobjective problem Differentmethods are used to solve this problem e most commonapproach is to transform the multiobjective optimizationproblem into one single-objective optimization problem byusing the linear weighted sum method [21] In the previousstudy some other classic approaches are adopted such asiterative technique [22] mixed-integer linear programming[23] design space concept [24] andmin-max approach [25]Considering that some objectives are mutually exclusive themetaheuristic optimization techniques are found to be moreacceptable than traditional classic methods for the optimi-zation of microgrid system because of their ability to searchglobal optimum fast convergence and good calculationaccuracy [26] which can be divided into two groups one isthe evolutionary algorithms (EAs) which is based on em-ulating the process of natural evolution and survival of thefittest such as genetic algorithm (GA) [27] and evolutionaryprogramming (EP) [28] and the other is the swarm intel-ligence algorithms (SIAs) whose operation is based on socialand cooperative behaviors of individuals such as particleswarm optimization (PSO) [29] bee algorithm [26] and antcolony algorithm [30]

Cagnano et al [31] proposed a new strategy thatmanages the active power reserve in isolated microgrid formaximization of the gridrsquos reservation is work is doneby adopting direct Lyapunov theorem and sensitivityanalysis but the cost function is not considered Wu et al[32] presented the dynamic economic dispatch model of acombined heat and power (CHP) microgrid system Inorder to minimize the total cost namely operating costand pollutant treatment cost the biobjective problem issimplified by summing these two costs directly An im-proved particle swarm optimization (PSO) algorithm isproposed to solve the objective function But the rela-tionship between the two costs is not discussed Karimiet al [33] presented a multiobjective operational model fora grid-connected microgrid considering the cost securityand reliability of the system simultaneously To solve theproposed model a set of Pareto solutions is obtained firstby using the weighted sum approach e hybrid multi-objective and multiattribute decision-making frameworkis applied to achieve the best operation status Moradi et al[34] developed a multiobjective optimization model in-cluding fuel consumption cost total voltage variation andthe voltage stability index A hybrid optimization algo-rithm combining the harmony algorithm (HS) and thegenetic algorithm (GA) is proposed to solve the probleme fuzzy method is employed to find the optimum so-lution among all the nondominated results Zhang et al[35] to minimize the total life cycle cost and increase theaccuracy of size optimization of the independent hybridrenewable energy systems proposed a new hybrid opti-mization algorithm based on three algorithms chaoticsearch harmony search and simulated annealing eforecasting weather data is used along with artificial neural

networks to improve the accuracy of the size optimizationalgorithm results

Although various studies on microgrid operation opti-mization from different aspects and different techniqueshave been reported almost all of them have included thebattery depreciation cost into the cost of power generationwithout considering it separately e energy storage batterysystem is critical to stand-alone microgrid on an islandBecause of the harsh environment of island and the frequentcharging and discharging of battery bank the lifespan ofbattery bank will be greatly affected which will accelerate thedepreciation of battery bank During the operation opti-mization process it is necessary to consider the batterysystem separately Also both the optimization techniquesand the optimal decision-making methods need furtherresearch

In this paper a mathematical model for each device ofthe microgrid system is introduced at first In order to usethe battery more reasonably a novel battery operation costmodel is proposed and chosen as one of the optimizationobjectives To realize the economic operation of stand-alonemicrogrid a multiobjective function is defined based onminimize the fuel cost operation and maintenance costenvironmental cost and battery depreciation cost subject toconstraint conditions An efficient method is needed to solvethis multiobjective function Due to the features of particleswarm optimization algorithm and simulated annealingalgorithm an improved hybrid SAPSO algorithm is devel-oped to obtain Pareto front solutions for the multiobjectiveoptimization problem e results are compared with thoseobtained by traditional particle swarm optimization algo-rithm In order to help user choose the optimal scheme thegrey target decision-making strategy based on entropyweight method is proposed to identify the best compromisesolution from the obtained Pareto solution set At last astand-alone microgrid containing wind PV battery anddiesel generator in Yongxing Island China is chosen as onecase study to verify the effectiveness of the proposedmethods

is paper is organized as follows e introduction isgiven in Section 1 In Section 2 description of the proposedmicrogrid system and modelling of major components arepresented e optimization problem is analysed in Section3 Section 4 explains the proposed methodology e resultsare discussed in Section 5 e conclusion is shown inSection 6

2 Model of Major Components

e stand-alone microgrid system is composed of photo-voltaic arrays wind power generation diesel generatorsenergy storage battery system power conversion system(PCS) loads and energy management system (EMS) asshown in Figure 1

e AC bus mode is used in this microgrid system andall micro sources are directly integrated into the commonAC bus e photovoltaic array contains multiple PVmodules each of which is directly incorporated into thecommon AC bus through a string inverter e wind

2 Journal of Electrical and Computer Engineering

generation consists of several permanent magnet direct-drive wind turbines that are connected to the AC bus byACDCAC converters e maximum power pointtracking (MPPT) control strategy is adopted for PV andwind generation which aims to maximize the utilizationof solar and wind energy e energy storage batterysystem is integrated into the AC bus via a bidirectionalpower conversion system (PCS) and plays the role of peakclipping and valley filling in the system Under normalcircumstances the diesel generators provide frequencyand voltage support for the system as the main powersource while the energy storage PCS adopts the constantpower control strategy When the diesel generator fails orthe load is low the diesel generator will be turned off andthe energy storage PCS becomes the main power sourceworking in VF control mode e whole microgridsystem achieves stable and economic operation under thecoordinated control of the energy management system(EMS)

21 PV System e PV system works by converting solarenergy into electrical energy erefore the output power isrelated not only to the solar irradiation but also to theperformance of the photovoltaic module itself e ambienttemperature also affects the output power of the componente temperature coefficient should be taken into consid-eration us the output of a PV system can be calculated bythe following equation [36]

PPV(t) Prate_PVηPVG(t) 1 + αTP TPV(t) minus TSTC( 11138571113858 1113859 (1)

where PPV(t) is the real output power of PV system Prate_PVis the nominal capacity of PV array ηPV is the deterioratingfactor G(t) is the actual solar irradiation on the PV panelαTP is the temperature factor (degC) TSTC is the ambienttemperature of PV cell under standard test conditionnormally 25degC and TPV(t) is the temperature on the surfaceof PV panel it is usually different from the ambient tem-perature which can be obtained from equation (2) as follows[37]

TPV(t) T(t) + TNOCT minus 20( 1113857((G(t))(08)) 1 minus ηSTC 1 minus 25αTP( 1113857( 1113857(09)( 1113857

1 + TNOCT minus 20( 1113857((G(t))(08)) αTPηSTC( 1113857(09)( 1113857 (2)

hellip

Diesel generator Load

EMS

ACDCAC BoxDCAC

DC

AC

DC

AC

AC bus

BMS

Battery systemPV systemWind turbine

ElectricityControl data

Figure 1 e schematic configuration of a PV-wind-battery-diesel stand-alone microgrid system

Journal of Electrical and Computer Engineering 3

where ηSTC is the efficiency at standard test condition TNOCT is the nominal operating temperature of PV cell andT(t) is the ambient temperature degC

22Wind Turbine Wind turbines convert the kinetic energyof wind into rotational kinetic energy of the blades and ul-timately into electrical energy [38] A type of permanentmagnet direct-drive wind turbine manufactured by GHRE-Power is adopted in this microgride output power of windturbine can be calculated by the following equation [39]

PWT(t)

0 vlt vcut in vgt vcut out

Prated WT timesv2 minus v2cut inv2R minus v2cut in

1113888 1113889 vcut in le vle vr

Prated WT vr le vle vcut out

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

where v is the wind speed vr is the rated wind speed of windturbine 13ms Prated_WT is the rated output power of WTand vcut_in and vcut_out refer to the cut-in and cut-out windspeed of WT 3ms and 25ms respectively

23 Diesel Generator Because of the randomness andvolatility of renewable resources there may be a mismatchbetween power generation and load demand in the re-newable energy generation system Especially for a stand-alone microgrid it is quite necessary to deploy one or morediesel generators [40] e fuel consumption rate of dieselgenerator is one of the most important parameters inmicrogrid operation since both the operating and main-tenance cost and the pollutant emission are directly de-pendent on fuel consumption e hourly fuelconsumption rate of diesel generator can be formulated asfollows [41]

F(t) F0Prate gen + F1Pgen(t) (4)

where F(t) is the hourly fuel consumption of diesel gen-erator Lh Prate_gen denotes the nominal power and Pgen(t)

is the real output power at time t and F0 and F1 are theintercept coefficient and slope of the fuel consumptioncurve LkW describing the relationship between the fuelconsumption and electrical power and are approximated to0084 and 024 respectively [42]

24BatterySystem e energy storage battery system is ableto balance the power of stand-alone microgrid system bystoring the excess energy or supplying the power deficit It isusually composed of one or more individual batteries estate of charge (SOC) of battery system at time t is deter-mined by the total available generation and the load demandas well as the SOC at time t minus 1 which can be calculated asfollows [43]

For battery charging

SOC(t) (1 minus δ) middot SOC(t minus 1) + Pgen(t) minus Pload(t)1113872 1113873

middot ηbsch middotΔt

Ebat

(5)

For battery discharging

SOC(t) (1 minus δ) middot SOC(t minus 1) minus Pload(t) minus Pgen(t)1113872 1113873

middotΔt

ηbsdisEbat

(6)

where δ is the self-discharging factor SOC(t) is the state ofcharge of battery Pgen(t) is the total available energy gen-erated by micro sources Pload(t) is the load demand in timeinterval Ebat is the capacity of the battery bank Δt is the timeinterval and ηbsch and ηbsdis are the battery charging anddischarging efficiency including the inverter respectivelye lead-acid battery GFM-800RC manufactured byNARADA is adopted in the microgrid system

3 Multiobjective Optimization Model

In order to minimize the economic cost the battery de-preciation cost and the environmental cost of microgridsystem a multiobjective optimizationmodel is established inthis paper e objective function is as follows

minF(x) min fc(x) fb(x) fe(x)1113858 1113859T

1113872 1113873

fc(x) 1113944T

t1CF + COM1113858 1113859

fb(x) 1113944T

t1CB

fe(x) 1113944T

t1CE

(7)

where fc(x) is the economic cost fb(x) is the batterydepreciation cost fe(x) is the environmental cost CF is thefuel cost of diesel generator COM is the equipment operationandmaintenance costCB is the battery depreciation costCE

is the environmental cost of pollutant emissions affecting theenvironment and T is the number of time intervals in theoptimization period which is 24 hours in this paper

Due to the stochastic and intermittent natures of solarirradiance and wind speed the output power of PV systemand wind turbines are uncontrollable erefore the outputpower of diesel generator and battery system are chosen asthe optimization decision variables in this paper e op-timization period contains 24 time intervals in one day sothe decision variables are 24-dimensional power vectors

31 Economic Cost Since PV and wind generations userenewable energy the cost of both is not considerede fuelconsumption cost of diesel generator can be expressed as


CF 1113944n

i1f Pi(t)( 1113857Cfuel (8)

where f(Pi(t)) represents the amount of diesel consumedby the diesel generator in time interval L and Cfuel is the unitprice of diesel $L

e operation and maintenance cost of the microgrid islinearly related to the electrical energy produced by thesystem e expression of COM is

COM 1113944n

i1Pi(t)KOMi (9)

where Pi(t) is the output power of unit i at time t KOMi isthe operation and maintenance cost per kilowatt of unit i$kWh and n is the number of generation units

32 BatteryDepreciation Cost Due to the fact that the harshnatural environment of the island will accelerate aging ofbattery the depreciation cost of battery system is adopted asone of the optimization objectives Meanwhile frequentcharging and discharging will reduce the lifespan of the lead-acid battery bank thereby indirectly increasing the operatingcost of the system Converting the replacement cost of thelead-acid battery into the operating cost can more accuratelyreflect the impact of the battery life on the operating cost Tothis end this paper designs a battery depreciation costobjective function that takes into account the replacementcost of lead-acid battery

CB 1113944T

t1CbatDP(t) + CbatOM(t)1113960 1113961 1113944

T

t1

Cbatrep

2ElifetimePbat(t)

11138681113868111386811138681113868111386811138681113868

+ 1113944T

t1KbatOM Pbat(t)

11138681113868111386811138681113868111386811138681113868

(10)

where CbatDP(t) is the battery depreciation cost CbatOM(t) isthe operation and maintenance cost of battery Cbatrep isbattery replacement cost Elifetime is the total charging anddischarging energy of battery lifetime kWh Pbat(t) is thecharging and discharging power of the battery at time tpositive at the time of discharging and negative at the time ofcharging and KbatOM is the unit operation and maintenancecost coefficient of the battery $kW

Generally the total amount of recyclable charging anddischarging energy in the battery lifespan is basically aconstant [43] e relationship of the total number of cyclesto failure and the depth of discharge can be described by adouble exponential function [44] e relationship curve ofboth is depicted in Figure 2

NDOD a1 + a2 middot eminus a3 middotDOD

+ a4 middot eminus a5 middotDOD

(11)

where NDOD is the number of cycles to failure DOD is thedepth of discharge of battery and parameters a1 to a5 areobtained via a regression on empirical lifetime test dataprovided by the battery manufacturer which are 150589968724 490 984509 and 659 respectively [44]

erefore at a given DOD the total charging and dis-charging energy during batteryrsquos lifetime is [42]

Elifetime 2Erated middot DOD middot NDOD (12)

33 Environmental Cost Diesel generators release pollutinggases such as SO2 CO2 CO and NOxe emission of thesegases will pollute the environment and the environmentalprotection department will levy a corresponding environ-mental damage penalty for environmental treatment eenvironmental cost CE namely the penalty fees of pollutantemission consisting of NOX CO2 CO and SO2 can becalculated as follows [45]

CE 1113944n

i11113944

m

j1Vej

Qij + Vj1113874 1113875 (13)

where Vejis the environmental value standard of pollutant

emission Qij is the amount of pollutant emission Vj is thepenalty factor of the jth gas emission by the ith micro powersource n is the number of micro power sources in themicrogrid system andm is the total number of the pollutinggases

34 Constraint Conditions Considering the system powerbalance and the physical limits of the power generationunits the above operation optimization model must besubject to the following constraints

Power generation and consumption should always bekept in balance

Pload(t) Ppv(t) + Pwt(t) + Pbat(t) + Pde(t) (14)

where Pload(t) is the load demand Pbat(t) is the outputpower of the battery and positive means discharging andnegative means charging Pde(t) is the output of the dieselgenerator and Ppv(t) and Pwt(t) are the output of PV systemand wind turbine respectively

e output constraints of PV system and wind turbineare

0lePpv(t)lePpvmax

0lePwt(t)lePwtmax(15)

where Ppvmax and Pwtmax are the maximum output power ofPV system and wind turbine respectively

00 02 04 06 08 100

5000

10000

15000

Depth of discharging

Recy

cle ti

mes

Figure 2 e relationship between NDOD and DOD


e constraints of battery system are

SOCmin le SOC(t)le SOCmax

minus Pbatmax lePbat(t)lePbatmax(16)

where Pbatmax is the maximum power of charging anddischarging the battery SOCmin and SOCmax are the lowerand upper limits of the SOC respectively

Moreover the initial SOC and the SOC at the end mustbe equal

SOCinitial SOCend (17)

e operating constraint of diesel generator is

kdeminPdemax lePde(t)le kdemaxPdemax (18)

where Pdemax is the output upper limit of diesel generatorkdemin and kdemax denote the minimum and maximum loadrates of the diesel generator respectively Considering theeconomical operation and spinning reserve of system thevalues of kdemin and kdemax are set to 03 and 08 based onmanufacturersrsquo suggestion

e block diagram of operating strategy is shown inFigure 3 Considering the systemrsquos operation efficiency andpower supply reliability and the fact that diesel generatorand storage battery system are controllable sources in orderto utilize renewable energy sources as much as possible theeconomic operation strategy of diesel generator is appliedand the chargingdischarging power of battery is dispatchedat first

When the net power is less than or equal to the lowerlimit of diesel generatorrsquos economic operating ranges it willrun at the lower limit or be shut down and the energystorage battery will balance system power When the netpower is between the upper and lower limits of dieselgeneratorrsquos economic operating ranges the state of charge ofbattery is kept at an appropriate level and the battery systemis charged or discharged to make sure diesel generator runswithin the economic operating ranges When the net poweris greater than the upper limit of diesel generatorrsquos economicoperating ranges and if the battery system has the ability toregulate it will share the excess load otherwise the unim-portant load will be cut off

4 Methodology

41 Improved SAPSO Algorithm e particle swarm opti-mization algorithm is derived from the simulation of for-aging behavior of flocks and fish populations Particlesdetermine the next move through their own experience andthe best experience of their peers Each particle in the swarmis a potential solution to the problem and corresponds to afitness value determined by its position e velocity of theparticle determines the direction and distance of its motionand the velocity is dynamically adjusted with the movementexperience of itself and other particles thus achieving theindividualrsquos optimization in the solvable space e speedand position update formula are expressed in followingequations

vij(k + 1) vij(k) + c1r1 pij(k) minus xij(k)1113872 1113873

+ c2r2 pgj(k) minus xij(k)1113872 1113873(19)

xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)

where c1 and c2 are the learning factors vij and xij are thevelocity and position of particles pi is the best position foundby each particle so far pg is the global best position found byall particles in the entire population and r1 and r2 arerandom numbers between 0 and 1

e basic idea of simulated annealing algorithm is touse a thermodynamic system to present optimizationprocess by gradually cooling the system to the lowestenergy state [46] e energy of the system is regarded asthe objective function of the optimization problemAccording to the principle of thermodynamics when thetemperature is T the likelihood of temperature drop withthe energy difference ΔP is P(ΔE) which is expressed as

P(ΔE) expΔET

1113874 1113875 (21)

where E is the internal energy of temperature T ΔE is energydifference

e Metropolis criterion is used to judge whether toaccept new solution or not e iteration process ofldquogenerating new solutions judging accepting or aban-doningrdquo was realized to find the optimal solution at thistemperature

x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)

where r is a random number in the range [0 1] x(i) is thesolution at an iteration E(x(i)) is the corresponding ob-jective function and xnew is the new solution

Although the particle swarm optimization (PSO) al-gorithm has a fairly fast convergence speed it is easy to fallinto a local optimum and produce premature convergencee simulated annealing (SA) algorithm has a simplecalculation process and strong robustness but the con-vergence speed is slow erefore the hybrid algorithmcombined the particle swarm optimization and the sim-ulated annealing algorithm is proposed to make up for thedefects of both algorithms

In this paper the SAPSO algorithm adopts PSO with acompression factor χ which is able to ensure the conver-gence of PSO algorithm and select the boundary of speed bychoosing appropriate parameters limits Since the optimalpopulation position is used in the speed update formula allparticles will move to the global best position of the entirepopulation If the best position of the population is at a localoptimum all particles will tend to the local optimumerefore in order to improve the ability of PSO algorithmto avoid falling into local extremum a roulette theory is usedto determine a globally optimal alternative value p

bull

g from piRewrite the speed update formula


vij(k + 1) χ vij(k) + c1r1 pij(k) minus xij(k)1113872 11138731113876

+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2

2 minus C minusC2 minus 4C

radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)

By borrowing the mechanism of simulated annealingalgorithm pi is a special solution that is worse than pg thejump probability of piwith respect to pg at temperature t canbe calculated as follows

P pi( 1113857 eminus fpiminus fpg( 1113857t

1113936Ni1 eminus fpiminus fpg( 1113857t

(25)

where N is the population size t is the current temperatureand f represents the objective function value

e calculation flowchart of SAPSO algorithm is shownin Figure 4 e penalty functions are used to handle theequality and inequality constraints e main steps ofSAPSO algorithm are as follows

Step 1 (initialization) set up the initial parameters suchas the output power of generation units randomcontrol parameters population size N maximumnumber of iterations M initial and minimum

annealing temperatures T0 and Tmin temperature at-tenuation coefficient k and learning factors c1 and c2respectively Initial population is generated randomly

SOC(t) lt SOCmax

Yes

|Pnet(t) ndash Pde(t)| lt Pbatmax

Yes

Pbat(t) = Pnet(t) ndash Pde(t)

End

Start

Pnet(t) = Pload(t) ndash Pwt(t) ndash Ppv(t)

Pnet(t) lt Pdemin Pdemin le Pnet(t) le kdemaxPdemaxNo

Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes

Pde(t) = Pnet(t) ndash Pbat(t)

Yes

End

Pnet(t) gt kdemax PdemaxNo

Yes

Pde(t) = Pdemin

Yes


Pnet(t) ndash Pbatmax gt Pdemax

|Pnet(t) ndash Pde(t)| lt PbatmaxNo

Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes

Cut unimportant load

Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End

Pbat = Pnet(t) ndash Pde(t)


Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No


Figure 3 e block diagram of operating strategy

Yes

Start

Set parameters

Initial population

Calculate the fitness of each particle

Search for pi and pg

Determine the initial annealingtemperature

Calculate the jumpprobability of each pi

Judge the acceptance of new solutionsbased on Metropolis criterion

Find the global optimalsubstitute value

Update the velocity andposition of particle

Calculate the new fitness ofeach particle

Update pi anf pg

T gt TminNo

No

Temperature annealingoperation

Number of iterationsreaches M

Yes

Output solutions

Terminate

Figure 4 Flowchart of SAPSO algorithm


Step 2 (fitness calculation) calculate the fitness valueof each particle in the initial population Find theoptimal value of the objective function and recordthe individual best position pi and global best positionpgStep 3 (probability) determine the initial annealingtemperature T0 and calculate the fitness of jumpprobability corresponding to each pi at the currenttemperature according to equation (25)Step 4 (selection) according to the Metropolis criterionto judge whether to accept the current solution or notuse the roulette theory to find the global optimalsubstitute value p

bull

g and update the global optimalposition from all individual extremumsStep 5 (updating) update the velocity and position ofthe particles by using equations (19) (23) and (24)Calculate the new fitness of each particle and updatethe best position pi of each particle and the global bestposition pg of the population Determine whether theannealing temperature is less than the terminationtemperature Tmin and if so jump to step 7 otherwisecontinue executionStep 6 (annealing) perform the temperature annealingoperationStep 7 (end) judge whether the iteration has reachedthe maximum number if it is not reached go to step 3otherwise stop iteration and output results

42 Grey Target Decision-Making eory In this paper amultiobjective grey target decision-making theory basedon entropy weight method is used to select a satisfactorysolution from the Pareto optimal solution set obtained bySAPSO algorithm Setting a target center in the grey targetregion formed by all the feasible solutions the distancebetween these solutions and the target center is an im-portant criterion for grey target decision e grey targetdecision sorts all the schemes according to the bullrsquos eyedistance of each scheme and chooses the shortest one asthe optimum Based on the information entropy theorythe weighting factor of each objective and the bullrsquos eyedistance of each scheme are obtained without relying onthe experience of experts or the preferences of decision-makers e credibility and realism of decision-making areimproved

Step 1 initialization of the sample matrixAssume that there are m decision-making schemesand each scheme has n objectives Based on the Paretooptimal solution set obtained by SAPSO algorithmthe initial sample matrix X can be established asfollows

X xij1113872 1113873mtimesn

x11 middot middot middot x1n

⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)

Step 2 calculation of the weighting factorsAccording to target values of each scheme differentspecificweights yij and entropy valuesEj are calculated andthe weighting factors are obtained by using equation (29)

yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m

i1xij lnyij Ej gt 0 (28)

ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)

Step 3 normalization of the sample matrixe decision matrix V is solved based on the ldquorewardand finerdquo operator zj and sample matrix X where theoperator zj is

zj 1m

1113944

m

i1xij j 1 2 n (30)

If the target value is a benefit indicator the normali-zation expression is as follows

vij xij minus zj

max max1leilem xij1113966 1113967 minus zj zj minus min1leilem xij1113966 11139671113966 1113967

(31)

If the target value is a cost indicator the normalizationexpression is as follows

vij zj minus xij


(32)

Step 4 definition of the target center vectorBased on the above transformation the decision matrixis V (vij)mtimesn e target center is

v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)

e target center vector is

v0

v01 v

02 v

0n1113966 1113967 (34)

Step 5 calculation of the bullrsquos eye distance

According to the definition of grey target theory v0 is thetarget center of an n-dimensional ellipsoid grey target ecloser the target value of each solution is to the target centerthe better the solution ise bullrsquos eye distance is expressed as


di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)

5 Results and Discussion

51 Case Study In order to evaluate the performance of theproposed multiobjective economic operation optimizationmodel for microgrid and the effectiveness of the improvedhybrid algorithm the windsolardieselbattery stand-alonemicrogrid system on Yongxing island in the South ChinaSea is adopted as a case study e optimal economic op-eration problem of this microgrid is solved by the SAPSOalgorithm using MATLAB software

e optimization model considers daily scheduling witha time interval of one hour e forecast temperature windspeed and solar irradiance are shown in Figure 5 Accordingto the mathematical model given in Section 2 using theforecast temperature wind speed and solar irradiance theoutput power of PV system and wind turbine are calculatedand presented in Figure 6 e hourly forecast load demandcurve in one day is shown in Figure 7

As can be seen from Figure 5 this island is rich in solarand wind energy resources with high average wind speedand long sunshine time which are 1036ms and 12 hoursrespectively However the wind speed fluctuates greatlyhour by hour In addition the island has a typical marineclimate with a high average temperature of 274degC As shownin Figure 7 there are two peaks of load on this island whichare at 11 orsquoclock am and 19 orsquoclock pm respectively

e operation limits and operation and maintenancecost of the stand-alone microgrid system are shown inTable 1 e parameters of the pollutant emission coeffi-cients and the penalty coefficients are presented in Tables 2and 3 respectively Other simulation input data are shown inTable 4 e parameters for algorithms are presented inTable 5

52 Results Analysis Based on the proposed SAPSO algo-rithm the Pareto solution set of the multiobjective opti-mization problem is obtained and the duplicate schemes aredeleted e eight feasible solutions are shown in Figure 8

It can be seen from Figure 8 that the projection of thePareto front on the XY plane is a straight line It means thatthe economic cost and the environmental cost are notmutually exclusive ey both reach the maximum orminimum at the same time e fuel cost of diesel generatoraccounts for the majority of the economic cost the windpower and photovoltaic power generations do not producepolluting gas while diesel generators release polluted ex-haust gases e more power generation from diesel gen-erator the higher economic cost and the highercorresponding environmental cost Meanwhile the eco-nomic cost and the environmental cost are both in generalconflict with the battery depreciation cost While the eco-nomic cost and the environmental cost decrease to the

lowest the battery depreciation cost increases to the higheste following eight schemes are given for further study

e economic cost the battery depreciation cost and theenvironmental cost of the above eight schemes are given inTable 6 When the battery depreciation cost is the highest27713$ the economic cost and the environmental cost arethe lowest 214397$ and 119109$ respectively when thebattery depreciation cost is lowest 20846$ the economiccost and the environmental cost are the highest 243073$and 135041$ respectively e real total cost increasesgradually from scheme one to scheme eight

In order to evaluate the performance of each scheme andchoose the optimal one from the above eight schemes threedecision-making methods are applied in this paper e firsttwo traditional methods use the subjective and objectivelinear weighted sum method to calculate the evaluationindex values respectively Method three is based on the greytarget decision-making theory en the results obtainedfrom these three methods are compared Since the orders ofmagnitude are different the linear normalization is per-formed at first

521 Method 1 Assume that each objective is equallyimportant to the whole objective thus the same weightingfactor is given to the three objectives that is each oneaccounts for 13 respectively As shown in Table 7 thecalculation results show that the evaluation index valuereduces at first and then gradually increases Although thetotal cost of scheme one is the lowest 361219$ the eval-uation index value is the largest 09213 e total cost ofscheme 1 361219$ is much less than that of scheme 839896$ while the index value of scheme 1 09213 is largerthan that of scheme 8 09174 e final results show that thefourth scheme has the lowest evaluation index value 09016which means scheme four is the best one

522 Method 2 Based on the simulation data obtained bythe hybrid SAPSO algorithm both the information entropyvalue and weighting factor of each objective are obtained byusing the entropy weight method As shown in Table 8 theweighting coefficient of the battery depreciation cost7202 is much larger than the other two objectives 1405and 1394 respectively From the information entropytheory the smaller the entropy value of an index is thegreater the degree of its variation is and the more infor-mation it can provide us it plays a more important role ina comprehensive evaluation and should be given a greaterweighting factor and vice versa e battery depreciationcost reduces from 27713$ to 20846$ a decrease of about33 while the other two indices increase by about 13 So agreater weighting factor is given to the battery depreciationcost e calculation results are presented in Table 9 eresults indicate that scheme 3 is the optimum whoseevaluation index value is 09051 It can also be seen fromTable 9 that the evaluation index value reduces at first andthen gradually increases e real total cost and the evalu-ation index value of scheme 8 are the largest at the sametime which are 39896$ and 09367 respectively


523 Method 3 Using the grey target decision-makingtheory based on entropy weight method mentioned inSection 42 the target center vector (minus 1 minus 1 minus 1) is calculated

at first en the bullrsquos eye distance of each scheme is ob-tained As shown in Table 10 the bullrsquos eye distance of theeight schemes decreases from 09420 to 09151 and thenincreases to 15122 Scheme 2 has the smallest bullrsquos eye

2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)

Figure 5e hourly forecast temperature and renewable resources (a)e temperature profile (b) the solar irradiance profile (c) the windspeed profile

2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)

Figure 6 Output power of PV system and wind turbines

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)

Figure 7 e hourly forecast load demand curve

Table 1 Operating parameters of the microgrid system

Type Pmin (kW) Pmax (kW) KOM ($kWh)PV 0 200 00096WT 0 100 00296DE 120 320 00524BS minus 400 400 00648

Table 2 Pollutant emission coefficients of different generationunits

TypePollutant emission (gmiddotkWminus 1middothminus 1)

PV WT DE BSCO2 0 0 232037 0SO2 0 0 0464 0NOx 0 0 4331 0CO 0 0 2320 0

Table 3 Environmental value and penalty rate of differentpollutants

Type Environmental value ($middotkgminus 1) Penalty rate ($middotkgminus 1)CO2 0002875 0210SO2 075 14842NOx 100 62964CO 0125 0125


distance which means the corresponding solution is closestto the target center So it is a satisfactory solution for thisdecision e total cost of scheme 8 39896$ is much largerthan scheme 2 362908$ the bullrsquos eye distance of scheme 815122 is also much larger than that of scheme 2 09151 It isalso shown that the real total cost and the value of theevaluation index are consistent which is closer to the actualsituation

For method one the total cost of scheme 4 is relativelyhigh and it is too subjective by artificially assigningweighting factorsWhat is more it cannot reflect preferences

by giving the same weighting factor For method two due tothe fact that the battery depreciation cost is one order ofmagnitude lower than the economic cost and the envi-ronmental protection cost the entropy weight method lacksa horizontal comparison between the indicators in theprocess of weighting However method two is more ob-jective than method one in dealing with the multiobjectivedecision-making problem For method three although theeconomic cost and the environmental cost of scheme 2 are

Table 4 Simulation input data

Parameter ValuePVNominal capacity of PV array (Prate_PV) 200 kWDeteriorating factor (ηPV) 98Temperature factor (αTP) degCAmbient temperature under standard testcondition (TSTC)

25degC

Efficiency at standard test condition (ηSTC) Nominal operating temperature of PV cell (TNOCT) 25degC

Wind turbineNominal capacity of wind turbine (Prate_WT) 100 kWRated wind speed of wind turbine (vr) 13msCut-in wind speed (vcut_in) 3msCut-out wind speed (vcut_out) 25ms

Diesel generatorNominal power of diesel generator (Prate_gen) 400 kWIntercept coefficient of the fuel consumption curve(F0)

0084

Slope of the fuel consumption curve (F1) 024Unit price of diesel (Cfuel) 12 $L

Battery systemNominal capacity of the battery system (Ebat) 1000 kWhTime interval (Δt) 1 hourSelf-discharging factor (δ) 001Minimum state of charge (SOCmin) 04Maximum state of charge (SOCmax) 09Initial state of charge (SOCin) 07Battery charging efficiency (ηbatch) 09Battery discharging efficiency (ηbatdis) 09

Battery replacement cost (Cbatrep)488 $kWh

Table 5 Parameters for algorithms

Algorithm ValueSAPSOPopulation size (N) 600Maximum iteration number (M) 100Learning factor (c1) 205Learning factor (c2) 205Initial temperature (T0) 100Annealing temperature factor (k) 05

IWPSOPopulation size (N) 600Maximum iteration number (M) 100Learning factor (c1) 205Learning factor (c2) 205

120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360

Environmental cost ($)

Economic cost ($)

Figure 8 Pareto front solutions by the SAPSO algorithm

Table 6 Costs of different schemes

Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041

Table 7 e calculation results of method 1

Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174

Table 8 Information entropy and weighting factors of differentobjectives

Objective f c f b f e

Information entropy 09996 09977 09996Weighting factors () 1405 7202 1394


not the lowest both are relatively low At the same time thisreflects the objectivity and the trade-off between sub-objectives of a multiobjective optimization problem

e output results of different generation units at theminimum economic and environmental cost the minimumbattery depreciation cost and the optimal scheme are shownin Figures 9ndash11 respectively During 1000ndash1600 the solarresource is rich the total available generation is greater thanload demand and the battery bank is charged While therenewable energy resource is poor from 1800 to 2100 thebattery bank is discharged In general because the unitgeneration cost of diesel generator is higher than that of thebattery system it will increase the output power and thegeneration cost of diesel generator to decrease the life losscost of battery system Because of the abundant renewableresources and the role of battery system the load rate ofdiesel generator is relatively low But it is always located inthe economic operating ranges of diesel generator (30sim80)Table 11 lists the daily power generation of diesel generatorthe charging capacity of storage battery when solar energy isrich and the discharging capacity of storage battery at thepeak of load demand at night respectively

Figure 9 shows that the battery starts charging from 10orsquoclock in the morning until 15 orsquoclock in the afternoonabsorbing about 26416 kWh of renewable energy within fivehours Meanwhile for the load peak during 1800ndash2000 pmthe energy storage system discharges 27054 kWh of elec-trical energy Among the whole optimization cycle althoughthe economic cost is the lowest 214397$ the batterycharging and discharging capacity is 90116 kWh which isthe highest and the corresponding battery depreciation costis also the largest

In Figure 10 it can be seen that the battery bank ischarged between 1200 and 1500 and the total 19204 kWhelectricity power is absorbede charging process lasts only

three hours During the load peak from 18 to 20 orsquoclock inthe evening only 9693 kWh of electricity is released be-cause the charging and discharging cost of energy storagesystem is much lower than generation cost of diesel gen-erator Although the battery cost is reduced only 20846$


Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367

Table 10 Bullrsquos eye distance of different schemes

Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)

Figure 9 Output power of generation units at the minimumeconomic and environmental cost

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)

Figure 10 Output power of generation units at the minimumbattery depreciation cost

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)

Figure 11 Output power of generation units for scheme 2


the cost of diesel generator is increased which is 243073$e total cycle charging and discharging electricity of batterysystem is the lowest in one day among all the schemes whichis just 75071 kWh at means the energy storage system isnot utilized reasonably in this scheme

Figure 11 shows the output power of generation units forthe optimal scheme At eight orsquoclock in the morning thebattery system starts to charge until 15 orsquoclock in the af-ternoon e charging process lasts even more than sixhours e total electrical energy absorbed by battery systemfrom renewable energy generation is 29488 kWh At theload peak between 1800 and 2000 in the evening the energystorage system discharges 25761 kWh of electrical energyFrom 22 to 2 orsquoclock in early morning the load is at a lowlevel and the output power of diesel generator is smoothedby charging the battery system e output power of thediesel generator is relatively stable and only fluctuates in avery small range Avoiding drastic fluctuations in power isbeneficial to reducing mechanical damage and prolonginglifespan of the diesel generator e energy storage batterysystem plays the role of ldquoshaving the peak and filling thevalleyrdquo in this microgrid system It is consistent with theexpected operation effect

Figure 12 shows the hourly SOC of energy storagebattery system in one day e battery system is charged forabout 6 hours until 1500 pm and the SOC reaches amaximum of 083 After the discharging during the loadpeak at night the SOC reaches daily lowest value which isabout 046 at 2100 pm e values of SOC satisfy the SOCconstraints

e microgrid cost distribution of the optimal scheme isshown in Figure 13 It can be seen that the two largestproportions of the whole operating cost are fuel cost andenvironmental cost which are 5349 and 3367 re-spectively e fuel cost accounts for more than one half ofthe whole operating expenses Once the fuel price ortransportation distance increases the fuel cost will risewhich will lead to a further increase in the proportion of fuelcosts to power generation costs erefore reducing the fuelconsumption is critical to improve the economics for remoteisland microgrid e battery depreciation cost only ac-counts for 572 of the entire operating cost that is becauseonly the replacement cost of the battery system is consid-ered while the construction labour and transportationcosts of replacing the battery system are not included in thispaper

To make a comparison of the performance differencebetween the simulated annealing particle swarm optimization

(SAPSO) algorithm and the inertia weight particle swarmoptimization (IWPSO) algorithm it is assumed that eachobjective is equally important and given the same weightingfactor to obtain the total expenses Each algorithm performs10 iterations and then compares the average of the fitnessvalues Convergence curves of both algorithms are shown inFigure 14 It can be seen that the SAPSO algorithm hasstronger search ability than the IWPSO algorithm in the earlystage In the whole search process the IWPSO algorithm isprone to fall into local optimum and produce prematureconvergence the final fitness value is about 3980$ Howeverthe SAPSO algorithm can quickly jump out after a short timeof iterative operation so as to avoid falling into the localoptimal solution the final fitness value is about 3760$ which

Table 11 e daily power generation of diesel generator and charging and discharging capacity of battery system

Scheme Diesel generator(kWh)

Battery system (kWh)Total charging anddischarging capacity

Charging capacity (whensolar energy is rich)

Discharging capacity (whenload peak is at night)

e minimum of economiccost 392767 90116 26416 27054

e minimum of batterydepreciation cost 416854 75071 19204 9693

e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO

CFigure 12 SOC of storage battery for scheme 2

3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost

Figure 13 Microgrid cost distribution of the optimal scheme


is 553 less than that of the IWPSO algorithm e SAPSOalgorithm tends to be stable after 25 iterations while IWPSOalgorithm tends to be stable after 9 iterations Although theIWPSO algorithm has a faster convergence the proposedSAPSO algorithm can search for a smaller global optimalobjective function fitness value and the convergence process ismore robust

6 Conclusion

In this study a novel economic operation optimizationmodel and optimization method are proposed for a stand-alone microgrid system which includes photovoltaic panelswind turbines diesel generators and energy storage batterysystem In the operation optimization model the outputpower of the storage battery system and diesel generator aretaken as the optimization decision variables For this pur-pose a multiobjective function is defined on minimizing thecosts of generation battery depreciation and environmentalprotection An improved hybrid SAPSO algorithm is pro-posed for optimal search for the two decision variables whilesatisfying the load demand e results are compared withthe results obtained by IWPSO algorithm en the greytarget decision-making theory based on entropy weightmethod is adopted to make the decision of the best trade-offscheme e results are compared with the results obtainedby two other traditional decision-making methods

e results show that the economic cost and the envi-ronmental cost are not mutually exclusive for the stand-alone microgrid on a remote islande battery depreciationcost is conflicting with both the economic cost and theenvironmental cost With the increased battery depreciationcost the economic cost and the environmental cost bothdecrease e simulation results demonstrate that the energystorage battery system can absorb the renewable energywhen the renewable energy is rich at daytime while releasingenergy during the peak load at night which plays the role ofldquoshaving the peak and filling the valleyrdquo as well as smoothingthe output power of traditional diesel generator e totalcharging and discharging capacity of the battery systemreaches the maximum when the economic cost is at the

minimum while the battery system is not used reasonablywhen the battery depreciation cost is at the minimum efuel cost in stand-alone microgrid is a key factor for thewhole operating expenses It is confirmed that the improvedhybrid SAPSO algorithm can find a better objective functionvalue and it exhibits better robustness than the traditionalPSO algorithm It is also shown that the proposed grey targetdecision-making theory based on entropy weight methodcan find optimal compromise solution e optimal schemeobtained by the grey target decision method is consistentwith the expected operation effect e proposed operationoptimization method and decision-making theory provide auseful tool for the stand-alone microgrid optimal operation

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is work was financially supported by ldquoNational Key RampDProgram of China (supported by Ministry of Science andTechnology of China no 2016YFC0305001)rdquo and ldquotheNational Science and Technology Support Programrdquo (sup-ported by Ministry of Science and Technology of China no2014BAC01B05)

References

[1] F Feijoo and T K Das ldquoEmissions control via carbon policiesand microgrid generation a bilevel model and Pareto anal-ysisrdquo Energy vol 90 pp 1545ndash1555 2015

[2] S M Mortazavi A Maleki and H Yousefi ldquoAnalysis ofrobustness of the Chinese economy and energy supplyde-mand fluctuationsrdquo International Journal of Low-CarbonTechnologies vol 14 no 2 pp 147ndash159 2019

[3] N Duic G Krajacic and M Dagracacarvalho ldquoRenewIslandsmethodology for sustainable energy and resource planning forislandsrdquo Renewable and Sustainable Energy Reviews vol 12no 4 pp 1032ndash1062 2008

[4] A S Bahaj ldquoGenerating electricity from the oceansrdquo Re-newable and Sustainable Energy Reviews vol 15 no 7pp 3399ndash3416 2011

[5] A Maleki and F Pourfayaz ldquoOptimal sizing of autonomoushybrid photovoltaicwindbattery power system with LPSPtechonology by using evolutionary algorithmsrdquo Solar Energyvol 115 no 1 pp 471ndash483 2015

[6] P Pal V Mukherjee and A Maleki ldquoEconomic and per-formance investigation of hybrid PVwindbattery energysystem for isolated Andaman and Nicobar islands IndiardquoInternational Journal of Ambient Energy pp 1ndash19 2018

[7] 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

[8] S G Sigarchian M S Orosz H F Hemond andA Malmquist ldquoOptimum design of a hybrid PVndashCSPndashLPG

0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue

Figure 14 Convergence curve for the basic PSO and the SAPSO


microgrid with particle swarm optimization techniquerdquoApplied ermal Engineering vol 109 pp 1031ndash1036 2016

[9] J Jung and M Villaran ldquoOptimal planning and design ofhybrid renewable energy systems for microgridsrdquo Renewableand Sustainable Energy Reviews vol 75 pp 180ndash191 2017

[10] A Maleki ldquoModeling and optimum design of an off-grid PVWTFCdiesel hybrid system considering different fuel pri-cesrdquo International Journal of Low-Carbon Technologiesvol 13 no 2 pp 140ndash147 2018

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

[12] L M Halabi S Mekhilef L Olatomiwa and J HazeltonldquoPerformance analysis of hybrid PVdieselbattery systemusing HOMER a case study Sabah Malaysiardquo Energy Con-version and Management vol 144 no 15 pp 322ndash339 2017

[13] J Manwell A Rogers G Hayman et al Hybrid2 A HybridSystem Simulation Model eory Manual Renewable EnergyResearch Laboratory Department ofMechanical EngineeringUniversity of Massachusetts Boston MA USA 2006

[14] B Yan B Wang L Zhu et al ldquoA novel stable and economicpower sharing scheme for an autonomous microgrid in theenergy internetrdquo Energies vol 8 no 11 pp 12741ndash127642015

[15] G-C Liao ldquoSolve environmental economic dispatch of smartmicrogrid containing distributed generation system usingchaotic quantum genetic algorithmrdquo International Journal ofElectrical Power amp Energy Systems vol 43 no 1 pp 779ndash7872012

[16] F A Mohamed and H N Koivo ldquoSystem modelling andonline optimal management of microgrid using meshadaptive direct searchrdquo International Journal of ElectricalPower amp Energy Systems vol 32 no 5 pp 398ndash407 2010

[17] Y Yi L Xia Y Tao et al ldquoMicrogrid energy optimal dispatchconsidering the security and reliabilityrdquo Proceeding of theCSEE vol 34 no 19 pp 3080ndash3088 2014

[18] L Guo N Wang H Lu X Li and C Wang ldquoMulti-objectiveoptimal planning of the stand-alone microgrid system basedon different benefit subjectsrdquo Energy vol 116 pp 353ndash3632016

[19] M Azaza and F Wallin ldquoMulti objective particle swarmoptimization of hybrid micro-grid system a case study inSwedenrdquo Energy vol 123 pp 108ndash118 2017

[20] W Zhang A Maleki and M A Rosen ldquoA heuristic-basedapproach for optimizing a small independent solar and windhybrid power scheme incorporating load forecastingrdquo Journalof Cleaner Production vol 241 Article ID 117920 2019

[21] G Carpinelli F Mottola D Proto and A Russo ldquoA multi-objective approach for microgrid schedulingrdquo IEEE Trans-actions on Smart Grid vol 8 no 5 pp 2109ndash2118 2017

[22] T Aziz N-A Masood S R Deeba W Tushar and C YuenldquoA methodology to prevent cascading contingencies usingBESS in a renewable integrated microgridrdquo InternationalJournal of Electrical Power amp Energy Systems vol 110pp 737ndash746 2019

[23] Y Zheng B M Jenkins K Kornbluth A Kendall andC Traeligholt ldquoOptimization of a biomass-integrated renewableenergy microgrid with demand side management underuncertaintyrdquo Applied Energy vol 230 pp 836ndash844 2018

[24] A S Jacob R Banerjee and P C Ghosh ldquoSizing of hybridenergy storage system for a PV based microgrid throughdesign space approachrdquoApplied Energy vol 212 pp 640ndash6532018

[25] L Wang Q Li R Ding M Sun and G Wang ldquoIntegratedscheduling of energy supply and demand in microgrids underuncertainty a robust multi-objective optimization approachrdquoEnergy vol 130 pp 1ndash14 2017

[26] A Mleki ldquoDesign and optimization of autonomous solar-wind-reverse osmosis desalination systems coupling batteryand hydrogen energy storage by an improved bee algorithmrdquoDesalination vol 435 pp 221ndash234 2018

[27] M B Shadmand and R S Balog ldquoMulti-objective optimi-zation and design of photovoltaic-wind hybrid system forcommunity smart DC microgridrdquo IEEE Transaction on SmartGrid vol 5 no 5 pp 2635ndash2643 2014

[28] A Maleki ldquoOptimal operation of a grid-connected fuel cellbased combined heat and power systems using particle swarmoptimisation for residential sectorrdquo International Journal ofAmbient Energy vol 47 pp 1ndash8 2019

[29] T Kerdphol K Fuji Y Mitani M Watanabe and Y QudaihldquoOptimization of a battery energy storage system usingparticle swarm optimization for stand-alone microgridsrdquoInternational Journal of Electrical Power amp Energy Systemsvol 81 pp 32ndash39 2016

[30] G Li X Zhai Y Li B Feng Z Wang and M Zhang ldquoMulti-objective optimization operation considering environmentbenefits and economy based on ant colony optimization forisolated micro-gridsrdquo Energy Procedia vol 104 pp 21ndash262016

[31] A Cagnano A Caldarulo Bugliari and E De Tuglie ldquoAcooperative control for the reserve management of isolatedmicrogridsrdquo Applied Energy vol 218 pp 256ndash265 2018

[32] H Wu X Liu and M Ding ldquoDynamic economic dispatch ofa microgrid mathematical models and solution algorithmrdquoInternational Journal of Electrical Power amp Energy Systemsvol 63 pp 336ndash346 2014

[33] H Karimi and S Jadid ldquoOptimal microgrid operationscheduling by a novel hybrid multiobjective and multi-at-tribute decision-making frameworkrdquo Energy vol 186 ArticleID 115912 2019

[34] M H Moradi M Abedini and S M Hosseinian ldquoOptimaloperation of autonomous microgrid using HSndashGArdquo Inter-national Journal of Electrical Power amp Energy Systems vol 77pp 210ndash220 2016

[35] W Zhang A Maleki M A Rosen and J Liu ldquoSizing a stand-alone solar-wind-hydrogen energy system using weatherforecasting and a hybrid search optimization algorithmrdquoEnergy Conversion and Management vol 180 pp 609ndash6212019

[36] J Lu W Wang Y Zhang and S Cheng ldquoMulti-objectiveoptimal design of stand-alone hybrid energy system usingentropy weight method based on HOMERrdquo Energies vol 10no 10 p 1664 2017

[37] G Li W Liu B Jiao and C Wang ldquoMulti-objective optimalplanning design method for stand-alone microgrid systemrdquoProceedings of the CSEE vol 34 no 4 pp 524ndash536 2014

[38] D omas O Deblecker and C S Ioakimidis ldquoOptimaldesign and techno-economic analysis of an autonomous smallisolated microgrid aiming at high RES penetrationrdquo Energyvol 116 pp 364ndash379 2016

[39] N Nikmehr and S N Ravadanegh ldquoHeuristic probabilisticpower flow algorithm for microgrids operation and plan-ningrdquo IET Generation Transmission amp Distribution vol 9no 11 pp 985ndash995 2015

[40] H Tazvinga B Zhu and X Xia ldquoEnergy dispatch theory for aphotovoltaic-wind-diesel-battery hybrid power systemrdquo SolarEnergy vol 108 pp 412ndash420 2014


[41] 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

[42] A M A Haidar P N John and M Shawal ldquoOptimalconfiguration assessment of renewable energy in MalaysiardquoRenewable Energy vol 36 no 2 pp 881ndash888 2011

[43] C Liu XWang and XWu ldquoAmulti-layer dispatch theory ofcombined wind-storage systems considering optimization ofbattery unitsrdquo Power System Technology vol 40 no 10pp 3029ndash3037 2016

[44] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system forsmall isolated gridsrdquo IEEE Transactions on Energy Conversionvol 26 no 3 pp 744ndash756 2011

[45] K Qian Y Yuan X Shi et al ldquoEnvironmental benefitsanalysis of distributed generationrdquo Proceedings of the CSEEvol 28 no 29 pp 11ndash15 2008

[46] G Zhang B Wu A Maleki and W Zhang ldquoSimulatedannealing-chaotic search algorithm based optimization ofreverse osmosis hybrid desalination system driven by windand solar energiesrdquo Solar Energy vol 173 pp 964ndash975 2018


forecast load information instead of past information foroptimally designing a hybrid renewable energy scheme(WTPVBAT) to minimize TLCC of the scheme

However the microgrid optimal scheduling model is amulticonstrained multiobjective problem Differentmethods are used to solve this problem e most commonapproach is to transform the multiobjective optimizationproblem into one single-objective optimization problem byusing the linear weighted sum method [21] In the previousstudy some other classic approaches are adopted such asiterative technique [22] mixed-integer linear programming[23] design space concept [24] andmin-max approach [25]Considering that some objectives are mutually exclusive themetaheuristic optimization techniques are found to be moreacceptable than traditional classic methods for the optimi-zation of microgrid system because of their ability to searchglobal optimum fast convergence and good calculationaccuracy [26] which can be divided into two groups one isthe evolutionary algorithms (EAs) which is based on em-ulating the process of natural evolution and survival of thefittest such as genetic algorithm (GA) [27] and evolutionaryprogramming (EP) [28] and the other is the swarm intel-ligence algorithms (SIAs) whose operation is based on socialand cooperative behaviors of individuals such as particleswarm optimization (PSO) [29] bee algorithm [26] and antcolony algorithm [30]

Cagnano et al [31] proposed a new strategy thatmanages the active power reserve in isolated microgrid formaximization of the gridrsquos reservation is work is doneby adopting direct Lyapunov theorem and sensitivityanalysis but the cost function is not considered Wu et al[32] presented the dynamic economic dispatch model of acombined heat and power (CHP) microgrid system Inorder to minimize the total cost namely operating costand pollutant treatment cost the biobjective problem issimplified by summing these two costs directly An im-proved particle swarm optimization (PSO) algorithm isproposed to solve the objective function But the rela-tionship between the two costs is not discussed Karimiet al [33] presented a multiobjective operational model fora grid-connected microgrid considering the cost securityand reliability of the system simultaneously To solve theproposed model a set of Pareto solutions is obtained firstby using the weighted sum approach e hybrid multi-objective and multiattribute decision-making frameworkis applied to achieve the best operation status Moradi et al[34] developed a multiobjective optimization model in-cluding fuel consumption cost total voltage variation andthe voltage stability index A hybrid optimization algo-rithm combining the harmony algorithm (HS) and thegenetic algorithm (GA) is proposed to solve the probleme fuzzy method is employed to find the optimum so-lution among all the nondominated results Zhang et al[35] to minimize the total life cycle cost and increase theaccuracy of size optimization of the independent hybridrenewable energy systems proposed a new hybrid opti-mization algorithm based on three algorithms chaoticsearch harmony search and simulated annealing eforecasting weather data is used along with artificial neural

networks to improve the accuracy of the size optimizationalgorithm results

Although various studies on microgrid operation opti-mization from different aspects and different techniqueshave been reported almost all of them have included thebattery depreciation cost into the cost of power generationwithout considering it separately e energy storage batterysystem is critical to stand-alone microgrid on an islandBecause of the harsh environment of island and the frequentcharging and discharging of battery bank the lifespan ofbattery bank will be greatly affected which will accelerate thedepreciation of battery bank During the operation opti-mization process it is necessary to consider the batterysystem separately Also both the optimization techniquesand the optimal decision-making methods need furtherresearch

In this paper a mathematical model for each device ofthe microgrid system is introduced at first In order to usethe battery more reasonably a novel battery operation costmodel is proposed and chosen as one of the optimizationobjectives To realize the economic operation of stand-alonemicrogrid a multiobjective function is defined based onminimize the fuel cost operation and maintenance costenvironmental cost and battery depreciation cost subject toconstraint conditions An efficient method is needed to solvethis multiobjective function Due to the features of particleswarm optimization algorithm and simulated annealingalgorithm an improved hybrid SAPSO algorithm is devel-oped to obtain Pareto front solutions for the multiobjectiveoptimization problem e results are compared with thoseobtained by traditional particle swarm optimization algo-rithm In order to help user choose the optimal scheme thegrey target decision-making strategy based on entropyweight method is proposed to identify the best compromisesolution from the obtained Pareto solution set At last astand-alone microgrid containing wind PV battery anddiesel generator in Yongxing Island China is chosen as onecase study to verify the effectiveness of the proposedmethods

is paper is organized as follows e introduction isgiven in Section 1 In Section 2 description of the proposedmicrogrid system and modelling of major components arepresented e optimization problem is analysed in Section3 Section 4 explains the proposed methodology e resultsare discussed in Section 5 e conclusion is shown inSection 6

2 Model of Major Components

e stand-alone microgrid system is composed of photo-voltaic arrays wind power generation diesel generatorsenergy storage battery system power conversion system(PCS) loads and energy management system (EMS) asshown in Figure 1

e AC bus mode is used in this microgrid system andall micro sources are directly integrated into the commonAC bus e photovoltaic array contains multiple PVmodules each of which is directly incorporated into thecommon AC bus through a string inverter e wind








hellip


EMS

ACDCAC BoxDCAC

DC

AC

DC

AC

AC bus

BMS







PWT(t)



1113888 1113889 vcut in le vle vr


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)










Ebat

(5)



middotΔt

ηbsdisEbat

(6)





1113872 1113873

fc(x) 1113944T

t1CF + COM1113858 1113859

fb(x) 1113944T

t1CB

fe(x) 1113944T

t1CE

(7)






CF 1113944n

i1f Pi(t)( 1113857Cfuel (8)



COM 1113944n

i1Pi(t)KOMi (9)



CB 1113944T


T

t1

Cbatrep

2ElifetimePbat(t)

11138681113868111386811138681113868111386811138681113868

+ 1113944T

t1KbatOM Pbat(t)

11138681113868111386811138681113868111386811138681113868

(10)





(11)





CE 1113944n

i11113944

m

j1Vej

Qij + Vj1113874 1113875 (13)








0lePpv(t)lePpvmax



00 02 04 06 08 100

5000

10000

15000


Recy

cle ti

mes














4 Methodology




xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)



P(ΔE) expΔET

1113874 1113875 (21)



x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)




bull




+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue


















































hellip


EMS

ACDCAC BoxDCAC

DC

AC

DC

AC

AC bus

BMS







PWT(t)



1113888 1113889 vcut in le vle vr


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)










Ebat

(5)



middotΔt

ηbsdisEbat

(6)





1113872 1113873

fc(x) 1113944T

t1CF + COM1113858 1113859

fb(x) 1113944T

t1CB

fe(x) 1113944T

t1CE

(7)






CF 1113944n

i1f Pi(t)( 1113857Cfuel (8)



COM 1113944n

i1Pi(t)KOMi (9)



CB 1113944T


T

t1

Cbatrep

2ElifetimePbat(t)

11138681113868111386811138681113868111386811138681113868

+ 1113944T

t1KbatOM Pbat(t)

11138681113868111386811138681113868111386811138681113868

(10)





(11)





CE 1113944n

i11113944

m

j1Vej

Qij + Vj1113874 1113875 (13)








0lePpv(t)lePpvmax



00 02 04 06 08 100

5000

10000

15000


Recy

cle ti

mes














4 Methodology




xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)



P(ΔE) expΔET

1113874 1113875 (21)



x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)




bull




+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue














































PWT(t)



1113888 1113889 vcut in le vle vr


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)










Ebat

(5)



middotΔt

ηbsdisEbat

(6)





1113872 1113873

fc(x) 1113944T

t1CF + COM1113858 1113859

fb(x) 1113944T

t1CB

fe(x) 1113944T

t1CE

(7)






CF 1113944n

i1f Pi(t)( 1113857Cfuel (8)



COM 1113944n

i1Pi(t)KOMi (9)



CB 1113944T


T

t1

Cbatrep

2ElifetimePbat(t)

11138681113868111386811138681113868111386811138681113868

+ 1113944T

t1KbatOM Pbat(t)

11138681113868111386811138681113868111386811138681113868

(10)





(11)





CE 1113944n

i11113944

m

j1Vej

Qij + Vj1113874 1113875 (13)








0lePpv(t)lePpvmax



00 02 04 06 08 100

5000

10000

15000


Recy

cle ti

mes














4 Methodology




xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)



P(ΔE) expΔET

1113874 1113875 (21)



x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)




bull




+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue












































CF 1113944n

i1f Pi(t)( 1113857Cfuel (8)



COM 1113944n

i1Pi(t)KOMi (9)



CB 1113944T


T

t1

Cbatrep

2ElifetimePbat(t)

11138681113868111386811138681113868111386811138681113868

+ 1113944T

t1KbatOM Pbat(t)

11138681113868111386811138681113868111386811138681113868

(10)





(11)





CE 1113944n

i11113944

m

j1Vej

Qij + Vj1113874 1113875 (13)








0lePpv(t)lePpvmax



00 02 04 06 08 100

5000

10000

15000


Recy

cle ti

mes














4 Methodology




xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)



P(ΔE) expΔET

1113874 1113875 (21)



x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)




bull




+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue























































4 Methodology




xij(k + 1) xij(k) + vij(k + 1) j 1 n (20)



P(ΔE) expΔET

1113874 1113875 (21)



x(i + 1)

xnew if expΔET

1113874 1113875gt r

x(i) ow

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(22)




bull




+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue













































+ c2r2 pbull

gj(k) minus xij(k)1113874 11138751113877

(23)

x 2


radic 11138681113868111386811138681113868111386811138681113868

C c1 + c2 Cgt 4

(24)




(25)





SOC(t) lt SOCmax

Yes


Yes


End

Start



Pbat(t) = Pnet(t)


No

Yes

Pde(t) = 0

End

Yes


Yes

End


Yes

Pde(t) = Pdemin

Yes




Yes

End

Pde(t) = Pnet(t)

Pnet(t) le Pdemax

Yes


Pde(t) = Pdemax

No

End

SOC(t) gt SOCmin

Yes

Pbat(t) = 0Yes

No

End

No

End



Pde(t) = Pdemax

End

Pbat(t) = Pbatmax

SOC(t) le SOCmax

Pbat(t) = 0

End

No



Yes

Start

Set parameters

Initial population









Update pi anf pg

T gt TminNo

No



Yes

Output solutions

Terminate




bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue













































bull






⋮ ⋱ ⋮

xm1 xmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (26)


yij xij

1113936mi1 xij

xij ge 0 (27)

Ej minus1

lnm1113944

m


ωj 1 minus Ej1113872 1113873

1113936nj1 1 minus Ej1113872 1113873

(29)


zj 1m

1113944

m

i1xij j 1 2 n (30)


vij xij minus zj


(31)


vij zj minus xij


(32)


v0j min vij

11138681113868111386811138681113868 1le ilem1113882 1113883 j 1 2 n (33)


v0

v01 v

02 v

0n1113966 1113967 (34)




di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue












































di vi minus v011138681113868111386811138681113868111386811138681113868

1113944

n

j1ωj vij minus v0j1113872 1113873

2

11139741113972

(35)
















2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue














































2 4 6 8 10 12 14 16 18 20 22 2424

26

28

30

32

Time (h)

Tem

pera

ture

(degC)

(a)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

8

10

12

14

16

Win

d sp

eed

(ms

)

(b)

2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

300

600

900

1200So

lar i

rrad

ianc

e (W

m2 )

(c)


2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Time (h)

WTPV

Out

put (

kW)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

0

100

200

300

400

Load

(kW

)















25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue

















































25degC




0084







120011602500

24002300

22002100

280

260

240

220

200

Batte

ry d

epre

ciat

ion

cost

($)

12401280

13201360


Economic cost ($)



Scheme fc ($) fb ($) fe ($)1 214397 27713 1191092 216376 26345 1201873 219634 25167 1221324 223071 24089 1239295 228214 22923 1267866 233007 21821 1294497 238179 21365 1323218 243073 20846 135041


Scheme Value1 092132 091343 090544 090165 090176 090477 091028 09174











Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue


















































Scheme Value1 091222 090773 090514 090535 091046 091727 092658 09367


Scheme Value1 094202 091513 094874 103325 116076 128317 140678 15122

2 4 6 8 10 12 14 16 18 20 22 24ndash100

0

100

200

300

400

Time (h)

DEPVWT

LoadBAT

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)


2 4 6 8 10 12 14 16 18 20 22 24Time (h)

DEPVWT

LoadBAT

ndash100

0

100

200

300

400

Pow

er (k

W)
















e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue

























































e optimal scheme 403499 86548 29488 25761

2 4 6 8 10 12 14 16 18 20 22 2404

05

06

07

08

09

10

Time (h)SO


3367

572712

5349

Fuel cost

OampM cost

Depreciation cost

Environmental cost




6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue













































6 Conclusion




Data Availability




Acknowledgments


References









0 20 40 60 80 1003500

4000

4500

5000

5500

6000

Iterations

IWPSOSAPSO

Obj

ectiv

e fun

ctio

n va

lue












































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