research article optimal economic operation of islanded microgrid...

Research ArticleOptimal Economic Operation of Islanded Microgrid byUsing a Modified PSO Algorithm

Yiwei Ma12 Ping Yang12 Zhuoli Zhao12 and Yuewu Wang12

1School of Electric Power South China University of Technology No 381 Wushan Road Tianhe District Guangzhou 510641 China2Guangdong Key Laboratory of Clean Energy Technology No 381 Wushan Road Tianhe District Guangzhou 510641 China

Correspondence should be addressed to Yiwei Ma mayiweimailscuteducn

Received 29 October 2014 Revised 18 February 2015 Accepted 18 February 2015

Academic Editor Gerhard-WilhelmWeber

Copyright copy 2015 Yiwei Ma et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An optimal economic operation method is presented to attain a joint-optimization of cost reduction and operation strategy forislanded microgrid which includes renewable energy source the diesel generator and battery storage system The optimizationobjective is tominimize the overall generating cost involving depreciation cost operation cost emission cost and economic subsidyavailable for renewable energy source while satisfying various equality and inequality constraints A novel dynamic optimizationprocess is proposed based on two different operation control modes where diesel generator or battery storage acts as the masterunit to maintain the system frequency and voltage stability and a modified particle swarm optimization algorithm is applied to getfaster solution to the practical economic operation problem of islanded microgrid With the example system of an actual islandedmicrogrid in Dongao Island China the proposed models dynamic optimization strategy and solution algorithm are verified andthe influences of different operation strategies and optimization algorithms on the economic operation are discussed The resultsachieved demonstrate the effectiveness and feasibility of the proposed method

1 Introduction

In recent years microgrid has received considerable atten-tions to improve the reliability and economy of power system[1] Researches and practices show that islanded microgridintegrated with renewable energy sources (RES) the syn-chronous generators and energy storage system has been aneffective approach to solving the power supply problem insmall rural or remote regions where these communities donot access the utility grid due to the technical and economicalreasons [2ndash4] However incorporation of renewable energysources and other distributed generations (DG) poses a bigchallenge to the economic operation problem of islandedmicrogrid [5]

Economic operation is a very important problem tobe solved in the planning and operation of power sys-tem and optimal modeling optimization and simulationhave received considerable attentions in the literature [6ndash8]Reference [9] presents a novel energy management system(EMS) to coordinate the power forecasting output powerof different generators and energy storage to minimize the

total operation cost Reference [10] proposes a multiobjectivelinear programming methodology to determine the oper-ating levels of various generation units by minimizing twoobjectives of annual energy cost and annual CO

2emissions

Similarly a differential evolution algorithm is used to min-imize the total cost comprising the emission cost and theoperation andmaintenance costs ofmicrogrid in [11] Clearlythe operation strategy has a significant influence on theactual performance of islanded microgrid system Reference[12] proposes an idealized predictive dispatch strategy as abenchmark in evaluating simple nonpredictive strategiesbased on assumed perfect knowledge of future load andwind conditions Reference [13] proposes an optimal dispatchstrategy considering the battery wear cost and the diesel fuelconsumption cost to determine the optimum values of setpoints for the starting and stopping of the diesel generator asto minimize the total operation costs of islanded microgridThe optimum control algorithm based on combined dispatchstrategies is developed to achieve the optimal unit cost ofislanded microgrid [14]

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 379250 10 pageshttpdxdoiorg1011552015379250

2 Mathematical Problems in Engineering

DCAC

PV array Inverter

Inverter

BS

Battery

PV

WT

DCAC

AC

DC AC

DC

Rectifier InverterWind turbine

Diesel generator

DE

Electric loads

AC bus

Figure 1 Structure of islanded microgrid

From the literature survey exposed above the economicoperations of islanded microgrid in those studies are per-formed under the preset control strategies for minimizingoperation cost In addition it can be clearly inferred that thecost of islanded microgrid depends on two factors the unitgenerating cost of various distributed generation units andthe operation strategy In fact there are two distinct levelsin the operation control of islanded microgrid system (1)dynamic control which deals with control of the frequencyand magnitude of the output voltage of the system (2) dis-patch control which deals with the energy flowmanagementfrom the various sources to load for cost minimizationThusthe master-slave control strategy is popularly adopted to dealwith the control of system frequency and voltage as well asthe energy flow management of islanded microgrid

This paper presents a joint-optimization of operationstrategy and cost reduction to allocate the load demandamong various generation units in an economic stable andreliable way for islanded microgrid which is integrated withwind turbine generator (WT) and solar PV generator (PV)the diesel generator (DE) and battery storage system (BS)Considering two different controlmodes whereDE or BS actsas the master unit to guarantee stable operation of islandedmicrogrid a novel dynamic optimization process integratedwith a modified PSO (MPSO) algorithm is developed to findboth optimal operating strategy and optimal cost optimiza-tion scheme for the practical economic operation problem ofislanded microgrid

2 Microgrid Operation Strategy

Figure 1 shows a typical system structure of hybrid energysources islanded microgrid where PV WT DE and BS unitsare all connected together to supply power to the electricload through the AC bus As we know WT and PV bothhave a remarkable drawback of their unpredictable natureand dependence on weather and climatic conditions andtheir intermittent output powers will cause the system powerfluctuation [15] BS has great advantages of peak shaving andenergy buffer to improve RES fluctuation but the existing bigbottleneck of higher cost and shorter lifetime causes the smallsize of BS in islanded microgrid [16] DE is still necessary

and important to improve the system reliability in case of badweather conditions that will cause little or zero RES powerhowever its higher fuel cost and pollution emission are stillmain concerns of economic operation in islanded microgrid

Themain concerns of islanded operation are to guaranteethe system operation stability and reliability as well as con-sider economic cost requirement of microgrid Combiningthe system operation requirement and control characteristicsof various DGs the master-slave control method is a popularand preferable choice for islanded microgrid to achieve anoptimal objective of stable operation and minimum gen-erating cost [17] In the master-slave control strategy thecontrollable microsource is selected as the master unit totrack the power fluctuation as to guarantee the stability ofsystem voltage and frequency and the other microsourcesdo not follow the system power fluctuation [18] As shownin Figure 1 DE and BS units both are qualified to act as themaster unit but the larger difference of their control responsecharacteristics causes them not to operate as the master unitat the same time [19] Thus there are two different operationcontrol modes as below

(1) Mode 1 BS is the master unit that employs Vf con-trol method to follow the system power fluctuationand guarantee the frequency and voltage stability ofislandedmicrogrid DE is off or operates at full powerto supply power to microgrid and BS as required

(2) Mode 2 DE is the master unit that uses droop controlmethod tomaintain the operation stability of islandedmicrogrid However as the slave unit BS just use PQmethod to absorb RES power or inject power to assistDE to keep system power balance according to theinstruction of microgrid energy management system

3 Economic Operation Model

The economic operation problem of islanded microgrid isto allocate the load demands among the various distributedgeneration units in such a secure and reliable manner as tominimize the overall system generating cost subject to a setof equality and inequality constraints while the controllablepower sources such as DE or BS act as the master unit tofollow system power fluctuation

31 Objective Functions The objective of microgrid eco-nomic operation is to determine generation levels ofWT PVDE and BS units to meet the load demand as to minimizethe overall system generating cost including the depreciationcost the operation cost the pollutant emission cost andeconomic subsidies available for RES over the entire dispatchperiod [0 NT] where 119879 is the sampling time interval and119873 is the number of the time intervals The operation costcomprises the fuel cost and maintenance and operating(MampO) cost

min119862 (119875) =

119873

sum

119905=1

119866

sum

119895=1

119862119895(119875119905

119895) (1)

Mathematical Problems in Engineering 3

where 119862(119875) is the total generation cost of microgrid toproduce 119875 during an entire dispatch period 119873119879 119866 is thenumbers of various distributed generation units 119895 119862

119895(119875119905

119895) is

the generation cost for unit 119895 to produce 119875119905119895 119875119905119895is the output

power of generation unit 119895 during the 119905th time interval [(119905 minus1)119879 119905119879]

311 RES Generating Cost The renewable energy sources ofWT and PV units incur only investment costs and exhibitvery little operating cost which can be expressed as a fractionof the corresponding initial capital costs [5] The economicsubsidies available forWT and PVunits are expressed as theirdifferent price subsidies per unit power according to the localgreen energy generating policy Thus the generating cost ofRES is formulated in the following

119862RES119894 (119875119905

119894) = 119862DC119894 (119875

119905

119894) + 119862MO119894 (119875

119905

119894) minus 119878ES119894 (119875

119905

119894)

=119862AIC119894 (1 + 120588

119894)

119864APG119894sdot 119875119905

119894minus 119896ES119894 sdot 119875

119905

119894

= (119862AIC119894 (1 + 120588

119894)

119864APG119894minus 119896ES119894) sdot 119875

119905

119894

(2)

where 119862DC119894 119862MO119894 and 119878ES119894 are the depreciation cost theMampO cost and the economic subsidy for RES unit 119894 toproduce 119875119905

119894 respectively 119862AIC is the annualized investment

cost () 120588 is MampO cost coefficients 119864APG is the estimatedtotal annual power generation (kWh) based on a typicalhistorical data 119896ES is the proportionality coefficient of pricesubsidy (kWh)

312 DE Generating Cost The generating cost of DE is madeup of the fixed cost and variable cost The fixed cost isexpressed as the depreciation cost however the variable costconsists of the fuel cost MampO cost and emission cost TheMampO cost is assumed to be proportional with the producedenergy The fuel cost is expressed as an inverse proportionfunction about the relationship between the nominal powerrating and actual output power [20] The pollution emissioncosts (NO

119909 SO2 and CO

2) are gained by their proportional

coefficients of the fuel cost [21] The unit depreciation costcan be equal to the annualized investment cost divided bythe estimated total annual power generation produced byDEThus the overall generating cost of DE is formulated in thefollowing

119862DE (119875119905

DE)

= 119862DC (119875119905

DE) + 119862MO (119875119905

DE) + 119862FC (119875119905

DE) + 119862EC (119875119905

DE)

= (119862AICDE

119864APGDE+ 119870MODE) sdot 119875

119905

DE

+ (0146 + 005415 sdot119875RDDE119875119905

DE) sdot (119888

119891119901+

3

sum

119896=1

119888119864119896)

(3)

where 119862DC(119875119905

DE) 119862MO(119875119905

DE) 119862FC(119875119905

DE) and 119862EC(119875119905

DE) are thedepreciation cost the MampO cost the fuel consumption costand the emission cost respectively for DE to produce 119875119905DE119862AICDE is the annualized investment cost () 119864APGDE is theestimated total annual power generation produced by DE(kWh) 119870MODE is the MampO cost coefficient (kWh) 119875RD

DEis the nominal power rating of DE (kW) 119888

119891119901is the fuel price

for DE (liter) 119888119864119896

is the environmental cost coefficient ofpollution emission 119896 of NO

119909 SO2 and CO

2(kg)

313 BS Wear Cost The wear cost of BS is expressed asa proportion of the life cycle cost divided by the totaldischarging power in the whole life time It is a simple andeffective way to calculate in microgrid economic operationcompared with the method in accordance with the batterycycle times Thus the wear cost of BS is expressed as follows

119862BS (119875119905

BS) = 120573BS sdot 119875119905

BSdc (4)

where 119862BS(119875119905

BS) is the wear cost of BS to discharge 119875119905BS at 119905time 120573BS is the unit wear cost coefficients of BS 119875119905BSdc is thedischarging power of BS

32 Constraint Conditions

321 System Power Balance The balance between powersupply and demand is necessary for islanded microgrid sothe equality constraint is expressed as follows

119866

sum

119895=1

119875119905

119895minus 119875119905

excessive = 119875119905

Load (5)

where 119875119905excessive is the system excessive power beyond the loaddemand 119875119905Load is the total system load demand

322 Spinning Reserve Capacity The necessary spinningreserve capacity of the controllable generation units availableis necessary to follow the system net load power fluctuationas to guarantee the secure and stable operation of islandedmicrogrid thus it is formulated as follows

119877

sum

119892=1

119875119905

CGSR ge Δ119875119905

MGSR

Δ119875119905

MGSR = 119890MG sdot 119875119905

net-load

(6)

where 119877 is the numbers of the controllable generation units119875119905

CGSR is the spinning reserve of the controllable generationunit (CG) available Δ119875119905MGSR is the required spinning reserveof microgrid (MG) 119890MG is the deviation ratio between thepredictive value and the actual value of system net load119875119905

net-load is the system net load which equals the system loadminus RES power

323 PowerGeneration Limits ofMicrosources As for variousgenerating units such as WT PV DE and BS their output


power ranges are subject to the functional roles in islandedmicrogrid

(1)MasterUnitThemaster unit is responsible for tracking thepower fluctuation as to guarantee the stability of system volt-age and frequency in islanded operation of microgrid Thusits output powers are subject to the following constraints

119875119905

119872ℎmax le 119875119905

119872ℎle 119875119905

119872ℎmin (7)

119875119905

119872ℎmax = 119875max119872ℎ

minus Δ119875119905

MGSR

119875119905

119872ℎmin = 119875min119872ℎ

+ Δ119875119905

MGSR(8)

where 119875119905119872ℎ

is the output power of ℎmaster unit (Mh) during119905th time interval 119875119905

119872ℎmax and 119875119905

119872ℎmin are the output powerupper and lower limits respectively 119875max

119872ℎand 119875

min119872ℎ

are thetechnicalmaximumandminimumpower limits respectively

(2) Slave UnitThe slave unit can operate within its technicalmaximum and minimum power limits as it does not needto follow system power fluctuation Thus its output power issubject to the following inequality constraint

119875min119878119897

le 119875119905

119878119897le 119875

max119878119897

(9)

where 119875119905119878119897is the output power of 119897 slave unit during 119905th time

interval 119875min119878119897

and 119875max119878119897

are the technical operation powerupper and lower limits of 119897 slave unit respectively

324 Start-Stop Time Constraints The minimum start-stoptime constraint such as DE or WT cannot be less than acertain number

119879rs119895 ge 119879minrs119895 (10)

where 119879rs119895 is the runningstop (rs) time of 119895 generation unit119879minrs119895 is the minimum continuous running or stop time of 119895

unit

325 BS Storage Capacity Limits In order to avoid anydeep discharge to decrease battery lifetime [22] this paperselects four key nodes of SOCmin SOClow SOChigh andSOCmax to divide the battery energy storage capacity into4 interval ranges The maximum SOC (SOCmax) is fullycharged (100of the SOC) and theminimumSOC (SOCmin)is recommended by the manufacturer below which theyshould not operate

SOCmin le SOClow le SOC (119905) le SOChigh le SOCmax (11)

where SOCmin and SOCmax are the minimum and maximumbattery storage capacity limits SOClow and SOChigh are thelow and high storage capacity limits of BS normal operationrange

4 MPSO-Based Dynamic Optimization

41 Dynamic Economic Optimization Concept Theeconomicoperation of islanded microgrid is commonly regarded as a

Output solution

Operation mode M(t998400)

t = t + 1 t998400= t

998400+ 1

t998400lt T

M(t998400 )min

M(t998400) = M(t

998400minus 1)

Start

Implement MPSO algorithm

No

Yes

No

Yes

tT = 24 hour

Read Ptload Pt

WT PtPV SOC(t)

Min CtMG(P

tload)

min CNTMG(P)

Figure 2 Dynamic economic optimization process

discrete cost optimization problem to sum up all minimumgeneration costs of sampling periods in the time domain[23] The operation strategy and cost reduction are two mainconcerns to the economic operation problem of islandedmicrogrid The operation strategy is mainly to select themaster unit tomaintain the system stable operation as well aspay critical influence on the cost reduction [14 24] As shownin Figure 1 there are two different control modes of DE or BSas the master unit In fact during the whole dispatch periodof islanded microgrid DE and BS might alternate to operateas the sole master unit to maintain the system frequency andvoltage stability Thus a novel dynamic economic operationoptimization process is proposed based on two potentialoperation control modes as shown in Figure 2 which adoptsa MPSO algorithm to find both optimum operation strategyand optimum cost minimization for the economic operationproblem of islanded microgrid This proposed operationstrategy is called the dynamic operation strategy

In the proposed dynamic optimization process as abovethere are two different time scales 119905 is for the cost optimiza-tion and 119905

1015840 is for the operation control mode or the typeof master unit It also indicates that the type of master unitwill change during dispatch period so the master unit119872(119905

1015840)

needs its own time-domain function (1199051015840 = 1199051015840+ 1) to evaluate

if its minimum start or stop time constraints are met or notIf the master unit is always fixed as DE or BS over the wholedispatch period or during the initial sampling periods thesetwo time scales are the same as 119905 = 119905

1015840 Moreover MPSOalgorithm is applied to get the optimal trade-off betweenthe minimum generating cost (119862119905MG(119875

119905

load)) for meeting loadpower (119875119905load) and the corresponding operation control mode


that determines the type of master unit (119872(1199051015840)) during 119905th

sampling period

42 MPSO Algorithm Particle swarm optimization (PSO) isa stochastic population-based algorithm which was origi-nally introduced by Kennedy and Eberhart [25 26] Com-pared to other optimization techniques such as geneticalgorithm (GA) PSO has themost outstanding advantages offew parameters to implement easily and faster convergencespeed In order to find a balance between accelerating theconvergence speed and retaining the diversity of the particlesa MPSO with dynamic adaptive inertia weight is adoptedto resolve the economic dispatch problem for it has theimproved convergence speed and solution accuracy [27] InMPSO a swarm contains a set of populationmembers whichis called the particle Every particle has both a position anda velocity and the position represents a candidate solutionin the multidimensional solution space and the velocitymoves it from one position to another over the solutionspace For the economic operation optimization of islandedmicrogrid each particle represents a candidate optimumoperation solution

In a119863-dimensional solution space the position vector ofthe 119898th solution is written as 119883

119898= (1199091198981

1199091198982

119909119898119863

)and the corresponding velocity vector is given by 119881

119898=

(V1198981

V1198982

V119898119863

) The position and velocity updatingmethods for the119889th dimension of119898th solution at the (119899+1)thiteration step are expressed as the following equations

119909119899+1

119898119889= 119909119899

119898119889+ V119899+1119898119889

(12)

V119899+1119898119889

= 119908 sdot V119899119898119889

+ 11988811199031(119901119887119898119889

minus 119909119899

119898119889) + 11988821199032(119892119887119889minus 119909119899

119898119889)

(13)

119908 = 1199080minus ℎ119899

119898sdot 119908ℎ+ 119904119899

119898sdot 119908119904 (14)

ℎ119905

119898=

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865 (119901119887119899minus1

119898) 119865 (119901119887

119899

119898))

max (119865 (119901119887119899minus1119898

) 119865 (119901119887119899119898))

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

119904 =

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865119899119899best 119865119899)

max (119865119899119899best 119865119899)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(16)

where 119909119899119898and V119899

119898are vectors representing the position and

velocity of the 119898th particle respectively 119889 isin 1 2 119863

represents the dimension of the particle 119908 is a dynamicallyadaptive inertia weight determining how much of particlersquosprevious velocity is preserved 119888

1and 119888

2are two positive

acceleration constants 1199031and 119903

2are two uniform random

sequences sampled from 119880(0 1) 119901119887119898

is the personal bestposition found by the 119898th particle 119892119887 is the best positionfound by the entire swarm 119908

0is the initial value of 119908 ℎ119899

119898

is the speed factor 119904 is the aggregation degree factor 119908ℎand

119908119904are two constants typically within the range [0 1] 119865(119901119887119899

119898)

is the fitness value of 119901119887119899119898 119865119899is the mean fitness value of all

particles in the swarm at the 119899th iteration 119865119899119899best is the best

fitness value achieved by the particles at the 119899th iteration

Initial population of the MPSO algorithm

Fitness computing and evaluating

Update the position of each particle by (12)

Calculate the new inertia

End criterion satisfied

No

Yes

Start

End

wn+1) and new

velocity (n+1md) by using(14) (15) and (16) n = n + 1

Update particle best (pbmd)

and global best (gbd)

weight (

Figure 3 Flowchart of MPSO optimization algorithm

43 The Process of the MPSO Algorithmic Solution As shownin Figure 2 the MPSO algorithm was adopted to find bothoptimal operation strategy and optimalminimum generationcost of islanded microgrid Thus the algorithm process isshown in Figure 3

The specific steps are described as follows

Step 1 The first step includes the following populationinitialization of MPSO parameters setting the total numberof the particles the maximum number of the generations119896max the maximum velocity Vmax two positive accelerationcoefficients 119888

1and 1198882 initial inertia weight119908

0 and two inertia

weight coefficients 119908ℎand 119908

119904

Step 2 Calculate and evaluate the fitness (1) evaluate thefitness of each particle in the population

Step 3 Compare the particlersquos fitness value with 119901119887119898119889

and119892119887119889 Update the 119901119887

119898119889and 119892119887

119889according to the comparison

result

Step 4 Calculate the new velocity V119899+1119898119889

by using (15)

Step 5 Update the position of each particle by using (14)

Step 6 Calculate the variance of all particlesrsquo fitness functions(1) and check if the converge criterion is met If it is met goto Step 7 otherwise go to Step 2

Step 7 End and output the optimization result


Table 1 System configuration of Dongao microgrid

Generation unit Power rating QTY (set)WT 750 kW 3PV 250 kW 3DE 1020 kW1275 kVA 4BS 500 kW times 6 h 1

Table 2 Control parameters of DGs

Type Parameter (pu) Type Parameter (pu)119875maxMU 1 pu SOCmin 02 pu119875minMU 02 pu SOCinitial 1000 kWh119875maxSU 1 pu 119879WTmin 30 minutes119875minSU 02 pu 119879PVmin 0

SOCmax 1 pu 119879DEmin 20 minutesSOChigh 090 pu 119879BSmin 0SOClow 03 pu

5 The Case of Study

51 The Example System For the purposes of validatingthe proposed methodology the simulations are executed inan actual islanded microgrid project which was built tosupply power for a new economic development experimentalregion in Dongao Island China The system configurationof Dongao microgrid is shown in Table 1 which was opti-mized based on the full consideration of the load demandand various distributed generation units such as WT PVDE and BS based on the historical data According to itspractical operation performance the unexpected problemshave higher electricity costs and lower utilization of RESgenerations when Dongao microgrid adopts an initial staticoperation strategy that just has the control mode 2 where DEalways acts as the master unit as discussed in Section 2

In order to reflect the dynamic scheduling of microgridbetter this paper set the calculation cycle as 1 day setting5min as a calculation period then the whole day couldbe divided into 288 periods The related parameters aboutMPSO were set as follows particle population size was 50dimensions were 30 andmax iterations were 100 (119888

1= 1198882= 2

119908ℎ= 05 and 119908

119904= 005) Moreover based on the developed

models the parameters for each distributed generation unitin Dongao microgrid project are given in Table 2

52 Results and Discussion

521 Comparative Analysis of the PSO Algorithm In orderto analyze the influence of the MPSO algorithm and thetraditional PSO algorithm on the microgrid operation com-bined with the proposed dynamic optimization process asshown in Figure 2 the results of adopting these two differentalgorithms to calculate the optimal models are shown inTable 3 and the convergence curves are shown in Figure 4

Table 3 shows that the calculation time of the MPSO isshorter than that of the traditional PSO algorithm because

Table 3 Result comparisons between the traditional PSO and theMPSO algorithm

Optimization type PSO MPSOCalculation time (second) 35058 16235Average convergence iteration 47 15Convergence value () 906843051 906325133

0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105

Figure 4 Convergence characteristics of PSO and MPSO

the adaptive inertia weight effectively improves the conver-gence speed It can also be seen from Figure 4 that theconvergence rate of the MPSO is faster than the traditionalPSO algorithm and it converges at about 15th generationMoreover theMPSO obtained the optimum result comparedto the traditional PSO algorithm In conclusion the MPSOalgorithm has the more rapid convergence rate and moreaccurate convergence value to resolve the optimumoperationof islanded microgrid

522 Comparative Analysis of the Operation Strategy Inthis paper we adopt the dynamic optimization strategywith mode 1 and mode 2 where DE and BS alternate asthe sole master unit as to minimize the generating costand improve RES utilization of islanded microgrid over theentire dispatch period In order to analyze the impact ofthe proposed dynamic strategy on the economic dispatch ofmicrogrid the results of adopting both the proposed dynamicstrategy and the original static strategy to calculate the modelof scheduling are shown in Table 4 and their economicoperation performances are demonstrated in Figures 5 and6 respectively Please note that the output power curvesof WT01 WT02 and 3 sets of PVs are not shown becausethey are all absorbed or not changed during the economicoperation

We can see from Table 4 that when we adopt the dynamicoperation strategy the total cost is much less than that underthe static strategy and the daily cost saving is RMB50475858Thus the annual cost reduction will be RMB1817130888because the ratio of similar weather is approximately 10


0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1

(a) Performance under dynamic strategy

0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03

(b) WT03 power under dynamic strategy

P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04

(c) DE power under dynamic strategy

0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)

(d) BS SOC under dynamic strategy

Figure 5 Optimal economic operation under dynamic strategy

Table 4 Result comparisons between two operation strategies

Optimization results Dynamic strategy Static strategyTotal cost () 906325133 95680099RES utilization () 100 9659Cost saving () 50475858

calculated based on historical data collected on DongaoIsland in 2013 Combined with Figures 5 and 6 it is easy toknow the root cause of their different cost levels

Figure 5 shows detailed operation performances of vari-ous distributed generation units under the proposed dynamicoperation strategy in which BS and DE alternate to operateas the master unit frequently according to different operationconditions Figure 5(b) shows a continuous generation ofWT which means a satisfied RES utilization effect Combin-ing Figures 5(a) and 5(c) it is easy to know the following(i) While BS runs as the master unit it absorbs the surplusRES power when RES power exceeds the load demand during000amndash455am and 2305pmndash2400pm and accordingly DE

is off In addition BS also runs the peak shaving function tomeet buffer instantaneous fluctuations around the net loadand meanwhile DE operates at full power during 525amndash735am 1155amndash1300pm 1720pmndash1755pm and 1945pmndash2125pm (ii) While DE acts as the master unit during othertime periods it operates at the higher power level as toreduce fuel and emission and sometimes it should get somenecessary power supplement from BS if needed The SOCcurve of BS also shows this clearly in Figure 5(d) In short thedynamic strategy achieves the higher RES utilization and thehigher power level of DE as well as reduction of DE run-timeaccording to different conditions which can further reducethe system generating cost

Figure 6 demonstrates detailed operation performancesunder the original static strategy inwhichDE always operatesas the master unit It is obvious to see that the static strategycauses the system to abandondump some wind power andto make DE run at lower power level in some times whichare shown in Figures 6(b) and 6(c) Moreover combined withFigure 6(a) we also know that BS can assist DE to improveits output power level to a certain extent as to reduce fuel and


P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1

(a) Performance under static strategy

0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03

(b) WT03 power under static strategy

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)

(c) DE power under static strategy

0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)

(d) BS SOC under static strategy

Figure 6 Optimal economic operation under static strategy

emission However DE could not operate at the full powerbecause of the necessary spinning reserve to cover systempower fluctuation indicated in (8) As a result the highersystem generating cost occurs resulting from the lower RESutilization as well as the more fuel and emission of DE

Based on the above it can be seen that the operatingstrategy has a critical influence upon the actual economicoperation performance of islanded microgrid Comparedto the static strategy the proposed dynamic strategy canmaximize BS advantages to improve the RES utilization andhelp DE reduce run-time and run at higher power levelcorrespondingly further reducing DE fuel cost and emissioncost so as tominimize the systemgenerating cost ofmicrogridas far as possibleThe root cause is to set BS as themaster unitto further reduce system generating cost which can not onlyjust utilize RES power to meet load but also run the systempeak shaving function as to minimize DE fuel and emissionIn addition the results show the following (i) RES unitshave the lowest generating cost as to be priority schedulingcompared to DE and BS (ii) There is a set point between

the generating cost of DE and the wear cost of BS when DEoutput power is higher than this set point its generating costis less than the wear cost of BS so as to be scheduled prior toBS If not BS has a higher priority than DE

6 Conclusion

This paper proposes an optimal economic operation methodfor islanded microgrid to attain a joint-optimization of costreduction and operation strategy that determine the type ofmaster unit to maintain the stability of system frequencyand voltage The time-series dynamic optimization processis designed according to two different master units of DEand BS as well as the discrete optimization characteristicsof economic operation in islanded microgrid The MPSOalgorithmpresented is capable of efficiently searching an opti-mum trade-off between the minimum generating cost andthe corresponding control mode of islanded microgrid Theproposed models and MPSO-based dynamic optimizationstrategy are verified by case studies based on a real islanded


microgrid in Dongao Island China The methodology pre-sented effectively improves the RES generation utilizationand the operational life of BS as well as minimizing the fuelconsumption cost and pollution emission cost resulting fromDE

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study was supported jointly by the National HighTechnology Research and Development Program (863 Pro-gram 2014AA052001) the Science and Technology Plan-ning Project of Guangdong Province (2012B040303005) theGuangzhou Nansha District Science and Technology Project(2013C006) and the China Southern Power Grid CompanyLimited Science and Technology Project (K-KY2014-009)

References

[1] N Hatziargyriou H Asano R Iravani and C Marnay ldquoMicro-grids an overview of ongoing research development anddemonstration projectsrdquo IEEE Power and EnergyMagazine vol5 no 4 pp 78ndash94 2007

[2] A N Celik ldquoOptimisation and techno-economic analysisof autonomous photovoltaicndashwind hybrid energy systems incomparison to single photovoltaic and wind systemsrdquo EnergyConversion and Management vol 43 no 18 pp 2453ndash24682002

[3] A M Eltamaly and M A Mohamed ldquoA novel design andoptimization software for autonomous PVwindbattery hybridpower systemsrdquo Mathematical Problems in Engineering vol2014 Article ID 637174 16 pages 2014

[4] B Zhao X Zhang P Li K Wang M Xue and C WangldquoOptimal sizing operating strategy and operational experienceof a stand-alone microgrid on Dongfushan Islandrdquo AppliedEnergy vol 113 pp 1656ndash1666 2014

[5] J P S Catalao Electric Power Systems Advanced ForecastingTechniques andOptimalGeneration Scheduling CRCPressNewYork NY USA 2012

[6] M G Ippolito M L Di Silvestre E R Sanseverino G Zizzoand G Graditi ldquoMulti-objective optimized management ofelectrical energy storage systems in an islanded network withrenewable energy sources under different design scenariosrdquoEnergy vol 64 pp 648ndash662 2014

[7] Y-H Chen S-Y Lu Y-R Chang T-T Lee and M-C HuldquoEconomic analysis and optimal energy management modelsfor microgrid systems a case study in Taiwanrdquo Applied Energyvol 103 pp 145ndash154 2013

[8] M Parvizimosaed F Farmani and A Anvari-MoghaddamldquoOptimal energy management of a micro-grid with renewableenergy resources and demand responserdquo Journal of Renewableand Sustainable Energy vol 5 Article ID 053148 pp 1ndash15 2013

[9] A Dukpa I Duggal B Venkatesh and L Chang ldquoOptimalparticipation and risk mitigation of wind generators in anelectricity marketrdquo IET Renewable Power Generation vol 4 no2 pp 165ndash175 2010

[10] H Ren W Zhou K Nakagami W Gao and Q Wu ldquoMulti-objective optimization for the operation of distributed energysystems considering economic and environmental aspectsrdquoApplied Energy vol 87 no 12 pp 3642ndash3651 2010

[11] H Vahedi R Noroozian and S H Hosseini ldquoOptimal man-agement ofMicroGrid using differential evolution approachrdquo inProceedings of the 7th International Conference on the EuropeanEnergy Market (EEM rsquo10) pp 1ndash6 IEEE Madrid Spain June2010

[12] C D Barley and C B Winn ldquoOptimal dispatch strategy inremote hybrid power systemsrdquo Solar Energy vol 58 no 4-6 pp165ndash179 1996

[13] MAshari andCVNayar ldquoAn optimumdispatch strategy usingset points for a photovoltaic (PV)-diesel-battery hybrid powersystemrdquo Solar Energy vol 66 no 1 pp 1ndash9 1999

[14] A Gupta R P Saini and M P Sharma ldquoModelling of hybridenergy system-Part II combined dispatch strategies and solu-tion algorithmrdquo Renewable Energy vol 36 no 2 pp 466ndash4732011

[15] O Ekren and B Y Ekren ldquoSize optimization of a PVwindhybrid energy conversion system with battery storage usingsimulated annealingrdquoApplied Energy vol 87 no 2 pp 592ndash5982010

[16] H Yang W Zhou L Lu and Z Fang ldquoOptimal sizing methodfor stand-alone hybrid solar-wind systemwith LPSP technologyby using genetic algorithmrdquo Solar Energy vol 82 no 4 pp 354ndash367 2008

[17] N Cai and J Mitra ldquoA multi-level control architecture formaster-slave organized microgrids with power electronic inter-facesrdquo Electric Power Systems Research vol 109 pp 8ndash19 2014

[18] J A P Lopes C L Moreira and A G Madureira ldquoDefiningcontrol strategies for microgrids islanded operationrdquo IEEETransactions on Power Systems vol 21 no 2 pp 916ndash924 2006

[19] L Guo X Fu X Li and C Wang ldquoCoordinated control ofbattery storage and diesel generators in isolated AC microgridsystemsrdquo Proceedings of the Chinese Society of Electrical Engi-neering vol 32 no 25 pp 70ndash78 2012

[20] O Skarstein and K Uhlen ldquoDesign considerations with respectto long-term diesel saving in winddiesel plantsrdquo Wind Engi-neering vol 13 no 2 pp 72ndash87 1989

[21] W Morgantown ldquoEmission rates for new DG technologiesrdquoThe Regulatory Assistance Project [EBOL] 2001 httpwwwraponlineorgdocumentdownloadid66

[22] G Cau D Cocco M Petrollese S Knudsen Kaeligr and CMilanldquoEnergy management strategy based on short-term generationscheduling for a renewable microgrid using a hydrogen storagesystemrdquo Energy Conversion and Management vol 87 pp 820ndash831 2014

[23] X Xia and A M Elaiw ldquoOptimal dynamic economic dispatchof generation a reviewrdquo Electric Power Systems Research vol 80no 8 pp 975ndash986 2010

[24] R Dufo-Lopez J L Bernal-Agustın and J Contreras ldquoOpti-mization of control strategies for stand-alone renewable energysystems with hydrogen storagerdquo Renewable Energy vol 32 no7 pp 1102ndash1126 2007

[25] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks pp 1942ndash1948 Perth Ausitalia December 1995

[26] Y Shi and R Eberhart ldquoA modified particle swarm opti-mizerrdquo in Proceedings of the IEEE International Conference on


World Congress on Computational Intelligence pp 69ndash73 IEEEAnchorage Alaska USA May 1998

[27] X Yang J Yuan J Yuan and H Mao ldquoA modified particleswarm optimizer with dynamic adaptationrdquoAppliedMathemat-ics and Computation vol 189 no 2 pp 1205ndash1213 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


DCAC

PV array Inverter

Inverter

BS

Battery

PV

WT

DCAC

AC

DC AC

DC

Rectifier InverterWind turbine

Diesel generator

DE

Electric loads

AC bus

Figure 1 Structure of islanded microgrid

From the literature survey exposed above the economicoperations of islanded microgrid in those studies are per-formed under the preset control strategies for minimizingoperation cost In addition it can be clearly inferred that thecost of islanded microgrid depends on two factors the unitgenerating cost of various distributed generation units andthe operation strategy In fact there are two distinct levelsin the operation control of islanded microgrid system (1)dynamic control which deals with control of the frequencyand magnitude of the output voltage of the system (2) dis-patch control which deals with the energy flowmanagementfrom the various sources to load for cost minimizationThusthe master-slave control strategy is popularly adopted to dealwith the control of system frequency and voltage as well asthe energy flow management of islanded microgrid

This paper presents a joint-optimization of operationstrategy and cost reduction to allocate the load demandamong various generation units in an economic stable andreliable way for islanded microgrid which is integrated withwind turbine generator (WT) and solar PV generator (PV)the diesel generator (DE) and battery storage system (BS)Considering two different controlmodes whereDE or BS actsas the master unit to guarantee stable operation of islandedmicrogrid a novel dynamic optimization process integratedwith a modified PSO (MPSO) algorithm is developed to findboth optimal operating strategy and optimal cost optimiza-tion scheme for the practical economic operation problem ofislanded microgrid

2 Microgrid Operation Strategy

Figure 1 shows a typical system structure of hybrid energysources islanded microgrid where PV WT DE and BS unitsare all connected together to supply power to the electricload through the AC bus As we know WT and PV bothhave a remarkable drawback of their unpredictable natureand dependence on weather and climatic conditions andtheir intermittent output powers will cause the system powerfluctuation [15] BS has great advantages of peak shaving andenergy buffer to improve RES fluctuation but the existing bigbottleneck of higher cost and shorter lifetime causes the smallsize of BS in islanded microgrid [16] DE is still necessary

and important to improve the system reliability in case of badweather conditions that will cause little or zero RES powerhowever its higher fuel cost and pollution emission are stillmain concerns of economic operation in islanded microgrid

Themain concerns of islanded operation are to guaranteethe system operation stability and reliability as well as con-sider economic cost requirement of microgrid Combiningthe system operation requirement and control characteristicsof various DGs the master-slave control method is a popularand preferable choice for islanded microgrid to achieve anoptimal objective of stable operation and minimum gen-erating cost [17] In the master-slave control strategy thecontrollable microsource is selected as the master unit totrack the power fluctuation as to guarantee the stability ofsystem voltage and frequency and the other microsourcesdo not follow the system power fluctuation [18] As shownin Figure 1 DE and BS units both are qualified to act as themaster unit but the larger difference of their control responsecharacteristics causes them not to operate as the master unitat the same time [19] Thus there are two different operationcontrol modes as below

(1) Mode 1 BS is the master unit that employs Vf con-trol method to follow the system power fluctuationand guarantee the frequency and voltage stability ofislandedmicrogrid DE is off or operates at full powerto supply power to microgrid and BS as required

(2) Mode 2 DE is the master unit that uses droop controlmethod tomaintain the operation stability of islandedmicrogrid However as the slave unit BS just use PQmethod to absorb RES power or inject power to assistDE to keep system power balance according to theinstruction of microgrid energy management system

3 Economic Operation Model

The economic operation problem of islanded microgrid isto allocate the load demands among the various distributedgeneration units in such a secure and reliable manner as tominimize the overall system generating cost subject to a setof equality and inequality constraints while the controllablepower sources such as DE or BS act as the master unit tofollow system power fluctuation

31 Objective Functions The objective of microgrid eco-nomic operation is to determine generation levels ofWT PVDE and BS units to meet the load demand as to minimizethe overall system generating cost including the depreciationcost the operation cost the pollutant emission cost andeconomic subsidies available for RES over the entire dispatchperiod [0 NT] where 119879 is the sampling time interval and119873 is the number of the time intervals The operation costcomprises the fuel cost and maintenance and operating(MampO) cost

min119862 (119875) =

119873

sum

119905=1

119866

sum

119895=1

119862119895(119875119905

119895) (1)



119895(119875119905

119895) is




119862RES119894 (119875119905

119894) = 119862DC119894 (119875

119905

119894) + 119862MO119894 (119875

119905

119894) minus 119878ES119894 (119875

119905

119894)

=119862AIC119894 (1 + 120588

119894)

119864APG119894sdot 119875119905

119894minus 119896ES119894 sdot 119875

119905

119894

= (119862AIC119894 (1 + 120588

119894)

119864APG119894minus 119896ES119894) sdot 119875

119905

119894

(2)





119909 SO2 and CO



119862DE (119875119905

DE)

= 119862DC (119875119905

DE) + 119862MO (119875119905

DE) + 119862FC (119875119905

DE) + 119862EC (119875119905

DE)

= (119862AICDE

119864APGDE+ 119870MODE) sdot 119875

119905

DE

+ (0146 + 005415 sdot119875RDDE119875119905

DE) sdot (119888

119891119901+

3

sum

119896=1

119888119864119896)

(3)

where 119862DC(119875119905

DE) 119862MO(119875119905

DE) 119862FC(119875119905

DE) and 119862EC(119875119905




for DE (liter) 119888119864119896


119909 SO2 and CO

2(kg)


119862BS (119875119905

BS) = 120573BS sdot 119875119905

BSdc (4)

where 119862BS(119875119905




119866

sum

119895=1

119875119905

119895minus 119875119905

excessive = 119875119905

Load (5)



119877

sum

119892=1

119875119905

CGSR ge Δ119875119905

MGSR

Δ119875119905

MGSR = 119890MG sdot 119875119905

net-load

(6)








119875119905

119872ℎmax le 119875119905

119872ℎle 119875119905

119872ℎmin (7)

119875119905

119872ℎmax = 119875max119872ℎ

minus Δ119875119905

MGSR

119875119905

119872ℎmin = 119875min119872ℎ

+ Δ119875119905

MGSR(8)

where 119875119905119872ℎ


119872ℎmax and 119875119905


119872ℎand 119875

min119872ℎ



119875min119878119897

le 119875119905

119878119897le 119875

max119878119897

(9)


interval 119875min119878119897

and 119875max119878119897



119879rs119895 ge 119879minrs119895 (10)


unit






Output solution


t = t + 1 t998400= t

998400+ 1

t998400lt T

M(t998400 )min

M(t998400) = M(t

998400minus 1)

Start


No

Yes

No

Yes

tT = 24 hour

Read Ptload Pt

WT PtPV SOC(t)

Min CtMG(P

tload)

min CNTMG(P)





1015840)




119905




sampling period



119898= (1199091198981

1199091198982

119909119898119863


119898=

(V1198981

V1198982

V119898119863


119909119899+1

119898119889= 119909119899

119898119889+ V119899+1119898119889

(12)

V119899+1119898119889

= 119908 sdot V119899119898119889

+ 11988811199031(119901119887119898119889

minus 119909119899

119898119889) + 11988821199032(119892119887119889minus 119909119899

119898119889)

(13)

119908 = 1199080minus ℎ119899

119898sdot 119908ℎ+ 119904119899

119898sdot 119908119904 (14)

ℎ119905

119898=

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865 (119901119887119899minus1

119898) 119865 (119901119887

119899

119898))

max (119865 (119901119887119899minus1119898

) 119865 (119901119887119899119898))

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

119904 =

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865119899119899best 119865119899)

max (119865119899119899best 119865119899)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(16)

where 119909119899119898and V119899




1and 119888

2are two positive






119898



119898)









No

Yes

Start

End

wn+1) and new




weight (






0 and two inertia


119904



and119892119887119889 Update the 119901119887

119898119889and 119892119887


result


by using (15)










5 The Case of Study



1= 1198882= 2

119908ℎ= 05 and 119908








0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105






0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119895(119875119905

119895) is




119862RES119894 (119875119905

119894) = 119862DC119894 (119875

119905

119894) + 119862MO119894 (119875

119905

119894) minus 119878ES119894 (119875

119905

119894)

=119862AIC119894 (1 + 120588

119894)

119864APG119894sdot 119875119905

119894minus 119896ES119894 sdot 119875

119905

119894

= (119862AIC119894 (1 + 120588

119894)

119864APG119894minus 119896ES119894) sdot 119875

119905

119894

(2)





119909 SO2 and CO



119862DE (119875119905

DE)

= 119862DC (119875119905

DE) + 119862MO (119875119905

DE) + 119862FC (119875119905

DE) + 119862EC (119875119905

DE)

= (119862AICDE

119864APGDE+ 119870MODE) sdot 119875

119905

DE

+ (0146 + 005415 sdot119875RDDE119875119905

DE) sdot (119888

119891119901+

3

sum

119896=1

119888119864119896)

(3)

where 119862DC(119875119905

DE) 119862MO(119875119905

DE) 119862FC(119875119905

DE) and 119862EC(119875119905




for DE (liter) 119888119864119896


119909 SO2 and CO

2(kg)


119862BS (119875119905

BS) = 120573BS sdot 119875119905

BSdc (4)

where 119862BS(119875119905




119866

sum

119895=1

119875119905

119895minus 119875119905

excessive = 119875119905

Load (5)



119877

sum

119892=1

119875119905

CGSR ge Δ119875119905

MGSR

Δ119875119905

MGSR = 119890MG sdot 119875119905

net-load

(6)








119875119905

119872ℎmax le 119875119905

119872ℎle 119875119905

119872ℎmin (7)

119875119905

119872ℎmax = 119875max119872ℎ

minus Δ119875119905

MGSR

119875119905

119872ℎmin = 119875min119872ℎ

+ Δ119875119905

MGSR(8)

where 119875119905119872ℎ


119872ℎmax and 119875119905


119872ℎand 119875

min119872ℎ



119875min119878119897

le 119875119905

119878119897le 119875

max119878119897

(9)


interval 119875min119878119897

and 119875max119878119897



119879rs119895 ge 119879minrs119895 (10)


unit






Output solution


t = t + 1 t998400= t

998400+ 1

t998400lt T

M(t998400 )min

M(t998400) = M(t

998400minus 1)

Start


No

Yes

No

Yes

tT = 24 hour

Read Ptload Pt

WT PtPV SOC(t)

Min CtMG(P

tload)

min CNTMG(P)





1015840)




119905




sampling period



119898= (1199091198981

1199091198982

119909119898119863


119898=

(V1198981

V1198982

V119898119863


119909119899+1

119898119889= 119909119899

119898119889+ V119899+1119898119889

(12)

V119899+1119898119889

= 119908 sdot V119899119898119889

+ 11988811199031(119901119887119898119889

minus 119909119899

119898119889) + 11988821199032(119892119887119889minus 119909119899

119898119889)

(13)

119908 = 1199080minus ℎ119899

119898sdot 119908ℎ+ 119904119899

119898sdot 119908119904 (14)

ℎ119905

119898=

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865 (119901119887119899minus1

119898) 119865 (119901119887

119899

119898))

max (119865 (119901119887119899minus1119898

) 119865 (119901119887119899119898))

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

119904 =

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865119899119899best 119865119899)

max (119865119899119899best 119865119899)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(16)

where 119909119899119898and V119899




1and 119888

2are two positive






119898



119898)









No

Yes

Start

End

wn+1) and new




weight (






0 and two inertia


119904



and119892119887119889 Update the 119901119887

119898119889and 119892119887


result


by using (15)










5 The Case of Study



1= 1198882= 2

119908ℎ= 05 and 119908








0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105






0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119875119905

119872ℎmax le 119875119905

119872ℎle 119875119905

119872ℎmin (7)

119875119905

119872ℎmax = 119875max119872ℎ

minus Δ119875119905

MGSR

119875119905

119872ℎmin = 119875min119872ℎ

+ Δ119875119905

MGSR(8)

where 119875119905119872ℎ


119872ℎmax and 119875119905


119872ℎand 119875

min119872ℎ



119875min119878119897

le 119875119905

119878119897le 119875

max119878119897

(9)


interval 119875min119878119897

and 119875max119878119897



119879rs119895 ge 119879minrs119895 (10)


unit






Output solution


t = t + 1 t998400= t

998400+ 1

t998400lt T

M(t998400 )min

M(t998400) = M(t

998400minus 1)

Start


No

Yes

No

Yes

tT = 24 hour

Read Ptload Pt

WT PtPV SOC(t)

Min CtMG(P

tload)

min CNTMG(P)





1015840)




119905




sampling period



119898= (1199091198981

1199091198982

119909119898119863


119898=

(V1198981

V1198982

V119898119863


119909119899+1

119898119889= 119909119899

119898119889+ V119899+1119898119889

(12)

V119899+1119898119889

= 119908 sdot V119899119898119889

+ 11988811199031(119901119887119898119889

minus 119909119899

119898119889) + 11988821199032(119892119887119889minus 119909119899

119898119889)

(13)

119908 = 1199080minus ℎ119899

119898sdot 119908ℎ+ 119904119899

119898sdot 119908119904 (14)

ℎ119905

119898=

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865 (119901119887119899minus1

119898) 119865 (119901119887

119899

119898))

max (119865 (119901119887119899minus1119898

) 119865 (119901119887119899119898))

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

119904 =

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865119899119899best 119865119899)

max (119865119899119899best 119865119899)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(16)

where 119909119899119898and V119899




1and 119888

2are two positive






119898



119898)









No

Yes

Start

End

wn+1) and new




weight (






0 and two inertia


119904



and119892119887119889 Update the 119901119887

119898119889and 119892119887


result


by using (15)










5 The Case of Study



1= 1198882= 2

119908ℎ= 05 and 119908








0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105






0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











sampling period



119898= (1199091198981

1199091198982

119909119898119863


119898=

(V1198981

V1198982

V119898119863


119909119899+1

119898119889= 119909119899

119898119889+ V119899+1119898119889

(12)

V119899+1119898119889

= 119908 sdot V119899119898119889

+ 11988811199031(119901119887119898119889

minus 119909119899

119898119889) + 11988821199032(119892119887119889minus 119909119899

119898119889)

(13)

119908 = 1199080minus ℎ119899

119898sdot 119908ℎ+ 119904119899

119898sdot 119908119904 (14)

ℎ119905

119898=

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865 (119901119887119899minus1

119898) 119865 (119901119887

119899

119898))

max (119865 (119901119887119899minus1119898

) 119865 (119901119887119899119898))

10038161003816100381610038161003816100381610038161003816100381610038161003816

(15)

119904 =

10038161003816100381610038161003816100381610038161003816100381610038161003816

min (119865119899119899best 119865119899)

max (119865119899119899best 119865119899)

10038161003816100381610038161003816100381610038161003816100381610038161003816

(16)

where 119909119899119898and V119899




1and 119888

2are two positive






119898



119898)









No

Yes

Start

End

wn+1) and new




weight (






0 and two inertia


119904



and119892119887119889 Update the 119901119887

119898119889and 119892119887


result


by using (15)










5 The Case of Study



1= 1198882= 2

119908ℎ= 05 and 119908








0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105






0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















5 The Case of Study



1= 1198882= 2

119908ℎ= 05 and 119908








0 20 40 60 80 10008

1

12

14

16

IterationO

bjec

tive f

unct

ion

valu

e

PSOMPSO

times105






0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

P (M

W)

LoadWTPV

DEBS

192

21

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


P (M

W)

P (M

W)

P (M

W)

P (M

W)

00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE01DE02

DE03DE04


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










P (M

W)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (hour)

LoadWTPV

DEBS

17518

185

7

6

5

4

3

2

1

0

minus1


0 2 4 6 8 10 12 14 16 18 20 22 240

150

300

450

600

750

900

Time (hour)

P (k

W)

WT03


00612

00612

00612

0 2 4 6 8 10 12 14 16 18 20 22 240

0612

Time (hour)

DE04DE03

DE02DE01

P (M

W)

P (M

W)

P (M

W)

P (M

W)


0 2 4 6 8 10 12 14 16 18 20 22 240

02

04

06

08

1

Time (hour)

SOC

(pu

)






6 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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