Research Article Optimal Capacity Allocation of Large

Research ArticleOptimal Capacity Allocation of Large-ScaleWind-PV-Battery Units

Kehe Wu12 Huan Zhou2 and Jizhen Liu12

1 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power UniversityBeijing 102206 China

2 School of Control and Computer Engineering North China Electric Power University PO Box 570 Beijing 102206 China

Correspondence should be addressed to Huan Zhou shenarder163com

Received 10 December 2013 Revised 5 February 2014 Accepted 19 February 2014 Published 17 April 2014

Academic Editor Mahmoud M El-Nahass

Copyright copy 2014 Kehe Wu 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 capacity allocation of large-scale wind-photovoltaic- (PV-) battery units was proposed First an output power modelwas established according to meteorological conditionsThen a wind-PV-battery unit was connected to the power grid as a power-generation unit with a rated capacity under a fixed coordinated operation strategy Second the utilization rate of renewable energysources and maximum wind-PV complementation was considered and the objective function of full life cycle-net present cost(NPC) was calculated through hybrid iterationadaptive hybrid genetic algorithm (HIAGA) The optimal capacity ratio amongwind generator PV array and battery device also was calculated simultaneously A simulation was conducted based on the wind-PV-battery unit in Zhangbei China Results showed that a wind-PV-battery unit could effectively minimize the NPC of power-generation units under a stable grid-connected operation Finally the sensitivity analysis of the wind-PV-battery unit demonstratedthat the optimization result was closely related to potential wind-solar resources and government support Regions with rich windresources and a reasonable government energy policy could improve the economic efficiency of their power-generation units

1 Introduction

Wind and solar energy are forms of green energy withtremendous application prospects At present some coun-tries have started research on the key technical problems ofwind-photovoltaic- (PV-) battery units [1ndash4] In 2011 Chinaestablished a demonstration wind-PV-battery unit in Zhang-bei this project aims to explore the stability and economicefficiency of large-scale power grids with renewable energysources [5]

Numerous studies on optimizing the capacity of wind-PV-battery units have been reported These studies can bemainly divided into single and multiple objective optimiza-tions The former primarily considers power distributionreliability as a constraint and targets minimum investmentcost For example aiming to reduce net present cost of dis-tribution systemsMohammadi et al suggested using particleswarm optimization to optimize the capacities of distributedgenerators in a microgrid under different market policies[6] To minimize the annual cost of a system Yang et al

considered the expected power shortage rate as a constraintand established an independent capacity optimization modelfor wind-PV-battery units He applied the model in a com-munication relay station in the southeastern coastal areas inChina and thus confirmed the feasibility of his model [7ndash9]Diaf et al established an independent economic optimizationmodel for wind-PV-battery units to minimize the levelizedcost of energy (LCE) and to analyze the sensitivity factors ofwind-PV-battery units [10]

Multiple objective optimizations mainly aim to improveinvestment cost and power distribution reliability Moreoverthey consider environmental protection such as reducingexhaust emissions For example Kazem and Khatib calcu-lated the optimal capacity ratio of a wind-PV-diesel-batterypower-generation system through a numerical algorithm tominimize cost and maximize power distribution reliabilityThey verified the economic efficiency and feasibility of theiroptimal capacity ratio through the power supply systemin several communities in Oman [11] Aiming at a mini-mum life cycle cost with no load shedding Li et al used

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 539414 13 pageshttpdxdoiorg1011552014539414

2 International Journal of Photoenergy

Meteorologicalobservatory

InternetPower grid dispatching automation system

Power grid

Physical connection lineSignals of control and measuring

Weather forecast

Combined powergeneration monitoring

system

Intelligentsubstation

PV array

Battery bank

Wind turbines

Figure 1 Basic structure of wind-PV-battery units

a simple sizing algorithm to calculate the capacity allocationof an independent wind-PV-battery unit and determinedthat the state of charge (SOC) of a battery should beperiodically invariant They confirmed the reliability andeconomic efficiency of the algorithm through a case studyin Zhoushan Island China [12] To minimize the LCE andCO2emissionswithin equivalent life cycles Dufo-Lopez et al

adopted a multiobjective evolutionary algorithm to calculatethe optimal capacity ratio of a wind-PV-diesel-battery power-generation system [13 14] To minimize system cost andloss of power supply probability Khatiba et al calculatedthe optimal capacity ratio of a wind-PV-battery unit in amicrogrid environment by using a genetic algorithm (GA)Moreover they further optimized the hub height of a windturbine and the optimal tilt angle of the PV array [15]

Previous studies on the capacity allocation of wind-PV-battery units have mainly focused on allocating appropriatewind-PV capacity ratios to achieve a wind-PV output powerthat is as close as possible to the load curve as well as to reducecharge-discharge times and the discharge depth of the batteryThe capacity allocation and characteristics of the overalloutput power are closely related to the load variation trendthus significantly restricting its application in large-scalewind-PV-battery units During the grid-connected operationof a large-scale wind-PV-battery unit the power grid has

to consider the unit as a power plant with a particularrated capacity to perform corresponding dispatcher tasks Inthe present study an optimal capacity allocation of wind-PV-battery units based on a rate capacity was proposed tominimize the net present cost (NPC) The optimal capacityof each wind-PV-battery unit under a rated capacity wascalculated by using a HIAGA

2 Operating Model of theWind-PV-Battery Units

21 System Structure The wind-PV-battery units mainlyconsist of a combined power-generation monitoring systema wind generator a PV array and a battery-energy storagedevice The basic structure is shown in Figure 1

The wind generator and the PV array are primarilyresponsible for generating power from renewable energysources such as wind and solar energy whereas the batteryis responsible for maintaining a stable overall power outputof the wind-PV-battery units through peak clipping andvalley filling The combined power-generation monitoringsystem provides a reasonable arrangement of the power-generation devices according to dispatching commands andweather forecasts (eg wind speed illumination intensity

International Journal of Photoenergy 3

0 5 10 15 20 25 300

05

1

15

2

25

3

Wind speed (ms)

Out

put p

ower

(MW

)

Figure 2 Output power characteristics of the wind generator

and temperature) thus ensuring the stable grid-connectedoperation of the wind-PV-battery units

22 Output Power Model of the Wind Generator The outputpower model of the wind generator is closely related to siteconditions such as surface roughness and tower height Giventhat the actual wind speed at the hub is different from that atthemonitoring point [16] themeasured wind speed has to beconverted through

V (119896) = Vref[119867

119867ref]

120572

(1)

where Vref and V(119896) are the measured wind speed at themonitoring point and the wind speed at the hub at 119896 119867and 119867ref are the hub height and the monitoring heightrespectively and 120572 (17 to 14) is the descriptive factorof surface roughness which is determined by the surfaceenvironment of the wind generator

The actual output power of the wind generator is closelyrelated to wind speed (Figure 2)The output power character-istics of the wind generator can be expressed as

119875wd (119896) =

0 V (119896)ltVmin or V (119896) gt Vmax

119875rated Vrated le V (119896) le Vmax

119875ratedV(119896)2 minus V2minV2rated minus V2min

Vmin le V (119896) lt Vrated

(2)

where 119875wd(119896) is the output power of the wind generator at 119896119875rated is the rated power of the wind generator and Vmin Vmaxand Vrated are the minimum start-up wind speed cutoff windspeed andminimum rated wind speed of the wind generator

23 Output PowerModel of the PVModule Theoutput powermodel of the PVmodule is determined by solar radiation andenvironmental temperature as follows [6]

119875PV (119905) = 119860PV119866 (119905) 120578PV (119905) 120578inv (3)

where 119860PV (m2) is the area of the PV panel exposed to solarradiation 119866(119905) (Wm2) is the value of solar radiation 120578PV(119905)is the energy conversion efficiency of the PVmodule and 120578inv

is the conversion efficiency of the inverter 120578PV(119905) is influencedby environmental temperature

120578PV (119905) = 120578ref [1 minus 120573 (119879119862 (119905) minus 119879119862ref)] (4)

where 120578ref is the reference energy conversion efficiency ofthe PV module under a standard temperature 120573 is theinfluence coefficient of the temperature for energy conversionefficiency 119879

119862(119905) is the temperature of the PV module at 119905

and 119879119862ref

is the reference standard temperature of the PVmodule The temperature of the PV module changes underthe influence of solar radiation absorption and environmentaltemperature as follows

119879119862(119905) minus 119879ambient =

119879rated800

119866 (119905) (5)

where 119879ambient is the ambient temperature and 119879rated is therated temperature of the PV module

24 Battery Model Given that the battery devices of large-scale wind-PV-battery units can be concentrated in an inde-pendent plant with a constant indoor temperature the chargeand discharge efficiencies of the battery are not affected bytemperatureThe output power model of the battery is [17] asfollows

(1) charge

Soc (119905) = Soc (119905 minus 1) (1 minus 120590) +119875119888(119905) Δ119905120578

119888

119864max (6)

(2) discharge

Soc (119905) = Soc (119905 minus 1) (1 minus 120590) minus119875119889(119905) Δ119905

119864max120578119889 (7)

where Soc(119905) is the battery level after 119905 120590 is the self-dischargeper hour of the battery119875

119888and119875119889are the charge and discharge

powers of the battery in 119905 respectivelyΔ119905 is the length of 119905 120578119888

and 120578119889are the charge and discharge efficiencies of the battery

respectively and119864max is themaximumcapacity of the batteryThe modeling of the life cycle of a battery will affect

the calculation of total system cost Existing literature hasestablished the life cycle expectancy model of batteries basedon battery operations and charge-discharge strategies undera constant temperature [18] The present study adopts themethod of Lopez [11] which estimates cycles to failure ofbatteries by calculating the number of charge and dischargewithin an interval of several discharge depths (Figure 3)

The life cycle of a battery can be calculated according tothe following equation

Lifebat =1

sum119898

119894=1(119873119894CF119894) (8)

where 119898 is the total interval119873119894is the number of charge and

discharge of the battery within interval 119894 and CF119894is the cycles

to failure within interval 119894


10 20 30 40 50 60 70 80 900

10002000300040005000600070008000

Depth of discharge ()

Cycle

s to

failu

re

Figure 3 Battery cycle

The replacement cycle of a battery (119884RES) can be expressedas

119884RES = min Lifebat Lifefloat (9)

where Lifefloat is the float life of a battery that is provided bymanufacturers

3 Optimization Model

31 Coordinated Operating Strategy The wind-PV-batteryunit controls the battery device through the principle of max-imum utilization of renewable energy sources and constantoutput power When the wind-PV output power is smallerthan the dispatching demand (119875ref) the remaining power isreplenished through battery discharge Battery devices stopactive output power until they reach the maximum dischargedepth (Socmin)

Consider

119875119889(119905) = 119875ref minus [119875wd (119905) + 119875PV (119905)]

Soc (119905) gt Socmin(10)

where 119875119889(119905) can be deduced from (7)

When the wind-PV output power is higher than 119875refsurplus energy is stored in the battery Battery devices stopcharging when they are fully charged (Socmax)

Consider

119875119888(119905) = [119875wd (119905) + 119875PV (119905)] minus 119875ref

Soc (119905) lt Socmax(11)


32 Optimization Variables The numbers of wind genera-tors (119873wd) PV modules (119873PV) and battery devices (119873bat)involved in the wind-PV-battery unit are selected as opti-mization variables and recorded as

119883 = [119873wd 119873PV 119873bat]119879

(12)

33 Objective Function The reliable and high-quality elec-tric power supply with renewable energy sources optimalenvironmental protection and maximum economic benefits

are the development goals of new-energy power enterprisesThe goals of the optimal capacity allocation of large-scalewind-PV-battery power-generation unit designed in thispaper include minimum total investment cost maximumutilization rate of renewable energy sources minimum envi-ronmental cost maximum power distribution reliability

From the analysis of these goals we can conclude thatfirstly wind-PV-battery unit does not include the traditionalfossil energy Therefore environmental pollution will notbe taken into consideration Secondly the guarantee of theconstant output power is beneficial to the improvement ofthe grid-connected operation reliability of large-scale newenergy Finally the maximum utilization rate of renewableenergy sources and less installed capacity of battery con-tribute to the reduction of total investment cost In thefollowing analysis the reliability and energy utilization rateare considered as the constraints of the system performanceinstead of the optimal goals In this way it can not onlyshrink the scope of algorithmic search solution space but alsoenable the system performance of each component to reach arelative balance The designed wind-PV-battery unit aims tominimize the NPC as follows [19]

119862NPC =119870

sum119896=1

119862OUT (119896) minus 119862IN (119896)

(1 + 119903)119896

(13)

where 119870 is the service life of the project 119903 is discount rateand 119862OUT(119896) and 119862IN(119896) are the costs and revenues of theunit at 119896th year respectively which are calculated through thefollowing equations

119862OUT = 119862119868 + 119862119874119872 (119896) + 119862119877 (119896)

119862119874119872

(119896) =

3

sum119894=1

119862119874(119909119894 119905119874

119894) +

3

sum119894=1

119862119872(119909119894 119905119872

119894)

119862119877(119896) =

3

sum119894=1

119862119877(119909119894 119896)

119862IN (119896) = 119875119878 int119879

0

119875wpb (119905) 119889119905 + 119862salvage

(14)

where 119862119868is the initial cost 119862

119874and 119862

119872are the operation

and maintenance costs of equipment respectively 119905119874119894and 119905119872119894

are the operation time and maintenance time of equipment 119894respectively 119862

119877(119909119894 119896) is the replacement cost of equipment 119894

at 119896th year119875wpb(119905) is the accessing power of renewable energyat 119905 119875

119878is the corresponding feed-in tariff and 119862salvage is the

remanent value of equipment

34 Performance Constraints

(1) Power Balance Constraint The overall accessing powerof the wind-PV-battery unit should be consistent with theexpected accessing power (119875ref) during dispatching at alltimes that is

119875ref = 119875wd (119905) + 119875PV (119905) + 119875bat (119905) (15)

where 119875wd(119905) 119875PV(119905) and 119875bat(119905) are the output power of thewind generator the PV module and the battery devices at 119905respectively


0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 000 1 0

Wind turbine number PV panel number Battery bank number

Figure 4 Binary coding of optimization variables

(2) Loss of Produced Power Probability Constraint The wind-PV-battery unit should take full advantage of renewableenergy sources to reduce waste of energy and to limit lossof produced power probability (119877LPPP) [20] within a certainrange

119877LPPP =119864LPP119864119899

lt 120576 (16)

where 119864LPP and 119864119899are the loss of produced power and the

total dispatching demand respectively and 120576 is themaximumreference loss of power supply probability of the unit

(3) Wind-PV Complementary Constraint The overall outputpower can be kept stable and the number of charge-dischargeas well as the discharge depth of the battery devices can bereduced by applying wind-PV complementation

Consider

119863wp =1

119875refradic1

119879

119879

sum119905=1

(119875wd PV(119905) minus 119875ref)2lt 120582 (17)

where 119863wp is the wind-PV output powerexpected dispatch-ing output power 119875wd PV is the wind-PV output power at 119905and 120582 is themaximum reference fluctuation ratio of wind-PVcomplementation

4 The Hybrid IterationAdaptiveGenetic Algorithm

41 Basic Idea of the Algorithm The optimal capacity alloca-tion of large-scale wind-PV-battery unit was solved throughiterationadaptive hybrid genetic algorithmThis algorithm isdivided into 2 stages as follows

Stage 1On the basis of the specification parameters of equip-ment meteorological conditions and expected dispatchingoutput power and taking formulas (1)ndash(11) as the constraintsof the equipment and formulas (15)ndash(17) as the constraints ofthe global performance the iteration method was adopted tocalculate the feasible solutions and feasible solution set PSSsatisfying the system performance indexes

Stage 2 On the basis of the elements and economic param-eters in PSS and taking formulas (13)-(14) as objectivefunction adaptive genetic algorithm was utilized to solve theoptimal capacity allocation result from PSS

42 ImprovedAdaptiveGenetic Algorithm Genetic algorithmwas firstly proposed by Professor Holland in University of

Michigan in 1975 [21]This algorithm searches for an optimalsolution by simulating the natural evolutionary processwhichcan offset nondifferentiation and discontinuity of functionsIn consideration of abundant variables a discontinuousvariable domain of definition multiple constraints andother characteristics of the optimal capacity allocationmodelof wind-PV-battery unit genetic algorithm owns obviousadvantage to solve its optimal capacity allocation issueHowever a lot of studies and practices have demonstratedthat the traditional genetic algorithm has poor local searchcapacity premature convergence and other defects To solvethe above problems Srinivas and Patnaik proposed adaptivegenetic algorithm which could dynamically adjust crossoverprobability 119901

119862and mutation probability 119901

119872according to

the changes of fitness [22] This paper adopted hybriditerativegenetic algorithm fromKhatib et al [15] andNeung-matcha et al fuzzy logic controlmethod to dynamically adjust119901119862and 119901

119872and improve from group initialization selection

crossover mutation and other aspects [23] In this way theconvergence rate can be speeded up the search efficiency canbe optimized and further the locally optimal solution can beavoided

(1) Individual CodingBinary codingwas used to express threeoptimization variables the numbers of wind generators PVmodules and batteries The lengths of these three optimiza-tion variables can be determined according to the constraintswhich will be connected together to form an integral 119871wpblong binary coding shown as in Figure 4

(2) Generation of Initial Group Guaranteeing the variety ofinitial group contributes to the search of the whole solutionspace of the algorithm and avoids the premature conver-gence This paper adopted the absolute Hamming distance119867(119909119894 119909119895) between different individuals as the measurement

of group in the individual distribution and the Hammingdistance between all the individuals in the groupwas required119867(119909119894 119909119895) (119894 119895 = 1 2 119871wpb 119894 = 119895) ge 119863 At this time the

group size119873Group with individual length of 119871wpb was noted as2119871wpb minus119863+1 Distance119863was determined by the complexityof the issue and generally it fell approximately between 30 and200

(3) Selection Strategy Selection crossover mutation andother random operations may destroy the optimal individualin the current group which may have adverse effects onthe operating efficiency and convergence This paper utilizedthe elitist retention mechanism to keep the individualswith stronger fitness to the next group At the same time


there was common competition between the parent groupand offspring group and they were ordered from strongerfitness to poor ones The high-quality individuals in theformer proportion of 119875CH can be directly copied to the nextgeneration

(4) Adaptive Crossover and Variation Operator The tradi-tional genetic algorithm sets the constant values of crossoverand mutation probability Thus the values of crossoverand mutation probabilities usually greatly affect the searchefficiency of the algorithm Thus this paper adopted Neung-matcha fuzzy logic control method to dynamically adjustthe genetic operators to enable crossover probability 119901

119862

and mutation probability 119901119872

to adjust with the changesof individual fitness relative to average group fitness Theadjustment method is as follows

Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)

where Δfitavg(119905) is the average fitness of 119905-generation groupΔ119888 and Δ119898 are offset of crossover and variation popSize andoffSize are parent group size and offspring group size 119896 is theparticle ID 120572 and 120573 are the maximum offset range of eachcrossover and variation and 119885(119894 119895) is the fuzzy control rulewhich is determined by Δfitavg(119905) and Δfitavg(119905 minus 1)

43 Steps of the Algorithm

Stage 1

Step 1 Obtain meteorological data specifications of equip-ment and system expected output power data Set the valuerange of optimization variables to reduce the cycle times ofiterative algorithmAmong them the lower limit of wind unitand PV unit is set as 1 while their upper limit is constrainedby the planned site and 119875wd119873wd + 119875PV119873PV gt 119875ref The lowerlimit of the number of batteries is set as 1 and its upper limitis set as 119875ref119875bat

Step 2 Preset 120576 120582 and calculate each capacity combinationto obtain the feasible solutions satisfying the constraintsAlso the system performance indexes of each group aregathered for example service hours of wind generator grossgeneration charge-discharge times of battery and loss ofpower supply probability

Stage 2

Step 1 Obtain feasible solution set corresponding systemperformance indexes and economic parameters Code eachset of feasible solutions according to Figure 4 and set

the minimum group Hamming distance as 119863 Obtain theinitial values of the group size (119873Group) the number ofiterations (Iter) proportion of high-quality individuals (119875CH)crossover probability (119901

119862) and mutation probability (119901

119872)

The initial group (119866) is gained

Step 2 According to formulas (13)-(14) calculate the eco-nomic efficiency of individual capacity allocation plan Inconsideration of the energy waste and wind-PV comple-mentation the individual fitness is calculated according toformula (19)

One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582

2are loss of produced power probability and

penalty coefficient of wind-PV complementationAccording to the selection strategy and crossover and

mutation strategy in Section 42 the group is updated and 119866119894

is got

Step 3 Judgewhether the terminal condition of the algorithmis satisfied If not turn to Step 2 If so select the individual119866Iter with the strongest fitness and output capacity allocationplan1198831015840 = [1198731015840wd 1198731015840PV 1198731015840bat]

119879 and costs of each unit as wellas the overall performance index of the systemTheprocedureof the algorithm was shown in Figure 5

5 Case Study

51 Basic Data A simulation calculation was conducted inZhangbei county Zhangjiakou city Hebei province Zhang-bei is located in 114∘211015840E to 114∘271015840E 40∘591015840N to 41∘071015840Nand meteorological condition data in 2003 were used Theexpected constant dispatching output power was set as 119875ref =100MW and the specification parameters of equipmenteconomic parameters and algorithm parameters were shownas in Tables 1 2 and 3 PV panels of the same type areconnected to the independent inverter chamber to form PVunit Battery energy storage unit is formed by connectingseveral battery cabinets into a battery pack series and thenconnecting other battery pack series in parallel The divisionof PV unit and energy storage unit is good for the operatorsrsquocontrol of the large-scale power generation unit

52 Optimization Results and Analysis

(1) The Optimization Results Analysis A simulation was con-ducted based on the proposed optimal capacity allocationThe final optimization results are shown in Figures 6 to 8

Figure 6 presents the wind-PV output power curve andthe overall output power curve of the wind-PV-battery unitin a year Under a fixed coordinated operation and controlstrategy the wind-PV-battery unit can output constant powerat any time thus ensuring stable grid-connected operationof renewable energy sources Table 4 lists the optimal capac-ity allocation 242MW for the wind generator 81MW forthe PV module and 72MW for the battery thus showing


Table 1 Specification parameters of equipment

Wind generator PV module BatteryParameter Value Parameter Value Parameter ValueSerial no GW2000A Serial no STP300 Model no KYN61Rated power (MW) 20 Peak power (MWp) 05 Rated capacity (MWsdoth) 1Cut-in wind speed (ms) 43 Open-circuit voltage (V) 446 Maximum charge depth () 70Rated wind speed (ms) 108 Short-circuit current (A) 833 Charge efficiency () 90Cut-out wind speed (ms) 256 Size (mm) 1966 times 982 times 50 Nominal voltage (KV) 405Hub height (m) 80 Peak temperature coefficient (∘C) minus047 Maximum power (MW) 1

Start

Obtain specifications of equipment meteorological data and expected dispatching output power

ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y

Obtain FSS SPIS and economic data

Individual coding initialize the population

Calculate the fitness and order from high to low

Select individual for crossovers by a random number

Move Pch percent of individual to next generation

Calculate the rate of crossover and mutation

Crossover and mutation

Individuals in FSSEliminate infeasible individual

Meet the termination conditions

Find the best individual

Cost detail System performance indicators

End

Iterative finished

NN

N

Phase two

Best combination

Set parameters (120576 120582 etc)

Set number of wind turbine 1 step 1 max Nwd max

Join the feasible solution set FSS and save the system performance index to SPIS

Update currentbattery SOC

Set number of battery bank 1 step 1 max PrefPbat

Infeasible solution

Update the numbervalue next iteration

t = 1

Pbat(t) = Pref minus [Pwd(t) +

Pbat(t) ge 0

SOC(t) ge SOCmin SOC(t) le SOCmax

SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582

Adaptive genetic algorithmIterative algorithm

Phase one

NwdNPVNbat

Set parameters (DNgroup Iter

RLPPP le 120576

PCH Pc Pm)

Set number of PV array (Pref minus PwdNwd)PPV step 1 max NPV max

PPV(t)]

Figure 5 The HIAGA procedure


Table 2 Economic parameters

Equipmentno Price (US$) Operating maintenance cost

(US$Y)Downtime maintenance cost

(US$Y)Feed-in tariff(US$KWsdoth)

GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)

Wind and PV powerExpected power

Figure 6 Annual output power curve of the wind-PV-battery unit

Table 3 HIAGA parameters

Index Parameter valueIter 60119873Group (119871wpb) 30sim200119875CH () 5120582 15120576 () 101205821

5 times 108

1205822

2 times 108

a ratio of 061 021 018 Based on these values the windgenerator has a relatively higher installed capacity comparedwith the PV module and the battery The local output powercurve of the wind-PV-battery unit (Figure 7) explores thereason for the higher installed capacity of the wind generatorin Zhangbei county Zhangbei county has rich and evenwind resources throughout the year thus resulting in strongmatching between the output power of the wind generatorand the expected dispatching demand Solar resources haveless dispatching demand because they are only availableduring daytime In particular during the summer rainyseason sunlight time shortens but temperature increases thussignificantly decreasing the energy conversion efficiency ofPV modules and decreasing PV output

According to the comparison of electricity generation(Figure 8) wind is the major source of electricity genera-tion and PV is used nearly equally throughout the yearwhereas battery is mainly used during summer Furtheranalysis (Figures 9-10) demonstrates frequent battery charge-discharge from June to August because weather changes oftenduring the rainy season Consequently the wind-PV outputfluctuates violently thus requiring the battery to charge and

discharge frequently to smooth power fluctuation and toensure the constant output of the wind-PV-battery unit

(2) Contrastive Analysis with Hocaoglu Optimization Algo-rithm [24]Thecapacity allocation results under the conditionof 100MW expected output power of the optimizationalgorithm proposed in this paper andHocaoglu optimizationalgorithm are shown as Table 4 It can be seen from thecomparative results that the installed capacity of wind unitallocated by Hocaoglu optimization algorithm was higherthan those of PV and battery units The reason is that inHocaoglu optimization computation process the model ofbattery life cycle was not established Instead it was simplifiedinto a replacement every 5 years Furthermore this methoddid not consider the influence of wind-PV power outputfluctuation range on the life cycle of battery This kind ofallocation had a lower initial investment cost while the accu-racy degree of the model was poorer As seen from the totalinvestment cost in Table 4 compared with the optimizationalgorithm proposed in this paper Hocaoglu optimizationalgorithm decreased 12 but its total investment cost of theentire project term may not be optimal Table 5 providesthe costs of each unit through simulation calculation onthe basis of 2003ndash2013 meteorological data It can be seenfrom the cost details in Table 5 that the initial investmentand construction year was 2003 Thus the costs of bothalgorithms in 2003 were high and the costs left years wereconstituted of operation costs and replacement costs Every 5years there was one peak in cost for Hocaoglu optimizationalgorithmwhich was related to the 5-year life cycle of batteryThe annual expense of the optimization algorithm proposedin this paper was average and there was no large-scale batteryreplacement During the allocation process thismethod fullyconsidered wind-PV complementation which contributedto decreasing the wind-PV output fluctuation range and


Table 4 The contrast of optimal configuration result

Optimizer Wind turbine PV unit Battery unit TotalNumber Capacity (MW) Number Capacity (MW) Number Capacity (MW) Ratio Cost (US$)

Hocaoglu 129 258 144 72 70 70 065 018 017 351230000Proposed 121 242 162 81 72 72 061 021 018 355670000

Table 5 The comparison of cost detail

Year Hocaoglu ProposedExpense (US$) Income (US$) NPC (US$) Expense (US$) Income (US$) NPC (US$)

2003 360369200 12210800 331579400 364809200 12755100 3352896002004 3846600 11780100 minus7195900 3380800 13483300 minus91632652005 2532500 13283900 minus9287400 2979000 12869600 minus85438002006 2332600 13344700 minus9059600 4021500 12719300 minus71557002007 9687600 12424100 minus2144100 3994000 11925700 minus62146002008 2019500 11699800 minus7223500 2461800 12691600 minus76336002009 3464900 12710000 minus6570300 3459100 13150900 minus68877002010 3450700 13256800 minus6637100 4017300 13090200 minus61408002011 2702300 11858600 minus5902200 2511100 13370200 minus69998002012 9457500 11795300 minus1435200 2998500 11809400 minus54091002013 2031000 11920000 minus5781800 2553500 13101200 minus6167000Total 401894400 136284100 270341800 397185800 140966500 264973700

0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)

Wind powerPV powerExpected power

(a) Output power curve on a certain day in spring

0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)


(b) Output power curve on a certain day in summer

0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)


(c) Output power curve on a certain day in autumn

0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)


(d) Output power curve on a certain day in winter

Figure 7 Output power curve on a certain day in different season


500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth

Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)

Figure 8 Comparison of the monthly electricity generation of wind PV and battery

0 1000 2000 3000 4000 5000 6000 7000 8000minus100minus80minus60minus40minus20

020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)

Figure 9 Output power curve of the battery

0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()

Figure 10 Battery SOC

frequency the charge-discharge times and discharge depthof battery which could extend the life cycle of battery andminimize the total cost in the whole life cycle From theaggregated data in the last line of Table 5 it can be seen thatthe total costs of the optimization algorithm proposed inthis paper were 397185800 (US$) 12 lower than that ofHocaoglu optimization algorithm Its NPC was 264973700(US$) decreasing by 2

Table 6 shows the system performance indexes throughsimulation calculation on the basis of 2003ndash2013 meteoro-logical data It is found that each index of the optimization

algorithm proposed in this paper was superior to that ofHocaoglu optimization algorithm Among them loss ofpower supply probability was 657 decreasing by 214wind-PV complementation was 122 increasing by 116charge-discharge times of battery were 676548 decreasingby 75 levelized cost of energy was 0215 (US$KWsdoth)decreasing by 36

(3) Convergence Analysis of the Algorithm To make an objec-tive and overall evaluation of the optimization algorithmproposed in this paper Hocaoglu optimization algorithm


Table 6 Performance indicators

Indicator Hocaoglu ProposedLoss of produced power probability () 836 657Wind-PV complementation characteristics 138 122Number of battery charge-discharge 730997 676548LCE (US$KWsdoth) 0223 0215

Khatib optimization algorithm [15] and the optimizationalgorithm proposed in this paper respectively carried out30 simulations Through the changes of the parameters ofthe algorithm the group number and CPU computationtime at the beginning of convergence were observed andgathered (shown as in Table 7) It can be seen that HIAGAoptimization algorithm was the fastest and started conver-gence at 22nd-generation group and its average convergencealgebra was 276 respectively 305 and 20 higher thanHocaoglu optimization algorithm and Khatib optimizationalgorithm In terms of CPU computation time the averageconvergence time of HIAGA optimization algorithm was858 s respectively 106 and 64 higher than Hocaogluoptimization algorithm and Khatib optimization algorithmThese indicated that the convergence rate of HIAGA opti-mization algorithm was faster and it owned certain advan-tages compared with the previous research results

53 Sensitivity Analysis

(1) Potential Wind-PV Resources Through simulations inseveral regions in China the optimal capacity allocationand costs of each component of the wind-PV-battery unitwhen 119875ref = 100MW were calculated as shown in Table 8and large-scale wind-PV-battery units in regions with richwind resources have high economic efficiency because wind-dominated units require less capacity for cost-ineffectivebattery (high cost but short life cycle) compared with PV-dominated units Furthermore the even distribution of windpower and appropriate PV output complementation enablethe entirewind-PV-battery unit tomaintain a constant outputwith only a small battery capacity

(2) Government Support China is experiencing an increasingnumber of hazy days because of the continuously worseningenvironment Consequently the country is paying significantattention to the development of green energies Howeverwind-PV-battery power generation is inferior to thermalpower generation because of its lower economic efficiencyAs such the government should formulate reasonable energypolicies to support the development of new energy-basedpower enterprises At present numerous countries world-wide support wind power and PV power generation Chinaalso adopted a fixed electricity price and increased subsidiesto PV power generation in 2008 However no policy aboutthe feed-in tariff of battery power has yet been released Therelationship curve between the feed-in tariff of battery powerand the NPC of the wind-PV-battery unit is presented inFigure 11

0 005 01 015 02 025 03130140150160170180190200210220230240

Battery power feed-in tariff ($)

NPC

(mill

ion

US

dolla

rs)

NPC valueValue fitting curve

Wind power feed-in tariffPV power feed-in-tariff

Figure 11 Impact of the feed-in tariff of battery power

According to Figure 11 the NPC of the wind-PV-batteryunit is more sensitive to the feed-in tariff of battery powerwhen the latter is smaller than the feed-in tariffs of windpower and PV power This finding is attributed to the loweconomic efficiency of battery power Moreover each charge-discharge requires high investment costs thus significantlyaffecting the NPC When the feed-in tariff of battery powerexceeds those of wind power and PV power the optimalcapacity allocation will involve an extremely large proportionof battery energy to absorb all wind-PV electricity thusinfluencing the NPC slightly However this process violatesthe practical significance of the wind-PV-battery unit

6 Conclusion

This study proposes an optimal capacity allocation of a large-scale wind-PV-battery unit in which the wind-PV-batterypower-generation system is connected to the power grid asa power-generating unit with a fixed rated capacity Thisfeature does not only ensure the stable output of the wind-PV-battery unit but is also convenient to the power grid forevaluating the power-generation capacity of the wind-PV-battery unit thus formulating a corresponding dispatchingplan and increasing acceptance of renewable energy sourcesAiming at minimum NPC and considering power distribu-tion reliability energy utilization rate and other indexes theiterationadaptive hybrid genetic algorithm was used to solvethe optimal capacity ratio of each component in the wind-PV-battery unit and a simulation analysis on the wind-PV-battery unit with a construction rated capacity of 100MW inZhangbei county (China) was carried out Then the compar-ative results between Hocaoglu optimization algorithm andHIAGA optimization algorithm indicated that HIAGA opti-mization algorithm could minimize the investment cost ofthe entire life cycle of the power-generation unit project andthe accuracy and validity of the model and algorithm werealso verified Through the multiple simulation calculationsthe optimization algorithm proposed in this paper ownedfaster convergence rate and search efficiency than Hocaogluand Khatib optimization algorithm Finally the sensitivityanalysis of the large-scale wind-PV-battery unit determines


Table 7 The algorithm convergence analysis

Optimizer Convergence at generation k CPU times of convergence(s)Minimum Maximum Average Minimum Maximum Average

Hocaoglu 28 54 397 923 1161 960Khatib 29 39 345 869 1146 917Proposed 22 31 276 821 943 858

Table 8 Comparative analysis of allocations in different regions

Region Annual averagewind speed (ms)

Annual average illuminationintensity (Wm2)

Annual averagetemperature (∘C)

Capacity allocation(119873wd119873PV119873bat)

NPC (US$)

Zhangbei 66 1040 26 12127 times 10572 188274000Chifeng 61 980 19 126295 times 10582 197463000Tangshan 36 1270 58 82594 times 105172 422198000Datong 41 1210 29 95531 times 105156 387579000Baotou 64 1025 22 82295 times 10582 195387000

that wind-solar resources and government energy policieshave a significant effect on the economic efficiency of theunit The wind-PV-battery unit in regions with rich windresources requires less battery capacity compared with thatin regions with rich solar resources thus exhibiting highereconomic efficiency A reasonable feed-in tariff for batterypower imposed by the government can improve the economicbenefits of new energy-based power enterprises The resultsof the sensitivity analysis also confirm the accuracy of theproposed model and algorithm

Conflict of Interests

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

Acknowledgment

The authors would like to acknowledge the support from theState Key Laboratory of Alternate Electrical Power Systemwith Renewable Energy Sources (North China Electric PowerUniversity)

References

[1] S Rehman M Mahbub Alam J P Meyer and L M Al-Hadhrami ldquoFeasibility study of a wind-pv-diesel hybrid powersystem for a villagerdquo Renewable Energy vol 38 no 1 pp 258ndash268 2012

[2] J S Silva A R Cardoso and A Beluco ldquoConsequences ofreducing the cost of PV modules on a PV wind diesel hybridsystem with limited sizing componentsrdquo International Journalof Photoenergy vol 2012 Article ID 384153 7 pages 2012

[3] D Amorndechaphon S Premrudeepreechacharn K Higuchiet al ldquoModified grid-connected CSI for hybrid PVwind powergeneration systemrdquo International Journal of Photoenergy vol2012 Article ID 381016 12 pages 2012

[4] M Engin ldquoSizing and simulation of PV-wind hybrid powersystemrdquo International Journal of Photoenergy vol 2013 ArticleID 217526 10 pages 2013

[5] G Mingjie H Dong G Zonghe et al ldquoPresentation ofnational windphotovaltaicenergy storage and transmissiondemonstration project and analysis of typical operationmodesrdquoAutomation of Electric Power Systems vol 37 no 1 pp 59ndash642013

[6] M Mohammadi S H Hosseinian and G B GharehpetianldquoOptimization of hybrid solar energy sourceswind turbinesystems integrated to utility grids as microgrid (MG) underpoolbilateralhybrid electricity market using PSOrdquo SolarEnergy vol 86 no 1 pp 112ndash125 2012

[7] H Yang ZWei and L Chengzhi ldquoOptimal design and techno-economic analysis of a hybrid solar-wind power generationsystemrdquo Applied Energy vol 86 no 2 pp 163ndash169 2009

[8] 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

[9] HYang L Lu andWZhou ldquoAnovel optimization sizingmodelfor hybrid solar-wind power generation systemrdquo Solar Energyvol 81 no 1 pp 76ndash84 2007

[10] S Diaf G Notton M Belhamel M Haddadi and ALouche ldquoDesign and techno-economical optimization forhybrid PVwind system under various meteorological condi-tionsrdquo Applied Energy vol 85 no 10 pp 968ndash987 2008

[11] H A Kazem and T Khatib ldquoA novel numerical algorithm foroptimal sizing of a photovoltaicwinddiesel generatorbatterymicrogrid using loss of load probability indexrdquo InternationalJournal of Photoenergy vol 2013 Article ID 718596 8 pages2013

[12] J Li WWei and J Xiang ldquoA simple sizing algorithm for stand-alone PVwindbattery hybrid microgridsrdquo Energies vol 5 no12 pp 5307ndash5323 2012

[13] R Dufo-Lopez J L Bernal-Agustın J M Yusta-Loyo et alldquoMulti-objective optimization minimizing cost and life cycleemissions of stand-alone PV-wind-diesel systems with batteriesstoragerdquo Applied Energy vol 88 no 11 pp 4033ndash4041 2011

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

[15] T Khatib A Mohamed and K Sopian ldquoOptimization of aPVwind micro-grid for rural housing electrification using a


hybrid iterativegenetic algorithm case study of Kuala Tereng-ganu Malaysiardquo Energy and Buildings vol 47 pp 321ndash331 2012

[16] F O Hocaoglu O N Gerek and M Kurban ldquoThe effect ofmodel generated solar radiation data usage in hybrid (wind-PV)sizing studiesrdquo Energy Conversion andManagement vol 50 no12 pp 2956ndash2963 2009

[17] B Li H Shen Y Tang andHWang ldquoImpacts of energy storagecapacity configuration of HPWS to active power characteristicsand its relevant indicesrdquo Power System Technology vol 35 no4 pp 123ndash128 2011

[18] H Wenzl I Baring-Gould R Kaiser et al ldquoLife predictionof batteries for selecting the technically most suitable and costeffective batteryrdquo Journal of Power Sources vol 144 no 2 pp373ndash384 2005

[19] L Mengxuan W Chengshan G Li et al ldquoAn optimal designmethod of multi-objective based islandmicrogridrdquoAutomationof Electric Power Systems vol 36 no 17 pp 34ndash39 2012

[20] G Xydis ldquoOn the exergetic capacity factor of a wind-solarpower generation systemrdquo Journal of Cleaner Production vol47 pp 437ndash445 2012

[21] J H Holland Adaptation in Natural and Artificial Systems AnIntroductory Analysis with Applications to Biology Control andArtificial Intelligence The University of Michigan Press 1975

[22] M Srinivas and L M Patnaik ldquoAdaptive probabilities ofcrossover and mutation in genetic algorithmsrdquo IEEE Transac-tions on Systems Man and Cybernetics vol 24 no 4 pp 656ndash667 1994

[23] W Neungmatcha K Sethanan M Gen et al ldquoAdaptive geneticalgorithm for solving sugarcane loading stations with multi-facility services problemrdquo Computers and Electronics in Agricul-ture vol 98 pp 85ndash99 2013

[24] F O Hocaoglu O N Gerek and M Kurban ldquoA novel hybrid(wind-photovoltaic) system sizing procedurerdquo Solar Energy vol83 no 11 pp 2019ndash2028 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


Meteorologicalobservatory

InternetPower grid dispatching automation system

Power grid

Physical connection lineSignals of control and measuring

Weather forecast

Combined powergeneration monitoring

system

Intelligentsubstation

PV array

Battery bank

Wind turbines

Figure 1 Basic structure of wind-PV-battery units

a simple sizing algorithm to calculate the capacity allocationof an independent wind-PV-battery unit and determinedthat the state of charge (SOC) of a battery should beperiodically invariant They confirmed the reliability andeconomic efficiency of the algorithm through a case studyin Zhoushan Island China [12] To minimize the LCE andCO2emissionswithin equivalent life cycles Dufo-Lopez et al

adopted a multiobjective evolutionary algorithm to calculatethe optimal capacity ratio of a wind-PV-diesel-battery power-generation system [13 14] To minimize system cost andloss of power supply probability Khatiba et al calculatedthe optimal capacity ratio of a wind-PV-battery unit in amicrogrid environment by using a genetic algorithm (GA)Moreover they further optimized the hub height of a windturbine and the optimal tilt angle of the PV array [15]

Previous studies on the capacity allocation of wind-PV-battery units have mainly focused on allocating appropriatewind-PV capacity ratios to achieve a wind-PV output powerthat is as close as possible to the load curve as well as to reducecharge-discharge times and the discharge depth of the batteryThe capacity allocation and characteristics of the overalloutput power are closely related to the load variation trendthus significantly restricting its application in large-scalewind-PV-battery units During the grid-connected operationof a large-scale wind-PV-battery unit the power grid has

to consider the unit as a power plant with a particularrated capacity to perform corresponding dispatcher tasks Inthe present study an optimal capacity allocation of wind-PV-battery units based on a rate capacity was proposed tominimize the net present cost (NPC) The optimal capacityof each wind-PV-battery unit under a rated capacity wascalculated by using a HIAGA

2 Operating Model of theWind-PV-Battery Units

21 System Structure The wind-PV-battery units mainlyconsist of a combined power-generation monitoring systema wind generator a PV array and a battery-energy storagedevice The basic structure is shown in Figure 1

The wind generator and the PV array are primarilyresponsible for generating power from renewable energysources such as wind and solar energy whereas the batteryis responsible for maintaining a stable overall power outputof the wind-PV-battery units through peak clipping andvalley filling The combined power-generation monitoringsystem provides a reasonable arrangement of the power-generation devices according to dispatching commands andweather forecasts (eg wind speed illumination intensity


0 5 10 15 20 25 300

05

1

15

2

25

3

Wind speed (ms)

Out

put p

ower

(MW

)




V (119896) = Vref[119867

119867ref]

120572

(1)



119875wd (119896) =





(2)



119875PV (119905) = 119860PV119866 (119905) 120578PV (119905) 120578inv (3)






and 119879119862ref


119879119862(119905) minus 119879ambient =

119879rated800

119866 (119905) (5)



(1) charge


119888

119864max (6)

(2) discharge


119864max120578119889 (7)








Lifebat =1

sum119898

119894=1(119873119894CF119894) (8)





10 20 30 40 50 60 70 80 900

10002000300040005000600070008000


Cycle

s to

failu

re







Consider

119875119889(119905) = 119875ref minus [119875wd (119905) + 119875PV (119905)]




Consider

119875119888(119905) = [119875wd (119905) + 119875PV (119905)] minus 119875ref




119883 = [119873wd 119873PV 119873bat]119879

(12)




119862NPC =119870

sum119896=1

119862OUT (119896) minus 119862IN (119896)

(1 + 119903)119896

(13)


119862OUT = 119862119868 + 119862119874119872 (119896) + 119862119877 (119896)

119862119874119872

(119896) =

3

sum119894=1

119862119874(119909119894 119905119874

119894) +

3

sum119894=1

119862119872(119909119894 119905119872

119894)

119862119877(119896) =

3

sum119894=1

119862119877(119909119894 119896)

119862IN (119896) = 119875119878 int119879

0

119875wpb (119905) 119889119905 + 119862salvage

(14)


119874and 119862










119875ref = 119875wd (119905) + 119875PV (119905) + 119875bat (119905) (15)



0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 000 1 0




119877LPPP =119864LPP119864119899

lt 120576 (16)




Consider

119863wp =1

119875refradic1

119879

119879

sum119905=1

(119875wd PV(119905) minus 119875ref)2lt 120582 (17)









119872according to












119862



Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)



Stage 1



Stage 2




119872)



One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582




is got



5 Case Study








Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 5 10 15 20 25 300

05

1

15

2

25

3

Wind speed (ms)

Out

put p

ower

(MW

)




V (119896) = Vref[119867

119867ref]

120572

(1)



119875wd (119896) =





(2)



119875PV (119905) = 119860PV119866 (119905) 120578PV (119905) 120578inv (3)






and 119879119862ref


119879119862(119905) minus 119879ambient =

119879rated800

119866 (119905) (5)



(1) charge


119888

119864max (6)

(2) discharge


119864max120578119889 (7)








Lifebat =1

sum119898

119894=1(119873119894CF119894) (8)





10 20 30 40 50 60 70 80 900

10002000300040005000600070008000


Cycle

s to

failu

re







Consider

119875119889(119905) = 119875ref minus [119875wd (119905) + 119875PV (119905)]




Consider

119875119888(119905) = [119875wd (119905) + 119875PV (119905)] minus 119875ref




119883 = [119873wd 119873PV 119873bat]119879

(12)




119862NPC =119870

sum119896=1

119862OUT (119896) minus 119862IN (119896)

(1 + 119903)119896

(13)


119862OUT = 119862119868 + 119862119874119872 (119896) + 119862119877 (119896)

119862119874119872

(119896) =

3

sum119894=1

119862119874(119909119894 119905119874

119894) +

3

sum119894=1

119862119872(119909119894 119905119872

119894)

119862119877(119896) =

3

sum119894=1

119862119877(119909119894 119896)

119862IN (119896) = 119875119878 int119879

0

119875wpb (119905) 119889119905 + 119862salvage

(14)


119874and 119862










119875ref = 119875wd (119905) + 119875PV (119905) + 119875bat (119905) (15)



0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 000 1 0




119877LPPP =119864LPP119864119899

lt 120576 (16)




Consider

119863wp =1

119875refradic1

119879

119879

sum119905=1

(119875wd PV(119905) minus 119875ref)2lt 120582 (17)









119872according to












119862



Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)



Stage 1



Stage 2




119872)



One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582




is got



5 Case Study








Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


10 20 30 40 50 60 70 80 900

10002000300040005000600070008000


Cycle

s to

failu

re







Consider

119875119889(119905) = 119875ref minus [119875wd (119905) + 119875PV (119905)]




Consider

119875119888(119905) = [119875wd (119905) + 119875PV (119905)] minus 119875ref




119883 = [119873wd 119873PV 119873bat]119879

(12)




119862NPC =119870

sum119896=1

119862OUT (119896) minus 119862IN (119896)

(1 + 119903)119896

(13)


119862OUT = 119862119868 + 119862119874119872 (119896) + 119862119877 (119896)

119862119874119872

(119896) =

3

sum119894=1

119862119874(119909119894 119905119874

119894) +

3

sum119894=1

119862119872(119909119894 119905119872

119894)

119862119877(119896) =

3

sum119894=1

119862119877(119909119894 119896)

119862IN (119896) = 119875119878 int119879

0

119875wpb (119905) 119889119905 + 119862salvage

(14)


119874and 119862










119875ref = 119875wd (119905) + 119875PV (119905) + 119875bat (119905) (15)



0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 000 1 0




119877LPPP =119864LPP119864119899

lt 120576 (16)




Consider

119863wp =1

119875refradic1

119879

119879

sum119905=1

(119875wd PV(119905) minus 119875ref)2lt 120582 (17)









119872according to












119862



Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)



Stage 1



Stage 2




119872)



One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582




is got



5 Case Study








Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 000 1 0




119877LPPP =119864LPP119864119899

lt 120576 (16)




Consider

119863wp =1

119875refradic1

119879

119879

sum119905=1

(119875wd PV(119905) minus 119875ref)2lt 120582 (17)









119872according to












119862



Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)



Stage 1



Stage 2




119872)



One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582




is got



5 Case Study








Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




119862



Δfitavg (119905) =1

popSize

popSize

sum119896=1

fit119896(119905) minus

1

offSize

offSizesum119896=1

fit119896(119905)

Δ119888 (119905) = 120572 times 119885 (119894 119895) Δ119898 (119905) = 120573 times 119885 (119894 119895)

119901119862(119905) = Δ119888 (119905) + 119901

119862(119905 minus 1)

119901119872(119905) = Δ119898 (119905) + 119901

119872(119905 minus 1)

(18)



Stage 1



Stage 2




119872)



One has

Fit (119909) = 1

119862NPC (119909) + 1205821119877LPSP + 1205822119863wp + 1 (19)

where 1205821and 120582




is got



5 Case Study








Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




Start


ChargeDischarge

Y

Y

Y

Y

Y

N

YN

Y

Y

N

N

N

N

Y












End

Iterative finished

NN

N

Phase two

Best combination






Infeasible solution


t = 1


Pbat(t) ge 0


SOC(t) = SOCmax

t le 8760 t = t + 1

Dwp le 120582


Phase one

NwdNPVNbat


RLPPP le 120576

PCH Pc Pm)


PPV(t)]







GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






GW2000A 1370000 6000 4000 014STP300 750000 37 12 019KYN61 950000 8000 1600 011

0 1000 2000 3000 4000 5000 6000 7000 80000

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





5 times 108

1205822

2 times 108












0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of








0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)



0 5 10 15 200

50100150200250300350

Time (h)

Out

put p

ower

(MW

)





500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


500

400

300

200

100

0

432

183

129

389

169

114

488

148

108

452

152

116

472

151121

439

139142

438

141

165

421

189

134

405

162153

440

178

126

450

173

97

475

181

88


Elec

tric

ity g

ener

atio

n

WindPVBattery

(MWmiddoth)



020406080

100

Time (h)

Out

put o

f bat

tery

(MW

)


0 1000 2000 3000 4000 5000 6000 7000 80000

102030405060708090

100

Time (h)

Batte

ry S

OC

()













0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of








0 005 01 015 02 025 03130140150160170180190200210220230240


NPC

(mill

ion

US

dolla

rs)





6 Conclusion











NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










NPC (US$)





Acknowledgment


References




































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





















Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Optimal Capacity Allocation of Large