Research Article Operation of a Wind Turbine-Flywheel ...

Research ArticleOperation of a Wind Turbine-Flywheel Energy Storage Systemunder Conditions of Stochastic Change of Wind Energy

Andrzej Tomczewski

Institute of Electrical Engineering and Industrial Electronics Poznan University of Technology Piotrowo 3A 60-965 Poznan Poland

Correspondence should be addressed to Andrzej Tomczewski andrzejtomczewskiputpoznanpl

Received 6 June 2014 Accepted 22 July 2014 Published 18 August 2014

Academic Editor Linni Jian

Copyright copy 2014 Andrzej TomczewskiThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The paper presents the issues of a wind turbine-flywheel energy storage system (WT-FESS) operation under real conditionsStochastic changes of wind energy in time cause significant fluctuations of the system output power and as a result have a negativeimpact on the quality of the generated electrical energy In the authorrsquos opinion it is possible to reduce the aforementioned effects byusing an energy storage of an appropriate type and capacity It was assumed that based on the technical parameters of awind turbine-energy storage system and its geographical location one can determine the boundary capacity of the storage which helps preventpower cuts to the grid at the assumed probability Flywheel energy storage was selected due to its characteristics and technicalparameters The storage capacity was determined based on an empirical relationship using the results of the proposed statisticaland energetic analysis of the measured wind velocity courses A detailed algorithm of the WT-FESS with the power grid systemwas developed eliminating short-term breaks in the turbine operation and periods when the wind turbine power was below theassumed level

1 Introduction

Environmental issues included in long term power strategiesof different countries and high accessibility of the renewablesources of energy and their significant potential are the mainreasons for an increase in the share of renewable sources ofenergy in the global generation of electrical energy Whenit comes to the widely available solar and wind energy oneshould however pay attention to great fluctuations of theconverters output power related to a stochastic nature ofthe irradiation changes 119864

119909and wind velocity V

119908in time

The instability has a negative impact on the cooperationof wind and solar sources with the power grid system [1ndash3] The issue is important for systems with a high percentshare of renewable sources of energy particularly in thosewithout output power stabilisation [2 4] The operation ofunsustainable sources of energy can cause problems relatedto stabilisation of a section of a power grid system and gen-erate additional costs related to maintaining the periodicallyactivated conventional sources in a standby mode [5 6]

Energy storage in industrial applications is a current issueand the research in the area led to some practical applications

of batteries artificial and natural compressed air energystorage (CAES) supercapacitors superconducting magneticenergy storage (SMES) flywheel energy storage and so forth[4 7ndash13] Despite technical sophistication and high coststheir application area in high power systems is graduallyextending There are a growing number of technical devicesincluding energy storage and further recovery as a part ofnormal operation for example emergency supply systemspumped storage power plants and hybrid and electrical carsDue to growing significance of such kind of solutions used ineconomics of highly developed countries the problem shouldbe considered with regard to widely understood optimizationand economic aspects [11 14]

An important issue of the practical application of windsources is to mitigate the effects of output power fluctuationsresulting from the stochastic nature of the wind energychanges in time when working with a power grid system[15] Long-lasting (eg for several hours) breaks in powergeneration inwind sources related to the decrease in the windkinetic energy can be determined with the use of computer-assisted systems of the output power prediction [16ndash18] Thesituation differs when the breaks are short (up to several

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 643769 16 pageshttpdxdoiorg1011552014643769

2 The Scientific World Journal

0

2

4

6

8

10

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

Win

d ve

loci

ty (m

s)

Time (h)

Vcut-in

Figure 1 Circadianwind velocity changes recorded on 1March 2008in Strzyzow (South Eastern Poland) at the height of ℎ

119901= 10mabove

the ground level

minutes) and impossible to predict due to their generationmechanism Moreover the frequency and duration of shortbreaks depend on the parameters of the implemented windturbinemdashmainly on its cut-in velocity Vcut-in

Figures 1 and 2 present two circadian curves of windvelocity changes obtained by measurements The measure-ments were made on 1 and 5 March 2008 in a meteorologicalstation in Strzyzow (South Eastern Poland) at the height ofℎ119901= 10m above the ground levelThe obtained values were recalculated for the height of

ℎWT = 60m above the land level corresponding to theposition of the wind wheel hub used for further analyses ofEnercon E53 turbine according to the following relationship

V119908WT = V

119908(ℎWTℎ119901

)

120572

(1)

where 120572 is the aerodynamic coefficient of terrain roughnessℎ119901 ℎWT are the heights of the wind velocity and wind wheel

hub measurement quoted in reference to the land level V119908is

the wind velocity at the measurement height ℎ119901 V119908WT is the

recalculated wind velocityThe model of wind velocity vertical profiles expressed in

the formula (1) is simplified but sufficient for the purpose ofthe study

The above-mentioned type of wind turbine with nominalpower of 119875WTN = 800 kW was used in all calculations andsimulations done for the purpose of the studyThe horizontalline marked in Figures 1 and 2 stands for the cut-in velocitywhich for the reference type of turbine is Vcut-in = 2ms Theanalysis of the curve presented in Figure 1 indicates an almost5-hour break (long-lasting break) in power generation andmany short turbine cut-outs from the power grid system Forthe course presented in Figure 2 the average wind velocitiesare higher which allows for the uninterrupted operationof the generator 247 In practice the nature of the windvelocity changing in time tends to include the features of bothcourses and the mean energy additionally depends on the

0

5

10

15

20

25

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

Win

d ve

loci

ty (m

s)

Time (h)

Vcut-in

Figure 2 Circadian wind velocity changes recorded on 5 March2008 in Strzyzow (South Eastern Poland) at the height of ℎ

119901= 10m

above the ground level

deterministic components circadian and annual changes andlong term trends

At the current technological level of energy storageproduction solving the problems related to the first type ofbreaks seems hard and economically not justified Never-theless short breaks in the operation of wind sources canbe effectively compensated with energy from appropriatelyselected energy storage resulting in a partial stabilisation ofthe output parameters of a wind power plant connected tothe grid and also contribute to improving the quality of thegenerated electrical energy [15 20 21]

2 Cooperation of Energy Storage withWind Turbine

21 Introduction With regard to the breaks in the windturbine operation caused by the stochastic nature of the windvelocity (energy) changes in time it is necessary to find someengineering solutions preventing the related power cuts tothe grid Considering significant technical difficulty relatedto eliminating long-lasting power cuts the methods allowingfor preventing power cuts with maximum duration119879MAX canbe considered sufficient but the parameter value is usuallydetermined for a range up to several minutes

One of the practically feasiblemethods is maintaining thepower supplied to the electrical energy system at the assumedlevel with the value of119875

3MIN in the reference periods In orderto maintain high quality of energy and stable operation ofthe system in the connection spot the change in the powerlevel supplied to the system from the value related to thewind turbine power curve to the value of 119875

3MIN should beas smooth as possible It is also recommended to implementmeasures aimed at partial stabilisation of the system outputpower at the level of 119875

3MIN in periods with reduced windenergy Such situations occur when the wind velocity valueis V10158401198753MIN

gt V119908

ge Vcut-in where V10158401198753MIN

is the velocitycorresponding to the power 119875

3MIN + 119875PW (119875PW is the house

The Scientific World Journal 3

load power of the analysed system) A complete stabilisationof the output power of the WT-ESS for all periods of theturbine operation at a reduced power requires using complexengineering systems and is economically not justified (veryhigh investment expenditure)

The paper assumes that the implementation of the pre-sented measure requires the use of energy storage withappropriate parameters and of appropriate type The basicaim is to compensate the reduced power supplied by thewind turbine generator in the assumed periods with durationup to 119879MAX The solution is of particular importance forgeographical areas with the values of the average windvelocity not much higher than the cut-in velocity Vcut-in ofthe applied type of turbine Appropriately selected turbineand energy storage leads to a creation of wind turbine-energystorage (WT-ESS) of a new quality connected to the powergrid whose features on the one hand result from its being arenewable source of energy but on the other hand are similarto the characteristics of conventional sources [20 22 23]

22 Characteristics of Energy Storage Systems Selecting theEnergy Storage Type Advantages and Disadvantages of KineticStorage Accumulation of energy is a topical and econom-ically expensive problem of high technological complexity[11 12] The studies carried out in this field result amongothers from aspiration to improve energetic safety andfrom the need of long-term accumulation of very largeamount of energy The difficulties in accumulation of electricenergy cause the indirect methods are most commonlyused Consequently it reduces the efficiency of the processAmong the systems that make most often use of the above-mentioned method there are accumulator batteries (lead-acid and lithium-ion batteries) kinetic storage (flywheels)supercapacitors superconducting magnetic energy storage(SMES) and compressed air energy storage (CAES) [4 11 1224]

In case of the storage designed for operation in renewableenergy systems the requirements related to their energeticcapacity rated power charging rate and durability andthe range of operating temperature results from specificconditions of wind turbine and photovoltaic panel operationcaused directly by weather conditions The changes in tem-perature humidity pressure and so forth not only directlyaffect the equipment but also contribute to stochastic changesof input values delivered by the aforesaid types of the sources

It was assumed for purposes of the research that func-tionality of the energy storage in electric power grids isdescribedwith the use of a set of parameters including powerand energy densities (WL and WhL resp)mdashdeterminingpossible recovery of usable current (power) and energeticcapacity durability (the number of charging-dischargingcycles) depth of discharge the range of operating tempera-ture discharge rate and transition rate between the operatingstates efficiency unit cost of the equipment converted topower or unit energy (costkW costkWh) and physicaldimension of the system Table 1 presents a comparison of themost important usable parameters of the above mentionedenergy storage types [10 12]

In order to carry into effect the algorithm proposed in thepaper and aimed at partial stabilization of the power deliveredto the system from a wind source a storage is necessarywhich renders possible a so-called short-term accumulationof energy It is designed for equalizing the output power ofthe system in time intervals below 1 h (usually 025 h) Suchsystems are required to deliver the energy to the electricpower grid immediately after activation of the storage (withvery short delay) and to maintain it at the rated power levelin the assumed time [10] Taking into account a single windturbine an energy storage cooperating with it should havethe average energetic capacity (usually from tens to hundredskWh) high charging rate (comparable to discharging ratemdashin the range ofminutes) rated power in the range from tens tohundreds kW very short time of transition between chargingand discharging stages (below 1 s) and the range of operatingtemperature corresponding to yearly temperature variationscharacteristic for the definite geographic location Moreoverthe storage should be composed of modules allowing forsimple development of the system [25]

The SMES storage must be excluded from cooperationwith wind turbines due to their low energy density (05WhLdivide 10WhL) Usable current value of a single module reacheseven several kA (the superconducting technology and signif-icant reduction of active power loss) nevertheless the timeof cooperation with the system is too short as compared tothe one required according to the assumption Similarly theCAES storage is excluded too due to the need of buildinglarge systems (pressure vessels) or using a precisely imposedlocation of the system (natural reservoirs eg old mineexcavations etc) and relatively poor efficiency of the systemSuch a type of the storage is characterized by too longdeployment time (from several to 10 minutes) as comparedto real dynamics of wind energy variations On the otherhand high power density is an advantage of this storage typeNevertheless in case of the time of energy recovery belowone hour this advantage is not decisive for the choice of thestorage type [10] From the group of considered solutions ofthe problem the supercapacitors must be removed too Thisis caused by very low energy density (2WhL divide 10WhL)which precludes gaining proper capacity andmaintaining theoutput power at required level within the time from ten totwenty minutes

Hence the most important types of energy storagefeasible for practical application of the proposed method ofequalizing the output power of a wind turbine with stochasticcharacter of the input function are secondary electrochemicalcellsmdashaccumulators and flywheels [10 12]

Among the advantages of the flywheels as compared toelectrochemical cells (lead-acid and lithium-ion batteries)there are constant value of energetic capacity in the wholerange of operational temperature (minus35∘C to +40∘C) coveringyearly variations of weather conditions very high numberof charging and discharging cycles reaching millions (life-time 15ndash20 years) and short duration of storage charging(approximating the discharging time with rated power) [1012 16] Two first features allow to locate the storage indirect proximity of the turbine and to operate it without anyrestrictions within the turbine lifetime (15ndash20 years) High


Table1Specificatio

nof

them

ostimpo

rtantu

sablep

aram

eterso

fselectedtypeso

fthe

energy

storage

[1012]

Energy

storage

type

Roun

d-trip

efficiency

[]

Energy

density

[Whl]

Power

density

[kW

l]Cy

clelifecalend

arlife

Depth

ofdischarge[]

Self-discharge

[]

Deploym

ent

time

Charging

time

Operatin

gtemperature

[∘

C]Flyw

heel

80ndash9

520ndash200

upto

10Manymillions15

yearsndash20

years

752ndash5h

10ms

Minutes

minus35

divide+4

0Supercapacito

r90ndash9

42ndash10

upto

15Upto

onem

illion15

years

75Ve

ryslo

wlt10ms

Second

sminus40

divide+6

5Lithium-io

nbatte

ry83ndash86

200ndash

350

01ndash35

5ndash20years(accordingto

temperature)

100

5mon

thly

3msndash5m

sHou

rsminus20

divide+5

0

Lead-acid

batte

ry75ndash80

50ndash100

001ndash0

5500ndash

2000

cycle

s5ndash15

years(according

totemperature)

7001ndash04daily

3msndash5m

sManyho

urs

0divide40

CAES

60ndash70

3ndash6

na

Unlim

ited25

years

35ndash50

05ndash1d

aily

3minndash10m

inHou

rsminus30

divide60

SMES

80ndash9

005ndash10

1ndash4

Unlim

ited20

years

100

10ndash15daily

1msndash10ms

Second

s-minutes

na


PT(t)

WT120596

P1(t)

CS

FESS

PW

(plusmn)P2(t)

P3(t)

P4(t)

Power system

PW(t) W(t)

PWTN

PPW

AES (t)

PESN AES MAX

AES

Figure 3 Construction diagram principles of operation and power flow in the WT-FESS (WTmdashwind turbine FESSmdashflywheel energystorage CSmdashcontrol system 119875

119879(119905)mdashmechanical power 119875WTNmdashwind turbine nominal power and 119875PWmdashthe system house load power)

charging rate [16] enables to use the wind energy even in caseof quick variations without the need of using faster energystorage devices as energetic buffers Additionally the kineticstorage is characterized by high efficiency (from 80 to 95)remarkably higher as compared to lead-acid batteries (75ndash80) For the recent solutions their efficiency is higher eventhan the one of lithium-ion batteries (83ndash86) It shouldbe noticed that the system occupies relatively small spacemdashagroup of modules may be often closed in a container readyfor transportation to another location [10 12]

One of the features of the kinetic storage that might beconsidered as a fault as compared to accumulator batteryis lower energy density (in case of lead-acid battery from50WhL to 100WhL while for the lithium-ion onemdashfrom200WhL to 350WhL) Another fault of them is due tohigh degree of self-discharge (several percent per hour)Nevertheless the above-mentioned features are not decisivefor cooperation between the wind turbine-energy storagesystem and the electric power grid since the storage is notrequired to be characterized by very large energetic capacityand the storage charging and discharging processes lastbelow 1 hourmdashusually no more than twenty minutes Theinvestment cost of flywheels converted to unit power or unitenergetic capacity is several times higher than that of thelead-acid or lithium-ion batteries Hence economical aspectsof the use of such systems must be considered as their faultworsens appraisal of the technology of kinetic storage [10 12]

Obtaining high energy values requires a high flywheelvelocity which entails the use ofmodern compositematerialsTheir density is several times lower than the density of steeland the boundary strength 120590max related to the presence ofhigh radiation forces is much higher which results in obtain-ing the value of characteristic energy several times higher(Wkg) Detailed information on this matter is presented inthe paper [26] Low idle changes and a relatively high totalsystem performance (usually of ca 86) are mainly achievedby using magnetic bearings and the rotor operation in avacuum with the pressure values of about 10minus3 bar [7]

Based on the comparison of technical parameters of theabove-mentioned types of energy storage and consideringthe economic aspects (periodical replacement of batteries) aflywheel type of energy storage was assumed for cooperationwith the wind turbine [9]

23 Algorithm of a Flywheel Energy Storage Cooperationwith a Wind Turbine (Farm) According to the establishedassumptions a wind turbine with the nominal power 119875WTNand specific power curve 119875

1= 119891(V

119908) working with flywheel

energy storage form a complex power system (WT-FESS)Its basic goal is to deliver a relevant level of active power tothe power grid system also in the periods when the windvelocity V

119908is below Vcut-in The basic diagram of a flywheel-

electrical system is presented in Figure 3 The kinetic energyof wind is transformed in the turbine wheel into the shaft (orgear) and generator rotary motion According to the turbinepower curve active power 119875

1(119905) is obtained at the system

outletThe storage operateswith the active output power1198752(119905)

variable in time the power can be positive (energy releasedto the power gridmdashunloading) negative (energy taken fromthe generatormdashloading) or zero energy (idle state of completeunloading of the storage) Hence the storage energy 119860ES(119905)also varies in time and its value ranges from zero to thenominal capacity 119860ES119873 The current energy value tends to beexpressed in the percentage of nominal value with the use offactor 119860ES(119905)

Active power 1198753(119905) which is an algebraic sum of momen-

tary powers 1198751(119905) and 119875

2(119905) with deducted house load power

119875PW is released to the system Due to an automatic changein the WT-FESS configuration its value also varies in time119875PW = 119891(119905) According to the assumptions given inSection 21 while releasing energy from the storage to thegrid the minimum output power value 119875

3MIN is obtainedHowever it covers periods of time with a specific duration(maximum duration 119879MAX) and depends on meeting severalconditions given further on in the algorithm

The system presented in Figure 3 depending on themomentary value of the wind velocity V

119908(119905) and the energy


storage loading119860ES(119905) can be in one of the four characteristicstates

(i) autonomic operation of the turbine generator(V119908(119905) gt V1015840

1198753MINand 119860ES(119905) ge 119860ESMIN) or

(V10158401198753MIN

gt V119908(119905) ge Vcut-in and 119860ES(119905) = 0)

1198753(119905) = 119875

1(119905) minus 119875PW (119905) (2a)

where 119860ESMIN is the minimum level of the storageenergy not resulting in its supplementary loadingunder favourable wind conditions

(ii) generator operation with supplementary loading ofthe energy storage (V

119908(119905) gt V1015840

1198753MIN 119860ES(119905) lt

119860ESMIN)

1198753(119905) = 119875

1(119905) minus 119875

2(119905) minus 119875PW (119905) (2b)

(iii) simultaneous operation of the generator and energystorage (V1015840

1198753MINgt V119908(119905) ge Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

1(119905) + 119875

2(119905) minus 119875PW (119905) (2c)

(iv) autonomic operation of the energy storage (V119908(119905) lt

Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

2(119905) minus 119875PW (119905) (2d)

The transition between the above-mentioned states is acontinuous and dynamic process depending on the stochas-tically changing atmospheric conditions and the current andprevious system arrangement A single continuous operatingperiod of energy collecting from flywheel energy storage islimited with the 119879MAX algorithm parameter

3 Selecting the Energy Storage Volume forWorking with a Wind Turbine

31 Statistical Energy Analysis of the Course of Wind VelocityChanges V

119908= 119891(119905) Based on theoretical analysis and the

conducted tests it was determined that the measurementcourses of the wind velocity changes V

119908= 119891(119905) can be

used for identifying the minimum capacity of the flywheelenergy storage 119860ESMIN that will meet the assumptions ofthe algorithm of WT-FESS cooperation with the power gridsystem according to Section 23 It was established thatthe knowledge of the output parameters of the WT-FESS(time 119879MAX power 119875

3MIN) and technical parameters of theturbine (nominal power 119875WTN cut-in velocity Vcut-in powercurve 119875

1= 119891(V

119908)) and of the energy storage (idle losses

Δ119860ES119895 performance at loading 120578119865+

and unloading 120578119865minus

nominal power 119875ES119873 continuous maximum power 119875ESMAX)are additionally required

Assuming the above-mentioned principle of the WT-FESS operation on a sample course of the wind velocitychanges (Figure 4) horizontal lines identifying the parame-ters characteristic of the systemaremarked the turbine cut-invelocity Vcut-in velocity V1198753MIN

of obtaining the power 1198753MIN +

0

5

10

15

20

25

30

0 5 10 15 20 25 30

Win

d ve

loci

ty (m

s)

Time (s)

Vcut-in

Vcut-out

Area 1

Area 2

Area 3

Area 4

VP3MIN

Figure 4 Course of wind velocity changes V119908= 119891(119905) with marked

areas used for determining the value of statistical and energeticparameters of WT-FESS

119875PW and the turbine cut-out velocity Vcut-out were markedThis way the course V

119908= 119891(119905) is divided into four areas

where a set of statistical and energy parameters characterisingthe WT-FESS in the specific geographical location can bedetermined

In the area 1 the wind velocity meets the requirementV119908(119905) lt Vcut-in and the generator power is 119875

1= 0 In practice

such periods can last from several seconds to many days Inorder to identify the required capacity of a flywheel energystorage 119860ESMIN information about subsequent breaks of thespecific type and their average duration is necessary Theparameters proposed and used in further analysis for the areainclude the average 119879

1AVG and maximum 1198791MAX duration of

power generation breaks (stochastic wind velocity changes)not exceeding the set value of the factor 119879MAX 1198961 seriescoefficient determining the average number of subsequentbreaks separatedwith one turbine operation interval at powerguaranteeing the energy storage loading (119875

1gt 1198753MIN + 119875PW)

and the summary turbine operation time in the area 1198791WT for

the assumed period of analysis 119879119886

Area 2 covers the wind velocity range meeting therequirement Vcut-in lt V

119908le V10158401198753MIN

Information concerning theaverage m 119879

2AVG and maximum 1198792MAX duration of intervals

not exceeding the set value of 119879MAX the average generatorpower 119875

1AVG2 and the total turbine operating time in the area1198792WT for the assumed period of analysis 119879

119886is determined in

the areaThe system operation in area 3 (wind velocity V

119908ge V10158401198753MIN

)allows for controlled loading of the storage according to itscurrent energy status 119860ES(119905) The average generator power1198751AVG3 and the total turbine operating time in the area 119879

3WTfor the assumed period of analysis 119879

119886is determined for the

areaArea 4 covers the turbine cut-out periods due to excess

wind velocity V119908

ge Vcut-out which can additionally causemechanical damage Moreover the following values of elec-trical energy generated by the reference type of turbine aredetermined for the total period 119879

119886and areas 2 and 3 119860WT

1198602WT and 119860

3WT respectively


According to the description above sets of measurementpoints whose values constitute the averagewind velocity fromthe period Δ119905

119898and the duration of 48 seconds are analysed

Hence 1800 measurement points are recorded within 24hours and their number amounts to 657 thousand withinone year For high power wind turbines (hundreds kW andmore) themoments of inertia of rotating elements are so highthat the quotedmeasurement period is sufficient for the goalspresented in the paper All measurements used in the paperwere made with a rotating anemometer placed at 10m abovethe land level

From the point of view of the analysed subject matter it isimportant to compare the values and relationships betweenthe suggested statistical energy parameters for two character-istic periods of a calendar year autumn-winter and spring-summer For many geographical locations including theSouth Eastern Europe the autumn-winter period has greaterwind energy that the spring-summer one and the differencescan be of several dozen percent Another important elementcovers determining the impact of the change in theWT-FESSinput and output parameters in particular in the parameterof time119879MAX and power1198753MIN on the proposed statistical andenergetic factors at the established course of wind velocitychanges and the type of the employed wind turbine

Tables 2(a) 2(b) 3(a) and 3(b) present a comparison ofthe results of a statistical-energetic analysis of the course ofwind velocity changes V

119908= 119891(119905) recorded for three periods in

2010 period I (autumn-winter 1 January 2010ndash31March 2010)period II (spring-summer 1 June 2010ndash31 August 2010) andperiod III (1 January 2010ndash31 December 2010) at the assumedtime 119879MAX = 600 seconds and two powers at the WT-FESSoutlet 119875

3MIN = 200 kW (Tables 2(a) and 2(b)) and 1198753MIN =

300 kW (Tables 3(a) and 3(b) in periods with reduced windenergy (V

119908(119905) lt Vcut-in and V1015840

1198753MINgt V119908(119905) ge Vcut-in) The

analysis was made for Enercon E53 turbine with nominalpower 800 kW at recalculating the wind velocity value to therotor hub centre (ℎ

119908= 60m) according to the relationship

(1)

32 Identifying the Boundary Capacity 119860ESMIN of a Fly-wheel Energy Storage The WT-FESS operation according tothe assumptions of the algorithm presented in Section 23requires using a flywheel energy storage with appropriatecapacityThe authorrsquos research on the analysis of themeasure-ment courses of the wind velocity changes V

119908= 119891(119905) for a

period of several years for one geographical location lead todetermining an empirical relationship identifying the value oftheminimumstorage capacity119860ESMIN that guarantees correctoperation of the analysed system The relationship includestechnical parameters of the storage and wind turbine andstatistical energy parameters of the measurement courses ofthe wind velocity changes defined in Section 31

The presented relationship consists of segments corre-sponding to the turbine operation areas separated in Figure 3A corrective segment related to the storage additional loadingconditions and its ability to use the excess energy generatedby the turbine (119875

1gt 1198753MIN) was also taken into account

Considering these elements in determining the minimum

capacity 119860ESMIN of a storage intended for working with aselected type of wind power plant in a specific geographicallocation the following relationship was proposed

119860ESMIN =1198961

120578ESminussdot 119879119892

1AVG sdot 1198753MIN

+1198961

120578ESminussdot 1198962sdot 119879119892

2AVG sdot (1198753MIN minus 119875

119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG

minus 1198963sdot 1198964sdot 120578ES+119879

119889

3AVG sdot (1198751AVG3 minus 119875

3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889

3AVG is the upper (119892 index) and lower(119889 index) confidence limit for the subsequent mean timevalues 119879

1AVG 1198792AVG and 119879

3AVG (Tables 2(a) 2(b) 3(a)and 3(b)) 119896ES119895 is the idle losses of the flywheel storageexpressed in percent of its nominal power 119875ES119873 119879

119892

119895AVG isthe upper confidence limit of the storage operation on idlegear (the value stands for the mean time between subsequentperiods of the storage energy use in areas 1 and 2 whoseduration does not exceed the maximum natural unloadingtime storage119879ESR119895) 120578ME+ 120578MEminusare the flywheel energy storageperformance in the loading and unloading process 119896

2is the

correction factor (1198962

= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889

2AVG) 1198963 is the coefficient of the storageadditional loading conditions

1198963=

119875WTN minus 1198754MIN


(4)

identifying the turbine powermargin that can be used duringthe storage additional loading where 119875

1MIN stands for theminimum turbine power value corresponding with the windvelocity Vcut-in 1198964 is the ability to use excess power

1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875

3MINfor 1198753AVG minus 119875

3MIN gt 119875ES119873(5)

The other factors and parameters used in the relationship (3)are described in the previous section of the paper

The first three components of the relationship (3) helpdetermine partial capacities related to stabilisation of a powerplant output power for areas 1 and 2 at the establishedmaximum continuous duration of the turbine operation withreduced power (119875

1lt 1198753MIN) and idle loses of the flywheel

energy storage Δ119875ES119895 (1198752 = 0 119860ES(119905) gt 0) The last element isof corrective nature and in special cases reduces the value ofthe identified capacity Additionally it happens that the realcapacity of the storage 119860ESMIN must not be lower than the119860ESMIN determined from the relationship (3) and in practicedepends on the nominal data of the modules availablefor the selected storage type and the possibility of theircombining


Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53

turbineℎ119908=60m1198753MIN

=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocitychangesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)

Maximum duration of power cuts (min)

P3MIN = 100 kWP3MIN = 200 kWP3MIN = 300kW

Figure 5 Family of characteristics 119860ESMIN = 119891(119879MAX) for EnerconE53 turbine height ℎ

119908= 60m for the period between 1 Jan 2010

and 31 Mar 2010

33 Changes in the Capacity 119860ESMIN in the Function of WT-FESS Parameters A computational application was devel-oped with the use of the analysis algorithm of the mea-surement courses of wind velocity changes V

119908= 119891(119905) pro-

posed in Section 31 and empirical relation (3) in the NETenvironment (language C) With regard to a large numberof measurement points covering the period of one yearand the related long times of statistical analysis the TaskParallel Library was used for parallel execution on multicoresystem which allowed to significantly reduce the total time ofcalculations

With the use of the developed application families ofcharacteristics 119860ESMIN = 119891(119879MAX) and 119896

1= 119891(119879MAX) were

determined for the established set of power values 1198753MIN

and particular geographical location Based on them it ispossible to evaluate the behaviour of the WT-FESS whenwind turbines with identical nominal power are used todifferentiate the mounting height of the wind wheel and toanalyse the system for different periods of the same year andto compare several years The above-mentioned families ofcharacteristics were determined separately for two periodsof the same year autumn-winter and spring-summer Theconducted calculations used the values of standard deviationsand confidence ranges assuming the confidence factor of095 which were determined for statistical and power param-eters presented in Tables 2(a) 2(b) 3(a) and 3(b)

Figures 5 6 7 and 8 present the discussed families ofcharacteristics determined for two periods from 1 January2010 to 31March 2010 and from 1 June 2010 to 31 August 2010assuming the mounting height of Enercon E53 wind turbineconverter of ℎ

119908= 60m and ℎ

119908= 73m and three power

values of the WT-FESS 1198753MIN = 100 kW 200 kW and 300 kW

Additionally the investigation covered the impact of thechange in the wind converter mounting height on the above-mentioned characteristics Two mounting heights of the E53

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)




119908= 60m for the period between 1 June 2010

and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m

Figure 7 Family of characteristics 119860ESMIN = 119891(119879MAX) for EnerconE53 turbine and the system power of 119875

3MIN 100 kW for the periodbetween 1 Jan 2010 and 31 Mar 2010

turbine converter quoted in the catalogue were employedwhile implementing the task (ℎ

119908= 60m and ℎ

119908= 73m)

alongside with a method of calculating the wind velocityagainst themeasurement height according to the relationship(1) Figures 9 and 10 present the results of calculating thechanges in 119860ESMIN capacity and 119896

1multiplication factor for

the system power 1198753MIN = 100 kW for the period between 1

January 2010 and 31 March 2010Extending the maximum acceptable time 119879MAX of the

turbine operation with a limited or zero power (1198751

lt

1198753MIN) results in an increase in the flywheel energy storage

119860ESMIN allowing for the WT-FESS operation according to


0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)

Figure 8 Family of characteristics 1198961= 119891(119879MAX) for Enercon E53

turbine height ℎ119908= 60m for the period between 1 Jan 2010 and 31

Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)


turbine height ℎ119908= 60m for the period between 1 June 2010 and

31 Aug 2010

the proposed algorithmmdashSection 23 The change is non-linear and reveals the greatest dynamics at lower time values119879MAX It mainly results from the nature of the changes in themultiplication factor 119896

1(Figures 7 and 8) The differences in

the characteristics curves 1198961= 119891(119879MAX) between the spring-

summer and autumn-winter period result from differentaverage wind velocity and the dynamics of the wind velocitychanges in time Analysing the obtained characteristics onecan note their similarities within the dynamics of the119860ESMINstorage capacity changes for both analysed periods Thedetermined capacity 119860ESMIN for the spring-summer periodis higher than for the autumn-winter period which ismainly caused by higher average values of the wind velocity

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)

Figure 10 Family of characteristics 1198961

= 119891(119879MAX) for EnerconE53 turbine and the system power of 119875

3MIN 100 kW for the periodbetween 1 June 2010 and 31 Aug 2010

(kinetic energy) in the winter period Lower values of themultiplication factor for the winter period can be attributedto higher dynamics of the wind velocity change V

119908in time

and the change in the speed of switching between the turbineoperating areas marked in Figure 3

4 Simulation of WT-FESSOperation under Conditions ofStochastic Wind Energy Change

41 Simulator Model Verification of the proposed algorithmof wind turbine cooperation with a flywheel energy storage(WT-FESS) required developing an analytical and numericalmodel and implementing a simulator of the analysed systemoperation With regard to the necessary application of pro-prietary computational methods covering statistical analysisof the wind change velocity measurement data identifyingthe minimum capacity of a flywheel energy storage andanalysing the changes in the storage energy in time it isreasonable to develop our own simulation application Theset goals include

(i) verifying the effectiveness of the proposed methodof determining the minimum capacity of a flywheelenergy storage 119860ESMIN intended for working with awind turbine at the established geographical location

(ii) carrying out tests of the system behaviour undersimulation and real conditions of the wind energychanges in time

(iii) analysing the results of WT-FESS operation as com-pared to the independent operation of the windturbine under constant wind conditions

It was assumed that the correctness of determining the min-imum capacity of a flywheel energy storage 119860ESMIN intendedfor working with a wind turbine is established based on the


value of a percentage factor of eliminating the acceptable cut-outs 119896

119871 It is the relationship between the summary workingtime of a generator with power below 119875

3MIN in unit periodsand duration not exceeding 119879MAX compensated with theflywheel storage energy and the summary time of all periodsof the generator operating at a power not exceeding119875

3MIN andduration not exceeding 119879MAX (including not compensatedperiods) in the assumed period of analysis 119879

119886 expressed in

percentA set of 119873 wind velocity values discrete in time is the

simulator input obtained by measurements According toSection 31 of the paper each measurement point makes theaverage wind velocity for the period Δ119905

11989848 seconds long

In the numerical algorithm of the simulator regardless ofthe energy storage operation state one should consider idlelosses related to mechanical resistance in the system feedingof magnetic bearings and maintaining the specific vacuumlevel in the rotating mass housing If the energy storage isin an idle state they are taken into account as 119896ES119895 factorAt loading and unloading the idle losses are included in theprocess efficiency whereby the efficiency was assumed asidentical in both cases and its value is 120578ES

The momentary power of a wind turbine generator 1198751(119905)

is determined with the use of the energy curve stored in adiscrete form in the database The values of the generatorpower are determined for each of the established points 119873separating the time periods Δ119905

119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)

periodwind velocities amounting to V

119908119904(119894)and V

119908119890(119894)respectively

and the generator power 1198751119904(119894)

and 1198751119890(119894)

related to them aredetermined The average turbine power in the range Δ119905

1015840

119898(119894)

and value 1198751AVG(119894) is used for the calculations made in the

WT-FESS operation simulator The changes in the energystorage power 119875

2(119905) are established based on the relationships

from (2a) to (2d) whereas the output power 1198753(119905) of the

system is identified based on the determined values of 1198751(119905)

and 1198752(119905) and the house load power 119875PW(119905)

The energy state of the storage in discrete moments oftime 119905

119896for 119896 = 0 1 2 119873 is determined based on the initial

storage loading condition (for 119896 = 0 119860ES119873 ge 119860ES0 ge 0)previous changes in the storage119875

2(119905) and turbine119875

1(119905) power

its efficiency and coefficient of idle lossesThe value of energyfor discrete time 119905

119896(119905119896= 119896 sdot Δ119905

119898) is determined by adding

(considering the sign) the energy gains in all time ranges Δ119905119898

preceding the 119905119896point The storage energy in the moment of

time 119905119896can thus be expressed as

119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)

sdot 120578ES sdot 1198752(119894) sdot Δ119905119898)

minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)

where 119894 is the time step index 119896 is the final time step indexused according to the relationship 119905

119896= 119896 sdot Δ119905

119898 to determine

the time 119905119896 119875ES119873 is the nominal power of energy storage

1198752(119894)

is the established value of the energy storage loadingor unloading power as the average value for the initial andfinal point of the time range Δ119905

119898 119887119894 119888119894 119889119894isin 0 1 are the

coefficients from sets 119887 119888 and 119889 respectively identifying thestorage state for the time periods (loading unloading idle)

For numerical implementation of proposed model NETplatform MS Visual C language and ADONET technologyfor handling the relational database of the wind turbinesparameters were used Elements of object-oriented softwarewere applied for building the programme structures Alibrary of classes intended for representing the structure andoperating principle of the followingWT-FESS elements windturbine flywheel energy storage control system method ofselecting 119860ESMIN storage capacity and identifying the storageenergy state at any moment of time 119905

119896were developed In

relation to a very time-consuming nature of the calculationscovering a statistical energy analysis of the discrete courseof wind velocity changes in time elements of calculationparalleling were used That is why Task class was used todivide the calculations onto logical cores of the processorintended for PCs and workstations

42 Results of Simulation Analyses Simulation tests of aWT-FESSworkingwith the power grid systemwere carried out fortwo types of inputs test input VWT = 119891(119905) and real input V

119908=

119891(119905) Two configurations of the systemwith different nominalpower 119875ES119873 limit capacities 119860ESMIN and initial loading states119860ES0 of the storage (option I and IImdashTable 4) were usedfor the tests The real input case is covered by parameterspresented in Table 4 as option III ENERCON E 53 turbinewith the power of119875WTN = 810 kWand established generationcharacteristics was used in all tests

The first part of the tests was done for the input VWT =

119891(119905) whose curve is presented in Figure 11(a) The analysiscovers changes in the wind velocity during 70 minutesincluding fluctuations from the cut-in velocity Vcut-in to thevelocity V

119873when the turbine reached the nominal power

119875WTNThe velocity changes VWT in time were selected so thatin the assumed period of analysis 119879

119886the system WT-FESS

reached all working states defined in the defined algorithm(Section 23) and shifted between them at diversified dynam-ics

The other part of the tests covered a simulation of theinvestigated system operation for a real input in a form ofthe curve of wind velocity changes from the one indicatedin the geographical location reference for the period between3 March and 6 March 2008 The nominal (limit) capacity119860ESMIN of the storage used for the tests was determined for anidentical location but usingmeasurement data for the spring-summer period in 2010

According to the assumptions presented in Section 23the numerical simulatormodel covers four operating states ofthe systemdepending on thewind energy systemparametersand current and previous values of the energy storage Theresults of the performed simulations were presented in aform of power curves of the generator 119875

1(119905) storage 119875

2(119905)

(considering the sign) and the output power of the system


Table 4 List of technical parameters of WT-FESS used in simulation tests

Option 119875ESN [kW] 119860ES0 [] 119860ESMIN [kWh] 119879MAX [s] 1198753MIN [kW] 119896119895 [] 119875PW []

I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200

P1P1P2-option IP2-option II

Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)

Figure 11 Courses of changes in WT-FESS parameters obtained in the developed simulator for the test input VWT = 119891(119905) and options I andII of calculations (Table 4) (a) wind velocity VWT (b) power 1198751 and 119875

2 (c) power 119875

3 (d) storage loading state 119860ES

1198753(119905) and a relative percent storage loading 119860ES(119905) for the

assumed period of analysis 119879119886

Figure 11 shows the results of WT-FESS operation sim-ulation conducted for the test input and two parameteroptions of the tested system (Table 4) With regard to theshort period under analysis and the related high readabilityin Figures 11(b)ndash11(d) the curves for the aforementionedparameters are presented simultaneously for two simulationoptions (Table 4)

As a result of the wind velocity drop below Vcut-in inthe period between 37 and 57 minutes if the turbine worksindependently it is disconnected from the power grid system(Figure 11(a)mdashcircled with an intermittent line) Howeverconsidering the turbine cooperation with the storage thebreak was eliminated thanks to the previously stored energy(Figures 11(b) and 11(c)) For option II considering theassumption of zero storage energy at the beginning of theanalysis period (119860ES0 = 0) the stored energy was notsufficient to eliminate the entire break which resulted in theturbine cut-out after 20minutes A similar situation occurred

in the first period of the system operation (to ca minute4) The enumerated periods are circled with an intermittentline in Figures 11(c) and 11(d) It is the evidence of toolow capacity of the applied energy storage resulting fromextremely difficult storage operating conditions not includedin the confidence ranges of statistical energy parameters usedin the relationship (3)

Figure 12 shows the curves of some selected simulatorparameters forWT-FESS operation at real input (option IIImdashTable 4)

The analysis of the systemoperation for a real input covers50 hours from the period between 3March 2008 and 6March2008 with diversified wind conditions (Figure 12(a)) Next tohigh wind energy periods (eg between the system operationhour 5 and 20) there are periods with boundary energy valuesfrom the point of view of the assumed WT-FESS operationparameters (eg between hour 20 and 30) This type ofperiods accumulates breaks in the turbine operation whichare short according to the definition presented in Section 1of the paper and should be additionally compensated with


0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)

Figure 12 Courses of changes in WT-FESS parameters obtained in the developed simulator for the test input VWT = 119891(119905) for the periodbetween 3 Marchndash6 March 2008 (calculation option III) (a) wind velocity V

119908 (b) power 119875

1(c) power 119875

2 and 119875

3(d) storage loading state

119860ES

energy stored in the storage Furthermore a period oflong-lasting decrease in the wind velocity below the cut-invelocity (between system operation hour 31 and 34) can beadditionally seen in Figure 12 whose impact on the systemoperation will not be analysed in detail

From the point of view of the developed algorithmthe most important periods are the ones with boundary(limit) values of the wind velocity (energy)The implementedalgorithm of WT-FESS cooperation with the power gridsystem assumes stabilisation of the output power 119875

3of the

system at the assumed level 1198753MIN besides eliminating short

breaks It applies to periods where the wind velocity allowsfor reaching the turbine power 119875

3MIN gt 1198751

gt 0 (area 2in Figure 4) and the assumed duration up to 119879MAX In theanalysed period 119879

119886the greatest number of wind velocity

changes corresponding to the transition between areas 1 and2 (Figure 4) occurs between hour 15 and 25 of the systemoperation This period is circled with an intermittent line inFigures 12(c)ndash12(e) Unloading of the storage energy is usedfor eliminating breaks in the turbine operation (119875

1= 0)

and equalising the system output power 1198753with the value

of 1198753MIN (Table 4 option III) assumed in the algorithm

It is also loaded between the storage unloading periods(positive power 119875

2) when the power values 119875

2are negative

(Figure 12(c))

5 Comments and Conclusions

Operation of wind sources in geographical locations withmoderate wind conditions may generate a number of prob-lems related to their cooperation with the power grid sys-tem The basic reason for such occurrence is stochasticallychanging kinetic energy of thewind and construction charac-teristics of the turbines One of the solutions to mitigate theeffect of frequent cut-outs of such sources from the grid isusing energy storage Implementing the proposed algorithmof the wind turbine can control the system operationmdashflywheel energy storage system cooperation with the gridthat allows for eliminating a large number of short breaksusing the previously stored energy The author proposedan algorithm using the features of flywheel energy storagemainly the short period of their loading and shifting betweenthe loading and unloading state as well as low dependenceof the real capacity on temperature Equalising the activepower released to the power grid system at the assumedlevel 119875

3MIN is done for the breaks in the turbine operationand periods when the turbine reaches the power 119875

1lt

1198753MIN at maximum duration 119879MAX The results obtained by

simulation (Figures 11 and 12) are the evidence of goodefficiency of the developed algorithm and improving theconditions of the wind turbine cooperation with the power


grid system The number of the turbine cut-outs from thegrid at appropriately selected flywheel energy storage capacitydecreases significantly which results in an improved qualityof electrical energy and the source stability

Correct operation of the above-mentioned systemrequires determining the minimum (boundary) capacity119860ESMIN of the applied energy storage The process can beconducted in different ways but the author of the papersuggests a proprietary concept based on statistical energyanalysis of the measurement time series of changes inthe wind velocity in the analysed geographical locationfor a period of at least one year (Tables 2(a) 2(b) 3(a)and 3(b)) The minimum capacity of the storage 119860ESMINrequired for the assumed algorithm at maintaining thespecified parameters of cooperation with the power gridsystem is established based on the empirical relationship (3)connecting the energy storage and wind turbine parametersand states as well as the results of statistical energy analysisof the measurement curves V

119908(119905) Seasonality of the average

wind energy demonstrated based on the tests (Tables 2(a)2(b) 3(a) and 3(b)) indicated the need to consider thisfact in determining the limit storage capacity 119860ESMIN Thesimulation results confirm that if this fact is accountedfor while establishing the value of 119860ESMIN the real percentindex of eliminating the acceptable breaks (duration up to119879MAX) is between 75 and 85 Not meeting this conditionresults in a significant decrease in the process of eliminatingshort breaks in the wind turbine operation defined in thepaper

In the authorrsquos opinion the statistical energy parametersproposed and determined for the measurement curves canbe compared and taken into account while designing WT-FESS systems in various geographical locations Based onthe values of the parameters presented in Tables 2(a) 2(b)3(a) and 3(b) one can drawmore detailed conclusions on thenature of wind conditions in the examined location (energydynamics of changes etc) similarly to the wind conditionsclass according to IEC 61400-1 As a result of implementingheuristic methods it is additionally possible to select theoptimum components of the WT-FESS (turbine type towerheight type and size of storage) as regards the unit cost ofelectrical energy generation

It was established based on the conducted statisticalenergy analyses of the curves V

119908= 119891(119905) (Tables 2(a) 2(b)

3(a) and 3(b)) and the tests according to the implementedmethod of determining the capacity119860ESMIN that for a specificgeographical location conclusions concerning mutual rela-tions between the parameters characterising the WT-FESSand cooperationwith the power grid can be formulated Withthis in mind a series of calculations was made whose resultsare presented as curves 119860ESMIN = 119891(119879MAX) at 1198753MIN = const(Figures 4 and 5) and 119860ESMIN = 119891(119879MAX) at ℎ119908 = const(Figure 6) The coefficient of series 119896

1has a major impact on

the capacity value 119860ESMIN and the shape of the enumeratedcharacteristics Considering the dependence of the coefficient1198961on the turbine construction wind conditions and the

assumed value 1198753MIN calculations were made and character-

istics determined for 1198961= 119891(119879MAX) at 1198753MIN = const (Figures

8 and 9) and 1198961= 119891(119879MAX) at ℎ119908 = const (Figure 10)

The families of the aforementioned curves are typicalof a particular geographical location the parameters of thesystem elements (119875WTN 119875ESN ℎTW) and its cooperation withthe power grid (119879MAX 1198753MIN) They can be used for anapproximate determination of the minimum (limit) capacityof the storage 119860ESMIN when different values of the windwheel mounting height power change 119875

3MIN and time of theeliminated breaks 119879MAX are used

The choice of energy accumulation system in the formof flywheels is an effective solution that enables to fulfillthe assumptions formulated for the algorithm of WT-FESSsystem cooperation with the electric power grid Exchange ofthe storage for accumulator batteries would worsen the sys-tem properties because of long charging time (the lead-acidbatteries) capacity variations (particularly in winter) andshorter lifetime (in higher temperature) On the other handthe use of supercapacitors would result in significant growthof the cost since they should be distinguished by high electriccapacity Hence it appears that despite the disadvantagesmentioned in Section 22 the kinetic energy storage complieswith the largest number of required qualities Moreoverdevelopment of the technology allows forecasting reductionof the kinetic storage prices in the future and their morecommon use particularly in the field of renewable powerengineering

The results presented in the paper are a basis for furtherresearch particularly in two basic spheres The first of themconsists in analysis of operation simulation of aWT-FESS sys-tem within one year with consideration of repeated changesin wind power The other includes optimization of the WT-FESS system aimed at definition of such structure of thesystem for which the unit cost of electric power productionis possibly the lowest for the considered geographic location

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] K Skowronek and G Trzmiel ldquoThe method for identificationof fotocell in real timerdquo Przegląd Elektrotechniczny vol 83 no11 pp 108ndash110 2007

[2] H Lee B Y Shin S Han S Jung B Park and G JangldquoCompensation for the power fluctuation of the large scalewind farm using hybrid energy storage applicationsrdquo IEEETransactions on Applied Superconductivity vol 22 no 3 2012

[3] M Delfanti D Falabretti M Merlo and G MonfredinildquoDistributed generation integration in the electric grid energystorage system for frequency controlrdquo Journal of Applied Math-ematics vol 2014 Article ID 198427 13 pages 2014

[4] Z Zhou M Benbouzid J Frederic Charpentier F Scuiller andT Tang ldquoA review of energy storage technologies for marinecurrent energy systemsrdquo Renewable and Sustainable EnergyReviews vol 18 pp 390ndash400 2013

[5] A Tomczewski ldquoSelecting thewind turbine for a particular geo-graphic location using statisticalmethodsrdquo Poznan University of


Technology Academic Journals Electrical Engineering no 67-68pp 81ndash93 2011

[6] MR PatelWind and Solar Power SystemsDesign Analysis andOperation Taylor amp Fracis Boca Raton Fla USA 2006

[7] F NWerfel U Floegel-Delor T Riedel et al ldquo250 kW flywheelwith HTS magnetic bearing for industrial userdquo Journal ofPhysics Conference Series vol 97 2008

[8] K Bednarek and L Kasprzyk ldquoFunctional analyses and appli-cation and discussion regarding energy storages in electricsystemsrdquo in Computer Applications in Electrical EngineeringR Nawrowski Ed pp 228ndash243 Publishing House of PoznanUniversity of Technology Poznan Poland 2012

[9] F Dıaz-Gonzalez A Sumper O Gomis-Bellmunt and RVillafafila-Robles ldquoA review of energy storage technologies forwind power applicationsrdquo Renewable and Sustainable EnergyReviews vol 16 no 4 pp 2154ndash2171 2012

[10] G Fuchs B Lunz M Leuthold and D U Sauer TechnologyOverview on Electricity Storage Overview on the Potential andon the Deployment Perspectives of Electricity Storage Technolo-gies Institut fur Stromrichtertechnik und Elektrische AntribeAachen Germany 2012

[11] S Sundararagavan and E Baker ldquoEvaluating energy storagetechnologies for wind power integrationrdquo Solar Energy vol 86no 9 pp 2707ndash2717 2012


[13] R Sebastian and R Pena Alzola ldquoFlywheel energy storagesystems review and simulation for an isolated wind powersystemrdquo Renewable and Sustainable Energy Reviews vol 16 no9 pp 6803ndash6813 2012

[14] L Kasprzyk A Tomczewski and K Bednarek ldquoEfficiencyand economic aspects in electromagnetic and optimizationcalculations of electrical systemsrdquo Electrical Review vol 86 no12 pp 57ndash60 2010

[15] F Islam H Hasanien A Al-Durra and S M Muyeen ldquoA newcontrol strategy for smoothing of wind farm output using short-term ahead wind speed prediction and Flywheel energy storagesystemrdquo in Proceedings of the American Control Conference(ACC rsquo12) pp 3026ndash3031 Montreal Canada June 2012

[16] P Pinson Estimation of the uncertainty in wind power forecast-ing [PhD thesis] Ecole des Mines de Paris Paris France 2006

[17] T Uchida T Maruyama and Y Ohya ldquoNew evaluationtechnique for WTG design wind speed using a CFD-model-based unsteady flow simulation with wind direction changesrdquoModelling and Simulation in Engineering vol 2011 Article ID941870 6 pages 2011

[18] N Chen Z Qian I T Nabney and X Meng ldquoWind powerforecasts using Gaussian processes and numerical weatherpredictionrdquo IEEE Transaction on Power Systems vol 29 no 2pp 656ndash665 2014

[19] ldquoENERCONProduct overviewrdquo httpwwwenercondeen-en88htm

[20] P Khayyer and U Ozguner ldquoDecentralized control of large-scale storage-based renewable energy systemsrdquo IEEE Transac-tion on Smart Grid vol 5 no 3 pp 1300ndash1307 2014

[21] M Khalid and A V Savkin ldquoMinimization and control ofbattery energy storage for wind power smoothing aggregateddistributed and semi-distributed storagerdquo Renewable Energyvol 64 pp 105ndash112 2014

[22] F Diaz-Gonzalez F D Bianchi A Sumper and O Gomis-Bellmunt ldquoControl of a flywheel energy storage system forpower smoothing in wind power plantsrdquo IEEE Transaction onEnergy Conversion vol 29 no 1 pp 204ndash214 2014

[23] G O Suvire and P E Mercado ldquoCombined control of adistribution static synchronous compensatorflywheel energystorage system for wind energy applicationsrdquo IET GenerationTransmission and Distribution vol 6 no 6 pp 483ndash492 2012

[24] G N Prodromidis and F A Coutelieris ldquoSimulations of eco-nomical and technical feasibility of battery and flywheel hybridenergy storage systems in autonomous projectsrdquo RenewableEnergy vol 39 no 1 pp 149ndash153 2012

[25] Power Beacon Product Overview httpbeaconpowercom[26] J L Perez-Aparicio and L Ripoll ldquoExact integrated and com-

plete solutions for composite flywheelsrdquo Composite Structuresvol 93 no 5 pp 1404ndash1415 2011

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


0

2

4

6

8

10

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

Win

d ve

loci

ty (m

s)

Time (h)

Vcut-in

Figure 1 Circadianwind velocity changes recorded on 1March 2008in Strzyzow (South Eastern Poland) at the height of ℎ

119901= 10mabove

the ground level

minutes) and impossible to predict due to their generationmechanism Moreover the frequency and duration of shortbreaks depend on the parameters of the implemented windturbinemdashmainly on its cut-in velocity Vcut-in

Figures 1 and 2 present two circadian curves of windvelocity changes obtained by measurements The measure-ments were made on 1 and 5 March 2008 in a meteorologicalstation in Strzyzow (South Eastern Poland) at the height ofℎ119901= 10m above the ground levelThe obtained values were recalculated for the height of

ℎWT = 60m above the land level corresponding to theposition of the wind wheel hub used for further analyses ofEnercon E53 turbine according to the following relationship

V119908WT = V

119908(ℎWTℎ119901

)

120572

(1)

where 120572 is the aerodynamic coefficient of terrain roughnessℎ119901 ℎWT are the heights of the wind velocity and wind wheel

hub measurement quoted in reference to the land level V119908is

the wind velocity at the measurement height ℎ119901 V119908WT is the

recalculated wind velocityThe model of wind velocity vertical profiles expressed in

the formula (1) is simplified but sufficient for the purpose ofthe study

The above-mentioned type of wind turbine with nominalpower of 119875WTN = 800 kW was used in all calculations andsimulations done for the purpose of the studyThe horizontalline marked in Figures 1 and 2 stands for the cut-in velocitywhich for the reference type of turbine is Vcut-in = 2ms Theanalysis of the curve presented in Figure 1 indicates an almost5-hour break (long-lasting break) in power generation andmany short turbine cut-outs from the power grid system Forthe course presented in Figure 2 the average wind velocitiesare higher which allows for the uninterrupted operationof the generator 247 In practice the nature of the windvelocity changing in time tends to include the features of bothcourses and the mean energy additionally depends on the

0

5

10

15

20

25

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

Win

d ve

loci

ty (m

s)

Time (h)

Vcut-in

Figure 2 Circadian wind velocity changes recorded on 5 March2008 in Strzyzow (South Eastern Poland) at the height of ℎ

119901= 10m

above the ground level

deterministic components circadian and annual changes andlong term trends

At the current technological level of energy storageproduction solving the problems related to the first type ofbreaks seems hard and economically not justified Never-theless short breaks in the operation of wind sources canbe effectively compensated with energy from appropriatelyselected energy storage resulting in a partial stabilisation ofthe output parameters of a wind power plant connected tothe grid and also contribute to improving the quality of thegenerated electrical energy [15 20 21]

2 Cooperation of Energy Storage withWind Turbine

21 Introduction With regard to the breaks in the windturbine operation caused by the stochastic nature of the windvelocity (energy) changes in time it is necessary to find someengineering solutions preventing the related power cuts tothe grid Considering significant technical difficulty relatedto eliminating long-lasting power cuts the methods allowingfor preventing power cuts with maximum duration119879MAX canbe considered sufficient but the parameter value is usuallydetermined for a range up to several minutes

One of the practically feasiblemethods is maintaining thepower supplied to the electrical energy system at the assumedlevel with the value of119875

3MIN in the reference periods In orderto maintain high quality of energy and stable operation ofthe system in the connection spot the change in the powerlevel supplied to the system from the value related to thewind turbine power curve to the value of 119875

3MIN should beas smooth as possible It is also recommended to implementmeasures aimed at partial stabilisation of the system outputpower at the level of 119875

3MIN in periods with reduced windenergy Such situations occur when the wind velocity valueis V10158401198753MIN

gt V119908

ge Vcut-in where V10158401198753MIN

is the velocitycorresponding to the power 119875

3MIN + 119875PW (119875PW is the house












Table1Specificatio

nof

them

ostimpo

rtantu

sablep

aram

eterso

fselectedtypeso

fthe

energy

storage

[1012]

Energy

storage

type

Roun

d-trip

efficiency

[]

Energy

density

[Whl]

Power

density

[kW

l]Cy

clelifecalend

arlife

Depth

ofdischarge[]

Self-discharge

[]

Deploym

ent

time

Charging

time

Operatin

gtemperature

[∘

C]Flyw

heel

80ndash9

520ndash200

upto

10Manymillions15

yearsndash20

years

752ndash5h

10ms

Minutes

minus35

divide+4

0Supercapacito

r90ndash9

42ndash10

upto

15Upto

onem

illion15

years

75Ve

ryslo

wlt10ms

Second

sminus40

divide+6

5Lithium-io

nbatte

ry83ndash86

200ndash

350

01ndash35


temperature)

100

5mon

thly

3msndash5m

sHou

rsminus20

divide+5

0

Lead-acid

batte

ry75ndash80

50ndash100

001ndash0

5500ndash

2000

cycle

s5ndash15

years(according

totemperature)

7001ndash04daily

3msndash5m

sManyho

urs

0divide40

CAES

60ndash70

3ndash6

na

Unlim

ited25

years

35ndash50

05ndash1d

aily

3minndash10m

inHou

rsminus30

divide60

SMES

80ndash9

005ndash10

1ndash4

Unlim

ited20

years

100

10ndash15daily

1msndash10ms

Second

s-minutes

na


PT(t)

WT120596

P1(t)

CS

FESS

PW

(plusmn)P2(t)

P3(t)

P4(t)

Power system

PW(t) W(t)

PWTN

PPW

AES (t)

PESN AES MAX

AES








1= 119891(V









tary powers 1198751(119905) and 119875










(V10158401198753MIN


1198753(119905) = 119875

1(119905) minus 119875PW (119905) (2a)



119908(119905) gt V1015840

1198753MIN 119860ES(119905) lt

119860ESMIN)

1198753(119905) = 119875

1(119905) minus 119875

2(119905) minus 119875PW (119905) (2b)



1198753(119905) = 119875

1(119905) + 119875

2(119905) minus 119875PW (119905) (2c)


Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

2(119905) minus 119875PW (119905) (2d)






119908= 119891(119905) can be



1= 119891(V







0

5

10

15

20

25

30

0 5 10 15 20 25 30

Win

d ve

loci

ty (m

s)

Time (s)

Vcut-in

Vcut-out

Area 1

Area 2

Area 3

Area 4

VP3MIN







1= 0 In practice




1gt 1198753MIN + 119875PW)




119908le V10158401198753MIN







119908ge V10158401198753MIN








1198602WT and 119860

3WT respectively











119908(119905) lt Vcut-in and V1015840




(1)


119908= 119891(119905) for a






119860ESMIN =1198961

120578ESminussdot 119879119892


+1198961



119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG


119889


3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889


1AVG 1198792AVG and 119879


119892


2is the


= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889


1198963=



(4)



1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875


3MIN gt 119875ES119873(5)






Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




























Table1Specificatio

nof

them

ostimpo

rtantu

sablep

aram

eterso

fselectedtypeso

fthe

energy

storage

[1012]

Energy

storage

type

Roun

d-trip

efficiency

[]

Energy

density

[Whl]

Power

density

[kW

l]Cy

clelifecalend

arlife

Depth

ofdischarge[]

Self-discharge

[]

Deploym

ent

time

Charging

time

Operatin

gtemperature

[∘

C]Flyw

heel

80ndash9

520ndash200

upto

10Manymillions15

yearsndash20

years

752ndash5h

10ms

Minutes

minus35

divide+4

0Supercapacito

r90ndash9

42ndash10

upto

15Upto

onem

illion15

years

75Ve

ryslo

wlt10ms

Second

sminus40

divide+6

5Lithium-io

nbatte

ry83ndash86

200ndash

350

01ndash35


temperature)

100

5mon

thly

3msndash5m

sHou

rsminus20

divide+5

0

Lead-acid

batte

ry75ndash80

50ndash100

001ndash0

5500ndash

2000

cycle

s5ndash15

years(according

totemperature)

7001ndash04daily

3msndash5m

sManyho

urs

0divide40

CAES

60ndash70

3ndash6

na

Unlim

ited25

years

35ndash50

05ndash1d

aily

3minndash10m

inHou

rsminus30

divide60

SMES

80ndash9

005ndash10

1ndash4

Unlim

ited20

years

100

10ndash15daily

1msndash10ms

Second

s-minutes

na


PT(t)

WT120596

P1(t)

CS

FESS

PW

(plusmn)P2(t)

P3(t)

P4(t)

Power system

PW(t) W(t)

PWTN

PPW

AES (t)

PESN AES MAX

AES








1= 119891(V









tary powers 1198751(119905) and 119875










(V10158401198753MIN


1198753(119905) = 119875

1(119905) minus 119875PW (119905) (2a)



119908(119905) gt V1015840

1198753MIN 119860ES(119905) lt

119860ESMIN)

1198753(119905) = 119875

1(119905) minus 119875

2(119905) minus 119875PW (119905) (2b)



1198753(119905) = 119875

1(119905) + 119875

2(119905) minus 119875PW (119905) (2c)


Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

2(119905) minus 119875PW (119905) (2d)






119908= 119891(119905) can be



1= 119891(V







0

5

10

15

20

25

30

0 5 10 15 20 25 30

Win

d ve

loci

ty (m

s)

Time (s)

Vcut-in

Vcut-out

Area 1

Area 2

Area 3

Area 4

VP3MIN







1= 0 In practice




1gt 1198753MIN + 119875PW)




119908le V10158401198753MIN







119908ge V10158401198753MIN








1198602WT and 119860

3WT respectively











119908(119905) lt Vcut-in and V1015840




(1)


119908= 119891(119905) for a






119860ESMIN =1198961

120578ESminussdot 119879119892


+1198961



119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG


119889


3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889


1AVG 1198792AVG and 119879


119892


2is the


= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889


1198963=



(4)



1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875


3MIN gt 119875ES119873(5)






Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















PT(t)

WT120596

P1(t)

CS

FESS

PW

(plusmn)P2(t)

P3(t)

P4(t)

Power system

PW(t) W(t)

PWTN

PPW

AES (t)

PESN AES MAX

AES








1= 119891(V









tary powers 1198751(119905) and 119875










(V10158401198753MIN


1198753(119905) = 119875

1(119905) minus 119875PW (119905) (2a)



119908(119905) gt V1015840

1198753MIN 119860ES(119905) lt

119860ESMIN)

1198753(119905) = 119875

1(119905) minus 119875

2(119905) minus 119875PW (119905) (2b)



1198753(119905) = 119875

1(119905) + 119875

2(119905) minus 119875PW (119905) (2c)


Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

2(119905) minus 119875PW (119905) (2d)






119908= 119891(119905) can be



1= 119891(V







0

5

10

15

20

25

30

0 5 10 15 20 25 30

Win

d ve

loci

ty (m

s)

Time (s)

Vcut-in

Vcut-out

Area 1

Area 2

Area 3

Area 4

VP3MIN







1= 0 In practice




1gt 1198753MIN + 119875PW)




119908le V10158401198753MIN







119908ge V10158401198753MIN








1198602WT and 119860

3WT respectively











119908(119905) lt Vcut-in and V1015840




(1)


119908= 119891(119905) for a






119860ESMIN =1198961

120578ESminussdot 119879119892


+1198961



119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG


119889


3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889


1AVG 1198792AVG and 119879


119892


2is the


= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889


1198963=



(4)



1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875


3MIN gt 119875ES119873(5)






Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















(V10158401198753MIN


1198753(119905) = 119875

1(119905) minus 119875PW (119905) (2a)



119908(119905) gt V1015840

1198753MIN 119860ES(119905) lt

119860ESMIN)

1198753(119905) = 119875

1(119905) minus 119875

2(119905) minus 119875PW (119905) (2b)



1198753(119905) = 119875

1(119905) + 119875

2(119905) minus 119875PW (119905) (2c)


Vcut-in 119860ES(119905) gt 0)

1198753(119905) = 119875

2(119905) minus 119875PW (119905) (2d)






119908= 119891(119905) can be



1= 119891(V







0

5

10

15

20

25

30

0 5 10 15 20 25 30

Win

d ve

loci

ty (m

s)

Time (s)

Vcut-in

Vcut-out

Area 1

Area 2

Area 3

Area 4

VP3MIN







1= 0 In practice




1gt 1198753MIN + 119875PW)




119908le V10158401198753MIN







119908ge V10158401198753MIN








1198602WT and 119860

3WT respectively











119908(119905) lt Vcut-in and V1015840




(1)


119908= 119891(119905) for a






119860ESMIN =1198961

120578ESminussdot 119879119892


+1198961



119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG


119889


3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889


1AVG 1198792AVG and 119879


119892


2is the


= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889


1198963=



(4)



1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875


3MIN gt 119875ES119873(5)






Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



























119908(119905) lt Vcut-in and V1015840




(1)


119908= 119891(119905) for a






119860ESMIN =1198961

120578ESminussdot 119879119892


+1198961



119889

1AVG2)

+ 119875ES119873 sdot

119896ES119895

100sdot 119879119892

119895AVG


119889


3MIN)

(3)

where 1198791198921AVG 119879

119892

2AVG 119879119889


1AVG 1198792AVG and 119879


119892


2is the


= 0 for 1198753MIN le 119875

119889

2AVG and 1198962

=

1 for 1198753MIN gt 119875

119889


1198963=



(4)



1198964=

1 for 1198753AVG minus 119875

3MIN le 119875ES119873

119875ES1198731198753AVG minus 119875


3MIN gt 119875ES119873(5)






Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Table2(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=200kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=200kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

592

149

3378

851

1141

1360

147

1Jun

e2010ndash

31Au

g2010

922564

100

898

350

1667

650

1193

1438

179

1Jan2010ndash

31Dec2010

365

15016

100

3147

210

11868

790

1214

1389

176

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

9161

424

6587

305

624

5140

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

15591

706

4271

193

554

3984

1292

1Jan2010ndash

31Dec2010

8760

100

11979

137

50834

580

24787

283

596

4823

1979


Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Table3(a)L

istof

statisticalandpo

wer

parametersd

etermined

forthe

course

ofwindvelocity

changesin2010

(Enercon

E53


=300kW

and

119879MAX=600s)(b)

Listof

statisticalandpo

wer

parametersd

etermined

forthe

course


(Enercon

E53


=300kW

and

119879MAX=600s)

(a)

Perio

d119879119886

119860WT

1198602WT

1198603WT

1198791AVG

[s]

1198792A

VG[s]

1198961[mdash]

[Days]

[MWh]

[

][MWh]

[]

[MWh]

[]

1Jan2010ndash

31Mar2010

903970

100

982

247

2988

753

1141

1374

154

1Jun

e2010ndash

31Au

g2010

922564

100

1313

512

1252

488

1193

1465

230

1Jan2010ndash

31Dec2010

365

15016

100

4879

325

10136

675

1214

1415

208

(b)

Perio

d119879WT

1198791W

T1198792W

T1198793W

T1198751AVG

2[kW

]1198751AVG

3[kW

]1198751AVG

[kW

][h]

[]

[h]

[]

[h]

[]

[h]

[]

1Jan2010ndash

31Mar2010

2160

100

5852

271

10751

498

4997

231

893

6020

2514

1Jun

e2010ndash

31Au

g2010

2208

100

2218

100

17297

783

2565

116

737

5032

1292

1Jan2010ndash

31Dec2010

876

100

11979

137

57899

661

17722

202

818

5791

1979

Thec

alculations

usethe

power

curvea

ndotherE

53turbinep

aram

etersp

resented

inthem

anufacturerrsquos

technicalcatalogue

[19]


0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Mar 2010


119908= 119891(119905) pro-



1= 119891(119879MAX) were




119908= 60m and ℎ




0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)





and 31 Aug 2010

0

50

100

150

200

0 10 20 30 40 50 60

Min

imum

capa

city

of t

he fl

ywhe

el (k

Wh)


hw = 60mhw = 73 m




119908= 60m and ℎ

119908= 73m)






lt




0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0

2

4

6

8

10

12

14

16

18

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



Mar 2010

0

4

8

12

16

20

24

0 10 20 30 40 50 60



Serie

s coe

ffici

ent (

mdash)



31 Aug 2010





0

2

4

6

8

10

12

14

0 10 20 30 40 50 60


hw = 60mhw = 73 m

Serie

s coe

ffici

ent (

mdash)





119908in time













119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















119886 expressed in







119898(119894)for 119894 = 1 2 119873 minus 1

For the initial 119905119898119904(119894)

and final 119905119898119890(119894)

time of the Δ119905119898(119894)


119908119904(119894)and V

119908119890(119894)respectively


and 1198751119890(119894)


1015840

119898(119894)










2(119905) and turbine119875

1(119905) power


119896(119905119896= 119896 sdot Δ119905





119860ES (119905119896 = 119896 sdot Δ119905119898) = 119860ES0 +

119896

sum

119894=1

(119887(119894)


minus

119896minus1

sum

119894=1

(119888(119894)

sdot1

120578ESsdot 1198752(119894)

sdot Δ119905119898)

minus

119896

sum

119894=1

(119889(119894)

sdot

119896ES119895 sdot 119875ES119873 sdot Δ119905119898

100)

(6)


119896= 119896 sdot Δ119905

119898 to determine


1198752(119894)


119898 119887119894 119888119894 119889119894isin 0 1 are the






119908=










1(119905) storage 119875

2(119905)





I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















I 200 50 100 1800 100 2 05II 100 0 75 1800 100 2 05III 100 0 150 600 100 2 05

024681012

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Win

d ve

loci

ty

(ms

)

(a)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

minus400

minus200


Activ

e pow

erP1P

2

(kW

)

(b)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Time (min)

Option IOption II

Activ

e pow

erP3

(kW

)

(c)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Stor

age e

nerg

y (

)

Time (min)

Option IOption II

(d)


2 (c) power 119875










0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0246810121416

0 5 10 15 20 25 30 35 40 45 50

Win

d ve

loci

ty (m

s)

Time (h)

(a)

0100200300400500600700800

0 5 10 15 20 25 30 35 40 45 50

P1

Time (h)

Activ

e pow

erP1

(kW

)

(b)

0

50

100

0 5 10 15 20 25 30 35 40 45 50

Time (h)

minus50

minus1000Activ

e pow

erP2

(kW

)

(c)

0

200

400

600

800

0 5 10 15 20 25 30 35 40 45 50

Time (h)

Activ

e pow

erP3

(kW

)

(d)

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40 45 50

Stor

age e

nerg

y (

)

Time (h)

(e)


119908 (b) power 119875

1(c) power 119875

2 and 119875


119860ES



3of the



3MIN gt 1198751




1= 0)





2are negative

(Figure 12(c))




1lt










119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























119908= 119891(119905) (Tables 2(a) 2(b)













References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of












































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Research Article Operation of a Wind Turbine-Flywheel ...

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Transcript of Research Article Operation of a Wind Turbine-Flywheel ...