Applied Energy 104 (2013) 1–9

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Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

A methodology for the low-cost optimisation of small wind turbine performance

A. Arroyo ⇑, M. Manana, C. Gomez, I. Fernandez, F. Delgado, Ahmed F. ZobaaUniversity of Cantabria, Department of Electrical and Energy Engineering, Av. Los Castros s/n, 39005 Santander, Spain

h i g h l i g h t s

" This paper presents a methodology to increase the efficiency of Small Wind Turbines." This methodology is tested in a commercial 3.5 kW Small Wind Turbine." An economic study is carried out using the Weibull Distribution." The efficiency increase can be close to 4%, if a capacitor bank is connected.

a r t i c l e i n f o

Article history:Received 6 April 2012Received in revised form 2 October 2012Accepted 24 October 2012

Keywords:CapacitorWind power generationPerformance optimisation

0306-2619/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.apenergy.2012.10.068

⇑ Corresponding author. Tel.: +34 942201371; fax:E-mail address: arroyoa@unican.es (A. Arroyo).

a b s t r a c t

The increasing use of small wind energy has made it necessary to develop new methods to improve theefficiency of this technology. This improvement is best achieved considering the interaction between thevarious components, such as the wind rotors, the electrical generators, the rectifiers and the inverters, asopposed to studying the individual components in isolation. This paper describes a methodology toincrease the efficiency of Small Wind Turbines (SWTs) equipped with a Permanent Magnet SynchronousMachine (PMSM). To achieve this objective, capacitor banks will be connected between the PMSM andthe rectifier. This methodology is motivated by two clear aims. The first one is to operate the SWT withits maximum power coefficient Cp. The second one is to select the most suitable capacitor bank for eachwind speed to optimise the energy supplied to the grid. The methodology will be tested on a commercial3.5 kW SWT, and the results will be studied to determine its feasibility.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The small wind industry is experiencing significant growth andis becoming increasingly competitive. Currently, robust equipmentthat maximises energy production and minimises manufacturingcosts is being sought.

Some studies to achieve these objectives have focused on:

� Improving the energy storage system [1].� Designing new Permanent Magnet Synchronous Machines

(PMSMs) [2].� Improving the aerodynamic design of Small Wind Turbines

(SWTs) [3,4].� Controlling the pitch angle [5].� Enhancing the inverter operation [6].

Previous works have used capacitors behind the rectifier to cre-ate a Power Factor Control (PFC) and to improve the SWT efficiency[7–9].

ll rights reserved.

+34 942201385.

This paper presents a methodology to optimise the efficiency ofSWTs based on a PMSM. To test this methodology, it is necessary tocreate a model of the whole system. The Simulink softwarepackage was used for this purpose [10]. To optimise the system,two aspects are considered:

1. The aerodynamic factor: the Maximum Power Point Tracker(MPPT) [11] is calculated to extract the maximum energy fromthe wind [12]. Using the MPPT and the SWT operating surfaces(obtained by means of the Simulink model), the optimal rela-tionship between the continuous voltage of the rectifier vdc

and the grid power Pgrid can be determined. This relationshipmust be set in the inverter, and it is known as the MaximumPower Characteristic Curve (MPCC).

2. The capacitor bank effect: when a capacitor bank is connected,the armature reaction produces a magnetising effect in thePMSM that is added to the magnetic field generated by themagnets. As a result, a higher voltage at the machine terminalsis generated [13,14].

This methodology will be tested in a commercial 3.5 kWSWT with a PMSM, and the system improvements will be verified.

2 A. Arroyo et al. / Applied Energy 104 (2013) 1–9

Finally, an economic study will be conducted, in which the well-known Weibull Distribution (WD) will be employed [15].

Fig. 1. PMSM schematic generated using Matlab.

Fig. 2. Wind power generation system.

2. System model

A system model is necessary to use the methodology presentedhere, and Simulink was used for this purpose [10]. This modelmakes it possible to analyse the SWT in detail and to evaluate itsperformance under various operating conditions.

First, a PMSM model must be created with the intention ofincluding it in the system model. This model was constructed usingthe electrical equations of synchronous machines. Eq. (1) definesthe flux at the stator of the PMSM:

weaðtÞ ¼ ðLre þMaaÞieaðtÞ þMeaiebðtÞ þMeaiecðtÞ þ wf cosðheðtÞÞ ð1Þ

where wea(t) is the total instantaneous flux in the stator phase ‘‘a’’,Lre the leakage inductance of a stator phase, Maa the inductance dueto the magnetisation flux generated by the phase ‘‘a’’ on itself, Mea

the inductance due to the magnetisation flux generated by the otherphases on the phase ‘‘a’’, wf the flux generated by the rotor, he(t) theelectrical angle between the rotor and the stator, iea(t), ieb(t), iec(t)are the instantaneous current flowing through the stator phases.if iea(t) = �(ieb(t) + iec(t)), then:

weaðtÞ ¼ ðLre þMaa �MeaÞieaðtÞ þ wf cosðheðtÞÞ ð2Þ

Given the geometry of the stator phases,

Mea ¼ Maacos2p3

� �¼ �Maa

2ð3Þ

and incorporating it into Eq. (2),

weaðtÞ ¼ Lre þ3Maa

2

� �ieaðtÞ þ wf cosðheðtÞÞ ð4Þ

the total flux at phase ‘‘a’’ can be expressed by the equation,

weaðtÞ ¼ LeieaðtÞ þ wf cosðheðtÞÞ ð5Þ

where Le is the stator phase inductance: Le ¼ Lre þ 3Maa2 .

Extending Eq. (5) to the remaining stator phases gives:

webðtÞ ¼ LeiebðtÞ þ wf cos heðtÞ �2p3

� �ð6Þ

wecðtÞ ¼ LeiecðtÞ þ wf cos heðtÞ þ2p3

� �ð7Þ

where web(t) is the total instantaneous flux in the stator phase ‘‘b’’,wec(t) the total instantaneous flux in the stator phase ‘‘c’’.

The voltage at the stator windings is,

veaðtÞ ¼ ReieaðtÞ þdweaðtÞ

dt

¼ ReieaðtÞ þ LedieaðtÞ

dt� wf xeðtÞsinðheðtÞÞ ð8Þ

where Re is the equivalent resistance of one stator phase, xe(t) is theangular speed of the electrical rotor.

Eq. (9) establishes the relationship between the angular speedsof the electrical and mechanical rotors:

dheðtÞdt

¼ xeðtÞ ¼ pxgðtÞ ð9Þ

where p is the number of pole pairs and xg(t) is the angular speed ofthe mechanical rotor.

Extending Eqs. (8) and (9) to the remaining phases and usingthe vectorial notation gives:

veaðtÞvebðtÞvecðtÞ

264

375 ¼ Re þ Le

ddt

� � ieaðtÞiebðtÞiecðtÞ

264

375� wf xeðtÞ

sinðheðtÞÞsin heðtÞ � 2p

3

� �sin heðtÞ þ 2p

3

� �264

375ð10Þ

The parameters Re and Le are required in Eq. (10). To obtain Re, ahigh-precision multimeter is used. To take into account the rela-tionship between the resistance and the temperature, Eq. (11) isused [16].

RTi¼ RTr

235þ Ti

235þ Trð11Þ

Here, RTiis the resistance at the desired temperature (X), RTr the

resistance at room temperature (X), Tr the room temperature (�C),Ti is the desired temperature (�C).

To obtain Le, the formulation proposed in [17–19] is used. ThePMSM model is shown in Fig. 1.

After obtaining the PMSM model, the effects of the inverter andthe grid must be incorporated into the system model. For this pur-pose, a variable resistor R will be defined (see Fig. 2). This resistor Rwill control the power injected into the grid.

To consider the efficiency of the inverter, a study of the inverterlosses DPinv was conducted (see Fig. 3). Thus, the relationship be-tween continuous current in the rectifier idc and the inverter lossesDPinv was obtained. Therefore, the grid power Pgrid can be calcu-lated as:

Pgrid ¼ Pdc � DPinv ¼ vdcidc � 16:06 e0:149 idc ð12Þ

where Pdc is the DC power of the rectifier and vdc is the DC voltage ofthe rectifier.

The final system model will be used to analyse the SWT perfor-mance when certain parameters are modified, such as the rotation

0 5 10 150

20

40

60

80

100

120

140

160

idc

[A]

ΔPin

v [

W]

ΔPinv=16.06·e0.149·idc

Fig. 3. DC current of the rectifier idc vs. inverter losses DPinv.

A. Arroyo et al. / Applied Energy 104 (2013) 1–9 3

speed n, the capacitance value C and the variable resistor R (seeFig. 2). Therefore, the following values can be obtained:

� The grid power Pgrid and the rectifier DC voltage vdc by combin-ing different values of R, C and n.� The MPCC for different operating conditions.

3. Maximum Power Point Tracker (MPPT)

A SWT converts the kinetic energy of wind into electrical en-ergy. A mechanical torque is produced when air passes throughthe turbine blades. This torque is used by the PMSM to producethree-phase power at a variable frequency. A back-to-back con-verter then transforms this AC power into AC power with fixedfrequency.

The equation that relates the wind speed uh with the mechani-cal power at the wind turbine rotor Pw is,

Pw ¼12

p d2

4q u3

h

!Cpðk; bÞ ð13Þ

where Cp is the power coefficient. The maximum value that can beachieved is 16/27, which is known as the Betz limit [20], Pw themechanical power at the wind turbine rotor (W), uh the wind speed(m/s), d the diameter of the swept area (m), q the air density (kg/m3), b the pitch angle (�), k is the tip speed ratio.

n [rpm]

P w [

W] uh4

uh5

uh6

uh1

uh2

uh3

MPPT

Fig. 4. Turbine rotation speed n vs. mechanical power Pw for different wind speedsuh.

Hence, the mechanical power obtained by the SWT is a functionof uh and of certain aerodynamic parameters. Eq. (13) depends onthe tip speed ratio k, and this parameter can be calculated with Eq.(14),

k ¼x d

2

uh¼

2pn60

d2

uhð14Þ

where x is the SWT angular speed (rad/s), n the SWT rotation speed(rpm).

Alternatively, Eq. (13) can be expressed in terms of torque by:

Pw ¼ Twx ð15Þ

where Tw is the SWT torque (Nm).For each SWT, there is a single value of k that provides the high-

est value of Cp and, according to Eq. (13), the highest mechanicalpower Pw. Thus, according to Eq. (14), each uh has an optimum va-lue of n that keeps k constant. Therefore, the example in Fig. 4shows the mechanical power Pw with respect to the SWT rotationspeed n. The wider line indicates the maximum mechanical powerat various wind speeds and is known as the Maximum Power PointTracker (MPPT) [12].

With Eq. (15), the associated mechanical torque Tw at variouswind speeds uh can also be obtained, which is known as the TorquePoint Tracker (TPT).

4. Methodology to calculate the optimal capacitor bank andMPCC

The flowchart to calculate the optimal capacitor bank and itsassociated MPCC is shown in Fig. 5. The steps of the methodologyare as follows:

Step 1: Perform several tests on the SWT. At a minimum, a no-load test and a rated load test should be conducted.

Step 2: Define a system model. Adjust the model parametersby comparing the simulation results with thoseobtained in Step 1.

Step 3: Calculate the TPT to extract the maximum mechanicalpower. Given Eq. (13),

Fig. 5. Flowchart of the methodology.

R [Ω]

C [F]

P grid

[W

]

Fig. 6. Grid power Pgrid vs. resistance R and capacitance C for the rated speed nrated. Fig. 8. Relationship R(C) not exceeding the restriction of ir,max for the rated speed ofthe SWT.

4 A. Arroyo et al. / Applied Energy 104 (2013) 1–9

Pw ¼ f ðd;q;n;uh;bÞ ) fd;q and b are constantsg) Pw ¼ f ðn;uhÞ ð16Þ

In this way, the maximum mechanical power Pwmaxiand its asso-

ciated rotation speed ni for each wind speed uhican be obtained by

deriving Pw with respect to n and setting the result to zero.

dPw

dn

����uhi

¼ 0) ½Pwmaxi;ni�uhi

ð17Þ

Using Eq. (15), the mechanical torque Tw;Pwmaxiassociated with

each Pwmaxican be calculated. Thus,

Tw;Pwmaxijniuhi¼

Pwmaxijniuhi

xið18Þ

Note that the TPT must remain unchanged for every value of thevariable resistor R. Therefore, the TPT in 3D can be represented as asurface parallel to axis R.

Step 4: Calculate a capacitance range [C1–C2] that contains theoptimal capacitor C. Using the Simulink model, per-form a simulation that varies R and C for the ratedspeed of the SWT (see the example in Fig. 6). The initialranges of R and C must be sufficiently wide to effec-tively analyse the SWT performance.

Looking at Fig. 6, it can be seen that by increasing the capaci-tance C (for a constant value of R) the power injected to the grid

Fig. 7. Winding current ir vs. resistance R and capacitance C.

Pgrid increases, up to reach a maximum capacitance value Cmax,from which point Pgrid decreases.

However, the value of Cmax must be controlled because it couldalso increase the current ir flowing into the PMSM windings andthereby cause damage.

ir ¼ f ðR; C; nÞ ) fn ¼ nratedg ð19Þ

Therefore, the winding wire diameter should be known todetermine the maximum current ir,max that can flow through wind-ings. Once the value of ir,max is known, the capacitance range [C1–C2] can be obtained by means of drawing a perpendicular surfaceto the axis ir (see the example in Figs. 7 and 8).

irjnrated¼ f ðR;CÞ ) ½C1 � C2�jir6ir;max

nratedð20Þ

Step 5: Obtain MPCCs for several values of Cj: (C1 6 Cj 6 C2).The greater the number of values of Cj that are tested,the more accurate the results will be. For each value ofCj, the following steps must be performed:

� Step 5.1: Use the system model to determine the operatingsurface Tw(R,n) of the SWT.

Fig. 9.

Tw ¼ f ðR; C; nÞ ) fC ¼ Cjg ) TwjCj¼ f ðR; nÞ ð21Þ

Then, obtain the intersection of that surface with the TPT (see theexample in Fig. 9). Thus, the relationship RðnÞjC¼Cj

Pwmaxfor maximum

mechanical power extraction from the wind is obtained (see Fig. 10).�

Step 5.2: Project the optimal relationship RðnÞjC¼CjPwmax

perpendic-ular to the R–n plane (see the example in Fig. 11).

Intersection between the TPT and the operating surface Tw(R,n) of the SWT.

Fig. 10. Optimal relationship R(n)jPwmax.Fig. 12. Intersection between the optimal relationship R(n) and the operatingsurface vdc(R,n) of the SWT.

vdc [V]

Pdirg

]W[ OPTIMAL

RELATIONSHIPPgrid(vdc)

Fig. 13. Maximum Power Characteristic Curve (MPCC): Grid power Pgrid vs. rectifierDC voltage vdc.

A. Arroyo et al. / Applied Energy 104 (2013) 1–9 5

� Step 5.3: Use the model to determine the SWT operating sur-faces Pgrid(R,n) (see the example in Fig. 11) and vdc(R,n) (seethe example in Fig. 12).

Pgrid ¼ f ðR;C;nÞ ) fC ¼ Cjg ) PgridjCj¼ f ðR;nÞ ð22Þ

vdc ¼ f ðR;C;nÞ ) fC ¼ Cjg ) vdcjCj¼ f ðR;nÞ ð23Þ

Then, obtain the intersection of those SWT surfaces with the surfaceobtained in Step 5.2. In this way, the optimal relationshipsPgridðnÞj

C¼CjPwmax

and vdcðnÞjC¼CjPwmax

can be determined.

� Step 5.4: Finally, the optimal relationship PgridðvdcÞjC¼CjPwmax

, alsoknown as the MPCC, can be determined easily with the val-ues of PgridðnÞj

C¼CjPwmax

and vdcðnÞjC¼CjPwmax

(see the example inFig. 13).

The additional MPCCs can be obtained by repeating steps 5.1–5.4for each value of Cj.

Step 6: Analyse the results and perform an economic study. Toperform the analysis, the well-known Weibull Distri-bution (WD) can be used [12,15]. This distribution isdefined as,

Fig. 11surface

WðuhÞ ¼Kuh

uh

um

� �K

e�uhumð Þ

K

ð24Þ

. Intersection between the optimal relationship R(n) and the operatingPgrid(R,n) of the SWT.

where K is the shape parameter of the WD, and um is the averagewind speed.

The National Renewable Energy Laboratory (NREL) defines se-ven different Wind Classes (WCs). Each WC is a function of theaverage wind speed um and the height at which the SWT is located(10 or 50 m) with respect to the ground [21]. These WCs are shownin Table 1.

The Weibull Distributions, Eq. (24), for a value of K = 1.9 and forthe average wind speeds listed in Table 1 (assuming a height of10 m) are shown in Fig. 14.

To compare the results obtained with different values of Cj, fourparameters will be used: Eðuhi

Þ; Etot ;DgjCjand D$jCj

.

Table 1Wind classification according to average speed. Adapted from [21].

Wind class um (10 m) um (50 m)

1 0–4.4 0–5.62 4.4–5.1 5.6–6.43 5.1–5.6 6.4–74 5.6–6 7–7.55 6–6.4 7.5–86 6.4–7 8–8.87 7–9.4 8.8–11.9

0 5 10 15 200

2

4

6

8

10

12

14

16

18

20

uh [m/s]

Win

d sp

eed

prob

abili

ty [

%]

Wind Class 1: um

=4.4

Wind Class 2: um

=5.1

Wind Class 3: um

=5.6

Wind Class 4: um

=6

Wind Class 5: um

=6.4

Wind Class 6: um

=7

Wind Class 7: um

=9.4

Fig. 14. Weibull Distribution for different WCs at a height of 10 m.

Fig. 15. System: PMSM + Rectifier + Inverter + Capacitor bank.

Fig. 16. SWT blo

6 A. Arroyo et al. / Applied Energy 104 (2013) 1–9

� EðuhiÞ is the annual grid energy for each wind speed uhi

and isdefined as,

ck diagr

EðuhiÞ ¼ 8760

hoursyear

� �Wðuhi

ÞPgridðuhiÞ ð25Þ

where PgridðuhiÞ is the SWT grid power for each wind speed uhi

.

� Etot is the annual total energy that can be produced by the SWT.It is obtained from the following equation:

Etot ¼Xn

i¼0

EðuhiÞ ð26Þ

� DgjCjrepresents the annual total energy increment injected into

the grid for different capacitor banks (C = Cj) compared to thecase without a capacitor bank (C = 0).

DgjCj¼

Etot;C¼Cj� Etot;C¼0

Etot;C¼0ð27Þ

� D$jCjrepresents the annual financial benefit obtained by using

different capacitor banks (C = Cj) compared to the case withouta capacitor bank (C = 0). In the calculations, an energy cost of0.2484 US$/kWh is assumed (including electricity taxes).

D$jCj¼ ðEtot;C¼Cj

� Etot;C¼0Þ0:2484US$

kWh

� �ð28Þ

5. Set-up facility

The architecture of the set-up facility is depicted in Fig. 15. Themain elements are as follows:

� DC motor to simulate wind effects (5 H.P. and 200 V).� PMSM of the SWT.� Rectifier (AC) DC).� Inverter (DC) AC).� Six-channel wattmeter.� Power quality analyser.� Torque and speed sensors.� Multimeter to measure the PMSM phase resistance.� Temperature sensors in windings.

am.

Table 2Results of steps 3 and 5 without a capacitor bank.

Step 3 Step 5

uhin Tw R Pgrid vdc

11.9 276.9 194.5 20 4346.1 299.210.1 233.2 138.8 30 2804.7 293.5

9.2 213.3 115.4 35 2170.3 278.88.4 194.9 97.7 40 1702.6 264.17.4 172.2 74.6 50 1171.0 245.16.0 139.2 50.2 65 644.0 208.35.0 116.0 33.9 85 361.2 180.14.1 95.0 23.3 105 197.2 150.93.1 72.7 13.0 150 75.1 118.5

A. Arroyo et al. / Applied Energy 104 (2013) 1–9 7

� PC to control the wattmeter, the temperature sensors and theinverter.

Fig. 16 shows the connection of the different devices.

6. Results

This methodology and the set-up facility were used to optimisea commercial SWT whose rated parameters are as follows:

� Number of blades: 3.� Power coefficient: 0.36.� Diameter: 4.2 m.� Rated speed of the wind: 11 m/s.� Rated speed: 250 rpm.� PMSM rated power: 3500 W.� Pole pairs: 10.

The results obtained were as follows:

Steps 1 and 2: Various tests were performed, and the resultswere compared with the simulated results.Fig. 17 represents the continuous voltage vdc andthe PMSM phase voltage vr versus the rotationspeed n. The simulated results show a high degreeof agreement with the real values.

Step 3: The TPT was calculated. Table 2 shows the resultsobtained when the methodology was applied.These results are for the case when no capacitorbank was connected (C = 0).

Step 4: The capacitance range was obtained. If the wind-ing wire diameter is 0.8 mm, the maximumallowed current is approximately 11 A. Thus, thecapacitance C is calculated to be between C1 = 0and C2 = 25 lF, for every value of R. The capaci-tances tested were 0, 4, 6, 8, 10, 12, 14, 16, 20,and 24 lF.

Step 5: MPCCs for several values of C were calculated. Thesimulated results without the use of capacitorbanks (C = 0) are shown in Table 2.The remaining MPCCs were determined by repeat-ing this step for the different capacitances. Thesecurves are shown in Fig. 18.Table 3 presents the values of Pgrid that wereobtained for different wind speeds uhi

for each

75 125 175 225 27550

100

150

200

250

300

350

n [rpm]

v dcv

&r

]V[

vdc

SWT

vdc

Simulink

vrSWT

vrSimulink

Fig. 17. Real and simulated results.

capacitance Cj. This table also shows the capaci-tance value that produces the highest Pgrid for eachwind speed uhi

(highlighted values).Step 6: An analysis of the results and an economic study

were performed. Using the WD Eq. (24) andassuming WC = 2 (height 10 m) lead to the resultsshown in Table 4. This table shows Eðuhi

Þ; Etot ;DgjCj

and D$jCj.

As Table 4 shows, the highest benefit ($41.51 USD) is producedby using a capacitance of 12 lF (4529 kW h). Given that capacitorscost approximately $14 USD, the total costs are covered in the firstyear. Thus, from the second year on, the capacitor bank would be-gin to make a profit.

The analysis of the system financial benefits for the remainingWCs (height = 10 m) led to the results shown in Table 5.

Table 5 shows that the investment can be recovered during thefirst year of use for WC values equal to or greater than three. Thevalue of the optimal capacitance varies for each WC. Hence, it isnecessary to know the location of the SWT to choose the capacitorbank that yields the maximum efficiency.

Table 6 shows the efficiency increase produced when using dif-ferent capacitor banks and WCs. For WC = 2 and height = 10 m, theefficiency increase was 3.83%.

Once the simulated results were obtained, an experiment wasconducted to verify them. The test consisted of connecting a capac-itor bank of 12 lF (delta connection) to the SWT. The simulatedand experimental results are shown in Fig. 19.

0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

vdc

[V]

P grid

[W

]

0 μF

4 μF

6 μF

8 μF

10 μF

12 μF

14 μF

18 μF

20 μF

24 μF

Fig. 18. MPCCs obtained with different capacitor banks.

Table 3Grid power improvement achieved by connecting capacitor banks (delta connection).

uhi(m/s) Pgrid (W)

0 lF 6 lF 8 lF 10 lF 12 lF 14 lF

5.0 360 361 360 358 358 3596.0 643 645 651 648 647 6507.0 995 1010 1008 1014 1010 10078.0 1464 1503 1496 1504 1500 14929.0 2054 2122 2141 2120 2143 2135

10.0 2763 2888 2877 2888 2900 287011.0 3572 3784 3817 3807 3846 380412.0 4401 4834 4822 4895 4855 4922

Table 4Annual benefits produced by placing different capacitors at a location with WC = 2,height = 10 m.

uhiEðuhi

Þ (kW h)

0 lF 6 lF 8 lF 10 lF 12 lF 14 lF

5 441.1 442.5 441.0 438.9 438.9 440.26 622.5 624.6 629.3 627.6 626.3 629.07 696.4 707.0 705.6 709.2 706.9 704.78 682.1 699.5 697.0 700.1 698.5 695.19 589.7 609.1 614.6 608.6 614.9 612.810 454.4 474.8 473.0 474.8 476.7 471.811 313.4 332.1 335.0 334.1 337.4 333.812 174.2 211.5 211.0 214.1 212.4 215.3

Etot 4362 4517 4523 4526 4529 4522Dg) 3.56 3.68 3.77 3.83 3.65D$) 38.65 39.92 40.82 41.51 39.56

Table 5Annual financial benefits produced by using different capacitors for all WCs at aheight of 10 m.

WC D$ (height = 10 m)

6 lF 8 lF 10 lF 12 lF 14 lF

1 15.4 15.9 16.1 15.8 15.12 38.6 39.9 40.9 41.5 39.73 66.2 67.1 69.3 70.4 68.34 94.0 94.3 98.2 99.3 97.55 124.2 125.5 131.3 132.2 131.16 175.1 176.4 185.6 185.8 186.37 356.8 357.3 380.2 375.4 385.5

Table 6Efficiency increase produced by using different capacitors for all WCs at a height of10 m.

WC Dg (%) (height = 10 m)

6 lF 8 lF 10 lF 12 lF 14 lF

1 2.21 2.25 2.25 2.26 2.132 3.62 3.68 3.77 3.83 3.673 4.76 4.83 4.99 5.06 4.924 5.67 5.74 5.97 6.03 5.935 6.54 6.61 6.91 6.95 6.906 7.73 7.79 8.19 8.20 8.227 10.96 10.97 11.68 11.53 11.84

0 50 100 150 200 2500

1000

2000

3000

4000

5000

n [rpm]

Pdirg

]W[

SimulinkReal

Fig. 19. Simulated and experimental results (C = 12 lF).

8 A. Arroyo et al. / Applied Energy 104 (2013) 1–9

7. Conclusions

The increasing development of small-wind energy systems hasmade it necessary to study new methods to improve the efficiencyof this technology. This paper presents a methodology to increasethe SWT efficiency by connecting a capacitor bank. This methodol-ogy involves the use of a Simulink model to simulate the system.

The results obtained with the Simulink model are suitable be-cause they show a high degree of agreement with the performanceof the real machine. As an example, the efficiency increases pre-dicted by the simulations were the same as those obtained in thereal tests. Given the accuracy of the Simulink model, all modifica-tions can be extrapolated to the SWT.

It has been shown that connecting different capacitor banks tothe system modifies the SWT performance and the MPCC. Thepower obtained from the SWT increases as a result of connectingcapacitor banks and is only limited by the maximum current thatcan flow through the PMSM windings. To connect the optimalcapacitor bank, the precise location of the SWT and the associatedaverage wind speed must be known. In this study, we found thatconnecting a capacitor bank of 12 lF increases the SWT efficiencyby 3.83%. Thus, in the PMSM design, an added shunt capacitancecould be a new parameter to bear in mind.

The methodology described in this paper could be used by elec-trical machine manufacturers to reduce the PMSM size. If the3.5 kW PMSM is redesigned using a capacitor bank, this new elec-trical machine will contain less copper (the capacitor bank de-creases the current that flows through the PMSM), a smallermagnet size (due to magnetising effect of the capacitors) and fewermagnetic plates to obtain the same electrical power Pgrid. If thesemodifications are included in the SWT design, the manufacturingcosts would decrease substantially, especially in the case of higherWCs.

Acknowledgments

The authors are grateful for the support from the Spanish Gov-ernment under the Project ENE2007-68032-C04-04, SODERCAN,ITEC and Sonkyo Energy.

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Glossaryb: pitch angle (�)DPinv: inverter losses (W)Dg: increment of Etot using different capacitor banks (%)D$: annual benefit ($)k: tip speed ratioC: capacitance of the capacitor banks (F)Cdc: DC bus capacitor (F)Cp: Power coefficientd: diameter of turbine blades (m)Etot: annual total energy extracted from the SWT (kW h)E(uh): annual grid energy for each wind speed (kW h)idc: DC rectifier current (A)ir, is, it: phase RMS current of the PMSM (A)n: SWT rotation speed (rpm)Pdc: rectifier DC power (W)Pgrid: grid power (W)Pw: mechanical power at the wind turbine rotor (W)R: variable resistor to simulate inverter and grid effects (X)Tw: torque in SWT shaft (Nm)Uh: wind speed (m/s)vdc: DC rectifier voltage (V)vr, vs, vt: phase RMS voltage of the PMSM (V)W(uh): Weibull Distribution