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Renewable Energy 36 (2011) 2655e2662

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Renewable Energy

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Maximum power point tracker of wind energy conversion system

M. Kesraoui a,*, N. Korichi b, A. Belkadi b

a Laboratory of applied automatics, Faculty of hydrocarbons and chemistry, M’hamed Bougara University, Avenue de l’indépendance, 35000, Boumerdès, AlgeriabDepartment of electronics and electrical engineering, Faculty of engineering sciences, M’hamed Bougara University, Avenue de l’indépendance, 35000, Boumerdès, Algeria

a r t i c l e i n f o

Article history:Received 22 March 2010Accepted 21 April 2010Available online 15 May 2010

Keywords:WECSPMSGMPPT algorithmPWM converters controllers

* Corresponding author. Tel.: þ213 669.53.34.86; faE-mail address: mkesraoui@umbb.dz (M. Kesraoui

0960-1481/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.renene.2010.04.028

a b s t r a c t

In this paper, a simple control strategy for an optimal extraction of output power from grid connectedvariable speed wind energy conversion system (WECS) is presented. The system consists of a variablespeed wind turbine coupled to a permanent magnet synchronous generator (PMSG) through a gear box,a diode bridge rectifier, a dc-to-dc boost converter and a current controlled voltage source inverter. Themaximum power point tracker (MPPT) extracts maximum power from the wind turbine from cut-in torated wind velocity by sensing only dc link power. The MPPT step and search algorithm in addition to theDCeDC and DCeAC converters PWM controllers are simulated using MATLAB-SIMULINK software. Theobtained simulation results show that the objectives of extracting maximum power from the wind anddelivering it correctly to the grid are reached.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Variable speed wind energy systems integrated with powerelectronic interfaces are becoming popular because they canextract maximum power from the wind, alleviate the load peak indrive train and supply reactive power on demand. For maximumenergy extraction, the speed of the turbine should be varied withwind speed so that the optimum tip-speed ratio is maintainedconstant. A maximum power point tracking (MPPT) algorithm isdeveloped. It extracts maximum power from the wind turbine forwind speeds from cut-in to rated, by generating a suitable referencevoltage to the dcedc converter. A separate controller generates thereference current for the inverter in such a way that the dc linkvoltage is maintained constant. The WECS used will be describedfirstly. It is followed by the presentation of the MPPT step andsearch algorithm and the used PWM inverter and dcedc converterscontrollers. Finally the MATLAB-SIMULINK models used as well asthe simulation results will be given.

2. Wind energy conversion system

The wind generator system is formed by a fixed pitch windturbine, a permanent magnet synchronous generator, a passiverectifier, a dc-to-dc boost converter and a current controlled voltagesource inverter. It is shown in Fig. 1.

x: þ213 24.81.91.72.).

All rights reserved.

2.1. Wind turbine system

The blades of a wind turbine extract the energy flow frommoving and deliver it via a gear box unit to the rotor of an electricgenerator. The wind power is estimated by [1]:

PWind ¼ 12rAy3 (1)

Where, r is the air density which varies with air pressure andtemperature. The power coefficient Cp is usually given as a functionof the tip speed ratio l and the blade pitch angle b. The pitch angleis the angle between the plane of rotation and the blade cross-section chord [3]. The tip speed ratio of awind turbine is defined as:

l ¼ uy1

¼ ruR

y1(2)

Where u is the tangential velocity of the blade pitch, uR the angularvelocity of the rotor, r the rotor radius in meters, and y1 the windspeed. For the wind turbine used in this paper, Cp as a function of lis given by the following equation [1]:

Cp ¼ 0:043� 0:108 lþ 0:146 l2 � 0:062 l3 þ 0:014 l4

� 0:0006 l5 (3)

The output power of the wind turbine Pt is calculated as:

Pt ¼ 12CpðlÞAy3 (4)

The mechanical power versus the generator rotor speed fordifferent wind speeds is shown in Fig. 2. The power extracted from

Fig. 1. WECS with MPPT and converters controllers.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e26622656

the wind is maximized when the power coefficient Cp is at itsmaximum. This occurs at a defined value of the tip speed ratio l.Hence for each wind speed there is an optimum rotor speed wheremaximum power is extracted from the wind. Therefore if the windspeed is assumed to be constant, the value of Cp depends on thewind turbine rotor speed. Thus, by controlling the rotor speed, thepower output of the turbine is controlled.

2.2. Electrical system

The electrical system schematic is shown in Fig. 1 [2]. The windturbine converts the power of the wind to mechanical power in therotor shaft. This is then converted to electricity using a permanentmagnet synchronous generator (PMSG). The output voltage isrectified using a three-phase diode bridge rectifier. The dc-to-dcconverter is used to control the dc voltage Vdc across capacitor C1.The MPPT controller delivers a voltage reference that is comparedto the actual value of Vdc. The result is fed into a PI controller whoseoutput is compared to a triangular waveform to determine when toturn the dcedc boost converter switch ON or OFF. The voltagesource PWM inverter interfaces the wind turbine system with thepower grid. It operates so that the amplitude of the output currentvaries in order to keep constant the dc side voltage V0 across thecapacitor Co.

Fig. 2. Typical power versus speed characteristics of a wind turbine.

3. Control systems

3.1. Maximum power tracking algorithm

Due to its monotonic characteristics, wind turbines can becontrolled to yield maximum power using search control methods.Before explaining the maximum power tracking controller, it isimportant to understand the basic physics of the system. Thegenerated mechanical power is given by [3e5]:

Pmech ¼ TmechðtÞuRðtÞ (5)

Where, Tmech is the mechanical torque. For simplification, thegenerated electric power of a one-phase generator is given by

PeðtÞ ¼ VaðtÞIaðtÞ (6)

Va and Ia are the generator voltage and current respectively.Assuming no losses in the system, then

TmechðtÞ$uRðtÞ ¼ VaðtÞIaðtÞ (7)

The basic electrical and motion equations are

Te ¼ kIaIf (8)

Fig. 3. Maximum power tracking process.

Fig. 4. Block diagram of a typical dc-to-dc converter controller.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e2662 2657

Ia ¼ Va � EaRa

(9)

Ea ¼ kIaue (10)

Where, ue ¼ p2uR and p is the number of poles of the generator.

Using (3)e(10), the power is obtained by

Pe ¼ uRkIfRa

�Va � kIfue

�(11)

Where, ue is the electrical angular speed, If the field current, Eaarmature voltage and Ra armature resistance. For a diode rectifier,the dc output voltage, Vdc is proportional to the generator phasevoltage Va, (11) can be expressed as:

Pe ¼ uRkIfRa

�Vdc � kIfue

�(12)

Maximum power is atdPedVdc

¼ 0 (13)

It is noticed from (12) that the power extracted from the windcan be controlled by varying the dc bus voltage, which is a func-tion of If and ue. Considering the wind turbine characteristicsgiven in Fig. 2, we know that the maximum power point isobtained when.

dPmechduR

¼ 0 (14)

Fig. 5. Block diagram of voltage

This equation can be written as:

dPmechduR

¼ dPmechdVdc

dVdcdue

due

duR¼ 0 (15)

According to (15), Maximum power point is when:

dPmechdVdc

¼ 0 (16)

The function Pmech (Vdc) has a single point where maximumpower extraction is achieved. It also means that the maximumpower can be tracked by searching the rectified dc power, ratherthan environmental conditions, such as wind speed and direction.The MPPT algorithm is as follows [6]:

One initiates the maximum power searching process by settingan arbitrary dc side voltage reference Vref. The controller thenmeasures both the dc side current and voltage, and calculates theinitial electric power Po ¼ VdcIdc. Next, the reference voltage Vref isincreased by DVdc so that.

Vref ðkÞ ¼ Vref ðk� 1Þ þ DVdc (17)

Then the dc power is calculated with P(k) ¼ Vdc(k)Idc(k).If P(k) is bigger than P(k� 1), the maximum power point has not

been reached therefore, the voltage reference needs to be increasedby DVdc and the dc power needs to be compared. This process willrepeat until maximum power is reached.

And if P(k) is less than P(k � 1), the dc voltage reference is thendecreased by DVdc. In order to search for maximum power at anywind speed four conditions must be met.

1. If PðkÞ � Pðk� 1Þ and VdcðkÞ � Vdcðk� 1Þ, the dc side voltagereference need to be increased by DVdc. This condition is metwhen the turbine operates on the low speed side of the powercurve, shown on Fig. 3.

2. If PðkÞ � Pðk� 1Þ and VdcðkÞ3Vdcðk� 1Þ, the wind turbine isbeing operated in the high speed side and the dc referencevoltage needs to be decreased by DVdc.

3. When PðkÞ3Pðk� 1Þ and VdcðkÞ � Vdcðk� 1Þ, the maximumpower point is passed and a step back must be taken,decreasing the reference voltage by DVdc. This condition is met

source inverter controller.

wind speed

wind speed

2.3

rotor radius

Continuous

powergui

[pmech]

pmech1

[pmech]

pmech

0

pitch angle

[[lambda]

lambda1[lambda]

lambda

1.08

air density

[Wr]

Wr

gen speed

pitch angle

wind speed

air density

rotor radius

tm

pmech

Cp

lamda

WIND TURBINE

[Wr]

W

Scope1

T

wm

te

Vo

Vo+

Vo-

PMSG+RECTIFIER+DC TO DC CONVERTER+CONTROLLER

Vo

v+

v-

INVERTER CONTROLLER+LOAD

[Cp]

Cp1

[Cp]

Cp

2/4*5

2/pG

1/5

1/G

Fig. 6. WECS simulation block diagram.

Fig. 7. PMS generator and dc-to-dc converter model.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e26622658

when the turbine is operated in the high speed side of thedome and the power is decreasing.

4. When PðkÞ3Pðk� 1Þ and VdcðkÞ3Vdcðk� 1Þ, the power isdecreasing on the low speed side, therefore the voltage refer-ence is to be increased by DVdc.

In Fig. 3, the power-speed plot is shown for three different windspeeds, where y1 < y2 < y3. The arrows show the trajectory inwhich

Fig. 8. Maximum power tracking a

the turbine will be operated using the maximum power trackingalgorithm explained above. If the wind speed is y1, the controllerwill search for the maximum power. If the wind changes to y3 theturbine is no longer being operated at the maximum power pointso the controller will search for the new maximum power point.After reaching the maximum point it will operate the wind turbineat the optimal point until wind changes, thus searching formaximum power at any wind speed. In order to optimize the

nd dc-to-dc controller model.

Fig. 9. Inverter controller model.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e2662 2659

maximum power search algorithm presented above, a step thatcombines speed of convergence and accuracy of results wasdeveloped. The variable step method is based on the New-toneRaphson method. The value of the root can be calculated as,

Xnþ1 ¼ Xn � f ðXnÞf ’ðXnÞ

(18)

Where Xn is the current known value of X, f(Xn) represents the valueof the function at Xn, and f0(Xn) is the derivative at Xn. The functionf(Xn) can be expressed as:

f ðXnÞ ¼ f ðVdcðkÞÞ ¼ dPedVdc

¼ PðkÞ � Pðk� 1ÞVdcðkÞ � Vdcðk� 1Þ ¼ SlopeðkÞ

(19)

And f’(Xn) as

f 0ðXnÞ ¼ f 0ðVdcðkÞÞ ¼ d2Ped2Vdc

¼ Slope ðkÞ � Slope ðk� 1ÞVdcðkÞ � Vdcðk� 1Þ (20)

Using (18), (19), and (20), DVdc can be express as follows:

DVdc ¼ f ðVdcðkÞÞf 0ðVdcðkÞÞ

¼PðkÞ�Pðk�1Þ

VdcðkÞ�Vdcðk�1ÞSlope ðkÞ�Slope ðk�1Þ

VdcðkÞ�Vdcðk�1Þ(21)

And hence,

DVdc ¼ PðkÞ � Pðk� 1ÞSlope ðkÞ � Slope ðk� 1Þ (22)

Using this variable step will allow the maximum power trackerto converge faster to the maximum power point and will decreasepower oscillations due to large values of DVdc when maximumpower is achieved. For protection the value of DVdc is limited. TheDVdc limit can be changed based on the generator size and designparameters.

Fig. 10. MPPT for a step change in wind speed.

3.2. Dc/dc converter controller

The maximum power tracker will generate a reference voltagethat will be used to control the dc voltage at the rectifier dc sideterminals. The dc-to-dc converter uses a simple feedback controller.The dc voltage reference is compared to the actual dc voltage, andthe error signal is fed to a PI controller. The output signal iscompared with a fixed frequency repetitive triangular waveform todeliver a signal that will turn ON or OFF the switch. This is shown inFig. 4.

3.3. Inverter controller

A current control voltage source pulse-width modulationcontrol strategy is used. The controller varies the amplitude of theoutput current of the inverter in order to keep the dc voltageconstant. Two feedback loops are used. The inner loop controls theamplitude of the current and the outer one controls the dc sidevoltage as shown in Fig. 5. The reference dc side voltage is sub-tracted from the actual dc voltage and the error is fed into a look-uptable. The look-up table outputs a gain that will then be multipliedby the utility grid ac voltage. This will generate a reference

Fig. 11. Simulation results for wind speed v ¼ 6 m/s.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e26622660

Fig. 12. Simulation results for wind speed v ¼ 8 m/s.

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e2662 2661

M. Kesraoui et al. / Renewable Energy 36 (2011) 2655e26622662

waveform for each phase current with unity power factor. Differentpower factors can be obtained by phase shifting the current refer-ence to lag or lead the voltage waveform. The actual value of thecurrent is then subtracted from the reference and the error is fedinto a PI controller. The output of the PI controller is compared witha repetitive triangular waveform to turn the inverter switches ONor OFF.

4. Simulation

The MATLAB-SIMULINK model of the WECS and the controlsystems are first presented. Simulation results with the MPPT inaddition to the comments will then be given for two wind speeds 6and 8 m/s. The electric machine and the dc-to-dc converterparameters are given in Appendix.

The dc-to-dc converter parameters were obtained by selectinga power rating based on the generated power capacity and voltageripple requirements for the output voltage of the converter. The Airdensity r¼ 1.08m3/Kg, radius r¼ 1.525m, initial Speed 20 rps, GearRatio G ¼ 5.

4.1. WECS MATLAB-SIMULINK model

The WECS model is shown in Fig. 6. The model of the generatorand dc-to-dc converter is represented in Fig. 7. The model of themaximum power tracking algorithm and the dc-to-dc controllerare given in Fig. 8. The inverter controller with a connection to thegrid is shown in Fig. 9.

4.2. Simulation results and comments

Simulation results of the WECS with MPPT algorithm are shown(with zooming) in Figs. 10e12.

It can be seen from Figs. 11 and 12 (a and b) that the inputcurrent of the rectifier is in phase with the voltage waveformtherefore, leading to a unity power factor. Dc link voltage is main-tained constant at 400 V as indicated in Figs. 11(e) and 12(e). Phase-A current of the PWM inverter is in anti-phase with the corre-sponding phase voltage according to Figs. 11 and 12(c and d). Withthe increase in wind speed the power fed to the grid also increaseswhich is indicated by an increase in magnitude of PMSG phasevoltage and phase current at Figs. 11 and 12(a and b) and inverteroutput phase current Figs. 11 and 12(c).

At t ¼ 10 s, wind speed is changed from 6 to 8 m/s in step,whereas tip-speed ratio is maintained at Cp maximum in steadystate conditions. It is noticed from Fig. 10(b and c) that thecontroller is able to search for maximum power and keep thepower coefficient of the wind turbine very close to its maximum.

5. Conclusion

A maximum power point tracker of a wind energy conversionsystem as well the dcedc converter and PWM inverter controllershave been presented and simulated for two wind speed profiles.The proposed wind energy conversion system has been describedand each of its components modeled in MATLAB-SIMULINK. Thestep and search algorithm for the MPPT has been developed andsimulated. The analysis and simulation have shown that thedeveloped step and search algorithm has reached the objective ofextracting maximum power from the air stream at any wind speedwithout the knowledge of wind speed or rotor speed. In addition,the knowledge of the wind turbine aerodynamic characteristics isunnecessary in order for the algorithm to work.

Appendix

Machine Parameters: Stator resistance Rs ¼ 1.5 U, Stator induc-tances Ld ¼ Lq ¼ 0.01 mH, Flux induced by magnets f ¼ 0.1194 Wb,moment of inertia J ¼ 2 Kg m, number of poles p ¼ 4.

Converter parameters: Low voltage side capacitor C1 ¼ 500 uF,High voltage side capacitor C0 ¼ 3600 uF, Inductor L ¼ 200 uH,Switching frequency fd ¼ 20 kHz.

References

[1] AB Raju, BG Fernandes, Kishore Chatterjee. A UPF Power Conditioner witha Simple Maximum Power Point Tracker for Grid Connected Variable SpeedWind Energy Conversion System, EPE2003. Toulouse, France; 2003.

[2] Kesraoui M. Optimization of a decentralized electrical energy supply system.Phd thesis. Austria: University of Leoben; 2006.

[3] Spera DA. Wind turbine technology: fundamental concept of wind turbineengineering. New York: ASHE Press; 1994.

[4] Bhadra SN, Kastha D, Banerjee S. Wind electrical systems. Oxford, UK: OxfordUniversity Press; 2005.

[5] Mohammad H. Rashid. Power electronics-circuit. Devices and application. 3rded; 2004.

[6] Koutroulis E, Kalaitzakis K. Design of a maximum power tracking system forwind-energy-conversion applications. IEEE Transactions on Industrial Elec-tronics April 2006;53(2):486e94.