ISSN 0003�701X, Applied Solar Energy, 2012, Vol. 48, No. 4, pp. 238–244. © Allerton Press, Inc., 2012.

238

1 INTRODUCTION

Due to the rising oil price and environmental regu�lations in the one hand and increasing of the worldenergy demand, due to the modern industrial societyand population growth on the other hand, the demandof utilizing alternative power sources is increased dra�matically. Alternative power energy and their applica�tions have been heavily studied for the last decade.Solar energy is a promising candidate in many appli�cations. Among solar energy applications, the PV hasreceived much attention with many feasible applica�tions. However, the performances of PV depend onsolar radiation, ambient temperature and load imped�ance. To achieve MPP output of a PV system is essen�tial for its application. Different approach to track theMPP has been addressed in many literatures. Amongthese algorithms, Hill climbing [1–3] and perturba�tion methods [3] and [4] were commonly used due totheir straightforward and low cost implementation.These two methods share the same principle by per�turbing duty cycle and observing the power output.The drawbacks of these methods are that, at steadystate, the operating point oscillates around MPPwhich leads to perturbation. Alternative approach toovercome this effect is called the increment induc�tance method [5–7]. However, both perturbation andincrement inductance didn’t perform well duringrapid changing of atmospheric conditions. Therefore,modified methods [8–11] have been also proposed toimprove tracking performance. Another approachcalled proportional open circuit voltage or short cir�cuit current is addressed in [12–14] which assumedthat the voltage and current of MPP is proportional toPV open circuit voltage and short circuit currentrespectively. However, the estimated optimal voltage is

1 The article is published in the original.

only an approximation of the true one and the propor�tional constant will change if the PV modules ages.

As it is shown with the Ppv–Vpv characteristic, if thePV current is optimal, the PV voltage is also optimal asthe Ipv = f(Vpv) characteristic is a bijective function.Based on this concept, a new MPPT algorithm is con�ceived. It is based on PV current control. Here, theoptimal PV current is estimated using the NewtonRaphson optimization algorithm.

Digital simulation results for a resistive load arepresented to highlight the improvement in perfor�mances of the presented MPPT approach.

PV GENERATOR (PVG) MODEL

The direct conversion of the solar energy into elec�trical power is obtained by solar cells. A PVG is com�posed of many strings of solar in series, connected inparallel in order to provide the desired values of outputvoltage and current [14]. Its equivalent circuit model isshown in Fig. 1. From which non linear P–Vpv charac�teristic can be deduced.

Based on the Kirchhoff law for current, the termi�nal current of PVG is given as:

Ipv = Iph – ID – IRsh. (1)

The light current Iph is related to radiation, temper�ature and the light current measured at some referenceconditions:

(2)

where, Iphs is the light current at reference conditions,G and Gs are the actual and reference condition radia�tions, respectively, T and Ts are the actual and refer�

IphGGs

����Iphs 1 Δi T Ts–( )–[ ],=

A Maximum Power Tracking Algorithm Based on Photovoltaic Current Control for Matching Loads

to a Photovoltaic Generator1

Ben Hamed Mouna and Sbita LassaâdNational Engineering School of Gabes, Tunisia

Received August 27, 2012

Abstract—In this paper, a novel maximum power point tracking (MPPT) approach is studied. It is based onthe photovoltaic (PV) current control. The last one is estimated using an estimation algorithm. It is estab�lished based on the Newton Raphson optimization algorithm. Digital simulation results for a resistive loadare presented to highlight the improvement in performances of the presented MPPT approach.

DOI: 10.3103/S0003701X1204007X

DIRECT CONVERSION OF SOLAR ENERGY TO ELECTRIC ENERGY

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

A MAXIMUM POWER TRACKING ALGORITHM 239

ence conditions temperatures, respectively, and i is thetemperature coefficient for current.

The diode saturation current ID is given by Shock�ley equation (3):

(3)

here Isat is the reverse saturation current, VD is thediode’s voltage and Vt is the thermal voltage.

Using the Kirchhoff law for voltage VD is defined as:

VD = Vpv + RsIpv. (4)

As the something, IRsh is:

(5)

Finally, the PVG’s electric characteristic is given interms of output current Ipv and voltage Vpv:

(6)

Now, the parameter Isat needs to be evaluated. Atopen circuit: Ipv = 0A and Vpv = Voc.

In these conditions, (6) can be written as:

(7)

ID IsatVD

Vt

�����⎝ ⎠⎛ ⎞exp 1– ,=

IshVpv RsIpv+

Rsh

��������������������� .=

Ipv Iph IsatVD

Vt

�����⎝ ⎠⎛ ⎞exp 1––

Vpv RsIpv+Rsh

��������������������� .–=

0 Iph IsatVoc

Vt

������⎝ ⎠⎛ ⎞exp 1––

Voc

Rsh

������.–=

This can be simplified as:

(8)

The Voc is related to temperature and Vocs measuredat some conditions:

Voc = Vocs – (9)

where Vocs is the temperature coefficient for voltage.

MPPT CONVERTER CONFIGURATION

Let’s consider a boost type converter connected tothe PVG as illustrated in Fig. 2.

The PVG characteristic presents three importantpoints: the short circuit current, the open circuit voltageand the optimal power delivered by the PVG when itoperates at its MPP. Figures 3a and 3b gives the Ipv–Vpv

and Ppv–Vpv characteristic of the PVG for different val�ues of radiation and temperature. The maximum out�put power is proportional to the radiation andreversely proportional to the temperature. The powercurves of Fig. 3 show that the optimal power point cor�responds to a load connected to the PVG that varieswith the radiation and temperature. In practice, thisvariable optimal load will be achieved through the useof a variable duty cycle of the control part of the

Isat

IphVoc

Rsh

������–

Voc

Vt

������⎝ ⎠⎛ ⎞exp 1–

�������������������������� .=

ΔVocT Ts–( ),

Rs Ipv

Rsh

Iph

ID

Vpv

IRsh

Fig. 1. Equivalent circuit model of PV generator.

Ipv Iout

Vout

L

SaC1 C2

Fig. 2. MPPT boost converter diagram.

Vpv

240

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

BEN HAMED MOUNA, SBITA LASSAÂD

MPPT converter which controls directly the operatingvoltage corresponding to this optimal load.

The system can be written in two sets of state equa�tion depend on control voltage Sa level. If the controlvoltage is set to 1, the output voltage Vout, the input volt�age Vpv, and the inductance current can be written as:

(10.a)

(10.b)

(10.c)

The last equations can be written as (10.a), (10.b)and (10.c) if the control voltage is at level zero:

(11.a)

(11.b)

(11.c)

By the averaging method using, (10) and (11) can becombined into one set of equations to represent thedynamic system. Two distinct equation sets are

Vpv1

C1

���� Ipv Il–[ ] t,d∫=

Vout1

C2

���� Iout–[ ] t,d∫=

dIL

dt������

Vpv

L������ .=

Vpv1

C1

���� Ipv Il–[ ] t,d∫=

Vout1

C2

���� IL Iout–[ ] t,d∫=

dIL

dt������ 1

L��� Vpv Vout–[ ].=

weighted by the control voltage Sa. Hence, the dynamicequation of the system can be described as:

(12.a)

(12.b)

(12.c)

where C1 and C2 are the capacities and L is the induc�tance.

In searching for the MPP and tracking this point inorder to minimize the spread between the operationpower and the optimal power in the event of change ofweather conditions, the optimal current is comparedto the actual one and the obtained signal feeds a cur�rent controller. The resulting output is then used by thePWM system to increase or decrease the duty cycle ofthe boost converter in order to change the operatingpoint of the PVG until the later reaches its optimalvalue.

NEW MPPT METHOD FOR PV SYSTEMS

As it is shown in Fig. 3, if PVG current is at optimalvalue, the PVG voltage is also at its optimal value as thecharacteristic Ipv = f(Vpv) is represented with a bijectivefunction. Based on this concept, a novel approach forMPPT is proposed. It is based on the regulation of the

Vpv1

C1

���� Ipv Il–[ ] t,d∫=

Vout1

C2

���� 1 Sa–( )IL Iout–[ ] t,d∫=

dIL

dt������ 1

L��� Vpv 1 Sa–( )Vout–[ ],=

15

0 50

10

5

150100 200

2000

0 100 200

1000

1000

0 100 200

500

0 50

2

150100 200

4

6

8

I pv,

AI p

v, A

Vpv, V Vpv, V

P,

WP

, W

Vpv, V Vpv, V

G:100:100:1800G:100:100:1800

T:10:10:100 T:10:10:100

(a)

(b)

Fig. 3. Solar radiation and temperature influences on the Ipv–Vpv and P–Vpv characteristics, (a) solar radiation influence,(b) temperature influence.

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

A MAXIMUM POWER TRACKING ALGORITHM 241

PVG current at its optimal value. This optimal value isdefined as:

(13)

where Iops is the optimal PVG current at standard testconditions and iop is the temperature coefficient forcurrent.

The error between the optimal and the actual PVGcurrent is analyzed with a current controller to get thecontrol voltage feeding the control part of the MPPTconverter. The used algorithm for the optimal PVGcurrent estimation is tested in simulation for differentvalues of solar radiation and temperature. Obtainedresults are reported in Figs. 4a and 4b. The waveformsdepicted through these figures show that estimatedoptimal PVG current follows the real one indicatingthe validity of the used estimation algorithm.

SIMULATION RESULTS

The effectiveness and the robustness of the pro�posed MPPT algorithm are investigated using simula�tions with Matlab/Simulink software. We have testedthe proposed approach for different values of radiation

IopGGs

����Iops 1 Δiop T Ts–( )–[ ],=

and temperature. The effect of load is also studied.The results obtained at various values of radiation andtemperatures under fixed load value are reported inFigs. 5 and 6. In this cases, the proposed MPPT con�troller acts on the variation of the PVG current by theuse of the variable duty cycle (Figs. 5b and 6b) of theconverter yielding to a variable optimal current. As theIpv = f(Vpv) is represented with a bijective function, thecorresponding voltage is the optimal one and so on, anoptimal power. The robustness of the proposed MPPTapproach is tested according to the load variation. Theobtained results are given in Fig. 7. It is shown that thePVG current response converges to the optimal one.An error occurs at the time of load variation. It is com�pensated thanks to the PVG current controller.

CONCLUSIONS

A new MPPT approach based on the PVG currentcontroller was developed. Using this approach, it ispossible to adopt the load to the PVG and to follow theMPP howsoever the weather conditions may vary.Simulations results of this new approach show thattracking efficiency of the MPP is with high perfor�mances. The implementation of the proposed MPPT

14

0 50 150100 200

12

10

8

6

4

2

250

14

0 50 150100 200

12

10

8

6

4

2

250

8

0 50 150100 200

7

6

5

4

2

1

250

3

300

8

0 50 150100 200

7

6

5

4

2

1

250

3

300

I pv,

A

I pv,

AI p

v, A

I pv,

A

Vpv, VVpv, V

Vpv, V Vpv, V

* Actual optimal current Estimated optimal current

* Actual optimal current Estimated optimal current

Increasing G:G = 100:100:1800 W/m2 Increasing G:

G = 100:100:1800 W/m2

Increasing temperature T:T = 10:10:100°C

Increasing temperature T:T = 10:10:100°C

G = 1000 W/m2 G = 1000 W/m2

T = 25°C

(b)

Fig. 4. Actual and estimated optimal currents, (a) under different solar radiation values, (b) under different temperature values.

(a)

242

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

BEN HAMED MOUNA, SBITA LASSAÂD

1200

0 50 150100 200

1000

800

600

400

200

Vpv, V

P,

W

... PV generator power

0.8

0 3.0

0.6

0.4

0.2

2.52.01.51.00.5Time, s

α

(b)

Fig. 5. Simulation results under different temperature values, (a) PV generator power in P = f(Vpv) characteristics and (b) boostchopper duty.

(a)

2000

0 50 150100 200

1500

1000

500

0 6

0.2

54321

0.4

0.6

0.8

Vpv, V

P,

W

... PV generator power

Time, s

α

(a)

(b)

Fig. 6. Simulation results under different solar radiation, (a) PV generator power in P = f(Vpv) characteristics and (b) boost chop�per duty cycle.

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

A MAXIMUM POWER TRACKING ALGORITHM 243

(a)

8

0 1.51.00.5

6

4

2

6.45

0.90.80.70.60.50.40.3

6.40

6.35

6.30

Optimal currentGPV current

Op

tim

al a

nd

GP

V c

urr

ents

, A

Time, s

200

0 1.51.00.5

150

100

50

175

0 0.3 0.50.4 1.00.90.80.70.60.2

170

165

160

155

150

0

0.1

1.51.00.5

0.2

0.3

0.4

0.5

0.6

0.7

Time, s

Time, s

Vpv

, V

Bo

ost

ch

op

per

du

ty c

ycle

(b)

(c)

Fig. 7. Simulation results under load variation, (a) target and actual optimal currents, (b) GPV voltage and (c) duty cycle.

244

APPLIED SOLAR ENERGY Vol. 48 No. 4 2012

BEN HAMED MOUNA, SBITA LASSAÂD

approach on an experimental set up is a follow upresearch work.

REFERENCES

1. Xiao, W. and Dunford, W.G., A Modified Adaptive HillClimbing MPPT Method for Photovoltaic Power Sys�tems, Proc. 35th Annu. IEEE Power Electronics SpecialistsConf., Aachen, 2004, pp. 1957–1963.

2. Koutroulis, E., Kalaitzakis, K., and Voulgaris, N.C.,Development of a Microcontroller�Based. Photovol�taic Maximum Power Point Tracking Control System,IEEE Trans. Power Electron., 2001, no. 16, pp. 46–54.

3. Veerachary, M., Senjyu, T., and Uezato, K., MaximumPower Point Tracking Control of IDB Converter Sup�plied PV System, IEE Proc. Electron. Power Appl., 2001,no. 148, pp. 494–502.

4. Hua, C. and Lin, J., Energy, 2003, pp. 1129–1142.

5. Femia, N., Petrone, G., Spagnuolo, G., and Vitelli, M.,Optimization of Perturb and Observe Maximum PowerPoint Tracking Method, IEEE Trans. Power Electron.,2005, vol. 20, pp. 963–973.

6. Kuo, Y.C., Liang, T.J., and Chen, J.F., Novel Maxi�mum Power Point Tracking Controller for PhotovoltaicEnergy Conversion System, IEEE Trans. Ind. Electron.,2001, vol. 48, pp. 594–601.

7. Hussein, K.H. and Mota, I., Maximum PhotovoltaicPower Tracking: An Algorithm for Rapidly ChangingAtmospheric Conditions, IEE Proc. GenerationTransm. Distrib., 1995, no. 1, pp. 59–64.

8. Yu, G.J., Jung, Y.S., Choi, J.Y., and Kim, G.S., SolarEnergy, 2004, vol. 76, pp. 455–463.

9. Simoes, M.G., Franceschetti, N.N., and Friedhofer, M.,A Fuzzy Logic Based Photovoltaic Peak Power TrackingControl, Proc. IEEE Int. Symp. on Industrial Electronics(ISIE’98), Pretoria, 1998, pp. 300–305.

10. Wilamowski, B.M. and Li, X., Fuzzy System BasedMaximum Power Point Tracking for PV System, Proc.28th Annu. Conf. on Industrial Electronics Society(IECON’02), Sevilla, 2002, pp. 3280–3284.

11. Hiyama, T., Kouzuma, S., and Imakubo, T., Identifica�tion of Optimal Operating Point of PV Modules UsingNeural Network for Real Time Maximum Power TrackingControl, IEEE Trans. Energy Convers., 1995, vol. 10,no. 2, pp. 360–367.

12. Noguchi, T., Togashi, S., and Nakamoto, R., Short�Current Pulse�Based Maximum Power Point TrackingMethod for Multiple Photovoltaic and Converter Mod�ule System, IEEE Trans. Ind. Electron., 2002, vol. 49,no. 1, pp. 217–223.

13. Chu, C.C. and Chen, C.L., J. Chin. Soc. Mech. Eng.,2008, no. 3, pp. 225–231.

14. Duru, H.T., Solar Energy, 2006, vol. 80, no. 7, pp. 812–822.