PV MPPT with Inductor.pdf

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 4, APRIL 2011 1031

A New Approach to Achieve Maximum Power PointTracking for PV System With a Variable InductorLonglong Zhang, Student Member, IEEE, William Gerard Hurley, Fellow, IEEE, and Werner Hugo Wolfle

Abstract—Maximum power transfer in solar microgrid applica-tions is achieved by impedance matching with a dc–dc converterwith maximum power point tracking by the incremental conduc-tance method. Regulation and dynamic control is achieved by op-erating with continuous conduction. It can be shown that understable operation, the required output inductor has an inductanceversus current characteristic, whereby the inductance falls off withincreasing current, corresponding to increasing incident solar ra-diation. This paper describes how a variable inductor whereby theinductor core progressively saturates with increasing current meetsthis requirement and has the advantage of reducing the overall sizeof the inductor by up to 75% and increases the operating range ofthe tracker to recover solar energy at low solar levels.

Index Terms—Impedance matching, maximum power pointtracking (MPPT), microgrid, photovoltaic (PV), variable inductor.

I. INTRODUCTION

THERE have been renewed interests in solar microgrids inrecent years, and thus, led to further studies in maximum

power point tracking (MPPT) [1]–[8]. MPPT in solar photo-voltaic (PV) microgrid systems is normally achieved either bythe perturb and observe method or by the incremental conduc-tance method (ICM). In the ICM approach, the output resistanceof the PV panel is equal to the load resistance as expected fromthe celebrated maximum power transfer theorem; this may beshown by linearizing the I–V output characteristic of a PV panelabout the operating point, as illustrated in Fig. 1. Thus, theequivalent resistance r at the maximum power point is given by

−r = −ΔV

ΔI= RLR =

VP

IP(1)

where RLR is the regulated resistance in order to achieve MPPT,VP and IP are the PV voltage and current at the MPP.

The actual load resistance is matched to r by a buck converterthrough the control of the duty cycle D, the regulated resistance

Manuscript received July 2, 2010; revised September 20, 2010 and August24, 2010; accepted October 10, 2010. Date of current version June 10, 2011.This paper appeared in part at the 2nd IEEE International Symposium onPower Electronics for Distributed Generation System (PEDG), Hefei, Chinain June 2010. This work was supported by the China Scholarship Council underGrant 2009102634.Recommended for publication by Associate Editor J. M.Guerrero.

L. Zhang is with the Institute of Power Electronics, Zhejiang University,Hangzhou 310027, China (e-mail: [email protected]).

W. G. Hurley is with the Department of Electrical and Electronic En-gineering, National University of Ireland, Galway, Galway, Ireland (e-mail:[email protected]).

W. H. Wolfle is with Convertec Ltd., Wexford, Ireland (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2010.2089644

RLR is as follows:

RLR =VP

IP=

1D2

VO

IO=

1D2 RL (2)

where D is the duty cycle of the buck converter and RL repre-sents the microgrid load connected to the PV panel.

The equivalent circuit of a PV module is shown in Fig. 2. Themain equations are summarized in Appendix A.

Consider two levels of illumination intensity at points ©1 and©2 in Fig. 1(c), the current at the MPP decreases going frompoint ©1 to point ©2 that changes the value of the PV resistanceat the MPP. In order to achieve MPPT, the regulated resistanceRLR should be adjusted by changing the duty cycle D in (2).

The buck converter should work in the continuous currentmode (CCM) in order to satisfy (2). In discontinuous conduc-tion mode (DCM), this relationship is not valid and the sta-ble operation of the converter is more complex. In continuousconduction, for a load power change, the duty cycle changestemporarily during a transient, but it reverts to Vout /Vin in thesteady state. On the other hand, in discontinuous conduction,the power is a function of the dead time, and therefore, a differ-ent control strategy is required that involves dual-control mov-ing from CCM to DCM and vice versa. This is particularlytrue for partially shaded conditions [9], where local peaks (forthe shaded regions) in the P–V characteristics exist alongsidethe global peak, the maintenance of continuous conduction inthese areas for low light levels ensures that the MPPT controllercan maintain a stable response.

The minimum inductance in a buck converter in CCM is givenby

Lmin =RL (1 − D)

2fs(3)

where fs is the switching frequency.The average input current in the buck converter IP and output

current IO is as follows:

IP = IO D. (4)

The output current IO is the average current in the inductorof the buck converter.

The minimum inductance may be restated by combining (1)–(4) to yield

Lmin =D(1 − D)VP

2fsIO=

D2(1 − D)VP

2fsIP. (5)

The PV voltage is relatively constant over the full range ofsolar intensity [10] (VP = 41.6 V in the example to follow),thus the minimum inductance is a function of duty cycle D andthe output current of the PV panel IP or a function of duty cycle

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1032 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 4, APRIL 2011

Fig. 1. (a) Maximum power transfer in a PV microgrid. (b) Thevenin equiva-lent circuit. (c) MPPT based on impedance matching.

Fig. 2. Equivalent circuit of a PV module.

D and the inductor current IO that feeds the microgrid undera constant switching frequency (fs = 20 kHz). The characteris-tics of the minimum inductance under different duty cycles areshown in Fig. 3.

Evidently, the minimum inductance to achieve CCM falls offas the solar intensity increases. Conversely, the higher value ofinductance required at light loads may be achieved without in-creasing the volume of the inductor. Variable inductance may beachieved using a sloped air gap, whereby the inductor core pro-

Fig. 3. Characteristics of the minimum inductance under different load con-ditions of the microgrid.

Fig. 4. Comparison of CCM conditions in an MPPT dc/dc converter with avariable inductance.

gressively saturates with increasing current [11]. Alternatively,a powered iron core may be used so that it is progressively sat-urated with increasing current to yield the L–i characteristics ofFig. 4. The use of a reconfigurable inductor in a boost circuitfor PV microgrid applications is described in [12].

In the example described in Section IV, the inductor currentrange is 2.27–4.61 A, corresponding to a solar insolation levelfrom 200 to 800 W/m2 . In this range, the minimum inductorfalls from 111 to 21.3 μH. A conventional inductor would have111 μH at 4.61 A corresponding to a stored energy of 1.2 mJ.With a variable inductor, the stored energy at 111 μH and 2.27A is 0.29 mJ and at 21.3 μH with 4.61 A, the stored energy is0.23 mJ. The size of an inductor is directly proportional to itsstored energy so that the variable inductor would occupy 25%of the volume of a conventional fixed inductor.

II. CHARACTERISTICS OF VARIABLE INDUCTOR

The role of the variable inductor in the stable operation of thebuck converter is explained by reference to Fig. 4. Continuousconduction can only be achieved with inductance values above

ZHANG et al.: NEW APPROACH TO ACHIEVE MAXIMUM POWER POINT TRACKING FOR PV SYSTEM WITH A VARIABLE INDUCTOR 1033

TABLE IPARAMETERS UNDER DIFFERENT LOAD CONDICTIONS

the dashed line in Fig. 4 (the shaded area is off limits). Thelower limit of load current (corresponding to low solar insola-tion) is given by IO 1 as long as the inductance is greater thanL1 . Evidently, at higher currents (and higher insolaton levels),say IO 2 , a smaller inductor L2 would suffice, with the addedadvantage of a reduced volume occupied by the inductor. Con-versely, setting the inductance at L2 would limit the lower loadrange to values of current (and solar insolation) greater thanIO 2 . The variable inductor with the L–i characteristic shown inFig. 4 has the advantages of increasing the load range [12]. Theincreased inductance at low insolation levels maintains con-tinuous conduction, and this, in turn, means that the controlstrategy of the MPPT controller extends to lower power levels;this facilitates the extension of the MPPT algorithm to partialshading.

The voltage across an inductor is related to its flux linkage,and this, in turn, is related to the current, the dependence of theinductance on its current must be taken into account

V =dλ

dt, λ = L(i)i

= Ldi

dt+ i

dL

dt

=(

L + idL

di

)di

dt

= Leffdi

dt. (6)

Leff in (6) is readily found from the L/i characteristic of the in-ductor. The Leff versus current characteristic is more insightful.For the purposes of this paper, we shall use Leff for characteriz-ing the inductor.

III. CIRCUIT SIMULATION

The circuit of Fig. 1 has been simulated for the purpose ofevaluating the response for the variable inductor described inSection IV. The method of simulation is based on the electro-magnetic transient program by Dommel [13]. The simulatedcircuit is shown in Fig. 5. The series coil resistance R, whichhas a damping effect on the inductor current, is included andfor convenience, the solar panels and MOSFET voltage arerepresented by a rectangular waveform with a variable dutycycle.

Fig. 5. Circuit for simulation.

Fig. 6. (a) Internal resistance. (b) Minimum inductance as a function of solarinsolation.


Fig. 7. Schematic of the prototype converter.

Fig. 8. Inductance of the core.

The general solution for the three nodes in Fig. 5, recognizingthat there are no input currents at nodes 2 and 3 is as follows:

⎡⎣ i1(tn )

00

⎤⎦=

⎡⎣Y11 Y12 Y13

Y21 Y22 Y23Y31 Y32 Y33

⎤⎦·

⎡⎣ v1(tn )

v2(tn )v3(tn )

⎤⎦+

⎡⎣ I1(tn−1)

I2(tn−1)I3(tn−1)

⎤⎦ .

(7)The details of Yii and I1(tn−1) are described in Appendix B.

The two quantities of interest are i1 and i3 . The circuit wassimulated for VP = 41.6 V, C = 80 μF, R = 1 Ω, and RL = 8Ω with the inductor described in Section IV and with the dutycycle given in Table I.

Simulation studies were carried out on a 210 W Sanyo HIP PVmodule. The solar insolation was varied from 200 to 800 W/m2 .The results are summarized in Table I for the PV panel voltageVP and current IP at the maximum power point as well as theinternal resistance and the required duty cycle D for continuousconduction at 20 kHz.

The variation in internal resistance at the maximum powerpoint is shown in Fig. 6 (a)and the corresponding value Lmin isshown in Fig. 6 (b).

Fig. 9. Simulation results of inductor current under different conditions: (a)21.3 μH at 800 W/m2 . (b) 21.3 μH at 200 W/m2 . (c) Variable inductor at 200W/cm2 .


Fig. 10. Experimental results of inductor current under different conditions:(a) 21.3 μH at 800 W/m2 . (b) 21.3 μH at 200 W/m2 . (c) variable inductor at200 W/m2 .

Fig. 11. Experimental results of inductor current under 800 W/m2 .

Fig. 12. Response of inductor current under step change in insolation200–800 W/m2 .

IV. EXPERIMENTAL RESULTS AND DISCUSSION

The circuit schematic of the converter used for the experi-mental validation of the role of the variable inductor is shownin Fig. 7.

The variable inductance tested is a MICROMETAL iron pow-der core T68-52 with 72 turns (The mechanical scale is as fol-lows: inside diameter = 9.4 mm, height = 4.83 mm, and corelength = 4.23 cm). The effective inductance of the variableinductor was measured and the results are shown in Fig. 8.

Fig. 9 (a) shows the inductor current for 21.3 μH at 800 W/m2

(see point “a” in Fig. 4) and the current is continuous. Fig. 9(b) shows the inductor current for 21.3 μH at 200 W/m2

(see point “b” in Fig. 4), and as expected, the converter isoperating in discontinuous mode. Repeating the simulation fora variable inductor (see Fig. 8) at 200 W/cm2 in Fig. 9 (c)shows that continuous conduction has been restored. The afore-mentioned simulation results are validated by the experimentalresults shown in Fig. 10.

Fig. 10 (a) and Fig. 10 (b) uses a fixed inductor to illus-trate the effect of CCM at 800 W/m2 and DCM at 200 W/m2 ,


respectively. In Fig. 10 (c), the variable inductor was used andthe onset of CCM is shown as expected at 200 W/m2 . Thesame variable inductor was used at 800 W/m2 in Fig. 11 andthe converter was observed to operate in CCM, however, it wasnot at the boundary of DCM because the inductance value wasapproximately 73 μH (see Fig. 8) and this is higher than thecritical value of 21 μH given in Table I.

Evidently, the MPPT controller with a variable inductance isrobust and reliable over the full operating range. Fig. 12 showsa simulated response to a step change in insolation from 200 to800 W/m2 and the dynamic response is stable.

V. CONCLUSION

This paper presents a new topology of an MPPT controller forsolar microgrid applications that incorporates a variable induc-tance. The salient characteristic of the variable inductor is thatthe inductance decreases with increasing current. This charac-teristic brings the following advantages to the dc–dc converterused for MPPT.

1 The overall size of the inductor is reduced by up to 75%.2 The range of operation is extended for low light levels or

partially shaded solar panels.3 The step response for a change in solar input is stable.

The merit of the paper is the self-adaption of the circuit to alarge range of solar input power (including partial shading). Theaddition of the variable inductance, while maintaining continu-ous conduction with its attendant advantages for the control ofthe circuit, does not affect the stability of a buck dc–dc converterin any way. The step response shows that the system is stable,however, further optimization with regard to regulation couldform the basis for future work.

APPENDIX A

MODEL OF SOLAR PANEL

The solar module output characteristics are represented by anequivalent circuit model in Fig. 2 with the following equations,the parameter values given are for the Sanyo HIP 210 W module.

The output current is given by

I = Iph − Isat [eqV /(nK Tc e l l N s ) − 1] (A1)

whereq charge on an electron (q = 1.6022 × 10−19 C);K Boltzmann constant (K = 1.38 × 10−23 m2 ·kg·s−2

K);n ideality factor (n = 1.5);I output current [calculated in (A1)];Iph photogenerated current [calculated in (A2)];Isat saturation current [calculated in (A3)];

V output voltage;NS number of cells in series (82);RS : series resistance (0.004 Ω);Tcell solar panel temperature (K).

The photo generated current Iph is given by

Iph = IscrefG

Gref[1 + αisc(Tcell − Tref )] (A2)

whereIscref short circuit current at standard conditions (5.57 A);G solar irradiance;Gref reference solar irradiance at standard conditions

(1000 W/m2);αisc short circuit current temperature coefficient (1.67

mA/˚C);Tref reference temperature at standard conditions (298 K).The saturation current Isat is given by

Isat =Iph

eqV /(nK Tc e l l N s ) − 1. (A3)

The open circuit voltage VOC is given as follows:

VO C

= Vocref + αV O C

(Tcell − Tref ) (A4)

whereVocref open circuit voltage at standard operating condi-

tions (50.9 V);αV OC open circuit voltage temperature coefficient

(–0.127 V/˚C).

APPENDIX B

PARAMETERS FOR CIRCUIT SIMULATION

The coefficients in admittance matrix are as follows:

Y11 =1R

Y12 = − 1R

Y13 = 0

Y21 = − 1R

Y22 =1R

+Δt

2LeffY23 = − Δt

2Leff

Y31 = 0Y32 = − Δt

2LeffY33 =

Δt

2Leff+

2C

Δt

tn = nΔt.

Leff must be calculated at i1(tn−1).The current sources Ii(tn−1) are known from past history

I1(tn−1) = 0

I2(tn−1) = I2(tn−2)+Δt

Leff[v2(tn−1)− v3(tn−1)] n= 2, 3 · · ·

I3(tn−1) = I30(tn−1) − I2(tn−1) +v3(tn−1)

RLn = 2, 3 · · ·

I30(tn−1)= −I30(tn−2) −4C

Δtv3(tn−1) n = 2, 3 · · · .

We define the initial conditions of voltages and currents equalto 0.

If i1 results in a negative value, it is reset to zero and I2 andI3 are adjusted, since in reality, the diode D series with the PV


panel as shown in the microgrid setup of Fig. 1 (a) will blockthe current flowing into the PV panel.

ACKNOWLEDGMENT

The authors would like to thank MICROMETALS, Inc., forthe material support. They would also like to thank L. Breuilof the University of Nantes, France, and A. Gambaro of theUniversity of Genoa, Italy, who made significant contributionsto this paper.

REFERENCES

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[6] M. Liserre, R. Teodorescu, and F. Blaabjerg, “Stability of photovoltaic andwind turbine grid-connected inverters for a large set of grid impedancevalues,” IEEE Trans. Power Electron., vol. 21, no. 1, pp. 263–272, Jan.2006.

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Longlong Zhang (S’09) was born in Shandong,China. He received the B.E. degree (first class honor)in electrical engineering and automation and theB.A. degree in english from China University ofPetroleum, Dongying, China, in 2006. He is currentlyworking toward the Ph.D. degree in electrical engi-neering at the Institute of Power Electronics, ZhejiangUniversity, Hangzhou, China. From September 2009to August 2010, he was engaged in research as a jointPh.D. student in Power Electronics Research Center,National University of Ireland, Galway, Ireland.

His research interests include power converters in renewable power systems,system integration and control of fuel cell system.

William Gerard Hurley (M’77–SM’90–F’07) wasborn in Cork, Ireland. He received the B.E. degreefrom the National University of Ireland, Dublin, Ira-land, in 1974, the M.S. degree from the MassachusettsInstitute of Technology, Cambridge, MA, in 1976,both in electrical engineering, and the Ph.D. degreefrom the National University of Ireland, Galway, Gal-way, Ireland, in 1988.

From 1977 to 1979, he was with Honeywell Con-trols, Canada,. From 1979 to 1983, he was with On-tario Hydro. From 1983 to 1991, he was a Lecturer

of electronic engineering at the University of Limerick, Limerick, Ireland. Heis currently a Professor of electrical engineering at the National University ofIreland, Galway, where he is also the Director of the Power Electronics ResearchCentre. From 1997 to 1998, he was a Visiting Professor of electrical engineeringat the Massachusetts Institute of Technology, Boston. His research interests in-clude high-frequency magnetics, power quality, and renewable energy systems.

Prof. Hurley was also engaged with invited presentations in Mexico, Japan,Singapore, Spain, Czech Republic, Hong Kong, China, and U.S. He was the re-cipient of the Best Paper Prize for the IEEE Transactions on Power Electronicsin 2000. He was shortlisted for the National Excellence Award by EngineersIreland in 2010. He has served as a member of the Administrative Committee ofthe Power Electronics Society of the IEEE and was General Chair of the PowerElectronics Specialists Conference in 2000.

Werner Hugo Wolfle was born in Bad Schussen-ried, Germany. He received the Dipl.Ing. degree inelectronics from the University of Stuttgart, Stuttgart,Germany, in 1981, and the Ph.D. degree in electricalengineering from the National University of Ireland,Galway, Galway, Ireland, in 2003.

From 1982 to 1985, he was a Development Engi-neer for power converters in space craft applicationsat Dornier Systems GmbH, Germany. From 1986 to1988, he was a Research and Development Managerfor industrial ac and dc power. Since 1989, he has

been the Managing Director of Convertec Ltd., Wexford, Ireland, which devel-ops high-reliability power converters for industrial applications. He is also anAdjunct Professor of electrical engineering at the National University of Ireland,Galway.

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PV MPPT with Inductor.pdf