Maximum power point trackerr

for a multiple-input Cukde-de converterSungwoo Bae 1 and Alexis Kwasinski

Dept. of Electrical and Computer Eng., The University of Texas at Austin, USA'F-mail: sbae@mail.utexas.edu

Abstract - Photovoltaic modules require a maximum powerpoint tracker in order to achieve maximum conversion efficiencywhen the maximum power point changes based on solarirradiance, tem perature, cells age, and other factors. The need totrack the maximum power point while combining multiple-inputsources has stimulated research on maximum power pointtrackers for multiple input de-de converters. When compared toprior work, a multiple-input Cuk de-de converter seems to be anadequate choice when combining PV modules with alternativeenergy sources, such as fuel cells, because it provides currentsource interface and is capable of stepping up and down inputvoltages. This paper proposes a multiple-input Cuk de-deconverter topology. Ripple correlation control is used to find themaximum power point of a photovoltaic array.

I. INTRODUCTION

A multiple-input (MI) converter allows a variety of energysources to combine their inputs using a single commonconverter. Future distributed generation-based power systemsmay require combining input sources using MI converters,which increases systems' flexibility as hybrid systemsintegrating different renewable and alternative energy sources,such as wind turbines and photovoltaics (PV), become morecommon. An MI converter has advantages over a combinationof single-input converters in terms of reduced components,compactness and centralized control [1].

Photovoltaic modules require a maximum power pointtracker in order to achieve maximum conversion efficiencywhen the maximum power point changes based on solarirradiance, temperature, cells age, and other factors. Inaddition, PV systems may typically need another source tocompensate incident energy variations. The need to track theMPP while combining multiple-input sources has stimulatedresearch on MPP trackers for MI de-de converters [2-4]. Incomparison to prior work, an MI Cuk de-de converter seemsto be an adequate choice when combining PV modules withalternative energy sources, such as fuel cells, because itprovides current source interface and is capable of stepping upand down input voltages.

This paper proposes an MI Cuk de-de converter topologywith nearly continuous input current waveforms and highflexibility; and investigates an MPP tracker for an MI Cukconverter using ripple correlation control (RCC) [4-7]. RCC ischosen because of its good performance and simplicity.

II. MULTIPLE-INPUT CUK DC-DC CONVERTER

Fig. 1 shows the proposed MI Cuk de-de convertertopology which has advantages when compared to previousMI buck-boost converters [8-11]: continuous input current andhigh flexibility [12, 13]. The proposed MI Cuk de-deconverter provides nearly continuous input current waveformsbecause each input leg has a current-source interface. Hence,the proposed converter provides more operational flexibilitythan those other similar topologies because it allows theintegration of input sources that require a relatively constantcurrent, such as fuel cells [14].

I

"'KJut•

Fig. 1. Proposed MI Cuk de-de converter

Fig. 2. Switching strategy

A. Formulae for Steady-State Operationin Continuous Conduction Mode

Assume all gate control signals whose initial edges aresynchronized at a fix switching frequency as shown in Fig. 2[9]. A capacitor in each input cell transfers the energy betweenan input and an output; consequently, the charges delivered toa transfer capacitor through an input inductor are equal to the

(3)

(13)

(12)

(11)

where D 1 is the duty cycle for the leg with an alternativesource ~nl; and D2 is the switching corresponding to the legwith a PV source ~n2. It is assumed that ~n] > ~n2.

The average input currents and input powers for each legare as follows:

D1lin 1 =--lout (10)

I-DzD Zeff

I inZ =--1 t1-o, au

T,T [ Dl~ut )~nl = YinlDl~nl + Deffz~nl

[

Deffz~ut )~nZ = ~nZ

D 1~nl + D eff z ~nl

where Ln] and Pin] are the average input current and the inputpower of an alternative source ~nl; Ln2 and P in2 are the averageinput current and the input power for the leg with a PV source~n2 respectively.

where De.r{(i) is the effective duty cycle of each input cell, i.e.the effective time in which switch (i) is conducting current [9].As assumed in [9], if the voltage indices are arbitrarily orderedsuch that V]> V2> ... > VN , then

charges dissipated through a sharing output inductor [12].Thus, the following equation is obtained at node A of thecommon output stage (Fig. 1).

N

lin (i) (1- Deff(i») =(L lin(J) + lout )Deff(i) (1)j r-i

The average input current for a generic leg, Ln(i), can beobtained by solving the N equations derived from (1):

I = Deff(i) Deff(i) I

in(i) 1-"'D . lout =1- (D.) out (2)L..J eff(j) m~x 1j 1

If ideal lossless components are assumed, the averageoutput voltage can be obtained from the energy conversion

rule (L ~n(i)Iin(i) = ~utlout) •

N

L Deff(i)~n(i)V = _i=_1 _

out 1- m~x(Di)1

B. Formulae for a maximum power point tracker

If a two input case is considered for simplicity, the steadystate output voltage for continuous conduction mode and idealcomponents is given by

»r: +Dzeff~nzV = (8)

out 1-o,D Zeff =o,- D 1 (9)

Fig. 3. Overall control scheme

Voutrej

C. Alternative Operational Modes

The proposed MI Cuk de-de converter can be used in abidirectional operation mode because a Cuk converter iscompletely symmetrical with respect to the input and outputterminals [12]. Thus, the proposed MI Cuk de-de convertercan be operated in bidirectional mode if the diode D in thecommon output stage is replaced with a switch and theappropriate control signals are applied to each switch.

III. CONTROL

Alternativesource Vin l

A. Overall Control Scheme

Fig. 3 depicts the overall control scheme in the proposedMI Cuk converter. To regulate the output voltage andsupplement the required load power, a proportional integralcontroller is used in input leg #1. It is assumed that the PVmodule is connected to input leg #2. In some cases, a PV arrayis not able to reach the MPP with this control in MI convertersstrategy because D2e.r{ cannot be controlled in a fullyindependent way.

(4)

(6)

(7)

i-I

, D i < L Deff(J)j=1

o

~n(i) = ~n(i)

Deff(i) = i-I i-I

D i - L Deff(i) ,Di ~ L Deff(J)j=1 j=1

The output voltage ripple is

Av J:z (1- m~x(Di)) n? (1- m~x(Di))(f JZa _ 1 _ 1 c (5)

Va 8LC 2 IsThe output voltage ripple can be minimized if the comer

frequency fc of the output filter is made significantly smallerthan the switching frequency Is [15].

The power supplied by each input is obtained from theproduct of the average input current given in (2) and the inputvoltage ~n(i):

p V [ Deff(i) I)inU) = Inri) I-m~(Di) out

If the output power Pout= Vourlour is plugged into (6), eachinput power is given by

B. Ripple Correlation Control

The switching action of the power converter attached to aPV array produces voltage and current ripple on the PV array.Hence, the PV array's power has also ripple due to theswitching action. Ripple correlation control (RCC) usesinformation contained in the current and voltage ripple of theconverter to track the PV array's MPP [3, 5-7].

According to [7], the time derivative of the time-varying

PV array power p is correlated with the time derivative of the

time-varying PV array current i or voltage ~. As indicated in

Fig. 4, if v or i is increasing (~> 0 or i> 0) and p is increasing

(p > 0), then the operating point is below the MPP (V < VMPP

or I < I MPp ) . On the other hand, if v or i is increasing ( ~ > 0 or

i > 0) and p is decreasing (p < 0), the operating point is

above the MPP (V> VMPP or I> IMPp ) . Thus, RCC tracks the PV

array's MPP based on the fact that p~ or pi is positive

below the MPP, negative above the MPP, and zero at the MPP.From (8) and (11), the increase on the effective duty cycle

D2e.ff of the input leg #2 also increases the average input current,but reduces the average input voltage. Hence, increasing theeffective duty cycle d2e.g(t) increases iin2(t), but decrease Vi1l2(t).Therefore, the effective duty cycle for the converter, which theRCC system is controlling, is given by

d (t) =-kJp' v dt (14)2eff in2 in2

or

d2ejf(t)

= kfp:n 2

ii~2 dt (15)

where k is a positive constant. Equation (14), rather than (15),was chosen to implement the RCC controller because theinput filter capacitor on the terminals of the PV array causes aphase shift in the current ripple at high switching frequency[3].

P

PMPP - - - - - - - - - - - - -

vMPP or IMPP V or I

Fig. 4. PV array's P-V and P-I characteristic curves

IV. RESULTS

A. Experimental Resultsfor Validating the Proposed Circuit Topology

A two-input Cuk de-de converter operating in continuousconduction mode was investigated without loss of generality

and for simplicity. Each input inductance was 402.1 flH (45mfz). The common output inductance was 300.2 ul-l (31 mfz),These inductors were realized with Micrometals [16] T300D­26 cores. The series capacitors in each input were high­frequency, 50-V, 33-flF electrolytic capacitors. The outputcapacitor was a 250- V, 1500-flF electrolytic capacitor. TheMOSFETs were 100-V, 31-A Fairchild IRFP140A and thediodes were Fairchild FESI6DT. The switching frequencywas fixed at 50 kHz.

Fig. 5 shows the ideal and measured output voltages incontinuous conduction mode. The output voltages weremeasured when the D2 was fixed at 0.5 and the D1 was varied.The input voltage of source 1 was 10 V, while the inputvoltage of source 2 was 5 V. In Fig. 5, the measured andcalculated data show the same trends. Diodes and seriescapacitors losses may be the main contributors to thedifferences in results.

14.00

12.00

E 10.00~OJ)

~ 8.00;,

1 6.00

-=o4.00

2.00

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

D1

Fig. 5. Output voltage in CCM (D} varied while D2=O.5)

Fig. 6 shows input current waveforms in continuousconduction mode. The input voltages were applied as in Fig. 5,but the D 1 and D2 were adjusted at 0.25 and 0.5. The inputcurrent waveforms (Ch3, Ch4), corresponding to each of theinputs (10V, 5V), can be seen with the switching functions(ChI, Ch2) in Fig. 6. Each input current waveform iscontinuous as expected. Fig. 7 shows the shared inductorcurrent (Ch2), the input currents (Ch3, Ch4) and the outputvoltage (ChI) at the same condition of Fig. 6. In Fig. 7, thetwo different increasing slopes in each current (Ch2, Ch3, andCh4) reflect the influence of each dissimilar input source (10V, 5V) during its effective duty cycle.

Fig. 6. Input currents and switching functions (qI,q::)

,,/~PV oytput pow-er

~4.2Cl.)

~3.6

~3.0cd~2.4

>1.8~

1.2

0.6

0.00

6.6 88------------6.0 -~-----____ ;' /\ 80

5.4 PV array curre~~ '.., 72", -"'\1

1~

<4.8 ./ \\ 64-<\\ 56~\\ ~

\\ 48"S-\\, 40-g

\\ 32 ~\\ ~

\,, 2 4 :E\;'1, 16~

'1;1

~8

2 4 6 8 10 12 14 16 180

PV array voltage [V]Fig. 8. I-V and P-V characteristics for the simulated PV circuit model

CH3Mean

326mA

MEASURE

MATH OftNone

M Pos:O,OOOs

WI 5.00»s10-Jan-m 07:35

JL.Tek

CH3+'OOmA

PV+

0.463 0

20013.60

14.40

6.5A tCH3

Mean327mA

MEAStH

:~ ~~~. if:ll.!ll',I, M5.00..usCH3+1()()rnA CH~ .. 100mA lo-Jan-GS 07:51

Ext r 2.38VSO,647tti1l Fig. 9. PV's circuit based model

PV -

Fig. 7. Current and output voltage waveforms

B. Simulated Photovoltaic Circuit Modelfor a Maximum Power Point Tracker

The I-V characteristic of a PV array is non-linear. Severalmodels have been proposed for modeling PV arrays in theliterature. For the simulation, a circuit-based model waschosen in this paper that uses a current source with threediodes and bypass resistors connected in series [17].

Fig. 8 shows I-V and P-V characteristics of the simulatedPV circuit based model in Fig. 9. One can see that themaximum power for this PV model is about 82 Watts. As thevoltage of the PV terminal increases, the current alwaysdecreases in this model. This means that there are no localmaximum power points, so the MPPT in this paper should beable to find the only true global maximum power point (MPP).This paper will not consider the somewhat rare problem oflocal maximum power points. The PV I-V curves in Fig. 8 areonly valid for one particular state of a PV cell or array. Forexample, if the solar irradiance decreases, the whole I-V curvewill shift down. In the circuit model simulation, it is assumedthat the I-V characteristics stay constant throughout theoperation.

C. Simulation Results for a Maximum Power Point Tracker

The same two-input Cuk de-de converter investigated inthe previous experimental section was used to simulate amaximum power point tracker. The switching frequency wasfixed at 20 kHz. To supplement the required load power, a 30­V de voltage source was used in input leg #1 with aproportional integral controller. The PV array whosecharacteristics are shown in Fig. 9 was connected to input leg#2. The output reference voltage was set to 24 Volts.

Fig. 10 shows the inputs and output of the RCC blockduring the simulation. As indicated in Fig. 10, RCC blockoutput (d2eff) is increasing while PV output power (Pin::) isincreasing and PV panel voltage (~n::) is decreasing. Thus, theoperating point of a PV array is moving toward the MPPbased on (14). After the transient response, RCC block output(d2eff) is settled at 0.13 and the PV array is operated at theMPP (82 Watts).

Fig. 10. RCC block output (d::e.f{) vs PV's output power and PV's voltage

The MI Cuk converter's output voltage (Vout) and the PVarray's output power (Pin2) during the transient response areshown in Fig. 11. As indicated in Fig. 11, the PV arrayreached the MPP at 82 Watts and the output voltage wasregulated to 24 Volts, same as the output reference voltage.

21 --96

°1 8 8

~ =:1"\\ PV outp~ower(Pin;) ~ ~.:@ -8· \ 56 -g~ -10 j \ 48 .;-

-g -12 1 \ 40 ~.g -14 \ ': 32 ~~ -16 ..\ 24~

;:::s 18 j " . 16 ~ j...u - '\ -~ -20 ~ -. '.' \. 8 ~

:;s -221Ii,' \--- Output voltage (VOlt!) 0 2§-24 ~~'---~"'~~~~-----~~-~~----'-'--'-'---.-"'---.-.-- -8

-260 4 8 12 16 ao 24 28 3'2 36 16

Simulation time [ms]

Fig. 11. MI CUk output voltage and PV output power (Pin::)

V. CONCLUSION

A steady-state analysis of the MI Cuk de-de convertertopology was investigated for renewable and alternative powerconversion systems. The analysis was based on continuousconduction mode and ideal components. Experimental resultswere presented for a two-input case to validate the circuittopology.

A maximum power point tracking method based on ripplecorrelation control was presented for an MI Cuk converterwith a photovoltaic input (Pin::). A de power source (PinJ) wasused in input leg #1 with a proportional integral controller toregulate the output voltage and to supplement the requiredload power. Compared to previous MI buck-boost converters,the proposed MI Cuk converter seems to be an adequatechoice when combining PV modules with alternative energy

sources, such as fuel cells, because it provides current sourceinterface and is capable of stepping up and down inputvoltages.

REFERENCES

[1] H. Tao, A. Kotsopoulos, 1. L. Duarte, and M. A. M. Hendrix,"Family of multiport bidirectional DC-DC converters," ElectricPower Applications, lEE Proceedings -, vol. 153, pp. 451-458,2006.

[2] H. Matsuo, K. Kobayashi, Y. Sekine, M. Asano, and W. Lin,"Novel solar cell power supply system using the multiple-input DC­DC converter," in Telecommunications Energy Conference, 1998.INTELEC. Twentieth International, 1998, pp. 797-802.

[3] N. D. Benavides, T. Esram, and P. L. Chapman, "RippleCorrelation Control of a Multiple-Input De-De Converter," inPower Electronics Specialists Conference, 2005. PESC '05. IEEE36th, 2005, pp. 160-164.

[4] L. Bin and A. Kwasinski, "Analysis of a flexible and ruggedphotovoltaic-based power system," in Telecommunications EnergyConference, 2008. INTELEC 2008. IEEE 30th International, 2008,pp.I-7.

[5] P. Midya, P. T. Krein, R. 1. Turnbull, R. Reppa, and 1. Kimball,"Dynamic maximum power point tracker for photovoltaicapplications," in Power Electronics Specialists Conference, 1996.PESC '96 Record., 27th Annual IEEE, 1996, pp. 1710-1716 vol.2.

[6] P. T. Krein, "Ripple correlation control, with some applications," inCircuits and Systems, 1999. ISCAS '99. Proceedings of the 1999IEEE International Symposium on, 1999, pp. 283-286 vol.5.

[7] T. Esram and P. L. Chapman, "Comparison of Photovoltaic ArrayMaximum Power Point Tracking Techniques," Energy Conversion,IEEE Transaction on, vol. 22, pp. 439-449,2007.

[8] H. Matsuo, L. Wenzhong, F. Kurokawa, T. Shigemizu, and N.Watanabe, "Characteristics of the multiple-input DC-DCconverter," Industrial Electronics, IEEE Transactions on, vol. 51,pp. 625-631,2004.

[9] B. G. Dobbs and P. L. Chapman, "A multiple-input DC-DCconverter topology," Power Electronics Letters, IEEE, vol. 1, pp. 6­9,2003.

[10] N. D. Benavides and P. L. Chapman, "Power budgeting of amultiple-input buck-boost converter," Power Electronics, IEEETransactions on, vol. 20, pp. 1303-1309,2005.

[11] A. Khaligh, "A multiple-input de-de positive buck-boost convertertopology," in Applied Power Electronics Conference andExposition, 2008. APEC 2008. Twenty-Third Annual IEEE, 2008,pp. 1522-1526.

[12] S. Cuk and R. D. Middlebrook, "Advances in Switched-ModePower Conversion Part I," Industrial Electronics, IEEETransactions on, vol. IE-30, pp. 10-19,1983.

[13] S. Cuk, "A new zero-ripple switching DC-to-DC converter andintegrated magnetics," Magnetics, IEEE Transactions on, vol. 19,pp. 57-75, 1983.

[14] O. H. A. Shirazi, O. Onar, and A. Khaligh, "A novel telecom powersystem," in Telecommunications Energy Conference, 2008.INTELEC 2008. IEEE 30th International, 2008, pp. 1-8.

[15] N. Mohan, T. Underland, and W. Robbins, Power Electronics;Converters, Applications, and Design, 3rd ed.: John Wiley andSons, 2003.

[16] Micrometals, Inc. (2008) Iron powder cores. Tech. Rep. [Online]Available: http://www.micrometals.com

[17] R. C. Campbell, "A Circuit-based Photovoltaic Array Model forPower System Studies," in Power Symposium, 2007. NAPS '07.39th North American, 2007, pp. 97-101.