Direct Duty Ratio Controlled MPPT Algorithm forBoost Converter in Continuous and Discontinuous

Modes of OperationPallavi Bharadwaj, Vinod John

Department Electrical Engineering, Indian Institute of Science Bangalore

Abstract—Demand of increased lifetime, compact size andreduced cost of PV systems has led to the incorporation of LCLfilters in the boost converter of a grid connected PV system.Additional filtering offered at the input by LCL filter reduces theinductance of boost converter. This calls for an algorithm whichcan track the maximum power in both discontinuous (DCM)and continuous conduction modes (CCM) of boost converteroperation accurately. Direct duty ratio based perturb and observealgorithm for MPPT has been implemented in real time usingVHDL based FPGA. The sensitivity of the algorithm to DCMand CCM operation of converter is analysed. It is shown thatthe duty ratio increment used in the MPPT algorithm needs toevaluate. The direct duty ratio based approach is found to workwell with both modes of operation, even with mode transitions.

Index Terms—Solar, photovoltaic, maximum powerpoint tracking (MPPT), boost DC-DC converter,continuous/discontinuous conduction mode, perturb andobserve (P & O).

I. INTRODUCTION

Power converters are normally connected at the output ofPV panels as an interface between panel and load. Use of DC-DC converters such as buck, boost and cuk converter have beenreported in literature. Buck converter as used in [11], may notbe suitable for low voltage PV systems, specially when gridconnection is involved. Cuk converter as used in [10], requiresan additional set of LC filter as compared to buck and boostconverters. In this work boost converter has been used as thePV system has an MPP voltage of 15V and DC bus voltageneeds to be higher for grid connection through an inverter. AnLCL filter has been included at the input of the boost converterwhich reduces the inductance of boost, which can further leadto design of an optimised converter having low cost, low sizeand high efficiency. But low inductance also leads to DCMoperation, therefore need arises for a robust MPPT algorithmwhich has tracking ability with mode transitions involved.

Maximum power point tracking (MPPT) is a method ofobtaining the maximum possible power out of static solarpanels for given irradiation and temperature conditions. Someof the commonly used MPPT techniques include perturband observe (P & O) algorithm, incremental conductancealgorithm, open circuit voltage and short circuit current basedmethods [7]. P & O is widely used in PV MPPT applications

This work is supported by Department of Information Technology, Govt ofIndia under NaMPET Phase 2 under Project on Mini Full Spectrum Simulator.

PVmodule

L D

Cdc

R0

Cf

Ls Rs

Sw

Req

Inverter

grid

Fig. 1. Circuit diagram of grid connected PV system.

because it is relatively simple and has real time tracking abilityof MPP [7]. P & O algorithm has several variations basedon control parameter involved. First is the voltage based P& O which is the most common [8], [10]–[12]. Second oneinvolves current perturbation instead of voltage [9]. In boththese methods duty ratio is commonly used as an indirectvariable to actually change the voltage or current [11]. Thirdkind of P & O is called as direct duty ratio control [8],[13], wherein duty ratio is the direct control variable and itundergoes step changes in order to achieve MPPT. Currentperturbation method is not commonly used as it involves shortcircuit current measurement, which poses difficulty in practicalimplementation. Out of voltage based and direct duty ratiobased P & O methods latter one is preferred for this workas direct duty ratio control offers better energy utilisation andimproved system stability than reference voltage control [8].

The main focus of this work is the detailed study of directduty ratio based algorithm, to study its behaviour for differentmodes of converter operation namely - continuous conductionmode (CCM) and discontinuous conduction mode (DCM). Ithas been shown that duty ratio based algorithm is effective forboth modes of operation for boost converter.

II. DUTY RATIO BASED MPPT ALGORITHM

A. Theoretical background

Fig. 1 shows a grid connected PV system wherein a PVpanel feeds a boost converter with input LCL filter, whichfurther feeds the grid via inverter. The input LCL filter consistsof stray inductance Ls and resistance Rs of cables connectingpanel on roof, to the converter located in laboratory. Addi-tional capacitor Cf and boost inductor L together form LCL

0 5 10 150

10

20

30

V(V)

P(W

)

0 5 10 150

2

4

V(V)

I(A

) d decd inc

- - load line--- panel characteristic

Fig. 2. Determination of operating point of a solar PV panel dependson irradiation, temperature and terminal load resistance. The projection ofoperating point is taken on panel’s Power-Voltage curve, shown for threeloading conditions obtained by operating at 3 different duty cycles.

filter. This combined LCL filter acts as an attenuator to highfrequency boost inductor current ripple and effectively onlyDC current flows from the PV source thereby enhancing itsefficiency. Due to the incorporation of LCL filter in the circuitboost inductor value can be reduced for same ripple current.This gives reduced cost and size benefits. However reductionin L value may cause discontinuous mode of operation ofboost converter. So the MPPT algorithm needs to have MPPtracking ability in both DCM/CCM. For this the working ofdirect duty ratio MPPT algorithm is analysed in continuousand discontinuous modes of operations of boost converter.

The basic principle behind any MPPT algorithm is digitalcontrol of converter in such a manner that the load seenby PV panel corresponds to the maximum possible poweroutput for any given load. Consider the current-voltage andcorresponding power-voltage characteristic of a PV panel,as shown in Fig. 2. The operating point is obtained by theintersection of solar panel’s current-voltage (I-V) curve andload line which is dependent on load connected. The solarpanel terminal equation [1] is written as

I = IL − Is(eV +IRsmnsVt − 1) − V + IRs

Rsh(1)

And the equation of load line for a load resistance ‘R’ can bewritten as

I = V/R (2)

The intersection of the two above mentioned equations isshown in Fig. 2 for three different cases of load resistance. Thecurrent gain, voltage gain and equivalent resistance reflectedat the source terminals depends on the mode of operation ofthe boost converter, as given in Table I. Symbols shown inTable I are:- k = 2L

RoTs, Ro =output resistance, Ts =switching

period, L = boost inductance, d = duty ratio of switch Sw =Ton

Toff+Ton. To visualise the effect of duty ratio on equivalent

resistance (Req) it is plotted in Fig. 3 for CCM mode andDCM mode. In DCM the equivalent resistance is dependenton ‘k’, therefore it is shown for two different values of ‘k’.

TABLE ICOMPARISON OF GAINS AND EQUIVALENT RESISTANCE FOR CCM AND

DCM OPERATION FOR A BOOST CONVERTER.

Equivalent Resistance CCM DCM

Current Gain (1− d)

(k +√k2 + 4kd2

2d

)(d+k +√k2 + 4kd2

2d

)Voltage Gain

1

(1− d)

(d+k +√k2 + 4kd2

2d

)(k +√k2 + 4kd2

2d

)Equivalent Resistance Ro(1− d)2 Ro

(k +√k2 + 4kd2

2d

)2

(d+k +√k2 + 4kd2

2d

)2

TABLE IICIRCUIT PARAMETERS FOR THREE DIFFERENT BOOST CONVERTER

CONFIGURATIONS

Case k Ro L TsA 0.024 160Ω 100µH 50µsB 0.14 200Ω 700µH 50µsC 0.16 300Ω 1200µH 50µs

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

1

Duty Ratio (d)

Req

/Ro

CCMDCM, k = 0.024DCM, k = 0.140

Fig. 3. Variation of equivalent resistance with duty ratio in CCM mode andDCM mode.

For values of ‘k’ higher than 0.15 converter operates in CCMalways and equivalent resistance in CCM mode is independentof ‘k’. In this paper analysis is done for 3 cases of boostconverter configurations corresponding to the three differentcombinations of Ro, L and Ts values. These are listed in TableII.

As discussed before, operating point of a PV panel de-pends on the panel’s current-voltage characteristic (for giventemperature and irradiation condition) and the load line. Theslope of the load line is inverse of equivalent resistance asseen by the PV panel. From Table I it can be observed thatReq is a function of duty ratio. By changing the duty ratio ofthe boost converter, operating point for the PV panel can becontrolled. For a particular set of load resistance, inductanceand switching frequency of the boost converter, there willbe a range of duty ratio for which converter will operate in

0.2 0.4 0.6 0.8 1

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

DutyCRatio(d)

d×(1

-d)2

d(1-d)2 vsCd

LC=C700µ

H,CRCo=C200ΩLC=C100

µH,CRCo=C160

ΩLC=C1200µH,CRCo=C300Ω

kC=C0.14

kC=C0.16

kC=C0.024

CCM

CCM DCM CCM

DCM DCM DCM CCMCCM

Fig. 4. DCM-CCM boundary is given by the intersection of d(1−d)2 = k =2L

RoTsfor boost converter. Here duty ratio range for CCM/DCM operation

are shown for three different sets of Ro, L values, with Ts fixed at 50µs.

CCM and in DCM for remaining range. CCM-DCM boundarycan be observed in Fig. 4, wherein three cases are showncorresponding to the ones listed in Table II.The parameter ‘k’ is directly proportional to inductance andswitching frequency. The value of ‘k’ falls for small inductancevalue as well as lower switching frequency. Lower inductancevalue leads to lower size as well as lower cost of converter.Also, the filtering objective can be met with a smaller inductorL, and this can also lead to higher efficiency. However if ‘k’value is small then range of DCM operation is large. If MPPcan be tracked effectively in DCM then the converter cost andsize can be minimised and higher efficiency can be achieved.

From Fig. 4 it is clear that for a given duty ratio, theoperation of converter in CCM or DCM mode is determinedby Ro, L, Ts values. Whether MPP falls within the rangespanned by ‘d’ variation in CCM region or DCM region,solely depends on Ro, L, Ts values. Also it can be observedfrom Table I and Fig. 3 that duty ratio affects the equivalentresistance differently in DCM and CCM. In other words, theeffect of duty ratio variation on the slope of load line differsfrom CCM to DCM. This effect is discussed in detail inFig. 5 corresponding to three different converter configurationsnamely case A, B and C as specified in Table II and for twodifferent conditions for solar panel irradiation. Solar panel wasirradiated with Sun and a 500W hallogen lamp separately toget different characteristics of 10W polycrystalline solar panel[4]. Consider case A of boost converter operation as specifiedin Table II. Owing to low value of ‘k’ DCM operation isobserved for a wide range of duty ratio from 0.05 to 0.85 asshown in Fig. 5(a). This is as expected from Fig. 4. For case B‘k’ value is higher, this gives narrow range of DCM operationas shown in Fig. 5(b). However for case C as ‘k’ value is largeenough, it doesnot intersect CCM-DCM boundary as shownin Fig. 4. Thus Fig. 5(c) shows complete CCM operation asduty ratio varies from 0 to 1. It can be observed that forboth CCM and DCM operation as d increases the slope ofload line increases, therefore even if there is a transition fromCCM to DCM still complete I-V curve can be traced. However

0 5 10 15 200

5

10

15

20

25

30

V(V)

P(W

) P increasesV increases

MPP

P decreases

V increases

W

X Y

Z

Fig. 6. Power voltage characteristics for an array of PV panels, marked withMPP and a boundary which divides two sides of hill. W, X, Y, Z mark fourpossible operating points on the power - voltage curve.

accuracy of tracking MPP will differ. This calls for definationof a term called as sensitivity of MPP tracking. This is definedas change in power compared to change in duty ratio aroundMPP. Sensitivity can be physically interpreted by how denselyload lines cover MPP region. Higher density corresponds tohigher sensitivity. Fig. 5(a) shows better sensitivity comparedto Fig. 5(b). Fig. 5(a) also corresponds case A with lowerinductance value compared to case B with higher inductance.Therefore for a system, selection of L can be done consideringeffective range of Ro which for this case is Ro ≥ 160Ω, assmaller L can give both cost and MPPT benefits.

Sensitivity can also be improved by going for a smallerstep size ∆d, but this increases tracking time. As step size isreduced from 0.05 in Fig. 5(c) to 0.01 in Fig. 5(d) sensitivityimproves from 0.15W for 0.05 to 0.02W for 0.01. Last twocases shown in Fig. 5 correspond to laboratory setup whereinbetter control over irradiation conditions is achieved by usinga hallogen lamp. Results for step size of 0.05 are shown inFig. 5(e) and for 0.01 in Fig. 5(f) showing better sensitivity.

B. The MPPT algorithm

Consider power-voltage curve of a PV panel as shown inFig. 6. On left side of MPP, power (P) and voltage (V) are inphase, on right side power and voltage are out of phase [3]. Bymaking a small perturbation in the duty ratio, a new operatingpoint is obtained. If P and V increase with this perturbationthe operating point is in the left side of MPP, and furthermovement in the direction of perturbation will lead it to topof the hill. If P reduces with perturbation, V either increasesor decreases. In both cases the direction of ‘d’ perturbationneeds to be changed. From Section II-A it is known that as‘d’ increases load line moves up in anti-clockwise direction.These facts can be combined in a flowchart as given in Fig. 7.Fig. 7 shows that for a ‘∆d’ there are 4 possibilities for powerand voltage to increase or decrease. Based on changes in Vand P one can judge the way the operating point has moved onthe sides of hill, and then increase or decrease ‘d’ further toreach the top of the hill which corresponds to the MPP. HereW, X, Y, Z correspond to operating points shown in Fig. 6.

0 5 10 15 20

0.20.40.60.81

I(A)

V(V)

0 5 10 15 200

10

20

P(W)

V(V)

DCM

(a)

0 5 10 15 200

0.20.40.60.8

I(A)

V(V)

0 5 10 15 200

10

20

P(W)

V(V)

DCM

(b)

0 5 10 15 20

0.20.40.60.81

I(A)

V(V)

0 5 10 15 200

5

10

P(W)

V(V)(c)

0 5 10 15 200

0.20.40.60.8

I(A)

V(V)

0 5 10 15 200

5

10

P(W)

V(V)(d)

0 5 10 150

0.1

I(A)

V(V)

0 5 10 150

1

2

P(W)

V(V)(e)

0 5 10 150

0.1

0.2

I(A)

V(V)

0 5 10 150

1

2

P(W)

V(V)(f)

Fig. 5. Measured Current-Voltage (I-V) characteristics of 10W solar panel superimposed with family of load lines for varying duty ratio for a boost converter.Duty ratio increases from 0 to 1 in fixed step ∆d. (a) Case A : Ro = 160Ω, L = 100µH , Ts = 50µs. ∆d = 0.05. Projection on P-V curve shows DCMoperation for d = 0.05 to 0.85. (b) Case B : Ro = 200Ω, L = 700µH , Ts = 50µs. ∆d = 0.05. Projection on P-V curve shows DCM operation for d =0.25 to 0.40. (c) Case C : Ro = 300Ω, L = 1200µH , Ts = 50µs. ∆d = 0.05. For complete d variation only CCM operation observed. Projection onP-V curve shows MPP region (d = 0.60-0.65). (d) Same as (c) with ∆d = 0.01. Projection on P-V curve shows MPP region covered more densely (d =0.62-0.64). MPP occurs at d = 0.63. (e) Case C, ∆d = 0.05, MPP region projected on P-V curve. (f) Boost converter case C. ∆d = 0.01. MPP tracked withhigher accuracy at d = 0.25. Panel’s I-V and P-V curve shown in (a), (b), (c) and (d) measured on 15/11/13, 12:30pm, Bangalore, panel temperature 40oC.Panel’s I-V and P-V curve in (e) and (f) measured with panel irradiated with 500W hallogen lamp placed at 0.3m height from panel.

OUT dn

IN Vn, InPn = Vn˟In

IS Pn>Pn-1

IS Vn>Vn-1

W to X Z to Y Y to Z X to W

ISVn>Vn-1

dn = dn-Δd dn = dn+Δd dn = dn-Δddn = dn+Δd

yes no

yes no yes no

Fig. 7. Flowchart for duty ratio based P & O MPPT algorithm.

TABLE IIIBOOST CONVERTER PARAMETERS

Output Load Resistance (Ro) 300ΩBoost Inductance (L) 1.2 mH

Switching Frequency (fsw) 20 kHzInput Filter capacitance (Cf ) 150 µF

Output Filter capacitance (Cdc) 4400 µFInput Stray Resistance (Rs) 22.23 mΩInput Stray Inductance (Ls) 7.08 µH

C. Implementation and results

1) Implementation: This algorithm was coded in VHDLand implemented on a FPGA platform, which further con-trolled the boost converter fed by a 10W PV panel via a LCLfilter. The LCL filter ensures that boost inductor current rippleis not carried over to the PV panel and hence leads to panel’slong life. To emulate sun, a 500W halogen lamp is arranged,which irradiates the panel at a distance of 0.3m. The intensityof light is controlled by an autotransformer which feeds thehalogen lamp. Converter parameters are chosen so as to ensureCCM operation throughout duty ratio variation, they are givenin Table III, circuit diagram along with MPPT block is shownin Fig. 8. Hardware setup is shown in Fig. 9.

2) Results: Table IV shows the results with the experimen-tally tracked maximum power point for laboratory setup. Thisincludes a 10W polycrystalline PV panel irradiated with a500W halogen lamp. Boost converter specifications are givenin Table III. Table IV quantifies the tracked maximum powerpoint for the given setup. Fig. 10 shows maximum power

PVmodule

L D

R0Cf

Ls Rs

Sw

MPPTI

Ipv

Vpv

V d

Cdc V0

Fig. 8. Circuit showing implementation of MPPT.

HalogenFLamp

10WFPVFPanel

InverterF+FBoostFConverter ResistiveFLoad

1.2mHFInductor

FPGA

ACFVariac

Fig. 9. Hardware setup for MPPT.

TABLE IVRESULTS WITH MPP TRACKED

Input Voltage 16.6VInput Current 0.12ADuty Ratio 0.24

Output Voltage theoretical(ideal) 21.8 VOutput Voltage theoretical(practical) 21 V

Output Voltage measured 20.4 V

point tracked in steady state for duty ratio perturbation stepsize of 0.01. It shows panel voltage, current and duty ratio.Results were also obtained for ∆d = 0.05 and that gives∆P = 0.2W , which matches theoretically expected value asmentioned in Section IIA. Fig. 11 shows filtering by LCL filter,it shows panel current, which is 0.12A dc and boost currentwhich has 0.2A peak-peak ripple. MPP tracking is shown onpower-voltage plane in Fig. 12. Fig. 13 shows effect of varyingintensity of light on tracking of maximum power point againon power-voltage plane. It shows as the light intensity reducesto zero, locus of MPP shifts from 16V, 2W to 0V, 0W.

CH1CH2

CH4

Fig. 10. Panel voltage (CH1), panel current (CH2) and duty ratio (CH4)using the boost switch gating pulse showing the tracking of MPP and steadystate operation. Scale :: CH1 - 2V/div, sensor gain - 0.3V/V, Vmpp = 16.6V;CH2 - 0.5V/div, sensor gain - 6.67V/A, Impp = 0.12A; CH4 - 5V/div, timescale - 10µs/div, duty ratio = 0.24.

CH1CH2

CH4

Fig. 11. Panel voltage (CH1), panel current (CH2) and boost inductor current(CH4) showing filtering by LCL filter at the input. Scale :: CH1 - 2V/div,sensor gain - 0.3V/V, Vmpp = 16.6V; CH2 - 0.5V/div, sensor gain - 6.67V/A,Impp = 0.12A; CH4 - 10mV/div, sensor gain - 0.1V/A, ILmean = 0.12A,ILpk−pk

= 0.2A.

V

P

Fig. 12. PV panel power voltage plane (power-y axis, voltage-x axis),showing traking of maximum power point with steady state operation.Scale :: X axis : CH1 - 2V/div, sensor gain - 0.3V/V, Vmpp = 16.6VY axis : CH2 - 0.5V/div, scaling - 0.4V/W, Pmpp = 2W.

III. CONCLUSION

The incorporation of LCL filter between PV panel andboost converter results in lower boost inductance value whichleads to reduced cost and size benefits. But reduction ininductance leads to higher probability of DCM operation ofboost converter. The direct duty ratio based MPPT algorithm isfound capable of tracking MPP despite of mode changes, as inboth modes duty ratio increase traverses I-V curve of PV panelin same direction. However it has been found that sensitivityof MPP tracking depends on the mode of operation. This issueis resolved by changing the perturbation step size of duty ratiofor desired sensitivity. Experimental results show the filteringaction of LCL filter and maximum power point tracking forCCM operation with a duty ratio perturbation step size of 0.01.It has been observed that a higher step size perturbs the powerin a wider range thereby giving lower tracking accuracy, lower

V

P

Fig. 13. Tracking of MPP with varying intensity of light, shown onpower-voltage plane. MPP moves towards origin as light intensity reduces.Scale :: X axis : CH1 - 2V/div, sensor gain - 0.3V/V, voltage varies from16.6V to 0V; Y axis : CH2 - 0.5V/div, scaling - 0.4V/W, power varies from2W to 0W.

average power output but higher tracking speeds.

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