research article design and implementation of...

Research ArticleDesign and Implementation of Three-Level DC-DCConverter with Golden Section Search Based MPPT forthe Photovoltaic Applications

Chouki Balakishan N Sandeep and M V Aware

Visvesvaraya National Institute of Technology Nagpur 440010 India

Correspondence should be addressed to N Sandeep sandeep1991inieeeorg

Received 11 August 2014 Revised 12 December 2014 Accepted 30 December 2014

Academic Editor Pavol Bauer

Copyright copy 2015 Chouki Balakishan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In many photovoltaic (PV) energy conversion systems nonisolated DC-DC converters with high voltage gain are desired The PVexhibits a nonlinear power characteristicwhich greatly depends on the environmental conditionsHence in order to drawmaximumavailable power various algorithms are used with PV voltagecurrent or both as an input for the maximum power point tracking(MPPT) controller In this paper golden section search (GSS) based MPPT control and its application with three-level DC-DCboost converter for MPPT are demonstrated The three-level boost converter provides the high voltage transfer which enables thehigh power PV system to work with low size inductors with high efficiencyThe balancing of the voltage across the two capacitors ofthe converter and MPPT is achieved using a simple duty cycle based voltage controller Detailed simulation of three-level DC-DCconverter topology with GSS algorithm is carried out in MATLABSIMULINK platform The validation of the proposed systemis done by the experiments carried out on hardware prototype of 100W converter with low cost ATrsquomega328 controller as a corecontroller From the results the proposed system suits as one of the solutions for PV based generation system and the experimentalresults show high performance such as a conversion efficiency of 94

1 Introduction

The photovoltaic systems are major contributors in theelectrical powerThese are utilized effectivelywith interface tothe existing systems through DC-DC converters The majorchallenge is to extract the power under varying operatingconditions which influence the output voltage [1 2]

Isolated converter structures with cascaded configurationenables to achieve high voltage gain [3] However these areused up to several kW applications [4 5] The multilevelbuck converters proposed are widely used in high frequencyDCDC power conversion [6 7] In the conventional boostconverters high voltage ratio is feasible without multistagecascading [8] The voltage ratios in these are limited by theparasitic elements and switching control used [9 10] Three-level boost converters have significant advantage as comparedto conventional boost converter The size of the inductor isreduced and switch voltage rating is half of the output volt-age This reduces the overall size and improves the efficiency

in three-level DC-DC converters However the voltage bal-ancing across the DC bus capacitors is required due to noni-dealities in the components This is feasible by sensing thevoltages across them with corrective feedback through con-trollers [11 12]The current sensing of inductor by dispensingthe voltage measurements is feasible to balance the voltagesacross the DC bus capacitors [13]

PV array in solar power conversion system operates at apoint havingmaximumpower transfer It is necessary to trackthis operating point by using the MPPT control algorithmsto maximize the utilization efficiency Various algorithms forMPPT are reported in the literature and used for the efficientenergy conversion process [14]These methods are derivativebased andnoise sensitive A computational easewith inherentrobust MPPT using golden section search (GSS) based algo-rithm is proposed in this paperThis is having noise and signalfluctuation immunity with fast convergence as comparedto many reported MPPT methods [15 16] This GSS basedMPPTmethod is easy to implement on the low cost hardware

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2015 Article ID 587197 9 pageshttpdxdoiorg1011552015587197

2 Advances in Power Electronics

Voltage balance control

S

T

L

D

Three-level DC-DC converter

MPPTcontroller

D1

S1

S2

C1

C2D2

IL

c1 c2D998400

carrier 1

carrier 2

+minus

+

minus

+

minus

+minus

0 RL

G1

G2

Figure 1 Proposed scheme with PV-fed three-level boost converter

with single current sensor The PV connected system withthree-level converter using GSS based MPPT is presented inFigure 1

In this paper GSSMPPT based three-level DC-DC boostconverter for PV energy conversion system is presented Asimple duty cycle based pulse width modulation (PWM) andcapacitor voltage controller are suggested The switching andreverse recovery losses are less in the three-level boost con-verter A hardware prototype of 100W converter is built andthe control is made cost effective using ATrsquomega based lowcost controller The steady state and dynamic behavior of thesystem are presented Both the simulation and hardwareresults are seen to have clear agreement with inherent robust-ness built using new MPPT algorithm

2 Three-Level Nonisolated DC-DC Converter

In high power rating PV systems with high voltage gainrequires boost converter with controller to maintain the DCbus voltage constant The interfacing PV with wide range ofvoltages with boost converter having three-level is advanta-geous due to reduce input filter size and current ripple cancel-lation In three-level boost converter switching devices volt-age rating is half of the output voltage this leads to increasethe power density efficiency and reduction in costThe three-level boost converter is shown in Figure 2 The voltage ofthe center point is 119881

1199002 as capacitors 119862

1and 119862

2are equal

which in turn reflects the voltage stress reduction across theswitching devices in these converters

21 Operating Principle Symmetrical operation of three-level boost converter is explained with its operating modesIn this converter V

1198881 V1198882are the voltage across the capacitors

1198621 1198622 respectively The switch 119878

1is upper switch and 119878

2is

lower switch and switching frequency is 119891119904 In this converter

carrier signals Vcarrier1 and Vcarrier2 for PWM generation aretriangular for both switches but those are in 180∘ phase shiftto each other With these carrier signals both switches can be

turning ON and OFF at the same time Therefore the con-verter operates in four distinct modes as shown in Figure 3

(1) Mode 1 both switches are turn ON as shown inFigure 2(a) and the voltage across inductor is (V

119871) =

input voltage (Vin gt 0) In this mode the inductoris always in charging mode and charged capacitorssupply the current to the load

(2) Mode 2 in thismode 1198781is ON and 119878

2is OFF as shown

in Figure 2(b) and voltage across the inductor is V119871=

Vin minus V1198882 In this mode inductor may be in chargingmode or discharging mode and charged capacitor 119862

1

supplies the current to the loadwhile1198622is in charging

mode(3) Mode 3 in this mode 119878

1is OFF and switch 119878

2is

ON as shown in Figure 2(c) and voltage across theinductor is V

119871= VinminusV1198881 In thismode inductormay be

in charging mode or discharging mode and chargedcapacitor 119862

2supplies the current to the load while 119862

1

is in charging mode(4) Mode 4 both switches are turned OFF as shown in

Figure 2(d) and inductor voltage is V119871= Vin minus V1198882 lt 0

Due to boosting operation V1198881+ V1198882gt Vin so in

this mode inductor always is in discharging modeand both capacitors are in charging mode and inputsupplies the current to the load

In modes 1 and 4 inductor is in charging mode anddischargingmode respectively but inmodes 2 and 3 inductorcurrents raising polarity depend on the voltages V

1198881and V1198882

depending upon the relation between Vin and half of theoutput voltage (V

02) there exist two operating regions

(1) Region 1 Vin gt V02(2) Region 2 Vin lt V02In region 1 Vin gt V

02 hence V

119871= Vin minus V02 gt 0 so

inductor current raising polarity is positive in modes 3 and 2as shown in Figure 3(a)This will occur only when duty ratiosof upper switch (119863

1) and of lower switch (119863

2) are less than

05 in this region both switches must not be ON at the sametime In region 2 119863

1= 1198632gt 05 input voltage is Vin lt V02

then inductor current raising polarity is negative V119871= Vin minus

V02 lt 0 in modes 2 and 3 as shown in Figure 3(b) In this

region both switches must not be OFF at the same time

3 Current Ripple and Efficiency

In boost converter maximum inductor current ripple (Δ119894max)occurswhen duty ratio (119863) is 05 at this duty ratio Vin = 05V119900The inductor current ripple is given by

Δ119894max =Vin119871119863119879119904=1198810119879119904

119871 (1)

In three-level boost converter equivalent switching fre-quency is twice the switching frequency of conventionalboost converter In region 1 maximum ripple occurs at Vin =025V119900and is given by

Δ119894max =Vin119871119863119879119904

1

2=1198810119879119904

16119871 (2)

Advances in Power Electronics 3

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(a)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(b)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(c)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(d)

Figure 2 Operating modes of three-level DC-DC converter

Mode 2 Mode 4 Mode 3 Mode 4 Mode 2Sampling instants

G1

G2

t

iL

(a)


iL

G1

G2

t

(b)

Figure 3 Operation waveforms (a) Region 1 (b) Region 2

From (1) and (2) it is observed that the inductor currentripple is less for three-level boost converter for the sameinductor value and inductor value is four times less than con-ventional boost converterThe inductor loss due to the resist-ance is a major design parameter The selection of the 119871119877ratio and switching devices losses are the major contributorsin the efficient operation of the converter

4 Proposed MPPT Scheme

In this MPPT technique maximum power is tracked by con-trolling PV current to maximum power point current whichis computed by golden section search (GSS) algorithm ThisGSS basedMPPT needs to sense the irradiance temperatureand PV current to maximize the power output from PVsystems

41 Golden Section Search Principle The golden sectionsearch is a technique for finding extremum (minimum ormaximum) by sequentially narrowing the range of valuesinside which extremum exists The main aim is to findmaximum functional value of 119891(119909) within the input interval[119886 119887] Two points 119909

1and 119909

2are selected in the interval [119886 119887]

and function 119891(119909) is evaluated at these points Points 1199091and

1199092are selected such that each point subdivides interval into

two parts and length of whole linelength of larger fraction =length of larger fractionlength of smaller fraction Assume aline segment [0 1] as shown in Figure 4(b)Then 1119903 = 1199031minus119903that is 1199032 + 119903 minus 1 = 0 hence 119903 = 0618

Consider1199091= 119887minus119903(119887minus119886) that is119909

1is 0618 of interval

away from 119887


Voltage (V)

1

2

3

4

Isc)Short circuit current (

Current at MPP (Impp)Open circuit voltage (Voc)

Voltage at MPP (Vmpp)

Maximum power point

Power (W)Current (A)

(a)

f(X2)

f(X1)

abX1 X2

r 1 minus r

(b)

Figure 4 (a) MPPT tracking with GSS algorithm (b) Division of interval on the characteristics

Consider1199092= 119886+119903(119887minus119886) that is119909


away from 119886

For a GSS based MPPT for photovoltaic system the 119875-119881characteristics are the operating characteristics wherein 119891(119909)corresponds to power whose maximum value has to betracked The range of operation is from zero to open circuitvoltage (119881oc) that is 119886 = 0 and 119887 = 119881oc as shown inFigure 4(b) The way of tracking maximum point is shownin Figure 4(a) The voltage corresponding to the maximumpower is obtained and mapped into the119881-119868 characteristics toobtain the current reference

42 Golden Section Search Algorithm Based MPPT MPPTis used to track the maximum power under different atmo-spheric conditions this method is robust and also has a fastresponse as compared to the conventional MPPT algorithmsThis algorithm has guaranteed convergence under contin-uous variable irradiance and temperatures This GSS basedMPPT has two parts one is PV emulator which plots thePV characteristics for given irradiance and temperature byusing mathematical model equations of PV cell this requiressolar PV parameters irradiance and temperature The algo-rithm for generating the PV characteristics is presented inFigure 5(a)

The description of the parameters in the flow chart is asfollows

119868sc short circuit current119877119904 series resistance119873119904 the number of cells of the array connected in

series119870119894 temperature coefficient of current119886 ideality factor of diode119902 carrier charge119878119899 nominal irradiance119879119899 nominal temperature119864119892 band energy

119878 irradiance

119879 temperature

1198680 photovoltaic saturation current

The second part of the algorithm is to find the PV currentat maximum power point (MPP) is shown in Figure 5(b)

The inductor current feedback is used to generate theerror by comparing it with the reference current 119868MPP gen-erated by the GSS algorithm and it is processed throughproportional (P) controllerThis P controller changes the dutyratio (119863) according to error and governs the PV to track themaximum power point on its characteristics Figure 6 showsthe block diagram of GSS MPPT based reference generator

43 Voltage Balancing Control Capacitors 1198621and 119862

2are

alternatively charged to their voltages V1198881

and V1198882 Even

though both capacitor values are equal there is a voltageunbalance between output capacitors due tomismatch of tworeal capacitors and equivalent series resistance The voltagebalancing controller is required tomaintain the equal voltagesacross these capacitors through duty cycle control and isimplemented as shown in Figure 7 119866

1and 119866

2are the gate

pulses for switches 1198781and 119878

2 respectively In the three-level

boost operation of the DC-DC converters with duty rationrelates the fact that the input and output voltage are given as

1198810

119881in=

1

1 minus 051198891minus 05119889

2

(3)

If 1198891= 1198892= 119863 then

1198810

119881in=1

1 minus 119863 (4)

where the input DC voltage 119881in is PV input voltage andvaries with respect to varying environmental conditionsThe duty ratio of the boost switch 119878

1is determined by the

MPPT control (119863) and duty ratio of the boost switch 1198782is

determined by the additional controller The PI generates


Start

Enter the values ofRsNs Ki Voc Isc a q K Eg Sn Tn

Enter the values of S T

Irs

Irs

= Isc e(qVoc(N119904lowastKlowastalowastT)) minus 1

Ipv = (SSn)(Isc + Ki(T minus Tn))

I0 = lowast (TTn) lowast e(qlowastE119892lowast(TminusT119899)(alowastKlowastT119899lowastT))

Initialize i = 0 I(i) = Iinit V(0) = 0

P(i) = V(i) lowast I(i)

Isi = Voc

Yes

No

A

V(i + 1) = V(i) + 1

i = i + 1

I(i + 1) = Ipv minus I0((V(i)+IR119904)(V119905lowasta)) minus minus ((V(i) + I(i)Rs)Rp)

3

Iinit = Ipv minus I0 e((V+IR119904)V119905lowasta) minus minus ((V + IRs)Rp)( 1)

1)(e

( )

I = 0

(a)

A

Select range of operation (0 Voc)

Compute X1X2

X1 = b minus r lowast (b minus a)

X2 = a + r lowast (b minus a)

IsP(x1) = P(x2)

IsP(x2) gt P(X1)

No

Yes

a = a

b = x2

a = x1

b = b

The MPP = x1

IMPP = I(x1)

End

Evaluate P(x1) P(x2) at x1 x2

a = 0 b = Voc

(b)

Figure 5 GSS MPPT flowchart (a) PV emulator and (b) GSS method

PV GSS MPPT controller P

DInsolation temperature

emulator

IL

IlowastMPP

minus

Figure 6 GSS MPPT control technique

the duty (119863) from the voltage error obtained from (V1198881minus V1198882)

Consider

Δ119863 = 119870119901+119870119894

119904(V1198881minus V1198882) (5)

GSS

PI

MPPT

minus

minus

minus

+

+

c2

c1 ΔD

D G1

G2

D998400 = D + ΔD

Figure 7 Block diagram of MPPT with voltage balance control

where 119870119901+ 119870119894119904 is the transfer function of the PI controller

The duty cycle 1198631015840 = 119863 + Δ119863 controls switch 1198782of the

converter to balance the voltage across the capacitors


6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)

Figure 8 (a) Maximum power tracking at 119878 = 1000Wm2 and 119879 = 298K (b) Voltage balancing under steady state

Table 1 Specifications of the solar panel

Maximum power (119875mpp) 100WVoltage at maximum power point (119881mpp) 34VCurrent at maximum power point (119868mpp) 294AShort circuit current (119868sc) 317 AOpen circuit voltage (119881oc) 42V

Table 2 Specifications of the hardware prototype

Parameter Valuepart numberInductor (119871) 14mH 08ΩCapacitor (119862

1and 119862

2) 1000 120583F

Switching frequency (119891SW) 30 kHzPower MOSFETs IRFP250 (200V 30A)Hyperfast power diodes 1200V 8A

5 Simulation Results

In this section the converter operation with the MPPT con-trol and voltage balancing is presented through simulationThe PV panel parameters are given in Table 1 The boostconverter is operated with MOSFET switches and the detailsof the component specification are given in Table 2 Thesteady state and dynamic operation are presented for thevarious operating conditions

51 Steady State Operation The simulated results understeady state are shown in Figure 8 The PV panel is operatingat a temperature 298K with irradiation level of 1000Wm2The converter operation with MPPT control and capacitorvoltage balance activation at 02 s is presented in Figure 8(a)Initially reference value is set to 2A (without MPPT) afterthat it is changed according toGSSMPPTThen power drawnfrom the PV is increased to 100W by controlling the PVcell current to the reference value generated by GSS MPPTalgorithm The DC bus capacitor voltage balance control isalso presented with forced unbalance created by choosingthe different values of 119862

1and 119862

2(1198621= 1000 120583F and 119862

2=

900 120583F) The voltages across these capacitors are maintainedat the same value after the balancing the voltage converges

6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

Figure 9 Maximum power tracking under step change in irradi-ance

to a 235 V within the 002 s while converter is operating in amaximum power tracking mode shown in Figure 8(b) Thisindicates the operation of the designed controller is effectivelymaintaining the power near to 100W at the 50V outputthrough the duty ratio control at 30 kHz switching frequency

52 Dynamic Operation of the Converter The MPPT algo-rithm with converter under varying irradiation levels andvarious loading condition is tested TheMPPT with a changein the irradiation level from 800Wm2 to 1000Wm2 ispresented in Figure 9

The voltage variation across the capacitors due to suddenloading on the converter (around 20 variation) is presentedin Figure 10 It is observed that the voltage is controlled afterthe load variation andmaintained to 235 V across each of thecapacitors

53 Performance Comparison with Other MPPT with PartialShading The proposed MPPT method is compared withPerturb and Observe and Incremental Conductance basedMPPT techniques The performance is evaluated under thepartial shading The partial shading 119875-119881 characteristics areused to test the performance with local and global peak asgiven in Figure 11

The reference voltage (119881ref) generated by these methodsare given in Figure 12 with the number of iterations required


05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2

Figure 10 Voltage balancing under load change

150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)

Local peak Global peak

Vref

Figure 11 119875-119881 characteristics under partial shading

by these methods It is observed that the iterations requiredfor the GSS are 4-5 nos as other methods take 7-8 nos Thevariation in the generated reference is stable in GSS as it istracking the local and global peak

6 Experimental Results

The proposed scheme is implemented in ATrsquomega328 con-troller with GSS based MPPT and duty ratio control Theparameters of the hardware are built with the same param-eters as given in Table 2

61 Hardware Circuit Description The block diagram ofhardware prototype built is shown in Figure 13 The DCDCconverter is built with theMOSFET IRFP250The interfacingdrivers with isolation circuit using TLP350 are built Thecapacitor voltage is sensed using voltage sensor LV-25Pand inductor current by current sensor (WCS 2705) Thecontroller ATrsquomega328 with built-in ADC is used to executethe MPPT algorithm and also the PI controller The IO pinsare interfacedwith the driving circuit to activate the switchingdevices The photograph of the hardware prototype built isshown in Figure 14

Figure 15 shows themeasured power generated by PV andcurrent and voltage across it The PV current is controlledto maximum power point current 294A which is computedfrom the proposed GSS MPPT algorithm maximum power

001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC

Figure 12 119881ref tracking using (a) GSS technique (b) Perturb andObserve and (c) Incremental Conductance with the given shadingpattern

PV Load

S

T

ATrsquomega328 core controller

iL c1 c2 G1 G2

Figure 13 Block diagram of hardware prototype built

100W is reached within 05 s The voltages across the capaci-tors are indicating different voltages and they are balanced asthe controller is activatedThe voltage balance across the twoDC capacitors at 24V is shown in Figure 16

The level of the irradiation is also set to test the effec-tiveness of the GSS-MPPT controller Figure 17 shows thecontroller tracking the maximum power with change in thecurrent The level of irradiation is changed from 800Wm2to 1000Wm2 and the response of the GSS-MPPT algorithmis observed

The voltage balancing loop is also tested under loadchange and response shown in Figure 18 The capacitor volt-ages are unbalanced before applying control loop After ena-bling voltage balance control loop both capacitor voltages V

1198881

and V1198882are converged to 24V

62 Performance Evaluation TheMPPT effectiveness ismea-sured by measuring the efficiencyThis is defined by the ratioof maximum power to the power tracking by MPPT Theproposed GSS based MPPT is evaluated for the efficiency In


1

2

3

4 5 6

7

8

Figure 14 Prototype of the proposed PV energy conversion system (1) Solar panels (2)AC power supply for gate drivers (3) TLP-250 basedgate driver board (4) Atrsquomega328 controller (5) Sensing circuitry board (6) DC-DC converter power circuit (7) Load (8) Supply terminalfrom PV panel

MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV

Figure 15 Performance of the DCDC converter at start-up ofMPPT

simulation for 119878 = 1000Wm2 119879 = 298K the maximumpower is 100W and tracking power using GSS MPPT is998W The efficiency of the DC-DC converter is calculatedfor design values given in Table 2The inductor (119871 = 14mH)used is found to have a resistance of 08Ω and the efficiencyobtained is 91The actual measured hardware efficiency forthe 30 kHz operation is 897 The variation of the inductorresistance by way of wire gauge selection influences theefficiency and it is indicated in Figure 19 Use of switchingdevice and its switching frequency in a converter has a trade-off with the losses in the inductor The operational efficiencyof these converters can be achieved up to 98

7 Conclusion

The three-level boost converter is used to interface the PVsystem for maximization of the power extraction The newmaximum power point tracking algorithm based on thegolden section search method is implemented This algo-rithm shows the better dynamic response with the faster con-vergence without any oscillations while tracking The voltage

c1

c2

200ms

5V

MPPT + voltage balancing loop

Figure 16 Voltages across capacitors with voltage balancing loopcontrol

PPV

VPV

IPV

1 s

50W

25V

1A

Irradiance level step to 1000Wm2

PPPPP VV

VPVV VV

IPII V

Figure 17 Dynamic response during change in irradiation from 800to 1000Wm2

balancing of the DC bus is executed through the PI con-troller and performance is observed to be satisfactory Thesecontrollers are implemented on the low cost ATrsquomega328controller The 100W prototype is built to demonstrate the


Step change in load Balance in voltage restored

c1

c2

200ms

25V

Figure 18 Capacitor voltage balance during load disturbance

02 03 04 05 06 07 08 09 180

85

90

95

100

Inductance resistance

Effici

ency

()

Operating point

L = 14mH and fs = 30kHz

Figure 19 Variation in efficiency versus inductor parasitic resis-tance

performance of this converterThe performance of theMPPTwith GSS based algorithm indicates the good agreement withthe simulated results The steady state performance of theconverter shows the balance voltage operation across the DCbus It is indicated that the performance of the presentedconverter with varying irradiation as well as the load changeis also in line with the simulation results This indicatesthe converter performance with its efficiency up to 94 isachieved in these converters with high voltage gains in thePV energy conversion systems

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M Elshaer A Mohamed and O Mohammed ldquoSmart optimalcontrol of DC-DC boost converter in PV systemsrdquo in Proceed-ings of the IEEEPES Transmission and Distribution Conferenceand Exposition Latin America (T and D-LA rsquo10) pp 403ndash410Sao Paulo Brazil November 2010

[2] W Li and X He ldquoReview of non-isolated high-step-up DCDCconvertersin photovoltaic grid-connected applicationsrdquo IEEETransactions on Industrial Electronics vol 58 no 4 pp 1239ndash1250 2011

[3] B Huang A Shahin J P Martin S Pierfederici and B DavatldquoHigh voltage ratio non-isolated DC-DC converter for fuel cellpower source applicationsrdquo in Proceedings of the 39th IEEEAnnual Power Electronics Specialists Conference (PESC rsquo08) pp1277ndash1283 June 2008

[4] A M Tuckey and J N Krase ldquoA low-cost inverter for domesticfuel cell applicationsrdquo in Proceedings of the IEEE 33rd AnnualPower Electronics Specialists Conference (PESC rsquo02) pp 339ndash346 June 2002

[5] C Smith M Gilliom D Urciuoli A Mclandrich E Pepa andJ S Lai ldquoLow-cost solid oxide fuel cell power conditioning withbidirectional chargingrdquo in Proceedings of the Fuel Cell Seminarpp 8ndash15 Miami Beach Fla USA November 2003

[6] M Velaerts ldquoNew development of 3-level PWM strategiesrdquo inProceedings of the EuropeanConference on Power Electronics andApplications 1989

[7] O Apeldoorn and L Schulting ldquo10 kVA four level inverter withsymmetrical input voltage distributionrdquo inProceedings of the 5thEuropean Conference on Power Electronics and Applications vol3 pp 196ndash201 September 1993

[8] M T Zhang Y Jiang F C Lee and M M Jovanovic ldquoSingle-phase three-level boost power factor correction converterrdquo inProceedings of the IEEE 10th Annual Applied Power ElectronicsConference vol 1 pp 434ndash439 March 1995

[9] C Hua C Leu Y Jiang and F C Lee ldquoNovel zero-voltage-transition PWM convertersrdquo IEEE Transactions on Power Elec-tronics vol 9 no 2 pp 213ndash219 1994

[10] V Yaramasu and B Wu ldquoThree-level boost converter basedmedium voltage megawatt PMSG wind energy conversion sys-temsrdquo in Proceedings of the 3rd Annual IEEE Energy ConversionCongress and Exposition (ECCE rsquo11) pp 561ndash567 Phoenix ArizUSA September 2011

[11] J-M Kwon B-H Kwon and K-H Nam ldquoThree-phase photo-voltaic system with three-level boosting MPPT controlrdquo IEEETransactions on Power Electronics vol 23 no 5 pp 2319ndash23272008

[12] E Ribeiro A J M Cardoso and C Boccaletti ldquoFault-tolerantstrategyfor a photovoltaic DC-DC converterrdquo IEEE Transac-tions on Power Electronics vol 28 no 6 pp 3008ndash3018 2013

[13] H-C Chen and W-J Lin ldquoMPPT and voltage balancingcontrol with sensing only inductor current for photovoltaic-fedthree-level boost-type convertersrdquo IEEE Transactions on PowerElectronics vol 29 no 1 pp 29ndash35 2014

[14] A N A Ali M H M Saied M Z Mostafa and T MAbdel-Moneim ldquoA survey of maximum PPT techniques of PVsystemsrdquo in Proceedings of the IEEE Energytech pp 1ndash17 May2012

[15] J Agrawal and M Aware ldquoGolden section search (GSS)algorithm for maximum power point tracking in photovoltaicsystemrdquo in Proceedings of the IEEE 5th India InternationalConference on Power Electronics (IICPE rsquo12) 6 p 1 Delhi IndiaDecember 2012

[16] R Shao and L Chang ldquoA new maximum power point trackingmethod for photovoltaic arrays using golden section searchalgorithmrdquo in Proceedings of the IEEE Canadian Conference onElectrical and Computer Engineering (CCECE rsquo08) pp 619ndash622May 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Voltage balance control

S

T

L

D

Three-level DC-DC converter

MPPTcontroller

D1

S1

S2

C1

C2D2

IL

c1 c2D998400

carrier 1

carrier 2

+minus

+

minus

+

minus

+minus

0 RL

G1

G2

Figure 1 Proposed scheme with PV-fed three-level boost converter

with single current sensor The PV connected system withthree-level converter using GSS based MPPT is presented inFigure 1

In this paper GSSMPPT based three-level DC-DC boostconverter for PV energy conversion system is presented Asimple duty cycle based pulse width modulation (PWM) andcapacitor voltage controller are suggested The switching andreverse recovery losses are less in the three-level boost con-verter A hardware prototype of 100W converter is built andthe control is made cost effective using ATrsquomega based lowcost controller The steady state and dynamic behavior of thesystem are presented Both the simulation and hardwareresults are seen to have clear agreement with inherent robust-ness built using new MPPT algorithm

2 Three-Level Nonisolated DC-DC Converter

In high power rating PV systems with high voltage gainrequires boost converter with controller to maintain the DCbus voltage constant The interfacing PV with wide range ofvoltages with boost converter having three-level is advanta-geous due to reduce input filter size and current ripple cancel-lation In three-level boost converter switching devices volt-age rating is half of the output voltage this leads to increasethe power density efficiency and reduction in costThe three-level boost converter is shown in Figure 2 The voltage ofthe center point is 119881

1199002 as capacitors 119862

1and 119862

2are equal

which in turn reflects the voltage stress reduction across theswitching devices in these converters

21 Operating Principle Symmetrical operation of three-level boost converter is explained with its operating modesIn this converter V

1198881 V1198882are the voltage across the capacitors

1198621 1198622 respectively The switch 119878

1is upper switch and 119878

2is

lower switch and switching frequency is 119891119904 In this converter

carrier signals Vcarrier1 and Vcarrier2 for PWM generation aretriangular for both switches but those are in 180∘ phase shiftto each other With these carrier signals both switches can be

turning ON and OFF at the same time Therefore the con-verter operates in four distinct modes as shown in Figure 3

(1) Mode 1 both switches are turn ON as shown inFigure 2(a) and the voltage across inductor is (V

119871) =

input voltage (Vin gt 0) In this mode the inductoris always in charging mode and charged capacitorssupply the current to the load

(2) Mode 2 in thismode 1198781is ON and 119878

2is OFF as shown

in Figure 2(b) and voltage across the inductor is V119871=

Vin minus V1198882 In this mode inductor may be in chargingmode or discharging mode and charged capacitor 119862

1

supplies the current to the loadwhile1198622is in charging

mode(3) Mode 3 in this mode 119878

1is OFF and switch 119878

2is

ON as shown in Figure 2(c) and voltage across theinductor is V

119871= VinminusV1198881 In thismode inductormay be

in charging mode or discharging mode and chargedcapacitor 119862

2supplies the current to the load while 119862

1

is in charging mode(4) Mode 4 both switches are turned OFF as shown in

Figure 2(d) and inductor voltage is V119871= Vin minus V1198882 lt 0

Due to boosting operation V1198881+ V1198882gt Vin so in

this mode inductor always is in discharging modeand both capacitors are in charging mode and inputsupplies the current to the load

In modes 1 and 4 inductor is in charging mode anddischargingmode respectively but inmodes 2 and 3 inductorcurrents raising polarity depend on the voltages V

1198881and V1198882

depending upon the relation between Vin and half of theoutput voltage (V

02) there exist two operating regions

(1) Region 1 Vin gt V02(2) Region 2 Vin lt V02In region 1 Vin gt V

02 hence V

119871= Vin minus V02 gt 0 so

inductor current raising polarity is positive in modes 3 and 2as shown in Figure 3(a)This will occur only when duty ratiosof upper switch (119863

1) and of lower switch (119863

2) are less than

05 in this region both switches must not be ON at the sametime In region 2 119863

1= 1198632gt 05 input voltage is Vin lt V02

then inductor current raising polarity is negative V119871= Vin minus

V02 lt 0 in modes 2 and 3 as shown in Figure 3(b) In this

region both switches must not be OFF at the same time

3 Current Ripple and Efficiency

In boost converter maximum inductor current ripple (Δ119894max)occurswhen duty ratio (119863) is 05 at this duty ratio Vin = 05V119900The inductor current ripple is given by

Δ119894max =Vin119871119863119879119904=1198810119879119904

119871 (1)

In three-level boost converter equivalent switching fre-quency is twice the switching frequency of conventionalboost converter In region 1 maximum ripple occurs at Vin =025V119900and is given by

Δ119894max =Vin119871119863119879119904

1

2=1198810119879119904

16119871 (2)


D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(a)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(b)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(c)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(d)



G1

G2

t

iL

(a)


iL

G1

G2

t

(b)






1and 119909







away from 119887


Voltage (V)

1

2

3

4




Maximum power point


(a)

f(X2)

f(X1)

abX1 X2

r 1 minus r

(b)




away from 119886






119878 irradiance

119879 temperature





2are


and V1198882 Even


1and 119866

2are the gate




1198810

119881in=

1

1 minus 051198891minus 05119889

2

(3)

If 1198891= 1198892= 119863 then

1198810

119881in=1

1 minus 119863 (4)






Start



Irs

Irs






Isi = Voc

Yes

No

A

V(i + 1) = V(i) + 1

i = i + 1


3


1)(e

( )

I = 0

(a)

A


Compute X1X2



IsP(x1) = P(x2)

IsP(x2) gt P(X1)

No

Yes

a = a

b = x2

a = x1

b = b

The MPP = x1

IMPP = I(x1)

End


a = 0 b = Voc

(b)




emulator

IL

IlowastMPP

minus



Consider

Δ119863 = 119870119901+119870119894

119904(V1198881minus V1198882) (5)

GSS

PI

MPPT

minus

minus

minus

+

+

c2

c1 ΔD

D G1

G2

D998400 = D + ΔD






6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)






1and 119862

2) 1000 120583F





1and 119862

2(1198621= 1000 120583F and 119862

2=


6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)








05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(a)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(b)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(c)

D1L

S1

S2

C1

C2

D2

+ +

+

minus minus

minus

+

minus

V0Vin

(d)



G1

G2

t

iL

(a)


iL

G1

G2

t

(b)






1and 119909







away from 119887


Voltage (V)

1

2

3

4




Maximum power point


(a)

f(X2)

f(X1)

abX1 X2

r 1 minus r

(b)




away from 119886






119878 irradiance

119879 temperature





2are


and V1198882 Even


1and 119866

2are the gate




1198810

119881in=

1

1 minus 051198891minus 05119889

2

(3)

If 1198891= 1198892= 119863 then

1198810

119881in=1

1 minus 119863 (4)






Start



Irs

Irs






Isi = Voc

Yes

No

A

V(i + 1) = V(i) + 1

i = i + 1


3


1)(e

( )

I = 0

(a)

A


Compute X1X2



IsP(x1) = P(x2)

IsP(x2) gt P(X1)

No

Yes

a = a

b = x2

a = x1

b = b

The MPP = x1

IMPP = I(x1)

End


a = 0 b = Voc

(b)




emulator

IL

IlowastMPP

minus



Consider

Δ119863 = 119870119901+119870119894

119904(V1198881minus V1198882) (5)

GSS

PI

MPPT

minus

minus

minus

+

+

c2

c1 ΔD

D G1

G2

D998400 = D + ΔD






6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)






1and 119862

2) 1000 120583F





1and 119862

2(1198621= 1000 120583F and 119862

2=


6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)








05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Voltage (V)

1

2

3

4




Maximum power point


(a)

f(X2)

f(X1)

abX1 X2

r 1 minus r

(b)




away from 119886






119878 irradiance

119879 temperature





2are


and V1198882 Even


1and 119866

2are the gate




1198810

119881in=

1

1 minus 051198891minus 05119889

2

(3)

If 1198891= 1198892= 119863 then

1198810

119881in=1

1 minus 119863 (4)






Start



Irs

Irs






Isi = Voc

Yes

No

A

V(i + 1) = V(i) + 1

i = i + 1


3


1)(e

( )

I = 0

(a)

A


Compute X1X2



IsP(x1) = P(x2)

IsP(x2) gt P(X1)

No

Yes

a = a

b = x2

a = x1

b = b

The MPP = x1

IMPP = I(x1)

End


a = 0 b = Voc

(b)




emulator

IL

IlowastMPP

minus



Consider

Δ119863 = 119870119901+119870119894

119904(V1198881minus V1198882) (5)

GSS

PI

MPPT

minus

minus

minus

+

+

c2

c1 ΔD

D G1

G2

D998400 = D + ΔD






6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)






1and 119862

2) 1000 120583F





1and 119862

2(1198621= 1000 120583F and 119862

2=


6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)








05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start



Irs

Irs






Isi = Voc

Yes

No

A

V(i + 1) = V(i) + 1

i = i + 1


3


1)(e

( )

I = 0

(a)

A


Compute X1X2



IsP(x1) = P(x2)

IsP(x2) gt P(X1)

No

Yes

a = a

b = x2

a = x1

b = b

The MPP = x1

IMPP = I(x1)

End


a = 0 b = Voc

(b)




emulator

IL

IlowastMPP

minus



Consider

Δ119863 = 119870119901+119870119894

119904(V1198881minus V1198882) (5)

GSS

PI

MPPT

minus

minus

minus

+

+

c2

c1 ΔD

D G1

G2

D998400 = D + ΔD






6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)






1and 119862

2) 1000 120583F





1and 119862

2(1198621= 1000 120583F and 119862

2=


6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)








05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










6080

100120

303540

015 016 017 018 019 02 021 022 023 024 025Time (s)

152535

152535

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)

(a)

015 016 017 018 019 02 021 022 023 024 02522

23

24

25

26

27

28

Time (s)

(V)

vc1

vc2

(b)






1and 119862

2) 1000 120583F





1and 119862

2(1198621= 1000 120583F and 119862

2=


6080

100120

303234

035 036 037 038 039 041 042 043 044

225

335

225

335

Time (s)04

Ppv

Vpv

Iref

Ipv

(V)

(A)

(A)

(W)








05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










05 0505 051 0515 05222

225

23

235

24

245

25

Time (s)

(V)

vc1

vc2


150

100

50

0

Pow

er (W

)

0 5 10 15 20 25 30

Voltage (V)


Vref







001 0015 002 0025 003 0035 004 0045 005 0055 0061030

Volta

ge

Time (s)

(a) GSS

10203040

Volta

ge

Time (s)001 0015 002 0025 003 0035 004 0045 005 0055 006

(b) PampO

10203040

Time (s)

Volta

ge

001 0015 002 0025 003 0035 004 0045 005 0055 006

(c) INCC


PV Load

S

T


iL c1 c2 G1 G2





1198881




1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

2

3

4 5 6

7

8


MPPT

PPV

VPV

IPV

500ms

20W

10V

1A

PPPVVV

VPVV VV

IPVV



7 Conclusion


c1

c2

200ms

5V



PPV

VPV

IPV

1 s

50W

25V

1A


PPPPP VV

VPVV VV

IPII V





c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











c1

c2

200ms

25V


02 03 04 05 06 07 08 09 180

85

90

95

100


Effici

ency

()

Operating point






References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article design and implementation of...

Documents