Research Article An Improved MPPT Algorithm for PV...

Research ArticleAn Improved MPPT Algorithm for PV GenerationApplications Based on 119875-119880 Curve Reconstitution

Yaoqiang Wang Meiling Zhang and Xian Cheng

School of Electrical Engineering Zhengzhou University Zhengzhou 450001 China

Correspondence should be addressed to Xian Cheng chengxianzzueducn

Received 22 January 2016 Revised 26 May 2016 Accepted 29 May 2016

Academic Editor Ahmed M Massoud

Copyright copy 2016 Yaoqiang Wang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The output power of PV array changes with the variation of environmental factors such as temperature and solar irradiationTherefore amaximumpower point (MPP) tracking (MPPT) algorithm is essential for the photovoltaic generation systemHoweverthe 119875-119880 curve changes dynamically with the variation of the environmental factors here the misjudgment may occur if a simpleperturb-and-observe (PampO) MPPT algorithm is used In order to solve this problem this paper takes MPPT as the main researchobject and an improved MPPT algorithm for PV generation applications based on 119875-119880 curve reconstitution is proposed Firstlythe mathematical model of PV array is presented and then the output dynamic characteristics are analyzed Based on this a 119875-119880curve reconstitution strategy is introduced and the improved MPPT algorithm is proposed At last simulation and comparativeanalysis are conducted Results show that with the proposed algorithm MPP is tracked accurately and the misjudgment problemis solved effectively

1 Introduction

It is universally acknowledged that photovoltaic power gen-eration as a new green technology has become one of thehot spots at home and abroad However the output powerof PV array is affected by the external environment factorsstrongly such as temperature and solar irradiationThereforein order to adjust the working performance it is particularlyimportant to output maximum power of PV array as much aspossible

There are many kinds of common MPPT control algo-rithms and the control process is not the same and thecorresponding control effect is also different [1] The com-monly used algorithms include the method based on opti-mization mathematical model the method based on theoutput control the method based on intelligent control andnonlinear control and the method based on perturbation ofoptimization [2]

The perturb-and-observe algorithm and incrementalconductance algorithm are the important branches of themethod based on perturbation of optimization which are

the most commonly used methods currently [3] The MPPis tracked by perturbing the output voltage of PV array withperturbation observation algorithm which is simple [4ndash8]Nevertheless the output voltage perturbation signal of PVarray changes when solar irradiation changes strongly sothe power output characteristic deteriorates The trackingaccuracy is not high and oscillation and misjudgment phe-nomena easily occur Incremental conductance algorithm isactually an improved perturb-and-observe algorithm [9ndash14]with which the MPP is tracked by incremental conductanceand instantaneous conductance of PV array In this methodthe physical concept is clear And compared with what wasmentioned above the MPP can be tracked quickly with thismethod when solar irradiation changes But misjudgmentproblem still exists when solar irradiation mutates

Until now many scholars study the MPPT algorithmbased on intelligent control and nonlinear control such asfuzzy algorithm [15] siding algorithm [16] Particle SwarmOptimization (PSO) [17] and genetic algorithm [18]Although these algorithms do not need to establish accuratemathematical model of the controlled object their control

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2016 Article ID 3242069 10 pageshttpdxdoiorg10115520163242069

2 Journal of Control Science and Engineering

Iph ID IP

Rs

IC

U RL

I0

VDD RP

Figure 1 Equivalent circuit of photovoltaic cell

The temperature remains constant

0 10 20 30 40 500

1

2

3

4

5

6

7

600Wm2

800Wm2

1000Wm2

U (V)

I(A

)

Figure 2 119880-119868 characteristic curves of PV cell with different solar irradiation values

algorithms are generally more complicated and are notconducive to realization of the system and are not conduciveto reduction of the unit costs as well

In this paper based on the mathematical model ofPV array and classical perturb-and-observe algorithm 119875-119880curve reconstitution is introduced to track the maximumpower point accurately Finally the proposed MPPT controlstrategy is verified by simulation Results show that themaximum power point is tracked accurately with the pro-posed MPPT algorithm and the misjudgment is eliminatedeffectively and the proposedMPPT algorithm also has a gooddynamic performance

2 Mathematical Model of PV Array

The photovoltaic cell is different from dry cell and bat-tery the latter can store the transformed energy Howeverphotovoltaic cell is a device based on photovoltaic effectwhich converts solar energy into electrical energy directlyand immediately Figure 1 shows an equivalent model of PVcell When solar irradiation is constant the photogeneratedcurrent 119868ph does not change with the working state of thephotovoltaic cell so it can be seen as a constant current

source 119877119871is the load added at both ends of the PV cell and

119880 is the terminal voltageBy Figure 1 the output current equation of the PV cell can

be described as

119868119862= 119868119878minus 1198680exp (

119902

119860119870119879119880) minus 1 (1)

where A is a P-N junction coefficient of semiconductordevices in photovoltaic cells 119870 is Boltzmannrsquos constant 119902 isunit charge119879 is absolute temperature 119868

119862is output current 119868

0

is diode reverse saturation current 119868119878is short-circuit current

(the corresponding 119868ph when 119880 is 0 in Figure 1)As can be seen from (1) the output characteristic curves

of PV cell change with external environment factors suchas solar irradiation and temperature Figure 2 shows 119880-119868characteristic curves when temperature is constant and solarirradiation changes It can be seen that short-circuit cur-rent reduces significantly and open-circuit voltage is almostunchanged when solar irradiation decreases Figure 3 shows119875-119880 characteristic curves with the same conditions Similarlyit can be seen from the figure that 119875-119880 characteristic curvehas a single peak and the maximum power point is itsextreme point and the output power increases with solarirradiation and reaches a maximum at a point

Journal of Control Science and Engineering 3


0 10 20 30 40 500

50

100

150

200

600Wm2

800Wm2

1000Wm2

U (V)

P(W

)


Solar irradiation intensity remains unchanged

0 10 20 30 40 500

1

2

3

4

5

6

7

U (V)

I(A

)

0∘C

25∘C

50∘C

Figure 4 119880-119868 characteristic curves of PV cell at different temperatures

0 10 20 30 40 500

50

100

150

200

U (V)

P(W

)

0∘C

25∘C

50∘C




U (V)

P(W

)ΔU ΔU

Maximum power point Pmax

Figure 6 Schematic diagram of the classical perturb-and-observe algorithm

Start

Return

Yes

Yes

Yes

No

No

No

U(k) minus U(k minus 1) gt 0 U(k) minus U(k minus 1) gt 0

Uref = Uref + ΔU

Uref = Uref + ΔU

Uref = Uref minus ΔU


P(k) minus P(k minus 1) gt 0

Simple U ICalculate P = U lowast I

Figure 7 The flowchart of classical perturb-and-observe algorithm

Keeping solar irradiation unchanged when temperaturechanges the output characteristic curves of PV array canbe obtained which are shown in Figures 4 and 5 It can beseen from the two figures that open-circuit voltage increasessignificantly and short-circuit current is a constantwhen tem-perature decreases The output power of PV array increaseswith the decrease of temperature and reaches the maximumat a certain point finally

It can be seen from the output characteristic analysis ofPV cell mentioned above that the output characteristic curvesof PV array change with external environmental factorssuch as solar irradiation and temperature Therefore MPPTalgorithm is added in the operating control of PV power

generation system to provide the maximum output power forload in different working conditions

3 Improved MPPT Algorithm Based on 119875-119880Curve Reconstitution

31 Classical Perturb-and-Observe Algorithm The workingprinciple of classical perturb-and-observe algorithm is shownas in Figure 6 and step search is adopted in this methodSuppose that the external environmental factors remainunchanged such as temperature and solar irradiation Δ119880is the voltage adjustment step and 119875max is the power ofmaximum power point


U (V)

P(W

)

P(k + 1)

P998400(k)

P(k + 12)

P(k)

(k + 1)T

(k + 12)T

(k)T

U(k) U(k + 1)

Figure 8 Power prediction schematic

0 10 20 30 40 500

1

2

3

4

5

6

|dPd

U|

800Wm2

1000Wm2

U (V)

Figure 9 Relation curve of |d119875d119880| against voltage U

0 10 20 30 40 500

1

2

3

4

5

6

Step

adju

stmen

t fac

torS

(k)

800Wm2

1000Wm2

U (V)

Figure 10 Relation curve of 119878(119896) against voltage 119880

Firstly an initial step is chosen perturbation is started onthe basis of the working voltage a forward perturbation stepis added Perturbation direction remains unchanged if thepower increases perturbation direction changes if the powerreduces Perturbation process is repeated as shown in Figure 6until the maximum power point is tracked Owing to the

fact that the perturbation step has a large impact on trackingaccuracy and speed it should be selected appropriately

The flowchart of classical perturb-and-observe algorithmis shown in Figure 7119880(119896) is the present voltage and 119868(119896) is thepresent current and119875(119896) is the corresponding power119880(119896minus1)is the last voltage and 119868(119896 minus 1) is the last current 119875(119896 minus 1)


Yes

No

Yes

No

Return

No

Yes

Start

Simple U(k) I(k) calculate P(k)

Simple U(k + 12) I(k + 12)

calculate P(k + 12) P998400(k)

simple U(k + 1) I(k + 1)

calculate P(k + 1)

Calculate ΔU = U(k + 1) minus U(k)

ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1

U(k + 1) = U(k) step

U(k + 1) = U(k) + S(k) step U(k + 1) = U(k) minus S(k) step

U(k + 1) = U(k)

Figure 11 Flowchart of improved MPPT algorithm

is the corresponding power 119880ref is reference voltage Δ119880 isvoltage adjustment step

Firstly Δ119875 and Δ119880 can be described as

Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)

When Δ119880 is positive if Δ119875 is also positive whichindicates that the current working point is on the left of themaximum power point then it should be in the perturbationmode of increasing voltage if Δ119875 is negative which indicates

that the current working point is on the right of themaximumpower point then it should be in the perturbation mode ofdecreasing voltage When Δ119880 is negative if Δ119875 is positivewhich indicates that the current working point is on theright of the maximum power point then it should be in theperturbation mode of decreasing voltage if Δ119875 is negativewhich indicates that the current working point is on theleft of the maximum power point then it should be in theperturbation mode of increasing voltage

It should be noted that the working point oscillates onboth sides of the maximum power point reciprocating due to


LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc

Figure 12 MPPT main circuit

a fixed perturbation step in which it is unable to be stabilizedat the maximum power point and sometimes misjudgmentphenomenon occurs When external conditions change theoutput characteristic curves of PV array change dynamicallyThus misjudgment may occur if a classical perturb-and-observe MPPT algorithm is used

32 Improved MPPT Algorithm In order to solve the mis-judgment problem of classical PampO algorithm power predic-tion is added which ensures the power points are in the same119875-119880 curve before and after the perturbation

Figure 8 shows a schematic diagram of power predictionWhen the sampling frequency is high enough assume thatthe change rate of solar irradiation in a sampling period isconstantWithout voltage perturbation at 119896119879 the power 119875(119896)is calculated Then the power 119875(119896 + 12) is calculated at(119896 + 12)119879 and the predicted power 1198751015840(119896) can be obtainedas follows

1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)

ThenΔ119880 is perturbed at (119896+1)119879 and the power is119875(119896+1)when perturbation voltage is 119880(119896 + 1) The measured power119875(119896 + 1) and the predicted power 1198751015840(119896) are on the same 119875-119880characteristic curve at the same solar irradiation theoreticallyTherefore the proposed MPPT algorithm in this paper doesnot exhibit misjudgment problem

At the same time in order to solve the contradictionbetween the tracking accuracy and speed a variable step isadopted

By (1) the output power of PV array can be approximatedas

119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)

Thus the derivative of power with respect to voltage canbe obtained as

d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)

Study shows that |d119875d119880| is suitable for perturbationstep Then the curve of |d119875d119880| and voltage 119880 are shownin Figure 9 It shows that the curves are different when solarirradiation varies greatly so it is difficult to get the normalizedfunction of the perturbation step to achieve the above goal

However as shown in Figure 9 |d119875d119880| and short-circuitcurrent are similar to the positive correlation on the left sideof MPP Therefore in order to find the normalized functionof voltage perturbation step (3) can be divided by outputcurrent of PV array after the absolute value operation whichcan be calculated as

119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)

where 119878(119896) is the step adjustment factorRelation curve of 119878(119896) against voltage U is shown in

Figure 10 Take 119878(119896) as the normalization factor of voltageperturbation step size According to the actual workingcondition of PV cell the perturbation step is adjusted in timewhich is described as

119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)

Note that step adjustment factor 119878(119896) increases sharplyon the right of MPP In order to make the MPPT algorithmable to be converged on the right of MPP in the 119875-119880 curvehere adjustment factor is limited 119878(119896) isin [0 1] And Figure 11shows a flowchart of the improved MPPT algorithm

4 Simulation Results and Analysis

The PV generation system consists of PV array moduleMPPT module DCDC converter module and so forthwhich is shown in Figure 12

The simulation conditions are as follows short-circuitcurrent is 345A open-circuit voltage is 435 V maximumpower point voltage is 35V maximum power point currentis 315 A temperature is 25∘C the initial step is 0005 andsimulation time is 06 s


0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )

(a) The solar irradiation curve

0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)

(b) The output voltage curve

0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)

(c) The output current curve

0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)

(d) The output power curve

0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD

(e) The duty-cycle curve

Figure 13 The classical PampO algorithm curves

Figure 13(a) shows the curve of solar irradiation changesover 119905 Figures 13(b)ndash13(e) are the simulation results accord-ing to Figure 13(a) where Figure 13(b) is the output voltagecurve Figure 13(c) is the output current curve Figure 13(d)is the output power curve and Figure 13(e) is the duty-cycle curve The figures show that the working point reaches

themaximumpower point at 003 s and themaximumpoweris 110W When solar radiation mutates the output power isnot stable and has an oscillation around MPP

Figure 14 shows the improved MPPT algorithm sim-ulation results Figure 14(a) is the output voltage curveFigure 14(b) is the output current curve Figure 14(c) is


0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)

(a) The output voltage curve

0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)

(b) The output current curve

0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)

(c) The output power curve

0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD

(d) The duty-cycle curve

Figure 14 The improved MPPT algorithm curves

the output power curve and Figure 14(d) is the duty-cyclecurve The figures show that MPP is tracked at 001 s andthe maximum power is 11025W MPP can be tracked fasterand smoother and the fluctuation of tracking process is verysmall

Compared with Figures 13 and 14 the classical PampOalgorithm oscillates around MPP and maximum powercannot be tracked accurately when solar irradiation mutatesWith the improvedMPPT algorithm the output power curveis smoother under the same conditions and MPP is trackedin a shorter time

5 Conclusion

In this paper the variable PampO MPPT algorithm basedon 119875-119880 curve reconstitution has been proposed to trackMPP And the proposed algorithm has been verified withthe simulation Compared with the classical PampO algorithmresults show thatMPP is tracked accuratelywith the proposedalgorithm and themisjudgment is eliminated effectively andthe contradiction between tracking speed and accuracy is also

relievedThe simulation result verifies the effectiveness of theproposed algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant E07060251507155 ChinaPostdoctoral Science Foundation under Grant 2013M541990Key Project of Science andTechnologyResearch of EducationDepartment of Henan Province under Grant 14A470002 andFundamental andCutting-EdgeTechnologyResearch Projectof Henan Province under Grant 152300410046

References

[1] M A G de Brito L Galotto L P Sampaio G de AzevedoeMelo and C A Canesin ldquoEvaluation of the main MPPTtechniques for photovoltaic applicationsrdquo IEEE Transactions onIndustrial Electronics vol 60 no 3 pp 1156ndash1167 2010


[2] D Zhou andC Chen ldquoMaximumpower point tracking strategybased on modified variable step-size incremental conductancealgorithmrdquo Power System Technology vol 39 no 6 pp 1492ndash1498 2015

[3] Y Yang and K Zhou ldquoPhotovoltaic cell modeling and MPPTcontrol strategiesrdquo Transactions of China Electrotechnical Soci-ety vol 26 no 1 pp 229ndash234 2011

[4] G-C Hsieh H-I Hsieh C-Y Tsai and C-H Wang ldquoPho-tovoltaic power-increment-aided incremental-conductanceMPPT with two-phased trackingrdquo IEEE Transactions on PowerElectronics vol 28 no 6 pp 2895ndash2911 2013

[5] Z M Dalala Z U Zahid and J-S Lai ldquoNew overall controlstrategy for small-scale wecs in mppt and stall regions withmode transfer controlrdquo IEEE Transactions on Energy Conver-sion vol 28 no 4 pp 1082ndash1092 2013

[6] M A Elgendy B Zahawi and D J Atkinson ldquoAssessment ofperturb and observe MPPT algorithm implementation tech-niques for PV pumping applicationsrdquo IEEE Transactions onSustainable Energy vol 3 no 1 pp 21ndash33 2012

[7] B Liu S Duan F Liu and P Xu ldquoPhotovoltaic array maximumpower point tracking based on improved perturbation andobservation methodrdquo Power System Technology vol 2 no 46pp 91ndash94 2009

[8] R Garg A Singh and S Gupta ldquoPV cell models and dynamicsimulation of MPPT trackers in MATLABrdquo in Proceedings ofthe 8th International Conference on Computing for SustainableGlobal Development (INDIACom rsquo14) pp 6ndash12 New DelhiIndia March 2014

[9] Q Mei M Shan L Liu and J M Guerrero ldquoA novel improvedvariable step-size incremental-resistanceMPPTmethod for PVsystemsrdquo IEEETransactions on Industrial Electronics vol 58 no6 pp 2427ndash2434 2011

[10] Z Peng J He G Ma C Zhou and F Li ldquoSampling periodoptimization design of output power of photovoltaic powergeneration MPPT systemsrdquo Proceedings of the Chinese Societyof Electrical Engineering vol 32 no 34 pp 24ndash29 2012

[11] D Sera L Mathe T Kerekes S V Spataru and R TeodoresculdquoOn the perturb-and-observe and incremental conductancemppt methods for PV systemsrdquo IEEE Journal of Photovoltaicsvol 3 no 3 pp 1070ndash1078 2013

[12] R Faraji A Rouholamini H R Naji R Fadaeinedjad andM R Chavoshian ldquoFPGA-based real time incremental con-ductance maximum power point tracking controller for pho-tovoltaic systemsrdquo IET Power Electronics vol 7 no 5 pp 1294ndash1304 2014

[13] A Hmidet N Rebei and O Hasnaoui ldquoExperimental studiesand performance evaluation of MPPT control strategies forsolar-powered water pumpsrdquo in Proceedings of the 10th Interna-tional Conference on Ecological Vehicles and Renewable Energies(EVER rsquo15) pp 1ndash12 Monte-Carlo Monaco April 2015

[14] Y Zhou F Liu J Yin and SDuan ldquoStudy on realizingMPPTbyimproved incremental conductance method with variable step-sizerdquo in Proceedings of the 3rd IEEE Conference on IndustrialElectronics and Applications (ICIEA rsquo08) pp 547ndash550 Singa-pore June 2008

[15] D Wu and X Wang ldquoA photovoltaic MPPT fuzzy controllingalgorithmrdquo Acta Energiae Solaris Sinica vol 32 no 6 pp 808ndash813 2011

[16] A Costabeber M Carraro and M Zigliotto ldquoConvergenceanalysis and tuning of a sliding-mode ripple-correlationMPPTrdquoIEEE Transactions on Energy Conversion vol 30 no 2 pp 696ndash706 2015

[17] S Li X Zhang H Zhang W Zhao and H Ni ldquoGlobal MPPTmethod based on power closed-loop control and PSO algo-rithmrdquo Proceedings of the Chinese Society of Electrical Engineer-ing vol 34 no 28 pp 4809ndash4816 2014

[18] P Kumar G Jain and D K Palwalia ldquoGenetic algorithm basedmaximum power tracking in solar power generationrdquo in Pro-ceedings of the International Conference on Power and AdvancedControl Engineering (ICPACE rsquo15) pp 1ndash6 Bengaluru IndiaAugust 2015

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Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Iph ID IP

Rs

IC

U RL

I0

VDD RP

Figure 1 Equivalent circuit of photovoltaic cell


0 10 20 30 40 500

1

2

3

4

5

6

7

600Wm2

800Wm2

1000Wm2

U (V)

I(A

)


algorithms are generally more complicated and are notconducive to realization of the system and are not conduciveto reduction of the unit costs as well

In this paper based on the mathematical model ofPV array and classical perturb-and-observe algorithm 119875-119880curve reconstitution is introduced to track the maximumpower point accurately Finally the proposed MPPT controlstrategy is verified by simulation Results show that themaximum power point is tracked accurately with the pro-posed MPPT algorithm and the misjudgment is eliminatedeffectively and the proposedMPPT algorithm also has a gooddynamic performance

2 Mathematical Model of PV Array

The photovoltaic cell is different from dry cell and bat-tery the latter can store the transformed energy Howeverphotovoltaic cell is a device based on photovoltaic effectwhich converts solar energy into electrical energy directlyand immediately Figure 1 shows an equivalent model of PVcell When solar irradiation is constant the photogeneratedcurrent 119868ph does not change with the working state of thephotovoltaic cell so it can be seen as a constant current

source 119877119871is the load added at both ends of the PV cell and

119880 is the terminal voltageBy Figure 1 the output current equation of the PV cell can

be described as

119868119862= 119868119878minus 1198680exp (

119902

119860119870119879119880) minus 1 (1)

where A is a P-N junction coefficient of semiconductordevices in photovoltaic cells 119870 is Boltzmannrsquos constant 119902 isunit charge119879 is absolute temperature 119868

119862is output current 119868

0

is diode reverse saturation current 119868119878is short-circuit current

(the corresponding 119868ph when 119880 is 0 in Figure 1)As can be seen from (1) the output characteristic curves

of PV cell change with external environment factors suchas solar irradiation and temperature Figure 2 shows 119880-119868characteristic curves when temperature is constant and solarirradiation changes It can be seen that short-circuit cur-rent reduces significantly and open-circuit voltage is almostunchanged when solar irradiation decreases Figure 3 shows119875-119880 characteristic curves with the same conditions Similarlyit can be seen from the figure that 119875-119880 characteristic curvehas a single peak and the maximum power point is itsextreme point and the output power increases with solarirradiation and reaches a maximum at a point



0 10 20 30 40 500

50

100

150

200

600Wm2

800Wm2

1000Wm2

U (V)

P(W

)



0 10 20 30 40 500

1

2

3

4

5

6

7

U (V)

I(A

)

0∘C

25∘C

50∘C


0 10 20 30 40 500

50

100

150

200

U (V)

P(W

)

0∘C

25∘C

50∘C




U (V)

P(W

)ΔU ΔU



Start

Return

Yes

Yes

Yes

No

No

No


Uref = Uref + ΔU

Uref = Uref + ΔU












U (V)

P(W

)

P(k + 1)

P998400(k)

P(k + 12)

P(k)

(k + 1)T

(k + 12)T

(k)T

U(k) U(k + 1)


0 10 20 30 40 500

1

2

3

4

5

6

|dPd

U|

800Wm2

1000Wm2

U (V)


0 10 20 30 40 500

1

2

3

4

5

6

Step

adju

stmen

t fac

torS

(k)

800Wm2

1000Wm2

U (V)






Yes

No

Yes

No

Return

No

Yes

Start


Simple U(k + 12) I(k + 12)



calculate P(k + 1)


ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1



U(k + 1) = U(k)




Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)





LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0 10 20 30 40 500

50

100

150

200

600Wm2

800Wm2

1000Wm2

U (V)

P(W

)



0 10 20 30 40 500

1

2

3

4

5

6

7

U (V)

I(A

)

0∘C

25∘C

50∘C


0 10 20 30 40 500

50

100

150

200

U (V)

P(W

)

0∘C

25∘C

50∘C




U (V)

P(W

)ΔU ΔU



Start

Return

Yes

Yes

Yes

No

No

No


Uref = Uref + ΔU

Uref = Uref + ΔU












U (V)

P(W

)

P(k + 1)

P998400(k)

P(k + 12)

P(k)

(k + 1)T

(k + 12)T

(k)T

U(k) U(k + 1)


0 10 20 30 40 500

1

2

3

4

5

6

|dPd

U|

800Wm2

1000Wm2

U (V)


0 10 20 30 40 500

1

2

3

4

5

6

Step

adju

stmen

t fac

torS

(k)

800Wm2

1000Wm2

U (V)






Yes

No

Yes

No

Return

No

Yes

Start


Simple U(k + 12) I(k + 12)



calculate P(k + 1)


ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1



U(k + 1) = U(k)




Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)





LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










U (V)

P(W

)ΔU ΔU



Start

Return

Yes

Yes

Yes

No

No

No


Uref = Uref + ΔU

Uref = Uref + ΔU












U (V)

P(W

)

P(k + 1)

P998400(k)

P(k + 12)

P(k)

(k + 1)T

(k + 12)T

(k)T

U(k) U(k + 1)


0 10 20 30 40 500

1

2

3

4

5

6

|dPd

U|

800Wm2

1000Wm2

U (V)


0 10 20 30 40 500

1

2

3

4

5

6

Step

adju

stmen

t fac

torS

(k)

800Wm2

1000Wm2

U (V)






Yes

No

Yes

No

Return

No

Yes

Start


Simple U(k + 12) I(k + 12)



calculate P(k + 1)


ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1



U(k + 1) = U(k)




Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)





LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










U (V)

P(W

)

P(k + 1)

P998400(k)

P(k + 12)

P(k)

(k + 1)T

(k + 12)T

(k)T

U(k) U(k + 1)


0 10 20 30 40 500

1

2

3

4

5

6

|dPd

U|

800Wm2

1000Wm2

U (V)


0 10 20 30 40 500

1

2

3

4

5

6

Step

adju

stmen

t fac

torS

(k)

800Wm2

1000Wm2

U (V)






Yes

No

Yes

No

Return

No

Yes

Start


Simple U(k + 12) I(k + 12)



calculate P(k + 1)


ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1



U(k + 1) = U(k)




Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)





LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Yes

No

Yes

No

Return

No

Yes

Start


Simple U(k + 12) I(k + 12)



calculate P(k + 1)


ΔP = P(k + 1) minus P998400(k)

S(k) = |ΔPΔU|I(k)

ΔP = 0

ΔPΔU gt 0

S(k) gt 1



U(k + 1) = U(k)




Δ119875 = 119875 (119896) minus 119875 (119896 minus 1)

Δ119880 = 119880 (119896) minus 119880 (119896 minus 1)

(2)





LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LoadPVarray

L

DCDC converter

MPPT PWM

Cpv

Ipv Upv

Cdc





1198751015840(119896) = 2119875 (119896 +

1

2) minus 119875 (119896) (3)




119875 = 119868119878119880 minus 1198680119880exp [

119902

119860119870119879119880] minus 1 (4)


d119875d119880= 119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0 (5)



119878 (119896) =1

119868

10038161003816100381610038161003816100381610038161003816

d119875d119880

10038161003816100381610038161003816100381610038161003816

=1

119868

1003816100381610038161003816100381610038161003816119868119878minus 1198680exp [119902

119860119870119879119880] lowast [1 +

119902

119860119870119879119880] minus 119868

0

1003816100381610038161003816100381610038161003816

(6)



119880 (119896 + 1) = 119880 (119896) plusmn 119878 (119896) step (7)






0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06

500

600

700

800

900

1000

t (s)

Sola

r irr

adia

tion

(Wm

2 )


0 01 02 03 04 05 0605

101520253035404550

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD







0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 060

5

10

15

20

25

30

35

40

t (s)

U(V

)


0 01 02 03 04 05 0615

2

25

3

35

t (s)

I(A

)


0 01 02 03 04 05 060

20

40

60

80

100

120

t (s)

P(W

)


0 01 02 03 04 05 060

01

02

03

04

05

06

07

08

09

1

t (s)

Dut

y-cy

cleD





5 Conclusion



Competing Interests


Acknowledgments


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 An Improved MPPT Algorithm for PV...

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Transcript of Research Article An Improved MPPT Algorithm for PV...