MPPT Algorithms

8102019 MPPT Algorithms

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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 2

is not known This is the problem for MPPT

There are numerous methods that address the issue of

operating the PV module at the MPP The open voltage method

measures the open circuit voltage and operates at a voltage

around 76 of that value [2] This is based on the observation

that the MPP voltage is almost directly proportional to the

open circuit voltage The short circuit method is similar but

uses current instead operating near 85 of I sc [3] Fuzzy

controllers may also be used [4] [5] However the hill

climbing methods PampO and IncCond appear to be the most

common in the literature and are what are discussed in this

paper

I I SOM E I NCONSISTENCIES

Before getting to the comparison it seems worth mentioning

a couple inconsistencies that appear in the literature This sup-

ports the notion that the difference between the two algorithms

isnrsquot as well known as it should be

Many papers claim that the PampO method oscillates at steady

state even though it seems this was never really an issue A

1983 paper [6] shows it can be made to converge at steadystate as well as being acknowledged by [7] the paper that

introduces the IncCond method However many articles state

that the PampO method oscillates at steady state [8] [9] It is

not necessarily wrong to state that the PampO method oscillates

at steady state However the implication is that this is not

a problem with the standard IncCond algorithm However it

is also an issue with the IncCond in its original form as is

sometimes acknowledged [10] If one looks at both of the

flowcharts (see figures 2 and 4) it is easy to see that neither

algorithm in their most basic form change the value of ∆V Another inconsistency with these methods comes in the

discussion of the needed sensors For example [11] states 4

sensors are needed for the IncCond method which is morethan needed for the PampO method but they donrsquot expand on

this claim In [12] it is stated that the same number of variables

are measured in both IncCond and PampO In [9] they just say

ldquoA disadvantage of the INC algorithm with respect to PampO is

in the increased hardware and software complexity moreover

this latter leads to increased computation times and to the

consequent slowing down of the possible sampling rate of

array voltage and currentrdquo

It would seem that the same number of sensors would be

required for both methods Current and voltage need to be

measured for both of the algorithms to work as seen in the

flowcharts It is true that the IncCond algorithm is slightly

more complex but this isnrsquot really much of an issue since mostmicrocontrollers should have plenty of memory to hold either

algorithm Also as will be seen later the MPPT algorithm

should not be run at a very high speed anyway and so a

slight increase in computation time should not be an issue The

frequency of the switching and perhaps even the sampling

will likely be much faster than the actual running of the

algorithm

In this paper the algorithms will be discussed in more detail

than is normally given The IncCond method will be seen to

be slightly better than the PampO method and the reason for

this will be mathematically justified

III THE MPPT CONTROL A LGORITHMS

1) Perturb and Observe The PampO method gets its name

from how it works The algorithm will change (perturb) the

voltage of the PV panel (by changing the duty cycle) and

then measure (observe) how the power changes If the power

increases the voltage will continue to be changed in this

direction If a change in voltage causes a decrease in power

the voltage will then be changed in the other direction Acondensed PampO algorithm is shown in Figure 21

983117983141983137983155983157983154983141 983158983151983148983156983137983143983141 983137983150983140 983139983157983154983154983141983150983156

983158983080983150983081983084 983145983080983150983081

983152983080983150983081983085983152983080983150983085983089983081983101983088983103

983152983080983150983081983102983152983080983150983085983089983081 983137983150983140 983158983080983150983081983102983158983080983150983085983089983081

983119983122

983152983080983150983081983100983152983080983150983085983089983081 983137983150983140 983158983080983150983081983100983158983080983150983085983089983081

983126983155983141983156983101983126983155983141983156983083Δ983126 983126983155983141983156983101983126983155983141983156983085Δ983126

983122983141983156983157983154983150

983129983109983123

983118983119

983129983109983123

983118983119

Fig 2 Perturb and Observe MPPT algorithm

The PampO method may sometimes move in the wrong

direction To illustrate this for a fixed IV curve (the case

of changing conditions will be considered later) consider a

scenario in which the voltage is increasing Suppose going

from v1 to v2 caused the power of the system to increase and

moving to v3 decreases the power This could happen in two

ways as illustrated in the figures (3a) and (3b) Either v2 lt V mor v2 gt V m In the scenario in Figure 3b the voltage should

be decreased not increased from v2 because V m has been

passed Once it moves to v3 it will then without a decreasing

voltage step size move back to v2 which is at a higher power

and so on again to v1 For the scenario in Figure 3a when the

algorithm goes from v3 to v2 it should then turn around but it

will go to v1 instead This does not seem too terrible In either

case the algorithm oscillates around 3 points The bigger issue

is how tracking occurs during changing irradiance conditions

The IncCond method is supposed to have better behavior inthis regard This will be discussed more later

2) Incremental Conductance In [7] the authors state that

the PampO method has a problem at steady state namely that

it continually oscillates around the maximum power point

since the voltage is always being changed However they

acknowledge that this can easily be remedied by decreasing

the perturbation step size This paper states that the main

problem with the PampO method occurs during rapidly changing

atmospheric conditions The problem is that for example a

1The open source program Dia was used to make the flowcharts in thispaper




24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v1

v2

v3

(a) v2 lt V m

24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v2

v3

v1

(b) v2 gt V m

Fig 3 Increasing power and being left of MPP and being

right of MPP

decrease in power may be due to a decrease in irradiance

rather than because the operating point moved further from

the MPP Suppose for example that the voltage is increased

but is still to the left of the MPP Then it should continue

to increase However due to a sharp decrease in irradiance

the algorithm incorrectly decreases the voltage (This will be

illustrated later) To remedy this they introduce the IncCondmethod illustrated in Figure 4

The IncCond method claims to make use of the fact that

dPdv = 0 at the MPP dPdv gt 0 to the left of the MPP

and dPdv lt 0 to the right of the MPP Using dPdV =d(IV )dV = I + V dIdV inequalities in terms of i and vare obtained The derivatives are approximated numerically by

sampling quickly enough

IV MODELING THE P V SYSTEM

Before comparing the algorithms a brief discussion of the

PV system is given This is so that the origin of the figures

983117983141983137983155983157983154983141 983158983151983148983156983137983143983141 983137983150983140 983139983157983154983154983141983150983156

983158983080983150983081983084 983145983080983150983081

983126983155983141983156983101983126983155983141983156983083Δ983126 983126983155983141983156983101983126983155983141983156983085Δ983126

983122983141983156983157983154983150

983129983109983123

983118983119

983129983109983123

983118983119

983140983145983101983145983080983150983081983085983145983080983150983085983089983081

983140983158983101983158983080983150983081983085983158983080983150983085983089983081

983140983158983101983088983103

983140983145983087983140983158983101983085983145983087983158983103 983140983145983101983088983103

983140983145983102983088983103983140983145983087983140983158983102983085983145983087983158983103

983126983155983141983156983101983126983155983141983156983085Δ983126 983126983155983141983156983101983126983155983141983156983083Δ983126

983129983109983123983129983109983123

983129983109983123

983118983119 983118983119

983118983119

Fig 4 Incremental Conductance MPPT algorithm

given later will be better understood In particular a model for

the PV module as well as a converter are given It is to thisPV-converter system that the MPPT algorithms will be applied

For more details on the PV system setup in this section one

may refer to [13] [14]

A Model of PV module

Perhaps the most widely used model for the PV module is

given in Figure 5 This is the single diode model

983158

983145

983122983152

983122983155983113983143

Fig 5 A circuit representation of a PV module

The equation of the circuit in Figure 5 is

i = I g minus I s(ev+iRs

a minus 1)minusv + iRs

R p

(1)

In this equation i is the PV current v is the PV voltage

Rs is the series resistor R p is the parallel resistor I g is the

light-generated current I s is the diodersquos saturation current

and a = AkTq where A is the diode ideality factor k is

Boltzmannrsquos constant T is the temperature and q is the charge

of an electron

For simulation purposes the no resistor model (NRM)

(Rs = 0 R p = infin) is adequate [13] The module that will

be used for the simulations in this work is shown in Table

I Its parameter values for the single diode model with no

resistors (NRM) is given in Table II




Model V oc(V ) I sc(A) V m(V ) I m(Ω)BP-SX3195 307 86 244 796

TABLE I PV module used for testing

I g(A) I s(A) a(V ) Rp(Ω) Rs(Ω)86 27307e-5 24249 infin 0

TABLE II Parameter values for BP PV model

B Model of PV system

In this paper a buck converter with a fixed voltage output

will be used This circuit is shown in Figure 6 In the figure

the two PV resistors were kept though they are not used in

the simulation as discussed previously Using the equation of

the buck converter v = voutd

where d is the duty cycle vis the PV voltage and vout is the fixed output voltage one

can obtain Equation 2 as a means of changing the PV module

voltage for use with the MPPT algorithms

v2 = v1 + ∆v lArrrArr d2 = vout

voutd1

+ ∆v

(2)

983158

983116

983126983151983157983156

983145983116

983107

983145

983113983143

983122983155

983122983152

Fig 6 The PV model connected to a buck converter

V TESTING AT A FIXED IRRADIANCE AND TEMPERATURE

To begin with a number of comparisons will be made at

standard test conditions (STC) In other words the MPP is

fixed and so the algorithms need only converge to a point on

a fixed IV curve rather than deal with changing conditions

and so a changing MPP

A PampO vs IncCond

It is easy to see that dP dv

gt 0 is equivalent to didv gt minusiv

as shown in Equation 3 (the cases where ldquogtrdquo is replaced with

rdquoltldquo and rdquo=ldquo are the same)

0 lt dP dv

= d(iv)dv

= v didv

+ i lArrrArr didv

gt minus iv

(3)

Since the PampO algorithm looks at dPdv gt 0 and the

IncCond looks at didv gt minusiv they appear to be equivalent

The PampO algorithm checks on increase (or decrease) in power

relative to changes in voltage and the IncCond method checks

whether change in current over change in voltage (ie a

change in conductance which is where the name of the

algorithm likely comes from) is greater (or less or equal)

than the negative of current over voltage However when the

two algorithms were compared their behavior is seen to be

different This comparison can be seen in Figure 7

0 5 10 15 20 25 3024

245

25

255

26BP NRM with Buck Converter and control

time (s)

P V V

o l t a g e

PampO

IncCond

(a) PV voltage output

0 5 10 15 20 25 30194

1942

1944

1946

1948


time (s)

P V

P o w e r

PampO

(b) PV power output

Fig 7 Results of PampO and IncCond methods using a fixed

voltage step size of 01 volts

The original paper [7] does not explain the differences (nor

any other papers that were considered in this research) but

an explanation will be given presently Suppose the PampO

algorithm moved from position 1 to position 2 (v1 to v2)

Then that algorithm is comparing the powers P 2 vs P 1 at

voltages 2 and 1 More exactly one is comparing v2i2 to v1i1

Suppose one wishes to see if the change was positive That isthe following is checked

v2i2 minus v1i1 gt 0

Compare this to the IncCond case where the following in-

equality is checked

di

dv =

i2 minus i1v2 minus v1

gt minusi2v2

lArrrArr 2i2v2 minus i1v2 minus i2v1 gt 0

The fact that the derivatives are not being used but rather

numerical methods is what makes the algorithms different

In the original paper [7] it is stated ldquoHence the PV array




terminal voltage can be adjusted relative to the [MPP] voltage

by measuring the incremental and instantaneous array conduc-

tances (dIdV and IV respectively)rdquo The derivatives were

approximated using the differences between the voltages and

currents at positions 1 and 2 Many other papers seem to reuse

this explanation as if PampO and IncCond were not equivalent

in the differential form One should use ∆i∆v rather than

the derivative notation since it is the difference equation form

that sets the two algorithms apart not the differential form

Now that the equations have been seen to appear differently

it will be shown mathematically that the IncCond is better in

turning around once the MPP is passed

To do this a comparison is made for the cut off case of the

PampO algorithm the case where v1 = v2 but P 1 = P 2 It is

this case where the algorithm is at the threshold of moving

the voltage left or right Suppose that v2 gt v1 as the other

case is similar If the voltage were a pinch more to the left

power would have increased and so voltage would have been

increased after v2 if it were a pinch to the right power would

have decreased and so voltage would have been decreased

after v2

How does the IncCond algorithm fare for this caseIn this case

v1i1 = v2i2 v2 gt v1

Now looking at the power curve it should be clear that v2must be to the right of the MPP and v1 to the left (remember

at this point STC is assumed) However the PampO algorithm

does not know this What about the IncCond method For it to

work better it would be necessary that ∆i∆v lt minusiv Some

simple algebra (requiring the substitution of v1i1 = v2i2)

yields equation 4 which is clearly true


lt minusi2v2hArr (v1 minus v2)2 gt 0 (4)

For the other case (v2 lt v1) the math is quite similar Now

v2 minus v1 is negative so when multiplying be sure to flip the

inequality sign and the result is the same This explains the

slight difference between PampO and IncCond This is a strong

equality Hence it is possible for a situation like that illustrated

in Figure 3b to move left instead of right at v2 even if the

power is greater at v2 This explains why the IncCond turns

around quicker than the PampO algorithm in Figure 7 Note

that the IncCond method does not always turn around when

it should but only better than PampO

Consider Figure 8 The power at v2 is more than that at

v1 and so the PampO algorithm will perturb once more to the

right (which in this case would cause it to go far off the plot -though it should be stated that a 3 volt step might be a bit larger

than normal) What about the IncCond algorithm It is easy

to calculate ∆i∆v

= minus0293 and minus i2v2

= minus0283 Hence ∆i∆v

lt

minus i2v2

and so the voltage will move left Assuming the step size

doesnrsquot change it will go back to v1 Since minus i1v1

= minus0358 it

will then move back to the right In other words the IncCond

will bounce around v1 and v2 whereas the PampO algorithm

will bounce around v1 v2 and v3 (not shown) causing more

power loss It is important to note that if v2 were slightly

smaller but still at a larger power then IncCond would have

failed just as PampO did

22 23 24 25 26 27 28

175

180

185

190

195

200

X 2484Y 1946

Power Curve

Voltage

P o w e r

X 23Y 1895

X 26Y 1914

v1

vm

v2

Fig 8 An example of IncCond behaving better than PampO

It should also be mentioned though it wonrsquot be proven here

that the IncCond method does not turn around too early Forexample if V m gt v2 gt v1 then v3 will be greater than v2

The algorithm wonrsquot cause the voltage to turn around before

getting to the MPP

See Figure 7 for how the two compare using a step size of

01 volts Notice that the IncCond voltage doesnrsquot go as high

above V m as the PampO voltage does at steady state It should be

noted that it took a handful of simulations to get good results

like these The original results obtained were used a step size

of 03 volts and an average sampling method (discussed later)

to obtain the measured value The results of this are shown in

Figure 9 In this case the two algorithms were different but

just as bad with the PampO going one more voltage to the right

of the MPP than the IncCond method but the IncCond methodgoing one more to the left This is likely due to an issue with

the measured sample (some transient affecting the results) It

is not because the IncCond method behaves more poorly than

the PampO when decreasing the voltage In the model used in

this work the transient behavior is more pronounced than it

would be in practice Some current work is being done by the

author showing how converter losses bring down the transient

drastically Hence with a real system and smarter sampling

this shouldnrsquot be an issue The other tested cases had identical

results for the PampO and IncCond methods So the advantage

of the IncCond method is not that pronounced

VI TESTING WITH CHANGING CONDITIONS

There are many papers that compare algorithms [3] [7]ndash

[9] but the method of comparison is usually not well-defined

and there is no standard method for comparison Recently a

standard method for testing the algorithms was presented [15]

This proposal suggests the irradiance input shown in Figure

10 Temperature changes are relatively slow and so the effects

of these changes are not considered

The times when it changes are at the following seconds

60140200204264266386388448452512592 starting at

0 and ending at 652




0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

In the paper introducing the IncCond method [7] it was

claimed that this algorithm was developed to deal with poor

tracking of the PampO algorithm during changing irradiance

conditions One can show mathematically that the IncCond

is better during changing conditions The mathematics are the

same as in the STC case except this time v1 is on IV curve 1and v2 is on IV curve 2 where assuming conditions changed

during this time the curves are not the same However as

stated before the differences arenrsquot that great The results of

the two algorithms are given in figures 11 and 12 where a step

size of 03 volts was used The steady state behavior appears

the same The only noticeable difference appears to be around

500 seconds where the IncCond is at a slightly lower voltage

during the first part of the downward ramp

The PampO algorithm had an efficiency of 9881 and the

IncCond algorithm gets 9885 efficiency The efficiency is

calculated starting at 60s since initial conditions should not

983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156

Fig 10 Changing Irradiance Input for MPPT testing

0 100 200 300 400 500 6000

5

10

15

20

25

30

BP NRM with Buck Converter and PampO method

time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150

200BP NRM with Buck Converter and PampO method

time (s)

P V

P o w e r

(b) Power

Fig 11 Results of PampO algorithm with Ropp input




count against the algorithms used (since the algorithms donrsquot

have a standard for how they start) It is seen that the IncCond

method is better but not substantially so Still if there is no

disadvantage to using the IncCond method in place of the PampO

method it should be done

0 100 200 300 400 500 6000

5

10

15

20

25

30

BP NRM with Buck Converter and IncCond method

time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150

200BP NRM with Buck Converter and IncCond method

time (s)

P V

P o w e r

(b) Power

Fig 12 Results of IncCond algorithm with Ropp input

Notice that the algorithms move in the wrong direction near

the beginning This is due to the fact that increased irradiance

might give an increase in power even if moving in the wrongdirection In other words the increase in energy due to increase

in irradiance is greater than the decrease in energy due to

moving away from V m Even though the IncCond is better at

recognizing when it passes the MPP it is not perfect Both

also fail to track the decreasing ramp that occurs around 500s

This is because the power is decreasing due to irradiance

regardless of what direction you move in (this is dependent

on slope of ramp as well as step size chosen) Another issue

as stated previously with regards to the unmodified version

of these algorithms is the oscillation at steady state (for both

algorithms not just PampO)

VII REMARKS ON SAMPLING

In the description of the algorithms little is said about

how the sampling is done Papers claim to be comparing

measured voltage and current values to the prior measured

values but not how these values are obtained In the above

averages were used and were a second apart In particular 05

seconds was given for the transient to end and then voltages

and currents were recorded for 05 seconds at 1kHz Thesevalues were then averaged (Originally checking the standard

deviation was also done to make sure one was at steady state

before changing the voltage but this proved not to work well

during changing irradiance conditions) In this section only

one sample will be used to calculate the voltage and current

used within the algorithm This will make use of voltage and

current values sampled at 10ms 100ms and 1s with the

algorithm running after each sample The results for the PampO

algorithm (the IncCond are similar) are shown in Figure 13

for steady irradiance conditions

0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms

Fig 13 Results of PampO method using one voltagecurrent

sample

Why do the shorter sampling times yield worse results

Suppose one is trying to increase the voltage Then sampling

too soon reads a smaller voltage due to transient delay than

what the actual steady state value is Perhaps now the voltage

is set to the right of the MPP but the actual value was still

left of the MPP So the voltage is increased again perhaps

a couple more times Now the voltage is finally sampled to

be to the right of the MPP and so the algorithm starts tryingto go back The voltage is decreased but it is still swinging

up and so the power decreases So now it tries increasing

again etc This type of behavior can result in going far past

the MPP before everything is aligned enough to begin coming

back A slightly slower sampling may cause the values to be

sampled nearer the overshoot ie beyond where the voltage

is set rather than premature It may now try to turn around

sooner than it should Once again resulting in going the wrong

way a bit though not quite as bad as sampling too soon

It appears that sampling every second yields the best results

In fact those results using just one sample yield slightly




better results than the averaging used previously Averaging

might still be preferable in actual system where noise could

interfere depending on sensitivity of equipment used Perhaps

a smaller interval of averaging could also be considered The

best approach will depend on the frequency of the switch as

well as L and C values Also as mentioned before a real

system may have slightly better transient behavior allowing

for quicker sampling and running of the MPPT algorithm

Regardless it seems that neither of the algorithms will

be operating at a very high frequency (the switch converter

perhaps and maybe even sampling for measurements but

not the actual running of the MPPT algorithm) Perhaps

the IncCondrsquos slightly increased computational time has a

negligible penalty

VIII CONCLUSION

For non-varying conditions the two algorithms performed

similarly and both oscillated around the MPP The IncCond

method has a slight advantage and could potentially oscillate

slightly less due to turning around quicker once passing the

MPP However for a small step size the difference would befairly negligible For varying conditions the IncCond method

also did slightly better for the same reason However it does

not seem to have a large advantage to the PampO method

Assuming there are no added costs in implementing the

IncCond method over the PampO method it should be the

preferred method However if some of the claims that the

IncCond method indeed adds a performance or cost penalty

then it may not be worth it

REFERENCES

[1] R Messenger and J Ventre Photovoltaics Systems Engineering 2nd edCRC 2004

[2] D-Y Lee H-J Noh D-S Hyun and I Choy ldquoAn improved mpptconverter using current compensation method for small scaled pv-applicationsrdquo in 18th Annual IEEE Applied Power Electronics Confer-ence and Exposition 2003

[3] V Salas E Olias A Barrado and A Lazaro ldquoReview of the maximumpower point tracking algorithms for stand-alone photovoltaic systemsrdquo

Solar Energy Materials amp Solar Cells vol 90 2006[4] X Wei and H Jing ldquoMppt for pv system based on a novel fuzzy controlstrategyrdquo in 2010 International Conference on Digital Manufacturing amp

Automation 2010[5] F Bouchafaa D Beriber and M S Boucherit ldquoModeling and simula-

tion of a g[ri]d connected pv generation system with mppt fuzzy logiccontrolrdquo in 2010 7th International Multi-Conference on Systems Signalsand Devices 2010

[6] O Wasynczuk ldquoDynamic behavior of a class of photovoltaic powersystemsrdquo IEEE Transactions on Power Apparatus and Systems volPAS-102 no 9 September 1983

[7] K H Hussein I Muta T Hoshino and M Osakada ldquoMaximum pho-tovoltaic power tracking an algorithm for rapidly changing atmosphericconditionsrdquo Proc Inst Elect Eng vol 142 no 1 January 1995

[8] D P Hohm and M E Ropp ldquoComparative study of maximumpower point tracking algorithms using an experimental programmablemaximum power point tracking test bedrdquo in Photovoltaic Specialists

Conference 2000[9] N Femia G Petrone G Spagnuolo and M Vitelli ldquoOptimization of perturb and observe maximum power point trackingrdquo IEEE Transactionson Power Electronics vol 20 no 4 July 2005

[10] F Liu S Duan F Liu B Liu and Y Kang ldquoA variable step sizeinc mppt method for pv systemsrdquo IEEE Transactions on Industrial

Electronics vol 55 no 7 July 2008[11] C Hua and C Shen ldquoStudy of maximum power tracking techniques

and control of dcdc converters for photovoltaic power systemrdquo in 29th Annual IEEE Power Electronics Specialists Conference 1998

[12] J Pan C Wang and F Hong ldquoResearch of photovoltaic chargingsystem with maximum power point trackingrdquo in The Ninth InternationalConference on Electronic Measurement amp Instruments 2009

[13] T Bennett A Zilouchian and R Messenger ldquoPhotovoltaic model andconverter topology considerations for mppt purposesrdquo Solar Energyvol 86 2012

[14] T Bennett ldquoDeveloping a photovoltaic mppt systemrdquo DissertationAugust 2012

[15] M Ropp J Cale M Mills-Price M Scharf and S G HummelldquoA test protocol to enable comparative evaluation of maximum powerpopint trackers under both static and dynamic irradiancerdquo in IEEE 37thPhotovoltaic Specialist Conference 2011

Thomas Bennett Thomas received his bachelorrsquos

degree in mathematics from Florida Gulf CoastUniversity in 2006 and his masters in mathematicsfrom Florida Atlantic University in 2008 He is setto finish his PhD in electrical engineering fromFlorida Atlantic University in 2012 His currentresearch is in the areas of renewable energy powersystems power electronics and control




Ali Zilouchian Ali Zilouchian received his PhDfrom George Washington University WashingtonDC in 1986 He has been with the College of En-gineering and Computer Science at Florida AtlanticUniversity for the past 26 years He is currently theAssociate Dean for Academic Affairs and a Profes-sor in the Department of Computer and ElectricalEngineering and Computer Science

His recent projects have been funded by Deptof Energy FPL National Science Foundation and

the Broward County School district In addition tohis current research in the area of alternative energy and sustainability hehas conducted research on the applications of soft computing methodologiesto industrial processes including desalination processes oil refineries jetengines model reduction of multivariable systems and 2-D digital filters

Dr Zilouchian is a senior member of IEEE since 1995 and currentlyan associate editor of the International Journal of Electrical and ComputerEngineering out of Oxford UK

Roger Messenger Roger Messenger received hisPhD in electrical engineering from the Universityof Minnesota He is Professor Emeritus of ElectricalEngineering at Florida Atlantic University where he

taught for 35 years During his time at FAU heworked his way through the academic ranks and alsoserved in administrative posts for 11 years includingDepartment Chair Associate Dean and Director of the FAU Center for Energy Conservation

He is author along with Dr Jerry Ventre of theFlorida Solar Energy Center of the book Photo-

voltaic Systems Engineering now in its 3rd edition Since his retirement fromFAU in 2005 he has been involved in the design of more than 200 PV systemsranging from small stand-alone systems to complex battery-backup grid-connected systems as well as several systems in the megawatt capacity rangeHe is currently serving as Senior AssociatePV Specialist at FAE Consultingin Boca Raton FL where he spends most of his time supervising the designof PV systems for residential commercial and government use




is not known This is the problem for MPPT

There are numerous methods that address the issue of

operating the PV module at the MPP The open voltage method

measures the open circuit voltage and operates at a voltage

around 76 of that value [2] This is based on the observation

that the MPP voltage is almost directly proportional to the

open circuit voltage The short circuit method is similar but

uses current instead operating near 85 of I sc [3] Fuzzy

controllers may also be used [4] [5] However the hill

climbing methods PampO and IncCond appear to be the most

common in the literature and are what are discussed in this

paper

I I SOM E I NCONSISTENCIES

Before getting to the comparison it seems worth mentioning

a couple inconsistencies that appear in the literature This sup-

ports the notion that the difference between the two algorithms

isnrsquot as well known as it should be

Many papers claim that the PampO method oscillates at steady

state even though it seems this was never really an issue A

1983 paper [6] shows it can be made to converge at steadystate as well as being acknowledged by [7] the paper that

introduces the IncCond method However many articles state

that the PampO method oscillates at steady state [8] [9] It is

not necessarily wrong to state that the PampO method oscillates

at steady state However the implication is that this is not

a problem with the standard IncCond algorithm However it

is also an issue with the IncCond in its original form as is

sometimes acknowledged [10] If one looks at both of the

flowcharts (see figures 2 and 4) it is easy to see that neither

algorithm in their most basic form change the value of ∆V Another inconsistency with these methods comes in the

discussion of the needed sensors For example [11] states 4

sensors are needed for the IncCond method which is morethan needed for the PampO method but they donrsquot expand on

this claim In [12] it is stated that the same number of variables

are measured in both IncCond and PampO In [9] they just say

ldquoA disadvantage of the INC algorithm with respect to PampO is

in the increased hardware and software complexity moreover

this latter leads to increased computation times and to the

consequent slowing down of the possible sampling rate of

array voltage and currentrdquo

It would seem that the same number of sensors would be

required for both methods Current and voltage need to be

measured for both of the algorithms to work as seen in the

flowcharts It is true that the IncCond algorithm is slightly

more complex but this isnrsquot really much of an issue since mostmicrocontrollers should have plenty of memory to hold either

algorithm Also as will be seen later the MPPT algorithm

should not be run at a very high speed anyway and so a

slight increase in computation time should not be an issue The

frequency of the switching and perhaps even the sampling

will likely be much faster than the actual running of the

algorithm

In this paper the algorithms will be discussed in more detail

than is normally given The IncCond method will be seen to

be slightly better than the PampO method and the reason for

this will be mathematically justified

III THE MPPT CONTROL A LGORITHMS

1) Perturb and Observe The PampO method gets its name

from how it works The algorithm will change (perturb) the

voltage of the PV panel (by changing the duty cycle) and

then measure (observe) how the power changes If the power

increases the voltage will continue to be changed in this

direction If a change in voltage causes a decrease in power

the voltage will then be changed in the other direction Acondensed PampO algorithm is shown in Figure 21

983117983141983137983155983157983154983141 983158983151983148983156983137983143983141 983137983150983140 983139983157983154983154983141983150983156

983158983080983150983081983084 983145983080983150983081

983152983080983150983081983085983152983080983150983085983089983081983101983088983103

983152983080983150983081983102983152983080983150983085983089983081 983137983150983140 983158983080983150983081983102983158983080983150983085983089983081

983119983122

983152983080983150983081983100983152983080983150983085983089983081 983137983150983140 983158983080983150983081983100983158983080983150983085983089983081

983126983155983141983156983101983126983155983141983156983083Δ983126 983126983155983141983156983101983126983155983141983156983085Δ983126

983122983141983156983157983154983150

983129983109983123

983118983119

983129983109983123

983118983119

Fig 2 Perturb and Observe MPPT algorithm

The PampO method may sometimes move in the wrong

direction To illustrate this for a fixed IV curve (the case

of changing conditions will be considered later) consider a

scenario in which the voltage is increasing Suppose going

from v1 to v2 caused the power of the system to increase and

moving to v3 decreases the power This could happen in two

ways as illustrated in the figures (3a) and (3b) Either v2 lt V mor v2 gt V m In the scenario in Figure 3b the voltage should

be decreased not increased from v2 because V m has been

passed Once it moves to v3 it will then without a decreasing

voltage step size move back to v2 which is at a higher power

and so on again to v1 For the scenario in Figure 3a when the

algorithm goes from v3 to v2 it should then turn around but it

will go to v1 instead This does not seem too terrible In either

case the algorithm oscillates around 3 points The bigger issue

is how tracking occurs during changing irradiance conditions

The IncCond method is supposed to have better behavior inthis regard This will be discussed more later

2) Incremental Conductance In [7] the authors state that

the PampO method has a problem at steady state namely that

it continually oscillates around the maximum power point

since the voltage is always being changed However they

acknowledge that this can easily be remedied by decreasing

the perturbation step size This paper states that the main

problem with the PampO method occurs during rapidly changing

atmospheric conditions The problem is that for example a

1The open source program Dia was used to make the flowcharts in thispaper




24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v1

v2

v3

(a) v2 lt V m

24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v2

v3

v1

(b) v2 gt V m


right of MPP















983117983141983137983155983157983154983141 983158983151983148983156983137983143983141 983137983150983140 983139983157983154983154983141983150983156

983158983080983150983081983084 983145983080983150983081

983126983155983141983156983101983126983155983141983156983083Δ983126 983126983155983141983156983101983126983155983141983156983085Δ983126

983122983141983156983157983154983150

983129983109983123

983118983119

983129983109983123

983118983119

983140983145983101983145983080983150983081983085983145983080983150983085983089983081

983140983158983101983158983080983150983081983085983158983080983150983085983089983081

983140983158983101983088983103

983140983145983087983140983158983101983085983145983087983158983103 983140983145983101983088983103

983140983145983102983088983103983140983145983087983140983158983102983085983145983087983158983103

983126983155983141983156983101983126983155983141983156983085Δ983126 983126983155983141983156983101983126983155983141983156983083Δ983126

983129983109983123983129983109983123

983129983109983123

983118983119 983118983119

983118983119









983158

983145

983122983152

983122983155983113983143





R p

(1)






of an electron























voutd1

+ ∆v

(2)

983158

983116

983126983151983157983156

983145983116

983107

983145

983113983143

983122983155

983122983152








A PampO vs IncCond





0 lt dP dv

= d(iv)dv

= v didv

+ i lArrrArr didv

gt minus iv

(3)











0 5 10 15 20 25 3024

245

25

255


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30194

1942

1944

1946

1948


time (s)

P V

P o w e r

PampO

(b) PV power output












equality is checked

di

dv =


gt minusi2v2




























after v2




























lt

minus i2v2



= minus0358 it







22 23 24 25 26 27 28

175

180

185

190

195

200

X 2484Y 1946

Power Curve

Voltage

P o w e r

X 23Y 1895

X 26Y 1914

v1

vm

v2





getting to the MPP






























60140200204264266386388448452512592 starting at

0 and ending at 652




0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

















983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156


0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power










0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES


































24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v1

v2

v3

(a) v2 lt V m

24 245 25 2551935

194

1945

195

Voltage

P o w e r

Power Curve

v2

v3

v1

(b) v2 gt V m


right of MPP















983117983141983137983155983157983154983141 983158983151983148983156983137983143983141 983137983150983140 983139983157983154983154983141983150983156

983158983080983150983081983084 983145983080983150983081

983126983155983141983156983101983126983155983141983156983083Δ983126 983126983155983141983156983101983126983155983141983156983085Δ983126

983122983141983156983157983154983150

983129983109983123

983118983119

983129983109983123

983118983119

983140983145983101983145983080983150983081983085983145983080983150983085983089983081

983140983158983101983158983080983150983081983085983158983080983150983085983089983081

983140983158983101983088983103

983140983145983087983140983158983101983085983145983087983158983103 983140983145983101983088983103

983140983145983102983088983103983140983145983087983140983158983102983085983145983087983158983103

983126983155983141983156983101983126983155983141983156983085Δ983126 983126983155983141983156983101983126983155983141983156983083Δ983126

983129983109983123983129983109983123

983129983109983123

983118983119 983118983119

983118983119









983158

983145

983122983152

983122983155983113983143





R p

(1)






of an electron























voutd1

+ ∆v

(2)

983158

983116

983126983151983157983156

983145983116

983107

983145

983113983143

983122983155

983122983152








A PampO vs IncCond





0 lt dP dv

= d(iv)dv

= v didv

+ i lArrrArr didv

gt minus iv

(3)











0 5 10 15 20 25 3024

245

25

255


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30194

1942

1944

1946

1948


time (s)

P V

P o w e r

PampO

(b) PV power output












equality is checked

di

dv =


gt minusi2v2




























after v2




























lt

minus i2v2



= minus0358 it







22 23 24 25 26 27 28

175

180

185

190

195

200

X 2484Y 1946

Power Curve

Voltage

P o w e r

X 23Y 1895

X 26Y 1914

v1

vm

v2





getting to the MPP






























60140200204264266386388448452512592 starting at

0 and ending at 652




0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

















983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156


0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power










0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES
















































voutd1

+ ∆v

(2)

983158

983116

983126983151983157983156

983145983116

983107

983145

983113983143

983122983155

983122983152








A PampO vs IncCond





0 lt dP dv

= d(iv)dv

= v didv

+ i lArrrArr didv

gt minus iv

(3)











0 5 10 15 20 25 3024

245

25

255


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30194

1942

1944

1946

1948


time (s)

P V

P o w e r

PampO

(b) PV power output












equality is checked

di

dv =


gt minusi2v2




























after v2




























lt

minus i2v2



= minus0358 it







22 23 24 25 26 27 28

175

180

185

190

195

200

X 2484Y 1946

Power Curve

Voltage

P o w e r

X 23Y 1895

X 26Y 1914

v1

vm

v2





getting to the MPP






























60140200204264266386388448452512592 starting at

0 and ending at 652




0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

















983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156


0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power










0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES






















































after v2




























lt

minus i2v2



= minus0358 it







22 23 24 25 26 27 28

175

180

185

190

195

200

X 2484Y 1946

Power Curve

Voltage

P o w e r

X 23Y 1895

X 26Y 1914

v1

vm

v2





getting to the MPP






























60140200204264266386388448452512592 starting at

0 and ending at 652




0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

















983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156


0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power










0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES


































0 5 10 15 20 25 3020

22

24

26

28


time (s)

P V V

o l t a g e

PampO

IncCond


0 5 10 15 20 25 30190

191

192

193

194


time (s)

P V

P o w e r

PampO IncCond

(b) PV power output



A PampO vs IncCond

















983088 983089983088983088 983090983088983088 983091983088983088 983092983088983088 983093983088983088 983094983088983088 983095983088983088983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983089983088983088983088

983089983089983088983088

983156983145983149983141 983080983155983081

983113 983154 983154 983137 983140 983145 983137 983150 983139 983141 983080 983127 983087 983149 983090 983081

983122983151983152983152 983113983150983152983157983156


0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power










0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES







































0 100 200 300 400 500 6000

5

10

15

20

25

30


time (s)

P V V

o l t a g e

(a) Voltage

0 100 200 300 400 500 6000

50

100

150


time (s)

P V

P o w e r

(b) Power
































0 2 4 6 8 10 12 1420

22

24

26

28


time (s)

P V V

o l t a g e

Vm 100ms

1000ms

10ms


sample



































negligible penalty

VIII CONCLUSION













REFERENCES















































negligible penalty

VIII CONCLUSION













REFERENCES










































Documents

MPPT Algorithms