8102019 MPPT Algorithms
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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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 3
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 4
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
195BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 5
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
i2 minus i1v2 minus v1
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
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 3
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 4
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
195BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 5
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
i2 minus i1v2 minus v1
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 3
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 4
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
195BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 5
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
i2 minus i1v2 minus v1
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 49
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 4
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
195BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 59
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 5
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
i2 minus i1v2 minus v1
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 69
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
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IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 89
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 59
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 5
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
i2 minus i1v2 minus v1
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 69
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 79
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 89
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 69
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 6
0 5 10 15 20 25 3020
22
24
26
28
30BP 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 30190
191
192
193
194
195BP NRM with Buck Converter and control
time (s)
P V
P o w e r
PampO IncCond
(b) PV power output
Fig 9 Results of PampO and IncCond methods using a fixed
voltage step size of 03 volts
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 79
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 89
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 79
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 7
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
30BP NRM with Buck Converter and control
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 89
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 89
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 8
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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
8102019 MPPT Algorithms
httpslidepdfcomreaderfullmppt-algorithms 99
IEEE TRANSACTIONS ON POWER SYSTEMS VOL NO DATE YEAR 9
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