Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques

Abstract

The many different techniques for maximum power point tracking of photovoltaic (PV) arrays are discussed. The techniques are taken from the literature dating back to the earliest methods. It is shown that at least 19 distinct methods have been introduced in the literature, with many variations on implementation. This paper should serve as a convenient reference for future work in PV power generation.

Full text

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 2, JUNE 2007 439
Comparison of Photovoltaic Array Maximum Power
Point Tracking Techniques
Trishan Esram, Student Member, IEEE, and Patrick L. Chapman, Senior Member, IEEE
Abstract—The many different techniques for maximum power
point tracking of photovoltaic (PV) arrays are discussed. The tech-
niques are taken from the literature dating back to the earliest
methods. It is shown that at least 19 distinct methods have been
introduced in the literature, with many variations on implementa-
tion. This paper should serve as a convenient reference for future
work in PV power generation.
Index Terms—Maximum power point tracking (MPPT), photo-
voltaic (PV).
I. INTRODUCTION
TRACKING the maximum power point (MPP) of a pho-
tovoltaic (PV) array is usually an essential part of a PV
system. As such, many MPP tracking (MPPT) methods have
been developed and implemented. The methods vary in com-
plexity, sensors required, convergence speed, cost, range of ef-
fectiveness, implementation hardware, popularity, and in other
respects. They range from the almost obvious (but not necessar-
ily ineffective) to the most creative (not necessarily most effec-
tive). In fact, so many methods have been developed that it has
become difficult to adequately determine which method, newly
proposed or existing, is most appropriate for a given PV system.
Given the large number of methods for MPPT, a survey of
the methods would be very beneficial to researchers and practi-
tioners in PV systems. Fig. 1 shows the total number of MPPT
papers from our bibliography per year since the earliest MPPT
paper we found. The number of papers per year has grown
considerably of the last decades and remains strong. However,
recent papers have generally had shorter, more cursory literature
reviews that largely summarize or repeat the literature reviews
of previous work. This approach tends to repeat what seems to
be conventional wisdom that there are only a handful of MPPT
techniques, when in fact there are many. This is due to the sheer
volume of MPPT literature to review, conflicting with the need
for brevity.
This survey is a single reference of the great majority of papers
and techniques presented on MPPT. We compiled over 90 papers
pertaining to different MPPT methods published up to the date of
submission of this manuscript. It is not our intention to establish
a literal chronology of when various techniques were proposed,
since the publication date is not necessarily indicative of when a
method was actually conceived. As is typical of review papers,
Manuscript received September 24, 2004; revised September 8, 2005. This
work wase supported by the National Science Foundation ECS-01-34208. Paper
no. TEC-00276-2004.
The authors are with the Grainger Center for Electric Machinery and Elec-
tromechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-
2918 USA (e-mail: esram@uiuc.edu; chapman@ece.uiuc.edu).
Digital Object Identifier 10.1109/TEC.2006.874230
Fig. 1. Total number of MPPT papers per year, since 1968.
we have elected not to reference patents. Papers referencing
MPPT methods from previous papers without any modification
or improvement have also been omitted. It is possible that one
or more papers were unintentionally omitted. We apologize if
an important method or improvement was left out.
This manuscript steps through a wide variety of methods with
a brief discussion and categorization of each. We have avoided
discussing slight modifications of existing methods as distinct
methods. For example, a method may have been first presented
in context of a boost converter, but later on shown with a boost-
buck converter, otherwise with minimal change. The manuscript
concludes with a discussion on the different methods based on
their implementation, the sensors required, their ability to detect
multiple local maxima, their costs, and applications they suit. A
table that summarizes the major characteristics of the methods
is also provided.
II. PROBLEM OVERVIEW
Fig. 2 shows the characteristic power curve for a PV array.
The problem considered by MPPT techniques is to automati-
cally find the voltage VMPP or current IMPP at which a PV array
should operate to obtain the maximum power output PMPP under
a given temperature and irradiance. It is noted that under partial
shading conditions, in some cases it is possible to have multiple
local maxima, but overall there is still only one true MPP. Most
techniques respond to changes in both irradiance and temper-
ature, but some are specifically more useful if temperature is
approximately constant. Most techniques would automatically
respond to changes in the array due to aging, though some are
open-loop and would require periodic fine-tuning. In our con-
text, the array will typically be connected to a power converter
that can vary the current coming from the PV array.
0885-8969/$25.00 © 2006 IEEE

440 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 2, JUNE 2007
Fig. 2. Characteristic PV array power curve.
TABLE I
SUMMARY OF HILL CLIMBING AND P&O ALGORITHM
III. MPPT TECHNIQUES
We introduce the different MPPT techniques below in an
arbitrary order.
A. Hill Climbing/P&O
Among all the papers we gathered, much focus has been on
hill climbing [1]–[8], and perturb and observe (P&O) [9]–[25]
methods. Hill climbing involves a perturbation in the duty ratio
of the power converter, and P&O a perturbation in the operating
voltage of the PV array. In the case of a PV array connected to
a power converter, perturbing the duty ratio of power converter
perturbs the PV array current and consequently perturbs the
PV array voltage. Hill climbing and P&O methods are different
ways to envision the same fundamental method.
From Fig. 2, it can be seen that incrementing (decrement-
ing) the voltage increases (decreases) the power when operating
on the left of the MPP and decreases (increases) the power
when on the right of the MPP. Therefore, if there is an increase
in power, the subsequent perturbation should be kept the same
to reach the MPP and if there is a decrease in power, the per-
turbation should be reversed. This algorithm is summarized in
Table I. In [24], it is shown that the algorithm also works when
instantaneous (instead of average) PV array voltage and current
are used, as long as sampling occurs only once in each switching
cycle.
The process is repeated periodically until the MPP is reached.
The system then oscillates about the MPP. The oscillation can
be minimized by reducing the perturbation step size. However,
a smaller perturbation size slows down the MPPT. A solution
to this conflicting situation is to have a variable perturbation
size that gets smaller towards the MPP as shown in [8], [12],
[15], and [22]. In [24], fuzzy logic control is used to optimize
the magnitude of the next perturbation. In [20], a two-stage
algorithm is proposed that offers faster tracking in the first stage
Fig. 3. Divergence of hill climbing/P&O from MPP as shown in [9].
and finer tracking in the second stage. On the other hand, [21]
bypasses the first stage by using a nonlinear equation to estimate
an initial operating point close to the MPP.
Hill climbing and P&O methods can fail under rapidly chang-
ing atmospheric conditions as illustrated in Fig. 3. Starting from
an operating point A, if atmospheric conditions stay approxi-
mately constant, a perturbation ∆Vin the PV voltage Vwill
bring the operating point to B and the perturbation will be re-
versed due to a decrease in power. However, if the irradiance
increases and shifts the power curve from P1to P2within one
sampling period, the operating point will move from A to C.
This represents an increase in power and the perturbation is
kept the same. Consequently, the operating point diverges from
the MPP and will keep diverging if the irradiance steadily in-
creases. To ensure that the MPP is tracked even under sudden
changes in irradiance, [18] uses a three-point weight compari-
son P&O method that compares the actual power point to two
preceding ones before a decision is made about the perturbation
sign. In [22], the sampling rate is optimized, while in [24], sim-
ply a high sampling rate is used. In [8], toggling has been done
between the traditional hill climbing algorithm and a modified
adaptive hill climbing mechanism to prevent deviation from the
MPP.
Two sensors are usually required to measure the PV array
voltage and current from which power is computed, but de-
pending on the power converter topology, only a voltage sensor
might be needed as in [7] and [23]. In [25], the PV array current
from the PV array voltage is estimated, eliminating the need for
a current sensor. DSP or microcomputer control is more suit-
able for hill climbing and P&O even though discrete analog and
digital circuitry can be used as in [4].
B. Incremental Conductance
The incremental conductance (IncCond) [9], [26]–[36]
method is based on the fact that the slope of the PV array
power curve (Fig. 2) is zero at the MPP, positive on the left of
the MPP, and negative on the right, as given by



dP /dV =0,at MPP
dP /dV > 0,left of MPP
dP /dV < 0,right of MPP.
(1)

ESRAM AND CHAPMAN: COMPARISON OF PV ARRAY MAXIMUM POWER POINT TRACKING TECHNIQUES 441
Fig. 4. IncCond algorithm as shown in [29], [32], [33], and [36].
Since
dP
dV =d(IV )
dV =I+VdI
dV
∼
=I+V∆I
∆V(2)
(1) can be rewritten as



∆I/∆V=−I/V, at MPP
∆I/∆V>−I/V, left of MPP
∆I/∆V<−I/V, right of MPP.
(3)
The MPP can thus be tracked by comparing the instantaneous
conductance (I/V )to the incremental conductance (∆I/∆V)
as shown in the flowchart in Fig. 4. Vref is the reference voltage
at which the PV array is forced to operate. At the MPP, Vre f
equals to VMPP. Once the MPP is reached, the operation of the
PV array is maintained at this point unless a change in ∆Iis
noted, indicating a change in atmospheric conditions and the
MPP. The algorithm decrements or increments Vre f to track the
new MPP.
The increment size determines how fast the MPP is tracked.
Fast tracking can be achieved with bigger increments but the
system might not operate exactly at the MPP and oscillate about
it instead; so there is a tradeoff. In [31] and [35], a method
is proposed that brings the operating point of the PV array
close to the MPP in a first stage and then uses IncCond to
exactly track the MPP in a second stage. By proper control of the
power converter, the initial operating point is set to match a load
resistance proportional to the ratio of the open-circuit voltage
(VOC) to the short-circuit current (ISC)of the PV array. This
two-stage alternative also ensures that the real MPP is tracked
in case of multiple local maxima. In [37], a linear function is
used to divide the I–Vplane into two areas, one containing all
the possible MPPs under changing atmospheric conditions. The
operating point is brought into this area and then IncCond is
used to reach the MPP.
A less obvious, but effective way of performing the IncCond
technique is to use the instantaneous conductance and the incre-
mental conductance to generate an error signal
e=I
V+dI
dV (4)
as suggested in [27] and [28]. From (1), we know that egoes to
zero at the MPP. A simple proportional integral (PI) control can
then be used to drive eto zero.
Measurements of the instantaneous PV array voltage and cur-
rent require two sensors. IncCond method lends itself well to
DSP and microcontroller control, which can easily keep track of
previous values of voltage and current and make all the decisions
as per Fig. 4.
C. Fractional Open-Circuit Voltage
The near linear relationship between VMPP and VOC of the
PV array, under varying irradiance and temperature levels, has
given rise to the fractional VOC method [38]–[45].
VMPP ≈k1VOC (5)
where k1is a constant of proportionality. Since k1is dependent
on the characteristics of the PV array being used, it usually has to
be computed beforehand by empirically determining VMPP and
VOC for the specific PV array at different irradiance and tem-
perature levels. The factor k1has been reported to be between
0.71 and 0.78.
Once k1is known, VMPP can be computed using (5) with VOC
measured periodically by momentarily shutting down the power
converter. However, this incurs some disadvantages, including
temporary loss of power. To prevent this, [40] uses pilot cells
from which VOC can be obtained. These pilot cells must be
carefully chosen to closely represent the characteristics of the
PV array. In [44], it is claimed that the voltage generated by
pn-junction diodes is approximately 75% of VOC. This elimi-
nates the need for measuring VOC and computing VMPP. Once
VMPP has been approximated, a closed-loop control on the array
power converter can be used to asymptotically reach this desired
voltage.
Since (5) is only an approximation, the PV array technically
never operates at the MPP. Depending on the application of the
PV system, this can sometimes be adequate. Even if fractional
VOC is not a true MPPT technique, it is very easy and cheap to
implement as it does not necessarily require DSP or microcon-
troller control. However, [45] points out that k1is no more valid
in the presence of partial shading (which causes multiple local
maxima) of the PV array and proposes sweeping the PV array
voltage to update k1. This obviously adds to the implementation
complexity and incurs more power loss.
D. Fractional Short-Circuit Current
Fractional ISC results from the fact that, under varying atmo-
spheric conditions, IMPP is approximately linearly related to the

442 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 2, JUNE 2007
Fig. 5. Membership function for inputs and output of fuzzy logic controller.
ISC of the PV array as shown in [40], [42], and [45]–[48]
IMPP ≈k2ISC (6)
where k2is a proportionality constant. Just like in the fractional
VOC technique, k2has to be determined according to the PV
array in use. The constant k2is generally found to be between
0.78 and 0.92.
Measuring ISC during operation is problematic. An addi-
tional switch usually has to be added to the power converter to
periodically short the PV array so that ISC can be measured us-
ing a current sensor. This increases the number of components
and cost. In [48], a boost converter is used, where the switch in
the converter itself can be used to short the PV array.
Power output is not only reduced when finding ISC but also
because the MPP is never perfectly matched as suggested by
(6). In [46], a way of compensating k2is proposed such that
the MPP is better tracked while atmospheric conditions change.
To guarantee proper MPPT in the presence of multiple local
maxima, [45] periodically sweeps the PV array voltage from
open-circuit to short-circuit to update k2. Most of the PV sys-
tems using fractional ISC in the literature use a DSP. In [48], a
simple current feedback control loop is used instead.
E. Fuzzy Logic Control
Microcontrollers have made using fuzzy logic control
[49]–[58] popular for MPPT over the last decade. As mentioned
in [57], fuzzy logic controllers have the advantages of working
with imprecise inputs, not needing an accurate mathematical
model, and handling nonlinearity.
Fuzzy logic control generally consists of three stages: fuzzifi-
cation, rule base table lookup, and defuzzification. During fuzzi-
fication, numerical input variables are converted into linguistic
variables based on a membership function similar to Fig. 5.
In this case, five fuzzy levels are used: NB (negative big), NS
(negative small), ZE (zero), PS (positive small), and PB (posi-
tive big). In [54] and [55], seven fuzzy levels are used, probably
for more accuracy. In Fig. 5, aand bare based on the range
of values of the numerical variable. The membership function
is sometimes made less symmetric to give more importance to
specific fuzzy levels as in [49], [53], [57], and [58].
The inputs to a MPPT fuzzy logic controller are usually an
error Eand a change in error ∆E. The user has the flexibility of
choosing how to compute Eand ∆E. Since dP/dV vanishes
TABLE II
FUZZY RULE BASE TABLE ASSHOWN IN [50]
at the MPP, [58] uses the approximation
E(n)= P(n)−P(n−1)
V(n)−V(n−1) (7)
and
∆E(n)=E(n)−E(n−1).(8)
Equivalently, (4) is very often used. Once Eand ∆Eare
calculated and converted to the linguistic variables, the fuzzy
logic controller output, which is typically a change in duty ratio
∆Dof the power converter, can be looked up in a rule base table
such as Table II [50].
The linguistic variables assigned to ∆Dfor the different com-
binations of Eand ∆Eare based on the power converter being
used and also on the knowledge of the user. Table II is based on
a boost converter. If, for example, the operating point is far to
the left of the MPP (Fig. 2), that is Eis PB, and ∆Eis ZE, then
we want to largely increase the duty ratio, that is ∆Dshould be
PB to reach the MPP.
In the defuzzification stage, the fuzzy logic controller output
is converted from a linguistic variable to a numerical variable
still using a membership function as in Fig. 5. This provides an
analog signal that will control the power converter to the MPP.
MPPT fuzzy logic controllers have been shown to perform
well under varying atmospheric conditions. However, their ef-
fectiveness depends a lot on the knowledge of the user or control
engineer in choosing the right error computation and coming up
with the rule base table. In [55], an adaptive fuzzy logic control
is proposed that constantly tunes the membership functions and
the rule base table so that optimum performance is achieved. Ex-
perimental results from [51] show fast convergence to the MPP
and minimal fluctuation about it. In [57], two different mem-
bership functions are empirically used to show that the tracking
performance depends on the type membership functions con-
sidered.
F. Neural Network
Along with fuzzy logic controllers came another technique
of implementing MPPT—neural networks [59]–[63], which are
also well adapted for microcontrollers.
Neural networks commonly have three layers: input, hidden,
and output layers as shown in Fig. 6. The number of nodes in
each layer vary and are user-dependent. The input variables can
be PV array parameters like VOC and ISC, atmospheric data
like irradiance and temperature, or any combination of these.
The output is usually one or several reference signal(s) like a

ESRAM AND CHAPMAN: COMPARISON OF PV ARRAY MAXIMUM POWER POINT TRACKING TECHNIQUES 443
Fig. 6. Example of neural network.
duty cycle signal used to drive the power converter to operate at
or close to the MPP.
How close the operating point gets to the MPP depends on
the algorithms used by the hidden layer and how well the neural
network has been trained. The links between the nodes are all
weighted. The link between nodes iand jis labeled as having
a weight of wij in Fig. 6. To accurately identify the MPP, the
wij ’shave to be carefully determined through a training process,
whereby the PV array is tested over months or years and the
patterns between the input(s) and output(s) of the neural network
are recorded.
Since most PV arrays have different characteristics, a neural
network has to be specifically trained for the PV array with
which it will be used. The characteristics of a PV array also
change with time, implying that the neural network has to be
periodically trained to guarantee accurate MPPT.
G. RCC
When a PV array is connected to a power converter, the
switching action of the power converter imposes voltage and
current ripple on the PV array. As a consequence, the PV array
power is also subject to ripple. Ripple correlation control (RCC)
[64] makes use of ripple to perform MPPT. RCC correlates the
time derivative of the time-varying PV array power ˙pwith the
time derivative of the time-varying PV array current ˙
ior voltage
˙vto drive the power gradient to zero, thus reaching the MPP.
Referring to Fig. 2, if vor iis increasing ( ˙v>0or ˙
i>0)
and pis increasing (˙p>0), then the operating point is below
the MPP (V<V
MPP or I<I
MPP). On the other hand, if vor
iis increasing and pis decreasing ( ˙p<0), then the operating
point is above the MPP (V>V
MPP or I>I
MPP). Combining
these observations, we see that ˙p˙vor ˙p˙
iare positive to the left
of the MPP, negative to right of the MPP, and zero at the MPP.
When the power converter is a boost converter as in [64],
increasing the duty ratio increases the inductor current, which
is the same as the PV array current, but decreases the PV array
voltage. Therefore, the duty ratio control input is
d(t)=−k3˙p˙vdt (9)
or
d(t)=k3˙p˙
idt (10)
where k3is a positive constant. Controlling the duty ratio in
this fashion assures that the MPP will be continuously tracked,
making RCC a true MPP tracker.
The derivatives in (9) and (10) are usually undesirable, but
[64] shows that ac-coupled measurements of the PV array cur-
rent and voltage can be used instead since they contain the
necessary phase information. The derivatives can also be ap-
proximated by high-pass filters with cutoff frequency higher
than the ripple frequency. A different and easy way of obtaining
the current derivative in (10) is to sense the inductor voltage,
which is proportional to the current derivative. The nonideal-
ities in the inductor (core loss, resistance) have a small effect
since the time constant of the inductor is much larger than the
switching period in a practical converter.
Our present undocumented work has shown that (10) can fail
due to the phase shift brought about by the intrinsic capacitance
of the PV array at high switching frequencies. However, cor-
relating power and voltage as in (9) is barely affected by the
intrinsic capacitance.
Simple and inexpensive analog circuits can be used to im-
plement RCC. An example is given in [64]. Experiments were
performed to show that RCC accurately and quickly tracks the
MPP, even under varying irradiance levels. The time taken to
converge to the MPP is limited by the switching frequency of
the power converter and the gain of the RCC circuit. Another
advantage of RCC is that it does not require any prior informa-
tion about the PV array characteristics, making its adaptation to
different PV systems straightforward.
There are other papers in the literature that use MPPT methods
that resemble RCC. For example, [65] integrates the product of
the signs of the time derivatives of power and of duty ratio.
However, unlike RCC, which uses inherent ripple present in
current and voltage, [65] disturbs the duty ratio to generate
a disturbance in power. In [66] and [67], a hysteresis-based
version of RCC is used. A low frequency dithering signal is
used to disturb the power in [68]. In [68], a 90◦phase shift in
the current (or voltage) with respect to power at the MPP is
discussed, just like in RCC. The difference in [68] is that the
injection is an extra, low-frequency signal and not an inherent
converter ripple.
H. Current Sweep
The current sweep [69] method uses a sweep waveform for
the PV array current such that the I–Vcharacteristic of the PV
array is obtained and updated at fixed time intervals. The VMPP
can then be computed from the characteristic curve at the same
intervals.
The function chosen for the sweep waveform is directly pro-
portional to its derivative as in
f(t)=k4
df (t)
dt (11)
where k4is a proportionality constant. The PV array power is
thus given by
p(t)=v(t)i(t)=v(t)f(t).(12)
.

444 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 2, JUNE 2007
Fig. 7. Topology for dc-link capacitor droop control as shown in [71].
At the MPP
dp(t)
dt =v(t)df (t)
dt +f(t)dv(t)
dt =0.(13)
Substituting (11) in (13) gives
dp(t)
dt =v(t)+k4
dv(t)
dt df (t)
dt =0.(14)
The differential equation in (11) has the following solution
f(t)=Cexp [t/k4].(15)
Cis chosen to be equal to the maximum PV array current Imax
and k4to be negative, resulting in a decreasing exponential
function with time constant τ=−k4. Equation (15) leads to
f(t)=Imax exp [−t/τ].(16)
The current in (16) can be easily obtained by using some
current discharging through a capacitor. Since the derivative of
(16) is nonzero, (14) can be divided throughout by df (t)/dt and,
with f(t)=i(t), (14) simplifies to
dp(t)
di(t)=v(t)+k4
dv(t)
dt =0.(17)
Once VMPP is computed after the current sweep, (17) can be
used to double check whether the MPP has been reached. In
[69], the current sweep method is implemented through analog
computation. The current sweep takes about 50 ms, implying
some loss of available power. In [69], it is pointed out that this
MPPT technique is only feasible if the power consumption of
the tracking unit is lower than the increase in power that it can
bring to the entire PV system.
I. DC-Link Capacitor Droop Control
DC-link capacitor droop control [70], [71] is an MPPT tech-
nique that is specifically designed to work with a PV system
that is connected in parallel with an ac system line as shown in
Fig. 7.
The duty ratio of an ideal boost converter is given by
d=1−V
Vlink
(18)
where Vis the voltage across the PV array and Vlink is the
voltage across the dc link. If Vlink is kept constant, increasing
Fig. 8. Different load types. 1: voltage source, 2: resistive, 3: resistive and
voltage source, 4: current source, as shown in [78].
the current going in the inverter increases the power coming
out of the boost converter and consequently increases the power
coming out of the PV array. While the current is increasing, the
voltage Vlink can be kept constant as long as the power required
by the inverter does not exceed the maximum power available
from the PV array. If that is not the case, Vlink starts drooping.
Right before that point, the current control command Ipeak of
the inverter is at its maximum and the PV array operates at the
MPP. The ac system line current is fed back to prevent Vlink from
drooping and dis optimized to bring Ipeak to its maximum, thus
achieving MPPT.
DC-link capacitor droop control does not require the compu-
tation of the PV array power, but according to [71], its response
deteriorates when compared to a method that detects the power
directly; this is because its response directly depends on the re-
sponse of the dc-voltage control loop of the inverter. This control
scheme can be easily implemented with analog operational am-
plifiers and decision-making logic units.
J. Load Current or Load Voltage Maximization
The purpose of MPPT techniques is to maximize the power
coming out of a PV array. When the PV array is connected to
a power converter, maximizing the PV array power also maxi-
mizes the output power at the load of the converter. Conversely,
maximizing the output power of the converter should maximize
the PV array power [72]–[78], assuming a lossless converter.
In [78], it is pointed out that most loads can be of voltage-
source type, current-source type, resistive type, or a combina-
tion of these, as shown in Fig. 8. From this figure, it is clear
that for a voltage-source type load, the load current iout should
be maximized to reach the maximum output power PM.Fora
current-source type load, the load voltage vout should be maxi-
mized. For the other load types, either iout or vout can be used.
This is also true for nonlinear load types as long as they do not
exhibit negative impedance characteristics [78]. Therefore, for
almost all loads of interest, it is adequate to maximize either
the load current or the load voltage to maximize the load power.
Consequently, only one sensor is needed.

ESRAM AND CHAPMAN: COMPARISON OF PV ARRAY MAXIMUM POWER POINT TRACKING TECHNIQUES 445
In most PV systems, a battery is used as the main load or
as a backup [73]–[77]. Since a battery can be thought of as a
voltage-source type load, the load current can be used as the
control variable. In [73], [74], and [76], positive feedback is
used to control the power converter such that the load current
is maximized and the PV array operates close to the MPP. Op-
eration exactly at the MPP is almost never achieved because
this MPPT method is based on the assumption that the power
converter is lossless.
K. dP/dV or dP/dI Feedback Control
With DSP and microcontroller being able to handle com-
plex computations, an obvious way of performing MPPT is to
compute the slope (dP/dV or dP/dI) of the PV power curve
(Fig. 2) and feed it back to the power converter with some control
to drive it to zero. This is exactly what is done in [79]–[83].
The way the slope is computed differs from paper to paper.
In [79], dP/dV is computed and its sign is stored for the past
few cycles. Based on these signs, the duty ratio of the power con-
verter is either incremented or decremented to reach the MPP.
A dynamic step size is used to improve the transient response
of the system. In [80], a linearization-based method is used to
compute dP/dV. In [81]–[83], sampling and data conversion are
used with subsequent digital division of power and voltage to
approximate dP/dV. In [82], dP/dI is then integrated together
with an adaptive gain to improve the transient response. In [83],
the PV array voltage is periodically incremented or decremented
and ∆P/∆Vis compared to a marginal error until the MPP is
reached. Convergence to the MPP was shown to occur in tens
of milliseconds in [81].
L. Other MPPT Techniques
Other MPPT techniques include array reconfiguration [84],
whereby PV arrays are arranged in different series and parallel
combinations such that the resulting MPPs meet specific load
requirements. This method is time consuming and tracking MPP
in real time is not obvious.
In [85], a linear current control is used based on the fact that
a linear relationship exists between IMPP and the level of irradi-
ance. The current IMPP is thus found by sensing the irradiance
level and a PI controller is used such that the PV array current
follows IMPP.
In [86], IMPP and VMPP are computed from equations involv-
ing temperature and irradiance levels, which are not usually easy
to measure. Once IMPP or VMPP is obtained, feedback control is
used to force the PV array to operate at the MPP.
A state-based MPPT is introduced in [87], whereby the sys-
tem is represented by a state space model, and a nonlinear time-
varying dynamic feedback controller is used to track the MPP.
Simulations confirm that this technique is robust and insensitive
to changes in system parameters and that MPPT is achieved
even with changing atmospheric conditions and in the presence
of multiple local maxima caused by partially shaded PV array or
damaged cells. However, no experimental verification is given.
Unlike common topologies that consist of two power stages
(usually a dc–dc converter followed by an inverter), a single-
stage inverter that performs both MPPT and output current reg-
ulation for utility grid distribution is introduced in [88]. Based
on the voltage of the PV array, one-cycle control (OCC) is used
to adjust the output current of the single-stage inverter such that
MPPT is attained. The control circuit consists of discrete digital
components but it can also use an inexpensive DSP. Operation
is shown to be close to the MPP throughout a day-time period.
The slight discrepancy is due to the inability of the controller to
account for temperature variation.
The best fixed voltage (BFV) algorithm is introduced in [89].
Statistical data is collected about irradiance and temperature
levels over a period of one year and the BFV representative of
the MPP is found. The control sets either the operating point of
the PV array to the BFV or the output voltage to the nominal
load voltage. Operation is therefore never exactly at the MPP
and different data has to be collected for different geographical
regions.
The PV array characteristic equation, which needs to be
solved iteratively for the MPP, is manipulated to find an ap-
proximate symbolic solution for the MPP in [90]. This method,
called linear reoriented coordinates method (LRCM), requires
the measurement of VOC and ISC to find the solution. Other
constants representing the PV array characteristic curve are also
needed. The maximum error in using LRCM to approximate
the MPP was found to be 0.3%, but this was based only on
simulation results.
In [91], a slide control method with a buck-boost converter is
used to achieve MPPT. The switching function uof the converter
is based on the fact that dP/dV > 0on the left of the MPP and
dP/dV < 0on the right; uis expressed as
u=0 S≥0
u=1 S<0(19)
where u=0means the switch is open and u= 1 the switch
close and Sis given by
S=dP
dV =I+VdI
dV .(20)
This control was implemented using a microcontroller that
senses the PV array voltage and current. Simulation and exper-
imental results showed that operation converges to the MPP in
several tens of milliseconds.
IV. DISCUSSION
With so many MPPT techniques available to PV system users,
it might not be obvious for the latter to choose which one better
suits their application needs. The main aspects of the MPPT
techniques to be taken into consideration are highlighted in the
following subsections.
A. Implementation
The ease of implementation is an important factor in deciding
which MPPT technique to use. However, this greatly depends
on the end-users’ knowledge. Some might be more familiar with
analog circuitry, in which case, fractional ISC or VOC, RCC, and
load current or voltage maximization are good options. Others
might be willing to work with digital circuitry, even if that

446 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 22, NO. 2, JUNE 2007
TABLE III
MAJOR CHARACTERISTICS OF MPPT TECHNIQUES
may require the use of software and programming. Then, their
selection should include hill climbing/P&O, IncCond, fuzzy
logic control, neural network, and dP/dV or dP /dI feedback
control. Furthermore, a few of the MPPT techniques only apply
to specific topologies. For example, the dc-link capacitor droop
control works with the system shown in Fig. 7 and the OCC
MPPT works with a single-stage inverter.
B. Sensors
The number of sensors required to implement MPPT also
affects the decision process. Most of the time, it is easier and
more reliable to measure voltage than current. Moreover, cur-
rent sensors are usually expensive and bulky. This might be
inconvenient in systems that consist of several PV arrays with
separate MPP trackers. In such cases, it might be wise to use
MPPT methods that require only one sensor or that can esti-
mate the current from the voltage as in [25]. It is also uncom-
mon to find sensors that measure irradiance levels, as needed in
the linear current control and the IMPP and VMPP computation
methods.
C. Multiple Local Maxima
The occurrence of multiple local maxima due to partial shad-
ing of the PV array(s) can be a real hindrance to the proper
functioning of an MPP tracker. Considerable power loss can
be incurred if a local maximum is tracked instead of the real
MPP. As mentioned previously, the current sweep and the state-
based methods should track the true MPP even in the presence
of multiple local maxima. However, the other methods require
an additional initial stage to bypass the unwanted local maxima
and bring operation to close the real MPP; such examples are
given in [31] and [35].
D. Costs
It is hard to mention the monetary costs of every single MPPT
technique unless it is built and implemented. This is unfortu-
nately out of the scope of this paper. However, a good costs
comparison can be made by knowing whether the technique
is analog or digital, whether it requires software and program-
ming, and the number of sensors. Analog implementation is
generally cheaper than digital, which normally involves a mi-
crocontroller that needs to be programmed. Eliminating current
sensors considerably drops the costs.
E. Applications
Different MPPT techniques discussed earlier will suit differ-
ent applications. For example, in space satellites and orbital sta-
tions that involve large amount of money, the costs and complex-
ity of the MPP tracker are not as important as its performance
and reliability. The tracker should be able to continuously track
the true MPP in minimum amount of time and should not require
periodic tuning. In this case, hill climbing/P&O, IncCond, and
RCC are appropriate. Solar vehicles would mostly require fast
convergence to the MPP. Fuzzy logic control, neural network,
and RCC are good options in this case. Since the load in solar
vehicles consists mainly of batteries, load current or voltage
maximization should also be considered. The goal when using
PV arrays in residential areas is to minimize the payback time

ESRAM AND CHAPMAN: COMPARISON OF PV ARRAY MAXIMUM POWER POINT TRACKING TECHNIQUES 447
and to do so, it is essential to constantly and quickly track the
MPP. Since partial shading (from trees and other buildings) can
be an issue, the MPPT should be capable of bypassing multiple
local maxima. Therefore, the two-stage IncCond [31], [35] and
the current sweep methods are suitable. Since a residential sys-
tem might also include an inverter, the OCC MPPT can also be
used. PV systems used for street lighting only consist in charg-
ing up batteries during the day. They do not necessarily need
tight constraints; easy and cheap implementation might be more
important, making fractional VOC or ISC viable.
For all other applications not mentioned here, we put together
Table III, containing the major characteristics of all the MPPT
techniques. Table III should help in choosing an appropriate
MPPT method.
V. C ONCLUSION
Several MPPT techniques taken from the literature are dis-
cussed and analyzed herein, with their pros and cons. It is shown
that there are several other MPPT techniques than those com-
monly included in literature reviews. The concluding discussion
and table should serve as a useful guide in choosing the right
MPPT method for specific PV systems.
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Trishan Esram (S’00) received the B.S. degree from
Northeastern University, Boston, MA, in 2003, in
electrical engineering, and the M.S. degree in elec-
trical engineering from the University of Illinois
at Urbana-Champaign, Urbana, IL, in 2004. Cur-
rently, he is working toward the Ph.D. degree in op-
timal control of power converters and alternative en-
ergy sources at the University of Illinois at Urbana-
Champaign, as a Research Assistant for Prof. P. L.
Chapman.
Patrick L. Chapman (S’94–M’00–SM’05) received
the B.S. and M.S. degrees from the University of
Missouri-Rolla, Rolla, MO, in 1996 and 1997, re-
spectively, and the Ph.D. degree from Purdue Uni-
versity, West Lafayette, IN, in 2000, all in electrical
engineering.
Currently, he is a Grainger Associate and Assis-
tant Professor in the Department of Electrical and
Computer Engineering at the University of Illinois at
Urbana-Champaign, Urbana, IL. He is a co-founder
of SmartSpark Energy Systems, Inc. His research in-
terests, within power electronics, include integrated design, automated model-
ing, hybrid energy systems, and energy harvesting.
Dr. Chapman is a Senior Member of the IEEE, an Associate Editor for
IEEE TRANSACTIONS ON POWER ELECTRONICS, and a Member-at-Large for the
IEEE Power Electronics Society Administrative Committee. He is the recipient
of the National Science Foundation CAREER Award and the Office of Naval
Research Young Investigator Award. He was named the Richard M. Bass Out-
standing Young Power Electronics Engineer in 2006.