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A reliable, fast and low cost maximum power point tracker

for photovoltaic applications

J.M. Enrique

*

, J.M. Andu

´jar, M.A. Boho

´rquez

Departamento de Ingenierı

´a Electro

´nica, de Sistemas Informa

´ticos y Automa

´tica, Universidad de Huelva, Spain

Received 19 February 2009; received in revised form 22 July 2009; accepted 16 October 2009

Communicated by: Associate Editor Elias Stefanakos

Abstract

This work presents a new maximum power point tracker system for photovoltaic applications. The developed system is an analog

version of the “P&O-oriented”algorithm. It maintains its main advantages: simplicity, reliability and easy practical implementation,

and avoids its main disadvantages: inaccurateness and relatively slow response. Additionally, the developed system can be implemented

in a practical way at a low cost, which means an added value. The system also shows an excellent behavior for very fast variables in

incident radiation levels.

Ó2009 Published by Elsevier Ltd.

Keywords: Analog system; Eﬃciency; Low cost; Maximum power point tracker; Photovoltaic array; “P&O”algorithm

1. Introduction

In the specialized literature numerous proposals of MPP

tracking systems can be found. Most of them have similar

eﬃciency, which can also be considered acceptable for most

applications. As a result, the interest of the authors when

implementing this work has focused on achieving a certain

added value in the proposed system, which can be found in

the accurateness, speed and low cost. This allows its appli-

cation even to household installations, where investment

costs may be the most determining factor for decision mak-

ing. The developed system presents the advantage of its

high speed which also helps to improve the photovoltaic

system eﬃciency.

A photovoltaic (PV) array that functions under uniform

radiation and temperature conditions presents an I–V and

P–V characteristic as the one shown in Figs. 1(a) and (b),

respectively. As can be observed, there is a single point,

called “MPP”(Maximum Power Point), where the array

provides the maximum power possible for these environ-

mental conditions (radiation and temperature), and so

functions with the maximum performance. When a load

is connected directly to a PV array (direct coupling), the

operation point is deﬁned by the intersection of its I–V

characteristics, as shown in Fig. 1(a).

In general, this operation point does not coincide with

the MPP. Thus, in direct coupling systems, the array must

be over-dimensioned to guarantee the power demand of the

load. Obviously, this implies a more expensive system. To

solve this problem, a DC/DC (Xiao et al., 2007) converter

with an algorithm for the automatic control of its duty

cycle “d”is inserted between the photovoltaic array and

the load (see Fig. 2), resulting in what is known as MPPT

(Maximum Power Point Tracker) system.

The MPPT must control the voltage or current (through

the dof the converter) of the PV array regardless of the

0038-092X/$ - see front matter Ó2009 Published by Elsevier Ltd.

doi:10.1016/j.solener.2009.10.011

*

Corresponding author. Address: Departamento de Ingenierı

´a Electro

´-

nica, de Sistemas Informa

´ticos y Automa

´tica, Universidad de Huelva,

Huelva, Spain. Tel.: +34 959 217374/7656/7671; fax: +34 959 217348.

E-mail addresses: juanm.enrique@diesia.uhu.es (J.M. Enrique), andu

jar@diesia.uhu.es (J.M. Andu

´jar), bohorquez@diesia.uhu.es (M.A. Bo-

ho

´rquez).

www.elsevier.com/locate/solener

Available online at www.sciencedirect.com

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Energy (2009), doi:10.1016/j.solener.2009.10.011

load, trying to place it in the MPP. The DC/DC converter

presents an input impedance (R

i

) which depends basically

on the load impedance (R

L

) and the duty cycle (d)(Enrique

et al., 2005a,b, 2007; Dura

´n et al., 2008, 2009). Therefore,

the MPPT must ﬁnd the optimal dfor the operation point

of the PV array to coincide with the maximum power point

(MPP).

Although the solution to operating in the MPP may

seem immediate, it is not. This is because the location of

the MPP in the I–V curve of the PV array is not known

a priori. This point must be located, either by mathematical

calculations over a valid model, or by using some search

algorithm. This implies even more diﬃculty if we consider

the fact that the MPP presents non-linear dependencies

with temperature and radiation, as observed in Fig. 3.

Fig. 3(a) shows a set of I–V curves for diﬀerent levels of

radiation and constant temperature. In Fig. 3(b), the same

set of curves is presented at a higher temperature. Observe

the change in the voltage and, especially, in the current of

the MPP.

Numerous MPPT algorithms have been proposed and

developed in the literature. Among them, the “Perturbation

and Observation (P&O)”algorithm is probably the most

Fig. 1. (a) I–Vcharacteristic of a PV array, MPP and system operation point. (b) P–Vcharacteristic of the PV array.

Fig. 2. Basic diagram of an MPPT system.

Fig. 3. (a) I–Vcharacteristic of a PV array at 40 °C and diﬀerent radiation levels (200–400 to 600–800 and 1000 W/m

2

). (b) I–Vcharacteristic of a PV

array at 60 °C and diﬀerent radiation levels (200–400 to 600–800 and 1000 W/m

2

).

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Energy (2009), doi:10.1016/j.solener.2009.10.011

extensively used in commercial MPPT systems. However,

there is no clear agreement on which algorithm is best.

Hohm and Ropp (2002) presented a study that basically

concludes with not very diﬀerent performances for most

of the diﬀerent algorithms and where the traditional P&O

is quite successful.

To establish the quality of a given MPPT system (and to

be able to compare it with other systems), it is necessary to

deﬁne the “tracking eﬃciency (g)”, given by Eq. (1) (Hohm

and Ropp, 2002):

gMPPT ¼Rt

0PinstðtÞdt

Rt

0PmaxðtÞdt ð1Þ

where, for radiation and temperature conditions in the gi-

ven time period, P

inst

(t) is the instantaneous power supplied

by the MPPT system controlled PV array, and P

max

(t)is

the actual MPP power.

2. Algorithms for MPP tracking

A very short revision of the most usual algorithms for

MPP tracking is presented below.

2.1. Perturbation and Observation (P&O)

The Perturbation and Observation (P&O) algorithm is

probably the most frequently used in practice, mainly due

to its easy implementation (Kim et al., 1996). Its operation

is brieﬂy explained as follows: assume that the PV array

operates at a given point, which is outside the MPP. The

PV array operational voltage is perturbed by a small DV,

and then the change in the power (DP) is measured. If

DP> 0, the operation point has approached the MPP,

and therefore, the next perturbation must take place in

the same direction as the previous one (same algebraic

sign). If, on the contrary, DP< 0, the system has moved

away from the MPP and, consequently, the next perturba-

tion must be performed in the opposite direction (opposed

algebraic sign).

As stated before, the advantages of this algorithm are its

simplicity and easy implementation. However, it has limita-

tions that reduce its tracking eﬃciency. When the light

intensity decreases considerably, the P–Vcurve becomes

very ﬂat. This makes it diﬃcult for the MPPT to locate

the MPP, since the changes that take place in the power

are small as regards perturbations occurred in the voltage.

Another disadvantage of the “P&O”algorithm is that it

cannot determine when it has exactly reached the MPP.

Thus, it remains oscillating around it, changing the sign

of the perturbation for each DPmeasured. It has also been

observed that this algorithm can show misbehavior under

fast changes in the radiation levels (Kawamura et al.,

1997).

Several improvements in the “P&O”algorithm have

been proposed (Enslin et al., 1997; Andujar et al., 2005;

Xiao et al., 2007). One of them is the addition of a waiting

time if the system identiﬁes a series of alternate signs in the

perturbation, meaning that it is very close to the MPP. This

allows reducing the oscillation around the MPP and

improves the algorithm eﬃciency under constant radiation

conditions. However, this algorithm causes the MPPT to

be very slow, making its misbehavior more noticeable in

partly cloudy days.

Other modiﬁcations to the “P&O”algorithm, as the

ones detailed below, directly aﬀect the perturbation sign

according to whether certain conditions are given.

2.1.1. “P&O”oriented algorithm

The “P&O”oriented algorithm (Andujar et al., 2005)is

able to distinguish with certain accuracy whether the sys-

tem is operating to the right or left of the MPP and act con-

sequently, so increasing tracking eﬃciency. However, it is

observed that whenever there is a sudden variation in the

incident radiation (caused, for example, by the passing of

a cloud) and, therefore, in the power supplied by the pho-

tovoltaic generator, the system is unable to distinguish

instantaneously the appropriate direction of the change

in d(Hohm and Ropp, 2002). This algorithm is discussed

in detailed in Section 3.

2.1.2. “P&O”modiﬁed algorithm

To correct the defect caused by sudden radiation varia-

tions in the previous algorithm, a slight variation has been

proposed (Andujar et al., 2005). As already known, varia-

tions in the light radiation have an eﬀect mainly and

directly on the current supplied by the photovoltaic array

(Alonso, 1998). Thus, an increase in radiation will cause

a rise in the value of the MPP current (see Fig. 3). When

the algorithm detects a variation in radiation over a certain

threshold, its response is an immediate increase in d. In this

way, the DC/DC converter decreases its input impedance

R

i

, and so obliges the photovoltaic generator to move to

higher current points close to the MPP. An advantage of

this algorithm is that it does not require precise measure-

ments of radiation (this would remarkably increase the

price of its practical implementation), since it only needs

the sign of the radiation increase within an interval of mea-

sures. A simple photodiode can be useful for this purpose.

2.2. Constant voltage and current

The “Constant Voltage (CV)”algorithm (Hohm and

Ropp, 2002; Koizumi et al., 2006) is based on the fact that

in the I–Vcurves of a PV array the ratio between the max-

imum power point voltage and that of the open circuit is

roughly constant (something similar occurs with the ratio

between the current of the maximum power point and that

of the short circuit) (Noguchi et al., 2002; Mutoh et al.,

2006; Mutoh and Inoue, 2007), that is:

VMPP

VOC

ﬃK<1ð2Þ

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Energy (2009), doi:10.1016/j.solener.2009.10.011

where V

MPP

is the maximum power point voltage and V

OC

is

the open circuit voltage. The PV array is temporarily isolated

by the MPPT system to measure V

OC

. Next, the MPPT cal-

culates the correct operation point using Eq. (2) and adjusts

the voltage of the PV array until it reaches the MPP. This

operation is repeated periodically to track the MPP.

Although this method is simple, choosing the optimal K

value, which, on the other hand, is not totally constant,

may be diﬃcult. The literature indicates good values for

Kwithin the range 0.73–0.80 (Andersen and Alvsten,

1995; van der Merwe and van der Merwe, 1998; Abou El

Ela and Roger, 1984).

This method can be implemented in a relatively easy

way using analog software. However, its eﬃciency is lower

than that of other methods (Hohm and Ropp, 2002). The

main reasons are:

(I) Errors in the Kvalue.

(II) The measure of V

OC

(I

SC

) requires the momentary

interruption of the power supplied by the array.

2.3. Incremental conductance

The so called “incremental conductance”method

(Hohm and Ropp, 2002) derives directly from the power

equation, which will be given in the MPP by:

dP

dV MPP

¼dðVIÞ

dV MPP

¼0)I

V¼dI

dV ð3Þ

If instantaneous conductance g

L

, and increasing conduc-

tance g

P

, are deﬁned as:

gL¼I

V;gp¼dI

dV ð4Þ

Then, expression (3) can be re-written in the form of:

dP

dV MPP

¼0)gL¼gPð5Þ

The previous equation indicates that in the MPP the

instantaneous and incremental conductance must be equal.

If the operation point does not coincide with the MPP,

then a series of inequations directly derived from expres-

sion (5) (Hohm and Ropp, 2002; Koizumi et al., 2006)

allow us to know whether the operation voltage is higher

or lower than V

MPP

, and so to act consequently.

Once the MPP has been reached, every time a change

occurs in the radiation on the array the MPPT will tend

to increase or decrease the operation voltage to follow

the MPP.

The disadvantage of this method is that it needs a pre-

cise calculation of g

L

and g

P

, which makes the MPPT more

diﬃcult and relatively slow.

2.4. Parasitic capacity

This algorithm is similar to the previous one, except that

in this algorithm the eﬀect of the parasitic capacity of the

junction p–n is included. This eﬀect can be modeled (Bramb-

illa et al., 1998) as a condenser connected between the termi-

nals of each cell. By connecting cells in parallel the parasitic

capacity observed by the MPP will increase. As a result, the

diﬀerences between the tracking eﬃciencies of the MPP

between “Increasing Conductance”and “Parasitic Capac-

ity”algorithms are more outstanding in high power arrays,

where there are numerous modules connected in parallel.

The practical implementation of this algorithm is com-

plex, especially for the diﬃculty entailed by the calculation

of increasing conductance g

P.

. A detailed study of this algo-

rithm is shown in Brambilla et al. (1998).

2.5. Model-based algorithms

If a suitable model is available for a cell or photovoltaic

array and there are precise radiation and temperature mea-

sures available (which implies a signiﬁcant increase in the

price of the system, although there have recently been devel-

oped sensors of temperature and radiation at a low cost

(Martı

´nez and Andu

´jar, 2009; Martı

´nez et al., 2009), the

MPP voltage and current may be directly calculated by solv-

ing equation dP/dV = 0 (for example, using a numeric

method). Then, the MPPT would just have to adjust voltage

and current values to those calculated ones (Xiao et al., 2006).

Even so, the model-based MPPTs are not practical,

since the values for the cell parameters are not known with

accuracy and, in fact, can vary signiﬁcantly between cells

from the same production series. Moreover, only the cost

of a precise light radiation sensor (pyranometer) can cause

this MPPT system to be non-viable in practice.

Having revised the most usual algorithms and methods

for MPP tracking, it seems that the P&O algorithm and,

more speciﬁcally, its “oriented”variant, is the one with

the best ratio eﬃciency/easiness of practical implementa-

tion. This is mainly due to its proper operation, simplicity

and low cost (note that it needs no radiation and tempera-

ture sensors). Nonetheless, as already mentioned, it has the

disadvantage of its instantaneous confusion when facing

sudden variations in the incident radiation. This disadvan-

tage could be overcome with a system fast enough to make

its reaction speed higher than the speed of the incident radi-

ation change – which is the main reason in the MPP move-

ment. To achieve this without losing the advantages of the

P&O-oriented algorithm, the authors have developed a sys-

tem which is described below.

3. P&O oriented analog system

A completely analog system able to implement the algo-

rithm for MPP tracking, known as “P&O-oriented”algo-

rithm, is presented in this section (Andujar et al., 2005).

3.1. Operation of the P&O-oriented algorithm

Consider Fig. 4, where the P–V characteristic of a pho-

tovoltaic array at a given temperature and radiation is

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ARTICLE IN PRESS

Energy (2009), doi:10.1016/j.solener.2009.10.011

shown. Assume that, due to a modiﬁcation in the duty

cycle (d) of the converter, the system evolves from V

A

to

V

B

(DV> 0 and DP> 0). As observed in Fig. 4, the MPP

voltage, V

MPP

, is higher than V

B

, and therefore, the output

voltage must keep increasing. Now assume that the pertur-

bation has moved the operation point from V

B

to V

A

.In

this case, the voltage of the array must increase again to

approach V

MPP

. All possible combinations are shown in

Table 1.

The only variable to which the control system can access

is the duty cycle (d). Any increase in dimplies a decrease in

the input resistance R

i

of the DC–DC converter (and sub-

sequently, a decrease in the operation voltage of the photo-

voltaic generator) and vice versa (Enrique et al., 2005a,b,

2007; Dura

´n et al., 2008, 2009). The system starts from

an initial value (for example d= 0.5) that varies at constant

increase (Dd) according to expressions (6) and (7).

bi¼sign½ðDVÞðDPÞ ð6Þ

di¼di1þbiDdð7Þ

In each iteration “i”,DPand DVmeasures are obtained.

Next, the value of dis adjusted to approach it to the MPP.

Note that no temperature and solar radiation measures are

needed to do the tracking, which reduces the price of the

control system. The ﬂow chart diagram of this algorithm

is shown in Fig. 5.

3.2. The developed system

The whole developed system is shown in Fig. 11.To

explain its operation, the system will be analyzed by blocks.

Fig. 6 shows the circuit that, from the voltage and current

measures at the PV array output, generates a reference sig-

nal, V

ref

, which will then be used in another block to gen-

erate a PWM signal.

From the voltage and current measures at the array out-

put (V, I), the variable power, P, is generated by using the

multiplier “Mult. 1”. Two diﬀerentiators followed by two

comparators generate the value of the functions sign(dV)

and sign(dP). These two signals are multiplied and com-

pared again to generate the analog equivalent of the bit

Fig. 4. P–Vcharacteristic of a photovoltaic array. The developed MPPT

algorithm is able to distinguish whether the system is operating to the right

or left of the MPP and act consequently.

Table 1

Possible cases and control law to enable the photovoltaic system follow the MPP.

Case System evolution Control law (V?V

MPP

)

sign(DV)sign(DP)b

i

=sign((DV)(DP)) V sign(DV)d

V

A

?V

B

+1 +1 1"+1 ;

V

B

?V

A

111"+1 ;

V

C

?V

D

+1 1+1 ;1"

V

D

?V

C

1+1+1 ;1"

Fig. 5. Flow chart of the MPPT P&O-oriented algorithm.

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Energy (2009), doi:10.1016/j.solener.2009.10.011

“b

i

”. The iterations of expression (3) are formed by inte-

grating the subsequent b

i

. Finally, the output signal is lim-

ited in order to maintain it within the appropriate range,

generating V

ref

. This signal can be used as control signal

of a PWM generating system (Enrique et al., 2005a,b).

To perform the practical implementation of the devel-

oped system, the chip AD633J has been selected as multi-

plier block. For the comparators, the cheap (approx.

0.5 $) and extensively used op-amp TL082 has been

selected. The integrator and diﬀerentiator blocks are shown

in Fig 7. Both structures are basic in analog electronics.

The op-amp TL082 has also been used for their

implementation.

A lowpass RC ﬁlter has been inserted before each diﬀer-

entiator block to remove part of the harmonic content of

the input signals. The output signal, V

ref

, of the system in

Fig. 6 is used as reference voltage for a PWM generator

(see Fig. 8), so that its duty cycle can be adjusted.

The output PWM signal of the circuit in Fig. 8 allows

controlling the behavior of the DC/DC converter. This

converter (boost-type, in this case) is shown in Fig. 9 con-

nected to a 25 Xload.

To reduce the price of the sensors, the voltage input is

taken from the photovoltaic array using a high impedance

voltage divider with a voltage follower. The measurement

of the current variable is performed by measuring the volt-

age fall in a very low value resistance, located at one of the

PV array terminals. This measure must be ampliﬁed before

reaching the multiplier. For this purpose, a very low oﬀset

voltage precision op-amp OP27 has been used (see Fig. 10).

Fig. 11 shows the diagram of the whole developed

MPPT system.

4. Simulations

The developed system has been veriﬁed using PSpice

Ò

.

The photovoltaic generator has been implemented using

ABM blocks (Analog Behavioral Modeling). The parame-

ters of the generator model correspond to the “BP

Saturno”module (ns = 60 and np = 1) (CIEMAT, 2000).

Fig. 12 presents the model and I–V and P–V curves of

the module used at 21 °C and 1000 W/m

2

.Table 2 shows

the MPP power and current (P

MPP

and I

MPP,

respectively)

for diﬀerent levels of radiation and constant temperature.

To verify the correct operation of the system, fast vari-

ations in the incident radiation have been applied to it

(see Fig. 13). Observe that during start-up, an initial rise

of 688.7 W/m

2

in the incident radiation (P

MPP

= 55.2 W)

is reached by the system in approximately 10 ms. Once

the maximum power point has been reached, the system

maintains it even for variations higher than 5 10

3

W/

m

2

/s, much higher than those present in nature. Addition-

ally, it can be observed that the system presents a high pre-

cision, since the actual trajectory of the MPP and the one

intended do not have practically noticeable diﬀerences.

Fig. 14 shows the current obtained with the tracker system.

Fig. 6. System generating the reference signal.

Fig. 7. Diﬀerentiator and integrator blocks used.

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With this sudden start-up, the tracking system is able to

obtain eﬃciencies superior to 97.2% in the ﬁrst 100 ms.

Once the MPP has been reached (during the ﬁrst millisec-

onds of the start-up) the system presents a tracking eﬃ-

ciency ghigher than 99% (99.99%), even for variations in

the incident radiation as fast and extreme as those shown

in Fig. 13. This eﬃciency is superior to 81–85% of a classi-

cal “P&O”system (Perturb and Observed), superior to 88–

89% of an “InC”system (Incremental Conductance) and to

73–85% of a “CV”system (Constant Voltage)(Hohm and

Ropp, 2002). In Fig. 15, note how the system is able to

adjust automatically the duty cycle of the PWM signal.

Fig. 9. Boost converter used.

Fig. 8. System generating the PWM signal.

Fig. 10. Measure of variables Vand I.

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Energy (2009), doi:10.1016/j.solener.2009.10.011

Fig. 11. Diagram of the whole developed system.

Fig. 12. Model and I–Vand P–Vcurves of the “BP Saturno”module.

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Energy (2009), doi:10.1016/j.solener.2009.10.011

5. Conclusions

In this work, the design of a new maximum power point

(MPP) tracking system for photovoltaic systems has been

developed. The system is an analog version of the tracking

“P&O-oriented”algorithm. From the results obtained by

simulation, it can be concluded that the developed system

presents an excellent precision and speed in the MPP track-

Table 2

P

MPP

and I

MPP

for diﬀerent levels of radiation and constant temperature

corresponding to the “BP Saturno”generator.

Temperature (°C) Radiation (W/m

2

)P

MPP

(W) I

MPP

(A)

21 688.7 55.2 1.86

21 1000 80.6 2.71

21 1721.8 136.2 4.76

Fig. 13. Top chart: applied variations in the incident radiation. Bottom chart: comparative between the actual trajectory of the MPP and that followedby

the developed system for variations in the incident radiation.

Fig. 14. Current supplied by the system for variations in the incident radiation.

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Energy (2009), doi:10.1016/j.solener.2009.10.011

ing, even for very sudden variations in the levels of incident

radiation, so increasing the total energy performance of the

installation. The system is able to reach the MPP in the ﬁrst

10 ms, getting high eﬃciency values practically from the

start-up. Once the system has reached the MPP, the eﬃ-

ciency is superior to 99%, improving the ones obtained

by other methods (“P&O”,“InC”,“CV”). This quality,

along with its high simplicity and low price, makes the pro-

posed system highly suitable for use in any kind of photo-

voltaic installation.

Acknowledgment

The present work is a contribution of the DPI2007

62336/project, funded by The Spanish Ministry of

Education.

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