Low-Complexity MPPT Technique Exploiting the PV Module MPP ...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009

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Low-Complexity MPPT Technique Exploiting the PV Module MPP Locus Characterization Vladimir V. R. Scarpa, Student Member, IEEE, Simone Buso, Member, IEEE, and Giorgio Spiazzi, Member, IEEE

Abstract—This paper proposes a method for tracking the maximum power point (MPP) of a photovoltaic (PV) module that exploits the relation existing between the values of module voltage and current at the MPP (MPP locus). Experimental evidence shows that this relation tends to be linear in conditions of high solar irradiation. The analysis of the PV module electrical model allows one to justify this result and to derive a linear approximation of the MPP locus. Based on that, an MPP tracking strategy is devised which presents high effectiveness, low complexity, and the inherent possibility to compensate for temperature variations by periodically sensing the module open circuit voltage. The proposed method is particularly suitable for low-cost PV systems and has been successfully tested in a solar-powered 55-W battery charger circuit. Index Terms—Maximum power point (MPP) tracking, standalone photovoltaic (PV) systems.

I. I NTRODUCTION

I

N ORDER to ensure the optimal use of the available solar energy, the tracking of the maximum power point (MPPT) is an essential part of any photovoltaic (PV) system [1]. This function is implemented by suitably controlling the power processing circuit which is almost always used as an interface between the PV generator and the load or the energy accumulator. In the last few years, several novel MPPT methods have been proposed, as well as improvements for the already established ones [2]–[6]. Many of those methods aim at tracking the maximum power operating point of a PV generator by satisfying, in a closed loop regulation, the condition dPPV /dVPV = 0, where PPV and VPV represent the PV module output power and voltage, respectively. As an example, the very popular Perturb and Observe (P&O) [7]–[10] and the Incremental Conductance (IncCond) [11]–[13] make use of this relation. Due to the complexity of the required mathematical operations, a digital signal processor or a relatively powerful microcontroller are typically needed to implement them, which increases the cost of the power processing circuit. Manuscript received April 21, 2008; revised October 17, 2008. First published November 25, 2008; current version published April 29, 2009. This work was supported by the Program Alban, the European Union Program of High Level Scholarships for Latin America, under Scholarship E05D049801BR. V. V. R. Scarpa and G. Spiazzi are with the Department of Information Engineering, University of Padova, 35131 Padova, Italy (e-mail: [email protected]; [email protected]). S. Buso is with the Department of Technology and Management of Industrial Systems, University of Padova, 36100 Vicenza, Italy (e-mail: simone. [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2008.2009618

A less complicated way of tracking the maximum power point (MPP) is through a convenient estimation technique, based on an offline module characterization. In these methods, the optimal value of the PV voltage (VMPP ) or current (IMPP ) is estimated as a function of the module short circuit current (ISC ) [14], [15], open circuit voltage (VOC ) [16]–[18], or temperature (T ) [19]. Although estimation methods are generally much cheaper and simpler than those previously mentioned based on hill climbing algorithms, they often rely on approximated relations which, in certain operating conditions, can drive the system excessively far from the true MPP, thus significantly reducing the effectiveness of the power processing circuit. Therefore, their use has been limited mainly to low-cost low-power PV applications. Intermediate solutions can also be devised, as the one discussed in [20], where a linear relation between the values of module voltage and current at the MPP is used to reduce the convergence time in the P&O and IncCond methods. This paper shows how and why the relation exploited in [20] can actually be used as an alternative estimation technique, allowing the implementation of a novel low-complexity MPPT method. The analytical derivation of the estimation equation from the electrical model of a PV module allows one to identify its parameters, expressing them in terms of module quantities. Furthermore, the proposed solution suggests a simple and effective way to compensate the estimation equation for temperature variations, which only requires the periodic sensing of the VOC . As it will be further demonstrated, the proposed method presents better results when compared to other offline methods of comparably low complexity. This paper is organized as follows. In the first part, Section II, the mathematical analysis of a PV module electrical model is presented, which clarifies the underlying physical background and derives the analytical expression of the MPP locus. In the following part, comprising Sections III–V, the method is presented, the effect of temperature on its performance is discussed, and its effectiveness is compared with that of the very popular Fractional VOC method. Finally, in Sections VI and VII, the experimental application of the proposed strategy to a 55-Wp PV-powered battery charger is discussed. II. MPP L OCUS C HARACTERIZATION In a PV module, the MPP locus can be defined as the couple (VMPP , IMPP ), expressed as a function of module irradiation at a given operating temperature. The basic result presented in this paper is how to find a linear equation that approximates the

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TABLE I PV MODULE DATA AND SIMULATION PARAMETERS

Fig. 1. Equivalent electrical model of a PV module with N series-connected cells.

MPP locus and consequently allows one to implement a lowcomplexity MPPT method. We start the analytical derivation of the module MPP locus from the usual equivalent electrical model shown in Fig. 1. The model represents a generic PV module, composed by N series-connected cells, each of them presenting an equivalent series resistance RS and shunt resistance RSH . As usual, the current source Ig represents the photogenerated current, while series-connected diodes Di are lumped representations of the internal electron-hole recombination processes. We can write the following expression for the module current IPV :  V +N ·R I  PV S PV VPV + N · RS IPV IPV = Ig − Isat · e N ·(nVT ) −1 − N · RSH (1) where Isat = C · T e 3

−Eg VT

Fig. 2. Difference between VOC and VMPP for several irradiation conditions in a 55-Wp PV module (dots) and in the corresponding model (solid line), according to (6).

(6), which expresses the difference between VOC and VMPP and determines the relation between the variables (VMPP , IMPP )    VMPP ∼ VOC − VMPP = N · RS IMPP + nVT · ln +1 N · nVT = N · (RS IMPP + VDO ) .

(2)

is the cell inverse saturation current, and n is the so-called ideality factor. In (2), C is a suitable constant (in Ampere/◦ K−3 ), VT = kT /q is the temperature equivalent voltage, being k the Boltzmann’s constant, q the electron charge, T the temperature in kelvin, and Eg represents the energy gap of silicon in electronvolts. Since in almost all practical cases the cell shunt resistance RSH is relatively high, the current through it can be neglected and, consequently, the module output power can be well approximated by   V +N ·R I  PV S PV − 1 . (3) PPV ∼ = VPV · Ig − Isat · e N ·(nVT ) Calculating the partial derivative of (3) with respect to VPV and imposing it to be zero, it is possible to derive the following relation, valid at the MPP:   VMPP +N ·RS IMPP Ig VMPP N ·nVT +1=e · 1+ . (4) Isat N · nVT Equation (1) can now be rearranged to approximate the value of VOC as   Ig +1 (5) VOC ∼ = N · nVT · ln Isat where the term related to RSH has been neglected once again. Combining (4) and (5) and rearranging the terms, we obtain

(6)

In (6), the term named Differential Offset Voltage (VDO ) has been implicitly defined. We will now introduce the hypothesis, which we will verify in the immediate following, that VDO variations with irradiation can be neglected, and hence, the difference between VOC and VMPP , expressed by (6), increases linearly with IMPP . Experimental verification of (6) has been done on a 36-cell module by Helios Technology (Model H580) whose data, given by the manufacturer [21], are presented in Table I. The same table also shows the parameter values needed to emulate the module’s characteristics with the model of Fig. 1. The obtained results are shown in Fig. 2. As can be seen, the measured values follow the linear trend corresponding to (6). However, the relation between VMPP and IMPP with respect to irradiation is not linear, because VOC is a logarithmic function of Ig , as clearly shown by (5). Nonetheless, it is possible to linearize this relation for an interval where the value of VOC is sufficiently insensitive to irradiation. Indeed, from (5), it is possible to derive the sensitivity of VOC to Ig (SVOC ,Ig ) as SVOC ,Ig =

dVOC Ig 1 . · ≈  Ig VOC dIg ln Isat + 1

(7)

If we predefine a threshold value for SVOC ,Ig (e.g., 5%), from (7), we can calculate a minimum irradiation condition, corresponding to a photogenerated current Ig∗ , above which the sensitivity is lower than the selected threshold, at a given ∗ , temperature T ∗ . Associated to Ig∗ and T ∗ are the values VOC ∗ ∗ ∗ IMPP , VMPP —shown in Fig. 3 —, and VT . Now, the desired

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SCARPA et al.: MPPT TECHNIQUE EXPLOITING THE PV MODULE MPP LOCUS CHARACTERIZATION

Fig. 3. (Black lines) I–V curves for several irradiation conditions, (blue line) the MPP locus curve, and (red line) the VLR, calculated for Ig∗ = 2.5 A.

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Fig. 4. Simulated effectiveness of the VLR as a function of irradiation, for three different values of RS .

TABLE II VLR PARAMETERS AT T ∗ = 25 ◦ C

linear relation, approximating the MPP, will be defined as the tangent to the MPP locus curve for Ig = Ig∗ . The tangent line is named Voltage Linear Reference (VLR), and is shown in Fig. 3. As can be seen, the choice of the irradiation range guarantees a maximum relative VOC variation of about 4.9%. The VLR can also be analytically derived from (6) as

 dVOC − N · RS IMPP + VOFFSET (8) VLR ≡ dIMPP Ig =Ig∗ ∗ VOC

∗ (VDO

VT∗ )

∗ VDO

where VOFFSET = −n· + and is calculated for Ig = Ig∗ . Considering that IMPP is roughly proportional to Ig (see [14] and [15]), dVOC /dIMPP can be calculated as   dVOC dVOC dIg n · VT∗ = · ≈ . (9) ∗ dIMPP Ig =Ig∗ dIg dIMPP Ig =Ig∗ IMPP The parameters used to analytically derive the VLR for the simulated PV module are presented in Table II. According to (8) and (9), for the particular case where ∗ > RS , the VLR has negative slope. However, this nVT∗ /IMPP is not a necessary condition for the proposed method to operate properly, since (6) is valid independently from the value of RS . Nevertheless, as will be seen in Section VI, the slope sign has a role in the way the method is implemented. In order to evaluate the accuracy of the proposed approximation, the electrical power of each point of the VLR was calculated and compared with the power of the MPP locus at the same irradiation condition. The ratio between these two values, which we can define as the effectiveness (ε) of the VLR approximation, is shown in Fig. 4. As can be seen, in order to assess the sensitivity of the achievable effectiveness to different values of RS , two other VLRs were calculated through (8). In the three cases, the effectiveness is very near to unity for

Fig. 5. (VDO + n · VT ) obtained through simulation, with the parameters of Table I, for three different temperature conditions.

any Ig > Ig∗ . Beneath this value, the effectiveness decreases, reaching a value of ε = 0.9 for Ig = 0.3 A. III. P ROPOSED M ETHOD Based on the previous analysis, it is possible to implement a simple MPPT method by forcing the PV module to operate over the VLR. The MPPT can be based on any dc–dc switching converter, driven by a suitable input voltage (or input current) control circuitry that, using the VLR equation over the values of module voltage and current, automatically drives the module to the point where the VLR intercepts the current I–V curve. At that point, the equilibrium condition VPV ∼ = VMPP (or IPV ∼ = IMPP ) holds. Of course, the effectiveness of the method is conditioned by the accuracy of (8), which can be very high for high irradiation—and thus high power—conditions, as shown in Fig. 4. Furthermore, in order to guarantee the same performance for any temperature condition, the proposed method must also include some kind of compensation for temperature variations. This will be discussed in the next section. IV. E FFECT OF T EMPERATURE V ARIATIONS It is known that, assuming constant irradiation, the value of VOC in a PV module varies by about −2.5 mV/◦ C per cell ∗ is a function of temperature. [19], and thus the value of VOC In addition, according to (6), it is expected that the MPP locus is shifted by the same amount, since it is normally acceptable to consider RS independent from temperature and, from Fig. 5,

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Fig. 6. MPPs for T = 0 ◦ C, T = 25 ◦ C, T = 50 ◦ C, and (black lines) their respective VLRs calculated through (7).

one can observe that VDO variation with temperature can also be neglected. ∗ variation with temperaFurthermore, if we neglect the IMPP ture, and considering that, as shown in Fig. 5, the sum (VDO + n · VT ) varies only about 6% for a 50 ◦ C temperature variation, one can conclude that not only the characterization for the VLR calculation can be done at any temperature condition, but also that it is possible to compensate for temperature variations ∗ (T ). This is demonstrated simply by sampling the value of VOC by Fig. 6, where the VLR, calculated for T = T ∗ = 25 ◦ C, approximates the MPP locus with similar accuracy for any ∗ is updated. temperature condition, as long as VOC Hence, to take advantage of this property, a practical implementation of the method would require the periodic sensing of VOC at the irradiation condition that corresponds to Ig = Ig∗ . However, this solution would not be convenient, since it requires the additional sensing of Ig or the use of an irradiation sensor. Therefore, this paper proposes a simpler and cost-effective implementation: the value of VOC is sensed and simply inserted in (8), without any concern about temperature or irradiation conditions at the moment of sensing. As it will be further discussed in the next section, it will not only determine the required compensation, but also inherently increase the effectiveness of the estimation, particularly for lower irradiation conditions, i.e., those below Ig∗ . Given the relatively slow thermal time constants, this only requires the periodic sampling of VOC at a very low frequency, which helps to minimize the negative impact on the effectiveness of the temperature compensation process. V. S TUDY OF THE M ETHOD E FFECTIVENESS This section presents the study of the effectiveness of the proposed method. First, the impact of the proposed solution for temperature compensation on the effectiveness of the method will be considered. Later, the VLR method will be compared to the very popular Fractional VOC (F racVOC ) method, to evaluate the effectiveness improvement obtained with respect to a method with similar implementation complexity. A. Influence of Irradiation at VOC Sampling As explained above, during operation, VOC is periodically sensed, and VOFFSET is adjusted accordingly. The slope of

Fig. 7. Effectiveness of the VLR method for several values of irradiation condition at Voc sensing (marked with points).

Fig. 8. (Blue lines) Effectiveness of the VLR method and (red lines) the Fractional Voc method for three different temperature conditions.

the VLR, instead, remains the same one, calculated offline. Therefore, in the presence of variable irradiation conditions, the system moves across several effectiveness curves, each related to the particular, more recently sampled, VOC value. Using the parameters of Table I and temperature T = 25 ◦ C, Fig. 7 shows several effectiveness curves of the proposed method for the entire Ig range. The curves differ in the value of Ig at which VOC has been sensed, given by the marked point on each curve. As an example, assuming that VOC is sensed for Ig = 1.5 A (point A in Fig. 7), if the value of Ig decreases to Ig = 0.2 A (point B), the operation point will go far from the MPP, as predicted in Section II. However, if a new sample of VOC is taken, this will result in more suitable parameters for the estimation equation, increasing the effectiveness. Please note that the same fact is observed in the inverse situation, i.e., if irradiation increases between two VOC samples. B. Comparison With the Fractional VOC Method The proposed solution will now be compared with the F racVOC method ([12] and [13]) that estimates the VMPP value as VFrac = kFrac · VOC .

(10)

The idea is to compare the effectiveness of each method as a function of irradiation and temperature. Parameter kFrac was defined as kFrac = 0.75, and the VLR has the same parameters presented in Table I. For each value of Ig , the VOC was sampled and the effectiveness of each method, for the three values of temperature, was calculated and reported in Fig. 8.

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TABLE III COMPARISON OF THE MEAN EFFECTIVENESS FOR VLR AND F racVOC METHODS

The average value of the effectiveness (εm ) for each method and for the range of Ig defined above can be calculated as m 

εm ≡

εi

i=1

m

(11)

where m is the total number of Ig samples. Applying (11) to the results, the mean effectiveness of each method for the three simulated temperature conditions can be derived, and is presented in Table III. As can be seen, in any condition, the proposed solution offers better results than the F racVOC method. VI. M ETHOD I MPLEMENTATION For a given PV module, it might be not so immediate to measure all the parameter values required by (8). A more convenient way to implement the proposed solution consists in the graphic determination of the VLR over offline measured I–V curves. Then, the VLR can be arranged to generate a reference value for the module voltage, through an equation of the form S − Veq Vref = Req · IPV + VOC

(12)

S represents the periodically sampled VOC while where VOC Req and Veq are the parameters extracted from the analysis of the I–V curves. Their physical interpretation is given by the comparison of (12) and (8). Since the parameters Req and Veq are related to physical characteristics of the considered PV module, it is expected that they will be only affected by fabrication process tolerances, resulting in a reasonable repeatability, at least within the same production lot. If needed, (12) can also be straightforwardly transformed to give a reference value for the module current Iref

S S Iref = VPV −VOC +Veq /Req = VPV −VOC +Veq · Geq . (13)

With the help of Fig. 9, we would now like to illustrate the method’s convergence to the MPP. In doing that, we assume that we are dealing with a current controlled dc–dc converter, whose controller has, at least, an integral characteristic and is designed to guarantee a suitable stability margin, in particular when (13) is used to determine the current set point. In addition, we suppose the pulse width modulation (PWM) modulator is organized so that, when the PV module is such that Req < 0, IPV increases for a negative current error. The opposite must occur if Req > 0, so that we are always closing a negative feedback loop.

Fig. 9. Convergence process of the proposed MPPT strategy. (a) Explanation of the process. (b) Example of convergence to the MPP (simulation: VMPP = 16 V, IMPP = 2.3 A).

As shown in Fig. 9(a), starting from the condition VPV = S , both the calculated Iref and the error are negative. As VOC the value of IPV increases, thanks to the integral controller’s action and to a proper organization of the modulator, the error decreases in absolute value, until the steady-state equilibrium point is reached, at the intersection between the VLR and the module I–V curve. It is worth recalling that, if the VLR estimation error is low, the equilibrium point will be very close to the MPP, as we have shown in Section V. Once the equilibrium point is reached, a further increase of the current is prevented by the error sign reversal. Therefore, the equilibrium point is inherently stable. An interesting consequence of this fact is that, with the proposed method, phenomena like oscillations around the MPP or control losses due to sudden illumination variations (that can take place with other methods, e.g., P&O and IncCond) are not possible. As can be recognized, the situation shown in Fig. 9(a) is general and applies to all the operating conditions. Therefore, the convergence to the equilibrium point is guaranteed by the hardware organization, i.e., the system will always move toward the equilibrium point, independently from its initial conditions. Of course, we need to make sure that the small signal stability around the equilibrium point is guaranteed as well. Indeed, the current reference generation is based on the measured module voltage and, therefore, represents a further feedback loop, with a purely proportional compensator in it, whose gain is equal to Geq (13). In order to guarantee the small signal stability of this controller, i.e., its capability to steadily maintain the module on the equilibrium point of Fig. 9(a), rather than oscillating around it, the crossover frequency and phase margin of the external

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TABLE IV CONVERTER COMPONENT VALUES

Fig. 10. Battery charger schematic with the proposed control strategy.

loop have to be properly chosen. As the loop gain cannot be modified (it is imposed by the VLR), a simple and robust way to do that is by limiting the loop bandwidth, to give to the loop gain a first-order compensated behavior. This result can be obtained reducing the current controller speed of response, i.e., adjusting the current controller gain until a properly damped response is achieved. Please note that this does not imply any real performance penalization, as the required speed of response for an effective MPPT does not need to be very high. As we will show in the following (Fig. 10), in our implementation, the reference current is digitally generated, even if the current controller is still implemented by an analog circuit. In this case, to avoid any stability problem, it is only required to keep the digital controller update, or iteration, frequency fMPPT high enough to introduce a negligible delay in the reference generation loop. We observed that setting the reference update frequency, at least, two or three times higher than the current controller bandwidth guarantees a satisfactory response. Indeed, in these conditions, the digital implementation of the current reference generator behaves very much like the sampled data version of an analog one and does not pose any additional stability problem. Of course, the iteration frequency must also be compatible with the reference computation time, which is limited by the A/D and D/A conversion speed and by the time required for the numerical calculation of Iref (13). However, unless a very low-performance digital control hardware is adopted, there is normally no problem to achieve an acceptable speed of response. An example of the typical response that can be obtained with a proper design is shown in Fig. 9(b), where the module voltage, current and power are shown, together with the current reference, digitally generated according to the VLR equation (13). The reference update frequency is, in this case, equal to 200 Hz, as in our experimental prototype. In order to validate the proposed method, an experimental setup was built, based on the buck–boost topology, that operates as a battery charger, as shown in Fig. 10. The implementation is conventional, except for an additional logic switch, inserted in the output of the PWM block. It determines if the MOSFET will be driven by the duty cycle D, if Req > 0, or by its complement (1-D), if Req < 0,

for the reasons explained above. This guarantees the required negative feedback for the convergence process shown in Fig. 9. The parameters of the circuit are presented in Table IV. It is worth noting that the proposed method is not in any way topology dependent and can be adapted to all types of converters with input current or input voltage control. The choice of the buck–boost topology is only motivated by practical reasons, as it allows both series and parallel connection of batteries. In particular applications, the choice of an optimized topology is, of course, recommended. As shown in Fig. 10, even though Iref is calculated by a microcontroller, it passes through a D/A converter and feeds an analog closed loop current controller, to avoid the need for fast A/D conversion and digital PWM modulation. Given the simple operations involved in the Iref calculation—sum and multiplication between a sensed variable and a predefined constant—and the low repetition frequency— typically below 1 kHz—a simple 8-bit microcontroller has been used, whose high quantity price is below 1USD. This is, in fact, one of the advantages of the proposed solution when compared to more sophisticated methods, such as P&O and IncCond. These algorithms need the calculation of the module power, i.e., the multiplication of two sensed variables, and, therefore, cannot take advantage of any of the optimized multiplication routines that can be generally used, in low-cost microcontrollers, when one of the multiplication parameters is a constant. A flow chart of the algorithm executed by the microcontroller is shown in Fig. 11. The frequency of the MPPT calculation, according the aforementioned considerations, has been defined as fMPPT = 200 Hz, while the value of VOC is sampled every 5 minutes. VII. E XPERIMENTAL R ESULTS The aforementioned, practical way to obtain the equation of the VLR is shown in Fig. 12, where, after defining the value of Ig∗ = 2.5 A, the MPPs at this condition and at two other ones in the vicinity of Ig∗ are connected by a straight line. This line represents the VLR. As can be seen, the process can be repeated for any temperature condition, since, as we have shown, the slope of the VLR is practically insensitive to this parameter. Once the control parameters are extracted, the proposed method can be applied straightforwardly. Fig. 13(a) shows the dynamic behavior of the system for an irradiation decrease. As it can be observed, while the irradiation

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Fig. 11. Flowchart of the Iref computation algorithm. Fig. 13. (a) Dynamic behavior of the system for an irradiation decrease. (From top to bottom) Module voltage (2 V/div), module power (20 W/div), module current (0.5 A/div), current reference (1.2 A/div). Horizontal scale: 50 ms/div. (b) Same transition over the I–V plane.

Fig. 12. VLR determination for two different temperature conditions.

varies, the module operation smoothly moves over the VLR. The Iref oscillation visible in the steady state condition is due to the limit cycle caused by the finite resolution of the calculation. In Fig. 13(b), the same process is represented in the I–V plane. Since the irradiation step occurs between two samples of VOC , the effectiveness obviously decreases in the new irradiation condition, from ε = 0.99 to ε = 0.91. The effectiveness of the circuit for an entire sunny day measurement is shown in Fig. 14. It was calculated as the ratio between maximum available power and extracted power (thus not including the converter efficiency, by the way about 85% on average). As can be seen, it is very close to 100% in the higher irradiation conditions, remaining above 90% even for the lower irradiation conditions. VIII. C ONCLUSION This paper has presented an MPPT method that is based on the offline characterization of the MPP locus of a PV module.

Fig. 14. (Lower black line) Maximum available power, (gray line) average extracted power, and (upper black line) the effectiveness of the MPPT.

This paper has shown why and under what hypotheses the MPP locus can be well approximated by a line. Once the parameters of the estimation equation are extrapolated from offline measurements, the method allows one to track the MPP of the module requiring only the measurement of the input voltage and current. As any other estimation method, its effectiveness can be impaired by variations in the operating conditions. However, due to the effect of the module series resistance, the method will present better results in the high irradiation, high power conditions, with respect to the conventional solutions. Furthermore, this paper shows how, by simply measuring the module open circuit voltage, it is possible to compensate for temperature variations. The method has been implemented in a low-cost 8-bit microcontroller and tested in a battery charger application with satisfactory results.

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Vladimir V. R. Scarpa (S’05) was born in Uberlândia, Brazil, in 1980. He received the B.Sc. and M.Sc. degrees in electrical engineering from the Federal University of Uberlândia, Uberlândia, in 2003 and 2005, respectively. He is currently working toward the Ph.D. degree in information engineering at the University of Padova, Padova, Italy. His research interests include power electronics applied to renewable energy sources and digital control of switching power supplies.

Simone Buso (M’97) received the M.Sc. degree in electronic engineering and the Ph.D. degree in industrial electronics from the University of Padova, Padova, Italy, in 1992 and 1997, respectively. He is currently an Associate Professor of electronics with the Department of Technology and Management of Industrial Systems, University of Padova. His main research interests are in the industrial and power electronics fields and are specifically related to dc/dc and ac/dc converters, digital control and robust control of power converters, solid-state lighting, and renewable energy sources.

Giorgio Spiazzi (S’92–M’95) received the M.Sc. degree (cum laude) in electronic engineering and the Ph.D. degree in industrial electronics from the University of Padova, Padova, Italy, in 1988 and 1993, respectively. He is currently an Associate Professor with the Department of Information Engineering, University of Padova. His main research interests are in the fields of power-factor correctors, soft-switching techniques, lamp ballasts, renewable energy applications, and electromagnetic compatibility in power electronics.

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