PV, leakage currents, leakage current, PWM, PV systems, transformer, MODULATION TECHNIQUES, Recife, output voltage, vector, maximum amplitude, techniques, modulation technique, inverter, inverters, transformerless PV systems, RSPWM techniques, PV array, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, output voltages, grid voltage, proposed solution, frequency component, COMPARISON RESULTS, open circuit voltage, reference voltage, IC, PV system, Brazil, power systems, Federal University of Pernambuco, electrical engineering, parasitic capacitance, IEEE, transformerless, renewable energy systems, Power Systems Department, VBN, vectors, Francisco A. S. Neves, Federal University of Minas Gerais, research interests, power quality, SVPWM
Content:
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IEEE TransACTIONS ON
Industrial Electronics, VOL. 57, NO. 4, APRIL 2010
Modulation Techniques to Eliminate Leakage Currents in Transformerless ThreePhase Photovoltaic Systems Marcelo C. Cavalcanti, Member, IEEE, Kleber C. de Oliveira, Alexandre M. de Farias, Student Member, IEEE, Francisco A. S. Neves, Member, IEEE, Gustavo M. S. Azevedo, Student Member, IEEE, and Felipe C. Camboim
AbstractIn some photovoltaic (PV) applications, it is possible to remove the transformer of a system in order to reduce losses, cost, and size. In transformerless systems, the PV module parasitic capacitance can introduce leakage currents in which the amplitude depends on the converter topology, on the pulsewidth modulation, and on the
resonant circuit comprised by the system components. Based on the commonmode voltage model, modulation techniques are proposed to eliminate the leakage current in transformerless PV systems without requiring any modification on the converter and any additional hardware. The main drawback is that the proposed modulation technique for twolevel inverters can only be used with 650V dc link in the case of a 110V (rms) grid phase voltage. Comparisons among the modulation techniques are discussed, and it is proven that the proposed modulation for two and threelevel inverters presents the best results. To validate the models used in the simulations, an experimental threephase inverter is used. Index TermsEnergy conversion, photovoltaic (PV)
power systems, pulsewidthmodulated power converters. I. INTRODUCTION P HOTOVOLTAIC (PV) power systems have become more widespread in the world. Most of these systems are singlephase installations [1], [2]. However, in singlephase systems, there is a pulsating ac power on the output, and large dc capacitors are required. In threephase systems, there is a constant ac power on the output, and small dc capacitors can be used, improving the reliability and the lifetime of the systems [3]. Most of the topologies for PV systems have a transformer that adjusts the dc voltage input for the inverter and isolates the PV panels from the grid. The transformer can be used in line or high frequency, but the linefrequency transformer has large size and weight. The highfrequency transformer is used in PV systems with some stages, decreasing the efficiency and making the system more complex [3][5]. Topologies without a transformer generally have lower cost, size, and weight than topologies with transformers. The main disadvantage is the connection of the PV array to the grid Manuscript received January 16, 2009; revised July 27, 2009. First published August 18, 2009; current version published March 10, 2010. The authors are with the
electrical engineering and Power Systems Department,
Federal University of Pernambuco, 50730540 Recife, Brazil (email:
[email protected];
[email protected];
[email protected] rocketmail.com;
[email protected];
[email protected];
[email protected] yahoo.com.br). Digital Object Identifier 10.1109/TIE.2009.2029511
without galvanic isolation, which rises the leakage current through the parasitic capacitance of the PV array. Due to this capacitance and depending on the inverter topology and the switching strategy, fluctuations of the potential between the PV array and the ground can appear. These fluctuations inject a capacitive leakage current, and this current can cause grid current distortion, losses in the system, and safety problems [5]. In transformerless PV systems that use the connection between the neutral of the grid and the central point of the dc link, the leakage currents have low values because the potential between the PV array and the ground is constant. However, the connection between the neutral and the central point of the dc link is not ideal, and a small inductance has to be considered [3]. This inductance is sufficient to make the potential oscillate with high frequency and the leakage currents increase, having higher values than that recommended in standards. Without connection, high currents also appear because of the conventional pulsewidth modulation (PWM), and threephase inverters are not suitable for transformerless PV applications. Based on the commonmode (CM) voltage, some techniques to reduce the CM currents in motor drives were discussed in [6] and [7]. Depending on the choice of voltage vectors, the reduced CM voltage techniques can be grouped in two types [7]: remotestate PWM (RSPWM) [6] and active zerostate PWM (AZSPWM). In RSPWM, the
output voltage is synthesized from three active vectors. In AZSPWM, two active vectors are complimented with two opposing active vectors with equal time to create a zero vector. In this paper, RSPWM techniques are proposed to eliminate the leakage current in the conventional threephase inverter for PV applications. In RSPWM, the maximum amplitude of the phasetoneutral voltages is reduced, but it does not require any modification on the converter and any additional hardware. Using Matlab/Simulink, comparisons of the leakage currents for threephase PWM techniques are discussed, and it is proven that the PWM proposed for threephase inverters presents the best results. To validate the models used in the simulations, an experimental inverter is used in a threephase setup to evaluate the leakage currents. On the other hand, in PV systems where series PV arrays are connected to a conventional twolevel inverter, the occurrence of partial shades and the mismatching of the arrays lead to a reduction in the generated power [8], [9]. To overcome these problems, the connection of the arrays can be made using a
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Fig. 1. Threephase gridconnected PV inverter with stray elements.
Fig. 3. Model of the PV inverter: Case 1(a) step 1 and (b) step 2 [3].
Fig. 2. Model of the threephase gridconnected PV inverter.
multilevel converter [10][12]. The multilevel converter maximizes the power obtained from the arrays, reduces the device voltage stress, and generates a lower output voltage harmonic distortion [10]. The CM voltage model for twolevel inverters can also be applied to multilevel inverters. Using the proposed PWM (with constant CM voltage) for threelevel inverters guarantees low leakage currents with a gain of 50% of the maximum amplitude of the voltages in relation to twolevel inverters with the RSPWM. Therefore, the proposed PWM is specially suitable if threelevel inverters are used. II. LEAKAGE CURRENTS IN THREEPHASE TRANSFORMERLESS PV SYSTEMS Without a transformer, there is a galvanic connection of the grid and the dc source, and, thus, a leakage current appears. For the transformerless gridconnected system in Fig. 1(a), a resonant circuit is created if the PV array is grounded [3], [4]. This resonant circuit includes the PV array stray capacitance (CPV), the filter and grid inductances (L), the inverter stray capacitances (C), and the inductance between the ground connection of the inverter and the grid (LG). The magnitude of the PV array leakage capacitance depends on the weather conditions, changing from nanofarads up to microfarads [5]. Therefore, the leakage current can reach high values, becoming an important issue in transformerless PV systems. The model of a threephase gridconnected PV inverter is shown in Fig. 2. In the case of a threephase system, the CM and differentialmode (DM) voltages are derived between each phase, resulting in three cases [3]: case 1 (CM and DM voltages for phases A and B), case 2 (CM and DM voltages for phases B and C), and case 3 (CM and DM voltages for phases C and A). Only case 1 is shown in the calculation because the other two cases are
Fig. 4. Model of the PV inverter: Case 1(a) step 3 and (b) step 4 [3].
similar. The CM (VCMAB) and DM (VDMAB) voltages for phases A and B can be defined as
VCMAB
=
VAN
+ 2
VBN
(1)
VDMAB = VAN  VBN
(2)
where VAN and VBN are the voltages between the inverter outputs and the negative terminal of the PV array. Using (1) and (2), the inverter outputs can be expressed as
VAN
=
VDMAB 2
+ VCMAB
(3)
VBN
=

VDMAB 2
+ VCMAB.
(4)
A model for the system can be developed using (3) and (4) as shown in Fig. 3(a). Since the CM voltage is present in both legs, the circuit in Fig. 3(a) can be modified as shown in Fig. 3(b). The influence of the output inductors and the inverter stray capacitances can be separated as shown in Fig. 4(a). A
system modeling using different output inductances was developed in [3]. In this paper, it is considered that the output inductances of the three phases are identical. Considering that the inverter stray capacitances are also identical, the model can be simplified as shown in Fig. 4(b). It can be observed in Fig. 4(b) that the leakage current can be attenuated or eliminated by the control of the CM voltage. Therefore, in a balanced system, the DM does not contribute for the leakage currents in the PV system. To understand how to link the simplified twophase circuit (case 1) with a final model for the threephase system, the equivalent model shown in Fig. 5 is used. This figure can be used because the same development made for phases A and B
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Fig. 5. Simplified model of the threephase PV inverter.
Fig. 7. Switching patterns and CM voltage for the SVPWM. TABLE II SWITCHING PATTERNS FOR THE PWM TECHNIQUES
Fig. 6. Space vectors in the output of a threephase inverter.
TABLE I CORRESPONDING SPACE VECTOR FOR THE EIGHT POSSIBLE COMBINATIONS OF THE INVERTER SWITCHES
(case 1) can be applied for phases B and C (case 2) and phases C and A (case 3). The total CM voltage for the threephase inverter is calculated as
VCM
=
VCMAB
+ VCMBC 3
+ VCMCA .
(5)
Using (1) and similar equations for cases 2 and 3 in (5), it is possible to write the total CM voltage as
VCM
=
VAN
+ VBN 3
+ VCN .
(6)
III. MODULATION TECHNIQUES TO ELIMINATE LEAKAGE CURRENTS IN THREEPHASE INVERTERS The spacevector PWM (SVPWM) is generally used to control the threephase inverter output voltages (Fig. 1). The eight possible combinations are composed of six active (V1, V2, V3, V4, V5, and V6) and two zero (V0 and V7) vectors of voltage (Fig. 6). In the SVPWM, the plane is divided in six sectors, delimited by the active vectors. The zero and active vectors that define the sector, where the reference is placed, are used to comprise, in average values, the reference voltage vector.
Table I presents the eight possibilities of the inverter switches and the total CM voltage for the threephase inverter using (6). It can be seen in Table I that, using SVPWM, the CM voltage will change everytime that a different space vector is used. For example, in sector I, the SVPWM uses the vectors V0, V1, V2, and V7. Therefore, the CM voltage assumes four values: 0, VP N /3, 2VP N /3, and VP N as shown in Fig. 7. The SVPWM has one switching in each vector change, totaling six if the switching pattern is defined in such a way to reduce the harmonic distortion. The output voltage in relation to the central point of the dc link is intentionally modulated with a third harmonic component of the fundamental to increase the voltage in the ac side. The maximum amplitude of the phasetoneutral voltages is VP N / 3 in the linear region, where the
fundamental frequency component in the output voltage varies linearly with the voltage gain. In the AZSPWM, the active vectors are complimented with two opposing active vectors with equal time to create a zero voltage vector. Depending on the choice of the voltage vectors, the AZSPWM can be grouped in two types [7]: AZSPWM1 and AZSPWM2. The differences between the two types are illustrated in Table II for sectors I, II, and III in Fig. 6. It can be seen in Table I that, using AZSPWM1 or AZSPWM2, the CM voltage will change with high frequency. A. Proposed Modulation RSPWM eliminates the high frequency components of the CM voltage. The technique consists in using only the odd active vectors or only the even active vectors to comprise the reference. Therefore, V1, V3, and V5 are used in the case of choosing the odd vectors, and V2, V4, and V6 are used in the
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Fig. 10. Threephase setup to evaluate the leakage currents. Fig. 8. Switching patterns and CM voltage for the RSPWM1.
Fig. 9. CM voltage during a fundamental period for the RSPWM3.
case of choosing the even vectors. Depending on the choice of the voltage vectors, the RSPWM can be grouped in two types [7]: RSPWM1 and RSPWM2 (Table II). The switching pattern and the CM voltage for the RSPWM1 are shown in Fig. 8. The RSPWM presents two switchings in each vector change, and the switching pattern to reduce the harmonic distortion (eight switchings per period) is used. The maximum amplitude of the phasetoneutral voltages is VP N /3, which is 57.7% of the voltages that can be obtained with the SVPWM. However, applying the RSPWM is the only condition in which the leakage currents have low values. Another pattern (RSPWM3) can be applied using odd or even active vectors depending on the place of the reference vector [7]. For example, the vectors V1, V3, and V5 are used within 30 and 30 (last 30 of sector VI and first 30 of sector I). The vectors V2, V4, and V6 are used within 30 and 90 (last 30 of sector I and first 30 of sector II). Using this pattern, the maximum amplitude of the phasetoneutral voltages is 2VP N /(3 3), which is 15.5% higher than the amplitude that can be obtained with the RSPWM1 or RSPWM2. For the RSPWM3 technique, the CM voltage during a fundamental period is shown in Fig. 9. B.
simulation results The simulations were done in Matlab/Simulink using the threephase setup shown in Fig. 10. The grid voltages have values of 110 V (rms), and the output inductance is L = 1.8 mH.
Fig. 11. Simulated leakage impedance voltage and current of the threephase PV inverter: (a) SVPWM and (b) AZSPWM1. The PV array was simulated with a dc
voltage source of 650 V. The leakage capacitance between the cells and the grounded one was modeled with a simple capacitance between the PV array terminals and the ground. This capacitance (CPV) has a value of 220 nF, and the ground resistance (RG) is 10.75 . The results in Figs. 11(a) and 12(b) show the leakage impedance voltage and current (vL and iL in Fig. 10) for different techniques. The SVPWM and AZSPWM techniques to reduce the CM currents in motor drives [7] are not suitable for transformerless PV applications, as shown in Fig. 11(a) and (b). The RSPWM techniques [Fig. 12(a) and (b)] present the best results for threephase inverters because, using the SVPWM and AZSPWM techniques, the PV array terminals are varying between different levels with the switching frequency,
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Fig. 12. Simulated leakage impedance voltage and current of the threephase PV inverter: (a) RSPWM1 and (b) RSPWM3.
Fig. 13. Grid currents of the PV inverter: (a) SVPWM and (b) RSPWM1. TABLE III COMPARISON RESULTS FOR THE SVPWM AND AZSPWM TECHNIQUES
which would generate high leakage currents. During the transitions between the two levels of the CM voltage in RSPWM3 [Fig. 12(b)], there are some fluctuations in this voltage caused by the components of the system. Therefore, the RSPWM1 and RSPWM2 techniques are preferred in relation to eliminate the leakage currents. The results in Fig. 13(a) and (b) show the grid currents (iA, iB, and iC in Fig. 10) for the SVPWM and RSPWM techniques. The switching frequency was set to 10 kHz in SVPWM and 7.5 kHz in RSPWM in such a way to keep the same switching count. The drawback of the RSPWM1 and RSPWM2 is that the space vector will rotate within the triangle described by V1  V3  V5 or V2  V4  V6, and this circle has a radius that is 50% of the dclink voltage. However, it is shown in Fig. 13(b) that, using RSPWM, it is possible to inject a sinusoidal current into the threephase grid (110 V) with 650 V in the dc link. In this case, the PV array has a VMPP (maximum power point voltage) of 650 V with a VOC (
open circuit voltage) of 800 V. The comparison results of the PWM techniques are shown in Tables III and IV. In the tables, the techniques are compared considering the following: switchings per period (Ts), maxi
mum amplitude voltage, CM voltage, leakage current, and total harmonic distortion (THD) that is defined as
THD =
h=2 F12
Fh2
100%
(7)
where F is the rms value of the inverter output voltage or current and h is each frequency component. Two possibilities are shown in Tables III and IV for the THD calculation: THD20 means that only the harmonics up to 20 were considered, and THD200 means that harmonics up to 200 were considered. It is worthwhile to mention that the SVPWM has superior performance for THD200, but the analysis of THD20, which takes into account only the lower order harmonics, shows that the
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TABLE IV COMPARISON RESULTS FOR THE RSPWM TECHNIQUES
TABLE V COMPARISON OF EFFICIENCY FOR THE CONVERTERS
RSPWM and SVPWM techniques have similar performance. As the modulation techniques suggested for the inverter are both linear, the lowfrequency THD is expected to be low in both cases. It is the harmonic content at the switching and higher frequencies which mainly determines the current ripple and also the power efficiency of the modulation technique. The RSPWM3 presents the variable (low frequency) CM voltage resulting in low leakage current but with spikes in the transitions of the CM voltage.
C. Losses Calculation A study of losses is presented, and the methodology is used to compare the SVPWM and RSPWM techniques for gridconnected PV systems. The losses produced in switching devices consist mainly of conduction and switching losses. The technique used in this paper is based on the following methodology: Build the loss tables from the results in the data sheets; generate the loss equations; introduce these models into a simulation program for the PWM converter; and calculate the losses for a complete cycle of operation. This methodology allows comparing the losses of the converters by simulation. Conduction losses for a switch or a diode can be calculated by
EC = UC · IC · tC
(8)
where EC is the conduction energy, UC is the conduction voltage, IC is the collector current, and tC is the conduction time. At a given temperature, the relationship between UC and IC is usually characterized by a linear equation
UC = aC + bC · IC
(9)
where aC and bC are coefficients from the curve fitting provided from the device data sheets. Switching losses for turnon and turnoff of devices can be calculated by
ESW = a + b · IC + c · IC2
(10)
where a, b, and c are coefficients imposed by the curve fitting provided from the device data sheets and ESW is the switching loss energy. Inverter efficiencies have been calculated from the described models with the same parameters of the simulation results. The devices are insulatedgate bipolar transistors and diodes with
nominal values of 1200 V and 60 A. The switching frequency was set to 10 kHz in both techniques (SVPWM and
RSPWM). The SVPWM presents the best efficiency (97.4%) for the threephase inverter when compared to the RSPWM (97%). This is expected since only one switching is used in each vector change in the SVPWM. However, only one stage is used in the conversion process when using the RSPWM. Using the SVPWM in PV systems, a twostage topology or a linefrequency transformer is normally used. Since a linefrequency transformer has large size and weight, a twostage topology using SVPWM is compared to a onestage topology using the RSPWM. The differences among the efficiencies of the twostage topologies are significant when changing the dcdc topology. In Table V, hypothetical cases are considered with dcdc topologies having efficiencies changing from 97% to 99%. The global efficiency (a dcdc converter plus a threephase inverter) would present efficiencies changing from 94.5% to 96.4%. Therefore, the transformerless PV system using only one stage (threephase inverter) with the RSPWM has better results since it presents an efficiency of 97%. Other advantage of the RSPWM techniques is that the PV system has a
minimal number of components, decreasing the cost and complexity of the system. D.
experimental results For the experimental measurements, the same simulation threephase setup (Fig. 10) was used. The grid voltages have values of 10 V (rms), and the output inductance is L = 1.8 mH. The dc voltage source is 60 V, the leakage capacitance (CPV) has a value of 220 nF, and the ground resistance (RG) is 10.75 . The complete system control was executed in discrete time using the TMS320F2812 DSP from
Texas Instruments with sampling and switching frequencies of 10 kHz. It can be seen in Fig. 14(a) and (b) that only the RSPWM technique makes the leakage current have low values. A good agreement can be seen between the simulation and the experiment, showing that the theoretical assumptions used in the simulations are valid. The results indicate that the RSPWM technique has potential for using in gridconnected transformerless threephase PV systems. IV. MODULATION TECHNIQUES TO ELIMINATE LEAKAGE CURRENTS IN THREELEVEL INVERTERS The constant CM voltage technique for the twolevel inverter can also be used for an N level inverter. In this paper, the technique is explained for the threelevel inverter (Fig. 15). The SVPWM is generally used to control the threelevel inverter output voltages, and there are 27 possible combinations of voltage as shown in Fig. 16. The combinations are composed of six long vectors (V1, V2, V3, V4, V5, and V6), six medium vectors (V8, V9, V10, V11, V12, and V13), six small vectors (V15,
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Fig. 15. Diodeclamped threelevel inverter.
Fig. 16. Space vectors in the output of a threelevel inverter.
Fig. 14. Experimental leakage impedance voltage and current of the threephase PV inverter: (a) SVPWM and (b) RSPWM1.
TABLE VI CORRESPONDING SPACE VECTOR FOR THE POSSIBLE COMBINATIONS OF THE INVERTER SWITCHES FOR THE FIRST 150
V16, V17, V18, V19, and V20) with two possibilities for each one, and three zero vectors (V0, V7, and V14) of voltage. Table VI presents the space vectors associated to the possibilities of the inverter switches for the first 150 of the plane  and the total CM voltage for the threelevel inverter using (6). The proposed technique consists in using only the medium vectors and the zero vector V14 to comprise the reference vector. Therefore, in the region between the vectors V8 and V9, the vectors V8, V9, and V14 are used. Other option is to use always the three medium vectors. Considering the same region, the vectors V8, V9, and V10 would be used in this case. In any option, it can be seen that the CM voltage always assumes the values VP N /2. For the threelevel inverters, the proposed PWM can be applied with the maximum amplitude of the phasetoneutral voltages equal to VP N /2, resulting in 86.6% of the voltages that can be obtained with the SVPWM (VP N / 3). Therefore, using the proposed PWM for threelevel inverters guarantees low leakage currents with a gain of 50% of the voltage amplitude in relation to twolevel inverters with the RSPWM. It is important to mention that, increasing
the number of levels with the proposed PWM, the maximum amplitude voltage also increases, but the best gain occurs when there is a change of two to threelevel inverter. There are other combinations that guarantee a constant CM voltage using long and small vectors, but, in this case, the amplitude of the output voltages will be lower than the amplitude of the voltages
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TABLE VII COMPARISON OF THE TRANSFORMERLESS THREEPHASE INVERTERS
Fig. 17. Simulated leakage current of the threelevel PV inverter: (a) SVPWM, (b) proposed PWM (medium vectors), and (c) neutral connected to the middle point (L = 20 µH). using the technique with medium vectors if sinusoidal phasetoneutral voltages are desired. The results in Fig. 17 show that, using the proposed PWM, the threelevel inverters present low leakage currents in transformerless PV systems. In this figure, the proposed solution is compared to the traditional solution that uses the threelevel inverter as a threephase halfbridge structure, that is, with the neutral connected to the middle point of the PV generator. The connection between the neutral and the middle point of the dc link is not ideal, and a small inductance has to be considered [3]. This inductance is sufficient to make the leakage currents increase. V.
comparative analysis In this section, the transformerless threephase inverters are compared. The comparison is based on the number of switching devices and auxiliary diodes, the voltage rating of the devices, the output voltage amplitude, the CM voltages, and the leakage currents. The comparison is shown in Table VII. In terms of power devices, it can be said that the diodeclamped threelevel inverter needs twice the switching elements and six extra diodes in relation to the twolevel inverter. The advantage in this case is that the switching elements need only half of the voltage rating compared to those in the case of the twolevel inverter. Using the proposed PWM for threelevel inverters guarantees a gain of 50% of the output voltage amplitude in relation to twolevel inverters with the RSPWM. Considering the leakage current, the two and threelevel inverters are suitable in the case of applying the proposed techniques. Using SVPWM, the PV array terminals are jumping between different levels with the switching frequency resulting in high leakage currents. VI. CONCLUSION In this paper, the leakage current in threephase transformerless PV systems connected to the grid has been studied. Without
the transformer, the capacitance of the PV array can allow the circulation of the leakage current above the permissible levels. Modulation techniques designed for threephase transformerless PV systems have been proposed. The techniques guarantee a constant total CM voltage, improving the behavior of the two and threelevel inverters in terms of leakage currents without additional hardware. The behavior of the techniques has been validated on a threephase inverter prototype. Using the proposed modulation for threelevel inverters guarantees low leakage currents with a gain of 50% of the maximum amplitude of the voltages in relation to twolevel inverters with the proposed modulation. Therefore, the technique is specially suitable if threelevel inverters are used. REFERENCES [1] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, "Overview of control and grid synchronization for distributed
power generation systems," IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 13981409, Oct. 2006. [2] M. Liserre, A. Pigazo, A. Dell'Aquila, and V. M. Moreno, "An antiislanding method for singlephase inverters based on a grid voltage sensorless control," IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 14181426, Oct. 2006. [3] T. Kerekes, R. Teodorescu, and M. Liserre, "Common mode voltage in case of transformerless PV inverters connected to the grid," in Proc. IEEE ISIE, Jun. 2008, pp. 23902395. [4] E. Gubнa, P. Sanchis, A. Ursъa, J. Lуpez, and L. Marroyo, "Ground currents in singlephase transformerless photovoltaic systems," Prog. Photovolt., Res. Appl., vol. 15, no. 7, pp. 629650, Nov. 2007. [5] O. Lopez, R. Teodorescu, F. Freijedo, and J. DovalGandoy, "Eliminating ground current in a transformerless photovoltaic application," in Proc. IEEE Power Eng. Soc. Gen. Meet., Jun. 2007, pp. 15. [6] M. Cacciato, A. Consoli, G. Scarcella, and A. Testa, "Reduction of commonmode currents in PWM inverter motor drives," IEEE Trans. Ind. Appl., vol. 35, no. 2, pp. 469476, Mar./Apr. 1999. [7] E. Ьn and A. M. Hava, "Performance analysis and comparison of reduced common mode voltage PWM and standard PWM techniques for threephase voltage source inverters," in Proc. IEEE APEC, 2006, pp. 303309. [8] M. Garcнa, J.M. Maruri, L. Marroyo, E. Lorenzo, and M. Pйrez, "Partial shadowing, MPPT performance and inverter configurations: Observations at tracking PV plants," Prog. Photovolt., Res. Appl., vol. 16, no. 6, pp. 529536, Sep. 2008. [9] P. Sanchis, J. Lуpez, A. Ursъa, E. Gubнa, and L. Marroyo, "On the testing, characterization, and evaluation of PV inverters and dynamic MPPT performance under real varying
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Marcelo C. Cavalcanti (M'07) was born in Recife, Brazil, in 1972. He received the B.S. degree in electrical engineering from the Federal University of Pernambuco, Recife, in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the Federal University of Campina Grande, Campina Grande, Brazil, in 1999 and 2003, respectively. Since 2003, he has been with the Electrical Engineering and Power Systems Department, Federal University of Pernambuco, where he is currently a Professor of electrical engineering. His
research interests are
renewable energy systems, power quality, and threephase matrix converters.
Francisco A. S. Neves (M'00) was born in Campina Grande, Brazil, in 1963. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Pernambuco, Recife, Brazil, in 1984 and 1992, respectively, and the Ph.D. degree in electrical engineering from the Federal University of
Minas Gerais, Belo Horizonte, Brazil, in 1999. Since 1993, he has been with the Electrical Engineering and Power Systems Department, Federal University of Pernambuco, where he is currently a Professor of electrical engineering. His research interests are
renewable energy systems, power quality, and grid synchronization methods.
Kleber C. de Oliveira was born in Recife, Brazil, in 1980. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Pernambuco, Recife, in 2005 and 2007, respectively, where he is currently working toward the Ph.D. degree. Until December 2009, he was a Visiting Scholar at the University of Minho, Braga, Portugal. His research interests are renewable energy systems and power quality.
Gustavo M. S. Azevedo (S'08) was born in Belo Jardim, Brazil, in 1981. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Pernambuco, Recife, Brazil, in 2005 and 2007, respectively, where he is currently working toward the Ph.D. degree. Until May 2009, he was a Visiting Scholar at the
Polytechnic University of Catalonia, Barcelona, Spain. His research interests are renewable energy systems and power quality.
Alexandre M. de Farias (S'09) was born in Recife, Brazil, in 1983. He received the B.S. degree in electrical engineering from the Federal University of Pernambuco, Recife, in 2008, where he is currently working toward the M.S. degree. His research interests are renewable energy systems and power quality.
Felipe C. Camboim was born in Recife, Brazil, in 1982. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Pernambuco, Recife, in 2007 and 2009, respectively. He is currently with the Electrical Engineering and Power Systems Department, Federal University of Pernambuco. His research interests are threephase power converters and digital control.
MC Cavalcanti, KC De Oliveira