Assessment and Mathematical Modeling of Energy Quality Parameters of Grid Connected Photovoltaic Inverters

Assessment and mathematical modeling of energy quality parametersof grid connected photovoltaic inverters

Giuliano A. Rampinelli a, Fabiano P. Gasparin b,n, Alexandre J. Bühler c, Arno Krenzinger d,Faustino Chenlo Romero e

a Federal University of Santa Catarina (UFSC), Florianópolis, Brazilb State University of Rio Grande do Sul (UERGS), Porto Alegre, Brazilc Federal Institute of Rio Grande do Sul (IFRS), Farroupilha, Brazild Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, Brazile Research Center for Energy, Environment and Technology (CIEMAT), Madrid, Spain

a r t i c l e i n f o

Article history:Received 26 February 2014Received in revised form30 January 2015Accepted 18 July 2015

Keywords:Solar energyGrid connected photovoltaic systemsInverter

a b s t r a c t

The insertion of photovoltaic solar energy has increased considerably over the past few years, withremarkable growth since 2005. It is essential that the electrical energy delivered by the photovoltaicsystem to the grid has an acceptable quality level. This paper presents test results of power factor andharmonic distortion content in grid connected inverters for photovoltaic systems. Several tests of tencommercially available inverter models from three different manufacturers were performed at theLaboratory of Solar Energy (Labsol) at the Federal University of Rio Grande do Sul (UFRGS), using a testbench with a power analyzer. The power factor and total harmonic distortion in current curves weremathematically modeled as a function of relative power in order to be used in computer simulation ofphotovoltaic systems. For power loads close to the nominal values, the harmonic content was found tobe low and in accordance with the standard requirements. Nevertheless, at low loading levels theinverters may inject high levels of harmonics into the grid.

& 2015 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1332. The inverter and energy quality parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

2.1. Power factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1342.2. Total harmonic distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3. Methodology and results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1353.1. Power factor tests and proposed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1353.2. Total harmonic distortion tests and proposed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

1. Introduction

Grid connected photovoltaic systems (GCPVS) are the applicationof photovoltaic (PV) solar energy that have shown the most growth inthe world. Since 1997, the amount of GCPVS power installed annually

is greater than that all other terrestrial applications of PV technologycombined [1]. Currently, the installation of grid connected systemsrepresents nearly 100% of the market [1]. The PV installed capacity in2013 was approximately 38 GW and the cumulative installed capacityin the world by the end of 2013 was almost 139 GW [2]. This datapoints to the success of photovoltaic solar energy in several countries.

Although Brazil has a great deal of potential solar energy, theinsertion of PV technology is presently in the very initial stagesand currently there are no support programs or feed in tariff

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Renewable and Sustainable Energy Reviews

http://dx.doi.org/10.1016/j.rser.2015.07.0871364-0321/& 2015 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: [email protected] (F.P. Gasparin).

Renewable and Sustainable Energy Reviews 52 (2015) 133–141

specifically for PV systems. Support programs and governmentalincentives create an economy of scale that consequently reducecosts and improve the market. Although incentive programs areonly designed to be temporary, they are critical to the formation ofa stable market [3,4]. The regulation of the electric sector plays animportant role in assuring the availability of energy according tothe country’s future needs, encouraging its production consideringthe mid and long term needs as well as the necessity of offeringcleaner energy sources.

A regulatory framework was released on April 17, 2012 when theBrazilian national electric regulatory agency (ANEEL) issued resolutionno. 482 to regulate the installation of micro-generation (up to100 kW) and mini-generation (from 100 kW up to 1 MW) systemsconnected to the grid as well as to establish net metering for thesesystems. In Brazil, public concessions of electric power plants aredefined based on the result of public bidding. The first time thisoccurred specifically for photovoltaic energy plants was in October2014, when approximately 889MW of PV installations were grantedto different parties.

The energy produced by photovoltaic systems is converted byelectronic inverters and the energy quality is a constant issue forthe electric authority. In this work, energy quality parameters ofinverters up to 3800 W were analyzed.

2. The inverter and energy quality parameters

A grid connected photovoltaic system is basically constituted of aPV array, the inverter and other components needed to run thesystem. An inverter is the electronic device that converts DC powerfrom the PV array to AC power that is injected into the grid withacceptable quality. The development of power electronic technologyhas provided a considerable increase in the efficiency and reliability ofconversion and subsequently cost reduction. The inverters currentlyavailable in GCPVS feature important control functions such asmaximum power point tracking, anti-islanding grid fault conditiondetection, energy measurement, etc. These inverters have differentenergy conversion circuits and topologies and they can have transfor-mers for high or low frequencies, or they may not even havetransformers at all. Each topology has its own characteristics, withits particular advantages and disadvantages. In general, transformer-less inverters are more efficient but those with transformers havegalvanic isolation from the DC to AC side [5–7].

Early grid connected PV systems were designed to work at lowvoltages at the DC side and the inverter had a low frequencytransformer in the output. However, in addition to being heavy andexpensive, the transformers impeded the ability of manufacturers toincrease the inverter’s efficiency. Now most of the photovoltaic plantswork at higher voltages and transformerless inverters have gainedmarket share and are more efficient than those with transformers.Since 2007, the Photon Laboratory has performed regular tests ofinverter models from different manufacturers, finding transformerlessinverters to be the most efficient [8]. Their use depends on the localgrid regulations and can vary according to the country. In some places,for example, galvanic isolation between the DC and AC sides ismandatory.

The power injected into the grid by the PV system must complywith quality requirements in order to avoid major disturbances to thegrid. A power quality problem can be defined as any event thatmanifests electrical disturbances in voltage, current or frequencycausing damage or incorrect operation of equipment. Power qualityis evaluated based on certain parameters set by the local electricauthority. These parameters are usually low harmonic content,sinusoidal waveform with a frequency of 60 Hz (in Brazil) and powerfactor higher than a specified value. Failures or defects in the gridshould not result in damage to the PV system and if this should occur,

the equipment must ensure safe disconnection. Similarly, a failure ordefect in the PV system should be identified by protective devices andshould not affect other consumers of the electric system.

The impact on quality of electricity injected into the griddistribution is the subject of several studies [9–11]. They mainlyexplore the electrical characteristics of the inverters, such asharmonic distortion and power factor. For example, Infield andSimmons and Infield et al., analyze the energy quality injected intothe grid by PV systems [12,13]. Kourtesi et al., evaluate strategiesto reduce the harmonic content [14]. Caamaño-Martin et al.,explore the impact of PV systems on the electrical grid [15] andWoyte et al., study the fluctuations in voltage that occur when PVsystems inject power into the grid [16]. Several papers presentstudies and reviews of the state of the art of inverters used in gridconnected photovoltaic systems [17,18]. Reviews of islandingdetection techniques for renewable distributed generation sys-tems are also the subject of many scientific studies [19–21].

2.1. Power factor

In purely resistive alternating current circuits, the voltage andcurrent waveforms are in phase. However, in the presence ofreactive loads such as inductors and capacitors, the energy storagein these loads results in a phase difference between the voltageand current waveforms. In switching or non-linear devices, thevoltage and current waveforms are quite different and generateharmonic distortion. The power factor (PF) of an electrical systemis defined as the ratio between the active power (P) and apparentpower (S) as presented in Eq. (1).

PF ¼ PS¼

1T

RVi tð ÞU Ii tð ÞUdtVRMS U IRMS

ð1Þ

where Vi and Ii are the voltage and current at time t, VRMS and IRMS

are the root mean square of voltage and current and T is the periodof the waveform which corresponds to the integration time usedto calculate the power.

2.2. Total harmonic distortion

The total harmonic distortion in current (Eq. (2) left) is defined asthe ratio of the RMS value of the harmonic components in the currentand the RMS value of the fundamental component of the current.Similarly, the total harmonic distortion in voltage is defined as theratio between the RMS value of the harmonic components in voltageand the RMS value of the fundamental component of the voltage (Eq.(2) right).

THDI ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiP1n ¼ 2

I2n

s

I1THDV ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1n ¼ 2

V2n

s

V1ð2Þ

where THDI is the total harmonic distortion in current, In is the currentcomponent of the nth harmonic, I1 is the fundamental component ofcurrent, THDV is the total harmonic distortion in voltage, Vn is thecomponent of the voltage of the nth harmonic and V1 is thefundamental component of the voltage.

Power factor and harmonic distortion are topics of interest inseveral scientific studies [22,23]. Cardona and Carretero present amathematical model to the total harmonic distortion in invertercurrent according to Eq. (3) [24].

THDI ¼ AUPCA

PNOM

� ��B !

ð3Þ

where A and B are fitting parameters of the mathematical model,PCA is the output power of the inverter and PNOM is the nominalinverter power.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141134

3. Methodology and results

The tests were performed in ten different inverter models fromthree different manufacturers. Five models were manufactured bySMA, three by Fronius and two by Mastervolt. A test bench consistingof a Fluke 434 power analyzer and a computer to acquire data wasused for this task. In order to perform the measurements of theelectrical characteristics of the photovoltaic inverters, the connectionsto the power analyzer were made according to the schematic diagrampresented in Fig. 1, which shows the device input connections.

The power analyzer Fluke 434 is in conformity with IEC/EN61010-1-2001. The uncertainty of the instrument is presented in Table 1.

The variables measured were both DC and AC voltage and current.The power analyzer determines power factor and harmonic distortion

in voltage and current. Table 2 presents the main nominal character-istics of the inverters tested at Labsol—UFRGS.

The main electrical characteristics of grid connected inverters are:DC to AC efficiency, maximum power point tracking (MPPT) efficiency,power factor and harmonic distortion [25]. The mathematical modelsdeveloped in this work were obtained by testing inverters and thenplotting, fitting and obtaining the coefficients of the mathematicalmodels from the experimental data. The equation used for eachmathematical model was chosen among several possibilities availablein the curve fitting software that best matched the experimental data.

3.1. Power factor tests and proposed model

The power analyzer simultaneously measures and records theactive power, apparent power, reactive power and therefore the powerfactor of the inverter. Similar to the efficiency, this parameter alsodepends on the relative power. The curve of the power factor isobtained from measuring this parameter at different levels of relativepower. Figs. 2 and 3 show the measured and mathematical curve ofthe power factor of the inverters Fronius IG 15 and MastervoltSunmaster QS3200.

The mathematical model used to represent the measured curves ofthe power factor is presented in Eq. (4), which is determined as afunction of the relative power of the inverters.

PF¼C0 UC1þ C2 U

PACPNOM

� �C3� �

C1þ PACPNOM

� �C3ð4Þ

where C0, C1, C2 and C3 are coefficients of the mathematical model.

Fig. 1. Power analyzer input connections.

Table 1Uncertainty of the power analyzer Fluke 434.

Power and energy Variable Uncertainty

W–VA–VAR 71%kW h–kVA h–kVAr h 71.5%PF—cosφ 70.03

Harmonic distortion THDV 72.5%Harmonic distortion THDI 72.5%Voltage V 70.5% of Vnom

Current A 71%

Table 2DC and AC electrical power data from the inverters that were tested at Labsol—UFRGS.

Manufacturer Model DC power (W) AC power (W) Topology (transformer)

Maximum Nominal Maximum Nominal

SMA SB 700U 1000 780 700 700 Low frequencySMA SB 1100E 1210 1100 1100 1000 Low frequencySMA SB 2100 2450 2000 2100 1900 Low frequencySMA SB 2500 3000 2480 2500 2300 Low frequencySMA SB 3800U 4800 4040 3800 3800 Low frequencyFronius IG 15 2000 1400 1500 1300 High frequencyFronius IG 20 2700 1940 2000 1800 High frequencyFronius IG 30 3600 2690 2650 2500 High frequencyMastervolt QS 2000 1800 1700 1725 1600 High frequencyMastervolt QS 3200 2950 2750 2750 2600 High frequency

Fig. 2. Power factor of Fronius IG 15 as a function of relative power.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141 135

The proposed mathematical model requires the determination offour coefficients that are established by fitting the measured curve.Table 3 shows the power coefficients obtained for the mathematicalmodel that best match the data measured from the inverters. Table 4shows the power factor of the inverters based on different weightingfactors of relative power chosen according to the European andCalifornian efficiency curves.

The power factor of the inverter is a function of the load leveland increases proportionally to the relative power, approaching100% close to the rated output power. Table 5 presents theminimum relative power, where the power factor is larger than90% for the European and Californian power factors.

It can be seen that beginning at approximately 30% of nominalpower, inverters already present power factor values greater than 90%.On the other hand, the power factor of the inverter operating at lowpower can vary significantly depending on the model and manufac-turer. For example, if it is recommended that the inverter operateswith a power factor greater than 90%, the minimum relative powerwould ensure that it would vary between 0.08 and 0.32 of thenominal power among the tested inverters.

3.2. Total harmonic distortion tests and proposed model

In control devices such as inverters, harmonic distortions aremainly due to the odd harmonic components. The power analyzermeasures and records up to the fiftieth harmonic in voltage,current and power which are electrical parameters that alsodepend on the loading level of the inverter and the grid connec-tion point. The harmonic distortion curve is obtained from themeasurement of this parameter at different levels of relative

power. Figs. 4 and 5 show the measured and fitted curves of THDI

for the SMA Sunny Boy 2100 and SMA Sunny Boy 2500.The current harmonic distortion curve is described by the

mathematical model presented in Eq. (5).

THDI ¼ T0 Uexp �T1 UPAC

PNOM

� �� �þT2 Uexp �T3 U

PAC

PNOM

� �� �ð5Þ

where T0, T1, T2 and T3 are coefficients that are obtained by fittingmeasured curves.

The total harmonic distortion in current depends on the totalharmonic distortion in voltage and inverter operating power. TheTHDV depends on the power grid and varies throughout the day.To enable comparison among inverters, THDI values were mea-sured with the same amount of THDV (2.7%). Table 6 shows theadjustment coefficients for total harmonic distortion in current foreight of the ten inverters tested, obtained from the proposedmodel and from the model proposed by Cardonna e Carretero [24].

Table 3Power factor coefficients used in the mathematical model.

Manufacturer Model C0 C1 C2 C3 R2

SMA SB 700U 0.0464 0.0221 1.021 1.593 0.99SMA SB 1100E 0.0422 0.0067 1.007 1.4 0.99SMA SB 2100 0.0344 0.0016 0.999 1.787 0.98SMA SB 2500 0.1138 2.55�10�5 0.997 3.283 0.99SMA SB 3800U 0.1703 0.0012 0.998 1.902 0.99Fronius IG 15 0.0935 0.0137 0.997 1.696 0.99Fronius IG 20 0.0602 0.0139 1.006 1.473 0.97Fronius IG 30 0.2156 0.0039 0.997 1.853 0.99Mastervolt QS 2000 0.0781 0.0075 0.997 1.595 0.99Mastervolt QS 3200 0.0442 0.0126 0.993 1.449 0.98

Table 4Power factor determined by European and Californian weighting.

5% 10% 20% 30% 50% 75% 100%

SB 700U 31.6 56.8 80.3 89.3 96.0 98.8 99.9SB 1100E 71.0 86.8 94.9 97.3 99.0 99.7 100.0SB 2100 75.5 91.2 97.2 98.5 99.3 99.6 99.7SB 2500 71.2 95.5 99.2 99.5 99.6 99.7 99.7SB 3800U 77.9 92.5 97.7 98.8 99.4 99.6 99.7IG 15 37.5 63.1 84.0 91.0 95.8 97.7 98.4IG 20 50.1 73.0 88.3 93.4 97.0 98.6 99.3IG 30 60.5 82.7 94.1 96.9 98.6 99.2 99.3QS 2000 56.3 78.7 91.5 95.2 97.6 98.6 99.0QS 3200 52.6 74.4 88.4 92.9 96.1 97.5 98.1

Table 5Minimum relative power in which the inverter can operate to ensure a powerfactor larger than 90% and the European and Californian power factors.

Manufacturer Model Relative power PFEU PFCAL

SMA SB 700U 0.32 89.8 94.5SMA SB 1100E 0.13 96.9 98.5SMA SB 2100 0.10 97.9 99.0SMA SB 2500 0.09 98.5 99.5SMA SB 3800U 0.28 98.1 99.1Fronius IG 15 0.23 90.6 94.5Fronius IG 20 0.15 93.2 96.2Fronius IG 30 0.18 95.9 97.9Mastervolt QS 2000 0.22 94.5 96.9Mastervolt QS 3200 0.08 92.6 95.3

Fig. 4. THDI of SMA Sunny Boy 2100 as a function of relative power.

Fig. 3. Power factor of Mastervolt Sunmaster QS 3200 as a function ofrelative power.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141136

Table 7 presents the values of the total harmonic distortion incurrent at different levels of relative power. The relative powervalues where the THDI is less than 5% are highlighted in the table.

When the inverter is operating at nominal power, the totalharmonic distortion in the current must be less than 5% of thefundamental current and each individual harmonic should belimited based on the technical standards [26]. When the voltageis sinusoidal, the current injected into the grid by the inverter isalso sinusoidal with low harmonic content when the inverter isoperating with relative power greater than 20%. Thus, a highquality inverter may have harmonic content levels limited to thoseestablished by technical standards in the highest possible powerrange. However, it must be noted that in relative power of lessthan 10% or 20%, depending on the manufacturer, the inverters canpresent current with levels of harmonic distortion higher than thevalues established by technical standards, even when the voltagehas low harmonic content.

The first odd harmonics are primarily responsible for the levelof harmonic distortion. According to the standards, the distortionlimit provided by odd harmonics of order three, five, seven andnine must be less than 4% when the inverter is operating atnominal power. The first three odd harmonics content of the SMASunny Boy 2100 and SMA Sunny Boy 2500 inverters are shown inFigs. 6 and 7.

The first odd harmonics content of the SMA Sunny Boy 3800Uand Fronius IG 30 inverters are shown in Figs. 8 and 9.

The first odd harmonics of the Fronius IG 15 and Fronius IG 20inverters are shown in Figs. 10 and 11. The first odd harmonics ofthe Mastervolt Sunmaster QS 2000 and Mastervolt Sunmaster QS3200 inverters are shown in Figs. 12 and 13.

The distribution of harmonic components in the inverters’current and voltage was also analyzed and two distributionsobtained at different loading levels were compared. Figs. 14–17show the harmonic components in current and voltage of theFronius IG 30 inverter at different levels of power. Figs. 18–21show the harmonic components in current and voltage of the SMASunny Boy 2100 inverter operating at different levels of power.

The harmonic distortion in voltage at the inverters’ connectionpoint is due exclusively to the fifth harmonic, since the remainingharmonics have values less than 0.5% VRMS. However, it is possibleto find very different harmonic distributions in voltage whereother orders contributed to the total harmonic distortion [26].

Fig. 5. THDI of SMA Sunny Boy 2500 as a function of relative power.

Table 6Coefficients of the mathematical models of THD in current.

Model Proposed model Cardonna e Carretero

T0 T1 T2 T3 R² A B R²

SB 2100 6.071 0.579 49.629 10.467 0.994 2.700 0.916 0.984SB 2500 36.753 6.413 4.996 0.133 0.972 4.630 0.667 0.913SB 3800U 8.284 1.535 23.438 11.104 0.998 2.394 0.776 0.995IG 15 15.376 1.112 50.829 16.036 0.994 5.302 0.652 0.993IG 20 20.735 5.473 5.849 0.099 0.998 5.021 0.547 0.989IG 30 7.088 0.330 26.026 10.804 0.988 4.218 0.555 0.987QS 2000 3.514 0.792 10.339 8.796 0.997 1.635 0.65 0.995QS 3200 3.436 0.451 10.233 5.577 0.998 2.42 0.562 0.976

Table 7Total harmonic distortion in current of the tested inverters at different levels ofrelative power.

5% 10% 20% 30% 50% 75% 100%

SB 2100 35.3 23.1 11.5 7.2 4.8 3.9 3.4SB 2500 31.6 24.2 15.0 10.1 6.1 4.8 4.4SB 3800U 21.1 14.8 8.6 6.0 3.9 2.6 1.7IG 15 37.3 23.9 14.3 11.4 8.8 6.7 5.0IG 20 21.5 17.7 12.6 9.6 6.9 5.8 5.3IG 30 22.1 15.7 9.6 7.4 6.1 5.5 5.1QS 2000 10.0 7.5 4.7 3.5 2.5 1.9 1.6QS 3200 11.1 9.1 6.5 4.9 3.3 2.6 2.2

Fig. 6. SMA Sunny Boy 2100 current harmonics.

Fig. 7. SMA Sunny Boy 2500 current harmonics.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141 137

Figs. 22–25 show the harmonic components in current and voltageof the Mastervolt Sunmaster QS 3200 inverter operating atdifferent levels of power.

In values close to the nominal power output, the harmoniccontent in the current is generally small and mainly due to low

order odd harmonics. The total harmonic distortion tends toincrease when the inverter’s load level decreases, regardless theimpedance of the grid. Nevertheless, it is possible to find situationswhere reactive electric loads at the point of connection interfere inthe harmonic current injected by the inverter into the grid. The

Fig. 8. SMA Sunny Boy 3800U current harmonics.

Fig. 9. Fronius IG 30 current harmonics.

Fig. 10. Fronius IG 15 current harmonics.

Fig. 11. Fronius IG 20 current harmonics.

Fig. 12. Mastervolt Sunmaster QS 2000 current harmonics.

Fig. 13. Mastervolt Sunmaster QS 3200 current harmonics.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141138

presence of reactive loads can even prevent the connection of theinverters to the grid, creating a fault on the AC side [26].

The contribution of the harmonic components in low, mediumor high power can vary according to the inverter model and gridconditions. Yet, the total harmonic distortion is essentially depen-dent on the inverter’s power load level.

4. Conclusion

This work presented a study of electrical characteristics ofinverters used in grid connected PV systems from a theoretical andexperimental approach. Experimental tests of inverters allowedfor the characterization of power factor and total harmonicdistortion. The tests were performed to measure and analyzeinverters’ different electrical characteristics in order to developtheoretical mathematical models that describe these features. Thetests indicate that the power factor and total harmonic distortionin current are dependent on the relative power. The curves

Fig. 14. Fronius IG30 current harmonics at 10% of nominal power.

Fig. 15. Fronius IG30 current harmonics at 100% of nominal power.

Fig. 16. Fronius IG30 voltage harmonics at 10% of nominal power.

Fig. 17. Fronius IG30 voltage harmonics at 100% of nominal power.

Fig. 18. SMA Sunny Boy 2100 current harmonics at 10% of nominal power.

Fig. 19. SMA Sunny Boy 2100 current harmonics at 100% of nominal power.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141 139

described by the proposed mathematical models primarily presentcoefficients of determination (R2) greater than 0.9, indicating anexcellent correlation between measured points and theoreticalcurves. The characteristics were analyzed individually and theresults aided in understanding the process of interaction betweenthe PV system and the inverter, as well between the inverter andthe grid.

The mathematical models and coefficients obtained can easilybe introduced in PV system simulation software to improve the

results of simulations through a detailed model of the whole rangeof the inverter’s operation.

Acknowledgments

The authors wish to acknowledge the National Council forScientific and Technological Development of Brazil (CNPq) and the

Fig. 20. SMA Sunny Boy 2100 voltage harmonics at 10% of nominal power.

Fig. 21. SMA Sunny Boy 2100 voltage harmonics at 100% of nominal power.

Fig. 22. Mastervolt Sunmaster QS 3200 current harmonics at 10% of nom-inal power.

Fig. 23. Mastervolt Sunmaster QS 3200 current harmonics at 100% ofnominal power.

Fig. 24. Mastervolt Sunmaster QS 3200 voltage harmonics at 10% ofnominal power.

Fig. 25. Mastervolt Sunmaster QS 3200 voltage harmonics at 100% ofnominal power.

G.A. Rampinelli et al. / Renewable and Sustainable Energy Reviews 52 (2015) 133–141140

Centro de Investigaciones Energéticas Medioambientales y Tecno-lógicas (CIEMAT)—España.

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