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Solar Energy 83 (2009) 1026–1039

Experimental assessment of the waveform distortionin grid-connected photovoltaic installations

Gianfranco Chicco a,*, Jurgen Schlabbach b, Filippo Spertino a

a Politecnico di Torino, Dipartimento di Ingegneria Elettrica, corso Duca degli Abruzzi 24, 10129 Torino, Italyb University of Applied Sciences, Power System Engineering, – FB2, POB 10 11 13, 33511 Bielefeld, Germany

Received 29 July 2008; received in revised form 30 December 2008; accepted 6 January 2009Available online 12 February 2009

Communicated by Associate Editor: Dr. Arturo Morales-Acevedo

Abstract

This paper provides a multi-faceted view on the characterization of the waveform distortion in grid-connected photovoltaic (PV)plants from experimental results. The focus is set on the characterization of the waveform distortion occurring under different operatingconditions in field measurements and laboratory tests. The assessment is carried out by considering the system-based point of view, onthe basis of the measurements gathered at the interface between the PV plant and the grid or the supply point in the laboratory. Newmethodological hints on the formulation of the experimental tests are provided. The results of the waveform distortion analysis for har-monic currents and voltages are compared to the requirements of present power quality standards, indicating that in practical cases thecurrent distortion can be significantly higher than in normal test conditions. Furthermore, the key aspect concerning harmonic and inter-harmonic modelling of multiple grid-connected PV inverters is addressed. Experimental results on plant configurations with multiple PVinverters show that low-order harmonics sum up almost arithmetically, whereas the higher-order harmonics and the interharmonics sumup in an almost Euclidean way.� 2009 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic systems; Grid connection; Waveform distortion; Harmonics; Interharmonics; Experimental analysis

1. Introduction

The present evolution of the distribution system applica-tions is characterised by increasing diffusion of scatteredlocal sources, forming the so-called Distributed Generation(DG) Jenkins et al., 2000; Ackermann, 2007. As local sourcesof renewable energy, grid-connected photovoltaic (PV)plants are contributing to the increased DG penetration intothe distribution systems (Jager-Waldau, 2007). In recentyears, a significantly high growth of PV installations hasbeen experienced in countries like Germany and Spain(REN21, 2006). The economic barriers that typically limit

0038-092X/$ - see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2009.01.005

* Corresponding author. Tel.:+ 39 011 090 7141; fax: + 39 011 090 7199.E-mail addresses: gianfranco.chicco@polito.it (G. Chicco), juergen.

schlabbach@fh-bielefeld.de (J. Schlabbach), filippo.spertino@polito.it (F.Spertino).

the use of PV systems have been in some cases reduced by sig-nificant regulatory or governmental incentives towardswider use of PV systems. In particular, the incentives referto building-integrated solutions (Sick and Erge, 1995;German Government, 2004) or to the introduction of spe-cific feed-in tariffs (Munoz et al., 2007; Aste et al., 2007).

On the system point of view, the connection of PVplants to the grid allows for operation in peak-shaving

mode (i.e., reducing the load demand seen at the grid inter-face), or in net metering mode (with local power productionexceeding the local load). However, PV systems cannotperform island operation, i.e., supplying any portion ofthe distribution systems in the absence of the grid supply.Islanding prevention requires the PV system disconnectionwhenever the grid is switched off or excessive voltage or fre-quency deviations with respect to the reference valuesoccur (DIN V VDE 0126-1-1, 2006).

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1027

Besides energy efficiency and islanding issues (Islamet al., 2006; Macedo and Zilles, 2007), specific aspects con-cerning the operation of grid-connected PV systems refer topossible voltage increase at the distribution system nodes,reduction of distribution system losses, and voltage andcurrent waveform distortion (Islam et al., 2006; Bhowmiket al., 2003). Recent studies have pointed out that withthe present and foreseeable penetration of PV systems thevoltage increase is likely to remain relatively limited(Thomson and Infield, 2007). Loss reduction has a majorimpact in the absence of reverse power flows (Jenkinset al., 2000). Concerning the waveform distortion, varioussituations can be found depending on the characteristics ofthe inverter-based interface (Abete et al., 2001; Rooij,2002) and of the grid to which the PV plant is connected.The distortion of a voltage or current waveform, describedin terms of harmonics and interharmonics (Schlabbachet al., 2001), depends on the nonlinearities emerging fromthe coupling of the PV plant to the grid (Infield et al.,2004). The variety of actual operating conditions makesit difficult to set up suitable specifications for carryingout the laboratory tests (Chicco et al., 2004). Severalresearch efforts are aimed at reproducing test conditionsmore representative of the real PV inverter operation dur-ing laboratory tests (Sanchis et al., 2007) and at assistingthe development of upgraded regulatory requirements(Oliva et al., 1998; Oliva and Balda, 2003; Enslin andHeskes, 2004). Results coming from field measurementsare of key interest for the PV component manufacturers,in order to determine the effectiveness of the adoption oftheir products in real applications under a wide range ofoperating conditions (Schlabbach and Kammer, 2006).

This paper deals with the characterization of the wave-form distortion from grid-connected PV plants under dif-ferent operating conditions, on the basis of several fieldand laboratory tests. New contributions with respect tothe analyses available in the literature are presented, in par-ticular concerning:

� the relationships among the individual harmonic distor-tion of voltage and current from field and laboratorytests;� the discussion on how real PV plants perform in real

operating conditions when compared to their perfor-mance in standard test environments, with specific meth-odological indications on the assessment of thecompliance to the power quality standards in the worstacceptable conditions;� the characterization of the waveform distortion at differ-

ent harmonic orders by means of the harmonic andinterharmonic summation ratios, resulting from theaggregation of multiple PV inverters.

All these issues are addressed by highlighting the meth-odological aspects taken into account for setting up andcarrying out suitable experimental analyses, summarizingthe relevant general results obtained.

Section 2 introduces the waveform distortion indicatorsand discusses some particularities of the distortion in thepresence of PV systems. Section 3 deals with the harmonicassessment of PV inverters from field tests. Section 4 dis-cusses the results of specific laboratory tests carried outby reproducing supply voltage waveforms similar to theones found in real conditions, compared to the resultsobtained in test conditions specified by the standards.Section 5 highlights some specific issues depending on thepresence of a circuit for network impedance assessment.Section 6 deals with the connection of multiple invertersto the grid, highlighting the evaluation of harmonics andinterharmonics for the aggregation of inverters connectedto the same node of the grid. The last section containsthe concluding remarks.

2. Waveform distortion indicators and aspects concerning PV

systems

The voltage and current waveform distortion is charac-terised by various indicators. Besides the classical individ-ual harmonic distortion and Total Harmonic Distortion(THD) Schlabbach et al., 2001, further distortion factorsare defined in the IEC Std. 61000-4-7 (International Elect-rotechnical Commission, 2002) on the basis of the applica-tion of the Fast Fourier Transform (FFT) on thewaveforms recorded for 10 successive periods, in order toget a number of spectral lines of 5 Hz width each (for 50Hz systems) or 6 Hz (for 60 Hz systems) Aiello et al.,2006. For this purpose, the waveform is recorded for 10successive periods (Tw = 200 ms), then the Fast FourierTransform (FFT) is performed in order to get a numberof spectral lines of width 1/Tw = 5 Hz each. Consideringthe value ch f 0 of the central line of the FFT at the har-monic order h, the contribution of the generic harmonicgroup is

C2h ¼

1

2ðc2

h f 0� 5T wÞ þ

X4

i¼�4

c2h f 0þ i

T wþ 1

2ðc2

h f 0þ 5T wÞ ð1Þ

and the contribution of the generic harmonic subgroup is

S2h ¼

X1

i¼�1

c2h f 0þ i

T wð2Þ

For the maximum harmonic order H = 40, the group totalharmonic distortion (THDG) is then defined as:

THDG ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXH

h¼2

ðCh

C1

Þ2vuut ð3Þ

and the subgroup total harmonic distortion (THDS) is:

THDS ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXH

h¼2

ðSh

S1

Þ2vuut ð4Þ

The use of these factors improves the accuracy of theresults and their comparability, mitigating the diversity

1028 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

due to the actual value of the fundamental frequency andto the lack of stationary waveforms. The THDG andTHDS indicators embed the effects of the waveform varia-tion within the recording time interval. The resulting valuesare greater than the ones of the classical THD expressed inthe framework of the IEC Std. 61000-4-7 as

THD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXH

h¼2

ðch f 0

c1f 0

Þ2vuut ð5Þ

Similar expressions are provided for the interharmonics, bydefining the contribution of the hth interharmonicsubgroup to the RMS current

S2hþ0:5 ¼

X8

i¼2

c2h f 0þ i

T wð6Þ

Fig. 1 shows the block structure of the grid-connected PVplant, composed of arrays of PV modules, interfaced tothe external grid through a Power Conditioning Unit(PCU). The PCU is composed of a number of stages. Atthe DC side, besides DC filtering, it is possible to find aDC/DC converter or a DC/AC/DC converter (with anintermediate high frequency AC transformation), and abuffering (e.g., capacitive) stage, up to the DC/AC con-verter (inverter). The DC side also includes the control cir-cuits for tracking the maximum power point of the current/voltage characteristic with the highest possible accuracy(Maximum Power Point Tracker – MPPT). At the AC side,there are possible solutions with or without coupling trans-former, and the AC filtering stage (e.g., EMC-filters).

The harmonic distortion, originated from PV systems atthe Point of Common Coupling (PCC) with the LowVoltage (LV) or Medium Voltage (MV) external grid,depends on the combined harmonic characteristics of thedistribution system, where the PV system is installed, andon the PCU performance (Vasanasong and Spooner,2000). The typical maximum harmonic order H = 40defined in the power quality standards corresponds to amaximum frequency of 2 kHz (with 50 Hz as fundamentalfrequency). However, the typical commutation frequencyof DC/DC and DC/AC converters, usually operated withthe Pulse Width Modulation (PWM) technique, is higherthan 5 kHz. Hence, the commutation frequencies are notrepresented in the harmonic indicators. Nevertheless, inpractice there are substantial contributions at low-orderharmonics (mainly for h = 3, h = 5 and h = 7) in the har-monic currents injected into the grid.

In principle, the analysis of the harmonic distortion issimilar to the one that could be carried out for any

DC filtering

DC/DC or

DC/AC/DC converter

buffer

Fig. 1. Block structure of the

inverter-interfaced system. However, some peculiarities ofPV systems are the dependence of their operating condi-tions on climatic variables (e.g., temperature, irradianceand shading effect), which limit the time interval of opera-tion during a day and significantly impact on the shape ofvoltage and current waveforms. The climatic variables mayprovide significant correlation among the operational char-acteristics of closely located PV modules, resulting instrong similarities among the waveforms at the inverteroutput. Yet, particular cases, like the operation of somePV modules under shaded conditions, may result in strongunbalance of the phase currents provided by the PV sys-tems with different string or module integrated invertersconnected to the grid (Batrinu et al., 2006; Woyte et al.,2003). All these aspects appear in the field tests, but notin the laboratory tests, in which the PV array is substitutedby a controlled power supply, with no dependence on theclimatic variables. The comparison between the resultsobtained in field and laboratory tests is then conceptuallymeaningful to highlight possible discrepancies.

3. Harmonic assessment from field tests

3.1. Harmonics and generated power

The contributions to harmonic distortion are increas-ingly important at low active power level (e.g., for gener-ated power below approximately 20% of the ratedpower). In these conditions, the MPPT and power factorcontrols of the PCU are deactivated. At higher activepower level, specific closed-loop current controls are intro-duced with the goal of minimising the harmonic content(Groß, 2005). However, at high levels of generated power,the harmonic distortion is relatively low. Therefore, inthese conditions the type of inverter control may have verylittle impact on the harmonic distortion.

Several field measurements carried out on PV invertershave shown a similar dependence of the harmonic currentemission on the generated power. Similar harmonic behav-iour appeared both for PV systems interfaced to the gridthrough a transformer and for PV systems without cou-pling transformer (Holz, 2005; Haberlin, 2007; Gubiaet al., 2007). Fig. 2 shows the THD of the current (THDI)and the generated power of a 5 kW inverter without cou-pling transformer, measured over 1 day in the summer sea-son. In the morning and evening hours, the THDI is up tofive times higher than during the rest of the day. The shapeof the THDI is characterised by a comparative high valueunder low power generation conditions, with a sharp decayfor increased generation; the THDI remains below 10%

DC/AC converter

transformer AC filtering

grid

grid-connected PV plant.

0

10

20

30

40

50

0.00 4.00 8.00 12.00 16.00 20.00 0.00time

THD

I (%

)

0

1000

2000

3000

4000

5000

pow

er (W

)

THD I

power

Fig. 2. THDI (upper curve) and generated power (lower curve) of the PV inverter (rated AC power 5 kW).

0

2

4

6

8

10

12

3 5 7 9 11 13 15 17 19 21harmonic order

I h/I 1

(%)

0-5% Pr5-10% Pr10-15% Pr15-20% Pr20-40% Pr40-60% Pr60-100% Pr>100% Pr

22.7%

Fig. 4. Relative values of the 95%-probability harmonic currents of thePV inverter (rated AC power 5 kW) for different loading conditionsmeasured during 4 days (3rd harmonic truncated).

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1029

when the inverter loading exceeds approximately 18% �20% of the rated power. The individual harmonic currentsshow a similar behaviour, especially for low-order harmon-ics (Dress et al., 2005).

From the methodological point of view, in order toinvestigate the harmonic behaviour of the PV inverter invariable conditions of power generation, the ratio P/Pr ofthe generated power P with respect to the AC rated powerPr has been partitioned into a number of classes, with P/Pr

6 5%; 5% � 10%; 10% � 15%; 15% � 20%; 20% � 40%;40% � 60%; 60% � 100%; > 100%. The statistical analysisof each harmonic obtained from a detailed evaluation ofthe measured data has been carried out. The 95%-probabil-ity values of the odd harmonic currents referred to the clas-ses of P/Pr ratio are shown in Fig. 3, the relative values ofthe harmonic currents for different loading conditions areoutlined in Fig. 4. By increasing the PV inverter loading,the relative harmonic currents are decaying, whereas theabsolute current values are increasing. This behaviour hasbeen more generally found for all types and ratings ofthe investigated inverters. The harmonic currents show astrong dependence on the inverter loading. From the valuesused to build Fig. 4, comparing a loading below 5% of therated loading of the inverter to the rated loading itself, thecurrent emission is more than 10 times higher for the odd

0.00

0.10

0.20

0.30

0.40

0.50

3 5 7 9 11 13 15 17 19 21harmonic order

curr

ent (

A)

0-5 % Pr5-10% Pr10-15 % Pr15-20 % Pr20-40 % Pr40-60 % Pr60-100 % Pr>100 % Pr

Fig. 3. 95%-probability harmonic currents of the PV inverter (rated ACpower 5 kW) for different loading conditions measured during 4 days.

harmonics up to the 9th order, and generally it is more that6 times higher for all odd order harmonics.

3.2. Harmonic currents and harmonic voltages

Detailed evaluation of the measurement results has beencarried out to highlight the relationships between theharmonic currents of the PV inverter and the harmonicvoltages prevailing in the LV system. Again, different clas-ses of generated power have been set up in function of theP/Pr ratio. Fig. 5 and Fig. 6 indicate the results of thisassessment for a PV inverter loading of about 47% of therated power, for two types of PV inverters, one with ratedpower 3 kW (with coupling transformer) and the other withrated power 5 kW (without coupling transformer). Therespective power ranges are 1.38 kW � 1.43 kW and 2.35kW � 2.45 kW. Within these ranges, a sufficiently highnumber of data (over 50) of measured harmonic voltagesand currents was available. The average increase of the har-monic currents for increasing harmonic voltage has beencalculated by means of the least-square-error (linear regres-sion) method. The results are outlined by the straight linesin Fig. 5 and Fig. 6. The harmonic currents increase for

0

40

80

120

160

200

0.0 0.5 1.0 1.5 2.0 2.5

harmonic voltage (%)

harm

onic

cur

rent

(mA

)

3rd

5th

7th

9th

11th

Fig. 5. Harmonic currents of a 3 kW PV inverter (with couplingtransformer) for different harmonic voltages. Generated power 1.38 kW� 1.43 kW.

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5

harmonic voltage (%)

harm

onic

cur

rent

(mA

) 3rd

5th

7th

9th

11th

Fig. 6. Harmonic currents of a 5 kW PV inverter (without couplingtransformer) for different harmonic voltages. Generated power 2.35 kW �2.45 kW.

Table 1Increase of harmonic current related to per cent harmonic voltage (valuesin mA/% of voltage).

Harmonic order Values of nh

inverter 3 kW inverter 5 kW

3 53.0 �27.45 18.7 35.07 74.2 79.39 66.6 62.311 42.0 42.7

1030 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

higher harmonic voltages, whereas the differences betweenthe two inverters are small, mainly due to the similar makeof the inverters. Yet, the dependence of the 3rd harmoniccurrent on the harmonic voltage is largely different forthe two PV inverters.

The slope nh of the linear regression characteristic, rep-resenting the increase of harmonic current related to theper cent harmonic voltage, has been evaluated as a furtherparameter. Table 1 shows the values of nh obtained fromthe data of Fig. 5 and Fig. 6. The results reported in Table1 indicate that the harmonic currents depend on the pre-vailing harmonic voltages in the system. Furthermore, theharmonic currents are increasing with increasing harmonicvoltages, with the exception of the 5 kW PV inverter, whichshows a decreasing 3rd harmonic current with increasingharmonic voltage. In addition, the slope nh is quite similarfor harmonics of the 7th and higher-orders for both PVinverters.

The difference of the dependence of the 3rd harmoniccurrent on the harmonic voltage for the two invertersmay be attributable to the presence of the coupling

transformer (not installed in the 5 kW PV inverter), to adifferent design of the EMC-filter on the AC side, or to adifferent current control strategy. More specific detailscould not be obtained from the manufacturer. The negativeslope of the 3rd harmonic could not be recognized from themeasurement results of other inverters. The only inverterindicating this negative slope was the 5 kW inverter fromthe unnamed manufacturer.

In order to gain further insights, it is therefore essentialto measure the harmonic currents of the PV inverter undertest conditions in laboratory, with a voltage source havingadjustable harmonic voltages in a suitable range coincidentto the harmonic voltages that can be found in real condi-tions of grid connection, as shown in the next section.

4. Harmonic assessment from laboratory tests

4.1. Standards for harmonic current emission and harmonic

voltages

Various international standards define voltage test con-ditions to carry out measurements of harmonics emitted byelectronic loads and generation equipped with power elec-tronics. These standards have to be applied to PV invertersas well. In the standards applied to low-voltage systems,PV inverters with low rating (Pr 6 3.68 kW; Ir 6 16A,IEC Std. 61000-3-2 (International ElectrotechnicalCommission, 2000) are allowed to be tested under morerestrictive conditions than inverters with high rated power(Pr 6 17.25 kW per phase connection; Ir 6 75 A, IEC Std.61000-3-12 (International Electrotechnical Commission,2003). Equipment passing successfully the test for har-monic current emission (besides other tests) are permittedto wear the CE-certificate (European Union, 1993). Themeasurement results under normal test conditions, docu-mented in the CE-certificate of the PV inverter, are thebasis to assess the suitability of connection of the PV instal-lations to the power system. In Table 2, the second andthird columns outline the maximum values of the harmonicvoltages for normal test conditions (permissible harmonicvoltages, as defined in the IEC Std. 61000-3-2 and in theIEC Std. 61000-3-12). Furthermore, the maximum accept-able harmonic voltage values in real power systems aredefined according to the Standard EN 50160 (CENELEC,1994) as the 95%-probability values of harmonic voltages.

Table 2Permissible harmonic voltages as per IEC 61000-3-2 and IEC 61000-3-12,maximum acceptable values as per EN 50160.

Harmonic order Voltage in% of the rated voltage

61000-3-2 61000-3-12 EN 50160

3 0.9 1.25 5.05 0.4 1.5 6.07 0.3 1.25 5.09 0.2 0.6 1.511 – 0.7 3.513 – 0.6 3.0even (2 � 10) 0.2 0.4 2.0 � 0.5other (11 � 39) 0.1 – 3.5 � 1.5other (12 � 40) – 0.3 –

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1031

The corresponding values are indicated in the last columnof Table 2 and are not connected to the CE-certificate.From Table 2 it is immediate to notice that the harmonicvoltages defined in the normal test conditions are remark-ably lower than the maximum harmonic voltages accept-able in the power system. Some aspects of thesedifferences are discussed in the sequel, on the basis ofexperimental results obtained from laboratory tests.

4.2. Test equipment and settings

Several laboratory tests have been carried out withcontrolled AC voltage harmonics. The layout of the labo-ratory setting is shown in Fig. 7. The equipment used forthe tests includes:

� a constant voltage DC source with maximum outputvoltage 300 V and maximum output current 10A,replacing the PV array;� a waveform-generator with programmable individual

harmonics up to the 40th order and minimum imped-ance of the voltage source Zs = (0.03 + j 0.03) X;� the AC loads, consisting of small electrical heating

appliances, with power between 200 W and 2 kW,switched on and off according to the required load;� the harmonic measurement system (Haag Euro-Quant

with assessment software DAMON EWS 130 (HAAG,0000).

DC

harmonicmeasurement

AC

AC source and load

L

N

+

-

=

∼∼

A V

constant voltage source

+-

PV inverter

Fig. 7. Layout of the laboratory test system.

Here we report the test results obtained on the 5 kW PVinverter used in Section 3.2. In order to compare the resultswith those obtained from the field test, for all tests thepower of the PV inverter has been set to the range 2.35� 2.45 kW by adjusting the constant voltage DC source.This example is explained in detail to show the methodol-ogy used for the analysis that can be easily replicated toother power ranges.

During the tests, the harmonic voltages of the AC sourcehave been modified individually to different values startingfrom zero up to the maximum values of the individual har-monic voltages taken according to the Standard EN 50160(CENELEC, 1994). In order to make the testing uniform,the test voltage at each harmonic has been adjusted startingfrom the sinusoidal case and using the same number of stepsfor increasing the voltage. In particular, the sinusoidal case islabelled as S0, and the 10 further steps used are labelled as S1,. . ., S10, respectively. It is important to notice that the stepsrefer to different voltage values for different harmonics, sincestep S10 is always the maximum value of harmonic voltagedefined in the Standard EN 50160. For instance, for the5th harmonic order the maximum harmonic voltage is 6%(Table 3), so that the test harmonic voltage is adjustedbetween 0% and 6% in 10 steps of 0.6% each. Likewise, forthe 11th harmonic order the maximum harmonic voltage is3.5% (Table 3), so that the test harmonic voltage has beenadjusted from 0% up to 3.5% in 10 steps of 0.35% each,and so forth. For the even order harmonics, in more detailthe voltage limits imposed by the EN 50160 are 2% for the2nd harmonic, 1% for the 4th harmonic and 0.5% for thehigher-order harmonics (CENELEC, 1994).

4.3. Results of the laboratory tests

The laboratory tests have been carried out for severalminutes for each individual harmonic and adjustment,leading to a set of 15 measured data per harmonic orderand harmonic voltage step. The calculation of each individ-ual harmonic has shown negligibly small variety betweenthe individual measurements for the same harmonic (thestandard deviation of the 15 measured data has notexceeded 0.3% of the average value). Thus, the average val-ues of each group of 15 measured data are considered inthe sequel. Fig. 8 contains an overall view of the results.Looking at more specific cases, the representations of theresults in Fig. 9 and Fig. 10 indicate the different behaviourof the PV inverter with respect to a number of individualharmonics. The step corresponding to the voltage limitsimposed by the IEC Std. 61000-3-12 (i.e., the referenceStandard for the 5 kW PV inverter) are represented inFig. 9 and Fig. 10 as vertical lines with the indication ofthe corresponding harmonic; moreover, the behaviour ofthe individual harmonics for test voltages exceeding theselimits is drawn with dashed lines. For instance, for the11th harmonic the step for the test voltage is 0.35% (asalready shown) and the limit of the IEC Std. 61000-3-12

Table 3Harmonic voltages during laboratory tests corresponding to the minimum harmonic currents (odd order).

Harmonic order uh [%] EN 50160 Minimum harmonic current location

step of test voltage uh [%] test voltage

3 5% >10 >5%5 6% 4 2.4%7 5% 2–3 1% � 1.5%9 1.5% 5 0.75%11 3.5% 1 0.35%13 3% 1 0.3%15 0.5% 4–5 0.2% � 0.25%17 2% 1 0.2%19 1.5% – –

0

100

200

300

400

curr

ent (

mA

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40S0S1S2S3S4S5S6S7S8S9S10

harmonic order

1317 25239

19

27

11

7

29

voltagestep

Fig. 8. Harmonic currents of a PV inverter for increasing harmonic voltage during laboratory tests.

0

100

200

300

400

Sine Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10

voltage step

harm

onic

cur

rent

(mA

)

3rd

13th

11th

17th

7th

19th

5th

9th

15th

voltage limits from IEC 61000-3-123rd

5th

7th

9th11th

13th15th

17th

19th

Fig. 9. Odd order harmonic currents of a PV inverter for increasing harmonic voltage during laboratory tests.

1032 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

(from Table 2) is 0.7%, thus corresponding to step 2; theline representing the 11th harmonic is drawn in dashedform after Step 2.

The odd order harmonics, outlined in Fig. 9 up to the19th order, show a minimum at different voltage steps.With reference to Fig. 9, the last two columns of Table 3

0

30

60

90

120

Sine Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10

voltage step

harm

onic

cur

rent

(mA

)

20th

18th

16th

14th

12th

10th

4th

8th

6th

2nd

voltage limits from IEC 61000-3-122nd 4th 12th÷20th 6th

8th

10th

Fig. 10. Even order harmonic currents of a PV inverter for increasing harmonic voltage during laboratory tests.

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1033

outline the step (column 3) and the per cent voltage (col-umn 4) at which the minimum harmonic currents occur.For instance, for the 5th harmonic (with steps of 0.6%each, as indicated in Section 4.2) the minimum harmoniccurrent occurs at Step 4, thus corresponding to a per centharmonic voltage of 2.4%. The 3rd harmonic decreasesbut never reaches the minimum harmonic current condi-tion when the harmonic voltages increase within the testrange, so that the indication is that the minimum has tobe located over the last step, namely, at harmonic voltagehigher than 5%. In particular, the 3rd harmonic is charac-terised by a constant decay with increasing harmonic volt-age. The slope associated to this decay is �34.9 mA/% ofvoltage, reproducing a similar behaviour with respect tothe slope �27.4 mA/% of voltage referred to the first orderinterpolation line of the field test case reported in Fig. 6.

For the even order harmonic currents (Fig. 10), the mini-mum always occurs at Step 1 of the harmonic voltage exceptfor the 2nd order harmonic, for which the minimum occursbetween step 2 and step 3. The minimum harmonic currentconditions occur at harmonic voltages u2 = 0.4% (step S2for the 2nd harmonic), u4 = 0.1% (Step S1 for the 4th har-monic), and 0.05% (Step S1) for higher-order harmonics.

The higher-order harmonics (over the 25th order) showa moderate increment for even and odd order harmonics.The increment of the even order harmonics is lower thanthe increment of the odd order ones.

4.4. Comparison between normal test conditions and real

operating conditions

As the harmonic currents also depend on the prevailingharmonic voltages in the AC system, the measurementsunder normal test conditions generally provide harmoniccurrents lower than those emitted by the inverter in realoperating conditions. Comparing the results of Table 3 to

the normal test conditions in Table 2, it can be argued thatthe control strategy of the PV inverter under investigationis almost optimised for the normal test conditions, in orderto fulfil the requirements of the emission standards. In fact,the minimum harmonic current is generally obtained forharmonic voltages near the permissible harmonic voltageunder normal test conditions (with the exception of the3rd harmonic). However, the harmonic voltages appliedto the PV inverters in real power system operation are verylikely to exceed the permissible harmonic voltages, beingconceptually acceptable up to reaching the limits imposedby the Standard EN 50160. Correspondingly, the actualcurrents could exceed even significantly the currentsobtained from the tests for CE-certificate compliance. Thissituation is evident by looking at the dashed lines in Fig. 9and Fig. 10, representing the harmonic behaviour in theconditions exceeding the voltage limits imposed by theIEC Std. 61000-3-12 but still acceptable for the EN50160. Furthermore, in order to give numerical evidenceto this issue, Table 4 shows the relationship between theminimum harmonic current I 0h, obtained by applying themaximum permissible harmonic test voltage according tothe IEC Std. 61000-3-12, and the harmonic current I 00hoccurring under the maximum expected harmonic voltageconditions on the basis of the Standard EN 50160. The lastcolumn of Table 4 contains the ratio ch ¼ I 00h=I 0h. The resultsclearly show that the harmonic currents under the worstacceptable conditions according to the Standard EN50160 can largely exceed the harmonic currents of the PVinverter obtained in normal test conditions (even over 10times for the 11th and the 13th harmonic orders).

5. Experimental results on a medium-size PV plant

An experimental testing concerning harmonics andinterharmonics has been carried out on a medium-size

Table 4Comparison of harmonic currents under normal test conditions (IEC 61000-3-12) and in case of maximum harmonic voltages (EN 50160).

Harmonic order Minimum current I 00h (mA) (uh values as per IEC 61000-3-12) Harmonic current I 00h (mA) (uh values as per EN 50160) ch ¼I 00hI 0h

3 203.0 74.3 0.375 65.8 193.8 2.97 30.4 285.9 9.49 15.1 69.2 4.611 29.6 349.9 11.813 31.5 365.8 11.6

0

10

20

30

40

50

60

70

0 10 20 30 40 50measurement

dist

ortio

n in

dica

tor (

%)

THDG_A1 (%)THDS_A1 (%)THD_A1 (%)

Fig. 11. Distortion indicators recorded for the inverter A1 connected atphase a.

Fig. 12. Current waveforms recorded in the measurement #6 for the threeinverters connected at phase a.

1034 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

PV plant, whose characteristics are indicated in Table 5(Plant F). The plant contains 8 single-phase invertersconnected to the three phases with a group of 3 invertersat phase a, another group of 3 inverters at phase b, and 2inverters at phase c. The results shown here refer to thethree inverters connected to phase a (denoted as A1, A2and A3).

The measurements have been carried out in the after-noon of a cloudy day, starting around 3 pm, with 50measurements of 10 cycles (200 ms) each at almost regularcadence within a total time interval of about 15 min. Thesolar irradiance was slowly decreasing during the measure-ments. Slight improvement in the solar irradiance occurredonly in a very short time period, corresponding to the mea-surements #32 and #33. Fig. 11 shows the evolution of theharmonic distortion indicators for the current of inverterA1. The increased solar irradiance at measurements #32and #33 resulted in lower distortion indicators. TheTHD, THDG and THDS indicators assume similar valuesin many cases, but increase largely during some measure-ments. This effect is related to the action of the networkimpedance measurement circuit (Schulz and Hanitsch,2001), based on the temporary switching of a RC circuitat time cadence of about 5 s for islanding detection (Chiccoet al., 2005).

From the experimental results, it emerges that there is anon-synchronous switching of the RC circuit, that maycause the presence of none, one or more current spikes atphase a within the 10 measured cycles. Fig. 12 shows anexample with two current spikes appearing for the invertersA1 and A2. By repeating the measurements over a day indifferent operating conditions, the effect of the many cur-rent spikes on the THD of the currents in the three phases

Table 5Data of the PV Plant F.

PV plant Data

Total installed PV power PPV,plant [kW] 16.3Rated voltage at the LV side [kV] 0.4Number of PV arrays 8Single module rated power PPV,mod [W] 102Number of inverters 8Single inverter rated AC power Pr,INV,AC [kW] 1.5Rated voltage of the single-inverter [V] 230Number of strings for each inverter 2Number of modules for each string 10Installed power PINV,DC,ins [kW] 13

is immediately visible, as in Fig. 13. More generally, thetransients introduced by the switching of the RC circuitproduce relevant interharmonics in the measured wave-forms. Fig. 14 provides a detailed view of the interharmon-ic subgroups. Considering (6), the label S1 represents theinterharmonic S1þ0:5, the label S2 corresponds to the inter-harmonic S2þ0:5, and so forth. The effects of the transientdisturbances due to the switchings during the measure-ments from #1 to #15 are clearly visible.

The deterioration of the current THD due to action ofthe network impedance measurement circuit is confirmedby considering a series of measurements gathered duringa bright day on the three phases of Plant F (Fig. 13). A

0

5

10

15

20

25

0 5 10 15 20

current [A]

THD

%

phase a

current

voltage

0

5

10

15

20

25

0 5 10 15 20

current [A]TH

D%

phase b

current

voltage

0

5

10

15

20

25

0 5 10 15 20

current [A]

THD

%

phase c

current

voltage

Fig. 13. Current measurements on the three phases of Plant F containing PV inverters with network impedance measurement.

1 7 13

S1S10

S19

S28

S370

0.1

0.2

0.3

0.4

0.5

inte

rhar

mon

ic s

ubgr

oup

cont

ribut

ion

(A)

measurement

interharmonic subgroup

Fig. 14. Contribution of the inverter A1 to the various interharmonicsubgroups.

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1035

significantly high number of points are affected by the cur-rent THD worsening.

6. Grid-connected operation of multiple inverters in large-

size photovoltaic plants

6.1. Definition of harmonic and interharmonic indicators

Let us consider a PV plant containing N inverters ofequal type and size, connected to the same point at theAC side. In common situations the PV inverters could bemany, or could be located in such a way to give no possi-bility of obtaining simultaneous measurements of the totalcurrent together with the currents from all the individualPV inverters. In such cases, it is possible to follow theapproach described here, based on measuring the totalRMS current provided by the N inverters and the RMS

current of a single inverter. Let us first consider the casewith inverters of equal type and size. This procedureassumes that the single inverter subject to measurement isrepresentative of any of the N inverters (Chicco et al.,2007). From measurements and subsequent Fourier trans-form, the total RMS current I ðNÞh provided by the N invert-ers and the RMS current I ð1Þh of a single inverter areobtained at each harmonic order h = 1,. . ., H.

In order to represent the effect of the presence of N

inverters connected to the point of common coupling, letus define the harmonic summation ratio at the harmonicorder h

fðNÞh ¼ I ðNÞh

N I ð1Þh

ð7Þ

Conceptually, the inequalities 0 6 fðNÞh 6 1 should hold. Inpractice, the upper limit is not strictly limited to unity, sincethe actual value of fðNÞh depends on the choice of the indi-vidual inverter subject to the measurement. However, thevalues obtained are indicative of the harmonic summationcharacteristics at the given harmonic order. Values of fðNÞh

close to unity mean that the corresponding harmonic cur-rents of order h tend to sum up arithmetically, namely,all the current phasors �Ih for the various inverters areapproximately in phase. Conversely, values fðNÞh close tozero are representative of the maximum dispersion (espe-cially concerning the phase angles) of the current phasors.The extreme case fðNÞh = 0 would be obtained by summingup a number of phasors with equal amplitudes and regularphase angle shifts.

Similarly, it is possible to define the interharmonic

summation ratio, corresponding to the interharmonic orderq = h + 0.5, for h = 0, 1,. . ., H:

fðNÞq ¼I ðNÞq

N I ð1Þq

ð8Þ

1036 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

6.2. Experimental assessment of the harmonic and

interharmonic summation ratios

The investigation on the harmonic distortion due to theoperation of multiple PV inverters connected to the gridhas been carried out with reference to two PV plants, iden-tified as Plant D and Plant E, whose characteristics aresummarized in Table 6. Both plants are connected throughMV/LV transformers to the respective MV distributionsystem. Plant D is connected to the MV system, with noconsumer at the LV side. Plant E is connected to the LVsystem. In both plants, the current waveforms have beensimultaneously gathered for a single PV inverter and forthe whole group of PV inverters. The measurement of thegroup of inverters has been possible due to their close con-nection points at the AC side.

Measurements of current harmonics and interharmonicsaccording to the IEC Std. 61000-4-7 have been carried outfor frequencies up to 2 kHz. The results for Plant D andPlant E are shown in Figs. 15, Figs. 16 and Fig. 17 respec-tively. The harmonic summation ratio for the harmonic

Table 6Data of the PV Plants D and E.

PV plant D E

Total installed PV power PPV,plant [MW] 1.06 2Rated voltage at the MV side [kV] 15 20Rated voltage at the LV side [kV] 0.4 0.4Number of PV modules 3200 7046Single module rated power PPV,mod [W] 330 283Number of inverters 4 7Single inverter rated AC power Pr,INV,AC [kW] 250 250Rated voltage of the single inverter [V] 405 405Number of strings for each inverter 50 84Number of modules for each string 16 12Installed power PINV,DC,ins [kW] 264 283Max. recorded generated power PAC,max [MW] 0.93 1.75Short-circuit power (MV side) S”

k,MV [MVA] 76.73 112Short-circuit power (LV side) S”

k,LV [MVA] – 21.63Voltage level of the point of common coupling MV LV

0

6

12

18

24

30

2 4 6 8 10 12 14 16 18 20 22

harmonic o

curr

ent [

A]

(4 inverte

(1 inverte

harmonic

Fig. 15. Harmonic currents of the single inverter and of the aggregation ofinverters).

currents up to the order h � 9 of the inverters operatedin parallel is close to unity. The corresponding harmonicsare approximately added arithmetically, that is,

I ðNÞh �XN

i¼1

I ðiÞh ð9Þ

The harmonic summation ratio for the harmonics withorder h > 17 is close to 1=

ffiffiffiffiNp

(that is, to 0.5 for Plant D

and to 0.378 for Plant E). Then, the corresponding currentsare approximately added in an Euclidean way:

I ðNÞh �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

i¼1

ðI ðiÞh Þ2

vuut ð10Þ

The same type of analysis has been conducted for whatconcerns the interharmonics. The experimental results arepresented here for Plant D with 4 inverters. Fig. 17 showsthat, in spite of the different amplitude of the various inter-harmonics, the interharmonic summation ratio is relativelyclose in all cases and is slightly higher than 0.5, namely,with overall average value (computed from all the interhar-monic orders) of 0.569 (i.e., 1.137 times higher than 0.5)and standard deviation of 2.8%. Hence, the Euclideanmodel for the interharmonic summation could be appliedat first approximation to every interharmonic up to 2 kHz.

7. Concluding remarks

This paper has presented the results of an experimentalassessment of the waveform distortion in grid-connectedPV plants. A novel view on some specific aspects coveringa set of issues currently under discussion in the researchcommunity has been illustrated. A dedicated method ofanalysis has been developed to carry out laboratory testsby imposing voltages with programmable harmonic con-tents. The specific tests performed on a 5 kW PV inverterhave shown that in real operating conditions (applyingthe maximum permissible harmonic test voltages indicatedby the Standard EN 50160) the harmonic currents from PV

24 26 28 30 32 34 36 38 40

rder

0

0.2

0.4

0.6

0.8

1

harm

onic

sum

mat

ion

ratio

rs) current [A]

r) current [A]

summation ratio (4 inverters)

the 4 inverters, and resulting harmonic summation ratio for Plant D (4

0

10

20

30

40

50

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40harmonic order

curr

ent [

A]

0

0.2

0.4

0.6

0.8

1

harm

onic

sum

mat

ion

ratio

(7 inverters) current [A]

(1 inverter) current [A]

harmonic summation ratio (7 inverters)

Fig. 16. Harmonic summation ratio for Plant E (7 inverters).

0

1

2

3

4

5

0.5 3.5 6.5 9.5 12.5

15.5

18.5

21.5

24.5

27.5

30.5

33.5

36.5

39.5

42.5

45.5

48.5

interharmonic

curr

ent [

A]

0

0.2

0.4

0.6

0.8

1

inte

rhar

mon

ic s

umm

atio

n ra

tio

(4 inverters) current [A]

(1 inverter) current [A]

interharmonic summation ratio (4 inverters)

Fig. 17. Interharmonic currents and interharmonic summation ratio for Plant D (4 inverters).

G. Chicco et al. / Solar Energy 83 (2009) 1026–1039 1037

inverters, especially for higher harmonic orders, couldexceed up to 10 times the currents measured in the normaltest conditions defined to release the CE-certificate.Furthermore, a significant worsening of the current wave-form distortion, observed from field measurements, hasbeen related to the action of the network impedance mea-surement circuit. This aspect has to be taken into properaccount while carrying out harmonic analysis of the realdata gathered from the field.

Nowadays, the specifications provided by the manufac-turers concerning current harmonic distortion are referredto rated power conditions. In PV system operation close tothe rated power, harmonic distortion is generally low, anda few harmonics of order lower than the maximumharmonic order considered in the power quality standards(i.e., 40) appear, due to the characteristics of the PV inver-ter control. In these conditions, the presence of PV systemscould even provide benefits to the reduction of the har-monic distortion at the PCC. Hence, a rated condition-based analysis would conclude that PV systems cause noproblem concerning harmonic distortion.

However, the PV system operation is in most cases farfrom the rated conditions, and at lower level of power

production the harmonic current emission is much higherthan that at rated power. This conclusion is supported bythe specific analysis carried out in this paper by using the95%-probability harmonic currents. This analysis hasshown that below 20% of the rated power the harmonicto fundamental current ratio can be over 3 times higherthan in rated conditions at most harmonic orders. On theother hand, the harmonic currents in rated conditions areless than double with respect to the values occurring below20% of the rated power. As a result, at low power levels theoverall harmonic distortion effect could even be larger thanthe corresponding effects of PV systems operated at rela-tively high power generation and thus introducing rela-tively low harmonic distortion. Low power conditionstypically occur during autumn, winter and spring, but alsoin the early morning and late evening hours duringsummer.

If the size of the PV system is relatively low with respectto the short-circuit power of the grid, there is no significantinfluence on the grid voltage quality. With the increase ofthe PV system diffusion, the installed power could becomeclose or even exceed the load seen from the PCC (which isonly some hundreds of kW in LV power systems). In such

1038 G. Chicco et al. / Solar Energy 83 (2009) 1026–1039

cases, significant harmonic distortion effects could comefrom PV systems operating at relatively low power; thecompatibility level for harmonic voltages might beexceeded, and also the voltage quality limits defined inthe Standard EN 50160 could not be respected.

The results obtained from the system point of view canbe of major interest for the regulators, with the purpose ofdefining more stringent requirements in the standards alsoat lower power levels. Such requirements could be usefulfor the manufacturers as well. In fact, in the presence of sig-nificant variability in the operating conditions, currentlythe manufacturers have no ultimate indications on howto set up the control strategies of the PV inverters. Withoutmore specific hints, a general solution can be found by opti-mising the control strategies for the normal test conditions.The practice of setting up a unique control strategy isclearly reasonable when the volume of products sold tothe market is relatively low. However, at present the mar-ket of grid interface equipment for PV systems is evolvingfast, and the number of products is considerably increas-ing. In this context, there is a growing need for adoptingmore suitable solutions in terms of both complying withthe standards and guaranteeing efficient performance inthe specific operational environment. In response to thisneed, the manufacturers could diversify the productionby developing dedicated equipment for different applica-tions (e.g., with control strategies variable with respect tothe type of waveform distortion occurring in the specificcase). Major benefits of this product diversification couldarise for connection points with relatively low distortion,with the possibility of simplifying the equipment, reducingtheir cost, and even increasing the total power that can beconnected to the grid before reaching the waveform distor-tion limits. Likewise, it would be possible to develop spe-cific compensation circuits only for grid connections withhigh waveform distortion.

As a further result, this paper has shown that, in the pres-ence of multiple PV systems connected to the PCC, low-order harmonic currents tend to sum up arithmetically,whereas currents at higher-order harmonics and interhar-monics tend to sum up in an almost Euclidean way. Thisresult, especially of the lower harmonic orders, reflects thecorrelated behaviour of the PV inverters, depending on thesimilar impact of the meteorological variables on the PVinverters located in relatively close positions. In fact, the sim-ilar variation of quantities such as solar irradiance or temper-ature generates a coupling effect on the current waveforms atthe outputs of the PV inverters. The aggregated harmonicbehaviour is then different with respect to the one observablein applications with harmonic loads such as personal com-puters or fluorescent lamps. Further activities are in progressto define harmonic summation models adapt to represent thespecific case of multiple PV inverters.

On the basis of the results shown in this paper, the test-ing procedures of the PV inverters could be extended inorder to test such inverters under more detailed and restric-tive conditions reflecting the PV system operation with

respect to the prevailing harmonic voltages. The depen-dence of the harmonic current emission on the partial-loadconditions of the PV inverter, as well as the summationeffects of PV inverters operated in parallel, should be takeninto account in the formulation of the specific test condi-tions to be introduced into the standards. The harmoniccurrent emission of PV inverters shall be tested at full loadand partial-load, increasing the maximum permissible har-monic voltages under test conditions to reflect the har-monic voltages expected in the power system. The voltagevalues defined in voltage quality standards such as theStandard EN 50160 are suggested to be adopted for thispurpose.

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