research article reliability assessment of transformerless

Research ArticleReliability Assessment of Transformerless PV Invertersconsidering Mission Profiles

Yongheng Yang Huai Wang and Frede Blaabjerg

Department of Energy Technology Aalborg University Pontoppidanstraede 101 9220 Aalborg Denmark

Correspondence should be addressed to Yongheng Yang yoyetaaudk

Received 27 October 2014 Revised 26 January 2015 Accepted 9 February 2015

Academic Editor Mahmoud M El-Nahass

Copyright copy 2015 Yongheng Yang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Due to the small volume and high efficiency transformerless inverters have gained much popularity in grid-connected PVapplications where minimizing leakage current injection is mandatory This can be achieved by either modifying the modulationschemes or adding extra power switching devices resulting in an uneven distribution of the power losses on the switching devicesConsequently the device thermal loading is redistributed and thus may alter the entire inverter reliability performance especiallyunder a long-term operation In this consideration this paper assesses the device reliability of three transformerless inverters undera yearly mission profile (ie solar irradiance and ambient temperature)Themission profile is translated to device thermal loadingwhich is used for lifetime prediction Comparison results reveal the lifetime mismatches among the power switching devicesoperating under the same condition which offers new thoughts for a robust design and a reliable operation of grid-connectedtransformerless PV inverters with high efficiency

1 Introduction

Power electronics converter technology has enabled moreand more renewable energy installations in recent yearswhich is also associatedwith an increasing demand for higherefficiency and higher reliability [1ndash7] In order to reduce thecost of energy the demand will be further strengthened inthe future energy mix dominated by wind turbine systemsand photovoltaic (PV) systems [8ndash11] Transformerless PVinverters have gained much reputation in the Europeanmarket in terms of high efficiency small size and low weightcompared to their counterparts [7 12ndash16] Its popularityand its magnificence in conversion efficiency induce a shiftin inverter technology in the United States recently [17]Therefore an evenwide-scale adoption of transformerless PVinverters in the future grid-friendly systems is predictable

Till now a vast of transformerless PV inverters have beendeveloped [13ndash20] and many of those topologies have beensuccessfully commercialized in residential PV applicationswhere size and efficiency are the main concerns Howeverldquotransformerlessrdquo are also required to minimize the leakagecurrent injections for safety due to the removal of the galvanicisolation This is typically achieved by either developing

a special suitable modulation scheme or adding extra powerswitching devices [18] For instance in [19 20] optimizationapproaches have been proposed to improve the performanceof transformerless PV inverters while in [12ndash14] additionalpower switching devices have been introduced to the tra-ditional full-bridge PV inverter However such software orhardwaremodifications will alter the power loss distributionson the power switching devices thus contributing to uneventhermal loading in the PV inverters

Due to the intermittency of solar energy transformerlessPV inverters have to handle a fluctuating power Thus thethermal loading on each power switching device will bedifferent under a long-term mission profile (eg a yearlysolar irradiance and ambient temperature profile) [21ndash24]The varying thermal loading (appears as fluctuating junctiontemperature) of the power switching devices is one of themain failure contributors for the power electronics devices[22ndash29] As a consequence the thermal stress differenceamong the power switching devices will possibly make theentire transformerless PV inverter fail to operate [25ndash32]Although more advanced transformerless inverters with amain focus on efficiency are coming on market there isstill a lack of a reliability-oriented investigation considering

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015 Article ID 968269 10 pageshttpdxdoiorg1011552015968269

2 International Journal of PhotoenergySo

lar i

rrad

ianc

eA

mbi

ent t

empe

ratu

re

PV stringsmodules Full-bridge

∘C

iPV

CPV

O

iCMVCMVCP

Cf

LCL-filter

Grid

Ground

S1

S2

S3

S4

D1

D2

D3

D4

L1 L2

A

B

Figure 1 A single-phase single-stage grid-connected full-bridge PVinverter systemwith an LCL-filter where VCMV is the commonmodevoltage and 119862

119875is the stray capacitor

mission profiles for those PV inverters However such aninvestigation allows new thoughts for a robust design anda reliable operation of PV system As a result a reductionof the cost can be attained since both the efficiency and thereliability of transformerless PV inverters are enhanced

Taking the above into consideration this paper exploresthe thermal performance of three selected transformerless PVinverters under a yearly mission profile which thus allows aqualitative reliability assessment of the PV inverters beyondefficiency achievements Firstly a description of the selectedtransformerless PV topologies is presented in Section 2Focus has been put on the mission profile translation to thecorresponding device thermal loading of the transformerlessinverters in Section 3 where a mission profile based relia-bility evaluation approach is also introduced In accordancewith the translated thermal loading profiles Section 4 thusconducts an assessment of the device reliability in those PVinverters before the conclusions

2 Selected Transformerless PV Inverters

Depending on the power ratings transferring PV energy toan AC power grid has several possibilities [1 7 33] It can bemodular PV converters which typically harvest the energyusing DC-DC converters (maximum power point tracking)[34ndash36] while the string or central inverters can be directlyconnected to the grid Since the grid-connected PV systemsare still dominantly designed for residential applications[33] the single-phase transformerless PV inverter system isanalyzed

Figure 1 shows the most commonly used single-phasefull-bridge (FB) PV inverter topology where the modulationschemes have to be modified for a smaller leakage current(119894CMV) As it is shown in Figure 1 an LCL-filter is used fora better power quality In some cases a DC-DC converter isadopted to boost up the PV output voltage to an acceptablelevel for the PV inverters Conventionalmodulationmethodsfor the single-stage FB inverter topology include the bipolarmodulation the unipolar modulation and the hybrid mod-ulation When considering the leakage current injection intransformerless applications the bipolar modulation schemeis preferable [12 21] which is chosen in this paper Notablyoptimizing the modulation patterns is an alternative toeliminate the leakage currents [19]

Asmentioned early transformerless structures aremostlyderived from the FB topology by providing an AC path ora DC path using additional power switching devices As aresult during the zero-voltage states isolation between thePV modules and the grid is achieved thus leading to a lowleakage current injection Figure 2 shows two examples oftransformerless PV inverters derived from the single-phaseFB topology As it can be seen in Figure 2(a) the H6 invertertopology [13] has a DC path which isolates the PV panelsfrom the grid at zero-voltage states In contrast although thehighly efficient and reliable inverter concept (HERIC) [14]inverter has the same number of power switching devices asthat of the H6 inverter it provides an AC path to eliminatethe leakage current injection

It should be pointed out that there are also many othertransformerless topologies reported in the literature in addi-tion to the above two solutions [12 16 37] For examplethe Conergy neutral point clamped (NPC) transformerlessPV inverter is based on the multilevel power convertertechnology [12 20] However only the FB inverter with abipolar modulation scheme (FB-Bipolar) the H6 inverterand the HERIC inverter are assessed in terms of reliability

3 Mission Profile Translation toThermal Loading

31 Mission Profile for PV Systems A mission profile isnormally referred to a simplified representation of relevantconditions under which the system is operating [27 32] As aresult for the grid-connected PV systems the mission profile(ie solar irradiance and ambient temperature) is actually areflection of the intermittent nature of the solar PV energy[38 39] and consequently it has an inherent relationshipwith the entire system performance including the thermalloading performance The mission profile can be a series ofmultitime scales for example a minute mission profile ora yearly mission profile and it is usually taken as the inputfor the reliability analysis in the field of power electronicsconverters [29 39ndash42] which is also focused on in this paperFigure 3 shows the mission profile applied to the above threetransformerless PV inverters

With more accumulative real-field experience and moreadvanced real-time monitoring technology better missionprofiles are available for a reasonable lifetime predictionHence a mission profile based analysis approach should beable to analyze the performance at different time scales asit is shown in Figure 4 It can be observed in Figure 4(a)that for short-term mission profiles at the level of millisec-onds to several seconds the thermal loading profile canbe directly and instantaneously obtained In contrast forlong-term mission profiles within a range of a few minutesto several months obtaining the instantaneous thermalloading will be very time-consuming or even impossiblewhen the mission profile has a high data-sampling rateAlternatively the thermal loading profile can be obtainedbased on lookup tables [43] which are created in accordancewith the short-term constantmission profiles as it is shown inFigure 4(b)

International Journal of Photoenergy 3

PV stringsmodules Full-bridgeiPV

CPV1

CPV2

CP

LCL-filter

DC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

D8

D7L1 L2

A

B

(a)


iPV

CPV

CP

LCL-filter

AC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

L1 L2A

B

(b)

Figure 2 Examples of single-phase transformerless PV inverters derived from the single-phase full-bridge topology by adding extra powerswitching devices (a) H6 inverter [13] and (b) HERIC inverter [14]

Sola

r irr

adia

nce (

kWm

2)

15

10

05

0Oct Nov Dec Jan Feb Mar Apr Jun Jul Aug SepMay

(a)

Am

bien

t tem

p (∘

C)

40

20

0

minus20Oct Nov Dec Jan Feb Mar Apr Jun Jul Aug SepMay

(b)

Figure 3 A yearly mission profile used for the selected transformerless PV inverters (1 secsample) (a) solar irradiance and (b) ambienttemperature

∘C

MPPTMiss

ion

profi

le GridElectricalsystem

PVmodels

PinPout

PlossTransformerlessPV inverters

(electrical andloss models)

TjTj

Thermalmodel

Thermalloading profile

(a)

∘C

Lookup tablebased

simulation (thermal) model

Miss

ion

profi

le

Tj Thermalloading profile

(b)

Figure 4 Approach of the mission profile translation to thermal loading at different time scales (MPPT maximum power point tracking 119879119895

junction temperature of the power devices) (a) short-term mission profiles and (b) long-term mission profiles

32 Thermal Modelling of Power Switching Devices As it isshown in Figure 4 the translation from a mission profileto the corresponding thermal loading profile requires athermalmodel which links the electrical performance (powerlosses 119875loss) and the thermal behavior (junction temperature119879119895) The coupled relationship is demonstrated in Figure 5

in a FB PV inverter system which shows that the powerlosses on the switching devices will introduce a temperaturerise due to the thermal impedance in the power switchingdevices The thermal impedance can be modeled as a Fostermodel [43ndash47] as it is shown in Figure 6 Details of thethermal modelling of power semiconductors can be found in[46 47]

Typically for such a model of the thermal impedance theparameter data is provided in the datasheet Table 1 showsthe thermal parameters of the power switching device froma leading manufacturer used in the paper Notably all thedevices are the same in the three transformerless PV invertersfor comparison in terms of thermal loading and thus thebenchmarking results indicating the critical components of

Table 1Thermal impedance parameters of power switching devicesfrom a leading manufacturer according to Figure 6

Impedance 119885th(119895-119888)

119894 1 2 3 4IGBT119877th119894 (KW) 0074 0173 0526 0527120591119894(s) 00005 0005 005 02

Diode119877th119894 (KW) 0123 0264 0594 0468120591119894(s) 00005 0005 005 02

transformerless PV inverters could be a guidance to selectappropriate power switching devices in such applications

33 Translated Thermal Loading to Lifetime Based on thethermal model simulations have been carried out in PLECS[43] according to Figure 4 where the system parameters are

4 International Journal of Photoenergy

Power losses Device temp

Electrical domain

Thermal domain

Junction Case Heat-sink Ambient

Pin Poutinvdc

(Ploss = Pin minus Pout)Tj Tc Th Ta

Zth(j-c)Zth(c-h) Zth(h-a)

Figure 5 Coupled relationship between power losses and the junction temperature of the power switching devices 119885th(119895-119888) junction to caseimpedance 119885th(119888-ℎ) case to heat-sink impedance and 119885th(ℎ-119886) heat-sink to ambient impedance

Tc

Tj

Ptot

Ta

Rth1 Rth2 Rth3 Rth4

C1 C2 C3 C4

Ci = 120591iRthiZth(j-c)

Figure 6 Foster model of the junction to case thermal impedance 119885th(119895-119888) shown in Figure 5

Table 2 System parameters for single-phase transformerless grid-connected PV systems

Parameter Symbol Value UnitGrid voltage V

119892RMS 230 VGrid frequency 119891

119892 50 Hz

LCL-filter1198711

36 mH119862119891 235 120583F

1198712

4 mHDamping resistor 119877

11988910 Ω

Switching frequency 119891119904

10 kHzParameters of PV strings (3 strings 15 panels for each string)

at 25∘C and 1 kWm2

Power at MPP 119875MPP 299 kWVoltage at MPP 119881MPP 405 VCurrent at MPP 119868MPP 738 A

shown in Table 2 In order to create the lookup tables forlong-termmission profiles several constant operating condi-tions (eg solar irradiance 08 kWm2 ambient temperature25∘C) have been simulated firstly where a perturb-and-observe maximum power point (MPP) tracking algorithmhas been used [33ndash35 38] Figure 7 exemplifies the simulationmodel for a full-bridge inverter system A proportional reso-nant current controller has been adopted to control the gridcurrent considering power quality requirements [2] Using

the lookup table model the yearly mission profile (Figure 3)has been resampled (5minssample) and translated intothe thermal loading of the corresponding power switchingdevices as it is presented in Figure 8

Although the transformerless PV inverters (both the H6and the HERIC) can maintain a higher efficiency as reportedin the literature in contrast to the FB-Bipolar inverter thethermal loading on those switching devices is unequal as itcan be seen in Figure 8 Specifically the maximum junctiontemperature of the extra devices in an H6 inverter is thehighest indicating high power losses since they are switchedat a high frequency However this is not the case for theHERIC inverter where only one of the extra switchingdevices is switched at the grid frequency during a half cycleTherefore the power losses are lower and thus the thermalloading as it is shown in Figure 8 From the above qualitativeanalysis it is implied that much attention has to be paid onthe extra switching devices in transformerless PV invertersParticularly for theH6 inverter power switching deviceswithlower conduction losses and higher rated maximum junctiontemperature are desirable while the total cost has to be takeninto consideration as well

When the thermal loading profile appearing in the powerswitching devices is available a quantitative prediction ofthe device lifetime under the mission profile is enabled by arain-flow counting algorithm [41 42]The rain-flow countingalgorithm is a quantitative representation of the thermalloading which extracts the temperature information in detailin terms of the mean junction temperature 119879

119895119898 temperature


STa

PV++

+++

+

minus

minus

A

CC

A

V VCPVC 11e minus 3

PV

iPV

PWM

1

2 345

Full-bridgeinverter

a

a

b

b

R1 R2L1 L2

Cf GridRd

s

ig

gControl system

Probe

Probe

Probe

Probe

Probe

Probe

Probe

Probe

ProbeVac

Iac

PV V I P

PV P V

AC grid

PV string

P versus V

s

+

minus

f(u)

f(u)

f(u)

f(u)

D1

D2 D4

D3

Heat sink

IGBT1

IGBT2

IGBT3

IGBT4

Scope

Thermal chain T tint

Figure 7 Simulation model of a single-phase full-bridge PV inverter system in PLECS

FB-bipolar

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

1011 0312 0912Time of a year (monthyear)



H6

Extra devices S56

Extra devices S56

HERIC

(a)

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

Extra devices S56

Extra devices S56

Time of a day (hoursmin)0000 1200 2400



(b)

Figure 8 Translated thermal loading (maximum junction temperature 119879119895max) of the power switching devices of the three different

transformerless grid-connected PV inverters under a yearly mission profile shown in Figure 3 (a) the yearly long-term thermal loadingand (b) details of the maximum junction temperature of the power switching devices in a cloudy day of the year


Table 3 Parameters of the lifetime model for power devices [48]

Parameter Value Unit Experimental condition119860 34368 times 1014 mdash120572 minus4923 mdash 64K le Δ119879

119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731

minus9012 times 10minus3 mdash119862 1434 mdash 007 s le 119905

119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861

86173324 times 10minus5 eVK

cycle amplitude 119879119895 cycle period 119905

119900119899 number of cycles n and

so forthThen the extracted temperature information can beused for the lifetime prediction according to a specific lifetimemodel For example a lifetime model of power switchingdevices is introduced in [48] and it can be expressed as

119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)

where119873119891is the number of cycles to fail119891

119889is the diode effect

119886119903 is the bond-wire aspect ratio 119896119861is the Boltzmann constant

119864119886is the activation energy and 119860 120572 120573

0 1205731 120574 and 119862 are

the lifetime model parameters as it is shown in Table 3 Thelifetime model also implies that the junction temperature hasa significant impact on the number of cycles to fail that is thereliability of the power switching devices

According to Minerrsquos rule [24 42 48] the life consump-tion LC the damage due to the thermal stress is the linearlyaccumulative damage from different thermal cycles The LCcan then be expressed as

119871119862 = sum

119894

119899119894

119873119891119894

(2)

in which 119899119894is the number of cycles at the stressΔ119879

119895119894extracted

by the rain-flow counting algorithm and 119873119891119894is the number

of cycles to fail based on (1) Subsequently the lifetime of thepower switching devices can be given as

119871119875=119905119872119875

119871119862(3)

with 119871119875being the predicted lifetime and 119905

119872119875being the

mission profile period (eg a year)Using the above reliability analysis procedure the lifetime

of the power switching devices in the transformerless PVinverters can then be estimated as long as a mission profileand a lifetimemodel of high confidence are available Figure 9summarizes the mission profile based analysis approachwhich can also be used in other power electronics convertersfor example wind turbine converters where the missionprofiles are available

Mission profile

Mission profiletranslation

Thermal loadinginterpretation

Lifetimeprediction

∘C

System models

Loading profilecounting

Lifetimemodels

Counting algorithms

Extracted thermal info

∙ Level crossing∙ Rain-flow∙ Simple range counting∙ middot middot middot

∙ middot middot middot

∙ Tjm-mean junction temp∙ ΔTj-temp cycle amplitude∙ ton -cycle period

Figure 9 Flowchart of the mission profile based reliability analysisapproach for transformerless PV inverters

4 Reliability Assessment

According to Figure 9 the lifetime of the power switchingdevices in the three transformerless PV inverters under theyearly mission profile shown in Figure 3 can be obtained andevaluated In order to benchmark the reliability quantita-tively the thermal loading profiles have to be interpreted firstaccording to (1) and Figure 9 A rain-flow counting algorithmhas been adopted and the results are presented in Figure 10It can be observed in Figure 10 that the additional devicesof the H6 inverter (ie S

5and S

6) have a larger number

of cycles compared to the other power switching devices ofthis topology (S

1sim4) This indicates that the extra devices to

realize an elimination of the leakage currents become themost critical components of the H6 inverter according to(2) and (3) As a consequence more reliable power devicesare preferable as the extra devices when designing an H6based transformerless PV system In the case of the HERICinverter based transformerless PV systems the extra deviceshave a smaller number of cycles compared to those of theH6 inverter Moreover the number of cycles of the otherpower switching devices of theHERC inverter is even smallerthan that of the FB-Bipolar inverter under the same missionprofile This means that the thermal stress on the powerswitching devices of the HERIC inverter is the lowest andthus the HERIC inverter can achieve the highest reliabilityif the same mission profile is applied to those invertercandidates while also maintaining a higher efficiency as itis reported in [12 14] The discussion is in agreement withthe analysis presented in Section 33 based on the translatedthermal loading profiles

It should be noted that the life consumption and thusthe lifetime of the power switching devices according to (2)and (3) can quantitatively be obtained on condition that thelifetime model of (1) and also the parameters given in Table 3are at a high confident level However those parameters are


Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Tjm (∘C)minus25minus15minus5 5 15 25 35 45 55 65 75

S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

Tjm (∘C)minus25minus15 minus5 5 15 25 35 45 55 65 75

S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)

Figure 10 Rain-flowing counting results (number of cycles distributions at the cycle amplitude Δ119879119895and the mean junction temperature 119879

119895119898)

of the thermal loading profiles shown in Figure 8 (a) FB-Bipolar inverter (b) H6 inverter and (c) HERIC inverter


ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)

Figure 11 Normalized life consumption (lifetime comparison) of the three transformerless PV inverters under the same mission profile (a)FB-Bipolar inverter (b) H6 inverter and (c) HERIC inverter

extracted under specific conditions (eg 007 s le 119905119900119899

le

63 s) for the power switching devices introduced in [48]Therefore quantitative prediction errors will be inevitableIn order to reduce the parameter dependency and also thereliability model dependency the life consumption given in(2) is normalized and substituting (1) yields

119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)

where 119871119862 is the normalized life consumption and LCb is thebase LC for normalization For example LCb can be chosenas the life consumption of the power switching devices of theFB-Bipolar inverter under the samemission profileThen thepredicted lifetime can be expressed as

119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840

119901is the predicted lifetime of the base system used

for normalizationFigure 11 shows the normalized life consumption of the

three transformerless PV inverters according to (4) and thecounting results enabled by a rain-flow algorithm The lifeconsumption of the power switching devices of the FB-Bipolar (ie S

1sim4) is selected as the base life consumption for

normalization in Figure 11 It can be seen in Figure 11 that theextra power switching devices of the H6 inverter consumemuch more life compared to the other devices and also thoseof the HERIC inverter It implies that the degradation of theadditional devices of the H6 inverter happens much fasterand then the entire H6 systemmay fail to operate earlier thanthe other two transformerless PV inverters This comparisonfurther confirms that the HERIC inverter would be the mostpromising solution in terms of reliability

In addition by comparing the rain-flow counting resultsshown in Figure 10 with the normalized life consumptionshown in Figure 11 one interesting conclusion can be drawnwhich is that although there are a few cycles of a largetemperature cycling amplitude (eg ten cycles of 55∘C to65∘C for the extra devices S

56of the H6 inverter) they do

contribute much more damage (eg 04 in Figure 11(b))when the lifetime model of (1) is adopted Large cyclingamplitude is mainly induced by the mission profile whichconfirms that the mission profile effect has to be taken intoaccount in a reliability-oriented design of power electronics


converters In a word the reliability assessment in this paperreveals that much attention has to be put on the thermaldesign of the critical components in an entire PV inverter inorder to reduce the cost of energy

5 Conclusions

In this paper a qualitative reliability assessment of threeselected single-phase transformerless PV inverters has beencarried out in accordance with a mission profile based reli-ability analysis approach A real-field yearly mission profilehas been applied to the selected transformerless candidatesfor the reliability assessment The comparison results haverevealed that although minimizing leakage currents as wellas maintaining a satisfactory efficiency has been targetedby those inverters the extra devices that are used fordisconnection of the PV panels or the PV inverters mightbe heated up during operation The high thermal loadingwill further induce failures of the power switching devicesbeing a big challenge to the entire system reliability As aconsequence many efforts should be devoted to a reliability-oriented design of the critical components in a PV inverterand thus a reduced cost of energy can be achieved

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] F Blaabjerg K Ma and Y Yang ldquoPower electronicsmdashthe keytechnology for renewable energy systemsrdquo in Proceedings ofthe 9th International Conference on Ecological Vehicles andRenewable Energies (EVER rsquo14) pp 1ndash11 Monte-Carlo MonacoMarch 2014

[2] F Blaabjerg R Teodorescu M Liserre and A V TimbusldquoOverview of control and grid synchronization for distributedpower generation systemsrdquo IEEE Transactions on IndustrialElectronics vol 53 no 5 pp 1398ndash1409 2006

[3] J M Carrasco L G Franquelo J T Bialasiewicz et al ldquoPower-electronic systems for the grid integration of renewable energysources a surveyrdquo IEEE Transactions on Industrial Electronicsvol 53 no 4 pp 1002ndash1016 2006

[4] J D vanWyk and F C Lee ldquoOn a future for power electronicsrdquoIEEE Journal of Emerging and Selected Topics in Power Electron-ics vol 1 no 2 pp 59ndash72 2013

[5] A Golnas ldquoPV system reliability an operatorrsquos perspectiverdquoIEEE Journal of Photovoltaics vol 3 no 1 pp 416ndash421 2013

[6] A Ristow M Begovic A Pregelj and A Rohatgi ldquoDevelop-ment of a methodology for improving photovoltaic inverterreliabilityrdquo IEEE Transactions on Industrial Electronics vol 55no 7 pp 2581ndash2592 2008

[7] E Romero-Cadaval G Spagnuolo L G Franquelo C ARamos-Paja T Suntio and W M Xiao ldquoGrid-connectedphotovoltaic generation plants components and operationrdquoIEEE Industrial ElectronicsMagazine vol 7 no 3 pp 6ndash20 2013

[8] REN21 ldquoRenewables 2014 global status reportrdquo Tech Rep 2014httpwwwren21net

[9] M Liserre T Sauter and J Y Hung ldquoFuture energy systemsintegrating renewable energy sources into the smart power

grid through industrial electronicsrdquo IEEE Industrial ElectronicsMagazine vol 4 no 1 pp 18ndash37 2010

[10] C-L Shen and S-H Yang ldquoMulti-input converter with MPPTfeature for wind-PV power generation systemrdquo InternationalJournal of Photoenergy vol 2013 Article ID 129254 13 pages2013

[11] F Blaabjerg and K Ma ldquoFuture on power electronics for windturbine systemsrdquo IEEE Journal of Emerging and Selected Topicsin Power Electronics vol 1 no 3 pp 139ndash152 2013

[12] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic and Wind Power Systems Wiley-IEEE Press 2011

[13] R Gonzalez J Lopez P Sanchis and L Marroyo ldquoTrans-formerless inverter for single-phase photovoltaic systemsrdquo IEEETransactions on Power Electronics vol 22 no 2 pp 693ndash6972007

[14] H Schmidt C Siedle and J Ketterer ldquoDCAC converter toconvert direct electric voltage into alternating voltage or intoalternating currentrdquo US Patent 7046534 2006

[15] T Kerekes M Liserre R Teodorescu C Klumpner and MSumner ldquoEvaluation of three-phase transformerless photo-voltaic inverter topologiesrdquo IEEE Transactions on Power Elec-tronics vol 24 no 9 pp 2202ndash2211 2009

[16] R Gonzalez E Gubıa J Lopez and L Marroyo ldquoTransformer-less single-phase multilevel-based photovoltaic inverterrdquo IEEETransactions on Industrial Electronics vol 55 no 7 pp 2694ndash2702 2008

[17] Advanced Energy ldquoWhatrsquos ahead for PV inverter technologyrdquoGreentechsolar 2014 httpwwwgreentechmediacom

[18] I Patrao E Figueres F Gonzalez-Espın and G GarceraldquoTransformerless topologies for grid-connected single-phasephotovoltaic invertersrdquo Renewable and Sustainable EnergyReviews vol 15 no 7 pp 3423ndash3431 2011

[19] N Achilladelis E Koutroulis and F Blaabjerg ldquoOptimizedpulse width modulation for transformerless active-NPC invert-ersrdquo in Proceedings of the 16th European Conference on PowerElectronics and Applications (EPE rsquo14-ECCE Europe) pp 1ndash10Lappeenranta Finland August 2014

[20] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal design ofmodern transformerless PV inverter topologiesdrdquo IEEE Trans-actions on Energy Conversion vol 28 no 2 pp 394ndash404 2013

[21] Y Yang H Wang F Blaabjerg and K Ma ldquoMission profilebased multi-disciplinary analysis of power modules in single-phase transformerless photovoltaic invertersrdquo in Proceedingsof the 15th European Conference on Power Electronics andApplications (EPE rsquo13) pp 1ndash10 IEEE Lille France September2013

[22] S E de Leon-Aldaco H Calleja F Chan and H R Jimenez-Grajales ldquoEffect of the mission profile on the reliability of apower converter aimed at photovoltaic applicationsmdasha casestudyrdquo IEEE Transactions on Power Electronics vol 28 no 6pp 2998ndash3007 2013

[23] H Wang M Liserre and F Blaabjerg ldquoToward reliable powerelectronics challenges design tools and opportunitiesrdquo IEEEIndustrial Electronics Magazine vol 7 no 2 pp 17ndash26 2013

[24] H Huang and P A Mawby ldquoA lifetime estimation techniquefor voltage source invertersrdquo IEEE Transactions on PowerElectronics vol 28 no 8 pp 4113ndash4119 2013

[25] P McCluskey ldquoReliability of power electronics under thermalloadingrdquo in Proceedings of the 7th International Conference onIntegrated Power Electronics Systems (CIPS rsquo12) March 2012


[26] H Lu C Bailey and C Yin ldquoDesign for reliability of powerelectronics modulesrdquoMicroelectronics Reliability vol 49 no 9ndash11 pp 1250ndash1255 2009

[27] M Ciappa ldquoLifetime prediction on the base ofmission profilesrdquoMicroelectronics Reliability vol 45 no 9-11 pp 1293ndash1298 2005

[28] F Chan and H Calleja ldquoReliability estimation of three single-phase topologies in grid-connected PV systemsrdquo IEEE Trans-actions on Industrial Electronics vol 58 no 7 pp 2683ndash26892011

[29] K Ma M Liserre F Blaabjerg and T Kerekes ldquoThermalloading and lifetime estimation for power device consideringmission profiles in wind power converterrdquo IEEE Transactionson Power Electronics vol 30 no 2 pp 590ndash602 2015

[30] S Harb and R S Balog ldquoReliability of candidate pho-tovoltaic module-integrated-inverter (PV-MII) topologiesmdashausagemodel approachrdquo IEEE Transactions on Power Electronicsvol 28 no 6 pp 3019ndash3027 2013

[31] P Zhang YWangW Xiao andW Li ldquoReliability evaluation ofgrid-connected photovoltaic power systemsrdquo IEEETransactionson Sustainable Energy vol 3 no 3 pp 379ndash389 2012

[32] S E De Leon-Aldaco H Calleja and J Aguayo ldquoReliability andmission profiles of photovoltaic systems a FIDES approachrdquoIEEE Transactions on Power Electronics vol 30 no 5 pp 2578ndash2586 2015

[33] S B Kjaer J K Pedersen and F Blaabjerg ldquoA review of single-phase grid-connected inverters for photovoltaicmodulesrdquo IEEETransactions on Industry Applications vol 41 no 5 pp 1292ndash1306 2005

[34] H Li J PengW Liu Z Huang andK-C Lin ldquoA newton-basedextremumseekingMPPTmethod for photovoltaic systemswithstochastic perturbationsrdquo International Journal of Photoenergyvol 2014 Article ID 938526 13 pages 2014

[35] D Sera L Mathe T Kerekes S V Spataru and R TeodoresculdquoOn the perturb-and-observe and incremental conductancemppt methods for PV systemsrdquo IEEE Journal of Photovoltaicsvol 3 no 3 pp 1070ndash1078 2013

[36] M Abdulkadir A H M Yatim and S T Yusuf ldquoAn improvedPSO-based MPPT control strategy for photovoltaic systemsrdquoInternational Journal of Photoenergy vol 2014 Article ID818232 11 pages 2014

[37] Y Zhou and H Li ldquoAnalysis and suppression of leakage cur-rent in cascaded-multilevel-inverter-based PV systemsrdquo IEEETransactions on Power Electronics vol 29 no 10 pp 5265ndash52772014

[38] A Hajiah T Khatib K Sopian and M Sebzali ldquoPerformanceof grid-connected photovoltaic system in two sites in KuwaitrdquoInternational Journal of Photoenergy vol 2012 Article ID178175 7 pages 2012

[39] M Musallam C Yin C Bailey and M Johnson ldquoMissionprofile-based reliability design and real-time life consumptionestimation in power electronicsrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2601ndash2613 2015

[40] Y Yang HWang F Blaabjerg and T Kerekes ldquoA hybrid powercontrol concept for PV inverters with reduced thermal loadingrdquoIEEE Transactions on Power Electronics vol 29 no 12 pp 6271ndash6275 2014

[41] A T Bryant P A Mawby P R Palmer E Santi and J LHudgins ldquoExploration of power device reliability using com-pact device models and fast electrothermal simulationrdquo IEEETransactions on Industry Applications vol 44 no 3 pp 894ndash903 2008

[42] M Musallam and C M Johnson ldquoAn efficient implementationof the rainflow counting algorithm for life consumption estima-tionrdquo IEEE Transactions on Reliability vol 61 no 4 pp 978ndash986 2012

[43] Plexim Gmbh ldquoPLECSmdashthe simulation platform for powerelectronics systemsrdquo Workshop Documentation 1 Aalborg2014

[44] I F Kovacevic U Drofenik and J W Kolar ldquoNew physicalmodel for lifetime estimation of powermodulesrdquo in Proceedingsof the International Power Electronics Conference (IPEC rsquo10) pp2106ndash2114 Sapporo Japan June 2010

[45] C Busca R Teodorescu F Blaabjerg et al ldquoAn overview ofthe reliability prediction related aspects of high power IGBTsin wind power applicationsrdquoMicroelectronics Reliability vol 51no 9ndash11 pp 1903ndash1907 2011

[46] ABB ldquoApplication NotemdashApplying IGBTsrdquo 2014 httpwwwabbcom

[47] A Volke and M Hornkamp IGBT ModulesmdashTechnologiesDriver and Application Infineon Technologies AG MunichGermany 2012

[48] U Scheuermann ldquoReliability of advanced power modules forextended maximum junction temperaturesrdquo Bodorsquos Power Sys-tems pp 26ndash30 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of

2 International Journal of PhotoenergySo

lar i

rrad

ianc

eA

mbi

ent t

empe

ratu

re


∘C

iPV

CPV

O

iCMVCMVCP

Cf

LCL-filter

Grid

Ground

S1

S2

S3

S4

D1

D2

D3

D4

L1 L2

A

B

Figure 1 A single-phase single-stage grid-connected full-bridge PVinverter systemwith an LCL-filter where VCMV is the commonmodevoltage and 119862

119875is the stray capacitor

mission profiles for those PV inverters However such aninvestigation allows new thoughts for a robust design anda reliable operation of PV system As a result a reductionof the cost can be attained since both the efficiency and thereliability of transformerless PV inverters are enhanced

Taking the above into consideration this paper exploresthe thermal performance of three selected transformerless PVinverters under a yearly mission profile which thus allows aqualitative reliability assessment of the PV inverters beyondefficiency achievements Firstly a description of the selectedtransformerless PV topologies is presented in Section 2Focus has been put on the mission profile translation to thecorresponding device thermal loading of the transformerlessinverters in Section 3 where a mission profile based relia-bility evaluation approach is also introduced In accordancewith the translated thermal loading profiles Section 4 thusconducts an assessment of the device reliability in those PVinverters before the conclusions

2 Selected Transformerless PV Inverters

Depending on the power ratings transferring PV energy toan AC power grid has several possibilities [1 7 33] It can bemodular PV converters which typically harvest the energyusing DC-DC converters (maximum power point tracking)[34ndash36] while the string or central inverters can be directlyconnected to the grid Since the grid-connected PV systemsare still dominantly designed for residential applications[33] the single-phase transformerless PV inverter system isanalyzed

Figure 1 shows the most commonly used single-phasefull-bridge (FB) PV inverter topology where the modulationschemes have to be modified for a smaller leakage current(119894CMV) As it is shown in Figure 1 an LCL-filter is used fora better power quality In some cases a DC-DC converter isadopted to boost up the PV output voltage to an acceptablelevel for the PV inverters Conventionalmodulationmethodsfor the single-stage FB inverter topology include the bipolarmodulation the unipolar modulation and the hybrid mod-ulation When considering the leakage current injection intransformerless applications the bipolar modulation schemeis preferable [12 21] which is chosen in this paper Notablyoptimizing the modulation patterns is an alternative toeliminate the leakage currents [19]

Asmentioned early transformerless structures aremostlyderived from the FB topology by providing an AC path ora DC path using additional power switching devices As aresult during the zero-voltage states isolation between thePV modules and the grid is achieved thus leading to a lowleakage current injection Figure 2 shows two examples oftransformerless PV inverters derived from the single-phaseFB topology As it can be seen in Figure 2(a) the H6 invertertopology [13] has a DC path which isolates the PV panelsfrom the grid at zero-voltage states In contrast although thehighly efficient and reliable inverter concept (HERIC) [14]inverter has the same number of power switching devices asthat of the H6 inverter it provides an AC path to eliminatethe leakage current injection

It should be pointed out that there are also many othertransformerless topologies reported in the literature in addi-tion to the above two solutions [12 16 37] For examplethe Conergy neutral point clamped (NPC) transformerlessPV inverter is based on the multilevel power convertertechnology [12 20] However only the FB inverter with abipolar modulation scheme (FB-Bipolar) the H6 inverterand the HERIC inverter are assessed in terms of reliability

3 Mission Profile Translation toThermal Loading

31 Mission Profile for PV Systems A mission profile isnormally referred to a simplified representation of relevantconditions under which the system is operating [27 32] As aresult for the grid-connected PV systems the mission profile(ie solar irradiance and ambient temperature) is actually areflection of the intermittent nature of the solar PV energy[38 39] and consequently it has an inherent relationshipwith the entire system performance including the thermalloading performance The mission profile can be a series ofmultitime scales for example a minute mission profile ora yearly mission profile and it is usually taken as the inputfor the reliability analysis in the field of power electronicsconverters [29 39ndash42] which is also focused on in this paperFigure 3 shows the mission profile applied to the above threetransformerless PV inverters

With more accumulative real-field experience and moreadvanced real-time monitoring technology better missionprofiles are available for a reasonable lifetime predictionHence a mission profile based analysis approach should beable to analyze the performance at different time scales asit is shown in Figure 4 It can be observed in Figure 4(a)that for short-term mission profiles at the level of millisec-onds to several seconds the thermal loading profile canbe directly and instantaneously obtained In contrast forlong-term mission profiles within a range of a few minutesto several months obtaining the instantaneous thermalloading will be very time-consuming or even impossiblewhen the mission profile has a high data-sampling rateAlternatively the thermal loading profile can be obtainedbased on lookup tables [43] which are created in accordancewith the short-term constantmission profiles as it is shown inFigure 4(b)



CPV1

CPV2

CP

LCL-filter

DC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

D8

D7L1 L2

A

B

(a)


iPV

CPV

CP

LCL-filter

AC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

L1 L2A

B

(b)


Sola

r irr

adia

nce (

kWm

2)

15

10

05


(a)

Am

bien

t tem

p (∘

C)

40

20

0


(b)


∘C

MPPTMiss

ion

profi


PVmodels

PinPout



TjTj

Thermalmodel


(a)

∘C

Lookup tablebased


Miss

ion

profi

le


(b)







Impedance 119885th(119895-119888)

119894 1 2 3 4IGBT119877th119894 (KW) 0074 0173 0526 0527120591119894(s) 00005 0005 005 02

Diode119877th119894 (KW) 0123 0264 0594 0468120591119894(s) 00005 0005 005 02





Electrical domain

Thermal domain


Pin Poutinvdc




Tc

Tj

Ptot

Ta

Rth1 Rth2 Rth3 Rth4

C1 C2 C3 C4






119892 50 Hz

LCL-filter1198711

36 mH119862119891 235 120583F

1198712


11988910 Ω











STa

PV++

+++

+

minus

minus

A

CC

A

V VCPVC 11e minus 3

PV

iPV

PWM

1

2 345

Full-bridgeinverter

a

a

b

b

R1 R2L1 L2

Cf GridRd

s

ig

gControl system

Probe

Probe

Probe

Probe

Probe

Probe

Probe

Probe

ProbeVac

Iac

PV V I P

PV P V

AC grid

PV string

P versus V

s

+

minus

f(u)

f(u)

f(u)

f(u)

D1

D2 D4

D3

Heat sink

IGBT1

IGBT2

IGBT3

IGBT4

Scope



FB-bipolar

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4




H6

Extra devices S56

Extra devices S56

HERIC

(a)

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

Extra devices S56

Extra devices S56




(b)






119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731


119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861





119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)





0 1205731 120574 and 119862 are



119871119862 = sum

119894

119899119894

119873119891119894

(2)





119871119875=119905119872119875

119871119862(3)


119872119875being the



Mission profile



Lifetimeprediction

∘C

System models


Lifetimemodels

Counting algorithms








5and S







Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



CPV1

CPV2

CP

LCL-filter

DC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

D8

D7L1 L2

A

B

(a)


iPV

CPV

CP

LCL-filter

AC path

Grid∘C

OSola

r irr

adia

nce

Am

bien

t tem

pera

ture

Cf

S1

S2

S3

S4

S5

S6

D3

D2

D1

D6

D5

D4

L1 L2A

B

(b)


Sola

r irr

adia

nce (

kWm

2)

15

10

05


(a)

Am

bien

t tem

p (∘

C)

40

20

0


(b)


∘C

MPPTMiss

ion

profi


PVmodels

PinPout



TjTj

Thermalmodel


(a)

∘C

Lookup tablebased


Miss

ion

profi

le


(b)







Impedance 119885th(119895-119888)

119894 1 2 3 4IGBT119877th119894 (KW) 0074 0173 0526 0527120591119894(s) 00005 0005 005 02

Diode119877th119894 (KW) 0123 0264 0594 0468120591119894(s) 00005 0005 005 02





Electrical domain

Thermal domain


Pin Poutinvdc




Tc

Tj

Ptot

Ta

Rth1 Rth2 Rth3 Rth4

C1 C2 C3 C4






119892 50 Hz

LCL-filter1198711

36 mH119862119891 235 120583F

1198712


11988910 Ω











STa

PV++

+++

+

minus

minus

A

CC

A

V VCPVC 11e minus 3

PV

iPV

PWM

1

2 345

Full-bridgeinverter

a

a

b

b

R1 R2L1 L2

Cf GridRd

s

ig

gControl system

Probe

Probe

Probe

Probe

Probe

Probe

Probe

Probe

ProbeVac

Iac

PV V I P

PV P V

AC grid

PV string

P versus V

s

+

minus

f(u)

f(u)

f(u)

f(u)

D1

D2 D4

D3

Heat sink

IGBT1

IGBT2

IGBT3

IGBT4

Scope



FB-bipolar

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4




H6

Extra devices S56

Extra devices S56

HERIC

(a)

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

Extra devices S56

Extra devices S56




(b)






119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731


119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861





119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)





0 1205731 120574 and 119862 are



119871119862 = sum

119894

119899119894

119873119891119894

(2)





119871119875=119905119872119875

119871119862(3)


119872119875being the



Mission profile



Lifetimeprediction

∘C

System models


Lifetimemodels

Counting algorithms








5and S







Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Electrical domain

Thermal domain


Pin Poutinvdc




Tc

Tj

Ptot

Ta

Rth1 Rth2 Rth3 Rth4

C1 C2 C3 C4






119892 50 Hz

LCL-filter1198711

36 mH119862119891 235 120583F

1198712


11988910 Ω











STa

PV++

+++

+

minus

minus

A

CC

A

V VCPVC 11e minus 3

PV

iPV

PWM

1

2 345

Full-bridgeinverter

a

a

b

b

R1 R2L1 L2

Cf GridRd

s

ig

gControl system

Probe

Probe

Probe

Probe

Probe

Probe

Probe

Probe

ProbeVac

Iac

PV V I P

PV P V

AC grid

PV string

P versus V

s

+

minus

f(u)

f(u)

f(u)

f(u)

D1

D2 D4

D3

Heat sink

IGBT1

IGBT2

IGBT3

IGBT4

Scope



FB-bipolar

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4




H6

Extra devices S56

Extra devices S56

HERIC

(a)

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

Extra devices S56

Extra devices S56




(b)






119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731


119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861





119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)





0 1205731 120574 and 119862 are



119871119862 = sum

119894

119899119894

119873119891119894

(2)





119871119875=119905119872119875

119871119862(3)


119872119875being the



Mission profile



Lifetimeprediction

∘C

System models


Lifetimemodels

Counting algorithms








5and S







Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


STa

PV++

+++

+

minus

minus

A

CC

A

V VCPVC 11e minus 3

PV

iPV

PWM

1

2 345

Full-bridgeinverter

a

a

b

b

R1 R2L1 L2

Cf GridRd

s

ig

gControl system

Probe

Probe

Probe

Probe

Probe

Probe

Probe

Probe

ProbeVac

Iac

PV V I P

PV P V

AC grid

PV string

P versus V

s

+

minus

f(u)

f(u)

f(u)

f(u)

D1

D2 D4

D3

Heat sink

IGBT1

IGBT2

IGBT3

IGBT4

Scope



FB-bipolar

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4




H6

Extra devices S56

Extra devices S56

HERIC

(a)

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

Max

imum

junc

tion

tem

pTjm

ax(∘

C)

80

60

40

20

0

minus20

S1ndash4

S1ndash4

S1ndash4

Extra devices S56

Extra devices S56




(b)






119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731


119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861





119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)





0 1205731 120574 and 119862 are



119871119862 = sum

119894

119899119894

119873119891119894

(2)





119871119875=119905119872119875

119871119862(3)


119872119875being the



Mission profile



Lifetimeprediction

∘C

System models


Lifetimemodels

Counting algorithms








5and S







Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




119895le 113 K

1205730

1942 mdash 019 le ar le 0421205731


119900119899le 63 s

120574 minus1208 mdash119891119889

06204 mdash119864119886

006606 eV 325∘C le 119879119895119898

le 122∘C119896119861





119873119891= 119860Δ119879

120572

119895(119886119903)1205731Δ119879119895+1205730 (

119862 + (119905119900119899)120574

119862 + 1) exp(

119864119886

119896119861119879119895119898

)119891119889

(1)





0 1205731 120574 and 119862 are



119871119862 = sum

119894

119899119894

119873119891119894

(2)





119871119875=119905119872119875

119871119862(3)


119872119875being the



Mission profile



Lifetimeprediction

∘C

System models


Lifetimemodels

Counting algorithms








5and S







Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

Num

ber o

f cyc

les

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95


S1ndash4

S1ndash4

(a)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4

S56

S56

(b)

Num

ber o

f cyc

les

105

104

103

102

101

100

10minus1

ΔTj (∘C)0 5 15 25 35 45 55 65 75 85 95

Num

ber o

f cyc

les

104

103

102

101

100

10minus1


S1ndash4

S1ndash4S56

S56

(c)


119895119898)



ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

(a)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4

S56

(b)

ΔTj (∘C)0 5 15 35 55 75 95

Nor

mal

ized

LC

()

20

16

12

08

04

0

S1ndash4S56

(c)



le


119871119862 =119871119862

119871119862119887

= (sum

119894

119899119894

(Δ119879119895119894)120572

(119886119903)1205731Δ119879119895119894 [119862 + (119905

119900119899119894)120574] 119890119864119886(119896119861119879119895119898119894))

sdot (sum

119897

119899119897

(Δ1198791015840

119895119897)120572

(119886119903)1205731Δ1198791015840

119895119897 [119862 + (1199051015840

119900119899119897)120574] 119890119864119886(1198961198611198791015840

119895119898119897)

)

minus1

(4)


119871119901=

1

1198711198621198711015840

119901(5)

in which 1198711015840











5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



5 Conclusions




References




























































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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