research article a novel inverter topology for single

Research ArticleA Novel Inverter Topology for Single-PhaseTransformerless PV System

Haiyan Cao

Department of Information Engineering Shijiazhuang University of Economics Shijiazhuang 050031 China

Correspondence should be addressed to Haiyan Cao beatles888126com

Received 18 October 2015 Revised 6 December 2015 Accepted 15 December 2015

Academic Editor Adrian Ioinovici

Copyright copy 2016 Haiyan Cao This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Transformerless photovoltaic (PV) power system is very promising due to its low cost small size and high efficiency One of itsmostimportant issues is how to prevent the commonmode leakage current In order to solve the problem a new inverter is proposed inthis paperThe system commonmodemodel is established and the four operationmodes of the inverter are analyzed It reveals thatthe commonmode voltage can be kept constant and consequently the leakage current can be suppressed Finally the experimentaltests are conducted The experimental results verify the effectiveness of the proposed solution

1 Introduction

The transformerless PV inverter has the prominent advan-tages of the small size low cost and high efficiency [1] Andmore and more commercial transformerless PV invertershave been developed in recent years However there is nogalvanic isolation between the input and output sides of thetransformerless inverter so it is prone to common modeleakage current problems [2] The common mode leakagecurrent not only affects the electromagnetic compatibility ofthe inverter [3] but also leads to the potential human safetyproblems [4]

In order to solve this problem Sunways Companydeveloped HERIC inverter [5] SMA Company developedH5 inverter [6] Xiao and Xie presented a leakage currentanalytical model [7] and then developed the new optimizedH5 [8] and split-inductor neutral point clamped inverters[9] Cavalcanti et al developed the space vector modulationtechniques for three-phase two-level [10] and three-level[11] inverters Guo et al developed the carrier modulationtechniques for three-phase inverters [12] Yang et al [13]Zhang et al [14] and San et al [15] developed the improvedH6 inverter And there is an increasing attention to developthe new inverter for transformerless PV applications

The main contribution of this paper is to develop a newsingle-phase transformerless PV inverter Compared with

HERIC in [5] only one auxiliary switch and gating driverare needed in the proposal While in HERIC two auxil-iary switches are needed Also two auxiliary gating driversshould be designed for two auxiliary switches Thereforethe proposal is more cost-effective and reliable due to lessauxiliary switches and gating drivers are used On the otherhand three semiconductors conduct current during modes 2and 4 While in Heric two semiconductors conducts currentduring modes 2 and 4 Therefore the main difference isthat one additional diode loss With the development ofthe commercially available Sic diode the diode loss will bevery small So this difference due to one additional diodeloss would be small Finally the theoretical analysis andexperimental results validate the proposed solution

2 Proposed Topology

Figure 1 illustrates the schematic diagram of the proposedsingle-phase inverter It consists of five switches and fourdiodes119862PV is the parasitic capacitance between PV array andground The capacitance value depends on many conditionssuch as the PVpanel frame structure weather conditions andhumidity and it is generally up to 50ndash150 nFkW 119881119892 is thegrid voltage and 119881119889 is the dc bus voltage 119871119886 and 119871119887 are filterinductors respectively

Hindawi Publishing CorporationActive and Passive Electronic ComponentsVolume 2016 Article ID 1962438 6 pageshttpdxdoiorg10115520161962438

2 Active and Passive Electronic Components

PV

P

Vd

S3 S1

S5

S4 S2

La

Lb

Vg

o

A

N

B

CPV

Figure 1 Schematic diagram of proposed inverter

UDM(Lb minus La)

2(Lb + La) UCMUCM

LaLb LaLb

Lb = La

CPV CPV

Figure 2 System common mode model

The commonmode voltage and differential mode voltageare defined as

119880CM =119880AN + 119880BN2

119880DM = 119880AN minus 119880BN

(1)

From (1) the following voltage equations can be obtained

119880AN = 119880CM +119880DM2

119880BN = 119880CM minus119880DM2

(2)

Figure 2 shows the system common mode model It canbe observed that the differential mode voltage has the effecton the system common mode current if 119871119887 = 119871119886 Thereforethe filter inductance of 119871119886 should be designed the same valueas that of 119871119887 that is 119871119886 = 119871119887 So the differential modevoltage will not contribute the common mode current asshown in Figure 2 [15] Note that the common mode currentis mainly due to the high frequency switching componentsTherefore the effect of grid voltage on the common modevoltage is neglected because its frequency is much lower thanthe switching frequency [2]

On the other hand from Figure 2 it can be observedthat the common mode leakage current will be eliminatedon condition that the common mode voltage 119880CM can bekept constant all the time The reason is that the commonmode leakage current which passes through 119862PV dependson 119862PV(119889119880119862PV119889119905) When the common mode voltage 119880CMis constant the voltage across 119862PV is constant as well Thatis 119889119880119862PV119889119905 = 0 Therefore the common mode leakagecurrent can be eliminated if the common mode voltage 119880CM

Table 1 Four operation modes and common mode voltage

11987811198782119878311987841198785119880AN 119880BN 119880CM

Mode 1 1 0 0 1 0 119881119889

0 1198811198892

Mode 2 0 0 0 0 1 1198811198892 119881

1198892 119881

1198892

Mode 3 0 1 1 0 0 0 1198811198891198811198892

Mode 4 0 0 0 0 1 1198811198892 119881

1198892 119881

1198892

S3

S1

S5

S4

S2

Vg

Figure 3 Switching state of the proposed inverter

is constant In order to achieve this goal the following willpresent the operation principle

The proposed inverter operates in four modes as shownin Figure 3 and Table 1

In Mode 1 the switches 1198781 and 1198784 turn on and otherswitches turn off The differential mode voltage 119880AB is equalto the dc bus voltage of 119881119889 while the common mode voltagecan be expressed as

119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889 + 0) =

119881119889

2 (3)

InMode 2 only the switch 1198785 turns on and other switchesturn offThe current flows through 1198785 and diodes In this casethe differential mode voltage 119880AB is 0 while the commonmode voltage remains unchanged as

119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889

2+119881119889

2) =119881119889

2 (4)

In Mode 3 the switches 1198782 and 1198783 turn on and otherswitches turn off The differential mode voltage 119880AB is minus119881119889while the common mode voltage can be expressed as

119880CM =1

2(119880AN + 119880BN) =

1

2(0 + 119881119889) =

119881119889

2 (5)


119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889

2+119881119889

2) =119881119889

2 (6)

From the above theoretical analysis it can be observedthat the common mode voltage remains constant duringthe whole operation cycle Consequently the common modeleakage current can be significantly suppressed according totheoretical analysis of Figure 2

Active and Passive Electronic Components 3

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(a) Mode 1

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(b) Mode 2

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(c) Mode 3

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(d) Mode 4

Figure 4 Operation modes of the proposed

The system design in terms of passive and active com-ponents is presented as follows The rated system power is15 kW dc bus voltage 119881119889 is 400V grid voltage 119881119892 is 220Vacgrid frequency is 50Hz and inverter switching frequency is10 kHz

First of all the active components such as the switches aredesigned in terms of the operating voltage on-state currentThe rated voltage and current stresses of switches (1198781 1198782 11987831198784 1198785) and diodes are 400V and 10A respectively There-fore the IRG4IBC30S IGBT from International Rectifier isselected for five switches (1198781 1198782 1198783 1198784 1198785) Its collector-to-emitter breakdown voltage is 600V and the continuouscollector currents are 235 A and 13A respectively in case of119879119862 = 25

∘C and 119879119862 = 100∘C The diode is FR20J02GN-ND

from GeneSiC SemiconductorAnother design consideration is the filter inductor Its

inductance can be calculated according to the commonlyused design criterion in which the maximum current ripplemagnitude is less than 10 of the rated current The filterinductor current ripple can be calculated from Figure 4 asfollows

In mode 1 the inductor current increases

119881119889 minus 119881119892 = 119881119889 minus 119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198681

1198791

(7)

where 119881119898 and 120596 is the amplitude and angular frequency ofthe grid voltage and 1198791 is the time interval of mode 1

In mode 2 the inductor current decreases

minus119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198682

1198792

(8)

where 1198792 is the time interval of mode 2 1198791 + 1198792 = 119879119904 and 119879119904is the switching cycle

In steady state |Δ1198681| = |Δ1198682| So (119881119889 minus 119881119898 sin120596119905)1198791 =(119881119898 sin120596119905)1198792 Considering 1198791 = 119879119904 minus 1198792 we can obtain

1198792 =(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904 (9)

Substituting (9) into (8) the inductor current ripple canbe calculated as follows

1003816100381610038161003816Δ11986821003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

minus119881119898 sin120596119905119871119886 + 119871119887

1198792

10038161003816100381610038161003816100381610038161003816

=119881119898 sin120596119905119871119886 + 119871119887

(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904

(10)

The current ripple reaches its maximum value when119881119898 sin120596119905 = 1198811198892 In this case the maximum current ripple is

Δ119868max =119881119889

4 (119871119886 + 119871119887)119879119904 (11)

In this paper 119881119889 is 400V 119879119904 is 100 us the rated current is10 A and themaximumcurrent ripple should be less than 1 Atherefore the filter inductor should be designed as follows

119871119886 + 119871119887 =119881119889

4Δ119868max119879119904 ge 001H (12)


Mode 2 Mode 1

Mode 2 Mode 1

99510

10511

I g(A

)

02468

100

100

200

300

40002468

1012

0

50

100

150

200

00848 00849 0085 00851 00852 00853 0085400847Time (s)

Vs 1

(V)

I s1

(A)

Vs 5

(V)

I s5

(A)

(a) Operation mode 1 and mode 2

Mode 3 Mode 4

Mode 3 Mode 4

00949 0095 00951 00952 00953 0095400948Time (s)

02468

1012

0

100

200

300

40002468

1012

0

50

100

150

200

minus11

minus105

minus10

minus95

minus9

I g(A

)Vs 2

(V)

I s2

(A)

Vs 5

(V)

I s5

(A)

(b) Operation mode 3 and mode 4

Figure 5 Simulation results showing the operation of the converter

3 Simulation and Experimental Results

In order to further verify the effectiveness of the pro-posed inverter the performance test is conducted in MAT-LABSimulink The components and parameters are listed asfollows system rated power is 15 kW dc bus voltage 119881119889 is400V grid voltage 119881119892 is 220Vac grid frequency is 50Hzswitching frequency is 10 kHz filter inductor is 119871119886 = 119871119887 =5mH and parasitic capacitor is 119862PV = 150 nF The leakagecurrent is obtained by measuring the current through theparasitic capacitor [10]

Figure 5 shows the operation of the proposed converterThe simulation results of the operation mode 1 and mode 2are shown in Figure 5(a) In agreement with the theoreticalanalysis in Figure 4(a) when the switches 1198781 and 1198784 turnon the collector-to-emitter voltage119881119904

1

of 1198781 is approximatelyzero and its current 119868119904

1

increases with a slope of (119881119889 minus119881119898 sin120596119905)(119871119886 + 119871119887) The simulation result waveforms of 1198784are the same as those of 1198781 in mode 1 and thus not duplicatedhere for simplicity

In mode 2 only the switch 1198785 turns on the collector-to-emitter voltage 119881119904

5

of 1198785 changes from 400V (in mode 1) to

zero (in mode 2) and its current 1198681199045

decreases with a slope ofminus119881119898 sin120596119905(119871119886 + 119871119887)

The last figure in Figure 5(a) shows the filter inductorcurrent it can be observed that the inductor current 119868119892charges (in mode 1) and discharges (in mode 2) duringa switching cycle and the current ripple is less than 1 Awhich is in good agreement with the design consideration inSection 2

The simulation results of the operation mode 3 andmode4 are shown in Figure 5(b) In agreement with the theoreticalanalysis in Figure 4(c) when the switches 1198782 and 1198783 turnon the collector-to-emitter voltage119881119904

2


2

increases in mode 3 In mode 4 onlythe switch 1198785 turns on the collector-to-emitter voltage 119881119904

5

of 1198785 changes from 400V (in mode 3) to zero (in mode 4)and its current 119868119904

5

decreases The last figure in Figure 5(a)shows the filter inductor current it can be observed that theinductor current 119868119892 charges anddischarges during a switchingcycle and the current ripple is less than 1 A which is in goodagreement with the design consideration in Section 2

Figure 6 shows the simulation results of output wave-forms in the time and frequency domains It can be observed


Fundamental (50Hz) = 10 THD = 329

times104

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 3 35 40Frequency (Hz)

0

005

01

015

02

Mag

(A)

minus10

minus5

0

5

10

Grid

curr

ent (

A)

Figure 6 Simulation results of output waveforms in the time and frequency domains

050

100150200250

Com

mon

mod

evo

ltage

(V)

011 012 013 014 015 016 01701Time (s)

(a) Common mode voltage

011 012 013 014 015 016 01701

Time (s)

minus350minus300minus250minus200minus150minus100minus50

Para

sitic

capa

cito

rvo

ltage

(V)

(b) Parasitic capacitor voltage

times104

minus03minus02minus01

0010203

Leak

age c

urre

nt (A

)

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 30Frequency (Hz)

0

0005

001

0015

Leak

age c

urre

ntm

ag (A

)

(c) Common mode leakage current and spectrum

Figure 7 Simulation results of common mode voltage and leakage current

that the output grid current is sinusoidal and its totalharmonic distortion (THD) is well below 5 as specified inIEEE Std 929-2000

The simulation results of the common mode voltage andleakage current are shown in Figure 7 It can be observed thatthe commonmode voltage is constant which is in agreementwith the theoretical analysis in Section 2 On the other handthe parasitic capacitor voltage does not include any highfrequency common mode voltage and therefore the leakagecurrent is significantly reduced as shown in Figure 7(c) Itspeak value is below 300mA and the RMS value is below30mAwhichmeets the international standardVDE 0126-1-1

As shown in Figure 8 with the proposed topology itcan be observed that the parasitic capacitor voltage has onlythe fundamental frequency component without any highfrequency componentsTherefore the leakage current can beeffectively reduced below 300mA which complies with theinternational standard VDE 0126-1-1

4 Conclusion

This paper has presented the theoretical analysis and experi-mental verification of a new inverter for transformerless PVsystems The proposed inverter has the following interesting

Figure 8 Experimental results of parasitic capacitor voltage andleakage current

features It can keep the system common mode voltageconstant during the entire operation cycle Consequently thecommon mode leakage current can be significantly reducedwell below 300mA which meets the international standardVDE 0126-1-1Therefore it is attractive and a promising alter-native topology for transformerless PV system applications

Conflict of Interests

The author declares that there is no conflict of interestsregarding publication of this paper


References

[1] X Guo H Wang Z Lu and B Wang ldquoNew inverter topologyfor ground current suppression in transformerless photovoltaicsystem applicationrdquo Journal ofModern Power Systems andCleanEnergy vol 2 no 2 pp 191ndash194 2014

[2] E Gubıa P Sanchis A Ursua J Lopez and L MarroyoldquoGround currents in single-phase transformerless photovoltaicsystemsrdquo Progress in Photovoltaics Research and Applicationsvol 15 no 7 pp 629ndash650 2007

[3] R Araneo S Lammens M Grossi and S Bertone ldquoEMCissues in high-power grid-connected photovoltaic plantsrdquo IEEETransactions on Electromagnetic Compatibility vol 51 no 3 pp639ndash648 2009

[4] J C Hernandez P G Vidal and A Medina ldquoCharacterizationof the insulation and leakage currents of PV generators rele-vance for human safetyrdquo Renewable Energy vol 35 no 3 pp593ndash601 2010

[5] S Heribert S Christoph and K Jurgen ldquoInverter for trans-forming a DC voltage into an AC current or an AC voltagerdquoEU Patent 1369985 (A2) 2003

[6] M Victor F Greizer S Bremicker et al ldquoMethod of convertinga direct current voltage from a source of direct current voltagemore specifically from a photovoltaic source of direct currentvoltage into a alternating current voltagerdquo US Patent 74118022008

[7] H Xiao and S Xie ldquoLeakage current analytical model andapplication in single-phase transformerless photovoltaic grid-connected inverterrdquo IEEE Transactions on ElectromagneticCompatibility vol 52 no 4 pp 902ndash913 2010

[8] H Xiao S Xie Y Chen and R Huang ldquoAn optimizedtransformerless photovoltaic grid-connected inverterrdquo IEEETransactions on Industrial Electronics vol 58 no 5 pp 1887ndash1895 2011

[9] H Xiao and S Xie ldquoTransformerless split-inductor neutralpoint clamped three-level PV grid-connected inverterrdquo IEEETransactions on Power Electronics vol 27 no 4 pp 1799ndash18082012

[10] M C Cavalcanti K C De Oliveira A M De Farias F A SNevesGM SAzevedo andFCCamboim ldquoModulation tech-niques to eliminate leakage currents in transformerless three-phase photovoltaic systemsrdquo IEEE Transactions on IndustrialElectronics vol 57 no 4 pp 1360ndash1368 2010

[11] M C Cavalcanti A M Farias K C Oliveira F A S Nevesand J L Afonso ldquoEliminating leakage currents in neutral pointclamped inverters for photovoltaic systemsrdquo IEEE Transactionson Industrial Electronics vol 59 no 1 pp 435ndash443 2012

[12] X Guo M C Cavalcanti A M Farias and J M GuerreroldquoSingle-carrier modulation for neutral-point-clamped invertersin three-phase transformerless photovoltaic systemsrdquo IEEETransactions on Power Electronics vol 28 no 6 pp 2635ndash26372013

[13] B Yang W Li Y Gu W Cui and X He ldquoImproved trans-formerless inverter with common-mode leakage current elim-ination for a photovoltaic grid-connected power systemrdquo IEEETransactions on Power Electronics vol 27 no 2 pp 752ndash7622012

[14] L Zhang K Sun Y Xing and M Xing ldquoH6 transformerlessfull-bridge PV grid-tied invertersrdquo IEEE Transactions on PowerElectronics vol 29 no 3 pp 1229ndash1238 2014

[15] G SanHQi andXGuo ldquoAnovel single-phase transformerlessinverter for grid-connected photovoltaic systemsrdquo PrzegladElektrotechniczny vol 88 no 12 A pp 251ndash254 2012

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Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



PV

P

Vd

S3 S1

S5

S4 S2

La

Lb

Vg

o

A

N

B

CPV

Figure 1 Schematic diagram of proposed inverter

UDM(Lb minus La)

2(Lb + La) UCMUCM

LaLb LaLb

Lb = La

CPV CPV

Figure 2 System common mode model

The commonmode voltage and differential mode voltageare defined as

119880CM =119880AN + 119880BN2

119880DM = 119880AN minus 119880BN

(1)

From (1) the following voltage equations can be obtained

119880AN = 119880CM +119880DM2

119880BN = 119880CM minus119880DM2

(2)

Figure 2 shows the system common mode model It canbe observed that the differential mode voltage has the effecton the system common mode current if 119871119887 = 119871119886 Thereforethe filter inductance of 119871119886 should be designed the same valueas that of 119871119887 that is 119871119886 = 119871119887 So the differential modevoltage will not contribute the common mode current asshown in Figure 2 [15] Note that the common mode currentis mainly due to the high frequency switching componentsTherefore the effect of grid voltage on the common modevoltage is neglected because its frequency is much lower thanthe switching frequency [2]

On the other hand from Figure 2 it can be observedthat the common mode leakage current will be eliminatedon condition that the common mode voltage 119880CM can bekept constant all the time The reason is that the commonmode leakage current which passes through 119862PV dependson 119862PV(119889119880119862PV119889119905) When the common mode voltage 119880CMis constant the voltage across 119862PV is constant as well Thatis 119889119880119862PV119889119905 = 0 Therefore the common mode leakagecurrent can be eliminated if the common mode voltage 119880CM

Table 1 Four operation modes and common mode voltage

11987811198782119878311987841198785119880AN 119880BN 119880CM

Mode 1 1 0 0 1 0 119881119889

0 1198811198892

Mode 2 0 0 0 0 1 1198811198892 119881

1198892 119881

1198892

Mode 3 0 1 1 0 0 0 1198811198891198811198892

Mode 4 0 0 0 0 1 1198811198892 119881

1198892 119881

1198892

S3

S1

S5

S4

S2

Vg

Figure 3 Switching state of the proposed inverter

is constant In order to achieve this goal the following willpresent the operation principle

The proposed inverter operates in four modes as shownin Figure 3 and Table 1

In Mode 1 the switches 1198781 and 1198784 turn on and otherswitches turn off The differential mode voltage 119880AB is equalto the dc bus voltage of 119881119889 while the common mode voltagecan be expressed as

119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889 + 0) =

119881119889

2 (3)


119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889

2+119881119889

2) =119881119889

2 (4)

In Mode 3 the switches 1198782 and 1198783 turn on and otherswitches turn off The differential mode voltage 119880AB is minus119881119889while the common mode voltage can be expressed as

119880CM =1

2(119880AN + 119880BN) =

1

2(0 + 119881119889) =

119881119889

2 (5)


119880CM =1

2(119880AN + 119880BN) =

1

2(119881119889

2+119881119889

2) =119881119889

2 (6)

From the above theoretical analysis it can be observedthat the common mode voltage remains constant duringthe whole operation cycle Consequently the common modeleakage current can be significantly suppressed according totheoretical analysis of Figure 2


P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(a) Mode 1

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(b) Mode 2

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(c) Mode 3

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(d) Mode 4








119881119889 minus 119881119892 = 119881119889 minus 119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198681

1198791

(7)



minus119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198682

1198792

(8)



1198792 =(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904 (9)


1003816100381610038161003816Δ11986821003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

minus119881119898 sin120596119905119871119886 + 119871119887

1198792

10038161003816100381610038161003816100381610038161003816

=119881119898 sin120596119905119871119886 + 119871119887

(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904

(10)


Δ119868max =119881119889

4 (119871119886 + 119871119887)119879119904 (11)


119871119886 + 119871119887 =119881119889

4Δ119868max119879119904 ge 001H (12)


Mode 2 Mode 1

Mode 2 Mode 1

99510

10511

I g(A

)

02468

100

100

200

300

40002468

1012

0

50

100

150

200

00848 00849 0085 00851 00852 00853 0085400847Time (s)

Vs 1

(V)

I s1

(A)

Vs 5

(V)

I s5

(A)


Mode 3 Mode 4

Mode 3 Mode 4

00949 0095 00951 00952 00953 0095400948Time (s)

02468

1012

0

100

200

300

40002468

1012

0

50

100

150

200

minus11

minus105

minus10

minus95

minus9

I g(A

)Vs 2

(V)

I s2

(A)

Vs 5

(V)

I s5

(A)






1


1



5






2


2


5


5





times104

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 3 35 40Frequency (Hz)

0

005

01

015

02

Mag

(A)

minus10

minus5

0

5

10

Grid

curr

ent (

A)


050

100150200250

Com

mon

mod

evo

ltage

(V)

011 012 013 014 015 016 01701Time (s)


011 012 013 014 015 016 01701

Time (s)


Para

sitic

capa

cito

rvo

ltage

(V)


times104


0010203

Leak

age c

urre

nt (A

)

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 30Frequency (Hz)

0

0005

001

0015

Leak

age c

urre

ntm

ag (A

)






4 Conclusion







References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(a) Mode 1

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(b) Mode 2

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(c) Mode 3

P

Vd

S3 S1

S5

S4 S2

Vg

A

N

B

Ig

(d) Mode 4








119881119889 minus 119881119892 = 119881119889 minus 119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198681

1198791

(7)



minus119881119898 sin120596119905 = (119871119886 + 119871119887)Δ1198682

1198792

(8)



1198792 =(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904 (9)


1003816100381610038161003816Δ11986821003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

minus119881119898 sin120596119905119871119886 + 119871119887

1198792

10038161003816100381610038161003816100381610038161003816

=119881119898 sin120596119905119871119886 + 119871119887

(119881119889 minus 119881119898 sin120596119905)119881119889

119879119904

(10)


Δ119868max =119881119889

4 (119871119886 + 119871119887)119879119904 (11)


119871119886 + 119871119887 =119881119889

4Δ119868max119879119904 ge 001H (12)


Mode 2 Mode 1

Mode 2 Mode 1

99510

10511

I g(A

)

02468

100

100

200

300

40002468

1012

0

50

100

150

200

00848 00849 0085 00851 00852 00853 0085400847Time (s)

Vs 1

(V)

I s1

(A)

Vs 5

(V)

I s5

(A)


Mode 3 Mode 4

Mode 3 Mode 4

00949 0095 00951 00952 00953 0095400948Time (s)

02468

1012

0

100

200

300

40002468

1012

0

50

100

150

200

minus11

minus105

minus10

minus95

minus9

I g(A

)Vs 2

(V)

I s2

(A)

Vs 5

(V)

I s5

(A)






1


1



5






2


2


5


5





times104

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 3 35 40Frequency (Hz)

0

005

01

015

02

Mag

(A)

minus10

minus5

0

5

10

Grid

curr

ent (

A)


050

100150200250

Com

mon

mod

evo

ltage

(V)

011 012 013 014 015 016 01701Time (s)


011 012 013 014 015 016 01701

Time (s)


Para

sitic

capa

cito

rvo

ltage

(V)


times104


0010203

Leak

age c

urre

nt (A

)

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 30Frequency (Hz)

0

0005

001

0015

Leak

age c

urre

ntm

ag (A

)






4 Conclusion







References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Mode 2 Mode 1

Mode 2 Mode 1

99510

10511

I g(A

)

02468

100

100

200

300

40002468

1012

0

50

100

150

200

00848 00849 0085 00851 00852 00853 0085400847Time (s)

Vs 1

(V)

I s1

(A)

Vs 5

(V)

I s5

(A)


Mode 3 Mode 4

Mode 3 Mode 4

00949 0095 00951 00952 00953 0095400948Time (s)

02468

1012

0

100

200

300

40002468

1012

0

50

100

150

200

minus11

minus105

minus10

minus95

minus9

I g(A

)Vs 2

(V)

I s2

(A)

Vs 5

(V)

I s5

(A)






1


1



5






2


2


5


5





times104

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 3 35 40Frequency (Hz)

0

005

01

015

02

Mag

(A)

minus10

minus5

0

5

10

Grid

curr

ent (

A)


050

100150200250

Com

mon

mod

evo

ltage

(V)

011 012 013 014 015 016 01701Time (s)


011 012 013 014 015 016 01701

Time (s)


Para

sitic

capa

cito

rvo

ltage

(V)


times104


0010203

Leak

age c

urre

nt (A

)

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 30Frequency (Hz)

0

0005

001

0015

Leak

age c

urre

ntm

ag (A

)






4 Conclusion







References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











times104

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 3 35 40Frequency (Hz)

0

005

01

015

02

Mag

(A)

minus10

minus5

0

5

10

Grid

curr

ent (

A)


050

100150200250

Com

mon

mod

evo

ltage

(V)

011 012 013 014 015 016 01701Time (s)


011 012 013 014 015 016 01701

Time (s)


Para

sitic

capa

cito

rvo

ltage

(V)


times104


0010203

Leak

age c

urre

nt (A

)

011 012 013 014 015 016 01701Time (s)

05 1 15 2 25 30Frequency (Hz)

0

0005

001

0015

Leak

age c

urre

ntm

ag (A

)






4 Conclusion







References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a novel inverter topology for single

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