research article space vector modulation technique for 3...
TRANSCRIPT
Research ArticleSpace Vector Modulation Technique for 3-Level NPC Converterwith Constant Switching Frequency
Imen Ouerdani1 Hafedh Ben Abdelghani1 Afef Bennani Ben Abdelghani12
Daniel Montesinos-Miracle3 and Ilhem Slama-Belkhodja1
1Ecole Nationale drsquoIngenieurs de Tunis LR11ES15 Laboratoire de Systemes Electriques Universite de Tunis El Manar1002 Tunis Tunisia2Institut National des Sciences Appliquees et de Technologie (INSAT) Universite Tunis Carthage Centre Urbain NordBP 676 1080 Tunis Tunisia3Centre drsquoInnovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA-UPC) Departament drsquoEnginyeria ElectricaUniversitat Politecnica de Catalunya ETS drsquoEnginyeria Industrial de Barcelona Avenida Diagonal 647 Pl 2 08028 Barcelona Spain
Correspondence should be addressed to Imen Ouerdani imenwardanigmailcom
Received 23 April 2016 Accepted 25 May 2016
Academic Editor Francesco Profumo
Copyright copy 2016 Imen Ouerdani 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
This paper presents a simple Space Vector Modulation (SVM) methodology for a three-level NPC converter Nearest three vectors(NTV) and corresponding duty cycles are deduced through simple generic mathematical expressions Extra degrees of freedom ofNPC converter are used to fully benefit from SVM advantages and to control the switching frequency Simulation and experimentalresults are presented and discussed to validate the proposed methodology
1 Introduction
Power conversion investigation attracted attention particu-larly inMediumVoltageHigh Power ranges [1 2] During thethree last decades advancements in power electronics fieldshave led to innovative converter topologies called multilevelconverters [3 4] In fact compared to classical two-levelconverters multilevel converters are an attractive solutionsince they support higher operation voltages reduce com-mon mode voltages minimize output current and voltagedistortions and optimize output filter size and cost One ofthe most widely used and investigated multilevel topologiesis the neutral point clamped converter This topology wasfirstly introduced by Richard Baker in the early eighties [5]Later on several converters based on the NPCwere proposedsuch as the Active NPC [6ndash9] and the Optimized NPC [10ndash12] These converters are classified as the Diode ClampedConverters [13]The three-phase119873-level NPC converter uses(119873minus1) series-connected capacitors to divide the DC bus intoa set of intermediary voltage levels as presented in Figure 1
Simultaneously classical modulation algorithms pro-posed for two-level converters such as Pulse Width Mod-ulation (PWM) [14] hysteresis current control [15] andselective harmonic elimination [16] have been extended tomultilevel topologies Among the proposed algorithms theSpace Vector Modulation (SVM) is the most widely used dueto its better utilization of theDC bus [9] and higher harmonicperformances in linear and nonlinear operating zones [17 18]compared to conventional PWM strategies Detecting thenearest three vectors (NTV) among the numerous availableones selecting and fully defining the corresponding switchesduty cycles with respect to possible additional criteria arethe main issues of SVM technique in multilevel convertercontext
In this paper a simple approach for a 3-level SpaceVectorModulation technique available for theNPC converteris presented In the proposed method the nearest threevectors and their corresponding on-times application aresimply expressed using generic mathematical expressionsThe choice of the Phase Level Sequence (PLS) is used as
Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2016 Article ID 6478751 13 pageshttpdxdoiorg10115520166478751
2 Advances in Power Electronics
Vdc
Vs
+
D1
C1
C2
DNminus3
DNminus2
D998400Nminus3
D998400Nminus2
D9984001
n1
nNminus3
nNminus2
CNminus3
CNminus2
CNminus1TNminus1
TNminus2
T2
T1
T1
T2
Tnminus1
Tnminus2
Figure 1119873-level neutral point clamped inverter leg
an extra degree of freedom in order to control the switchingfrequency Simulation and experimental results are presentedto verify the effectiveness of the proposed SVM strategy
2 NPC Converter and Space VectorModulation (SVM)
21 Neutral Point ClampedConverter Onephase of an 119899-levelneutral point clamped inverter consists of (119899 minus 1) capacitors6times(119899minus1) power switches and 6times(119899minus2) clamping diodes andis able to generate (119899 minus 2) capacitive midpoints The outputvoltage 119881
119904is equal to the voltage of the capacitive midpoint
connected to it Hence 119881119904can take (119899 minus 2) values as
119881dc119899 minus 1
2119881dc119899 minus 1
sdot sdot sdot119895 sdot 119881dc119899 minus 1
sdot sdot sdot(119899 minus 2)119881dc119899 minus 1
(1)
In order to generate the output voltage119881119904 the IGBTs 119879
1to 119879119896
and119879119896+1
to119879119899minus1
must beONThe current is then flowing fromthe diodes 119863
119896through the switches 119879
1to 119879119896to the output
119881119904 It is to note that any other configuration is not permitted
and each voltage level is realized by an only one configuration[19 20] In this paper the triplet (119883119884 119885) called Phase LevelSequence (PLS) is introduced for a three-phase multilevelneutral point clamped inverters where 119883 (119884 and 119885 resp) isthe phase level of phase a (phase b and phase c resp) Three-phase 119899-level NPC converters are able to generate 1198993 PLS and(3119899(119899 minus 1) + 1) space vectors
Hence 3-phase 3-level NPC converter presented in Fig-ure 2 is able to generate 27 PLS and 19 space vectors
For a single phase phase level is equal to 0 when bothcommutation cells are OFF-switched and is equal to 2 whenboth commutation cells areON-switchedThe correspondingoutput voltage for phase level 0 is minus119881dc2 whereas thecorresponding output voltage for phase level 2 is equal to119881dc2 Intermediate level is equal to 1 and is obtained when
C1 C3 C5
C2 C4 C6
R L
O
abc
+
+
C1 C3 C5
C2 C4 C6
Vdc2
Vdc2
Figure 2 Three-phase 3-level NPC converter
(2 0 0)(1 0 0)
(2 1 1)
(0 0 0)(1 1 1)
(2 2 2)(1 2 2)
(0 1 1)(0 2 2)
(0 2 1)
(0 2 0) (1 2 0) (2 2 0)
(2 1 0)(1 1 0)(2 2 1)
(0 1 0)(1 2 1)
(0 1 2)
(0 0 2)(1 0 2) (2 0 2)
(2 0 1)(1 0 1)(2 1 2)
(0 0 1)(1 1 2)
M
120572
Figure 3 Three-level inverter space vector diagram
only one commutation cell is ON-switched in which case theoutput voltage is equal to 0
Figure 3 shows the (120572 120573) frame of a 3-phase NPC 3-levelconverter
22 Space Vector Modulation (SVM) For a three-phase two-level converter the aim of the Space Vector Modulation isto select the appropriate space vectors to apply and theirrespective application times [21 22] Given a voltage referencevector 119881lowast
119904 the SVM strategy selects the two nearest active
vectors (119881119896and119881119896+1
) and the zero vectors (0 0 0) and (1 1 1)as shown in Figure 4(a) The application times for these 4vectors are calculated using the volt-second balance as
119879119896+1119881119896+1
+ 119879119896119881119896+ (119879SVM minus (119879119896+1 + 119879119896)) sdot 1198810
= 119879SVM sdot 119881lowast
119904
(2)
where 119881119896 119881119896+1
and 1198810are space vectors 119879
119896and 119879
119896+1are the
application times corresponding to 119881119896and 119881
119896+1 respectively
and 119879SVM is the SVM period 119879SVM minus (119879119896+1
+ 119879119896) is the
application time of zero voltages during the first half of thistime slot (0 0 0) is applied and during the second half (1 1 1)is applied if symmetrical SVPWM technique is used
Advances in Power Electronics 3
(1 0 0)(0 0 0)(0 1 1)
(1 1 0)(0 1 0)
(1 0 1)(0 0 1)
(1 1 1)
Vlowasts
120573
(a)
Vlowasts
Vk+1
VkTk middot Vk
Tk+1 middot Vk+1
V0
(b)
Figure 4 (a) Two-level inverter space vector diagram (b) SVM for a two-level inverter
Compared to conventional PWM strategies the SpaceVectorModulation leads to better dynamic performances anda higher modulation index even if the calculation complexityis comparatively increased
For an 119899-level converter the increased number of spacevectors and switching states further enhances the dynamicperformances but needs additional calculation capabilitiesand introduces considerable implementation complexity
In this paper a simple approach to implement a three-level SVM algorithm using mathematical analysis of theobtained (120572 120573) frame is proposed Active vectors to beapplied switching states and IGBT on-times calculation areeasily deduced using the proposed method
3 Proposed Algorithm
Figure 5 shows the block diagram of the proposed methodwhere the main task of each step is written in bold andcriterion for each task is written in italic in the neighboringbox
31 Step 1 Localization of 119881lowast119904 The aim of 119881lowast
119904Localization
block is to identify the appropriate three vectors 119881119894 119894 =
1 2 3 to apply and consequently their corresponding PLSin order to generate an output voltage with a mean value onthe switching period equal to the reference voltageThe spacevectors needed for the SVM are the nearest three vectors to119881lowast
119904In order to localize the reference voltage vector its mod-
ule and phase noted respectively as 119881lowast119904 and 120579
119904 are used
They are calculated using basic (abc-120572120573) transformationThe (120572 120573) frame is divided into 6 sectors and 4 quadrants
according to Figure 6 This sectorization represents the firststep to deduce to which triangle (among the available 24ones) the reference voltage vector belongs Once this triangleselected a lookup table gives the three nearest voltage vectorsthe inverter must generate
Quadrant
Sector
Triangle
calculation
PLS sequencing
PLS dispatching
Symmetric waveforms
Spectrum quality
Step 1
Step 2Primary on-times
calculation
Step 3Secondary on-times
calculation
Step 4Control signal
generation
Vlowasts localization
Active Vi
Ti
SCi dispatching within TSVM
fsw control
Vs = Vlowasts
Vlowast1 Vlowast
2 Vlowast3
Figure 5 Block diagram of the proposed scheme
Depending on the modulation depth119898 specific trianglesare used if 0 lt 119898 lt 075 space vector 119881
119904crosses triangles
T1 T5 T9 T13 T17 and T21 and if 075 lt 119898 lt 115 theremaining triangles (T2 T3 T4 T6 T7 T8 T10 T11 T12T14 T15 T16 T18 T19 T20 T22 T23 and T24) are used Itis to be noted that the modulation index 119898 = 119881
lowast
119904119881dc and
the maximum modulation index 119898 = 115 is obtained when119881lowast
119904 = 119881dcradic3
4 Advances in Power Electronics
Q1
Q4
Q2
Q3
120572
120573
(a)
S2
S1S3
S4
S5
S6
120572
120573
(b)
18
1
13
9
87
2
4
35
6
11
10
12
242317
19
2115
14
1620
22
120572
120573
(c)
Figure 6 (120572 120573) frame sectorization (a) 4 quadrants (b) 6 sectors (c) 24 triangles
2
610
14
1822
12
13 2117
5
7
311
23
19
15
84
12
24
1620
V1V1
V1
V1
V1V1
V1V1
V1
V1
V1V1
V1
V1 V1
V1
V1
V1
V1
V1
V1
V1
V2 V2
V2
V2V2
V2
V2
V2
V2V2
V2V2
V2
V2
V2
V2
V2
V2V2
V2
V2
V2
V3
V3V3 V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3V3
V3
V3
V3
120573
120573
120572
120572
Figure 7 Triangles division into 4 families
32 Step 2 Primary ON-Times Calculation The ldquoPrimaryON-Times Calculationrdquo block aims to determine the on-timefor each of the three vectors 119881
119894 119894 = 1 2 3 that is the
activation time over switching period 119879SVM Step 2 outputsare as follows
(i) The corresponding on-time 119879119894 119894 = 1 3 for the
three needed vectors the converter has to perform onthe next 119879SVMThese vectors 119881
119894 119894 = 1 3 correspond to the
localized trianglersquos vertices
(ii) The PLS leading to the specified space vectorsThe PLS choice affects the converter switching fre-quency
To perform a rigorous on-times calculation fine modelingof the three-level converter voltage vectors is needed Theproposed algorithm divides the 24 triangles among 4 familiesgiven by Figure 7 In fact the 3 vectors of all the trianglesbelonging to the same family can be expressed using a uniquegeneric form Thus on times are deduced as generic formsdepending on the selected family
Advances in Power Electronics 5
1
13
9
8
7
2
4
35
6
11
10
12
242317
19
2115
14
1618 20
22
120573
120572
(a)
19
13 21
17
5
V1
V1
V1
V1
V1V1 V2
V2
V2V2
V2
V2
V3
(b)
Figure 8 Family 1 (a) triangles (b) zoom on family 1 space vectors
321 119881119894Generic Expressions Family 1 is formed by triangles
1 5 9 13 17 and 21 as shown in Figure 8 1198811 1198812 and 119881
3
are represented for each triangle belonging to this family andtheir expressions are
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813= 0
(3)
where 119896 is the sectorrsquos index corresponding to each triangleFamily 2 is formed by triangles 2 6 10 14 18 and 22 as
shown in Figure 91198811 1198812 and 119881
3corresponding to this family are given
by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=2119881dc3119890119895(119896minus1)(1205873)
=2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(4)
2
610
14
1822
V1V1
V1
V1
V1
V1
V2V2
V2
V2 V2
V2
V3
V3
V3V3
V3
120573
120572
Figure 9 Family 2 space vectors
Family 3 is formed by triangles 3 7 11 15 19 and 23 as shownin Figure 10 and associated space vectors are given by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(5)
The remaining triangles labeled 4 8 12 16 20 and 24 formfamily 4 as shown in Figure 11
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
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Active and Passive Electronic Components
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
2 Advances in Power Electronics
Vdc
Vs
+
D1
C1
C2
DNminus3
DNminus2
D998400Nminus3
D998400Nminus2
D9984001
n1
nNminus3
nNminus2
CNminus3
CNminus2
CNminus1TNminus1
TNminus2
T2
T1
T1
T2
Tnminus1
Tnminus2
Figure 1119873-level neutral point clamped inverter leg
an extra degree of freedom in order to control the switchingfrequency Simulation and experimental results are presentedto verify the effectiveness of the proposed SVM strategy
2 NPC Converter and Space VectorModulation (SVM)
21 Neutral Point ClampedConverter Onephase of an 119899-levelneutral point clamped inverter consists of (119899 minus 1) capacitors6times(119899minus1) power switches and 6times(119899minus2) clamping diodes andis able to generate (119899 minus 2) capacitive midpoints The outputvoltage 119881
119904is equal to the voltage of the capacitive midpoint
connected to it Hence 119881119904can take (119899 minus 2) values as
119881dc119899 minus 1
2119881dc119899 minus 1
sdot sdot sdot119895 sdot 119881dc119899 minus 1
sdot sdot sdot(119899 minus 2)119881dc119899 minus 1
(1)
In order to generate the output voltage119881119904 the IGBTs 119879
1to 119879119896
and119879119896+1
to119879119899minus1
must beONThe current is then flowing fromthe diodes 119863
119896through the switches 119879
1to 119879119896to the output
119881119904 It is to note that any other configuration is not permitted
and each voltage level is realized by an only one configuration[19 20] In this paper the triplet (119883119884 119885) called Phase LevelSequence (PLS) is introduced for a three-phase multilevelneutral point clamped inverters where 119883 (119884 and 119885 resp) isthe phase level of phase a (phase b and phase c resp) Three-phase 119899-level NPC converters are able to generate 1198993 PLS and(3119899(119899 minus 1) + 1) space vectors
Hence 3-phase 3-level NPC converter presented in Fig-ure 2 is able to generate 27 PLS and 19 space vectors
For a single phase phase level is equal to 0 when bothcommutation cells are OFF-switched and is equal to 2 whenboth commutation cells areON-switchedThe correspondingoutput voltage for phase level 0 is minus119881dc2 whereas thecorresponding output voltage for phase level 2 is equal to119881dc2 Intermediate level is equal to 1 and is obtained when
C1 C3 C5
C2 C4 C6
R L
O
abc
+
+
C1 C3 C5
C2 C4 C6
Vdc2
Vdc2
Figure 2 Three-phase 3-level NPC converter
(2 0 0)(1 0 0)
(2 1 1)
(0 0 0)(1 1 1)
(2 2 2)(1 2 2)
(0 1 1)(0 2 2)
(0 2 1)
(0 2 0) (1 2 0) (2 2 0)
(2 1 0)(1 1 0)(2 2 1)
(0 1 0)(1 2 1)
(0 1 2)
(0 0 2)(1 0 2) (2 0 2)
(2 0 1)(1 0 1)(2 1 2)
(0 0 1)(1 1 2)
M
120572
Figure 3 Three-level inverter space vector diagram
only one commutation cell is ON-switched in which case theoutput voltage is equal to 0
Figure 3 shows the (120572 120573) frame of a 3-phase NPC 3-levelconverter
22 Space Vector Modulation (SVM) For a three-phase two-level converter the aim of the Space Vector Modulation isto select the appropriate space vectors to apply and theirrespective application times [21 22] Given a voltage referencevector 119881lowast
119904 the SVM strategy selects the two nearest active
vectors (119881119896and119881119896+1
) and the zero vectors (0 0 0) and (1 1 1)as shown in Figure 4(a) The application times for these 4vectors are calculated using the volt-second balance as
119879119896+1119881119896+1
+ 119879119896119881119896+ (119879SVM minus (119879119896+1 + 119879119896)) sdot 1198810
= 119879SVM sdot 119881lowast
119904
(2)
where 119881119896 119881119896+1
and 1198810are space vectors 119879
119896and 119879
119896+1are the
application times corresponding to 119881119896and 119881
119896+1 respectively
and 119879SVM is the SVM period 119879SVM minus (119879119896+1
+ 119879119896) is the
application time of zero voltages during the first half of thistime slot (0 0 0) is applied and during the second half (1 1 1)is applied if symmetrical SVPWM technique is used
Advances in Power Electronics 3
(1 0 0)(0 0 0)(0 1 1)
(1 1 0)(0 1 0)
(1 0 1)(0 0 1)
(1 1 1)
Vlowasts
120573
(a)
Vlowasts
Vk+1
VkTk middot Vk
Tk+1 middot Vk+1
V0
(b)
Figure 4 (a) Two-level inverter space vector diagram (b) SVM for a two-level inverter
Compared to conventional PWM strategies the SpaceVectorModulation leads to better dynamic performances anda higher modulation index even if the calculation complexityis comparatively increased
For an 119899-level converter the increased number of spacevectors and switching states further enhances the dynamicperformances but needs additional calculation capabilitiesand introduces considerable implementation complexity
In this paper a simple approach to implement a three-level SVM algorithm using mathematical analysis of theobtained (120572 120573) frame is proposed Active vectors to beapplied switching states and IGBT on-times calculation areeasily deduced using the proposed method
3 Proposed Algorithm
Figure 5 shows the block diagram of the proposed methodwhere the main task of each step is written in bold andcriterion for each task is written in italic in the neighboringbox
31 Step 1 Localization of 119881lowast119904 The aim of 119881lowast
119904Localization
block is to identify the appropriate three vectors 119881119894 119894 =
1 2 3 to apply and consequently their corresponding PLSin order to generate an output voltage with a mean value onthe switching period equal to the reference voltageThe spacevectors needed for the SVM are the nearest three vectors to119881lowast
119904In order to localize the reference voltage vector its mod-
ule and phase noted respectively as 119881lowast119904 and 120579
119904 are used
They are calculated using basic (abc-120572120573) transformationThe (120572 120573) frame is divided into 6 sectors and 4 quadrants
according to Figure 6 This sectorization represents the firststep to deduce to which triangle (among the available 24ones) the reference voltage vector belongs Once this triangleselected a lookup table gives the three nearest voltage vectorsthe inverter must generate
Quadrant
Sector
Triangle
calculation
PLS sequencing
PLS dispatching
Symmetric waveforms
Spectrum quality
Step 1
Step 2Primary on-times
calculation
Step 3Secondary on-times
calculation
Step 4Control signal
generation
Vlowasts localization
Active Vi
Ti
SCi dispatching within TSVM
fsw control
Vs = Vlowasts
Vlowast1 Vlowast
2 Vlowast3
Figure 5 Block diagram of the proposed scheme
Depending on the modulation depth119898 specific trianglesare used if 0 lt 119898 lt 075 space vector 119881
119904crosses triangles
T1 T5 T9 T13 T17 and T21 and if 075 lt 119898 lt 115 theremaining triangles (T2 T3 T4 T6 T7 T8 T10 T11 T12T14 T15 T16 T18 T19 T20 T22 T23 and T24) are used Itis to be noted that the modulation index 119898 = 119881
lowast
119904119881dc and
the maximum modulation index 119898 = 115 is obtained when119881lowast
119904 = 119881dcradic3
4 Advances in Power Electronics
Q1
Q4
Q2
Q3
120572
120573
(a)
S2
S1S3
S4
S5
S6
120572
120573
(b)
18
1
13
9
87
2
4
35
6
11
10
12
242317
19
2115
14
1620
22
120572
120573
(c)
Figure 6 (120572 120573) frame sectorization (a) 4 quadrants (b) 6 sectors (c) 24 triangles
2
610
14
1822
12
13 2117
5
7
311
23
19
15
84
12
24
1620
V1V1
V1
V1
V1V1
V1V1
V1
V1
V1V1
V1
V1 V1
V1
V1
V1
V1
V1
V1
V1
V2 V2
V2
V2V2
V2
V2
V2
V2V2
V2V2
V2
V2
V2
V2
V2
V2V2
V2
V2
V2
V3
V3V3 V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3V3
V3
V3
V3
120573
120573
120572
120572
Figure 7 Triangles division into 4 families
32 Step 2 Primary ON-Times Calculation The ldquoPrimaryON-Times Calculationrdquo block aims to determine the on-timefor each of the three vectors 119881
119894 119894 = 1 2 3 that is the
activation time over switching period 119879SVM Step 2 outputsare as follows
(i) The corresponding on-time 119879119894 119894 = 1 3 for the
three needed vectors the converter has to perform onthe next 119879SVMThese vectors 119881
119894 119894 = 1 3 correspond to the
localized trianglersquos vertices
(ii) The PLS leading to the specified space vectorsThe PLS choice affects the converter switching fre-quency
To perform a rigorous on-times calculation fine modelingof the three-level converter voltage vectors is needed Theproposed algorithm divides the 24 triangles among 4 familiesgiven by Figure 7 In fact the 3 vectors of all the trianglesbelonging to the same family can be expressed using a uniquegeneric form Thus on times are deduced as generic formsdepending on the selected family
Advances in Power Electronics 5
1
13
9
8
7
2
4
35
6
11
10
12
242317
19
2115
14
1618 20
22
120573
120572
(a)
19
13 21
17
5
V1
V1
V1
V1
V1V1 V2
V2
V2V2
V2
V2
V3
(b)
Figure 8 Family 1 (a) triangles (b) zoom on family 1 space vectors
321 119881119894Generic Expressions Family 1 is formed by triangles
1 5 9 13 17 and 21 as shown in Figure 8 1198811 1198812 and 119881
3
are represented for each triangle belonging to this family andtheir expressions are
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813= 0
(3)
where 119896 is the sectorrsquos index corresponding to each triangleFamily 2 is formed by triangles 2 6 10 14 18 and 22 as
shown in Figure 91198811 1198812 and 119881
3corresponding to this family are given
by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=2119881dc3119890119895(119896minus1)(1205873)
=2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(4)
2
610
14
1822
V1V1
V1
V1
V1
V1
V2V2
V2
V2 V2
V2
V3
V3
V3V3
V3
120573
120572
Figure 9 Family 2 space vectors
Family 3 is formed by triangles 3 7 11 15 19 and 23 as shownin Figure 10 and associated space vectors are given by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(5)
The remaining triangles labeled 4 8 12 16 20 and 24 formfamily 4 as shown in Figure 11
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
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Active and Passive Electronic Components
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RotatingMachinery
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Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
Advances in Power Electronics 3
(1 0 0)(0 0 0)(0 1 1)
(1 1 0)(0 1 0)
(1 0 1)(0 0 1)
(1 1 1)
Vlowasts
120573
(a)
Vlowasts
Vk+1
VkTk middot Vk
Tk+1 middot Vk+1
V0
(b)
Figure 4 (a) Two-level inverter space vector diagram (b) SVM for a two-level inverter
Compared to conventional PWM strategies the SpaceVectorModulation leads to better dynamic performances anda higher modulation index even if the calculation complexityis comparatively increased
For an 119899-level converter the increased number of spacevectors and switching states further enhances the dynamicperformances but needs additional calculation capabilitiesand introduces considerable implementation complexity
In this paper a simple approach to implement a three-level SVM algorithm using mathematical analysis of theobtained (120572 120573) frame is proposed Active vectors to beapplied switching states and IGBT on-times calculation areeasily deduced using the proposed method
3 Proposed Algorithm
Figure 5 shows the block diagram of the proposed methodwhere the main task of each step is written in bold andcriterion for each task is written in italic in the neighboringbox
31 Step 1 Localization of 119881lowast119904 The aim of 119881lowast
119904Localization
block is to identify the appropriate three vectors 119881119894 119894 =
1 2 3 to apply and consequently their corresponding PLSin order to generate an output voltage with a mean value onthe switching period equal to the reference voltageThe spacevectors needed for the SVM are the nearest three vectors to119881lowast
119904In order to localize the reference voltage vector its mod-
ule and phase noted respectively as 119881lowast119904 and 120579
119904 are used
They are calculated using basic (abc-120572120573) transformationThe (120572 120573) frame is divided into 6 sectors and 4 quadrants
according to Figure 6 This sectorization represents the firststep to deduce to which triangle (among the available 24ones) the reference voltage vector belongs Once this triangleselected a lookup table gives the three nearest voltage vectorsthe inverter must generate
Quadrant
Sector
Triangle
calculation
PLS sequencing
PLS dispatching
Symmetric waveforms
Spectrum quality
Step 1
Step 2Primary on-times
calculation
Step 3Secondary on-times
calculation
Step 4Control signal
generation
Vlowasts localization
Active Vi
Ti
SCi dispatching within TSVM
fsw control
Vs = Vlowasts
Vlowast1 Vlowast
2 Vlowast3
Figure 5 Block diagram of the proposed scheme
Depending on the modulation depth119898 specific trianglesare used if 0 lt 119898 lt 075 space vector 119881
119904crosses triangles
T1 T5 T9 T13 T17 and T21 and if 075 lt 119898 lt 115 theremaining triangles (T2 T3 T4 T6 T7 T8 T10 T11 T12T14 T15 T16 T18 T19 T20 T22 T23 and T24) are used Itis to be noted that the modulation index 119898 = 119881
lowast
119904119881dc and
the maximum modulation index 119898 = 115 is obtained when119881lowast
119904 = 119881dcradic3
4 Advances in Power Electronics
Q1
Q4
Q2
Q3
120572
120573
(a)
S2
S1S3
S4
S5
S6
120572
120573
(b)
18
1
13
9
87
2
4
35
6
11
10
12
242317
19
2115
14
1620
22
120572
120573
(c)
Figure 6 (120572 120573) frame sectorization (a) 4 quadrants (b) 6 sectors (c) 24 triangles
2
610
14
1822
12
13 2117
5
7
311
23
19
15
84
12
24
1620
V1V1
V1
V1
V1V1
V1V1
V1
V1
V1V1
V1
V1 V1
V1
V1
V1
V1
V1
V1
V1
V2 V2
V2
V2V2
V2
V2
V2
V2V2
V2V2
V2
V2
V2
V2
V2
V2V2
V2
V2
V2
V3
V3V3 V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3V3
V3
V3
V3
120573
120573
120572
120572
Figure 7 Triangles division into 4 families
32 Step 2 Primary ON-Times Calculation The ldquoPrimaryON-Times Calculationrdquo block aims to determine the on-timefor each of the three vectors 119881
119894 119894 = 1 2 3 that is the
activation time over switching period 119879SVM Step 2 outputsare as follows
(i) The corresponding on-time 119879119894 119894 = 1 3 for the
three needed vectors the converter has to perform onthe next 119879SVMThese vectors 119881
119894 119894 = 1 3 correspond to the
localized trianglersquos vertices
(ii) The PLS leading to the specified space vectorsThe PLS choice affects the converter switching fre-quency
To perform a rigorous on-times calculation fine modelingof the three-level converter voltage vectors is needed Theproposed algorithm divides the 24 triangles among 4 familiesgiven by Figure 7 In fact the 3 vectors of all the trianglesbelonging to the same family can be expressed using a uniquegeneric form Thus on times are deduced as generic formsdepending on the selected family
Advances in Power Electronics 5
1
13
9
8
7
2
4
35
6
11
10
12
242317
19
2115
14
1618 20
22
120573
120572
(a)
19
13 21
17
5
V1
V1
V1
V1
V1V1 V2
V2
V2V2
V2
V2
V3
(b)
Figure 8 Family 1 (a) triangles (b) zoom on family 1 space vectors
321 119881119894Generic Expressions Family 1 is formed by triangles
1 5 9 13 17 and 21 as shown in Figure 8 1198811 1198812 and 119881
3
are represented for each triangle belonging to this family andtheir expressions are
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813= 0
(3)
where 119896 is the sectorrsquos index corresponding to each triangleFamily 2 is formed by triangles 2 6 10 14 18 and 22 as
shown in Figure 91198811 1198812 and 119881
3corresponding to this family are given
by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=2119881dc3119890119895(119896minus1)(1205873)
=2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(4)
2
610
14
1822
V1V1
V1
V1
V1
V1
V2V2
V2
V2 V2
V2
V3
V3
V3V3
V3
120573
120572
Figure 9 Family 2 space vectors
Family 3 is formed by triangles 3 7 11 15 19 and 23 as shownin Figure 10 and associated space vectors are given by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(5)
The remaining triangles labeled 4 8 12 16 20 and 24 formfamily 4 as shown in Figure 11
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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DistributedSensor Networks
International Journal of
4 Advances in Power Electronics
Q1
Q4
Q2
Q3
120572
120573
(a)
S2
S1S3
S4
S5
S6
120572
120573
(b)
18
1
13
9
87
2
4
35
6
11
10
12
242317
19
2115
14
1620
22
120572
120573
(c)
Figure 6 (120572 120573) frame sectorization (a) 4 quadrants (b) 6 sectors (c) 24 triangles
2
610
14
1822
12
13 2117
5
7
311
23
19
15
84
12
24
1620
V1V1
V1
V1
V1V1
V1V1
V1
V1
V1V1
V1
V1 V1
V1
V1
V1
V1
V1
V1
V1
V2 V2
V2
V2V2
V2
V2
V2
V2V2
V2V2
V2
V2
V2
V2
V2
V2V2
V2
V2
V2
V3
V3V3 V3
V3
V3
V3
V3
V3
V3
V3
V3
V3
V3V3
V3
V3
V3
120573
120573
120572
120572
Figure 7 Triangles division into 4 families
32 Step 2 Primary ON-Times Calculation The ldquoPrimaryON-Times Calculationrdquo block aims to determine the on-timefor each of the three vectors 119881
119894 119894 = 1 2 3 that is the
activation time over switching period 119879SVM Step 2 outputsare as follows
(i) The corresponding on-time 119879119894 119894 = 1 3 for the
three needed vectors the converter has to perform onthe next 119879SVMThese vectors 119881
119894 119894 = 1 3 correspond to the
localized trianglersquos vertices
(ii) The PLS leading to the specified space vectorsThe PLS choice affects the converter switching fre-quency
To perform a rigorous on-times calculation fine modelingof the three-level converter voltage vectors is needed Theproposed algorithm divides the 24 triangles among 4 familiesgiven by Figure 7 In fact the 3 vectors of all the trianglesbelonging to the same family can be expressed using a uniquegeneric form Thus on times are deduced as generic formsdepending on the selected family
Advances in Power Electronics 5
1
13
9
8
7
2
4
35
6
11
10
12
242317
19
2115
14
1618 20
22
120573
120572
(a)
19
13 21
17
5
V1
V1
V1
V1
V1V1 V2
V2
V2V2
V2
V2
V3
(b)
Figure 8 Family 1 (a) triangles (b) zoom on family 1 space vectors
321 119881119894Generic Expressions Family 1 is formed by triangles
1 5 9 13 17 and 21 as shown in Figure 8 1198811 1198812 and 119881
3
are represented for each triangle belonging to this family andtheir expressions are
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813= 0
(3)
where 119896 is the sectorrsquos index corresponding to each triangleFamily 2 is formed by triangles 2 6 10 14 18 and 22 as
shown in Figure 91198811 1198812 and 119881
3corresponding to this family are given
by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=2119881dc3119890119895(119896minus1)(1205873)
=2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(4)
2
610
14
1822
V1V1
V1
V1
V1
V1
V2V2
V2
V2 V2
V2
V3
V3
V3V3
V3
120573
120572
Figure 9 Family 2 space vectors
Family 3 is formed by triangles 3 7 11 15 19 and 23 as shownin Figure 10 and associated space vectors are given by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(5)
The remaining triangles labeled 4 8 12 16 20 and 24 formfamily 4 as shown in Figure 11
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
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Electrical and Computer Engineering
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
Advances in Power Electronics 5
1
13
9
8
7
2
4
35
6
11
10
12
242317
19
2115
14
1618 20
22
120573
120572
(a)
19
13 21
17
5
V1
V1
V1
V1
V1V1 V2
V2
V2V2
V2
V2
V3
(b)
Figure 8 Family 1 (a) triangles (b) zoom on family 1 space vectors
321 119881119894Generic Expressions Family 1 is formed by triangles
1 5 9 13 17 and 21 as shown in Figure 8 1198811 1198812 and 119881
3
are represented for each triangle belonging to this family andtheir expressions are
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813= 0
(3)
where 119896 is the sectorrsquos index corresponding to each triangleFamily 2 is formed by triangles 2 6 10 14 18 and 22 as
shown in Figure 91198811 1198812 and 119881
3corresponding to this family are given
by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=2119881dc3119890119895(119896minus1)(1205873)
=2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(4)
2
610
14
1822
V1V1
V1
V1
V1
V1
V2V2
V2
V2 V2
V2
V3
V3
V3V3
V3
120573
120572
Figure 9 Family 2 space vectors
Family 3 is formed by triangles 3 7 11 15 19 and 23 as shownin Figure 10 and associated space vectors are given by
1198811=119881dc3119890119895(119896minus1)(1205873)
=119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
)
1198812=119881dc3119890119895(119896)(1205873)
=119881dc3(
cos(1198961205873)
sin(1198961205873)
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(5)
The remaining triangles labeled 4 8 12 16 20 and 24 formfamily 4 as shown in Figure 11
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
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VLSI Design
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Shock and Vibration
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Electrical and Computer Engineering
Journal of
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Volume 2014
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SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Advances in Power Electronics
7
311
23
19
15
V1
V1
V1
V1
V1
V1
V2V2
V2V2
V2
V2
V3
V3
V3
V3
120573
120572
Figure 10 Family 3 space vectors
Family 4 119881119894expressions are
1198811=119881dc3119890119895119896(1205873)
=119881dc3(
cos 1198961205873
sin 1198961205873
)
1198812=2119881dc3119890119895119896(1205873)
=2119881dc3
(
cos 1198961205873
sin 1198961205873
)
1198813=119881dcradic3
119890119895(119896minus05)(1205873)
=119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
)
(6)
322 119879119894Calculation 119879
119894correspond to the application time
of119881119894 119894 = 1 2 3They are the solutions of the three-level volt-
second balance given by1198791sdot 1198811+ 1198792sdot 1198812+ 1198793sdot 1198813= 119879SVM sdot 119881
lowast
119904(7)
and verifying1198791+ 1198792+ 1198793= 119879SVM (8)
The resolution of (7) and (8) for given 1198811 1198812 and 119881
3can
lead to a potentially complex calculation But thanks to theproposed families repartition described above 119879
119894calculation
can be easily performed As an example we detail this step forfamily 2
The substitution of (4) in (7) leads to
119879SVM sdot 119881119904119898 (cos 120579119904
sin 120579119904
) =[[
[
119881dc3(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198791
+2119881dc3
(
cos (119896 minus 1) 1205873
sin (119896 minus 1) 1205873
) sdot 1198792
+119881dcradic3
(
cos (119896 minus 05) 1205873
sin (119896 minus 05) 1205873
) sdot 1198793
]]
]
(9)
84
12
24
120
V1V1
V1
V1
V1
V1
V2
V2
V2V2
V2
V2
V3V3
V3
V3 V3
V3
120573
120572
Figure 11 Family 4 space vectors
Consequently
(
cos 120579119904
sin 120579119904
) =119881dc
3119879SVM sdot 119881119904119898sdot 119861 sdot (
1198791+ 21198792
radic3 sdot 1198793
) (10)
where
119861 = (
cos (119896 minus 1) 1205873
cos (119896 minus 05) 1205873
sin (119896 minus 1) 1205873
sin (119896 minus 05) 1205873
)
119861minus1
= 2 sdot (
sin (119896 minus 05) 1205873minus cos (119896 minus 05) 120587
3
minus sin (119896 minus 1) 1205873
cos (119896 minus 1) 1205873
)
(11)
From (10) and (11) it can be deduced that
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dc[sin((119896 minus 05) 120587
3) cos 120579
119904
minus cos((119896 minus 05) 1205873) sin 120579
119904]
(12)
1198793=2radic3119879SVM sdot 119881119904119898
119881dc[cos((119896 minus 1) 120587
3) sin 120579
119904
minus sin((119896 minus 1) 1205873) cos 120579
119904]
(13)
Equation (13) gives
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin(120579
119904minus (119896 minus 1)
120587
3) (14)
To simplify 119879119894expressions we introduce 120579
119894defined as
120579119894= 120579119904minus (119896 minus 1)
120587
3 (15)
Considering (15) 1198793final expression is
1198793=2radic3119879SVM sdot 119881119904119898
119881dcsin (120579119894) (16)
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
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Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Civil EngineeringAdvances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
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Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Power Electronics 7
Table 1 On-times calculation
Family 1 2 3 41198791
1198791198961
119879SVM minus 1198793 minus 1198792 119879SVM minus 1198791198962 119879SVM minus 1198792 minus 1198793
1198792
1198791198962
minus119879SVM + 1198791198961 119879SVM minus 1198791198961 minus119879SVM + 1198791198962
1198793
119879SVM minus 1198791 minus 1198792 1198791198962
119879SVM minus 1198791 minus 1198792 1198791198961
After substituting (15) in (12) one can write
1198791+ 21198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) (17)
Comparing (7) and (17) gives
1198791=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 2119879
2
= 119879SVM minus 1198793 minus 1198792
(18)
Consequently
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793 (19)
The final 119879119894expressions for family 2 are as follows
1198791= 119879SVM minus 1198793 minus 1198792
1198792=6119879SVM sdot 119881119904119898
119881dcsin(120587
6minus 120579119894) minus 119879SVM + 1198793
1198793=2radic3 sdot 119879SVM sdot 119881119904119898
119881dcsin (120579119894)
(20)
The same computation method is applied for the remaining3 families Consequently the obtained on-times vectorsapplications for the 4 families are summarized in Table 1where
119860 =2 sdot radic3 sdot 119881
119904119898sdot 119879SVM
119881dc
1198791198961= 119860 sin(120587
3minus 120579119894)
1198791198962= 119860 sin 120579
119894
(21)
33 Step 3 SecondaryON-Times Calculation As explained inSection 1 each vector can be reached bymultiple PLSThe aimof Step 3 is to choose which PLS has to be activated over itscorresponding on-time Obviously the inverter performancesignificantly depends on this PLS management
The aim of the PLS management is to operate with fixedswitching frequency this is easily reachable when each IGBTswitches once during a switching period In fact for a selectedtriangle the available PLS are applied so they are all usedduring a switching period and the transition from one PLSto the other requires only one commutation For example if119881lowast
119904is localized in triangle 4 the order of application of PLS is
(1 1 0) 997888rarr (2 1 0) 997888rarr (2 2 0) 997888rarr (2 2 1)
997888rarr (2 2 0) 997888rarr (2 1 0) 997888rarr (1 1 0)
(22)
Triangle 3T14T14 T14 T14 T24T22T24 T32T32
SC1
SC2
SC3
SC4
SC5
SC6
Figure 12 Switching signals for triangle 3
34 Step 4 Dispatching within 119879119878119881119872
According to thedescribed PLS management strategy each PLS is realizedfirst by defining the appropriate space vector (119881
1 1198812 or
1198813) Since the previously calculated on-times 119879
119894are the total
application time for the space vector119881119894within 119879SVM they are
evenly spread over the switching period For example if 119881lowast119904
is localized in triangle 4 1198811(of family 4) is applied 3 times
during 119879SVM and1198812 and1198813must be applied twiceTherefore1198791is equally divided into 3 time slots each PLS that generates
1198811is applied during 119879
13 1198792and 119879
3are also divided into 2
time slots equal to 11987922 and 119879
32 respectively The resulting
control signals of triangle 3 are shown in Figure 12
4 Simulation Results
The three-level NPC converter is simulated using PSIMsoftware where the converter is connected to an RL load asshown in Figure 13 Simulation parameters are presented inTable 2
As mentioned in Section 31 the triangles covered bythe space vector reference depend on the modulation depth119898 Figure 13 shows the sectors and triangles covered by thespace vector for a reference magnitude equal to 100V Thusmodulation depth119898 is equal to119898 = 100270 = 037
For 119898 = 037 when the space vector is circulating insector 1 (2 3 4 5 and 6 resp) the triangle containing thespace vector is T1 (T5 T9 T13 T17 and T21 resp) It is tobe noted that all of the 6 triangles are covered during 20mscorresponding to the reference voltagersquos frequency of 50Hz
Similarly Figure 14 presents the sectors and trianglescovered by the space vector when the reference magnitudeis equal to 250 that is119898 = 092
The lookup table implemented on PSIM generates theappropriate control signals depending on the selected sectorand triangle Figure 15 presents the converterrsquos control signalswhen the reference space vector is in triangle 3 and theresulting phase voltage It is seen in Figure 15(b) that the
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Advances in Power Electronics
Sector
Triangle
002 0040Time (s)
002 0040Time (s)
0
2
4
6
05
10152025
Figure 13 Space vectorrsquos sector and triangle for119898 = 037
Table 2 Simulation parameters
Item ValueSwitching frequency 119879SVM 50120583sDC link voltage 540VLine frequency 50HzLoad resistor 119877 10ΩLoad inductor 119871 2mH
proposed sequencing of the PLS ensures that the phaselevel (consequently voltage level) changes only once percommutation cell
In order to validate the converter performances of theproposed scheme the output line currents are presented inFigure 16 Maximum magnitude is equal to 28 A Line-to-line and phase leg voltages are shown in Figure 17 Theexpected multilevel waveforms insure the power qualityimprovement This is illustrated by line a current spectrumgiven in Figure 18 THD value is estimated to be 069 Onthis spectrum the main harmonic is equal to 20 kHz whichcorresponds to the switching frequency 119891sw
It is to be noted that thanks to the proposed SVMstrategy the converterrsquos switching frequency 119891
119888is constant
Moreover when the modulation depth 119898 is greater than0575 119891
119888is almost equal to 50 of 119891sw Thus the analysis of
the whole switching signals proves that each IGBT switchesonce per 119879sw during almost half of the reference period Forexample for switching signal SC1 it switches once per 119879sw ifthe vector119881
119904belongs to triangles T2 T3 T4 T6 T7 T19 T20
T22 T23 and T24When119881119904belongs to T8 T10 T11 T12 T14
T15 T16 and T18 SC1 does not switchThis leads to a mean switching frequency of 119879sw2
Figure 19 gives the simulated switching frequency of thethree converter legs A 20ms window is used to perform theswitching frequency calculation
Sector
Triangle
05
10152025
0
2
4
6
0 004002Time (s)
0 004002Time (s)
Figure 14 Space vectorrsquos sector and triangle for119898 = 092
Switching frequency 119891sw of one leg is presented as theaverage of 119891sw of the IGBTs in the same leg They arecalculated as
119891sw-a =119891sw1 + 119891sw2
2
119891sw-b =119891sw3 + 119891sw4
2
119891sw-c =119891sw5 + 119891sw6
2
(23)
where 119891sw119894 is the switching frequency of IGBTi119891sw-a (119891sw-band 119891sw-c resp) is leg a (leg b and leg c resp) switchingfrequency
It is shown in Figure 18 that 119891sw for each leg is a constantequal to 104 kHz The additional 400Hz compared to theSVM design (one commutation per IGBT within one 119879SVM)is due to the 119881
119904transition from one triangle to another
5 Experimental Results
The proposed algorithm is experimentally tested A 4 kWthree-phase three-level NPC converter laboratory prototypewas conceived as shown in Figure 20 The setup param-eters are listed in Table 3 The power devices are theF3L150R07W2E3 B11 from Infineon The proposed modula-tion method is implemented with a TI TMS320F2809 DSP
Figure 21 shows the triangles crossed by 119881119904for different
modulation depths When 119898 lt 05 119881119904crosses 6 triangles
which are T1 T5 T9 T13 T17 and T21 (Figure 21(a)) When119898 gt 05 119881
119904crosses the remaining triangles (Figure 21(b))
Figure 22 shows the steady state waveforms of the line-to-line voltages and line a current
The spectral analysis of the line current given in Figure 23shows that first carrier harmonics appear at 20 kHz and then40 kHz according to theoretical and simulation investiga-tions
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Power Electronics 9
Phase a
Phase b
Phase c
00408
00408
00408
00408
00408
00408
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
0006040006020006Time (s)
minus300minus200minus100
0
000602 0006040006Time (s)
000602 0006040006Time (s)
000602 0006040006Time (s)
minus300
minus200
minus100
0
0
100
200
300
(a) (b)
Vao
Vbo
Vco
C1
C2
C3
C4
C5
C6
Figure 15 Triangle 3 simulation results (a) control signals (b) 3 phases output voltages
minus30minus20minus10
0102030
001 002 003 0040Time (s)
IaIbIc
Figure 16 Output line currents
Figure 24 shows the control signals of one commutationcell of leg a during two switching periodsThe control signalsare complementary and the IGBTs switch once per period
Table 3 Parameters of the 3-phase 3-level NPC converter
Item ValueRated active power 4 kWSwitching frequency 20 kHzLine frequency 50HzDC link voltage 400VLine current amplitude 10A
6 Conclusion
This paper proposes a Space Vector Modulation (SVM)technique for a three-level NPC converter The proposedmethod consists in dividing the space vector diagram intofour categories leading to a simple nearest three-vectordetection and on-times calculation Moreover the choice ofthe converter Phase Level Sequence is used as an extra degreeof freedom in order to control the converterrsquos switchingfrequency In fact once the vectors to apply are detectedtheir corresponding Phase Level Sequences are dispatched
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 Advances in Power Electronics
minus300minus200minus100
0100200300
001 002 003 0040Time (s)
Vao
(a)
minus600minus400minus200
0200400600
001 002 003 0040Time (s)
Uap
(b)
Figure 17 NPC voltages (a) simple phase voltage (b) line-to-line voltage
Frequency (KHz) Frequency (KHz)20 40
0
5
10
15
20
25
30
6000040000 800000 20000Frequency (Hz)
0
002
004
006
008
0
002
004
006
008
(a)
(b) (c)
Ia
Ia Ia
Figure 18 (a) Line a current spectral analysis (b) zoom around 20 kHz (c) zoom around 40 kHz
006 008 01004Time (s)
0K4K8K
12KFsw-a
(a)
006 008 01004Time (s)
0K4K8K
12KFsw-b
(b)
006 008 01004Time (s)
0K4K8K
12KFsw-c
(c)
Figure 19 NPC legs switching frequencies (a) leg a (b) leg b (c) leg c
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Power Electronics 11
Figure 20 The experimental setup
(a) (b)
Figure 21 SVM triangles when (a)119898 lt 05 and (b)119898 gt 05
Figure 22 Line-to-line voltages and line a current
among the SVM period such that they are all applied and thetransition from one PLS to the following requires only onecommutation This SVM can be extended to higher levels if
Figure 23 Spectral analysis of line a current
the space vector diagram available triangles are appropriatelydefined
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 Advances in Power Electronics
Figure 24 Leg a commutation cell control signals
The proposed methodology is verified by simulationand through a 4 kW experimental test bed the resultingoutput currents show a constant switching frequency and areduced current THD For applications such as renewableenergies this is a valuable improvement since it reduces thecommutation power losses and lowers the output and gridconnection filters size
Nomenclature
NPC Neutral point clampedSVM Space Vector Modulation119881dc DC bus voltage119881119904 Space vector output voltage
THD Total Harmonic DistortionSC119894 119894th cell control signal
119883119884 119885 Phase level related to phase a b and crespectively
PLS Phase Level Sequence119881lowast
119904 Reference voltage vector
119881119896 Nonzero voltage space vector in the (120572 120573)
frame119879119896 Application time related to 119881
119896
119879SVM SVM periodPWM Pulse Width Modulation120579119904 Phase of the reference voltage vector
119891sw Switching frequency
Competing Interests
The authors declare that there are no competing interestsrelated to this paper
Acknowledgments
This work was partially supported by Tunisian-French Coop-eration project CMCU 12G 1120 LAPLACE (University of
Toulouse) and LSE (University of Tunis El Manar) Particu-larly the authors gratefully acknowledge Professor FredericRichardeau Professor Maria David-Pietrzak and EngineerJean-Marc Blaquiere from LAPLACE-University of Toulousefor their support for the experimental validation
References
[1] M Amirabadi ldquoA new class of high-power-density universalpower convertersrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo15) pp 2596ndash2602 MontrealCanada September 2015
[2] S Soumiah R P Vengatesh and S E Rajan ldquoPerformanceevaluation of single switch high frequency resonant powerconverter for alternative energy sourcesrdquo in Proceedings of theIEEE International Conference on Circuit Power and ComputingTechnologies (ICCPCT rsquo15) pp 1ndash10 Nagercoil India March2015
[3] N Mittal B Singh S P Singh R Dixit and D Kumar ldquoMul-tilevel inverters a literature survey on topologies and controlstrategiesrdquo in Proceedings of the 2nd International Conferenceon Power Control and Embedded Systems (ICPCES rsquo12) pp 1ndash11 Allahabad India December 2012
[4] A Christe and D Dujic ldquoState-space modeling of modularmultilevel converters including line frequency transformerrdquo inProceedings of the 17th European Conference on Power Electron-ics and Applications (EPE rsquo15) pp 1ndash10 Geneva SwitzerlandSeptember 2015
[5] R H Baker ldquoBridge converter circuitrdquo US4270163 A 1981[6] L Ma X Jin T Kerekes M Liserre R Teodorescu and P
Rodriguez ldquoThe PWM strategies of grid-connected distributedgeneration active NPC invertersrdquo in Proceedings of the IEEEEnergy Conversion Congress and Exposition (ECCE rsquo09) pp920ndash927 September 2009
[7] S Saridakis E Koutroulis and F Blaabjerg ldquoOptimal designof NPC and active-NPC transformerless PV invertersrdquo inProceedings of the 3rd IEEE International Symposium on PowerElectronics for Distributed Generation Systems (PEDG rsquo12) pp106ndash113 Aalborg Denmark June 2012
[8] J Li S Bhattacharya and A Q Huang ldquoA new nine-levelactive NPC (ANPC) converter for grid connection of largewind turbines for distributed generationrdquo IEEE Transactions onPower Electronics vol 26 no 3 pp 961ndash972 2011
[9] O Bouhali N Rizoug T Mesbahi and B Francois ldquoModelingand control of the three-phase NPC multilevel converter usingan equivalent matrix structurerdquo in Proceedings of the 7th IETInternational Conference on Power Electronics Machines andDrives (PEMD rsquo14) pp 1ndash6 April 2014
[10] CWang and Y Li ldquoA new balancing algorithm of neutral-pointpotential in the three-level NPC convertersrdquo in Proceedings ofthe IEEE Industry Applications Society AnnualMeeting (IAS rsquo08)pp 1ndash5 Edmonton Canada October 2008
[11] K Komatsu M Yatsu S Miyashita et al ldquoNew IGBT modulesfor advanced neutral-point-clamped 3-level power convertersrdquoin Proceedings of the International Power Electronics Conference-ECCE Asia (IPEC rsquo10) pp 523ndash527 Sapporo Japan June 2010
[12] T B Soeiro and J W Kolar ldquoThe new high-efficiency hybridneutral-point-clamped converterrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 5 pp 1919ndash1935 2013
[13] N Celanovic and D Boroyevich ldquoA fast space vector mod-ulation algorithm for multilevel three-phase convertersrdquo in
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Power Electronics 13
Proceedings of the Conference Record of the IEEE IndustryApplications Conference 34th IAS Annual Meeting vol 2 pp1173ndash1177 Phoenix Ariz USA October 1999
[14] B Zhang Q Ge L Tan X Wang Q Chang and J LiuldquoA new PWM strategy for three-level Active NPC converterrdquoin Proceedings of the International Conference on ElectricalMachines and Systems (ICEMS rsquo13) pp 1792ndash1795 BusanRepublic of Korea October 2013
[15] H Yi F Zhuo F Wang and Z Wang ldquoA digital hysteresiscurrent controller for three-level neural-point-clamped inverterwith mixed-levels and prediction-based samplingrdquo IEEE Trans-actions on Power Electronics vol 31 no 5 pp 3945ndash3957 2016
[16] M Sharifzadeh A Sheikholeslami H Vahedi H GhoreishyP Labbe and K Al-Haddad ldquoOptimised harmonic elimina-tion modulation extended to four-leg neutral-point-clampedinverterrdquo IET Power Electronics vol 9 no 3 pp 441ndash448 2016
[17] Z-B Yuan J-J Zhang J Hao and D-Y Lu ldquoPhase-shiftselective harmonic elimination pulse width modulation formultilevel converterrdquo in Proceedings of the 34th Chinese ControlConference (CCC rsquo15) pp 8981ndash8985 Hangzhou China July2015
[18] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) pp 1ndash8 Clemson UniversityMarch 2015
[19] A Nabae I Takahashi and H Akagi ldquoA new neutral-point-clamped PWM inverterrdquo IEEE Transactions on Industry Appli-cations vol IA-17 no 5 pp 518ndash523 1981
[20] Y-H Yu N-J Ku and D-S Hyun ldquoThe control algorithmof three-level NPC inverter under unbalanced input voltageconditionsrdquo in Proceedings of the IEEE Vehicle Power andPropulsion Conference (VPPC rsquo14) IEEE Coimbra PortugalOctober 2014
[21] V Dargahi A K Sadigh and K Corzine ldquoSelective harmonicelimination for extended cascaded multicell multilevel powerconvertersrdquo in Proceedings of the Clemson University PowerSystems Conference (PSC rsquo15) Clemson SC USA March 2015
[22] Y Deng Y Wang K H Teo and R G Harley ldquoA simplifiedspace vector modulation scheme for multilevel convertersrdquoIEEE Transactions on Power Electronics vol 31 no 3 pp 1873ndash1886 2016
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of