8122019 04510573

httpslidepdfcomreaderfull04510573 15

ANN control of Nine Level NPC Voltage

Inverter

Based on Selective Harmonics EliminationImarazene Khoukha Chekireb Hachemi Berkouk El Madjid

Faculteacute drsquoElectronique etDrsquoInformatique

Laboratoire de Commande des processus

Laboratoire de Commande des processus

USTHB Bp32 Departement de Geacutenie Electrique Departement de Geacutenie ElectriqueEl Alia Bab-Ezzouar Ecole Nationale Polytechnique drsquoAlger Ecole Nationale Polytechnique

10 Rue Hassen Badi Aj Harrach 10 Rue Hassen Badi Aj Harrach

ALGERIA BP- 182 ALGERIA BP- 182 ALGERIA khimarazeneyahoofr chekirebyahoofr Emberkoukyahoofr

Abstract - This paper is devoted to artificial neural network

(ANN) control of a nine levels neutral point clamped (NPC)

voltage inverter based on the selective harmonics elimination

Initially we determine all the adequate switching angles for the

control of the nine levels inverter switches in order to eliminate

the 5th 7th and 11th harmonics Then a multilayer ANN is

elaborated which is able to reproduce these angles according to

modulation index variations The aim of t

his technique is to improve the real-time control of the multilevel

inverter

Key words- Multilevel inverter Selective Elimination

Harmonics Artificial neurons network

I I NTRODUCTION

The fast development of very powerful algorithms for ACadjustable speed drives imposes a quite powerful mean forcontrolling the magnitude frequency and phase of inputvoltage of electric machines In high voltage powerapplications the most used converters for this objective are themultilevel inverters [1]-[4] In our case the studied converterconcerns the nine levels NPC voltage inverter

In high voltage high power applications using voltage sourceinverter (VSI) the switching frequency of electronic powerswitch is reduced around one KHz For this switchingfrequency and with techniques resulting from the carrier- based-sinusoidal PWM [5]-[7] and space vector modulation[8]-[10] the output voltage of the inverter might contain lowerharmonics which alter the current signal An alternativesolution is to use the selective harmonics elimination (SHE)which ensure the control of the fundamental and thecancellation of the undesirable lower harmonics [11]-[16]

This method exhibits the advantage of a low commutationfrequency for the electronic power switches

The selective elimination harmonics is generally implementedusing memory look up table to store the calculated switchingangles and their corresponding modulation index Hence largememories are required when the modulation index must varyin a wide interval with fine increment An alternativeimplementation solution is to utilize an ANNBeside the ANN proves their ability to handle effectively the

problems of classification memorization filtering andapproximation [17]-[19] It is also proven that the networkswith only one hidden layer have the universal approximation

propriety [20]-[22] With an ANN we attempt to reduce the memory size and thecomputing time involved with the SHE implementationMoreover the generalization property of the neurons network

might ensure the generation of the switching angles even forthe values that are not included in the look up table Therefore

the ANN is used to generate in real time the switching anglesaccording to the modulation index for the control of the ninelevels inverterIn the first section the structure of the nine levels NPC

inverter and the switch states leading to the inverter control aregiven The second section is devoted to the determination ofthe switching angles required to implement the SHE strategyfor the nine levels inverter In last section an ANN is

elaborated to recopy the SHE strategy in order to control thisinverter The tests results related to the inverter controlled bythese two methods allow to appreciate the efficiency of themethod

II NPC STRUCTURE OF NINE LEVEL I NVERTER

The NPC structure of three-phase nine levels inverter isrepresented in figure 1

It consists of three symmetrical arms with eight commutationcells Each arm comprises ten bidirectional switches in series

The two diodes (DD k0 DD k1) ensure zero voltage Eachswitch is constituted by an assembly a diode and a transistor inopposition Each cell is fed by a dc voltage Uc assumed to beconstant and is related to the input dc voltage Us by

8

S U

cU = (1)

The topological analysis carried out for this inverter revealsthat there are seven possible and controllable configurationsTable 1 gives logical states of the switches in the k arm k

(

th

k=1 2 3) according to the Vkm arm voltageTo ensure continuous operation of the inverter the switches

states must satisfy the complementary rule definite as follows

1-4244-0891-107 20009832092007 IEEE

8122019 04510573

httpslidepdfcomreaderfull04510573 25

0 90 180 270 360

1 α2 α3

Vkm

3Uc4Uc

Uc

2Uc

π2 π 3π2 2π

ωt

Fig2 Assigned form of the arm voltage for the nine

level inverter

T31

T32

T33

T34

T35

T310

T39

T38

T37

T36

D31

T312

D31

T311

D31

T316

T314

D31

T313

D31

D31

T315

T11

T12

T13

T14

T15

T110

T19

T18

T17

T16

D11

D12

D13

D14

D15

D11

D19

D18

D17

D16

D21

D19

D18

D17

D16

D31

D39

D38

D37

D36

D21

D22

D23

D24

D25

D31

D32

D33

D34

D35

T21

T22

T23

T24

T25

T210

T29

T28

T27

T26

D21

T212

D21

T211

D21

T 162

T2 41

D21

T213

D21

D21

T215

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

=

=

=

=

=

105

94

83

62

71

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

(2)

Uc1

Uc2

Uc3

Uc4

Uc8

Uc7

Uc6

Uc5

D11

T112

D11

T111

D11

T116

T114

D11

T113

D11

D11

T115

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

=

=

=

=

=

=

10987616

10987615

10987614

543213

543212

543211

1

1

1

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

(3)

VA VB

N

M

Table I gives logical states of the switches in the k

th

arm (k=12 3) according to the Vkm arm voltage

TABLE I

TYPOLOGICAL STATES OF THE SWITCHES FOR NINE LEVEL I NVERTER

Vkm Bk1 Bk2 Bk3 Bk4 Bk5 Bk6 Bk7 Bk8 Bk9 Bk10

4Uc 1 1 1 1 1 0 0 0 0 0

3Uc 1 1 1 1 0 0 0 0 0 0

2Uc 1 1 1 0 0 0 0 0 0 0

Uc 1 1 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0

-Uc 0 0 0 0 0 1 0 0 0 0

-2Uc 0 0 0 0 0 1 1 0 0 0

-3Uc 0 0 0 0 0 1 1 1 1 0

-4Uc 0 0 0 0 0 1 1 1 1 1

VC

III HARMONICS ELIMINATION STRATEGY

It is necessary to elaborate the control signals of the voltage

inverter in order to obtain an output voltage form nearest as

possible from the sinusoid For this goal several algorithms

have been developed In this work we are concerned with the problem of SHE in the case of the multi levels inverterThis method was developed initially for the case of the twolevels inverters [11] Sseveral works came after who were

devoted to the case of the multi levels inverters [12]-[16] In

general the algorithm of this control strategy is as followsi) The voltage arm desired at the output inverter is expanded

in Fourier series and the general expression of the nth harmonic

is determinated according to the switching angles αi withi=(1c)ii) Then the fundamental harmonic is imposed to the desiredvalue and the (c-1) selected undesirable harmonics arecancellediii) Finally a nonlinear algebraic system of c equations and c

unknowns is obtained

There are several methods for solving this nonlinear systemwe used the Newton-Raphson oneIn the case of a nine level inverter the shape of an arm voltageis imposed as shown in figure 2 Its signal expansion inFourier series leads to the expression of the n th harmonic

Fig1 Structure of the three-phase nine levels NPC voltageinverter

)]cos(

)cos()cos([42211

cc

n

n

nnn

U A c

α

α α

π

l

ll

+

++= (4)

Where n is the harmonic number c the considered number of

angles necessary to eliminate (c-1) harmonics and are

unitary coefficients depending on the form of the arm voltage

(Fig2)

il

In case of figure 2 these parameters are as follows n= 5 7and 11 c=4

8122019 04510573

httpslidepdfcomreaderfull04510573 35

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

15

Modulation Index r

T H

D

( )

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

Modulation Index r

T H D

( )

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

Modulation Index r

S w i t c h i n g

A n g l e s ( D e g r e e )

3α4α2

α1

055 06 065 07 075 08 085 09 095 110

20

30

40

50

60

70

80

90

100

Modulation Index r

S w i t c h i n g A n g l e s ( d e g r e e )

α3α4α2

α1

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-500

-400

-300

-200

-100

0

100

200

300

400

500

14

13

12

11

==== llll

Under the constraint

cα α α α lelelelele 0 321le

2

π

In this study the goal is to control the effective value of thefundamental and to eliminate the 5 7 and 11 harmonics The

development of the expression (3) for n = (1 5 7 and 11)according to the modulation index Uc

eff V2r = leads

to the following system

⎪⎪

⎩

⎪⎪

⎨

⎧

=++minus

=++minus

=++minus

=++minus

0)11cos()11cos()11cos()11cos(

0)7cos()7cos()7cos()7cos(

0)5cos()5cos()5cos()5cos(

)cos()cos()cos()cos(

4321

4321

4321

4321

α α α α

α α α α

α α α α

π α α α α r

(5)

Figure 3a gives the variation of the switching angles α1 α2

α3 and α4 according to r when the dc input voltage U S isequal to 889V

Time (S)

V o l t a g e ( V )

0 10 20 30 40 50 60 700

01

02

03

04

05

06

07

08

09

1

Harmonic Row

v o l t a g e p u

a) Switching angles given by Newton-Raphson

THD=735

b) THD given by a nine levels inverter

Fig3 Switching angles and the related THD for SHE control of the nine

levels inverter

a) Lowest THD exhibited by the nine levels inverter

b- Nine levels inverter switching angles related to the lowest THD

Fig4 Switching angles chosen and the related THD for SHE control of the

nine levels inverter

Fig5 Phase voltage waveform for r=08 with elimination harmonics 5 7 and

11

8122019 04510573

httpslidepdfcomreaderfull04510573 45

From theses curves it appears that this system exhibits two

solutions in the intervals [06 le r le 076] and [07 ler le 089]and only one solution elsewhere except for the interval

where there is no solution So a selection of the

adequate angles must be done in the double solution intervals

This selection is carried out on the basis of the best THDobtained for these two angle sets in these intervals (Fig3-b)

]93090[

Fig7 Switching angles given by ANN ( )

and by Newton-Raphson (-)

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

S w i t c h i n g A n g l e s ( D e g r e e )

Modulation Index r

α3

4α2

α1The figures (4-a) and (4-b) show respectively the selectedangles and their corresponding THDAfter this choice and in order to test the validity of the

obtained solutions the output voltage inverter is generatedusing the switching angles calculated for r = 08 Thus thegenerated voltage inverter and its spectrum are shown infigures 5

These results shows that the elimination of the undesirable 57 and 11 harmonics is effective with a good control offundamental

IV APPLICATION OF THE ARTIFICIAL NEURAL NETWORKS

In this section the goal is to utilize an ANN in place of thetabulated switching angles needed for the nine levels inverter based on the SHE

Several architectures of the ANN have been developed withdifferent training algorithms [17]-[19] A multi layers network

with supervised training is well suited for this kind of problemSince the network receives at its input the value of themodulation index r and must produce at its output the four

switching angles α i with i=(14) the network structure is oneneuron in its input layer four neurons in its output layer someneurons in its single hidden layer (Fig6) The training process

is performed off-line using the back-propagation algorithm[17]-[19] After several trying and errors tests we chose 15neurons for the hidden layer

hidden layer

ou rtput laye

r(k) α1

α4

Fig6 Architecture of the resulting network

Since the control characteristic (Fig4b) is not smooth enough

training of the network has taken an appreciate time and

necessited 1800 adaptation cycles in order to ensure theconvergence with a weak training errorThe switching angles according to and given by the elaboratednetwork are shown in figure 7 The response of the elaboratednetwork for (063 le r le1) given in figure 7 is practically

similar to that determined by Newton-Raphson method(Fig4b)

V CONCLUSION

The presented work consists in the elaboration of an ANN ableto generate the switching angles based on the SHE strategy tocontrol of a nine level inverter

In the first part we have determinate the switching angles inorder to cancel the 5 7 and 11 harmonic and to control thefundamental of the AC output voltage given by this consideredinverterThen an ANN is elaborated to reproduce these switching

angles without constrain for any value of the modulationindex For a real-time control it is enough to implement theobtained network after the training process

VI R EFERENCES

[1] R W Menzies P Steimer J K Steinke laquo Five GTO inverters for

large induction motor drivesrdquo IEEE Trans Industry ApplicationsVol 30 No 4 July 1994 pp938-944

[2] R W Menzies P Steimer J K Steinke laquo Five GTO inverters forlarge induction motor drivesrdquo IEEE Trans Industry Applications

Vol 30 No 4 July 1994 pp938-944

[3] R Teodorescu F Beaabjerg J K Pedersen E Cengelci S Sulistijo

B Woo and P Enjeti Multilevel converters- A survey in Proc

European power Electronics Conf [EPE99) Lausanne Switzerland

1999[4] J Rodriguez J-S Lai F Z Peng Multilevel inverters A survey of

topologies controls and applications 2002 IEEE[5] B S Suh G Sinha MD Manjrekar and T A Lipo Multilevel

power conversion ndashan overview of topologies and modulation

strategies International Conference on Optimization of Electrical andElectronic Equipment (OPTIM) Vol2 1998 ppAD11-AD24

[6] LTolbert and T G Habetler Novel multilevel inverter carrier-based

PWM method IEEE Trans Ind Applicat vol 35 pp 1098-1107

SeptOct 1999[7] Bor-Ren Lin Hsin-Hung Lu A novel multilevel PWM control

scheme of the ACDCAC converter for AC drives Proceedings of

the IEEE international Symposium on Industrial Electronics 1999ISIE99 Vol2 pp 795-800

8122019 04510573

httpslidepdfcomreaderfull04510573 55

[8] Sanmin Wei Bin Wu Fahai Li and Congwei Liu A general spacevector PWM control algoritm for multilevel inverters 2003 IEEE

[9] N Celanovic D Boroyevich A fast Space Vector modulation

algorithm for multilevel three-phase converter in Conf Rec IEEE

IAS Annual Meeting 1999 pp 1173-1177[10] B P MacGrath D G Holmes and T A Lipo Optimized space

vector switching sequences for multilevel inverters in Proc IEEE

Apec Anaheim CA Mar 4-8 2001 pp 1123-1129[11] HSPatel et RGHoft laquoGeneralized technique of harmonics

elimination and voltage control in thyristor inverter raquo IEEE Tran

Ind Appli pp 310-317 1973[12] John Nchiasson Leon MTolbert Keith JMckenzie et Zhong Du laquoA

unified approach to solving the harmonic elimination equations in

multilevel convertersraquo IEEE transactions on power electronics

Vol19 Ndeg2 March 2004[13] John NChiasson Leon Tolbert Keith JMckenzie et Zhong Du laquo A

complete solution to the harmonics elimination problem raquoDeacutepartement ECE universiteacute de Tennessee 2003 IEEE

[14] YSahali et MKFellah laquo Selective harmonic eliminated plusewidth

modulation technic (SHE PWM) applied to three-levelinverterconverter raquo IEEE International Symposium on Industrial

Electronics Rio de Janeiro Brasil 9-11 juin 2003

[15] Keith Jeremy Mckenzie laquo Elimination harmonics in a cascaded H- bridges multilevel inverter using resultant theory symmetric polynomials and power sums raquo thesis for the Master of science

degree University of Tennesse Knoxville May 2004

[16] SSirisukprasert laquo Optimized harmonic stepped-waveform formultilevel inverter raquo Master thesis submitted to the faculty of the

virginia politechnic institute and state university 1999

[17] J A Freeman and T Shibata Neural Networks Algorithms A pplications and Programming Techniques Addison-Wesley publication Cie 1992

[18] B Widrow and M A Lehr 30 years of adaptive neural networksPerceptron madaline and backpropagation Proc Of the IEEE 781415-14141

[19] P J Werbos Neural networks for control chapter 3 pp 67-95 MIT

Press Cambridge MA 1990[20] MJDPowell laquo Radial basis function for multivariable interpolation

A reviewraquo JCMason and MGCox Editors Algorithms forApproximation pp 143-167 Oxford University Press 1987

[21] K I Funahashi On the approximate realization of continuous

mappingd by neural networks Neural Networks 2 183-192[22] G Cybenko Approximation by superposition of a sigmoidal function

In penkaj Mehra and Benjamin W Wah Artificial Networks

Concepts and Theory pp 488-499 IEEE computer Society Press

Tutorial

8122019 04510573

httpslidepdfcomreaderfull04510573 25

0 90 180 270 360

1 α2 α3

Vkm

3Uc4Uc

Uc

2Uc

π2 π 3π2 2π

ωt

Fig2 Assigned form of the arm voltage for the nine

level inverter

T31

T32

T33

T34

T35

T310

T39

T38

T37

T36

D31

T312

D31

T311

D31

T316

T314

D31

T313

D31

D31

T315

T11

T12

T13

T14

T15

T110

T19

T18

T17

T16

D11

D12

D13

D14

D15

D11

D19

D18

D17

D16

D21

D19

D18

D17

D16

D31

D39

D38

D37

D36

D21

D22

D23

D24

D25

D31

D32

D33

D34

D35

T21

T22

T23

T24

T25

T210

T29

T28

T27

T26

D21

T212

D21

T211

D21

T 162

T2 41

D21

T213

D21

D21

T215

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

=

=

=

=

=

105

94

83

62

71

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

(2)

Uc1

Uc2

Uc3

Uc4

Uc8

Uc7

Uc6

Uc5

D11

T112

D11

T111

D11

T116

T114

D11

T113

D11

D11

T115

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

=

=

=

=

=

=

10987616

10987615

10987614

543213

543212

543211

1

1

1

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

k B

(3)

VA VB

N

M

Table I gives logical states of the switches in the k

th

arm (k=12 3) according to the Vkm arm voltage

TABLE I

TYPOLOGICAL STATES OF THE SWITCHES FOR NINE LEVEL I NVERTER

Vkm Bk1 Bk2 Bk3 Bk4 Bk5 Bk6 Bk7 Bk8 Bk9 Bk10

4Uc 1 1 1 1 1 0 0 0 0 0

3Uc 1 1 1 1 0 0 0 0 0 0

2Uc 1 1 1 0 0 0 0 0 0 0

Uc 1 1 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0

-Uc 0 0 0 0 0 1 0 0 0 0

-2Uc 0 0 0 0 0 1 1 0 0 0

-3Uc 0 0 0 0 0 1 1 1 1 0

-4Uc 0 0 0 0 0 1 1 1 1 1

VC

III HARMONICS ELIMINATION STRATEGY

It is necessary to elaborate the control signals of the voltage

inverter in order to obtain an output voltage form nearest as

possible from the sinusoid For this goal several algorithms

have been developed In this work we are concerned with the problem of SHE in the case of the multi levels inverterThis method was developed initially for the case of the twolevels inverters [11] Sseveral works came after who were

devoted to the case of the multi levels inverters [12]-[16] In

general the algorithm of this control strategy is as followsi) The voltage arm desired at the output inverter is expanded

in Fourier series and the general expression of the nth harmonic

is determinated according to the switching angles αi withi=(1c)ii) Then the fundamental harmonic is imposed to the desiredvalue and the (c-1) selected undesirable harmonics arecancellediii) Finally a nonlinear algebraic system of c equations and c

unknowns is obtained

There are several methods for solving this nonlinear systemwe used the Newton-Raphson oneIn the case of a nine level inverter the shape of an arm voltageis imposed as shown in figure 2 Its signal expansion inFourier series leads to the expression of the n th harmonic

Fig1 Structure of the three-phase nine levels NPC voltageinverter

)]cos(

)cos()cos([42211

cc

n

n

nnn

U A c

α

α α

π

l

ll

+

++= (4)

Where n is the harmonic number c the considered number of

angles necessary to eliminate (c-1) harmonics and are

unitary coefficients depending on the form of the arm voltage

(Fig2)

il

In case of figure 2 these parameters are as follows n= 5 7and 11 c=4

8122019 04510573

httpslidepdfcomreaderfull04510573 35

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

15

Modulation Index r

T H

D

( )

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

Modulation Index r

T H D

( )

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

Modulation Index r

S w i t c h i n g

A n g l e s ( D e g r e e )

3α4α2

α1

055 06 065 07 075 08 085 09 095 110

20

30

40

50

60

70

80

90

100

Modulation Index r

S w i t c h i n g A n g l e s ( d e g r e e )

α3α4α2

α1

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-500

-400

-300

-200

-100

0

100

200

300

400

500

14

13

12

11

==== llll

Under the constraint

cα α α α lelelelele 0 321le

2

π

In this study the goal is to control the effective value of thefundamental and to eliminate the 5 7 and 11 harmonics The

development of the expression (3) for n = (1 5 7 and 11)according to the modulation index Uc

eff V2r = leads

to the following system

⎪⎪

⎩

⎪⎪

⎨

⎧

=++minus

=++minus

=++minus

=++minus

0)11cos()11cos()11cos()11cos(

0)7cos()7cos()7cos()7cos(

0)5cos()5cos()5cos()5cos(

)cos()cos()cos()cos(

4321

4321

4321

4321

α α α α

α α α α

α α α α

π α α α α r

(5)

Figure 3a gives the variation of the switching angles α1 α2

α3 and α4 according to r when the dc input voltage U S isequal to 889V

Time (S)

V o l t a g e ( V )

0 10 20 30 40 50 60 700

01

02

03

04

05

06

07

08

09

1

Harmonic Row

v o l t a g e p u

a) Switching angles given by Newton-Raphson

THD=735

b) THD given by a nine levels inverter

Fig3 Switching angles and the related THD for SHE control of the nine

levels inverter

a) Lowest THD exhibited by the nine levels inverter

b- Nine levels inverter switching angles related to the lowest THD

Fig4 Switching angles chosen and the related THD for SHE control of the

nine levels inverter

Fig5 Phase voltage waveform for r=08 with elimination harmonics 5 7 and

11

8122019 04510573

httpslidepdfcomreaderfull04510573 45

From theses curves it appears that this system exhibits two

solutions in the intervals [06 le r le 076] and [07 ler le 089]and only one solution elsewhere except for the interval

where there is no solution So a selection of the

adequate angles must be done in the double solution intervals

This selection is carried out on the basis of the best THDobtained for these two angle sets in these intervals (Fig3-b)

]93090[

Fig7 Switching angles given by ANN ( )

and by Newton-Raphson (-)

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

S w i t c h i n g A n g l e s ( D e g r e e )

Modulation Index r

α3

4α2

α1The figures (4-a) and (4-b) show respectively the selectedangles and their corresponding THDAfter this choice and in order to test the validity of the

obtained solutions the output voltage inverter is generatedusing the switching angles calculated for r = 08 Thus thegenerated voltage inverter and its spectrum are shown infigures 5

These results shows that the elimination of the undesirable 57 and 11 harmonics is effective with a good control offundamental

IV APPLICATION OF THE ARTIFICIAL NEURAL NETWORKS

In this section the goal is to utilize an ANN in place of thetabulated switching angles needed for the nine levels inverter based on the SHE

Several architectures of the ANN have been developed withdifferent training algorithms [17]-[19] A multi layers network

with supervised training is well suited for this kind of problemSince the network receives at its input the value of themodulation index r and must produce at its output the four

switching angles α i with i=(14) the network structure is oneneuron in its input layer four neurons in its output layer someneurons in its single hidden layer (Fig6) The training process

is performed off-line using the back-propagation algorithm[17]-[19] After several trying and errors tests we chose 15neurons for the hidden layer

hidden layer

ou rtput laye

r(k) α1

α4

Fig6 Architecture of the resulting network

Since the control characteristic (Fig4b) is not smooth enough

training of the network has taken an appreciate time and

necessited 1800 adaptation cycles in order to ensure theconvergence with a weak training errorThe switching angles according to and given by the elaboratednetwork are shown in figure 7 The response of the elaboratednetwork for (063 le r le1) given in figure 7 is practically

similar to that determined by Newton-Raphson method(Fig4b)

V CONCLUSION

The presented work consists in the elaboration of an ANN ableto generate the switching angles based on the SHE strategy tocontrol of a nine level inverter

In the first part we have determinate the switching angles inorder to cancel the 5 7 and 11 harmonic and to control thefundamental of the AC output voltage given by this consideredinverterThen an ANN is elaborated to reproduce these switching

angles without constrain for any value of the modulationindex For a real-time control it is enough to implement theobtained network after the training process

VI R EFERENCES

[1] R W Menzies P Steimer J K Steinke laquo Five GTO inverters for

large induction motor drivesrdquo IEEE Trans Industry ApplicationsVol 30 No 4 July 1994 pp938-944

[2] R W Menzies P Steimer J K Steinke laquo Five GTO inverters forlarge induction motor drivesrdquo IEEE Trans Industry Applications

Vol 30 No 4 July 1994 pp938-944

[3] R Teodorescu F Beaabjerg J K Pedersen E Cengelci S Sulistijo

B Woo and P Enjeti Multilevel converters- A survey in Proc

European power Electronics Conf [EPE99) Lausanne Switzerland

1999[4] J Rodriguez J-S Lai F Z Peng Multilevel inverters A survey of

topologies controls and applications 2002 IEEE[5] B S Suh G Sinha MD Manjrekar and T A Lipo Multilevel

power conversion ndashan overview of topologies and modulation

strategies International Conference on Optimization of Electrical andElectronic Equipment (OPTIM) Vol2 1998 ppAD11-AD24

[6] LTolbert and T G Habetler Novel multilevel inverter carrier-based

PWM method IEEE Trans Ind Applicat vol 35 pp 1098-1107

SeptOct 1999[7] Bor-Ren Lin Hsin-Hung Lu A novel multilevel PWM control

scheme of the ACDCAC converter for AC drives Proceedings of

the IEEE international Symposium on Industrial Electronics 1999ISIE99 Vol2 pp 795-800

8122019 04510573

httpslidepdfcomreaderfull04510573 55

[8] Sanmin Wei Bin Wu Fahai Li and Congwei Liu A general spacevector PWM control algoritm for multilevel inverters 2003 IEEE

[9] N Celanovic D Boroyevich A fast Space Vector modulation

algorithm for multilevel three-phase converter in Conf Rec IEEE

IAS Annual Meeting 1999 pp 1173-1177[10] B P MacGrath D G Holmes and T A Lipo Optimized space

vector switching sequences for multilevel inverters in Proc IEEE

Apec Anaheim CA Mar 4-8 2001 pp 1123-1129[11] HSPatel et RGHoft laquoGeneralized technique of harmonics

elimination and voltage control in thyristor inverter raquo IEEE Tran

Ind Appli pp 310-317 1973[12] John Nchiasson Leon MTolbert Keith JMckenzie et Zhong Du laquoA

unified approach to solving the harmonic elimination equations in

multilevel convertersraquo IEEE transactions on power electronics

Vol19 Ndeg2 March 2004[13] John NChiasson Leon Tolbert Keith JMckenzie et Zhong Du laquo A

complete solution to the harmonics elimination problem raquoDeacutepartement ECE universiteacute de Tennessee 2003 IEEE

[14] YSahali et MKFellah laquo Selective harmonic eliminated plusewidth

modulation technic (SHE PWM) applied to three-levelinverterconverter raquo IEEE International Symposium on Industrial

Electronics Rio de Janeiro Brasil 9-11 juin 2003

[15] Keith Jeremy Mckenzie laquo Elimination harmonics in a cascaded H- bridges multilevel inverter using resultant theory symmetric polynomials and power sums raquo thesis for the Master of science

degree University of Tennesse Knoxville May 2004

[16] SSirisukprasert laquo Optimized harmonic stepped-waveform formultilevel inverter raquo Master thesis submitted to the faculty of the

virginia politechnic institute and state university 1999

[17] J A Freeman and T Shibata Neural Networks Algorithms A pplications and Programming Techniques Addison-Wesley publication Cie 1992

[18] B Widrow and M A Lehr 30 years of adaptive neural networksPerceptron madaline and backpropagation Proc Of the IEEE 781415-14141

[19] P J Werbos Neural networks for control chapter 3 pp 67-95 MIT

Press Cambridge MA 1990[20] MJDPowell laquo Radial basis function for multivariable interpolation

A reviewraquo JCMason and MGCox Editors Algorithms forApproximation pp 143-167 Oxford University Press 1987

[21] K I Funahashi On the approximate realization of continuous

mappingd by neural networks Neural Networks 2 183-192[22] G Cybenko Approximation by superposition of a sigmoidal function

In penkaj Mehra and Benjamin W Wah Artificial Networks

Concepts and Theory pp 488-499 IEEE computer Society Press

Tutorial

8122019 04510573

httpslidepdfcomreaderfull04510573 35

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

15

Modulation Index r

T H

D

( )

055 06 065 07 075 08 085 09 095 15

6

7

8

9

10

11

12

13

14

Modulation Index r

T H D

( )

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

Modulation Index r

S w i t c h i n g

A n g l e s ( D e g r e e )

3α4α2

α1

055 06 065 07 075 08 085 09 095 110

20

30

40

50

60

70

80

90

100

Modulation Index r

S w i t c h i n g A n g l e s ( d e g r e e )

α3α4α2

α1

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-500

-400

-300

-200

-100

0

100

200

300

400

500

14

13

12

11

==== llll

Under the constraint

cα α α α lelelelele 0 321le

2

π

In this study the goal is to control the effective value of thefundamental and to eliminate the 5 7 and 11 harmonics The

development of the expression (3) for n = (1 5 7 and 11)according to the modulation index Uc

eff V2r = leads

to the following system

⎪⎪

⎩

⎪⎪

⎨

⎧

=++minus

=++minus

=++minus

=++minus

0)11cos()11cos()11cos()11cos(

0)7cos()7cos()7cos()7cos(

0)5cos()5cos()5cos()5cos(

)cos()cos()cos()cos(

4321

4321

4321

4321

α α α α

α α α α

α α α α

π α α α α r

(5)

Figure 3a gives the variation of the switching angles α1 α2

α3 and α4 according to r when the dc input voltage U S isequal to 889V

Time (S)

V o l t a g e ( V )

0 10 20 30 40 50 60 700

01

02

03

04

05

06

07

08

09

1

Harmonic Row

v o l t a g e p u

a) Switching angles given by Newton-Raphson

THD=735

b) THD given by a nine levels inverter

Fig3 Switching angles and the related THD for SHE control of the nine

levels inverter

a) Lowest THD exhibited by the nine levels inverter

b- Nine levels inverter switching angles related to the lowest THD

Fig4 Switching angles chosen and the related THD for SHE control of the

nine levels inverter

Fig5 Phase voltage waveform for r=08 with elimination harmonics 5 7 and

11

8122019 04510573

httpslidepdfcomreaderfull04510573 45

From theses curves it appears that this system exhibits two

solutions in the intervals [06 le r le 076] and [07 ler le 089]and only one solution elsewhere except for the interval

where there is no solution So a selection of the

adequate angles must be done in the double solution intervals

This selection is carried out on the basis of the best THDobtained for these two angle sets in these intervals (Fig3-b)

]93090[

Fig7 Switching angles given by ANN ( )

and by Newton-Raphson (-)

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

S w i t c h i n g A n g l e s ( D e g r e e )

Modulation Index r

α3

4α2

α1The figures (4-a) and (4-b) show respectively the selectedangles and their corresponding THDAfter this choice and in order to test the validity of the

obtained solutions the output voltage inverter is generatedusing the switching angles calculated for r = 08 Thus thegenerated voltage inverter and its spectrum are shown infigures 5

These results shows that the elimination of the undesirable 57 and 11 harmonics is effective with a good control offundamental

IV APPLICATION OF THE ARTIFICIAL NEURAL NETWORKS

In this section the goal is to utilize an ANN in place of thetabulated switching angles needed for the nine levels inverter based on the SHE

Several architectures of the ANN have been developed withdifferent training algorithms [17]-[19] A multi layers network

with supervised training is well suited for this kind of problemSince the network receives at its input the value of themodulation index r and must produce at its output the four

switching angles α i with i=(14) the network structure is oneneuron in its input layer four neurons in its output layer someneurons in its single hidden layer (Fig6) The training process

is performed off-line using the back-propagation algorithm[17]-[19] After several trying and errors tests we chose 15neurons for the hidden layer

hidden layer

ou rtput laye

r(k) α1

α4

Fig6 Architecture of the resulting network

Since the control characteristic (Fig4b) is not smooth enough

training of the network has taken an appreciate time and

necessited 1800 adaptation cycles in order to ensure theconvergence with a weak training errorThe switching angles according to and given by the elaboratednetwork are shown in figure 7 The response of the elaboratednetwork for (063 le r le1) given in figure 7 is practically

similar to that determined by Newton-Raphson method(Fig4b)

V CONCLUSION

The presented work consists in the elaboration of an ANN ableto generate the switching angles based on the SHE strategy tocontrol of a nine level inverter

In the first part we have determinate the switching angles inorder to cancel the 5 7 and 11 harmonic and to control thefundamental of the AC output voltage given by this consideredinverterThen an ANN is elaborated to reproduce these switching

angles without constrain for any value of the modulationindex For a real-time control it is enough to implement theobtained network after the training process

VI R EFERENCES

[1] R W Menzies P Steimer J K Steinke laquo Five GTO inverters for

large induction motor drivesrdquo IEEE Trans Industry ApplicationsVol 30 No 4 July 1994 pp938-944

[2] R W Menzies P Steimer J K Steinke laquo Five GTO inverters forlarge induction motor drivesrdquo IEEE Trans Industry Applications

Vol 30 No 4 July 1994 pp938-944

[3] R Teodorescu F Beaabjerg J K Pedersen E Cengelci S Sulistijo

B Woo and P Enjeti Multilevel converters- A survey in Proc

European power Electronics Conf [EPE99) Lausanne Switzerland

1999[4] J Rodriguez J-S Lai F Z Peng Multilevel inverters A survey of

topologies controls and applications 2002 IEEE[5] B S Suh G Sinha MD Manjrekar and T A Lipo Multilevel

power conversion ndashan overview of topologies and modulation

strategies International Conference on Optimization of Electrical andElectronic Equipment (OPTIM) Vol2 1998 ppAD11-AD24

[6] LTolbert and T G Habetler Novel multilevel inverter carrier-based

PWM method IEEE Trans Ind Applicat vol 35 pp 1098-1107

SeptOct 1999[7] Bor-Ren Lin Hsin-Hung Lu A novel multilevel PWM control

scheme of the ACDCAC converter for AC drives Proceedings of

the IEEE international Symposium on Industrial Electronics 1999ISIE99 Vol2 pp 795-800

8122019 04510573

httpslidepdfcomreaderfull04510573 55

[8] Sanmin Wei Bin Wu Fahai Li and Congwei Liu A general spacevector PWM control algoritm for multilevel inverters 2003 IEEE

[9] N Celanovic D Boroyevich A fast Space Vector modulation

algorithm for multilevel three-phase converter in Conf Rec IEEE

IAS Annual Meeting 1999 pp 1173-1177[10] B P MacGrath D G Holmes and T A Lipo Optimized space

vector switching sequences for multilevel inverters in Proc IEEE

Apec Anaheim CA Mar 4-8 2001 pp 1123-1129[11] HSPatel et RGHoft laquoGeneralized technique of harmonics

elimination and voltage control in thyristor inverter raquo IEEE Tran

Ind Appli pp 310-317 1973[12] John Nchiasson Leon MTolbert Keith JMckenzie et Zhong Du laquoA

unified approach to solving the harmonic elimination equations in

multilevel convertersraquo IEEE transactions on power electronics

Vol19 Ndeg2 March 2004[13] John NChiasson Leon Tolbert Keith JMckenzie et Zhong Du laquo A

complete solution to the harmonics elimination problem raquoDeacutepartement ECE universiteacute de Tennessee 2003 IEEE

[14] YSahali et MKFellah laquo Selective harmonic eliminated plusewidth

modulation technic (SHE PWM) applied to three-levelinverterconverter raquo IEEE International Symposium on Industrial

Electronics Rio de Janeiro Brasil 9-11 juin 2003

[15] Keith Jeremy Mckenzie laquo Elimination harmonics in a cascaded H- bridges multilevel inverter using resultant theory symmetric polynomials and power sums raquo thesis for the Master of science

degree University of Tennesse Knoxville May 2004

[16] SSirisukprasert laquo Optimized harmonic stepped-waveform formultilevel inverter raquo Master thesis submitted to the faculty of the

virginia politechnic institute and state university 1999

[17] J A Freeman and T Shibata Neural Networks Algorithms A pplications and Programming Techniques Addison-Wesley publication Cie 1992

[18] B Widrow and M A Lehr 30 years of adaptive neural networksPerceptron madaline and backpropagation Proc Of the IEEE 781415-14141

[19] P J Werbos Neural networks for control chapter 3 pp 67-95 MIT

Press Cambridge MA 1990[20] MJDPowell laquo Radial basis function for multivariable interpolation

A reviewraquo JCMason and MGCox Editors Algorithms forApproximation pp 143-167 Oxford University Press 1987

[21] K I Funahashi On the approximate realization of continuous

mappingd by neural networks Neural Networks 2 183-192[22] G Cybenko Approximation by superposition of a sigmoidal function

In penkaj Mehra and Benjamin W Wah Artificial Networks

Concepts and Theory pp 488-499 IEEE computer Society Press

Tutorial

8122019 04510573

httpslidepdfcomreaderfull04510573 45

From theses curves it appears that this system exhibits two

solutions in the intervals [06 le r le 076] and [07 ler le 089]and only one solution elsewhere except for the interval

where there is no solution So a selection of the

adequate angles must be done in the double solution intervals

This selection is carried out on the basis of the best THDobtained for these two angle sets in these intervals (Fig3-b)

]93090[

Fig7 Switching angles given by ANN ( )

and by Newton-Raphson (-)

055 06 065 07 075 08 085 09 095 10

10

20

30

40

50

60

70

80

S w i t c h i n g A n g l e s ( D e g r e e )

Modulation Index r

α3

4α2

α1The figures (4-a) and (4-b) show respectively the selectedangles and their corresponding THDAfter this choice and in order to test the validity of the

obtained solutions the output voltage inverter is generatedusing the switching angles calculated for r = 08 Thus thegenerated voltage inverter and its spectrum are shown infigures 5

These results shows that the elimination of the undesirable 57 and 11 harmonics is effective with a good control offundamental

IV APPLICATION OF THE ARTIFICIAL NEURAL NETWORKS

In this section the goal is to utilize an ANN in place of thetabulated switching angles needed for the nine levels inverter based on the SHE

Several architectures of the ANN have been developed withdifferent training algorithms [17]-[19] A multi layers network

with supervised training is well suited for this kind of problemSince the network receives at its input the value of themodulation index r and must produce at its output the four

switching angles α i with i=(14) the network structure is oneneuron in its input layer four neurons in its output layer someneurons in its single hidden layer (Fig6) The training process

is performed off-line using the back-propagation algorithm[17]-[19] After several trying and errors tests we chose 15neurons for the hidden layer

hidden layer

ou rtput laye

r(k) α1

α4

Fig6 Architecture of the resulting network

Since the control characteristic (Fig4b) is not smooth enough

training of the network has taken an appreciate time and

necessited 1800 adaptation cycles in order to ensure theconvergence with a weak training errorThe switching angles according to and given by the elaboratednetwork are shown in figure 7 The response of the elaboratednetwork for (063 le r le1) given in figure 7 is practically

similar to that determined by Newton-Raphson method(Fig4b)

V CONCLUSION

The presented work consists in the elaboration of an ANN ableto generate the switching angles based on the SHE strategy tocontrol of a nine level inverter

In the first part we have determinate the switching angles inorder to cancel the 5 7 and 11 harmonic and to control thefundamental of the AC output voltage given by this consideredinverterThen an ANN is elaborated to reproduce these switching

angles without constrain for any value of the modulationindex For a real-time control it is enough to implement theobtained network after the training process

VI R EFERENCES

[1] R W Menzies P Steimer J K Steinke laquo Five GTO inverters for

large induction motor drivesrdquo IEEE Trans Industry ApplicationsVol 30 No 4 July 1994 pp938-944

[2] R W Menzies P Steimer J K Steinke laquo Five GTO inverters forlarge induction motor drivesrdquo IEEE Trans Industry Applications

Vol 30 No 4 July 1994 pp938-944

[3] R Teodorescu F Beaabjerg J K Pedersen E Cengelci S Sulistijo

B Woo and P Enjeti Multilevel converters- A survey in Proc

European power Electronics Conf [EPE99) Lausanne Switzerland

1999[4] J Rodriguez J-S Lai F Z Peng Multilevel inverters A survey of

topologies controls and applications 2002 IEEE[5] B S Suh G Sinha MD Manjrekar and T A Lipo Multilevel

power conversion ndashan overview of topologies and modulation

strategies International Conference on Optimization of Electrical andElectronic Equipment (OPTIM) Vol2 1998 ppAD11-AD24

[6] LTolbert and T G Habetler Novel multilevel inverter carrier-based

PWM method IEEE Trans Ind Applicat vol 35 pp 1098-1107

SeptOct 1999[7] Bor-Ren Lin Hsin-Hung Lu A novel multilevel PWM control

scheme of the ACDCAC converter for AC drives Proceedings of

the IEEE international Symposium on Industrial Electronics 1999ISIE99 Vol2 pp 795-800

8122019 04510573

httpslidepdfcomreaderfull04510573 55

[8] Sanmin Wei Bin Wu Fahai Li and Congwei Liu A general spacevector PWM control algoritm for multilevel inverters 2003 IEEE

[9] N Celanovic D Boroyevich A fast Space Vector modulation

algorithm for multilevel three-phase converter in Conf Rec IEEE

IAS Annual Meeting 1999 pp 1173-1177[10] B P MacGrath D G Holmes and T A Lipo Optimized space

vector switching sequences for multilevel inverters in Proc IEEE

Apec Anaheim CA Mar 4-8 2001 pp 1123-1129[11] HSPatel et RGHoft laquoGeneralized technique of harmonics

elimination and voltage control in thyristor inverter raquo IEEE Tran

Ind Appli pp 310-317 1973[12] John Nchiasson Leon MTolbert Keith JMckenzie et Zhong Du laquoA

unified approach to solving the harmonic elimination equations in

multilevel convertersraquo IEEE transactions on power electronics

Vol19 Ndeg2 March 2004[13] John NChiasson Leon Tolbert Keith JMckenzie et Zhong Du laquo A

complete solution to the harmonics elimination problem raquoDeacutepartement ECE universiteacute de Tennessee 2003 IEEE

[14] YSahali et MKFellah laquo Selective harmonic eliminated plusewidth

modulation technic (SHE PWM) applied to three-levelinverterconverter raquo IEEE International Symposium on Industrial

Electronics Rio de Janeiro Brasil 9-11 juin 2003

[15] Keith Jeremy Mckenzie laquo Elimination harmonics in a cascaded H- bridges multilevel inverter using resultant theory symmetric polynomials and power sums raquo thesis for the Master of science

degree University of Tennesse Knoxville May 2004

[16] SSirisukprasert laquo Optimized harmonic stepped-waveform formultilevel inverter raquo Master thesis submitted to the faculty of the

virginia politechnic institute and state university 1999

[17] J A Freeman and T Shibata Neural Networks Algorithms A pplications and Programming Techniques Addison-Wesley publication Cie 1992

[18] B Widrow and M A Lehr 30 years of adaptive neural networksPerceptron madaline and backpropagation Proc Of the IEEE 781415-14141

[19] P J Werbos Neural networks for control chapter 3 pp 67-95 MIT

Press Cambridge MA 1990[20] MJDPowell laquo Radial basis function for multivariable interpolation

A reviewraquo JCMason and MGCox Editors Algorithms forApproximation pp 143-167 Oxford University Press 1987

[21] K I Funahashi On the approximate realization of continuous

mappingd by neural networks Neural Networks 2 183-192[22] G Cybenko Approximation by superposition of a sigmoidal function

In penkaj Mehra and Benjamin W Wah Artificial Networks

Concepts and Theory pp 488-499 IEEE computer Society Press

Tutorial

8122019 04510573

httpslidepdfcomreaderfull04510573 55

[8] Sanmin Wei Bin Wu Fahai Li and Congwei Liu A general spacevector PWM control algoritm for multilevel inverters 2003 IEEE

[9] N Celanovic D Boroyevich A fast Space Vector modulation

algorithm for multilevel three-phase converter in Conf Rec IEEE

IAS Annual Meeting 1999 pp 1173-1177[10] B P MacGrath D G Holmes and T A Lipo Optimized space

vector switching sequences for multilevel inverters in Proc IEEE

Apec Anaheim CA Mar 4-8 2001 pp 1123-1129[11] HSPatel et RGHoft laquoGeneralized technique of harmonics

elimination and voltage control in thyristor inverter raquo IEEE Tran

Ind Appli pp 310-317 1973[12] John Nchiasson Leon MTolbert Keith JMckenzie et Zhong Du laquoA

unified approach to solving the harmonic elimination equations in

multilevel convertersraquo IEEE transactions on power electronics

Vol19 Ndeg2 March 2004[13] John NChiasson Leon Tolbert Keith JMckenzie et Zhong Du laquo A

complete solution to the harmonics elimination problem raquoDeacutepartement ECE universiteacute de Tennessee 2003 IEEE

[14] YSahali et MKFellah laquo Selective harmonic eliminated plusewidth

modulation technic (SHE PWM) applied to three-levelinverterconverter raquo IEEE International Symposium on Industrial

Electronics Rio de Janeiro Brasil 9-11 juin 2003

[15] Keith Jeremy Mckenzie laquo Elimination harmonics in a cascaded H- bridges multilevel inverter using resultant theory symmetric polynomials and power sums raquo thesis for the Master of science

degree University of Tennesse Knoxville May 2004

[16] SSirisukprasert laquo Optimized harmonic stepped-waveform formultilevel inverter raquo Master thesis submitted to the faculty of the

virginia politechnic institute and state university 1999

[17] J A Freeman and T Shibata Neural Networks Algorithms A pplications and Programming Techniques Addison-Wesley publication Cie 1992

[18] B Widrow and M A Lehr 30 years of adaptive neural networksPerceptron madaline and backpropagation Proc Of the IEEE 781415-14141

[19] P J Werbos Neural networks for control chapter 3 pp 67-95 MIT

Press Cambridge MA 1990[20] MJDPowell laquo Radial basis function for multivariable interpolation

A reviewraquo JCMason and MGCox Editors Algorithms forApproximation pp 143-167 Oxford University Press 1987

[21] K I Funahashi On the approximate realization of continuous

mappingd by neural networks Neural Networks 2 183-192[22] G Cybenko Approximation by superposition of a sigmoidal function

In penkaj Mehra and Benjamin W Wah Artificial Networks

Concepts and Theory pp 488-499 IEEE computer Society Press

Tutorial