The space vector PWM for voltage source inverters using artificial neural networks based on FPGA

The Space Vector PM for Voltage Source Inverters Using Artiicial Neural Networks Based on FPGA School of Electrical Engineering, University ofUlsan, Ulsan, Korea hhlee@mail.ulsan.ac.k

The Space Vector PM for Voltage Source Inverters Using

Artiicial Neural Networks Based on FPGA

School of Electrical Engineering,

University ofUlsan, Ulsan, Korea

hhlee@mail.ulsan.ac.kr

HCMC University of Technology

Ho Chi Minh City, Vietnam

pqdung@hcmut.edu.vn

HCMC University of Technology

Ho Chi Minh City, Vietnam Imphuong@hcmut.edu.vn

Le Dinh Khoa

HCMC University of Technology

Ho Chi Minh City, Vietnam

khoaledinh@hcmut.edu.vn

Nguyen Truong Dan Vu HCMC University of Technology

Ho Chi Minh City, Vietnam

ntdanvu@gmail.com

Abstract- This paper presents space vector PWM algorithm for

six- switch three-phase inverters (SSTPI) using Artiicial Neural

Networks (ANN) based on the ready-to-use ield-programmable

gate array (FPGA) technology ANN is used to calculate ON-OFF

time for six switches when given the angle and modulation index

of required voltage space vector This approach has the

advantage of very fast implementation of an Space Vector PWM

(SVPWM) algorithm that can increase the converter switching

frequency, particularly when the ield-programmable-gate-array

(FPGA) technology is used in the modulator This SVPWM is

also validated experimentally using FPGA-XUP VIRTEX II PRO

from Xilinx in SSTPI-IM system for under modulation mode and

over modulation mode 1 and 2, extended to six-step mode,

especially for 40khz-switching-frequency case

Kword: Space vector, Pulse-Width- Modulation, Artiicial

Neural Network, Voltage Source Inverter, undermodulation,

overmodulation

I INTRODUCTION

The applications of AN technique have been

developed strongly in power electronic ield in recent

years In the past, a neural network was implemented

in instantaneous curent control PWM [4-7] Nevertheless,

current control PWM does not give optimum performance

Several researches of ANN implementation of SVM had been

worked out [3,2] Although this ANN-SVM controller has the

advantage of fast calculation, the limitation of this approach is

the dificulty of training in the overmodulation range with

nonlinearity of modulation technique

To avoid this spot, the proposed back-propagation-type

feed-forward AN-SVM [12] successully has been trained

by using two principal approaches:

1) Method of linear modulation between two

limitary trajectories [8] (to overcome the diiculty of

nonlinearity of overmodulation range)

2) Individual training strategy with 8 Sub-nets (to

overcome the complexity of SVM for 3 modes:

undermodulation, overmodulation mode 1,

overmodulation mode 2)

VSI + - 1- - ,

Ud

1 + FPGA BASED ANN-SVPWM

CONTROLLER

c

Power system or Drive

Figure 1 NN- SVPM FPGA Bsed Controller for VSI

Because of highly parallel property and more resource demand of AN, FPGA is suitable to implement for experiments In this study, the FPGA implementation algorithm for ANN-SVPWM is presented Real number calculation and activation unction for ANN have been considered well The algorithm permits the accuracy of ANN about le-3 because of 3-ractional-digit loating point number model Experimental results of three modulation regions show that the parallel property of AN is guaranteed The switching requency is increased up to 40 hz

II SPACE-VECTOR PWM N UNDERMODULA TION AND OVERMODULATION REGIONS REVIEW The SVM technique has been well discussed and developed

in literature, and a number of authors [1], [8]-[10] have described its operation in the overmodulation Among these methods of modulation, method of modulation between trajectories [8] has the advantage of simplicity and linearity

A Undermodulation (0 < M < 0.907)

In the undermodulation, the rotating reference voltage remains within the hexagon The SVM strategy in this region

is based on generating three consecutive switching voltage vectors in a sampling period (Ts) such that the average output voltage matches with the reference voltage The equations for

efective duty cycle of the inverter switching states can be

described as following:

d, = 23 r M sin(r 1 3 -a)

d, = 23 r M sin( a)

do = I-d, -d,

where

(1)

dl - duty cycle (2tI/Ts) of switching vector that lags

d2 - duty cycle (2t2/Ts) of switching vector that leads

do - duty cycle (2tofT s) of zero-switching vector

M - modulation factor M = y* IY Isw (y* - magnitude of

reference voltage vector, Ylsw - the peak value of six­

step voltage wave )

The timing intervals re obtained by multiplying duty

cycles and period Tsl2 respectively

B vermodulation mode 1 (0.907 < M < 0.952)

This mode strts when the reference voltage y* exceeds the

inscribable circle in the hexagon nd atteints the sides of the

hexagon On the hexagon trajectoy, duty do vanish:

" 3cosa-sina

d, = ,3cosa+sina h

d," =I-d,

do" =0

(2)

Applying theory of linear modulation within trajectoy, the

fIrst trajectoy has been chosen with M = 0.907:

23 ( )

d, =-·0.907sinrI3-a r

(3)

23 ( )

d, =-·0.907sin a r

d; =I-d, -d,

The second one is the bounday of hexagon (2)

Coeficient of modulation is deined as following:

1= M,-M, M-M,

The duty cycles accordingly [8] are detemined as :

d, = d,' + 1(d," -di)

d, = d,' + 1(d," -d,')

do =d; +1(-d;)

vermodulation mode 2 (0.952 < M < 1)

(4)

(5)

In overmodulation mode 2, the reference vector y*

increases urther up to six-step mode

Applying theory of linear modulation within trajectory, the

fIrst trajectoy has been chosen with M = 0.952 :

d' _ , -3cosa+sina 3cosa-sina

(6) d,' =l-d,

d; =0

The second is divided in two cases:

For 0�a�r16 :

d," =I;d," = 0; do" =0

For r16�a�r13 :

(7)

Accordingly [8], the duty cycles are described linearly

as following:

d, = d,' + 1(d," -di)

d, =d,' +1(d," -d,')

do =0

(9)

Coeficient 1 is determined similarly (4) where MI=0.952, M2=1

In overmodulation region, this approach has the advantage of simplicity in comparison with other conventional method [2] III NEUL-NETWORK BASED SPACE VECTOR PWM

The SYM algorithm will be used to obtain training data for developed -AN-SYPWM

A Undermodulation Region Sub-net:

For any command angle c/, the duty cycles d), d2, do are given by (1) for sector 81• Similar duty cycles can be determined for all six sectors and the phase tum-on duty cycles can be calculated as [12]:

1 3 (

' )

1 3 (

' ) dB-ON = 2 + ;-M h20 a

1 3 (

' ) dC-ON = 2 + ;-M h30 a

where

( ,)_ [-sin(r 1 3 -a)+ sinal 8= 2

hIO a - [+ sin(r 13 _ a)+ sinal 8 = 3, 4

1[-sin(r 1 3 -a)-sin al 8 = I, 6

[+ sin(r 1 3 -a)-sinal 8 = 5

(11)

h2o(a\ h3o(a*) are obtained similarly Then, hIO,2o,3o(a*) have been used for creating databases which are needed for training

-oo -30 -SCO

f10: tansig; 20: purelin; 30: purelin O=sqt3)2; bO=1/2

Figure 2 Undermodulation region subnet

undermodulation region Sub-net with one input (a*) and three outputs (hIO' h2o, h30)' The angle step is 10

A two-layer network is used for implementing this Sub-net The sub-net is obtained by training (supervised) with trainlm

unction - Levenberg -Marquardt algorithm, the acceptable for training squared error is 10-4• The number of neurons of lSI

layer is 10 tansig neurons, the 2nd layer has 3 purelin neurons

So, the total number of neurons is 13 neurons (convergence obtained for 1077 epochs)

B vermodulation model Sub-net

The duty cycles d), d2, do are calculated by (5) for sector 81• Ater several subtitutions, the duty cycles can be described as :

d, =K,sm rl3-a +1 -K,sm rl3-a + ' ( ) [ ( ) K cosa-sina] K, cosa+sma

d ,= 1 K,cosa-sina [K' K,cosa+sma +1- ,sma+ -1 K,cosa+sma K,cosa-sina]

do =l-d,-d, where

(12)

Kl =3; K, = 3 ·0.907

r

Duty cycles can be determined for all six sectors and the phase

tum-on duty cycles can be calculated similar as (10)-(11) by

subtituting (12)

dA_oN =�+� [hl1a{a')+/.h'la{a')] (13)

dB_ON =�+ � [hl1b (a')+ / h'lb (a')]

dC_ON =� + � [hl1' (a')+ / h'k (a')]

where

and

u

K cosa-sina -K,s1O(r/3-a)-I+ 1 Kl cosa+s1Oa ' 8=1,6

-K, sin(r/3-a)+1 Kl cosa-sina Kl cosa+sina'

K (/3 ) 1 Kl cosa-sina

+ ,s1o r -a + Kl cosa+sina'

(/3 ) Kl cosa-sina

K,s1Or -a -I+ Kl cosa+s1Oa ,

8=2 8=3,4 8=5

(14)

-SA1

d 1 3 cosa+ sina / 3 cosa+ sin a 3cosa-sina + (1 3cosa-sina)

d ,--1 3cosa-sina [3cosa-sina 1]

3cosa+sina +/ 3cosa+sina

do =0

- For t/6 < a; I3 :

d 3cosa-sina 3cosa-sina

1 3cosa+sina +/ 3 cos a + sin a

3 cosa-sina 3 cosa-sina

d, =1 3 cos a + sina +/ .3 cos a + sina

(16)

(17)

-32 -SC2

]2

12: tansig; 22: purelin; 32: purelin 2=I; b2=O

Figure 4 Overnodulation mode 2 region subnet -31 Duty cycles can be expressed for all six sectors by using (15):

]1

11: tansig; 21: purelin; 31: pure Ii n Wl=l2; bl=112

Figure 3 Overnodulation mode 1 region subnet

-I + K, (sin(r 1 3-a)+sin a),

K cosa-sina 8=1,6 K,(s1O(r/3-a)+s1Oa)+1-2 1 . , 8=2

h'la a' = I-K, sin r/3-a +sina , ( ( ) ) 8=3,4

K cosa-sina -1+K,(s1O(r/3-a)+s1Oa)+2 1 . , 8=5

Kl cosa+s1Oa

SC1

(15)

hllb(a*), h2lb(a*),h11e(a*), h21e(a*) are obtained similarly

Then, h11, 211, 11b, 21b, 11e, 21e (a *) have been used for creating

databases which are needed for training overmodulation

region Sub-net with one input (a') and six outputs

(h11a,h2Ia,hllb,h2Ib,hlle,h2Ie)' The angle step is 1 degree

A two-layer network is used for implementing this Sub-net

The sub-net is obtained by training (supervised) with trainlm

unction - Levenberg -Marquardt algorithm, the acceptable

for training squared error is 10-4 The number of neurons of 1 sl

layer is 20 tansig neurons, the 2nd layer has 6 purelin neurons

So, the total number of neurons is 26 neurons (convergence

obtained for 1016 epochs)

vermodulation mode 2 Sub-net

The duty cycles in this mode dt d2, do are given by (9) for

sector 81 Ater several transformations, the duty cycles can be

written as:

- For 0 < a ; t/6 :

dA_oN = hI2a(a')+/ h".(a') (18)

dB_ON =hi2b (a')+ / h"b (a') dC_ON =h1"{a')+/.h,,,{a') where

h'la (a')=

and

h'la{a')=

0, 8=1,6

1 3 cos a -sin a 8=2

3 cosa+sina'

3 cos a-sin a 8=5

3 cosa+sina

0, 8=1,6

[1-.3 cosa -sina forO : a : f6

3 cosa + sin a 3cosa-sina f6< <f3 3cosa+sina' or _a_

D, 8=3,4

[1- 3 cosa -sin a forO 3 cosa + sin a : a : f6 3cosa-sina f6< <f3 3cosa+sina' or _a_

(19)

(20)

8= 2

8=5

h2lb( a*), h22b( a *),h2Ie( a *), h22e( a *) are obtained similarly Then, h2la, 22, 21b, 22b, 21e, 22e (a *) have been used for creating databases which are needed for raining overmodulation mode

2 Sub-net with one input (a *) and six outputs (h2Ia,h22a,h2Ib,h22b,h2Ie,h22e)' The angle step is 1 degree

A two-layer network is used for implementing this Sub-net The sub-net is obtained by training (supervised) with trainlm

unction - Levenberg -Marquardt algorithm, the acceptable for training squared error is 10-4• The number of neurons of 1 sl

m

]1

5: tansig; 8: purel i n Figure 5 Il calculation subnet

m

6: !ansig; 9: pure!in Figure 6 12 calculation subnet

e

eo

7: tansig: (13: purelin; (14: logsig; (15: pU"elin

Figure 7 Code of modulation mode Sub-net

layer is 20 tansig neurons, the 2nd layer has 6 purelin neurons

So, the total number of neurons is 26 neurons (convergence

obtained for 200 epochs)

D 71, 72 calculation Sub-nets

The coeficient 11 and 12 in overmodulation mode 1 and

mode 2 respectively are given by equation (4) This equation

had been used for generating neural network training data The

input M is varied rom 0.907 to 0.952 with step of 0.001, he

ouput is 11 and varied rom 0.952 to 1 with step of 0.001, the

ouput is 12

A 2 two-layer network is used for implementing these sub­

nets The sub-net is obtained by training (supervised) with

trainlm unction - Levenberg -Marquardt algorithm, the

acceptable for training squared error is 10-4• The number of

neurons of 1 st layer is 1 tansig neurons, the 2nd layer has 1

purelin neurons So, the total number of neurons is 2 neurons

Convergence is obtained for 57 epochs for 11-subnet and 46

epochs for 12-subnet) (Fig 5, 6)

Code of modulation mode Sub-net

The purpose of this subnet is to deine the code of

modulation mode:

Undermodulation : Cm = 3

Overmodulation mode 1 : Cm = 1

Overmodulation mode 2 : Cm = 2

The input M is varied rom 0 to 1 with step of 0.001, the

ouput is Cm•

TABLE I MODE SELECTION CODE

The sub-net is trained with trainlm unction Levenberg

-Marquardt algorithm, the acceptable for training squared error

is 10-10• The number of neurons of 1 st layer is 15 tansig

neurons; the 2nd layer has 1 purelin neurons So, the total

number of neurons is 16 neurons Convergence is obtained for

519 epochs

Mode Selection Code Sub-net

This subnet is used for determining which modulation mode

to be choice for generating duty cycles at outputs of AN­

SVM-Controller (SA, SB, Sc)

The input of this subnet is Cm, the ouput is eA, eB, ec (Table 1) (Fig.7)

The sub-net is trained with trainlm unction Levenberg -Mrquardt algorithm, the acceptable for training squared error

is 10-10• The number of neurons of 1 st layer is 2 logsig

neurons; the 2nd layer has 3 purelin neurons So, the total number of neurons is 5 neurons Convergence is obtained for

17 epochs

IV SIMULATION OF NN -SVPWM

A SimulinkiMatlab program with the toolbox of neural -network is used to train and simulate the complete AN­ SVPWM Controller with the above-mentioned sub-nets for diferent mode of operation: undermodulation, overmodulation mode 1,2

DC source voltage V d = 400V

1 Case stuy 1:

Modulation index: M = 0.5 when 0 ms ; t ; 40 ms; M = 0.93 when 40 ms ; t ; 80 ms; M = 0.97 when 80 ms ; t ; 120 ms;M= 1 when 120 ms;t; 160 ms

Figure 8 Simulation model for NN -SVPWM Controller

Figure 9 Simulation model of Voltage Source Inverter

TABLE II Table of simulation results for nn - controller

Modulation index M 0.5 0.93 0.97 1

(six-step)

Reference voltage V Ifef, [V] 127.3 236.8 247.0 254.6 Simulated output peak phase 126.7 236.7 246.3 254.6 voltge V INN, [V]

Tolerance e, [%] 0.471 0.042 0.283 0 Distortion factor THO, [%] 1.13 2.15 10.22 26.2

SImulatIOn results demonstrate the excellent performance

of the proposed AN-SVPWM for VSI, while the good responses of the output voltages are obtained (ig.l0 - 11, Table II)

Phase oltage waeform

10 12 14

ime, (us)

Figure 10 Phase voltage for undermodulation and overmodulation

mode 1,2 region

Figure 11 Line voltage for undermodultion nd overmodulation mode

1,2 regions

V ANN-SVPWM IMPLEMENTA nON USING FPGA

I ANN implementation summary

It is important to pay attention to Max-Min value of ANN­

parameters For used FPGA resource reduction, bias and

weights of ANN should to be declared in a speciic range

ANN has been initialized and trained in Matlab Next, ANN­

parameters have been got and declared in VHDL ANN is

created step by step with above algorithm for operations

2 NN application scheme for SVPWM (Fig.12-14)

For SVPWM, ANN is used to calculate ON-OFF time for

six switches when given alpha and modulation factor of

required space vector A speciic scheme for FPGA program is

presented in Fig 14

g·ak

Figure 12 ANN-SVPWM Scheme

VI EXPEIMENTAL AN-SVPWM

Experimental model includes: Kit XUP Virtex II pro of Xilinx;

Capacitor 5600lF, 450V; Driver circuit HCPL-3120; 6-switch

IGBT inverter circuit (Fairchild IGBT G60NlOO 60A, 1000V);

Induction motor has the follows parameters: f = 50 Hz, 380V,

Y, I HP, cosp =0.81, 1395 pm (Fig.15)

Figure 13 Data process for multiplication

Figure 14 Step-by-step NN

design

Figure 15 Experimental model

Case stuy 1: Undermodulation

1

41-5094 H2 4.9 U 99.7 or

00

4

:H1 s.oovw

50.3548 �� VOLTS W'§'¥ I.'IE -�

M 2.SCms CH1 f -":n,v= � � ������ �� ��;

Figure 16 Line voltage wave form nd spectrum in case switch requency is 40kHz, fou=50Hz, M=O.6, Vdc=100V

, 'I�

SODH� 3B7u

9 0 r

00

··;�o J, ·"· ···

Figure 17 Phase voltage wave form and spectrum in case switch requency is 2kHz, fout40Hz, M=O.7, Vdc=100V

rNxIYXY:YX:M ���t� so···· '''ri��:

1 3S8 H�

.127 n 99.7 or O·

" _ AlPS MH • p

Figure 18 Three- phase current waveforms and spectrum in case

switch requency is 2kHz, fout40Hz, M=O.7, Vdc=100V

Case study 2: Overmodulation mode 1

SrnsJd i v

50 V/ dlv

1 4 •

�.9B l�

718 U

940 r o·

�r�

m

_ _

··_�_·m.m_._

VOLTS iM

-Figure 19 Line voltage wave form and spectrum in case

switch frequency is 2kHz, fout=50Hz, M=0.94, Vdc=100V

'" i i

0 1 !.� �: lD KF

o •

1

19B Hz ese A

99.3 '

O·

-Figure 20 Three- phase current waveforms and spectrum in

case switch frequency is 2kHz, fou=40Hz, M=0.94, Vdc=100V

···�I··· o •

1 4'''

398 H:

4n7u

972%-00

I '[""

-Figure 21 Phase voltage wave form and spectrum in case

switch requency is 2kHz, fout40Hz, M=O.94, Vdc=100V

Case stuy 3: Overmodulation mode 2

,

190Hz 79

U

9S o· %

Figure 22 Line voltage wave form and spectrum in case

switch requency is 2kHz, fout=50Hz, M=O.985, Vdc=100V

1 4 •

1.90 HZ

9 9 %

o·

-Figure 23 Three- phase current waveforms and spectrum in case switch

requency is 2kHz, fout=50Hz, M=O.985, Vdc=IOOV

The results of output voltages nd currents are shown in

Fig 16-23 The Fig 16 shows the value of the undamentals

of the output line-voltage is 4S.9(V) while its theoretical value

is 46.78(V) So, the error of the output line voltage is 1.88%

In addition too, in the Overmodulation mode 1 (Fig 19) and

Overmodulation mode 2 (Fig 22) the voltage erors of

experiment implementation in compare with the theoretical

are 2.03% and 3.77%, respectively It can be seen rom these

results that implementing the proposed method the undamentals of the output voltages are ensured and the phase curents maintain symmetrical

VII CONCLUSION

This paper presents the algorithm of ANN implementation

in FPGA for SVPM The ANN in kit Virtex II pro of Xilinx operates very well in undemodulation as well as in overmodulation The implementation of the ANN-SVPM is done by simulation and in experiment to serve the practical production of the cost effective inverters in the ture based on FPGA

ACNOWLEDGMENT

The authors grateully acknowledge Vietnamese National University of Hochiminh City (U) and Network Based Automation Research Center (NARC) - Ulsan University for providing excellent supports and facilities

REFERENCES [1] 1 Holtz "Pulse width modulation for electric power conversion", Proc.lEEE, vo1.82, pp.l194-1214, Aug 1994

[2] 1 O P Pinto, B K Bose, L E B Silva, M P Karmierkowski "A Neural Network Based Space Vector PWM Controller for Voltage-Fed Inverter Induction Motor Drive", IEEE Trans on Ind Appl., vol.36, no

6, NovemberlDecember 2000

[3] A Bakhshai, 1 Espinoza, G loos, H lin "A combined NN and DSP approach to the implementtion of space vector modulation techniques",

in conf Rec.IEEE -lAS Annu Meeting, 1996, pp.934-940

[4] F Harashima et aI., "Applications of neural networks to power converter control", in conf Rec.lEEE -lAS Annu Meeting, 1989, pp.l086-1091 [5] M R Buhl nd R D Lorenz, "Design nd implementation of neural networks for digital current regulation of inverter drives", in conf Rec.lEEE -lAS Annu Meeting, 1991, pp.415-423

[6] 1 W Song, K C Lee, K B Cho, 1 S Won, " An adaptive lening current controller for ield - oriented controlled induction motor by neural network", in Proc IEEE -IECON'91, 1991, pp.469-474 [7] M P Karmierskowski et aI., " Neural network current control of VS­ PWM inverters ", in Proc IPE'95, 1995, pp.1415-1420

[8] N.V.Nho, M 1 Youn, "Two-mode overmodulation in two level VSI using principle control between limit trajectories", CD-ROM Proc PEDS 2003, pp.l274-1279

[9] 1 Holtz, W Lotzkat, M Khambadkone, "On continuous control of PWM inverters in the overmodulation rnge incIudingthe six-step mode", IEEE Trns Power Electron , vol.8, pp.546-553, Oct 1993 [10] S Bolognani, M Ziglitti, "Novel digital continuous control of SVM inverters in the overmodulation rnge", IEEE Trans Ind Applicat., vo1.33, pp.525-530, Mars/ April 1997

[11] S.Abramik, "Contribution a I'etude du diagnostic de defaillance des convertisseurs statiques en temps reelle» These du Doctorat, ENSEEIHT,2003

[12] Phn Quoc Dzung, Le Minh Phuong, Pham Qung Vinh, Nguyen Van Nho, Dao Minh Hien, "The Development of Artiicial Neural Network Space Vector PWM and Diagnostic Controller for Voltage Source Inverter", 2006 IEEE Power India Conference, New Delhi, India, April 10-12,2006

[13] Phn Quoc Dzung, Le Minh Phuong, Pham Qung Vinh, "The Development of Artiicial Neural Network Space Vector PWM for Four-Switch Three-Phase Inverter", PEDS 2007

[14] Volnei A.Pedroni, "Circuit Design with VHDL", MIT press, 2004