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Abstract - Space vector pulse width modulation (SVPWM) is an optimum pulse width modulation technique for an inverter used in a variable frequency drive applications. It is computationally rigorous and hence limits the inverter switching frequency. This paper discusses a time equivalent SVPWM and neural Network based SVPWM technique for a five-phase voltage source inverter in under modulation region. A neural network has the advantage of very fast implementation of an SVPWM algorithm that can increase the inverter switching frequency. The scheme has been simulated and comparative study is given with the existing PWM schemes. The simulation results are given to validate the concept of proposed schemes. Index Terms - Voltage source inverter (VSI), Time equivalent SVPWM, Artificial neural network (ANN), Total harmonic distortion (THD) and Weighted THD (WTHD).

I. INTRODUCTION ARIABLE frequency ac drives are increasingly replacing dc drives in a number of industrial applications due to

advantages in size, reliability and efficiency. One of the main components of an ac drive is power electronic converter in the form of voltage source inverter that takes dc voltage input (may be from a rectifier) and produces a sinusoidal ac waveform. This in turn is fed to the ac electric motor. The fundamental frequency of this waveform is adjusted to produce the desired speed. In modern electric drives the modulation of switching is carried out to achieve the required ac wave shape. This is met by incorporating the duration of ‘ON’ & ‘OFF’ methods [1, 2]. The techniques to get the duration of ON interval for a particular switch depend upon the control logic or PWM technique to be adopted. In a PWM scheme the output voltage and frequency can be controlled with the help of the switching inside the inverter. The switch may be MOSFET, IGBT etc with antiparallel connected diodes. Different PWM schemes such as sinusoidal PWM compares a high frequency triangular carrier with five sinusoidal reference signals, known as the modulating signals, to generate the gating signals for the

Shailesh Kumar Gupta is a M. Tech. student in Deptt. of Electrical & Electronics Engg., Krishna Institute of Engg. & Technology, Ghaziabad INDIA, (e-mail: geniousshailesh@gmail.com).

Mohd Arif Khan is with Deptt. of Electrical & Electronics Engg., Krishna Institute of Engg. & Technology, Ghaziabad INDIA, (e-mail: mdarif27@rediffmail.com).

Atif Iqbal is with Deptt. of Electrical Engg., Qatar University, Doha, QATAR. (e-mail: atif2004@gmail.com). Zakir Husain is with Department of Electrical and Electronics Engineering, NIT Hamirpur, INDIA. (email: zahusain2@gmail.com)

inverter switches but having a disadvantage that it contains third harmonic in output[3]. To the cancellation of the third-harmonic components and better utilization of the dc supply, the third harmonic injection PWM scheme is preferred in five-phase applications. Space vector modulation technique has advantage of an optimal output and also reduces harmonic content of the output voltage/current [4]. Space vector PWM (SVPWM) has the advantages of lower harmonics and a higher modulation index in addition to the features of complete digital implementation by a single chip microprocessor, because of it flexibility of manipulation; SVPWM has increasing application in power converters and motor control. An alternative and simple space vector pulse width modulation (SVPWM) scheme for a five-phase voltage source inverter (VSI) is proposed in this paper. The proposed PWM scheme generates the inverter leg switching times, from the sampled reference phase voltage amplitudes and centre the switching times for the middle vectors, in a sampling interval, as in the case of conventional space vector PWM. Similar technique has been reported in the literature [1] for a five-phase VSI. The proposed PWM scheme utilizes only the sampled amplitude of reference phase voltages for implementing the SVPWM. It does not involve any sector identification and a number of look up tables thus considerably reducing the computation time when compared to the conventional space vector PWM scheme. The proposed technique thus is simple and less demanding for use in real time DSP implementation. The application of artificial neural network (ANN) is recently growing in power electronic systems. A feed forward ANN implements nonlinear input–output mapping. The computational delay of this mapping becomes negligible, if parallel architecture of the network is implemented by an application-specific integrated circuit (ASIC) chip. A feed forward carrier-based PWM technique, Such as SVM, can also be looked upon as a nonlinear mapping phenomenon where the command phase voltages are sampled at the input and the corresponding pulse width patterns are established at the output. Therefore, it appears logical that a back propagation-type ANN that has high computational capability can implement an SVM algorithm. In this paper proposed ANN can be conveniently trained offline with the data generated by calculation of the TESVPWM algorithm. ANN has inherent learning capability that can give improved precision by interpolation unlike the standard lookup table method. [16-24]

Comparative Analysis of Pulse Width Modulation Schemes for Five Phase Voltage Source Inverter

Shailesh Kumar Gupta, Mohd. Arif Khan , Atif Iqbal, Senior Member, IEEE, and Zakir Husain

V

II. PWM SCHEMES FOR FIVE PHASE VSI – A REVIEW

Pulse Width modulation technique is the most basic method of energy processing in power electronic converters. The purpose here is to control the inverter to generate the variable voltage and variable frequency voltages/currents. This section describes the PWM techniques employed for controlling a five-phase voltage source inverter. Purpose here is to generate the five-phase sinusoidal output voltage. For this purpose different existing pulse width modulation techniques are

(a) Carrier based sinusoidal PWM (b) Fifth harmonic injection pulse width modulation scheme (c) Offset addition pulse width modulation scheme (d) Space vector pulse width modulation scheme

(a) Carrier based sinusoidal PWM Carrier-based sinusoidal PWM is the most popular and widely used PWM technique because of their simple implementation in both analogue and digital realization. The PWM signal is generated by comparing a sinusoidal modulating signal with a triangular (double edge) or a saw-tooth (single edge) carrier signal. The frequency of the carrier is normally kept much higher compared to the modulating signal. Principle of operation of a carrier-based PWM modulator is shown in Fig. 1 and the filtered output voltage is shown in Fig 2.

Carrier signal

+

+

+

+

-

-

-

-

-

1 6,S S

3 8,S S

5 10,S S

7 2,S S

9 4,S S

*av

*bv

*cv

*dv

*ev

+

+

+

+

-

-

-

-

-

+

Zero sequence

signal

Fig. 1 Principal of operation of carrier based PWM

Fig. 2 filtered output voltage for the carrier based PWM scheme

(b) Fifth harmonic injection based PWM

The effect of addition of harmonic with reverse polarity in any signal is to reduce the peak of the reference signal. Aim here is to bring the amplitude of the reference as low as possible, so that the reference can then be pushed to make it equal to the carrier, resulting in the higher output voltage and better dc bus utilisation. Using this principle, fifth harmonic injection PWM scheme is used in a five-phase VSI which results in increase in the fundamental output voltage to 0.5254 Vdc .

Fig. 3 Reference signal after third harmonic injection

(c) Offset addition based PWM

Another way of increasing the modulation index is to add an offset voltage to the references. The offset voltage addition is effectively adding 3n harmonic. This will effectively do the same function as above.

max min

2offestV VV += −

(1) In case of five-phase VSI the offset voltage is simply third harmonic triangular wave of 25% magnitude of fundamental.

Fig. 4 . Reference signal after Offset addition

(d) Space vector PWM

There are six switching devices and only five of them are independent as the operation of two power switches of the same leg are complimentary. The combination of these five

switching states gives out eight possible space voltage vectors. The space vectors forms a hexagon with 6 distinct sectors, each spanning 60 degrees in space. At any instant of time, the inverter can produce only one space vector. In space vector PWM a set of five vectors (two active and a zero) can be selected to synthesize the desired voltage in each switching period.

/ 5π

q-axis

d-axis

Fig. 5 - Space Vector representation of Line to Neutral Voltages

Fig. 6 Harmonic Spectrum for output voltage of the space vector based pulse

width modulation scheme

III. PROPOSED PWM SCHEMES FOR FIVE-PHASE VSI

(a) Time equivalent space vector pulse width modulation (TESVPWM) scheme

The presented SVPWM called here time equivalent space vector PWM (TESVPWM) utilises simply the sampled reference voltages to generate the gating time for which each inverter leg to yield sinusoidal output. The reference voltage is sampled at fixed time interval equal to the switching time. The sampled amplitude is converted to equivalent time signal. Thus a time offset is added to these signals to obtain the gating time of each inverter leg. This offset addition centre the active switching vectors within the switching interval. The algorithm is given below, Where Vx; x=a,b,c; is the sampled amplitudes of reference phase voltages during sampling

interval and Ts is the inverter switching period. Tx; x=a,b,c; are referred as time equivalents of the sampled amplitudes of reference phase voltages. Tmax and Tmin are the maximum and minimum values of Tx during sampling interval. To is the time duration for which the zero vectors is applied in the switching interval. Toffset is the offset time when added to time equivalent becomes gating time signal or the inverter leg switching time Tgx;x=a,b,c.

Algorithm of the proposed TESVPWM:

I Sample the reference voltages Va , Vb,& Vc, in every switching period Ts.

II Determine the equivalent times T1,T2& T3 given by expression, where x = a, b and c;

;dcVsT

xsVxsT ×=

III Determine Toffset ; dcV

TTSToffsetT minmax

2

+−=

IV Then the inverter leg switching times are obtained as ;offsetxgx TTT += x = a, b and c.

The TESVPWM is simulated using Matlab/Simulink model shown in Fig. 9. The five-phase voltage is provided with amplitude equals to ± 0.5 VDC and VDC is kept unity. The switching frequency is chosen equal; to 5 KHz.

Fig.7 Filtered output voltage for the time equivalent space vector based pulse

width modulation scheme

Fig. 8 Harmonic Spectrum for output voltage of the time equivalent space

vector based pulse width modulation scheme

Filtered output voltage after connecting a RL load at the output terminals for TESVPWM based scheme is shown in fig 7.and the harmonic spectrum for the output phase ‘a’ voltage is shown in Fig.8 shows that fundamental component appears at 50 Hz frequency. (b) Artificial neural network based space vector pulse

width modulation.

This section describes the ANN PWM based on TESVPWM scheme. The reference signal in TESVPWM is taken as input neuron values and the modulating signals in TESVPWM scheme is taken as the target values. Then the Matlab neural network tool is used for the training and simulation purpose which is later formed the ANN block for the above scheme

The complete implementation block diagram is illustrated in Fig.9. There are three layers in the neural network; one is input layer with five neurons in Fig 10 (a), one hidden layer with ten neurons in Fig 10 (b) and one output layer with five neurons in Fig 10 (c). Feed-forward back propagation type network is used and the Levenberg-Marquardt backpropagation “trainlm” training function is used for the simulation purpose. The Gradient descent with momentum weight and bias learning (LEARNGDM) adaptation learning function and Mean squared error (MSE) performance function have used. Transfer function is hyperbolic tangent sigmoid transfer function (TANSIG) type. Filtered output voltage and the harmonic spectrum for output voltage for the proposed scheme shown in Fig. 11 and Fig. 12.

Norm

alization

De-norm

alization

V*

α* Ts/4

UP/Down

Counter

Sa

Sb

Sc

Sd

Se

( )*Vf

( )*αg

Neural Network

Fig. 9 Functional Block Diagram of ANN Based SVM for a Five-Phase VSI

(a)

(b)

(c)

Fig.10 Artificial Neural Network Topology for five-phase VSI

y{1}

1

a{1}

Process Output 1

a y

Process Input 1

x p

Layer 2

a{1} a{2}

Layer 1

p{1} a{1}

a{1}

x{1}

1

iz {1,1}

1

dotprod 9

w

pz

dotprod 8

w

pz

dotprod 7

w

pz

dotprod 6

w

pz

dotprod 5

w

pz

dotprod 4

w

pz

dotprod 3

w

pz

dotprod 2

w

pz

dotprod 10

w

pz

dotprod 1

w

pz

Mux

Mux

IW{1,1}(9,:)'

weights

IW{1,1}(8,:)'

weights

IW{1,1}(7,:)'

weights

IW{1,1}(6,:)'

weights

IW{1,1}(5,:)'

weights

IW{1,1}(4,:)'

weights

IW{1,1}(3,:)'

weights

IW{1,1}(2,:)'

weights

IW{1,1}(10 ,:)'

weights

IW{1,1}(1,:)'

weights

pd {1,1}

1

lz{2,1}

1

dotprod 5

w

pz

dotprod 4

w

pz

dotprod 3

w

pz

dotprod 2

w

pz

dotprod 1

w

pz

Mux

Mux

IW{2,1}(5,:)'

weights

IW{2,1}(4,:)'

weights

IW{2,1}(3,:)'

weights

IW{2,1}(2,:)'

weights

IW{2,1}(1,:)'

weights

ad {2,1}

1

Fig. 11 Filtered output voltages for the ANN based

Fig. 12 Harmonic Spectrum for output voltage of the

scheme

IV. PERFORMANCE COMPARISOEXISITNG AND PROPOSED

The method of comparing the effectiveness by comparing the unwanted components i.ethe output voltage or current waveform, relaideal sine wave, it can be assumed that by ppositive and negative portions of the output(no DC or even harmonics). The total harmfactor reduces to,

THD = ∑∞

=⎟⎟⎠

⎞⎜⎜⎝

⎛

..7,5,3

2

1n

n

vv

(2)

Normalizing this expression with respect to i.e. fundamental, the weighted total har(WTHD) becomes defined as

WTHD = 1

..7,5,3

2

Vn

Vn

n∑∞

=⎟⎠

⎞⎜⎝

⎛

(3)

d PWM scheme

ANN based PWM

ON BETWEEN D SCHEMES

of modulation is . the distortion in ative to that of an proper control, the t are symmetrical monics distortion

the quantity (V1) rmonic distortion

Taking the advantage of MATLcontrol system is built up, and the the schemes mentioned above areThen the total harmonics distortischemes is obtained by FFT meswitching period is taken as 0.2msfrequency is designed as 50Hz. The schemes are same, executed in convenience of comparison, the THschemes are calculated at the samesimulation are shown in figure 13.

Fig. 13 comparison of existing and proposed P

THD & WTH

Seen from figure, the THD and scheme is the lowest from the rest schemes. The proposed ANN basedTHD lower than carrier based and spand higher than the offset additionTESVPWM. The offset addition bain the existing PWM schemes due toand WTHD than the carrier based PWM and space vector based PWManalysis it is shown that that the proscheme is best in the above meaddition based PWM scheme is the bPWM schemes.

V. CONCL

In this paper different existing Pphase voltage source inverter areschemes are proposed i.e. time equiand ANN based PWM. The algTESVPWM scheme is elaborated aMatlab/Simulink the scheme is simuresults are obtained. The simulatioutput contains fundamental comfrequency. ANN based scheme is data available from the TESVPWMlayer containing five neurons, one hneurons and output layer containingvoltage spectrum shows that thecomponent at 50 Hz frequency. Th

AB, five phase inverter output line voltages of all

e obtained by simulation. on (THD) rate of those ethod. In simulation the s, and the inverter output operating situations for all the simulation. For the

HD and WTHD of all the e time. The results of the

PWM schemes based on D

WTHD of TESVPWM of existing and proposed

d scheme has the value of pace vector based schemes n, harmonic injection and sed PWM scheme is good o the lower values of THD PWM, harmonic injection M. On the basis of above oposed TESVPWM based entioned schemes. Offset best scheme in the existing

USION

PWM schemes for a five-e studied and two new ivalent space vector PWM gorithm of the proposed and then with the help of ulated and their simulation on results show that the mponent at the 50 Hz proposed on the basis of

M scheme. There are input hidden layer containing ten g five neurons. The output e output contains single he performance of all the

schemes are evaluated on the basis of THD & WTHD and found that TESVPWM is the best proposed scheme and Offset addition based PWM scheme is best in the existing schemes.

VI. REFERENCES

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