Researchpaper Analysis and Simulation of Three Phase Sinusoidal PWM Inverter

8/18/2019 Researchpaper Analysis and Simulation of Three Phase Sinusoidal PWM Inverter

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Analysis and simulation of three phase sinusoidalPWM Inverter fed by PV array

E. Hendawi 1, 2 , I. Bedir 1, 3

1 Department of Electrical Engineering, Faculty of Engineering Taif University

2 Electronics Research Institute, Egypt

3 Electrical Power and Machines Engineering Department, Faculty of Engineering, Tanta University, Egypt

Abs tr act —Mathematical analysis and simulation of a three phase sinusoidal PWM (SPWM) inverter fed by PV array is presented.Modeling of SPWM using MATLAB-Simulink is introduced based on MATLAB function and m-files. The inverter is supplied from a PV arraythrough voltage controlled boost chopper to maintain the inverter input voltage within a specified range. Simulation results using MATLAB-Simulink introduce high performance of the system when a step change is carried out representing variation of PV array voltage.

Index Terms —Sinusoidal PWM Inverter, PV array, voltage controlled boost chopper

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1 I NTRODUCTION

HE main objective of DC/AC inverters is to convert theDC input voltage to a symmetrical AC output voltagehaving a suitable voltage magnitude and frequency. The

input of the inverter may be a constant or a variable DCvoltage. Most applications of DC/AC inverters utilizeconstant DC voltage [1-3]. The DC voltage may come throughcontrolled or uncontrolled rectifier and smoothing capacitors,PV arrays, Fuel cells, or batteries.DC/AC inverters based on their output waveform can beclassified into two types: voltage source inverters (VSI) andcurrent source inverters (CSI). VSIs are the most widely usedand they are applied in many industrial applications, such asadjustable speed drives ASDs, uninterruptible power supply(UPS) and induction heating [2, 4]. The output voltages of theinverters are desired to be very close to sinusoidal waveformespecially in variable speed drives. Deviations from thesinusoidal shape may result in speed fluctuations, torqueripples and motor heating [2]. According to the switchingtechnique and the requirements needed by the load, threephase VSIs can be classified into several categories [1-3]. Pulsewidth modulation (PWM) inverters are considered as the mostcommon inverters. In these inverters, the dc input voltage ischopped by six switches to achieve ac output voltage in a formof pulses [2, 3]. The duty cycle of these pulses are adjustedaccording to the type of the PWM technique. The frequencyand the amplitude of the output voltage are controlled to meetthe requirements of the load. SPWM inverters are still foundin many industrial applications although space vector PWM(SVPWM) scheme became more attractive in the recent years.The main problem of SPWM is the variation of switchingfrequency and the existence of very narrow pulses on theoutput waveform of the inverter. The dc input voltage of theinverter is required to be constant in most applications.However when the inverter is fed from PV array, this dcvoltage may vary. Therefore a voltage controlled chopper isutilized to maintain the output voltage of the inverter within a

specified value. This voltage controlled chopper can beapplied with a mathematical algorithm to achieve maximumpower tracking of the PV array where the maximum powerpoint of PV array occurs at a certain point on the V-Icharacteristic of the PV array [5-7]. This paper presentsanalysis and simulation of SPWM based on MATLAB functionand m-files. The method of simulation overcomes theproblem of variation of switching frequency. The inverter isfed from a PV array and voltage controlled chopper. Since theoutput voltage of the PV array may vary, it is represented by astep change having two levels of output voltage. This paper isorganized as follows. Section 2 concentrates on analysis ofSPWM. Section 3 presents modeling of SPWM in MATLAB.Simulation results are introduced and discussed in section 4Section 5 concludes the paper

2 A NALYSIS OF SPWM

The basic principle of operation of three phase SPWMinverter is shown in Fig. (1). In this method a triangular(carrier) wave having a frequency "f RcR" is compared with threephase sinusoidal waveforms which have the requiredfundamental frequency "f Rs R". The outputs of the threecomparators are utilized to generate the control signals of the

six switches. The relative levels of the carrier wave andsinusoidal waves determine the pulse widths and control theswitching of devices in each phase leg of the inverter [2, 3]. The modulation index (m RiR) is defined as the ratio of theamplitude of the sinusoidal waveform A Rs R (reference signal) tothe amplitude of the carrier wave A RcR.The modulation index is sometimes called amplitudemodulation. The modulation index can be controlled byvarying A Rs R. As a result the widths of pulses that control theinverter switches can be controlled and consequently the rmsof output voltage.

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International Journal of Scientific & Engineering Research, Volume 5, Issue 6, June-2014ISSN 2229-5518

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Fig. 1 Principle of operation of SPWM

= (1)

The frequency modulation (m f) is defined as the ratio of thefrequency of the carrier wave f c to the frequency of thesinusoidal waveform (reference signal) f s . The frequencyindex is sometimes called frequency modulation

= (2)

The frequency of the reference sinusoidal wave determines thefundamental frequency of the output waveform. Thefrequency of the carrier wave determines the number of pulsesin one cycle "n"

n = m f (3)

In SPWM, the harmonics of low order can be reducedsignificantly as the frequency modulation increases. Withm f = 9 the third and fifth harmonics are nearly eliminated.The third, fifth, seventh and ninth harmonics are nearlyeliminated with m f = 15. On the other hand increasing thefrequency modulation will increase the carrier frequencywhich is limited because this will result in higher switchinglosses and very narrow pulses.

3 M ODELING OF SPWM IN MATLAB

Conventional modeling of SPWM in MATLAB includesSimulink blocks for modeling carrier and reference signalsthen comparison between them is carried out to generate thecontrol signals. In this paper, another approach is presentedusing MATLAB function and m-files. This approach hasmany advantages over conventional modeling. Variation ofswitching frequency is overcome and the switching frequencybecame constant. The model is written in m-file usingcommands similar to C-language. This later advantage makesthe implementation of SPWM using microcontrollers easier.Moreover the model is simpler than conventional modelingsince several blocks are excludedIn the proposed model, three phase sine waves with 120 o outof phase are generated. Each cycle of sine wave is divided

into fixed number of samples (N sin ). If the frequency of thereference signal is denoted as f s , each sample period "T s" canbe determined as:

Ts = 1 / N sin f s (4)

The number of samples in one cycle of carrier wave "M" isdetermined as:

M = N sin / m f (5)

And the period of one cycle of the carrier wave "T c" iscalculated as:

Tc = 1 / f c (6)

The period of the carrier cycle can be divided into threeportions as seen in Fig. (2). The first portion is from beginningof the cycle to 0.25 T c. The second is from 0.25 T C to 0.75 T Cand the third portion is from 0.75 T C to T C. The three portionscan be represented by lines 1, 2 and 3 whose equations are:

Line 1 VC( t ) = 4 AT t (7) Line 2 VC( t ) = 2 A C 4 AT t (8) Line 3 VC( t ) = 4 ATt 4 AC (9)

Fig. 2 portions of carrier wave

If the period of the carrier wave is divided into samples andthe number of these samples is denoted as "M", thenEquations 7-9 can be rewritten as:

Line 1 VC(k ) = 4 k AM (10) Line 2 VC(k ) = 2 A C 4 k AM (11) Line 3 VC(k ) = 4k AM 4 AC (12)

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Where "k" is a counter starts from "one" to "M"

The three phase reference sinusoidal voltages are

VA = A S sin (ωt) (13) VB = A S sin (ωt-2π/3) (14) VC = A S sin (ωt 2π/3) (15) If the sine wave is sampled into "N sin " samples (N sin = m f *M), Equations 13-15 can be rewritten as:

VA = A S sin (2 π I /NS ) (16) VB = A S sin (2 π I /NS -2π/3) (17) VC = A S sin (2 π I /NS 2π/3) (18) Where "I" is a counter starts from "one" to "N S"

The algorithm of the m-file is described in the following steps:• Generating carrier wave form

Based on the current instant, the counter "k" is determined.Then equations 10-12 are utilized to calculate the value ofcarrier wave at the current instant

• Generating three phase sine-wavesBased on the current instant, the counter "I" is determined.Then equations 16-18 are utilized to calculate the value of thethree phase sine-waves at the current instant

• Generating logic control signalsThe three phase sine waves are compared with the carrierwaves. The following relations summarize the results of thecomparisons which are the states of the inverter six switches."1" means the switch is to be turned on and "0" means theswitch is to be turned off

if ( VA (I) > VC (k) ), S1 = 1 ; S4 = 0; else S1 = 0 ; S4 = 1;

if ( VB (I) > VC (k) ), S3 = 1 ; S6 = 0; else S3 = 0 ; S6 = 1;

if ( VC (I) > VC (k) ), S5 = 1 ; S2 = 0; else S5 = 0 ; S2 = 1;

The m-file is included in a matlab block named matlabfunction. The block receive the current instant as an input via

a sampled block whose sampling period is defined byequation (4). If the sampling period is kept constant, theswitching frequency becomes constant.

For practical implementation, if the required fundamentalfrequency is 50 Hz and the number of sampling in one sine-wave cycle N sin is 180 samples, the sampling period is 111 μ sand the switching frequency is constant of about 9 kHz whichis suitable in practical implementation.

The output phase voltages of the inverter are calculated basedon the states of the upper switches of the inverters (S 1, S3 andS5) as follows:

�VAVBVC

=�2 1 11 2 11 1 2 �

S1SS5

× Vdc / 3 (19)The inverter is supplied from a PV array through a voltagecontrolled boost chopper to maintain the inverter input

voltage within a specified range. The V-I characteristic of thePV is shown in Fig. (3). The characteristic is based on themodel of the PV array as in the following equation [5]:

VPV= AkTre ln + o− o RS IL (20)

Where “k”: Boltzmann constant, “T r”: reference celltemperature, “e”: electron charge, “A”: curve fitting factor,“IPV”: cell photocurrent, “I o”: diode reverse saturation current,“IL”: cell output current and “R S”: cell series resistance

Fig. 3 V-I characteristic of the PV array

Investigating fig. (3), it is noticed that the output voltage of thePV array varies with the array current. Several researches aimto operate the PV array at maximum power point [5-7]. In thispaper, a step function representing two voltage levels of thePV array is introduced. A voltage controlled boost chopper isutilized to control the dc voltage within a specified level.

4 S IMULATION RESULTS

The block diagram including model of SPWM inverter,

voltage controlled boost chopper and step function is shownin Fig. (4). The step function represents a step change of theoutput of the PV array from 15V to 20V. The boost chopper iscontrolled to keep the output voltage of the chopper around24 V which supply the inverter. The fundamental frequency is50 Hz and the frequency modulation is 9 which eliminates thethird and fifth harmonics. Figures 5-7 illustrate the outputphase voltages of the inverter, output line-line voltages andspectrum analysis of the output phase voltage. As discussed,the third and fifth harmonics are reduced significantly. Theload is 80 W, with power factor 0.8 lagging.

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Fig. 5 Output phase voltages of the inverter

(Vdc = 24 V, n = 9) time (sec)Fig. 6 output line-line voltage of the inverter

(Vdc = 24 V, n = 9) time (sec)

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Fig. 4 Block diagram including SPWM model, boost chopper and step function

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Researchpaper Analysis and Simulation of Three Phase Sinusoidal PWM Inverter