Design and Simulation of an Inverter with High Frequency Sinusoidal PWM Switching Technique for

Harmonic Reduction in a Standalone/ Utility Grid Synchronized Photovoltaic System

A.Z.M.Shahriar Muttalib, S.M.Ferdous Dept. of EEE

American International University- Bangladesh (AIUB) Banani, Dhaka-1213

E-mail: sadi_eece@yahoo.com

Ahmed Mortuza Saleque, Nawjif Md. Anamul Hasan,

Md. Masoom Chowdhury Dept. of EEE, (AIUB) Banani, Dhaka-1213

E-mail: tanzir68@gmail.com

Abstract—Inverters are one of the major parts of any Photovoltaic Systems which are intended to feed power to any isolated standalone ac loads or to synchronize with the utility power grid systems. This paper discusses the design and simulation of a typical 1kW experimental precise sinusoidal Photovoltaic inverter which is intended to feed ac power at a standard 50Hz frequency to a mini grid powered by Photovoltaic solar cells. The very well-known and popular sinusoidal pulse width modulation (SPWM) technique with very high carrier frequency (in the order of kHz) has been chosen as the control scheme of the inverter by which it is also possible to synchronize the module to feed power on the 1-phase utility power grid. The high carrier frequency switching scheme enables to design a low pass smoothing filter for harmonic elimination resulting a reduction in Total Harmonic Distortion (THD) with small sized inductors and capacitors. As a prototype, the proposed circuit has been designed to supply small ac power, where the same design can be adopted and implemented to feed high power on the same grid only by increasing the device power ratings.

Keywords-Inverter, Sinosudal Pulse width Modulation(SPWM), Total Harmonic Distortion (THD, Harmonic Reduction, Passive LC Filter

I. INTRODUCTION For any grid tied photovoltaic (PV) system, inverter is the

essential piece of equipment that changes the DC power from the PV array to AC power used in the electrical grid. For high efficiency DC-AC conversion and peak power tracking, it must have low harmonic distortion along with low electromagnetic interference (EMI) and high power factor [1]. An inverter is evaluated after design by using the Inverter performance and testing standards which are IEEE 929-2000 and UL 1741 in the US EN 61727 in the EU and IEC 60364-7-712 [2]. The total harmonic distortion (THD) generated by the inverter is regulated by international standard IEC-61000-3-2 [2]. It requires that the full current THD be less than 5% and voltage THD be less than 2% for harmonic spectra up to 49th harmonic. Now designed topologies will enable the inverter to operate with near unity P.F. and THD less than 3-5% [3].

II. TYPES OF PV POWER SYSTEMS PV systems can be classified according to their connection

and arrangement within them or based on integration with the grid. They are

A. Standalone System In general, stand-alone system is used in the rural areas

where there is no sufficient facility to get an access to the main grid due to the technical problem or economical unfeasibility. Inverter of standalone system should maintain some features such as sinusoidal voltage, good voltage regulation and low harmonics in the output.

Figure 1.Schematic principle of a stand-alone PV system supplying a building

B. Hybrid In order to provide ecumenical, reliable and continuous

power supply a combination of PV, wind and fossil foul generation are integrated to form a hybrid system which guarantees the same supply reliability as the public grid.

Figure 2.Schematic principle of a hybrid system with PV, wind, and diesel generators

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C. Grid Concept Grid connected PV system always have a

suitable inverter. Normally a highly PV integan adverse impact as the system is going to bnumber of nonlinear devices. In order undesirable situation properly designed filtermight not be an economical solution. designed inverter can be helpful for reducing

Figure 3. Block diagram of the power supply for a hous

PV system and grid connection

III. INVERTERS FOR STAN-ALONE / GRISYSTEMS

Inverters are used to convert the DC ostorage battery in to AC electricity, in order grid or to supply a standalone system. Mobidirectional those are capable of operatingand rectifying nodes. In many standalone alternating current is needed to operate appliances at 230 V, 50 Hz frequency. Geninverter operates at 12, 24, 48, 96, 120 odepending on the power level [6].

The first self-commutating inverters permodulation (SPWM – sinusoidal pulse widthe output current on the primary side and 50adapt the voltage level to grid voltage. In thtype of inverter is designed, modeled and anthe performance.

Figure 4.GeneralOverview of the designe

a connection via a grated network has be introduced with to eliminate this

r is required which So appropriately the harmonics.

se with a decentralized

ID CONNECTED

utput of PV or a to be fed in to the

odern inverters are g in both inverting

PV installations, household utility

nerally stand-alone or even 240V dc

rformed sine-wave dth modulation) of 0 Hz transformer to his paper, a similar nalyzed to observe

ed system

For this type of inverter whseparate DC-DC converter is nduty cycle is continuously vatracker along with an algorithmtask and that sort of discussiopaper.

IV. MODULA

In the inverter the input is din order to get an A.C voltagsystem where the amplitude acontrolled. For this kind of modulation) inverters are beingof PWM scheme which inclmultiple pulse modulation modulation (SPWM). But maSPWM scheme as it improvesdirectly controlling the outpfunction. For the full bridge incomparing the frequency of a hsine waves. These two sine waeach other. The control wavefoswitch is achieved by comparfrequency with a triangle wavehigher frequency. The comparavoltage is greater than the trvoltage is used to trigger the res

The ratio between the triangbe an integer N, the number osuch that

s

c

ffN =2

Figure 5. SPWM m

According to this scheme if than the half the triangular voltare eliminated. For higher valu

hich is using SPWM scheme, a needed for MPP tracking as the arying. The design of a MPP m is a tedious and cumbersome on is beyond the scope of this

ATION SCHEME dc which is constant voltage. So e it requires such a controlling

as well as the frequency can be operation PWM (pulse Width g used. There are various kinds ludes single pulse modulation,

and sinusoidal pulse width ainly we are going to focus on the situation of the inverter by

put voltage according to sine nverter the PWM is obtained by high frequency carrier with two

aves are 180O phase shifted with orm which is used to control the ring a sine wave at a particular e of fixed amplitude with much ator gives out a pulse when sign riangle voltage and this pulse spective switches [4, 8].

gular wave and sine wave must of voltage pulses per half-cycle,

(1)

modulation scheme

f the peak of sine voltage is less tage harmonics less than the 2N

ues of sinusoidal voltage, higher

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∑∞

=

=,..3,2

2

nnh VV

order harmonics appear with amplitude of 15% less the fundamental [9]. The following equations are used in the sinusoidal PWM scheme:

i. Percentage of individual harmonics is calculated by the equation,

)2(cos)1(2

4100)(%1

1⎟⎟⎠

⎞⎜⎜⎝

⎛−×= ∑

=

+fM

pi

i

dc

nnV

nrms απ

n = nth harmonics

ii. Total Harmonic Distortion (THD) is given by

1VV

THD h= (3)

where,

A. Generation of SPWM Signal Sinusoidal pulse width modulation(SPWM) means that, the

output voltage is controlled according to a sine function. The control signal is achieved by comparing a reference sine wave produced by an oscillator of a particular frequency fS with a triangular wave of fixed amplitude with a much higher frequency fC (generally in kHz range).

Both the sine and triangular waves are compared with each other by using a simple comparator circuit to generate the switching waveform S1 and S4 (i.e. for positive cycle switching). The comparator detects the crossing points of the two signals and produces there from the required control signal with desired duty cycle. This signal is applied to the gates of the switching devices of the inverter and thus producing the chopped PWM voltage at the output. An inverted version of the reference sine wave is again compared with the carrier wave to generate the switching waveform S2 and S3 (i.e. for negative cycle). The total circuit arrangement is shown in detail in Fig. 6.

Figure 6. Complete circuit diagram to generate the switching wave form (S1, S4) and (S2, S3) for the SPWM scheme.

For this inverter an unipolar switching scheme is used rather than bipolar switching to achieve a better performance from the inverter. The simulated sine wave and triangular wave obtained from the two oscillator circuit are shown in Fig. 7.

Figure 7.Simulated sinusoidal reference signal (50Hz) and triangular carrier signal (1.6 kHz) generated by the switching waveform genetation circuit of

Figure 6.

B. Reduction of harmonics of the inverter output Inverter output waveform may vary to a large extent

depending upon the application and the circuit used. In most cases, an AC load requires sinusoidal output but the majority of the inverters produce square wave voltages. Therefore, appropriate means are adopted to alter the waveform of the inverter output to a more or less sinusoidal waveshape. Harmonic attenuation can be achieved by several methods such as by resonating the load, by an LC filter, pulse width modulation, sinewave synthesis, selected harmonic reduction and by polyphase inveters [9].

C. Harmonic Attenuation by Pulse Width Modulation Generally several PWM scheme is employed to reduce

harmonics. Among them sinusoidal pulse width modulation is used for this inverter. Use of SPWM reduces further the harmonic content at the inverter output, the reduction being more with large number of pulses per half cycle. For the modulation scheme used here the value of N is equal to 1600/50 = 32; which implies that all harmonic voltages below the 64th harmonics should be absent [8, 9]. But as a bipolar triangular wave is used as carrier signal instead of unipolar signal, the number of eliminated harmonics will be upto 32 because of the presence of the negative cycles in the signal.

D. Harmonic Attenuation by LC filter In this filter, attenuation of the harmonic comonents increases

with frequency. The phase shift through the filter is also a function of frequency and is nearly zero at low frequencies and approaches 180º at higher frequencies. The filter should be designed to make a good compromisation between maximum inverter current and voltage regulation. The LC resonance frequency should be less than the lowest harmonic to be attenuated. At the same time the load power factor should be considered in selecting the individual values of L and C [9].

To get a pure sine wave output or an output with very low

THD (Total Harmonic Distortion)from a pure square wave, a

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Low pass filter with very sharpe response characteristic is required. At the same time the size of the filter components will be large to filter out the low frequency harmonic components specially the third and fifth harmonics. Modulation with a very high frequency signal shifts the harmonic components to a higher frequency points which enablethe filtering process much easier using a LC filter built with small sized inductor and capacitor with moderate frequency response characteristics as a very sharpe response is not that much needed.

The value of inductor is calculated such that the voltage drop

across the inductor is less than 3% of the inverter output voltage, V0 so that it satisfies the following equation [6]-

Iload max x 2πfL < 0.03V0 (4)

where Iload max is the maximum RMS load current and f is output voltage frequency (50Hz).

V. SEQUENTIAL APPROACH OF DESIGN AND SIMULATION OF THE INVERTER

The design of the inverter is done based on the following output specifications:

Power 1kW Input voltage (d.c) 12V

Output voltage (a.c) 240V Output frequency 50Hz Total harmonic distortion <5%

The output voltage should be free from harmonics within the range (150Hz-1.5 kHz).

A. Power Specification The power specification is needed to calculate so that the

current which the switch has to withstand can be determinded. For simulation purspose an ideal switch is used in order to observe the output without any kind of loss across the switch. In practice MOSFET or IGBT can be used in order to perform the switching task and at the same time the system will be self commutating instead of forced or grid commutating.

Input side: In the input side the voltage is 12V and power is 1kW. So

the current rating is (1000/12) = 83.33amp. So switch should be selected so that it can withstand that amount current. In the output the load is calculated from this power specification. In this case an ideal switch is selected so that there is no power loss for it.

Output Side: In the output it will experience the same amount of power

and the output voltage is 240V (rms). So the load should be, R = (240)2/1000 = 57.6

B. Input and output voltage specifation The input and output voltage specification is used to select the turn ratio of the transformer. The input voltage is 12V and the output voltage is 240V (rms). So it requires a step up transformer whose gain is = (240 X√2)/12 = 28.28. (i.e. on Primary side 100 turns and on secondary side 2828 turns). In

this case an ideal transformer is being used to step up the voltage to meet the specified output. In practical case there may be some sort of unpredictable change in the output depending on the time constant of the system. The transformer is placed before the filter for scaling down the filter size as the transformer it self takes part in filtering process.

C. Operation and simulation of the inverter circuit (without filtering)

As per design, the control scheme the circuit arrangement is simulated in the Pspice (version-16.3). The control signal of the (S1, S4) and (S2, S3) are shown in Figure 8 (a) and (b) respectively.

Figure 8 (a). Control signal for S1 and S4.

Figure 8 (b). Control signal for S2 and S3.

It can be seen that, S1 and S4 are not closing at the same time and also S2 and S3 are as well. So there is no short circuit exist in the whole operation. This is normally known as Blanking time.After the switching the following chopped wave shape is obtained at the output of the inverter as shown in Figure 9 (a).

Figure 9 (a). Output voltage waveshape of the inverter before filtering.

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The rms value of the output can be observed from the following wave shape of Figure 9(b). The voltage is around 240V when steady state point is achieved.

Figure 9(b). RMS value of the output voltage. The voltage is stepped up to a

value of 240Vac from 12Vdc. Stepping up of voltage is performed by a transformer.

The Fast Fourier Transformation(FFT) of the output voltage

can be found out using Pspice which is shown in Figure 10.

Figure 10. FFT of the output voltage of the inverter (without filtering).

It is to be noted that, all the harmonic components are

shifted towards the high frequency. Initially the frequency of the carrier signal was 800Hz which can easily be verified by the presence of the 15th harmonics at 800Hz point of the above figure.

D. Harmonic calculation before filtering The output voltage is,Vout = 240V. The amplitude of the fundamental component is 271.574V. So, from Fig.16-

)(031.1925741.2711 rmsVVV ==

VVVV outh 959.143031.192240 2221

2 =−=−=

%75031.192959.143(%)

1

===VVTHD h

According to the Pspice simulation, the percentage of the harmonic is 80.5 which are really close to the calculated value. Now this total harmonic distortion (THD) value has to be

reduced to less than 5% and to eliminate all the harmonics between 150 to 1.5 kHz. For this purpose two common harmonic reduction techniques are used [5,8,9]-

i. Increasing the frequency of the control signal ii. Using a low pass LC filter

E. Increasing the frequency of the control signal In SPWM scheme the harmonic reduction is more effective

with larger number of pulses per half cycle. To reduce the THD, the frequency of the carrier signal has been increased. By doing so the lower order harmonics will be shifted towards the high frequency. Before increasing the carrier frequency the THD value was 80.5% but afteroubling the frequency, THD has reduced to 55.29%. By increasing the carrier frequency the harmonics has been shifted to the higher frequency. Now this harmonics can be eliminated by using a low pass filter.

F. Using a low pass LC filter The output wave still contains a high amount of harmonics

which can easily be understood from the value of THD. But a simple low pass LC filter can be used to filter out this harmonics which have been shifted to high frequency point due to modulation. In LC filter, the capacitor maintains the load voltage constant whereas the inductor makes the current smoother. The calculation is done by using the following equation:

(5) 2

1LC

f offcut π=−

So the filter allows only the low frequency components to

pass [4]. The value for L and C need to be optimized otherwise there will be the problem of voltage regulation. So calculative trade-off between L and C is required and LC resonance frequency has to be less than the lowest harmonic to be attenuated.

In this case the inductor has been assumed to be 100μH. According to the output voltage specification it is given that there should not be any harmonics from 150Hz to 1.5Khz. So the cut-off frequency should be 150Hz. So the value of C is calculated as-

C= 1/ [(100m)*(2 *150)2] = 11.25μF

After connecting the filter in the output side the harmonics is reduced to 0.41817%. After connecting the filter the output voltage reduced to 184.46V. So the gain should be increased by |184.46-240|/184.46 = 0.301 factor. So the gain becomes 28.284*1.301=36.8

A better harmonics reduction can be possible through cascading LC filter and size reduction of the components can be partially achieved by using transformer in the filter. But none of the techniques is used as complexity and higher costing of the filter is avoided.

G. Final Voltage Output Final output voltage of the inverter is shown in Fig.11. (a).

The rms value, the harmonic content, calculated THD value

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and power outputs are shown in Fig.11. (b), (c), (d) and (e) respectively.

Figure 11.(a). Final Output voltage from the inverter circuit which is almost sinusoidal in nature with a very low THD value of 0.41876%.

Figure 11.(b). RMS value of the output voltage which is equal to 240V.

Figure 11.(c). Harmonic content of the output voltage. The figure shows that, there are almost negligible harmonic contents between 150Hz to 1.5 kHz. The following figure taken form PSpice result shows the final THD value:

Figure 11.(d). Calculated THD value using Pspice

The following figure shows that the output power is 1kW.

Figure 11.(e). Output power of the Inverter.

VI. CONCLUSION The inverter output totally depends on the switching

operation. The output voltage depends on the switch status. Here ideal switch has been used. In practical there should be a voltage drop across it. As here the ideal switch has been used there is no voltage drop. The transformer is also an ideal one. Because in this case neither linear nor non-linear transformer has given a nice value. The PWM sinusoidal Scheme proved to be very essential to reduce the harmonics in the output voltage. As the frequency of the carrier signal increase the THD value decreases. The harmonics in the output voltage is shifted in the higher frequency by giving the carrier frequency a high value but it has no link with the amplitude of the amplitude of the harmonics. Low pass filter has been used to eliminate harmonics after certain frequency. In the filter the inductors are actually smoothing the current whereas the capacitor is holding the output voltage constant. The LC combination has to be chosen like that way so it gives low impedance so that it can passes to the output side and gives high impedance for the higher frequency.

REFERENCES

[1] Arman Roshan, “A dq rotating frame controller for single phase full bridge Inverters used in small distributed generation system”, M.Sc. thesis, Faculty of Virginia Polytechnique institute and State University, Jun., 2006.

[2] Patel, Mukund R., “Wind and Solar Power System”, 2nd ed., CRC press, USA, 2008.

[3] E. Koutroulis, J. Chatzakis, K. Kalaitzakis and N.C. Voulgaris, “A bidirectional sinusoidal high frequency inverter design”, IEE Proc-Electr. Power Appl., vol.148, No. 4, Jul., 2001, pp. 315-321.

[4] Dehbonei H., Borle L and Nayar C.V., “A review and proposal for

optimal harmonic mitigation in single phase pulse width modulation”, Proceedings of 4th IEEE International Conference on Power Electronics and Drive System, 2001, Vol.1, Oct., 2001, pp.408-414.

[5] Khaled H. Ahmed, Stephen J. Finny and Barry W. Williams, “Passive Filter Design for Three- Phase inverter Interfacing in Distributed Generation”, Journal of Electrical Power Quality and Utisation, Vol.XIII, No. 2, 2007, pp. 49-58.

[6] A. Goetzberger, V.U. Hoffmann, “Photovoltaic Solar Energy Generation”, Springer 2005.

[7] Mohammad Darwish, “Inverter Circuist (AC/DC)”, School of

Engineering and Design, Brunel University, UK. [8] P.C. Sen, “Power Electronics”, Tata Mcgraw-hill, India [9] K.S. Rajashekara, Joseph Vithayathill, “Harmonics in the voltage

Source PWM Inverters”.

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