Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 319.

983

Implementing a Three Phase Nine-Level Cascaded Multilevel Inverter with low Harmonics Values

Hussein A. Konber and Osama I. EL-Hamrawy Mahmoud EL-Bakry Department of Electrical Engineering Department of Power Electronics

University of Al-Azhar Electronics Research Institute Cairo, Egypt, Cairo, Egypt

hamrawy@gmail.com mahmdali42@yahoo.com

Abstract – A three phase nine-level cascaded multilevel inverter with very low values of the undesired low order harmonics is implemented. The switching angles of the inverter power switches are calculated to obtain zero values of the low order harmonics till the 11th harmonic for different values of the output voltage. These values of the switching angles are then applied to the constructed multilevel inverter and the harmonics are measured till the 31st harmonic. The paper presents experimental results, which show very low values of these harmonics as well as for the total harmonic distortion under no load and inductive load.

Index Terms –Multilevel inverter implementation, Multilevel

inverter harmonics, Selective harmonic elimination, Total harmonic distortion.

I. INTRODUCTION

Multilevel inverters are widely used in high power industrial applications such as ac power supplies, static VAR compensators, drive systems, etc., [1]. One of the significant advantages of multilevel inverters is the low values of the produced undesired low order harmonics, even when using low switching frequencies, [2]. Cascaded multilevel inverter is a well-known multilevel inverter topology. It is superior to other multilevel inverter topologies, such as diode–clamped and flying capacitor multilevel inverters [3], due to its simple modular structure, ease of control, least number of component and no need for clamping diode or voltage balancing capacitors, [4, 5]. The selection of the level of a multilevel inverter is a critical issue, since multilevel inverters of higher levels produce lower values of undesired harmonics and need power switches of lower ratings, but at the cost of increasing the number of components and control complexity. In this paper a three phase nine-level cascaded multilevel inverter is considered. Fig. 1 shows the structure of a single phase of this inverter. It consists of four simple H-bridge inverters, each can produce three output voltages +Vdc, 0 or –Vdc, thus the whole inverter can produce nine voltage levels. Fig.2 shows an odd-sine symmetric waveform that each phase will be designed to produce. Each H-bridge will be switched on and off only once each half cycle of the main harmonic. The harmonics produced by this way will be the main harmonic in addition to odd sine harmonics only.

The switching angles α1, α2, α3, and α4 are first calculated at different values of the main harmonics, so as to obtain zero values of the 5th, 7th, and 11th harmonics, using a selective harmonic elimination technique [6, 7]. All the undesired low order harmonics till the 11th harmonic are eliminated in the output line voltage of the three phase cascaded multilevel inverter. Noting that the odd tripled harmonic, i.e. (3th, 9th, 15th, …etc.) are self cancelled by the three phase balancing. The harmonic values and total harmonic distortion till the 31st harmonic are registered. Next the construction of the implemented three phase nine- level cascaded multilevel inverter is described and experimental measures when applying the calculated switching angles are recorded under no load and inductive load.

Fig. 1 single-phase structure of a nine-level multilevel cascaded inverter

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Fig. 2 Output phase voltage waveform of a nine-level cascade inverter (taking equal values of the dc voltage sources)

II. CALCULATING THE SWITCHING ANGLES

A. Formulation of the problem The Fourier series of the general quarter wave symmetric waveform, similar to that of Fig.2, with switching angles α1, α2, α3..., αs per quarter cycle is given by

)( tVout ω = tma mm

)12sin(120

++

∞

=∑

with ttdmVa outm ωωπ

π

)12sin(4 2

012 += ∫+

k

s

kk mV

mα

π)12cos(

)12(4

1+

+= ∑

=

Where kV is the increase in voltage value from each switching angle to another. Assuming regular staircase waveform (V1=V2=.....=Vs=E), the amplitude of the harmonic voltage 12 +mv is given by the values of 12 +ma i.e.

k

s

km m

mEv α

π ∑=

+ ++

=1

12 )12cos()12(

4

For the nine level inverter four switching angles α1, α2, α3, α4 are available, and the first four non zero harmonics in the output line voltages of the three phase inverter are

]coscoscos[cos443211 αααα

π+++=

Ev

]5cos5cos5cos5[cos54

43215 ααααπ

+++=Ev

]7cos7cos7cos7[cos74

43217 ααααπ

+++=Ev

]11cos11cos11cos11[cos114

432111 ααααπ

+++=Ev

These four relations will be turned to be four equations that are solved to obtain the values of the switching angles α1, α2, α3, and α4; by setting:

=1v The required amplitude of the main harmonic

,05 =v ,07 =v 011 =v . B. Solution results The above four nonlinear equations are solved using the "Newton-Raphson method" [4, 8and 9] for the values

=1v 4E, 3.8E, 3.6E, 3.4E, 3.2E, and 2.8E Table 1 gives the obtained values of α1, α2, α3, and α4, as well as the percentage total harmonic distortion (THD) in the output line voltage till the 31st harmonic for each value of 1v , as defined by

100/)( 1

15

1

212 ×= ∑

=+ vvTHD

mm

Noting that the tripled odd harmonics (2m+1=3, 9, ….) are not considered.

Table 1.1the switching angles at different value of 1v

1v 4E

3.8E

3.6E

3.4E

3.2E

2.8E

α1

10.015°

11.549°

14.409°

19.099°

24.699°

36.118°

α2

22.140°

27.392°

33.539°

39.722°

45.530°

47.876°

α3

40.752°

46.720°

51.290°

55.586°

57.039°

61.072°

α4

61.768°

64.444°

66.546°

66.978°

68.888°

76.297°

THD %

5.1635

7.1598

5.3259

7.3345

6.2731

7.471

Figure 3 shows the variations of THD with 1v . Figures 4 and 5 show the harmonic spectrum of the line voltage till the 31st harmonic for 1v =4E and 2.8E respectively. It should be noted that under pure inductive load the total harmonic distortion in the current will be much lower, since it is given by:

100/)12

( 1

15

1

212 ×+

= ∑=

+ vmvTHD

m

m

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Fig.3 the voltage THD versus 1v

Fig.4 Harmonic spectrum of the line voltage at 1v =4E

Fig.5 Harmonic spectrum of the line voltage at 1v =2.8E

III. EXPERIMENTAL ANALYSIS

A. Experiment setup The construction of the three phase wye-connected, nine-level cascaded multilevel inverter is illustrated in Fig.6. The power electronics switch used for this particular multilevel inverter is IRFP260 MOSFET with voltage ratings of 200V and current ratings of 46A.

Fig.6 Construction of a three-phase nine-level cascaded inverter

The hardware prototype shown in Fig. 6 consists of four main parts as follows: 1) The control circuit; An Atmel AT89C52 microcontroller is used as the main processor, which provides the gate logic signals. The microcontroller board is a part of the control unit. It receives the control command from the key button to enter the value of the switching angles, and generates the control signals for the gate drives. The microcontroller board consists of one microcontroller chip as the master processor and three microcontrollers as slave processors for generating the control signal for each gates of the module board. The generation of the control signals is realized inside the microcontroller chip. To control the gate signals, the command program, which is implemented in C++ language, is generated on a personal computer and then transferred to the microcontroller on the control circuit board. 2) The gate-driver circuit: NE555 is used as a gate-driver, which receives a TTL logic signal from the microcontroller and provides +10 V for the turn on the gate signal and 0 V the for the turn off the gate signal to obtain the proper gate voltages necessary for proper switching of the MOSFET. It is important to isolate the output signal from the drive circuit to avoid the propagation of fault voltages. Isolation is achieved by using optocouplers (type 4N35). 3) The power stage: Four MOSFET, IRFP260, are used as the main switches, which are connected in full-bridge configuration. Each power stage is supplied by a separate dc source E=72 V. Figure 7 shows the experimental configuration

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Fig. 7 Experimental configuration

B. Experimental results 1-under no load: Figure8 shows the peak phase voltage of the inverter with no load at 1v =4E=288v and f=50Hz.

Figure9 shows the voltage harmonic spectrum at 1v =4E=288v The THD measured by a power harmonic analyzer is 4.48%. Figures 10, and 11 show the same at 1v =2.8E=200v. The THD measured by a power harmonic analyzer is 7.46%.

Fig. 8 No load peak phase voltage at 1v =4E=284v

Fig. 9 Harmonic spectrum of line voltage at 1v =4E

Fig. 10 No load peak phase voltage at 1v =2.8E=200v

Fig. 11 Harmonic spectrum of line voltage at 1v =2.8E

2-under inductive load: The inverter is loaded by a three phase step down transformer 380v/133v connect to a three phase inductive load each inductance has L=125mH, r =0.9Ω. Figures 12 and 13 show the phase voltage and phase current waveform respectively of the inductive load at the secondary output of the transformer at v1= 4E. Figures 14 and 15 show the harmonic content of phase voltage and phase current at different voltage values respectively. The experimental phase voltage THD measured by the power harmonic analyzer 5.79 %. The experimental phase current THD measured by the power harmonic analyzer is 2.67 %. The value of each of the dc voltage sources was taken 72 v. This value can be changed to obtain any desired value of the output voltage. It is clear that the inverter produces very low values, nearly negligible, of the undesired low order harmonics.

Separate DC source

H-bridge power stage

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Fig. 12 Output voltage with inductive load, 1v =4E

Fig. 13 Inductive load current, 1v =4E

Fig.14 Voltage harmonic spectrum at 1v =4E

Fig.15 Current harmonic spectrum at 1v =4E

IV. CONCLUSIONS

A three phase nine-level cascaded multilevel inverter is implemented that produces very low values of the low order harmonics. The switching angles of the inverter power switches are calculated such that the low order harmonics till the 11th harmonic are eliminated. Digital generation of switching signals using a microcontroller allows generating the required switching angles for different voltage values. The harmonics measured till the 31st harmonic are very low for different values of the output voltage, as well the value of the total harmonic distortion under no load and inductive load.

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