Faouzi Ben Ammar INSAT Centre Urbain Nord, BP 676,1080Tunis I. INTRODUCTION

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1 Proceedings of the 4 th International Middle East Power Systes Conference (MEPCON ), Cairo University, Egypt, Deceber 9-,, Paper ID 9. Haronic distortion rate analysis of H-bridges ultilevel inverter Mohaed Néjib Ben Nasr and Anis Kebir Unité de recherché C3S ESSTT 5av. Taha Hussein BP 56 Bab Mnara-8 Tunis nejib.bennasr@topnet.tn, kebir_anis@yahoo.fr Faouzi Ben Aar INSAT Centre Urbain Nord, BP 676,8Tunis faouzi.benaar@insat.rnu.tn Abstract - This paper deals with a coparison study for two controls techniques applied to H-bridges ultilevel inverter. The considered techniques are standard PWM and haronic eliination control. The perforances of these techniques are copared in ters of THD and coutation s losses in order to optiize the choice of power switches. Fro the siulation results, the haronic eliination technique exhibits better results than the standard PWM technique, sustained by the reduce of the coutation losses, and a power rise for the switches ensuring the use of GTOs, IGCTs. intrinsic reliability and a relatively low cost []. The inverter being able to generate a whole of levels given, each one can be regarded as constant, the adapted ethods of odulation are PWM [] [3]. Index ters PWM, haronic eliination control, THD, H-Bridges ultilevel inverter. I. INTRODUCTION To pass beyond the liit value of the break over voltage of switches, soe studies in conversion DC-AC propose divers structures of ultilevel power converters [] [] [6]. In this way we assist a new share for the control s techniques of hybrid ultilevel power conversion illustrated by figure, which constitutes a research of developent and optiization beyond the control s point of view. A lot of control strategies are used to optiize the right choice of power switches to enhance the output signal s quality of this converter in a way, and to increase power in the other way, without exceeding the theral liits of the individual active switch. Between these controls, we note the PWM control and the control by haronic eliination which well be the objective of our article. II. PWM CONTROL FOR H-BRIDGE MULTILEVEL INVERTER Figure shows that in order to increase the nuber of levels (+) ore cells have to be cascaded. As H- bridge ultilevel inverter is a very odular solution, one ore isolated source is required for each cell to eliinate possible shortcuts. This has a good repercussion on the reliability and the aintenance of the syste since the cells have high availability, Fig. + level wyes-configured cascaded inverter with cells Single structure three phase structure Fig. Definition of the associated sizes to the odulation for a cell The oents of coutations are given starting fro the intersection between the carriers and the reference voltage. So positive ultiple triangle odulation assure high couple s (T, T) control by positive odulate signal. Negative ultiple triangle one assure low couple s (T 3, T4) control by negative odulate signal. The various states of possible voltage of a cell are state V T(i,j) = E, i is the row of the switch in the cell and j 74

2 suarized in the following table : TABLE Relationship between configurations &output voltages V AB T T T 3 T 4 V AB +E -E Thus the output voltage of a cell takes three distinct levels. The nuber of possible coutation s configurations is N E = 3. By taking into account only the three distinct levels generated by each one of these cells; a series-connected H-bridges inverter with cells has 3 distinct coutation s states per phase. Therefore the PWM ust allow the control of cells in series per phase. The generation of an output voltage phase-neutral of + distinct levels, and a line-line output voltage of 4- distinct levels starting fro 3 cascaded cells while ensuring balancing between the cells. Indeed, we need carriers at fixed frequency. the nuber of the cell. The three line-line voltages generated by this converter are given by the following expressions: V AB = V AN - V BN =E* [(S.j. + S 4.j. ) - (S.j. + S 4.j. )] (4) V BC = V BN - V CN = E* [(S + S ) - (S S )].j. 4.j..j j.3 (5) V CA = V CN - V AN = E* [(S.j.3 + S4.j.3 ) - (S.j. + S4.j. )] (6) The axiu agnitude of the line-line output voltage is : V ABax = V BCax = V CAax = (-) E (7) II.. PWM CONTROL VALIDATION PWM control validation is siulated in Matlab siulink of a ultilevel inverter single-phase and threephase structure with 5 cascaded cells. The phase-neutral voltage and the line-line ones for 5 cascaded cells and for a star load coupled are given by following figures 4 and 5: 3 Tension de sortie pour = 5 Tension (v) Teps (s) Fig 3 : Representative wave fors for PWM, =5 cells by phase a) single-phase structure b) three-phase structure The phase leg voltage at the load s boundaries is given by the addition of the cells voltages steps. V AN = V A +V A +V A3 +V A4 + +V A () S(i, j) is the control signal of the switch T(i, j) V AN = E [S(,j) + S(4,j) ] () The agnitude of the output leg voltage is : V ANax = E (3) The terinal voltage of the switch T(i,j) in a blocked Fig.4 Output phase leg voltage haronic distortion rate spectru in % of the fundaental for =5. But we notice that the frequency of coutation is 75

3 Tension en ( v ) Tension coposée de sortie VAB Teps (s) very high copared to the frequency of the fundaental one, which carried significant coutation s losses on the one hand, on the other hand the liitation of the rise on power for the switches. II.. VECTOR V s REPRESENTATION The space vector V s is defined by the following relation: V s = ( VS + avs + a VS3 ), so 3 V s = 3 [ V S ( V S + V S 3 ) + j ( V S V S 3 )] 3 The precedent equation shows that the vector two coponents in the αβ space so V s has V S = V S α + jvsβ ; Fig.5 Output line-line voltage VAB Haronic distortion rate spectru in % of the fundaental for =5 cells per phase. The load current and the haronic distortion rate in % of the fundaental are given by the following figure 6: 5 Courant dans la charge pour =5 V S α V S β = VSα = VSβ 3 V AN V BN V CN [S(, j,) + S(4, j,) ] + [S(, j,) S(4, j,) ] [S(, j,3) S(4, j,3) ] (8) (9) courant (A) 5-5 Vsβ Teps (s) Vsα =3cells Vsβ / 3U e Fig.6 Load Current haronic distortion rate in % of the fundaental for =5 the results of siulation confir: - A agnitude voltage E without voltage constraint in a state blocked for the silicon coponent. - A significant reduction in the gradients of terinal voltage of the load. - The haronic distortion rate in % of the leg voltages (,99%) and line-line voltage (6,74%) as the load current (, 36%) decreases significantly. In this case, as shown in the figure 7 Nvs = 3 : / 3U e Vs α =5cells Fig.7 Voltage phasors of the syetric star connection with H- bridges in series condition: < < < 3 < 4 < 5 < The output voltage VAN is given by the voltage steps 76

4 different coplex voltage phases can be generated.; Nvd = 6 (-) +: distinct states; Nvn = : nuber of zero vectors ; Nvr= () 3-6 (-) +: redundant states. Several possibilities of iposing a vector V s. The nuber of redundant states Nvr is very significant. It ensures a flexibility and suppleness of control for switches. So thus several possibilities to help balance the supply condensers. III. HARMONIC ELIMINATION METHOD In applications where the voltage agnitude and the frequency are relatively fixed, we are not in need of a odulated voltage [4]. In this case, the fundaental wave is sufficient for the voltage generation whose haronic rate of distortion is weak. The haronic eliination ethod consists in quantifying this reference voltage, in a given nuber of steps [5]. This odulation technical will be used to control syetric ultilevel inverter with five series-connected H-bridges. It consists in foring the output wave of the inverter of a succession of crenels of variable widths [5]. Generally, we use a wave which has a double syetry copared to the quarter and the half-period. This wave is characterized by the nuber C of crenels or ipulses by alternation. Whether odd or even nuber, C is represents also the nuber of angles of overlap per quarter of period and deterines the width of the whole of the crenels. The angles of overlap are given in such way to eliinate certain haronics. In the present study we were interested to eliinate the first haronics (5, 7,, and 3). The figure 8 illustrates the wavefors and switching ethod of levels cascade inverter. VAN 5E -5E VA5 VA4 VA3 VA VA 3 4 / 3 / Fig. 8 Wavefors and switching ethod of levels cascade inverter The output wavefors have a double syetry copared to the quarter and the half period thus the angles of conduction ust satisfy the following =5.55, =6.3669, 3 =3.8, 4 =38.67, wavefor such as the one depicted in figure 8 with 5 steps, the Fourier transfor for this wavefor is as follows: 4E VAN( wt) = [cos( n) + cos( n) + () sin( nwt) cos( n3 ) + cos( n4 ) + cos( n5 )] n where n=,3,5,7, Fro (), the agnitude of the Fourier coefficients when noralized with respect to E is as follows: 4 H( n) = cos( n) + cos( n) + cos( n3) + n () cos( n4) + cos( n5)] The odulation index is defined by : V a = V * AN AN.ax () * V AN is the agnitude of the output voltage desired. V is the axiu agnitude of the ANax inverter, where V ANax = 5.E (3) III.. CONTROL STRATEGY The five switching angles, i (i=,, 3, 4, and 5), are calculated offline to iniize the haronics for each odulation index a in order to have a total output voltage with a haronic inial distortion rate. The correct solution to (4) eans that the output voltage of the -level inverter will not contain the 5 th, 7 th, th, and 3 th haronic coponents. cos(5 ) + cos(5 ) + cos(5 3) + cos(5 4) + cos(5 5) = cos(7 ) + cos(7 ) + cos(7 3) + cos(7 4) + cos(7 5) = cos( ) + cos( ) + cos( 3) + cos( 4) + cos( 5) = (4) cos(3 ) + cos(3 ) + cos(3 3) + cos(3 4) + cos(3 5) = cos( ) + cos( ) + cos( 3) + cos( 4) + cos( 5) = 5 a The evolution of conduction angles according to the odulation index a is such as depicted in figure 9. We distinguish 3 regions. First one a belongs to the interval [,.48[ in which 4 and 5 are ixed-up. Second area a belongs to the interval [.48,.93[ in which all the i values are distinct. Third zone a belongs to the interval [.93, [ in which and are ixed-up. SO for a better optiization of the wavefor of the output voltage, we choice odulation index a =.9, the conduction angles are as follows: allows yes indeed to have the coutation frequency of the switches equal to the fundaental frequency one, which iniizes the coutation losses, but different 77

5 5 = Evolution des angles en fontion d'indice de odulation a tetta tetta tetta3 tetta4 tetta5 cells don t have the sae conduction tie. It thus results so an unbalance in the distribution of the conduction losses. The output voltages in figure are as follows: Angles en (degré) Tension de sortie pour =5 par une coande pleine onde Indice de odulation a en % Tension en (v) 5-5 Fig. 9 Evolution of conduction angles according to odulation index We distinguish 3 regions. First one a belongs to the interval [,.48[ in which 4 and 5 are ixed-up. Second area a belongs to the interval [.48,.93[ in which all the i values are distinct. Third zone a belongs to the interval [.93, [ in which and are ixed-up. SO for a better optiization of the wavefor of the output voltage, we choice odulation index a =.9, the conduction angles are as follows: =5.55, =6.3669, 3 =3.8, 4 =38.67, 5 = The angles i (i =,,3,4,5) are used to start the switches, the control signals equivalent to these angles are shown in figure : Teps en (s) Fig. wave for voltage of syetrical ultilevel inverter with five series-connected H-bridges by eliination haronic ethod As shown in figures and, we note that: - With a syetrical supply we obtain an output voltage which has *5+ levels of output voltage peak to peak. - The output voltage has a good haronic distortion rate (THDv = 8.33%) with haronics eliination (5, 7,, 3). Figure : Haronic rates of the output voltage CONCLUSION Fig. : Different control signals for all cells [,,3,4,5] This strategy of control based on the conduction angles choices which satisfy the condition of syetry, in % of the leg voltages and line-line voltage as well as the one load current decrease significantly. Those of the This paper has shown that, the series connection of H-bridges exhibits two control odes: PWM and haronics eliination ethod. The best choice between these two odes is dictated by a coproise between the two control odes. The advantages of the first ode characterized by a agnitude voltage E without constraint voltage in the state blocked for the power switch; a significant reduction in the gradients of terinal voltage of the load, a haronic distortion rate 78

6 second ode characterized by a coutation frequency of the switches the sae that the fundaental frequency one, sustained by a reduce of the coutation losses, and a power rise for the switches ensuring the use of GTOs, IGCTs. REFERENCES [] J-S.Mariéthoz. Foral study for synthesis of asyetrical ulti-level converters Topology, Modulation and Drive. thesis doctorate, Lausanne, EPFL 5. [] A. M. Hava, S.-K. Sul, R. J. Kerkan and T. A. Lipo, Dynaic Over odulation Characteristics of Triangle Intersection PWM Methods, IEEE Trans. on Industry Applications, Vol. 35, No. 4, pp , July 999. [3] A. Nabae and H. Akagi. A new neutral-pointclaped PWM inverter. IEEE Transactions on Industry Applications, 7(5) :58 53, Septeber 98. [4] T. Meynard and H. Foch. Multi-level choppers for high voltage applications. Applications, EPE Journal, () :45 5, 99. [5] M. D. Manjrekar, P. Steier, T. A. Lipo, Hybrid Multilevel Power Conversion Syste: A Copetitive Solution for High Power Applications, IEEE-IAS Conference, 999. [6] Ien Jaafer, Faouzi Ben Aar, Med Elleuch Modelling and control of cascaded ultilevel converters for dynaic copensation. Copel, Vol 7//8 International journal and atheatics in Electric Engineering. 79