FAYÇAL CHABNI, RACHID TALEB, M HAMED HELAIMI

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1 Rev. Roum. Sci. Techn. Électrotechn. et Énerg. Vol. 6, 4,. 4 4, Bucarest, 7 OUTPUT VOLTAGE WAVEFORM IMPROVEMENT OF MODIFIED CASCADED H-BRIDGE MULTILEVEL INVERTER USING SELECTIVE HARMONIC ELIMINATION TECHNIQUE BASED ON HYBRID GENETIC ALGORITHM FAYÇAL CHABNI, RACHID TALEB, M HAMED HELAIMI Key words: Modified cascaded H-bridge (CHB) multilevel inverter, Selective harmonic elimination (SHE), Hybrid genetic algorithm, LC filter. The main objective of this work is to imrove the quality of voltage waveform generated by a modified cascaded H-bridge (CHB) multilevel inverter toology using selective harmonic elimination (SHE) control strategy and also using LC filters. This study resents a new toology of multilevel inverters that combines the conventional architecture of a cascade H-bridge inverter and LC filters. The SHE method is used to eliminate harmonics of chosen lower-order while controlling the amlitude of fundamental harmonic in CHB multilevel inverter. LC filters are added to the inverter in order to eliminate the high-order harmonics. Otimal switching angles are obtained by solving a non-linear equations system using hybrid genetic algorithm (HGA). and 7 level configurations for the new toology are resented in this work. The obtained simulation results are validated through exerimental results.. INTRODUCTION Multilevel dc to ac ower converter configuration can be achieved by connecting several individual converters in series. By increasing the number of converters and dc sources, the ac outut voltage become more similar to a sinusoidal waveform. There are three main categories of multilevel inverters, diode-clamed, flying caacitor and cascade H- bridge inverters []. The cascade H-bridge multilevel inverters are easy to control, and they have a simle modular structure, the number of voltage levels could be increased by connecting additional H-bridge modules in series without changing the inverter s structure. The cascade multilevel inverters rovide a lot of advantages such as low total harmonic distortion (THD), low electromagnetic interference [], low voltage stress on semiconductor switches and an outut voltage similar to a sinusoidal waveform which make them widely used in high and medium ower alications electrical transmission systems. Several modulation methods were used to control multilevel inverters such as sace vector and sinusoidal ulse width modulation (PWM) [3 ], a more effective and efficient modulation strategy called selective harmonic elimination PWM (SHEPWM) is also used in the control of multilevel inverters, the method rovides numerous advantages such as reducing low order harmonics and the ossibility of driving the semiconductor switches at low frequencies [6, 7]. In this work, a assive LC filter is added to the CHB multilevel inverter in order to eliminate high-order harmonics. Genetic algorithm (GA) is a very owerful algorithm that can solve almost all otimization roblems, it mimics the rocess of natural evolution, and it is frequently used to obtain otimal solutions [8 ]. The hybrid genetic otimization algorithm has been develoed to solve the fine-tuning roblem of a local search in GA. It is combination of local search and GA [ 3]. In this work, a HGA with local search method has been alied to determine the otimal switching angles for the roosed CHB multilevel inverter. Comuter simulations using MATLAB software and exeriments using a small scale laboratory were carried out to evaluate the results obtained by the roosed converter for and 7 level configurations. This aer is organized as follows: The structure of the roosed CHB multilevel inverter is resented in Section. In Section 3, a HGA based SHE strategy is exlained. The results obtained from simulations and exeriments of the control strategy are resented in Section 4. The conclusion is resented in Section.. PROPOSED CHB MULTILEVEL INVERTER Cascade H-bridge multilevel toology requires least number of semiconductor switches, gate-drives and rotection circuits comaring to other tyes and configurations of multilevel ower converters. The asymmetrical configuration for multilevel inverters rovides more voltage outut levels for the same number of semiconductor switches than the symmetrical configuration, therefore imroving the voltage waveform quality [4, ]. Figure illustrates the structure of the roosed singlehase inverter, it consists of two H-bridge modules connected in series, V dc and V dc are the isolated DC voltage sources for the H-bridge modules, V ac = V LC V LC is the ac outut voltage obtained via a two LC filter. Fig. Proosed single-hase CHB multilevel inverter. Hassiba Benbouali University, Faculty of Technology, Deartment of Electrical Engineering, Laboratoire Génie Electrique et Energies Renouvelables (LGEER), Chlef, Algeria, chabni.fay@gmail.com, rac.taleb@gmail.com, halimi976@yahoo.fr

2 46 Fayçal Chabni, Rachid Taleb, M hamed Helaimi 3 In this study the inverter is oerated in two configurations level and 7 level in order to observe the imact of adding more voltage levels on the quality of the outut ac waveform, and also adding and removing the filters to observe their effect on the outut voltage. The level configuration can be achieved by using equal dc sources (V dc = V dc ), whereas the 7 level is obtained by using the asymmetrical configuration by setting V dc = V dc, Table resent the outut voltage values (er unit) of different switching states for and 7 level inverters. Table Outut voltage level (.u.) with corresonding conducting switches of and 7 level inverters level inverter 7 level inverter (S,S3,S6,S7) 3 (S,S3,S6,S7) (S,S3,S6,S8) (S,S4,S6,S7) (S,S4,S6,S8) (S,S3,S6,S8) (S,S4,S6,S8) (S,S4,S6,S8) (S,S4,S,S8) (S,S4,S6,S8) (S,S4,S,S8) 3 (S,S4,S,S8) Considering the inverter direct outut fundamental, the transfer function of LC filter can be exressed as follows: VC T = =, () V LC x + jxy where x = ω LC, y = R C L, ω is the fundamental angular frequency and R reresents the internal inductors resistance. The transfer function magnitude of the filter is exressed by: T = ( x ) + x y The maximum value T max of T, can be exressed by: y Tmax = Tω = max y.. ωmax =.y RC The maximum angular frequency ω max exists if y <.44. The filter transfer function will resent a maximum value and then decreases to zero. Consequently, the fundamental and harmonic comonents are amlified, which leads to the undesirable effects, as it is shown in Fig... () (3) T x. Fig. Transfer function of the LC filter for the fundamental. 3. SELECTIVE HARMONIC ELIMINATION WITH HGA 3.. GENERAL FORMULATION OF SHE IN PROPOSED INVERTER The SHEPWM is based on the Fourier analysis of the voltage waveform resented in Fig. 3. Since the voltage waveform generated by the ower converter is symmetric in a half and a quarter of a eriod, the even harmonics are equal to zero. The Fourier exansion for the V ac voltage is thus: 4Vdc VAC = Vn sin( nωt), with Vn = cos( nθi ), (4) n=,3, nπ i= where V n is the amlitude of the harmonic term of rank n, = (N )/ is the number of firing angles er quarter waveform, N is the number of generated voltage levels and θ i is the switching angle of rank i. V dc V dc -V dc θ θ.. θ π/ -V dc π V AC. y 3π/ Fig. 3 Generalized outut voltage waveform of a CHB multilevel inverter. The switching angles in (4) are calculated by fixing the value of the fundamental term and canceling the other harmonic terms. These switching angles can be determined by solving the following system of non linear equations: i i = = cos( θ ) = i π r 4 cos( nθ ) = for n i. { 3, }, where r = V /V dc is the modulation index. The solution of () must also satisfy the following constraint: π ()

3 4 Waveform imrovement of a modified inverter toology 47 < < < < < π. (6) θ θ θ START An objective function is then needed for the otimization rocedure; the function must be formulated in such way that allows the elimination of targeted harmonics while maintaining the fundamental comonent at desired amlitude. The objective function is defined as follows: Randomize switching angles θ i (i = ) corresonding to No. of oulation Evaluate objective function given by equation 7 of each chromosome (θ θ ) F( θ) = F( θ θ ) = + i= π cos( θ ) i r 4 n= 3, i= cos( nθ ). i (7) Create new offsring using crossover and mutation oerations Perform a local search on each solution, evaluating F(θ) of each new location, and relace the solution if there exists a locally imroved solution The otimal switching angles are obtained by minimizing the objective function resented in (7) while resecting the constraint resented in (6). The biggest roblem is the non-linearity of the equations resented in (); multile comutational techniques were used to solve SHE roblems such as Newton-Rahson method [6, 7] and or the resultant theory [8 ], these methods are either comlicated or require an initial guess of the otimal solutions, which can be very difficult esecially for a large number of switching angles. It is, therefore, worth considering more techniques and simle techniques such as hybrid genetic algorithms (HGA). 3.. SOLUTION USING HYBRID GENETIC ALGORITHMS The hybrid genetic otimization algorithm has been develoed to solve the fine-tuning roblem of a local search in GA. The HGA is mixture of genetic otimization algorithm and a local search (LS) method [ 3]. In this work, a hybrid genetic algorithms with local search method has been alied to determine the otimal switching angles by using the MATLAB otimization toolbox. The value of the resented objective function is minimized by using hybrid function which oerates after the terminating of the GA. The determined final oint from GA is used for hybrid function as an initial oint. In this study, fmincon which is a local search method is referred as hybrid function; fmincon is used to find a minimum value of the roosed cost function. A flowchart of the HGA algorithm for SHE is shown in Fig. 4. This algorithm was used to find the otimal firing angles (θ, θ ) to eliminate the 3 rd harmonic for level inverter (i.e. = ), and (θ, θ, θ 3 ) to eliminate the 3rd and th harmonics for 7 level inverter (i.e. = 3). The results for the two inverters are lotted resectively in Figs. and 6 versus r, where.4 r.9 with a ste of.. The THD corresonding to the solutions given in Figs. and 6 is reresented by Fig. 7. Sw itching angles (deg.) Sw itching angles (deg.) N Designate which individuals to include in the next oulation Solution converged? Outut final otimal solution θ i (i = ) Y STOP Fig. 4 Flowchart of HGA for SHE θ θ Modulation index r Fig. Otimal switching angles versus r for -level inverter θ Modulation index r Fig. 6 Otimal switching angles versus r for 7 level inverter. θ θ 3

4 48 Fayçal Chabni, Rachid Taleb, M hamed Helaimi THD % Level 7-Level Modulation index r Fig. 7 THD versus r for otimal switching angles. 4. SIMULATION AND EXPERIMENTAL RESULTS A laboratory rototye of the roosed single-hase CHB multilevel inverter was built using IRF84 ( V, 8 A) MOSFETs as the switching devices, and IR as MOSFET gate drivers, 4N otoisolators for rotection, and two laboratory variable dc ower sulies. Atmel SAM3X8E microcontroller was used to generate control signals. SDS SIGLENT digital storage oscilloscoe was used to cature voltage signals. Fast Fourier transform (FFT) and THD calculations were erformed by comuter linked to the SDS digital oscilloscoe via USB connection. Figure 8 illustrates the laboratory rototye of the roosed multilevel converter built for this study. Figures 9 and show resectively simulated and exerimental outut voltages inverter and the corresonding FFT without LC filter (unfiltered outut voltage) and with LC filter (filtered outut voltage) of level inverter for r =.86 (i.e. θ = 7.4 o, θ = 67. o ) with V dc = V dc = V and the filter arameters y =.. Fig. 8 Exerimental setu. The waveform reresenting the exerimental results in Fig. is ractically identical to the one obtained by simulation in Fig. 9. The filtered voltage waveform is very close to a sinusoidal form. From the exerimental results of unfiltered FFT outut voltage, it is seen that the 3 rd harmonic is efficiently eliminated as obtained in the simulation. All high frequency harmonics of filtered FFT outut voltage are cancelled which roves the efficiency of the roosed inverter. The same remark is for Figs. and showing resectively simulated and exerimental unfiltered outut voltage and filtered outut voltage of 7-level inverter for r =.8 (i.e. θ = 8.7 o, θ = 9.6 o, θ 3 = 77.8 o ) with V dc = V dc = V and the filter arameters y =.. From the results of 7-level unfiltered FFT outut voltage, it is clear that the low-order harmonics 3 rd and th are totally eliminated, and all high-order harmonics are eliminated of filtered FFT outut voltage. Table resents the THD during exerimental testing, and it is found that there is a significant imrovement of the THD when increasing the number of voltage levels and using an LC filter. 3 3 Outut voltage (V) - - Outut voltage (V) Fig. 9 Simulated outut voltages and the corresonding FFT of level inverter without LC filter (left) and with LC filter (right) for r =.86,V dc = V dc = V and y =..

5 6 Waveform imrovement of a modified inverter toology 49 Fig. Exerimental outut voltages and the corresonding FFT of level inverter without LC filter (left) and with LC filter (right) for r =.86, V dc = V dc = V and y = Outut voltage (V) - - Outut voltage (V) Fig. Simulated outut voltages and the corresonding FFT of 7 level inverter without LC filter (left) and with LC filter (right) for r =.8, V dc = V dc = V and y =.. Fig. Exerimental outut voltages and the corresonding FFT of 7 level inverter without LC filter (left) and with LC filter (right) for r =.8, V dc = V dc = V and y =..

6 4 Fayçal Chabni, Rachid Taleb, M hamed Helaimi 7 Table Exerimental measurement of THD Unfiltered outut voltage Filtered outut voltage level 7.4 %.9 % 7 level 8.6 %.33 %. CONCLUSIONS In this aer, a single-hase CHB multilevel inverter is develoed by combining selective harmonic elimination and a assive LC filter to eliminate the outut voltage harmonics. The overall system model requires solving a set of nonlinear equations for the otimal switching angles calculation. The roosed CHB multilevel inverter architecture and the harmonic elimination control strategy based on hybrid genetic algorithms make the system very efficient. The low switching frequency rovided by the SHE control method will increase the reliability of the system and comonents life time. The use of the LC assive filler canceled significantly the higher order harmonics in the outut voltage waveform. Results and waveforms obtained from exerimental tests match erfectly the simulation results. 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