Analysis of Various Carriers Overlapping PWM Strategies for a Single Phase Ternary Multilevel Inverter

Received Jun 1, 2017 Revised Jan 9, 2018 Accepted Feb 17, 2018 Multilevel inverters are used in power conversion system due to improved voltage and current waveforms. This paper presents the comparison of various Carrier Overlapping Pulse Width Modulation (COPWM) Strategies for the three phase Cascaded Multi Level Inverter (CMLI). Various new schemes adopting the constant switching frequency and also variable switching frequency multicarrier control freedom degree combination concepts are developed and simulated for the chosen three phase CMLI. A single phase CMLI is controlled in this paper with Sinusoidal PWM (SPWM) reference along with Carrier Overlapping (CO) techniques and simulation is performed using MATLAB-SIMULINK. The variation of fundamental RMS output voltage and total harmonic distortion is observed for various carrier overlapping techniques. Among the various equal amplitude and unequal amplitude carriers carrier overlapping techniques such as COPWM-A, COPWM-B and COPWM-C, It is observed from Table 4 that all PWM method provides output with relative low distortion for equal amplitude carriers. If equal voltage sources are chosen then the THD will be less in the case of unequal amplitude carriers. But for the unequal voltage sources the THD is more in the case of unequal amplitude carriers. It is observed from simulation results that (Table-5) almost in all the strategies unequal amplitude carriers gives more fundamental RMS values compared to equal amplitude carriers. It is seen from table 6 that peak voltage is more in the case of unequal amplitude carriers compared to equal amplitude carriers. It is observed from the table 7 that dc components are less in both equal and unequal amplitude carriers. Keyword:

Multilevel inverters are used in power conversion system due to improved voltage and current waveforms. This paper presents the comparison of various Carrier Overlapping Pulse Width Modulation (COPWM) Strategies for the three phase Cascaded Multi Level Inverter (CMLI). Various new schemes adopting the constant switching frequency and also variable switching frequency multicarrier control freedom degree combination concepts are developed and simulated for the chosen three phase CMLI. A single phase CMLI is controlled in this paper with Sinusoidal PWM (SPWM) reference along with Carrier Overlapping (CO) techniques and simulation is performed using MATLAB-SIMULINK. The variation of fundamental RMS output voltage and total harmonic distortion is observed for various carrier overlapping techniques. Among the various equal amplitude and unequal amplitude carriers carrier overlapping techniques such as COPWM-A, COPWM-B and COPWM-C, It is observed from Table 4 that all PWM method provides output with relative low distortion for equal amplitude carriers. If equal voltage sources are chosen then the THD will be less in the case of unequal amplitude carriers. But for the unequal voltage sources the THD is more in the case of unequal amplitude carriers. It is observed from simulation results that (Table-5) almost in all the strategies unequal amplitude carriers gives more fundamental RMS values compared to equal amplitude carriers. It is seen from table 6 that peak voltage is more in the case of unequal amplitude carriers compared to equal amplitude carriers. It is observed from the table 7 that dc components are less in both equal and unequal amplitude carriers.

INTRODUCTION
Multi-level inverters play a key role in today's microgrids with renewable energy sources. It is a power electronic device that is used for high voltage and high power applications, with the added advantages of low switching stress and lower total harmonic distortion (THD), hence reducing the size and bulk of the passive filters. It gives the output current waveform which is nearly sinusoidal in nature. Jamaludin et al [1] suggested a multilevel voltage source inverter with optimised usage of bidirectional switches. Manjunatha and Anand [2] proposed a multilevel DC Link Inverter with reduced switches and batteries. Pharne [7] introduced a new multilevel converter topology with reduced number. Roshankumar et al [8] deals a five-level inverter topology with single-DC supply by cascading a flying capacitor inverter. James et al [9] proposed a multilevel inverter with reduced number of switches. Rahilal et al [10] evaluated a new 81 level inverter with reduced number of switches. Bayat and Babaei [11] introduced a new cascaded multilevel inverter with reduced number of switches. Nedumgatt et al [12] also introduced a multilevel inverter with reduced number of switches. Ho-Sun et al [13] proposed a multi-level inverter capable of power factor control with dc link switches. Adam et al [14] decribes a quasi-two-level and three-level operation of a diode-clamped multilevel inverter using space vector modulation. Gupta and Jain [15] made a topology for multilevel inverters to attain maximum number of levels from given DC sources. Lakshmi Ganesh and Chandra Rao [16] discussed the performance of symmetrical and asymmetrical multilevel inverters. Ebrahimi et al [17] introduced a new topology of cascaded multilevel converters with reduced number of switch count for high-voltage applications. Caballero et al [18] suggested a symmetrical hybrid multilevel inverter concept based on multi-state switching cells. Suroso and Toshihiko Noguchi [19] introduced a multilevel voltage-source inverter using h-bridge and twolevel power modules with a single power source. Balamurugan [20] made a comparision between simulation and dSPACE based implementation of various PWM strategies for a new H-type FCMLI topology. Balamurugan [21] introduced a nine level cascaded multi level inverter using embedded and flip flops. The above papers made a deep literature surevy on various multilevel invereters and its topologies. Figure 1 shows a circuit configuration of a cascaded H-bridge multilevel inverter employing trinary dc input source. It looks like a traditional cascaded H-bridge multilevel inverter except input dc sources. By using Vdc and 3Vdc, it can synthesize five output levels; -3Vdc, -Vdc, 0, Vdc, 3Vdc. The lower inverter generates a fundamental output voltage with three levels, and then the upper inverter adds or subtracts one level from the fundamental wave to synthesize stepped waves. Here, the final output voltage levels becomes the sum of each terminal voltage of H-bridge, and it is given as

TERNARY INVERTER
(1) Table 1 and 2 shows the different switching states for the ternary inverter and comparison between symmetrical and asymmetrical inverters. In the proposed circuit topology, if n number of H-bridge module has independent DC sources in sequence of the power of 3, an expected output voltage level is given as Vn = 3 n , n = 1,2,3 Table 1. Switching States for Ternary Output Vout S11 S12 S13 S14 S21 S22 S23 S24 4Vdc  Several CFDs exist in multi-carrier PWM strategies for MLIs. These strategies have more than one carrier option that can be triangular, saw tooth, a new function etc. As far as the particular carrier signals are concerned, there are multiple CFDs including function, frequency, amplitude, phase of each carrier and offset between carriers. Although multilevel inverter offers several advantages, the control strategies of MLI are quite challenging due to the complexity to cater the transitions between the voltage levels (or steps). A number of modulation strategies are used in multilevel power conversion applications. In this proposed topology two methods are used. 1. Equal Amplitude Carriers 2. Un Equal Amplitude Carriers (or) Variable Amplitude Carriers (VAC)

Equal Amplitude Carriers (EAC)
In this method, all the triangular carriers used will have the same amplitude. The PWM methods used are COPWM-A, COPWM-B AND COPWM-C WITH sine, THI, trapezoidal and stepped wave references. Figure. 4 to 6 shows the sample carrier arrangement, output voltage and FFT plot for COPWM-A strategy with sine reference (ma = 0.8 and mf=20). Where ma and mf are the amplitude and frequency modulation index.

Un Equal Amplitude Carriers (UEAC) (or) Variable Amplitude Carriers (VAC)
In this method, all the triangular carriers used will not have the same amplitude. The PWM methods used are UEAPD (Un Equal Amplitude Phase Disposition) PWM, UEAPODPWM, UEAAPODPWM, UEACOPWM, UEAPSPWM and UEAVFPWM with sine, THI, trapezoidal, TAR and stepped wave references. Figure 7 to 9 shows the sample carrier arrangement, output voltage and FFT plot for COPWM-A strategy with sine reference (ma = 0.8 and mf=20).

CARRIER OVERLAPPING PWM STRATEGIES
The COPWM method utilizes the CFD of vertical offsets among carriers. The principle of COPWM is to use several overlapping carriers with single modulating signal. For an m-level inverter, m-1 carriers with the same frequency fc and same peak-to-peak amplitude Ac are disposed such that the bands they occupy overlap each other. The overlapping vertical distance between each carrier is Ac/2 in this work. The reference wave has the amplitude Am and frequency fm and it is centered in the middle of the carrier signals. Within this COPWM strategy, combination of varied vertical and/or horizontal offsets are adopted to get different species such as COPWM-A, COPWM-B and COPWM -C.

The amplitude modulation index
Actually COPWM-B and COPWM-C can be looked on as a second control freedom degree change besides offset in vertical: the carriers have horizontal phase shift from COPWM -A. This formula is applicable only for the equal amplitude carriers.

COPWM-A strategy
The vertical offset of carriers for chosen five level inverter can be illustrated in Figure 10. It can be seen that the four carriers are overlapped with other and the reference sine wave is placed at the middle of the four carriers.

COPWM-B strategy
Carriers for chosen five level inverter with COPWM-B strategy are shown in Figure 11. It can be seen that they are divided equally into two groups according to the positive/negative average levels. In this strategy, the two groups are opposite in phase with each other while keeping in phase within the group.

COPWM-C strategy
Carriers for chosen five level inverter with COPWM-C strategy are shown in Figure 12. In this strategy, carriers invert their phase in turns from the previous one. It may be identified as PWM with amplitude overlapped and neighbouring phase interleaved carriers.

CONCLUSION
Various bipolar PWM strategies with equal amplitude carriers and unequal amplitude carriers have been developed using MATLAB-SIMULINK and tested for different modulation indices ranging from 0.8-1 for equal amplitude carriers and 0.6-1 for unequal amplitude carriers for the chosen single phase cascaded ternary multilevel inverter. It is observed from Table 4 that all PWM method provides output with relative low distortion for equal amplitude carriers. If equal voltage sources are chosen then the THD will be less in the case of unequal amplitude carriers. But for the unequal voltage sources the THD is more in the case of unequal amplitude carriers. It is observed from simulation results that (Table-5) almost in all the strategies unequal amplitude carriers gives more fundamental RMS values compared to equal amplitude carriers. It is seen from table 6 that peak voltage is more in the case of unequal amplitude carriers compared to equal