**ABSTRACT:**

This paper analyses synchronization strategy for cascaded H-Bridge multi level inverter (CHBMLI) topologies with carrier based sinusoidal phase shifted pulse width modulation (PSPWM) technique. In PSPWM technique a separate carrier is used for each H-Bridge (HB). The carriers are generally phase shifted from each other by π/x rad (x=No. of H-Bridges) for unipolar PWM. With the carrier frequency being an integer (odd/even) multiple of the fundamental frequency, it is observed that, the positions of zero crossings of the carriers with respect to the zero crossings of voltage references play an important role for maintaining quarter wave symmetry among multi level inverter (MLI) pole voltage waveforms. This paper analytically shows the conditions for half wave symmetry and quarter wave symmetry and experimentally verifies those conditions for PSPWM technique with a five level CHBMLI laboratory prototype.

**KEYWORDS:**

- Cascaded H-Bridge multilevel inverter
- Phase shifted carrier based PWM
- Synchronous PWM
- Half wave symmetry
- Quarter wave symmetry

**SOFTWARE:** MATLAB/SIMULINK

**CIRCUIT DIAGRAM:**

Fig. 1. (a) Single H-Bridge ; (b) Double cascaded H-Bridges.

** ****EXPECTED SIMULATION RESULTS**

** **

** **Fig. 2. (a) and (d) Ch.1:-CHB1, Ch.2:-CHB2, Ch.3:-R1 and Ch.4:-R2; (b) and (e) Ch.1:-VHB1, Ch.2:-VHB2 and Ch.3:-VHB and (c) and (f) Ch.1:-VRO, Ch.2:- VBO and Ch.3:-VYO when (i) the zero crossings of voltage references are in phase with the zero crossings of carrier CHB1 and (ii) the zero crossings of voltage references are placed at the midpoint of the positive zero crossings of carriers CHB1 & CHB2 for fc=3fs with a modulation index of 0.8 and fs=50Hz.

Fig. 3. (a) and (d) Ch.1:-CHB1, Ch.2:-CHB2, Ch.3:-R1 and Ch.4:-R2; (b) and (e) Ch.1:-VHB1, Ch.2:-VHB2 and Ch.3:-VHB and (c) and (f) Ch.1:-VRO, Ch.2:- VBO and Ch.3:-VYO when (i) the zero crossings of voltage references are placed at +π/12rad with respect to the zero crossings of carrier CHB1 for fc=3fs with a modulation index of 0.8 and fs=50Hz and (ii) for fc=160Hz with a modulation index of 0.8 and fs=50Hz.

Fig. 4. (a) and (c) Ch.1:-VRO, Ch.2:-VYO, Ch.3:-VRY and Ch.4:-iR; (b) and (d) Harmonic spectrum of VRY for (i) the zero crossings of voltage references are in phase with the zero crossings of carrier CHB1 and (ii) the zero crossings of voltage references are placed at the midpoint of the positive zero crossings of carriers CHB1 & CHB2 for fc=3fs with a modulation index of 0.8 and fs=50Hz.

Fig. 5. (a) and (c) Ch.1:-VRO, Ch.2:-VYO, Ch.3:-VRY and Ch.4:-iR; (b) and (d) Harmonic spectrum of VRY for (i) the zero crossings of voltage references are placed at +π/12 rad with respect to the zero crossings of carrier CHB1 for fc=3fs and (ii) fc=160Hz with a modulation index of 0.8 and fs=50Hz.

Fig. 6. (a) Ch.2:- VHB1, Ch.3:- VHB2 and Ch.4:- VHB; (b) Harmonic spectrum of VRO; (c) Ch.1:-VRO, Ch.2:-VYO, Ch.3:-VRY and Ch.4:-iR and (d) Harmonic spectrum of VRY when the zero crossings of voltage references are in phase with the zero crossings of carrier CHB1 for fc=6fs with a modulation index of 0.8 and fs=50Hz.

Fig. 7. (a) Ch.2:- VHB1, Ch.3:- VHB2 and Ch.4:- VHB; (b) Harmonic spectrums of VRO; (c) Ch.1:-VRO, Ch.2:-VYO, Ch.3:-VRY and Ch.4:-iR and (d) Harmonic spectrums of VRY when the zero crossings of voltage references are placed at the midpoint of the zero crossings of carriers CHB1 & CHB2 for fc=6fs with a modulation index of 0.8 and fs=50Hz.

Fig. 8. (a) and (b) Ch.1:-CHB1, Ch.2:-CHB2, Ch.3:-R1 and Ch.4:-R2 and (c) and (d) Ch.1:-VHB1, Ch.2:-VHB2 and Ch.3:-VHB when (i) the zero crossings of voltage references are placed at the midpoint of the positive zero crossings of carriers CHB1 & CHB2 and (ii) the zero crossings of voltage references are in phase with the zero crossings of carrier CHB2 for fc=9fs with a modulation index of 0.9 and fs=45Hz.

Fig. 9. (a) Ch.1:-Transition signal,Ch.2:-CHB1,Ch.3:-CHB2 and Ch.4:-R-Phase voltage reference and (b) Ch.1:-Transition signal,Ch.2:-CHB1,Ch.3:-CHB2 and Ch.4:-iR during the transition from p=9 to p=3.

Fig. 10. (a) and (d) Ch.1:-VHB1, Ch.2:-VHB2, Ch.3:-VHB3 and Ch.4:-VHB4; (b) and (e) Ch.1:-VHB and (c) and (f) Harmonic spectrum of VHB when (i) the positive zero crossing of one carrier co-incides with the zero crossing of fundamental voltage reference and (ii) the zero crossing of fundamental voltage reference is placed at the midpoint of two adjacent carriers with a modulation index of 0.8, fs=50Hz and p=3 for a single phase nine level CHBMLI.

**CONCLUSION: **

This paper shows analytically the possible positions of zero crossings of the carriers with respect to the zero crossings of voltage references for the CHBMLIs using the PSPWM technique for maintaining three phase symmetry, half wave symmetry and quarter wave symmetry. Three phase and half wave symmetries are maintained among the H-Bridge pole voltage waveforms for any position of zero crossing of carrier with respect to the zero crossing of the voltage references, as long as carrier frequency is 3n time the fundamental frequency with n being any integer (even/odd). But the positions of zero crossings of the carriers with respect to the zero crossings of voltage references are important for maintaining quarter wave symmetry among the pole voltage waveforms. This is analytically studied in this paper for single and two cascaded H-Bridges and generalized for x number of cascaded H-Bridges. The study is experimentally verified with the help of a three phase five level CHBMLI laboratory prototype and the results are presented.

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