Online harmonic elimination pulse width modulation technique for modular multilevel cascade converter

This paper presents a novel online technique, which simultaneously exploits the global search ability of differential evolution (DE) and rapid convergence of Newton Raphson (NR) methods (named as DE-NR) to solve intricate simultaneous transcendental trigonometric set of harmonic elimination pulse width modulation equations for modular multilevel cascade converters based power systems. Major contribution of this paper is a harmonically efficient online algorithm with rapid convergence. Switching angles for an extensive range of modulation index (M,0.86⩽M≤9.97) are computed online to demonstrate the harmonically efficient working of proposed method. Total harmonic distortion values of the filtered line-to-line output voltages during online operation are restricted to 0.35% of the fundamental component, which depict successful removal of unwanted harmonics and are significantly better than the values allowed by IEEE standard 519-2014. Comparison between DE-NR, differential evolution and Newton Raphson methods demonstrates the rapid convergence behavior of DE-NR as it requires only (on average) 4 iterations compared to 490 and 182 iterations respectively. It has also shown superior harmonic control than the recently devised online Middle-Level Selective Harmonic Elimination Pulse-Amplitude Modulation method. Successful simulation and experimental validations of DE-NR method have been done by developing three-phase modular multilevel cascade converter in MATLAB-Simulink and single-phase eleven-level modular multilevel cascade converter hardware prototype.