Newton-Raphson-based flying capacitor multilevel inverter modeling is investigated for capacitor voltage balancing. Without using voltage feedback, Newton-Raphson method determines the best switching pattern for maintaining nil mean current in all capacitors, hence minimizing the capacitor voltage fluctuation and eliminating certain harmonic orders. Flying capacitor multilevel inverter (FCMI) modeling is developed to work with the selective harmonic elimination (SHE) technique to obtain a programmable pulse generator for multilevel inverter commutation cell control. Theoretical results are verified by experiments and simulations for a flying capacitor four-level inverter. Results show that the proposed method does effectively eliminate a number of specific low order harmonics, and the output voltage is resulted in low total harmonic distortion and with balanced flying capacitors.