In this paper, SHE based on Newton Raphson algorithm is investigated for flying capacitor multilevel inverter control. Without measuring current and capacitor voltages, as well as not using any controller and voltage feedback the proposed strategy is capable of determining the best switching angles pattern in low switching frequency for maintaining nil mean current capacitor DC-link, hence balancing the capacitor voltages and eliminating certain harmonic orders while considering inverter R,L load power factor variation. Theoretical results are verified by simulations and experiments. Results show that the proposed method does effectively eliminate specific low order harmonics and the output voltage results in low total harmonic distortion with balanced flying capacitors.