Electrical Engineering https://doi.org/10.1007/s00202-020-00960-5 ORIGINAL PAPER Optimization-based selective harmonic elimination for capacitor voltages balancing in multilevel inverters considering load power factor Lazhar Manai 1,2 · Faouzi Armi 1,3 · Mongi Besbes 1,2 Received: 27 June 2019 / Accepted: 20 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract In this paper, SHE based on Newton–Raphson algorithm is used for open-loop control of flying capacitor multilevel inverter. Without measuring current and capacitor voltages, as well as not using any controller and voltage feedback, proposed control strategy generates accurate switching angles, capable of balancing flying capacitor voltage and eliminates lower order harmonics while considering load power factor variation. Efficiency and robustness of proposed algorithm are verified by simulation and experiments. Results show that proposed method does effectively eliminate specific low-order harmonics, and inverter output voltage is resulted in low total harmonic distortion with desired number of levels and balanced capacitor voltages. Keywords Newton–Raphson algorithm · Switching angles · Multilevel inverter · SHE · Lower order harmonics (LOH) · Flying capacitor voltage · Load power factor List of symbols ϕ Load current–voltage phase angle VC(i,j ) j th capacitor voltage of phase i C(i,j ) j th capacitor of phase i B Lazhar Manai manaii_lazhar@yahoo.fr Faouzi Armi armifaouzi@gmail.com Mongi Besbes mongi.besbes@gmail.com 1 Laboratory of Robotics, Informatics, and Complex Systems, and National Engineering School of Tunis, University of Tunis, El Manar, Le Belvédère, B.P N° 37, 1002 Tunis, Tunisia 2 Higher Institute of Information and Communication Technologies, University of Carthage, B.P N°123, 1164 Hammam Chatt, Tunisia 3 Laboratoire d’électronique et électromagnétisme (L2E), Campus Pierre et Marie Curie, Sorbonne Université, Paris, Île-de-France, France S(i,j ) Commutation cell T (i,j ) control signal E The DC bus link volt- age V T (i,j ) Inverter phase i volt- age across the j th commutation cell V AO (t ) Phase A-to-DC bus midpoint O voltage V BO (t ) Phase B-to-DC bus midpoint O voltage V CO (t ) Phase C-to-DC bus midpoint O voltage VAB Inverter line output voltage n Harmonic order ω Angular frequency θ 1, θ 2, θ 3 Switching angles to be calculated p Commutation cell number per inverter half arm M Modulation index Q C(1,1)charging and Q C(1,2)charging Electrical charge amount during 123