Electric Power Systems Research 108 (2014) 185–197 Contents lists available at ScienceDirect Electric Power Systems Research jou rn al hom e page: www.elsevier.com/locate/epsr On re-examining symmetry of two-level selective harmonic elimination PWM: Novel formulations, solutions and performance evaluation G. Konstantinou ∗ , V.G. Agelidis Australian Energy Research Institute (AERI) & School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia a r t i c l e i n f o Article history: Received 9 July 2013 Received in revised form 14 October 2013 Accepted 13 November 2013 Available online 6 December 2013 Keywords: Selective harmonic elimination Two-level converter Pulse-width modulation Half-wave symmetrical PWM Power electronics a b s t r a c t This paper analyzes the half-wave symmetrical two-level SHE-PWM, proposes two formulations of the SHE-PWM waveform with multiple solutions and evaluates the solutions for different cases of eliminated harmonics. Previous work on SHE-PWM focused on algorithms for calculating the solutions and only considered the quarter-wave symmetry in the formulation. In this paper two different formulations to the problem are considered and solutions for a number of eliminated harmonics are presented. The different formulations increase the solution space of the problem and the number of acquired solutions. A comparison of the solutions in terms of harmonic performance is also presented. When compared with the quarter-wave symmetrical solutions, certain half-wave symmetrical solutions exhibit better performance and additional benefits can be acquired for two-level converters operated under SHE-PWM techniques. The HW symmetrical solutions are experimentally verified on a laboratory setup in order to confirm the validity of the solutions sets. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Selective harmonic elimination pulse-width modulation (SHE- PWM) offers a tight control of the voltage harmonic spectrum of a switching converter, eliminating low order harmonics while main- taining the number of necessary switching instances (or switching angles) per period to a minimum. The reduced number of switch- ings leads to a reduction in the switching losses in medium and high-power systems. SHE-PWM is beneficial for and typically employed in utility-grade, high-power, low switching frequency grid connected applications, such as flexible alternating current transmission systems (FACTS), high-voltage direct current (HVDC) power transmission systems and high-power motor drives [1–25]. SHE-PWM is based on the Fourier decomposition of the out- put voltage waveform of a switching converter and has been dealt with in a number of previous papers for two- [1–18], three- and multilevel waveforms [19–23]. The modulation problem is ∗ Corresponding author at: Australian Energy Research Institute (AERI), Bldg H6 – Tyree Energy Technologies Building (TETB), University of New South Wales, Sydney, NSW 2052, Australia. Tel.: +61 2 9385 7405. E-mail addresses: g.konstantinou@unsw.edu.au (G. Konstantinou), vassilios.agelidis@unsw.edu.au (V.G. Agelidis). initially transformed to a number of non-linear, transcendental, trigonometrical equations and then the solutions to this system of equations are sought. A property of this system of equations is the fact that it exhibits multiple solutions. The number of solutions increases as the number of harmonics to be eliminated from the output spectrum and hence the complexity of the system increases. Various algorithms and approaches have been proposed in order to acquire the multiple solutions of SHE-PWM. The bipolar wave- form, with respect to harmonic elimination and voltage control techniques are analyzed in [1,2]. Ref. [3] presents a detailed catego- rization and analysis of the sets of solutions and a critical evaluation of the results for both single- and three-phase converter topologies. An accurate prediction of the initial values can simplify the process of solving the non-linear equations [4]. However, the prediction of initial values covers only a small number of the multiple solutions of the problem and cannot provide all possible solutions, particularly as the number of transitions per period increases. A systematic method for finding all harmonic elimination patterns based on a sequential homotopy-based computation is presented in [5]. For low number of transitions, the graphic method based on extrapolation of the values can accurately calculate the required solutions but the sequential approach based on previ- ous solutions becomes complicated as the number of transitions increases. The predicted number of solutions that is estimated 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.11.010