# An Improved Dingo Optimization Algorithm Applied to SHE-PWM Modulation Strategy
## 1 Introduction  
Due to the incremental use of renewable energy systems, (photovoltaics arrays, wind, fuel cells, just to mention a few), there is a need for power conversion systems that can transform their electrical output to the specific characteristics needed for a load to work [1]. Inverters are power electronic devices capable of transforming a direct current (DC) power source to an alternative current (AC) at a desired electrical characteristics output [2]. A multilevel inverter (MLI) is an inverter-type capable of generating a staircase output waveform synthesized at different voltage levels, where the levels are controlled by the correct angle switching of the MLI power switching devices. Due to their better electromagnetic compatibility, high power quality, low switching losses, and lower total harmonic distortion, they have been extensively used as industrial drivers, compensators, medium and high voltage inverters, and as an interface to renewable energy systems [3]. The multilevel inverters main advantage lies in the use of separate DC sources that are ideal for fuel cells and photovoltaics arrays applications. They can be classified in three basic types, cascaded H-bridge, diode clamped, and capacitor clamped inverters. Cascaded H-bridge inverters (CHBMLI) consist of a series of H-bridge cells connected in series, where the addition of each cell voltage is used to synthesize the desired output waveform [4]. Continuous research has aimed to reduce the MLIs harmonic content and to improve their structure by designing new topologies [5, 6]. On the operation of anMLI, the harmonic reduction mostly depends on the modulation strategy selected to control the inverter [6]. Selective harmonic elimination [4; 7; 8] (SHE) is a pulsed modulation (PWM) control strategy aimed to suppress low-order harmonics by determining the angles to control the switching sequence of the MLI power semiconductor devices. Then, the typical staircase output waveform is generated. The SHE-PWM formulation relies on the Fourier decomposition of this periodic output voltage waveform, giving a series of non-linear equations as a function of the inverter's switching angles for each level of the DC voltages [9; 10]. Finding the solution of these equations has been conducted by applying several methods such as iterative [11], stochastics [9], and metaheuristics [12; 13; 14], with the latter being highly used due to their ability to find the local optima and to avoid stagnation. On the metaheuristics side, many of them have been developed in recent years and can be classified as swarm-based, evolutionary, physics-based, human-based, and maths-based algorithms [15]. Several metaheuristics have been applied to solve the SHE-PWM formulation. [PERSON] et al. in [16] compared the flower pollination algorithm against particle swarm optimization (PSO), teaching learning-based optimization (TLBO), and cuckoo search algorithm (CSA) to establish the effectiveness of FPA in solving the selective harmonic elimination problem. Similarly, in [17; 18], the whale optimization (WOA) and modified version of the grey wolf optimization (GWO) were applied to solve the SHE formulation. In [19], they show that bio-inspired intelligent algorithms can effectively eliminate the undesired lower harmonics from the SHE-PWM control strategy. Researchers in [20] applied the asynchronous particle swarm optimization to solve the SHE-PWM formulation. Nowadays new optimization algorithms such as the black widow [21], harmony search [22], and the bacterial foraging algorithm [23] have been proposed to solve the SHE set of non-linear equations. Currently, no algorithm can efficiently and effectively solve every optimization problem in all engineering and research fields. The scientific community is still searching for new algorithms, which are then compared to those existing in the literature to prove their reliability. Good results can be achieved in a particular application but fail to find the global optimum in others [24; 25].