Selective harmonic elimination: An comparative analysis for seven level inverter

Selective Harmonic Elimination of Cascaded Multilevel Inverter Using BAT Algorithm

Multi‐level inverter (MLI) is a promising technology, able to generate high‐quality power with lower switching frequency. Therefore it leads to high conversion efficiency and low switching losses. Selective harmonic elimination is a fundamental frequency switching strategy that theoretically provides desirable output waveform for MLIs by elimination of low order harmonics. Unfortunately, complexity, non‐linearity and solvability features attached to this method have limited its industrial application. In this study, a particle swarm optimisation (PSO)‐based memetic algorithm (MA) guided by mesh adaptive direct search is introduced as a suitable choice for the harmonic optimisation problem. This algorithm is precise and applicable to any MLI. The results show that MA converges to the exact solution for feasible modulation index. When the problem has no exact solution, the algorithm finds a relatively proper solution to regulate the fundamental component of the voltage. Furthermore, the comparison between MA and other methods shows that the probability of convergence of MA is higher than others. For 48% of the analysed data MA reaches to a fitness value lower than 10−30 whereas this probability is 5% for PSO and almost zero for genetic algorithm and bee algorithm. The proposed method has been implemented on a cascade seven‐level inverter.

Multilevel inverters (MLIs) are widely recommended for DC to AC power conversion as per the load requirements. The MLIs are preferred over other types of multilevel and conventional converters due to their ability to produce staircase output voltage waveforms with superior harmonics profile. However, the performance of MLIs largely depends on the modulation strategy employed. Among the various modulation techniques, the selective harmonic elimination (SHE) method is more efficient in eliminating low-order harmonics from the voltage waveform produced by MLIs. Proper mitigation of the dominant low-order harmonics results in reduction in switching losses in the semiconductor devices and improves the efficiency of the inverter. However, the analytical solution of the nonlinear SHE equations constitutes the main challenge. Over last few decades, various solving algorithms and techniques such as algebraic methods such as resultant theory, numerical techniques and optimization algorithms have been developed and proposed for selective elimination of unwanted harmonics. This review paper presents the various aspects of the problem formulations for SHE technique. Moreover, the detailed principle operation for five different SHE problem-solving techniques is also discussed in this paper. Solution trajectories corresponding to multiple solutions, PWM waveforms with single and multiple transitions at each voltage level and also for pulse-width-amplitude modulation are evaluated and presented to help the researchers gain better insight into the SHE problem and its solution.

<span>In this paper, modified multilevel inverter, via addition of an auxiliary bidirectional switch, based on Newton Raphson (NR) and Particle Swarm Optimization (PSO) techniques is presented. The NR and PSO techniques were employed for selective harmonics elimination (SHE) solution in a modified Cascaded H Bridge Multilevel inverter (CHB-MLI). The Selective Harmonic Elimination Pulse-Width Modulation (SHE-PWM) is a powerful technique for harmonic minimization in multilevel inverter. The NR and PSO techniques were used to determine the switching angles by solving the non-linear equations of the output voltage waveform of the modified CHB-MLI in order to control the fundamental component and eliminate some low order harmonics. The proposed NR and PSO techniques are capable to minimize the Total Harmonic Distortion (THD) of the output voltage of the modified inverter within allowable limits. This paper aims to modeling and simulation by MATLAB of the modified topology of the CHB-MLI for a single-phase prototype for 13-levels. The inverter offers less THD and greater efficiency using PSO control algorithm compared with the NR algorithm. <br https://server9.kproxy.com/servlet/redirect.srv/sruj/snbzofspy/skvyzff/p1/> The performance of the proposed controllers based on NR and PSO techniques is verified through simulation.</span>

This article presents a hybrid method to solve the selective harmonic elimination (SHE) problem for an adaptive DC bus multilevel inverter (MLI) topology. The proposed hybrid method combines the Grey wolf optimization (GWO) technique and Newton-Raphson (NR) numerical method which drastically minimizes the computational time and further improves the accuracy of the SHE solution. The technique is essentially divided into two stages. In the exploration stage, GWO explores the entire search space of SHE problem and provides initial values of switching angles for a given modulation index with a fast rate of exploration. In the exploitation stage, the NR method uses these initial switching angles as input to iteratively determine the optimum value of the firing angles. This GWO-inspired iterative methodology is implemented on a hybrid MLI topology for photovoltaic (PV) system applications. The performance of proposed SHE method is compared with recently developed metaheuristic SHE techniques based on some key performance indices. From an application point of view, the 11-Level MLI is tested on a PV battery-based stand-alone system to determine the effectiveness of the proposed method in MATLAB/Simulink environment. Finally, a small-scale experimental prototype is developed to validate the proposed method.

A modified three phase symmetrical 5-level multilevel inverter structure, derived from a propounded auxiliary (AUX) inverter leg, is presented. The switch count and gate driver requirements are reduced compared to conventional topologies. An attempt is made to optimize the source requirement. The low switching frequency Selective Harmonic Elimination (SHE) method based on Bee algorithm is employed for generating gating signals. Simulations analysis is accomplished by MATLAB/SIMULINK To support the simulation results, experiment is conducted on a low power prototype.

Nowadays, voltage source multilevel inverters are being used extensively in industry due to its many advantages, compared to conventional two level inverters, such as higher output voltage at low switching frequency, low voltage stress(dv/dt), lower total harmonic distortion (THD), less electro-magnetic interference (EMI), smaller output filter and higher fundamental output. However, the evaluation of multilevel inverter losses is much more complicated compared to two level inverters. This paper proposes an on-line model for precise calculation of conduction and switching losses for cascaded h-bridge multilevel inverter. The model is simple and efficient and gives clear process of loss calculation. A singlephase 7-level cascaded h-bridge with IGBT's as switching devices has been used as a case study of the proposed model. The inverter has been controlled using selective harmonic elimination in which the switching angles were determined using the Genetic Algorithm (GA). MATLAB-SIMULINK is used for the modelling and simulation.

The paper presents non-traditional solutions to the problem of selective harmonic elimination (SHE) in induction motor drives fed by three-phase voltage-source inverter (VSI). The problem is independently solved using genetic algorithms (GA) and particle swarm optimisation (PSO). The inverter switching angles are determined such that the low-order harmonics up to the 17th are eliminated, while the fundamental component is set at a desired value. Findings of the research show that both routines could converge to accurate solutions. PSO outperforms GA in terms of the time of convergence and obtained value of the objective function, while GA is characterised with better robustness. The performance of the VSI-fed induction motor drive is studied under the SHE switching pattern. Results clearly show the merits of applying the SHE technique to the induction motor drive.

Selective Harmonics Elimination (SHE) technique of power electronic converters can be generally defined as calculation of the optimized switching angles at any desired output (fundamental) voltage component to eliminate a set of preferred lower order harmonic components. This low switching frequency method adds values to Multilevel Inverter (MLI) based systems for the reason that MLI’s have the ability to synthesize waveforms closer to sinusoidal with a better harmonics spectrum. The traditional method for finding the optimized switching angles is by solving the Fourier non-linear transcendental equations of the MLI output voltage and various algorithms like Newton-Raphson (NR) algorithm, Genetic algorithm (GA), Resultant theory, Walsh function etc. are available. This paper proposes a novel approach for performing SHE in MLI working with both equal and unequal dc voltages. The basic principle in which the proposed technique works is a combined effect of equal area criteria and negative harmonics injection techniques. The major advantage is that the proposed methodology comprises of four simple equations for performing SHE instead of solving the complex non-linear transcendental equation. The computational efficiency of this algorithm is evaluated through comparison with traditional NR and GA. In addition, a prototype of three-phase seven-level cascaded MLI is designed through which several informative results are investigated and the effectiveness of the proposed algorithm is proved.

This paper presents an implementation of selective harmonic elimination (SHE) modulation for a single-phase 13-level transistor-clamped H-bridge (TCHB) based cascaded multilevel inverter. To determine the optimum switching angle of the SHE equations, the Newton-Raphson method is used in solving the transcendental equation describing the fundamental and harmonic components. The proposed SHE scheme used the relationship between the angles and a sinusoidal reference waveform based on voltage-angle equal criteria. The proposed SHE scheme is evaluated through simulation and experimental results. The digital modulator based-SHE scheme using a field-programmable gate array (FPGA) is described and has been implemented on an Altera DE2 board. The proposed SHE is efficient in eliminating the <TEX>$3^{rd}$</TEX>, <TEX>$5^{th}$</TEX>, <TEX>$7^{th}$</TEX>, <TEX>$9^{th}$</TEX> and <TEX>$11^{th}$</TEX> order harmonics, which validates the analytical results. From the results, it can be seen that the adopted 13-level inverter produces a higher quality with a better harmonic profile and sinusoidal shape of the stepped output waveform.

The Selective Harmonic Elimination Pulse-Width Modulation (SHE-PWM) is an effective method for harmonic elimination in multilevel inverter. This paper presents the solutions of Selective Harmonic Elimination (SHE) problem based on Genetic algorithm (GA) and Particle Swarm Optimization (PSO) techniques. Total Harmonic Distortion (THD) of output voltage is minimized maintaining selected harmonics within allowable limits. A comparison has been drawn between GA and PSO techniques related to optimization.

Metaheuristic approaches receive a great interest in the area of optimization, especially when exact methods are missing, or the cost is extremely high. Besides the possibility to report good solutions in reasonable time, metaheuristic techniques are widely applicable. There are diverse categories of techniques that differ in number of search agents (or solutions), solution representation, and movement mechanism in search space. Just mentioned ingredients are determined according to the motivation or inspiration philosophy behind the technique. Nature-inspired optimization category is very popular and has proven high efficiency in many problems. It contains famous subclasses like evolutionary algorithms, swarm intelligence, and single-based techniques. Famous and classical examples of each subclass are genetic algorithm, particle swarm, and ant colony optimization, and simulated annealing, respectively. Nature-inspired optimization family grows so fast, and many members have joined it recently, for example, emperor penguin colony (2019), seagull optimization algorithm (2019), sailfish optimizer (2019), pity beetle algorithm (2018), emperor penguin optimizer (2018), multi-objective artificial sheep algorithm (2018), salp swarm algorithm (2017), electromagnetic field optimization (2016), sine cosine algorithm (2016), moth-flame optimization (2015), grey wolf optimizer (2014), flower pollination algorithm (2012), bat algorithm (2010), cuckoo search algorithm (2009), firefly algorithm (2008), and many others. There are many proposed hybridization and cooperation methods between techniques to produce improved versions of original ones. Nature-inspired techniques have been used in many application areas like theoretical computer science, engineering and control, forecasting, medical field, finance, management, operation research, and others. Also, new scientific disciplines like renewable energy, robotics, and navigation are feasible areas to make use of nature-inspired techniques. This chapter sheds light on six so recently new techniques that belong to nature-inspired optimization class.

This paper presents, ant colony optimization based hybrid algorithm for selective harmonic elimination in single phase seven level multilevel inverter with reduced switches. For high power and high voltage applications, multilevel structure with selective harmonic elimination (SHE) modulation scheme is used. The output voltage of multilevel inverter contains fundamental component along with harmonics. SHE technique aims to solve non-linear transcendental equations maintaining the fundamental harmonic component to its desired value and to eliminate lower order odd harmonics. Many optimization algorithms have been implemented to solve this problem. But these algorithms are complicated and time consuming. The Newton–Raphson algorithm is also very convergent for solving these non-linear equations. The main disadvantage of this method is, it requires strong initial guess. To overcome these drawbacks, hybrid optimization algorithm is used in this paper. This algorithm is performed in two stages, during first stage ant colony optimization has been run and in second stage the solutions obtained from ACO is used as a initial guess for Newton–Raphson algorithm which confirms the exact converged solution. Thus the drawback of Newton’s method i.e. requirement of good initial guess is overcomed by proposed hybrid algorithm. The MATLAB/SlMULINK software is used for comprehensive simulation of seven-level inverter. Experimental results validate the simulated results.

Multilevel inverters (MLIs) are increasingly used in real time applications. Among several pulse width modulation (PMW) techniques currently deployed for the control of MLIs, selective harmonic elimination PWM (SHEPWM) technique arguably gives the best performance due to its direct harmonic mitigation capability. However, real time application of SHEPWM technique is presently infeasible due to the heavy computational cost involved in solving the transcendental nonlinear equations known as selective harmonic elimination (SHE) equations, which characterize the harmonics that are selected for elimination or mitigation. This paper presents a twostage approach to the online generation of switching angles that mitigate selected lower-order harmonics in multilevel inverters. The first stage involves an offline solution of SHE equations using ant colony optimisation (ACO). In the second stage, ACO computed results are used to train an artificial neural network (ANN) predictive model. The results obtained from the simulation of the proposed method in MATLAB/SIMULINK environment show that the method is highly efficient and accurate.

This paper applies the selective harmonic elimination (SHE) technique to determine the switching angles for a multilevel inverter that cooperated with specially connected transformer, zig-zag connection. With the ability to direct controlling harmonics, SHE technique has the adaptability to associate with apparatus which are congenitally immune to specific harmonics, such as the zig-zag connection transformers. In this paper the two sets of primary windings of the transformers are supplied by two 6-switch full-bridge inverters with 30 electrical degrees phase shift. Prohibited by the transformers, harmonics with orders other than 12n±1 (n is positive integral) will not appear in the line-to-line voltage of the secondary side. Then, SHE technique is employed to handle harmonics with orders equal to 12n±1, and controls the amplitude of the fundamental. This paper obtains a set of precise switching angles through off-line calculation and then employs a digital signal processor to implement on-line calculation of the switching angles by an approximate method. Some selected analysis and experimental results are shown in this paper. A small-size prototype is built to verify the validity of the proposed system.