Number Of Switching Angles Research Articles

Multilevel Selective Harmonic Modulation via Optimal Control

We consider the Selective Harmonic Modulation (SHM) problem, consisting in the design of a staircase control signal with some prescribed frequency components. In this work, we propose a novel methodology to address SHM as an optimal control problem in which the admissible controls are piecewise constant functions, taking values only in a given finite set. In order to fulfill this constraint, we introduce a cost functional with piecewise affine penalization for the control, which, by means of Pontryagin’s maximum principle, makes the optimal control have the desired staircase form. Moreover, the addition of the penalization term for the control provides uniqueness and continuity of the solution with respect to the target frequencies. Another advantage of our approach is that the number of switching angles and the waveform need not be determined a priori. Indeed, the solution to the optimal control problem is the entire control signal, and therefore, it determines the waveform and the location of the switches. We also provide numerical examples in which the SHM problem is solved by means of our approach.

Symmetrical switching strategy based on reduced switching state in a three‐phase multilevel converter with a single faulty cell

AbstractDue to the possibility of the occurrence of a fault in converters, performance improvement of a converter under faulty conditions is important. In this paper, for improving the performance of the three‐phase cascaded H‐bridge multilevel converters (CHB‐MLCs) with a single faulty cell, the quarter‐and half‐wave symmetry selective harmonic mitigation (SHM) modulation method as well as reducing the number of switching angles (NSA) has been used. Consequently, it helps to reduce the switching frequency (fs) and the number of sentences of the Fourier series thus simplifies the objective function. In addition, the proposed method enables the switching angles of a faulty cell to be transferred to other normal cells per phase. For this purpose, the switching angles of the cells are optimized so that at least one of the cells does not overlap with the other cells in the same phase. By employing the maximum modulation index under the faulty condition, the maximum capacities of the remaining DC sources are used and consequently, the line voltage drop in the output voltage is prevented. To produce a balanced line voltage, the fundamental phase‐shift Compensation (FPSC) method is employed. Simulation and experimental results are presented to confirm the efficiency of the proposed strategy.

Implementation of SHE-PWM technique for single-phase inverter based on Arduino

This paper presents design and practical implementation of single-phase inverter based on selective harmonic elimination-pulse width modulation (SHE-PWM) technique. Microcontroller mega type Arduino used as a controller for producing the gate pulses. The optimized switching angles determination results in wide range of output voltage. Depending on number of switching angles, the lower order harmonics (LOHs) can be eliminated to improve the output voltage waveform. A comparison study using MATLAB/Simulink for sinusoidal-PWM and SHE-PWM techniques, which shows for the same LOH in the output voltage waveform, the SHE-PWM has less number of pulses per half cycle than sinusoidal-PWM strategy. The reduction in number of pulses results less switching losses. The simulation done using ten switching angles to drive R-L load. A prototype of SHE-PWM inverter with R-L load is used to validate the simulation results.

CC-LA: determining optimal switching angles in a cascaded H-bridge multilevel inverter with the aid of binary cat cubpool-based lion algorithm

A multilevel inverter (MLI) is a power electronic device that includes the capability to offer the preferred voltage level (alternating) in the output. Accordingly, selective harmonic elimination (SHE) or pulse width modulation (PWM) methodologies were deployed widely. However, these techniques are not appropriate in a certain situation which involves a huge number of switching angles if an excellent primary guess is not obtainable. Hence, this paper intends to determine the optimum switching angles of a cascaded H-bridge multilevel inverter (CH-MLI) using a hybrid lion optimization algorithm (LOA) and binary cat swarm algorithm (BCSO). The objective of optimizing the switching angle is to generate the needed fundamental voltage and minimize the harmonic content. This is done by resolving the transcendental equations characterizing the harmonic content. The switching angles, i.e., α1, α2.... αm, should be tuned in such a way that it satisfies the condition [Formula: see text]. Here, the optimal tuning of switching angles is done by the proposed binary cat cubpool-based lion algorithm (BCC-LA). In addition, the analysis is done for the proposed method over the state-of-the-art models in terms of total harmonic distortion (THD), and the impact of varying loads is also examined for the proposed and traditional models, and thus, the superior performance of the proposed model is validated.

Asynchronous Particle Swarm Optimization-Genetic Algorithm (APSO-GA) Based Selective Harmonic Elimination in a Cascaded H-Bridge Multilevel Inverter

In this article, a hybrid asynchronous particle swarm optimization-genetic algorithm (APSO-GA) is proposed for the removal of unwanted lower order harmonics in the cascaded H-bridge multilevel inverter (MLI). The APSO-GA is applicable to all levels of MLI. In the proposed method, ring topology based APSO is hybrid with GA. APSO is applied for exploration and GA is used for the exploitation of the best solutions. In this article, optimized switching angles are calculated using APSO-GA for seven-level and nine-level inverter, and results are compared with GA, PSO, APSO, bee algorithm (BA), differential evolution (DE), synchronous PSO, and teaching–learning-based optimization (TLBO). Simulation results show that APSO-GA can easily find feasible solutions particularly when the number of switching angles is high; however, the rest of all stuck at local minima due to less exploration capability. Also, the APSO-GA is less computational complex than GA, BA, TLBO, and DE algorithms. Experimentally, the performance of APSO-GA is validated on a single-phase seven-level inverter.

Analytical Evaluation and Reduction of Torque Harmonics in Induction Motor Drives Operated at Low Pulse Numbers

Induction motor drives operated with a low ratio of the switching frequency to the fundamental frequency (i.e., pulse number) are prone to have high magnitudes of low-order torque harmonics. This paper proposes a method to analytically evaluate the harmonic torque spectrum based on the pulsewidth-modulated voltage waveforms for low pulse number operation. The predicted torque harmonic spectra for different pulsewidth-modulated waveforms are validated through simulations and experiments. This paper also reports optimal switching angles to minimize the total rms value of torque harmonics of order 6, 12, 18 $,\dots,$ $6(N-1)$ , considering the number of switching angles per quarter ( $N$ ) to be 4 and 5. Compared to sine triangle pulsewidth modulation and selective harmonic elimination pulsewidth modulation with the same pulse number, the proposed optimal switching angles significantly reduce the total rms value of all harmonic torques of order lower than $6N$ . Extensive simulation and experimental results on a 3.7-kW induction motor drive are presented to demonstrate the superior performance of the proposed optimal pulsewidth modulation.

Simultaneous Selective Harmonic Elimination and THD Minimization for a Single-Phase Multilevel Inverter With Staircase Modulation

Power electronic converters for medium- and high-power/voltage applications employ low-frequency fundamental switching frequencies and, therefore, minimize switching losses. There are two main control techniques of switching angle estimation; total harmonic distortion (THD) minimization and selective harmonic elimination (SHE). In case of the first control technique, the switching angles are found based on THD minimization without being specifically focused on eliminating some exact harmonics. For the SHE control technique, all degrees of freedom, due to available number of switching angles, is used for the elimination of certain low-order harmonics. The basic idea of combining those two control techniques consists of using some degrees of freedom for eliminating certain harmonics and using the others for minimizing the remaining THD content. This generalized problem formulation includes classic minimal THD and SHE problems as special cases. Theoretical developments are verified by the set of experimental cases for the voltage and current THDs selecting characteristic working points over the modulation index range.

Fast closed‐form solution of line‐to‐line voltage total harmonic distortion for three‐level inverters

Harmonic emission to the network must be restricted below the predefined limits, avoiding power quality problems. Total harmonic distortion (THD) is a well-known criterion, which is used to determine harmonic content of each waveform, and extracting its exact value is very important. Three-level inverters produce a significant amount of harmonics and the exact closed-form expression for their line-to-line voltage THD has not yet been derived. All presented methods in this regard are based on an approximate approach. This study calculates line-to-line voltage THD of a three-level inverter by two different methods and presents their relevant formulas. The first method is usable for any number of controlled PWM switching angles, but the second method is limited to low number of switching angles. By the presented mathematical formulas in this study, the THD is computed simply, accurately and rapidly. The proposed methods are compared with the conventional methods and their advantages are verified by simulation and experimental results.

Multiple Switching Patterns for SHEPWM Inverters Using Differential Evolution Algorithms

An investigation on multiple patterns for both odd and even number of switching angles in a three-phase selective harmonic elimination pulse width modulation (SHEPWM) inverter is presented. The switching patterns are eand classified on the basis of the harmonic performance of the waveforms output from the inverter. Differen tial evolution algorithms are employed to calculate the optimum switching angl es. Selected cases are verified experimentally by a digital signal processorbased hardware implementation. The experimental res ults show that all types of the patterns offer low ha rmonic distortions on the inverter output after filtering. However, one tgives better harmonic performance is identified .

Harmonic Elimination of Cascade Multilevel Inverters with Nonequal DC Sources Using Particle Swarm Optimization

In this paper, the elimination of harmonics in a cascade multilevel inverter by considering the nonequality of separated dc sources by using particle swarm optimization is presented. Solving a nonlinear transcendental equation set describing the harmonic-elimination problem with nonequal dc sources reaches the limitation of contemporary computer algebra software tools using the resultant method. The proposed approach in this paper can be applied to solve the problem in a simpler manner, even when the number of switching angles is increased and the determination of these angles using the resultant theory approach is not possible. Theoretical results are verified by experiments and simulations for an 11-level H-bridge inverter. Results show that the proposed method does effectively eliminate a great number of specific harmonics, and the output voltage is resulted in low total harmonic distortion.

Selective Harmonic Mitigation Technique for High-Power Converters

In high-power applications, the maximum switching frequency is limited due to thermal losses. This leads to highly distorted output waveforms. In such applications, it is necessary to filter the output waveforms using bulky passive filtering systems. The recently presented selective harmonic mitigation pulsewidth modulation (SHMPWM) technique produces output waveforms where the harmonic distortion is limited, fulfilling specific grid codes when the number of switching angles is high enough. The related technique has been previously presented using a switching frequency that is equal to 750 Hz. In this paper, a special implementation of the SHMPWM technique optimized for very low switching frequency is studied. Experimental results obtained applying SHMPWM to a three-level neutral-point-clamped converter using a switching frequency that is equal to 350 Hz are presented. The obtained results show that the SHMPWM technique improves the results of previous selective harmonic elimination pulsewidth modulation techniques for very low switching frequencies. This fact highlights that the SHMPWM technique is very useful in high-power applications, leading its use to an important reduction of the bulky and expensive filtering elements.