Minimum Total Harmonic Distortion Research Articles

Calculation of Optimal Switching Angles for a Multilevel Inverter Using NR, PSO, and GA- a Comparison

Currently, multilevel inverters have been increased the number of applications in the industrial sector and renewable energy sources. Among its characteristics, the most remarkable are modular design, high performance, and low harmonic distortion in the output voltage waveform. For this paper, a single-phase Cascade H-Bridge Multilevel Inverters (CHB-MLI or CMLI) topology with independent DC sources, has been selected for the case study. Analyzing three scenarios: 5-level, 7-level, and 9-level applying the concept of the Optimized Harmonic Stepped-Waveform (OHSW) and comparing the results between the Selective Harmonic Eliminated-Pulse Width Modulation (SHE-PWM) and the Optimal Minimization of the Total Harmonic Distortion (OMTHD) are also presented. To compare the results obtained with classical and nature-inspired optimization methods, three techniques are used to solve transcendental nonlinear equations for the problem of Total Harmonic Distortion (THD) minimization: Newton Raphson (NR), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), which have been widely used for the problems of THD minimization in multilevel inverters.

Analytical formulation and optimization of Weighted Total Harmonic Distortion in three-phase staircase modulated multilevel inverters

Staircase Modulation (SCM) is a popular switching strategy for three-phase multilevel inverters (MLI) of higher voltage levels count (N). SCM is often combined with some harmonic mitigation strategy, such as a minimum of Total Harmonic Distortion (THD) in addition to output fundamental component adjustments. While voltage THD-based SCM is desirable in many applications, it is not a panacea for all applications, especially for motor drives and grid-connected MLIs, where minimization of current-THD is preferable. A THD alternative performance parameter, called frequency-Weighted Total Harmonic Distortion (WTHD) can serve as a strong indication of current-THD, especially in inductive loads. For three-phase MLIs with 3-wire loads, line voltage waveform has more significance than phase voltage waveform, as it directly impacts the load’s current quality. For this reason, the minimization of Line-voltage WTHD (WLTHD) may be preferred over the minimization of THD, Line-THD (LTHD) or WTHD. Since WLTHD involves complicated expressions, it is typically calculated and expressed using frequency-domain numerical approaches, often resulting in underestimation errors. In this paper, a novel analytical WLTHD formulation for three-phase SCM-based MLIs is revealed and used for subsequent WLTHD minimization with the aim of minimizing load current-THD for 3-wire inductive loads. The proposed WLTHD formulation is a function of all possible Phase Switching Angles (PSA), valid for any MLI topology with arbitrary values of N, either odd or even. Moreover, it is shown that the existing WLTHD minimization approach is a particular case of the proposed generic methodology. The derived formulation, which can produce mathematically exact symbolic WLTHD results, is verified against numerically obtained results in previous works. Controller + Hardware in Loop (C-HIL) based validation is also carried out for 7-level three-phase MLIs feeding an induction motor for current-THD optimization, revealing significant improvements compared to previously obtained methods. The proposed WLTHD minimization possess the highest correlation to current-THD, even for nearly resistive loads. Links for downloading MATLAB and Maple source files of proposed WLTHD formulations as well as pre-calculated optimum PSA results for 5 ≤ N ≤ 16, covering most of the practical cases, are also provided for reader’s convenience.

Hybrid Shark Smell Optimization based on World Cup Optimization algorithm for Minimization of Total Harmonic Distortion

Hybrid Shark Smell Optimization based on World Cup Optimization algorithm for Minimization of Total Harmonic Distortion

Implementation of FOC based speed control for an E-Rickshaw brushless DC drive

This paper describes an approach to implement Field Oriented Control (FOC) using PID Controller for a brushless direct control (BLDC) motor. The research proposes reduction in total harmonic distortion of the supply current using space vector pulse width modulation technique. Minimization of total harmonic distortion becomes mandatory for a smooth operation in electric vehicle applications. As the harmonics are generated in the supply current, caused by non-linear load in E-Rickshaw. The lower, the value of total harmonic distortion givers better performance of the motor when operated under light load. Here the different strategies employed for controlling BLDC motor speed is analyzed and compared. It also proved that the space vector pulse width modulation technique improves the reliability due to the balanced switching frequency achieved from the solid-state switches in the inverter. Through simulating, the proposed control strategy is analyzed and compared with the existing techniques results in smooth change in current during sudden loading, which improves system performance and as a result the torque ripple gets minimized. The comparative study was made in the Matlab/Simulink 2019b, by designing the mathematical model of motor, inverter and the switching sequence, and the max-min algorithm for the SVPWM.

Digital control strategy for SPWM MPPT of PV system with three-phase NPC three-level converter

<p><span>This paper is aimed at investigating MPPT of PV system controlled by SPWM which is generated by comparing sinusoidal wave with variable frequency sawtooth wave. Perturb and Observe (P&O) method is used for MPPT control of PV system. NPC three-phase three-level converter with LCL filter is designed to produce output voltage with minimum Total Harmonic Distortion (THD) and high efficiency. The simple and fast method to get MPP of PV system with variable irradiation is digital control where the maximum power point is obtained from look-up table for the values of optimum voltage that achieve the maximum power for each irradiance value is used for digital control signal in microcontroller. The output voltage harmonic of multi-level three-phase inverter is controlled using SPWM control. THD of output voltage of multi-level three-phase inverter is 22% of stand-alone and grid-connected PV system. Small rate LCL filter is used to limit voltage harmonics within medium and low voltage limits (5%). THD output voltage of LCL filter is 4.9% and 3.51% of stand-alone and grid-connected PV system respectively. </span></p>

Optimal total harmonic distortion minimization in multilevel inverter using improved whale optimization algorithm

Abstract This paper presents the solution to mitigate the total harmonic distortion (THD) in multilevel inverters (MLIs) using novel improved whale optimization algorithm (IWOA). The IWOA falls under the category of swarm-based nature inspired optimization algorithms. It uses a novel diffusion process using a random walk technique and utilizes an additional ranking system to estimate the optimum solution to minimize THD. Moreover, THD minimization is further accomplished through nine various meta-heuristic algorithms for investigation and comparative analysis. The selected algorithms along with the proposed IWOA are rigorously tested on single phase 5 and 7 level cascaded H-Bridge MLIs for various performance parameters such as consistency, computational efficiency and speed of convergence. It is found that the proposed algorithm outperforms the nine algorithms and is efficient for THD minimization for modulation index (MI) in the range of 0–1. The results are analyzed and reported after thorough verification using MATLAB simulation.

Meta-heuristic optimization algorithms based direct current and DC link voltage controllers for three-phase grid connected photovoltaic inverter

This paper deals with improving the effectiveness of the control system for the DC/AC grid connected photovoltaic (PV) inverter. The three-phase DC/AC grid connected PV inverter control system consists of two main control loops: (i) external loop to control the DC link voltage. (ii) An internal control loop for regulating the inverter current by controlling both direct and quadrature currents (Id, Iq) that are provided by the inverter phase-locked loop (PLL). The main component of each control loop is the proportional-integral (PI) controller, whose optimal gains are challenging tasks. The optimal PI controller gains should be selected to achieve multi-objectives such as increasing inverter efficiency, stability and power factor while decreasing the total harmonic distortion (THD) in the inverter output current as well as voltage. For this purpose, various meta-heuristic techniques (MHTs) are suggested with a comprehensive comparative study such as: (i) Whales Optimization Algorithm (WOA), (ii) Grey Wolf Optimization (GWO) algorithm, (iii) Antlions Optimization algorithm (ALO) and (iv) Moth Flame Optimization (MFO) algorithm. The numerical results attained through MatlabTM-Simulink reveal that the WOA technique is more superior than the three others studied MHTs in enhancing the inverter efficiency, stability and power factor with minimum THD.

Direct Power Control of a Single Stage Current Source Inverter Grid-Tied PV System

In this paper, a direct power predictive controller (DPPC) is derived for a current source inverter (CSI) based single stage photovoltaic (PV) system. The equations of the dynamics, including AC and DC filters, are formulated directly for the PV power and for the active and reactive power injected in the grid. Then, the prediction equations are synthesized straight for the power, and, at each time instant, the optimal switching vector that guarantees simultaneously the control of the power generated by the PV arrays, and the control of the reactive power in the connection to the grid is chosen. This approach aims to guarantee fast and accurate tracking of the power. The proposed system is then validated through simulation and experimental results, showing that the PV system is able to follow the power references, guaranteeing a fast response to a step in the power, and decoupled active and reactive power control, with minimum total harmonic distortion (<5%) of the currents injected in the grid.

Hybrid power generation system with Total Harmonic Distortion minimization using improved Rider Optimization Algorithm: Analysis on converters

Hybrid power generating system is the renowned renewable energy technology that is mainly meant for its reliable performance. This paper introduces a new phase for power quality output by analyzing three DC-DC converters. This work intends to reduce the Total Harmonic Distortion (THD) by proposing hybrid power generation system with the combination of solar-wind as well as converters and full bridge inverter. The analysis is conducted by connecting the converters like buck boost, Single Ended Primary Inductor Converter (SEPIC) and Cuk converter for DC to DC level conversion. As a major contribution, the proportional gain and the Integral gain parameters of the PI controller are optimized which, in turn minimizes THD. For this optimization, this paper introduces a new improved optimization algorithm termed as Fitness Oriented Rider Optimization Algorithm (FO-ROA), which is the improvement of Rider Optimization Algorithm (ROA). The optimized performance of the proposed control system is compared with other conventional models and the superiority of proposed work has been proved.

Three‐stage SiC‐based bi‐directional on‐board battery charger with titanium level efficiency

This Letter proposes a novel control and optimisation strategy for a bi-directional, three-stage, on-board battery charger (OBC) achieving 80 PLUS Titanium efficiency. The proposed strategy utilises the benefits of silicon carbide (SiC) devices and is based on direct current hysteretic control (DCHC) with optimisation of switching patterns and dead time. The OBC first stage is a solid-state transformer that provides the isolation barrier and is operated under zero-current switching/zero-voltage switching (ZVS) conditions. The second stage is a bi-directional buck–boost converter that operates in critical conduction mode (CRM) with automatic dead time optimisation to achieve ZVS operation. The third stage is an H-bridge inverter with a DCHC controlled current loop to optimise dynamic and steady-state performance and provide a smooth transition between CRM and continuous conduction mode. The DCHC is implemented using a hybrid software/hardware approach. The experimental results show that the OBC can not only change the power flow direction within a few milliseconds but can also provide reactive power support for the grid. Additionally, the OBC achieves a peak efficiency of 96.65% and a minimum total harmonic distortion equal to 1%.

Vortex search algorithm for designing hybrid active power filter

<p>This paper proposes a new multi-objective optimization design method for Hybrid Active Power Filter based on the Vortex Search algorithm. The Vortex Search algorithm belongs to the Single-Solution Based algorithm class of Metaheuristics algorithm. This design method has the advantage of fast execution time, high convergence speed and prevent local trap problems. The achieved results are multi-objective, such as minimum total harmonic distortion of the supply current and source voltage and satisfy many constraints such as system stability, resonance conditions of branches and limits of the parameters. Compared with the traditional design method, simulation results have proved that: the proposed design method is given with better results in minimizing total harmonic distortion of the supply current and source voltage.</p>

Thrust Ripple Force Minimization and Efficiency Analysis of Electromagnetic Actuator on Active Suspension

A novel electromagnetic actuator for active suspension is designed on an in-wheel motor electric vehicle in this paper. Aiming at reducing thrust ripple force and improving stability of the actuator, a method of calculating the optimum slot width and optimizing edge radian of end tooth is proposed. Firstly, a finite element model (FEM) of the actuator is modeled, and the correctness of FEM is verified through comparisons of simulation results and analytical ones, including counterelectromotive force of coil winding and force characteristic test of the actuator. Based on the FEM, the influence of slot width on electromagnetic thrust and total harmonic distortion (THD) is analyzed, and the slot width is improved. The side effect of the actuator is considered. By improving the edge radian, the fluctuation of the cogging force and thrust ripple is reduced. In addition, output efficiency and energy feed efficiency of the actuator after reducing thrust ripple are studied. The results show the minimum THD is 4.2%, which is obtained at the slot width 4.3 mm, and thrust ripple is 36.5 N. When the edge radian is 60°, the thrust ripple decreases to only 15.7 N, which is reduced by 57.0%. The maximum output efficiency and energy feedback efficiency of the actuator are 87.5% and 27.1%, respectively. Finally, according to actuator characteristic tests of two working modes, it is concluded that the maximum energy feedback efficiency is 25.6%. The input current and current frequency should be gradually increased with the increase of suspension speed under active mode, and the maximum output efficiency is 80.2%. The test results are basically consistent with the FEM analysis values, which verify the correctness of the FEM analysis.

Design and development of symmetrical super‐lift DC–AC converter using firefly algorithm for solar‐photovoltaic applications

The super-lift technique is an exceptional contribution to DC–DC conversion technology. A replacement approach of symmetrical super-lift multilevel inverter (SLMLI) DC/AC technology is proposed with a reduced number of elements compared with the traditional multilevel inverter. In this method, the firefly algorithm conveys a leading task for the SLMLI topology for solar-photovoltaic applications. It generates low distortion output and consumes the harmonic band of the fast Fourier transform framework by the employment of the proposed algorithm. The simulation circuit for 15 levels output uses single switch super-lift inverter feed with different kinds of load (R, RL and RLE) conditions. The power quality is improved in SLMLI with minimised harmonics underneath the various modulation indices while varied from 0.1 up to 0.8. The circuit is designed in a field-programmable gate array, which includes the firefly rule to help the multilevel output, to reduce the lower order harmonics and to find the best switching angle. As a result, the minimum total harmonic distortion from the simulation and hardware circuit is achieved. Due to the absence of bulky switches, inductor and filter elements expose the effectiveness of the proposed system.

A Symmetrical Multilevel Inverter Topology with Minimal Switch Count and Total Harmonic Distortion

A multilevel inverter (MLI) with reduced number of power devices, especially for the higher output levels, is presented in this paper. The generalized topology for ([Formula: see text]) level MLI is developed with symmetrical isolated dc sources and ([Formula: see text]) number of switches. A five-level MLI is developed with five power switches and then by adding each one additional switch two more levels are added in the output voltage waveform. With the help of lookup table, the working principle of the proposed five-level MLI topology is explained. Sinusoidal pulse width modulation–phase disposition control technique has been used to get a minimal total harmonic distortion (THD). The proposed MLI topology is simulated on the MATLAB platform. The laboratory prototype is developed for five-level MLI, and the experimental results obtained validate the simulation studies. The dSPACE 1104 is used for generating gate pulses in case of experimentation. The output voltage and current THDs obtained are 9.20% and 4.60%, respectively; the harmonics are mitigated more with five-level inverter. The proposed topology is compared with the cascaded H-bridge multilevel inverter.

An Interval Arithmetic Approach for Multilevel Converter Harmonic Minimization Using Parseval’s Theorem

Multilevel converters are used for DC/AC power supply conversion, which is often applied in electric vehicle (EV) motor drives. AC conversion is done by a stepped output voltage, which provides a near-sinusoidal voltage with its fundamental frequency, but contains some higher harmonics. The elimination of several harmonics is fully implemented and well described in numerous publications, see Chiasson et al. (2003, 2004, 2005); Li et al. (2010); Tarisciotti et al. (2014), and Majed et al. (2014). In these papers the first set of undesired harmonics was eliminated, which in general was done by solving an equivalent system of equations using different methods such as resultants, Newton-Raphson (Chiasson et al. (2003)) and Optimal Minimization of Total Harmonic Distortion (OMTHD) technique, see Li et al. (2010). Higher harmonics stayed unrecognized to these optimization algorithms and delivered an undesired power spectrum to the total harmonic distortion (THD) of AC conversion.This paper presents a novel approach to the global THD-optimization of three-phase systems taking into account all harmonics up to infinity. This global optimization is implemented using interval arithmetic, see Hansen and Walster (2003), which neither need a convex objective function nor continuous-differentiable function. Interval arithmetic computes guaranteed intervals containing the global minima. The optimum is computed with an algebraic objective function, which is derived from Parseval’s theorem on a 2π periodic function.

Optimum pulse-width modulation strategy for a symmetric cascaded multilevel inverter

This paper investigates for the most suitable PWM strategy for a symmetric cascaded multilevel inverter. The objective is to determine a PWM switching strategy which optimises inverter performance by ensuring higher DC link utilisation and minimum total harmonic distortion (THD) at low switching frequency to minimise switching power losses. Simulations carried out in MATLAB-Simulink environment has given an insight of inverter performance when carrier-based PWM techniques are applied. In this parametric evaluation, both odd and even multiples of 50 Hz modulating signal were applied for obtaining switching frequency for various multicarrier-based PWM strategies.

Analytical Formulation and Minimization of Voltage THD in Staircase Modulated Multilevel Inverters With Variable DC Ratios

Staircase Modulation (SCM) is a commonly employed switching strategy in Multilevel Inverters (MLI) with a high number of voltage levels (N). The main challenges in SCM are adjusting the Modulation Index (MI) to the desired value while minimizing the Total Harmonic Distortion (THD). This is achieved by solving an objective function for its optimum variables. These variables are the Switching Angles (SA) in the case of an MLI with Equal DC voltage Supply (EDCS), or both the SAs and the DC voltage supply Ratios (DCR), in the case of an MLI with Unequal DC voltage Supply (UDCS). Such an approach, which is referred to as Optimum Minimization of THD (OMTHD), relies on the accuracy of the THD expression used for the objective function. This paper reveals generic analytical closed-form formulations of both Phase-voltage THD (PTHD) for single-phase (1φ) MLIs and Line-voltage THD (LTHD) for three-phase (3φ) MLIs. The revealed THD expressions apply to SCM based MLIs of any topology, with either EDCS or UDCS voltage source configurations, which may be fixed or varying, and arbitrary value of N (odd and even). Given an arbitrary N value, the proposed unified formulations can be used to generate symbolic N-level PTHD or LTHD expressions, which are analytical functions of the SA and (optionally) DCR variables. The proposed THD expressions were used to form a generic OMTHD problem and solve for optimum SA and DCR variables, ensuring PTHD or LTHD minimization, subject to a set of optional constraints, such as the target MI, tolerable Modulation Error (ME), and the Maximum DCR (MDCR). Outcomes of the proposed OMTHD algorithm were successfully verified by Controller + Hardware-in-Loop (C-HIL) based experiments and compared against results of previous works, raveling significant improvement in THD accuracy and MLI's performance. A downloadable supplemental file containing Maple and MATLAB functions of the proposed THD expressions, as well as pre-calculated sets of optimum SAs and DCRs tables for 13 different values of N (4 ≤ N ≤ 16), is provided for readers' convenience.

Modified GSA for minimisation of THD of voltage source multilevel inverter

Optimisation techniques have always been a reliable friend while dealing with complex nonlinear problems. Among a wide gamut of available optimisation techniques, genetic algorithm (GA) has always stood out on account of its being flexible and adaptable. This paper is an attempt to find a worthy competitor to GA. In the process, a new heuristic algorithm, gravitational search algorithm (GSA) has been chosen for implementation. The new technique, GSA is based on the laws of gravity and mass interaction. In order to obtain an efficient solution and quick convergence to the problem of minimisation of THD of the 15 level MLI under study; the algorithm is further modified. In the modified GSA (MGSA), the initial gravitational constant (Go) and the updating constant (α) are suitably modified. In this paper, SHE equations are used to find the optimum switching angles in both GA and GSA to minimise the total harmonic distortion (THD) of the inverter output voltage. The simulation and hardware results rendered by sinusoidal pulse width modulation (SPWM), GA, GSA and MGSA are compared for validity with each other. It is found that hardware results are in concurrence with the simulation results.

Modified GSA for minimisation of THD of voltage source multilevel inverter

Optimisation techniques have always been a reliable friend while dealing with complex nonlinear problems. Among a wide gamut of available optimisation techniques, genetic algorithm (GA) has always stood out on account of its being flexible and adaptable. This paper is an attempt to find a worthy competitor to GA. In the process, a new heuristic algorithm, gravitational search algorithm (GSA) has been chosen for implementation. The new technique, GSA is based on the laws of gravity and mass interaction. In order to obtain an efficient solution and quick convergence to the problem of minimisation of THD of the 15 level MLI under study; the algorithm is further modified. In the modified GSA (MGSA), the initial gravitational constant (Go) and the updating constant (α) are suitably modified. In this paper, SHE equations are used to find the optimum switching angles in both GA and GSA to minimise the total harmonic distortion (THD) of the inverter output voltage. The simulation and hardware results rendered by sinusoidal pulse width modulation (SPWM), GA, GSA and MGSA are compared for validity with each other. It is found that hardware results are in concurrence with the simulation results.

Optimum pulse-width modulation strategy for a symmetric cascaded multilevel inverter

This paper investigates for the most suitable PWM strategy for a symmetric cascaded multilevel inverter. The objective is to determine a PWM switching strategy which optimises inverter performance by ensuring higher DC link utilisation and minimum total harmonic distortion (THD) at low switching frequency to minimise switching power losses. Simulations carried out in MATLAB-Simulink environment has given an insight of inverter performance when carrier-based PWM techniques are applied. In this parametric evaluation, both odd and even multiples of 50 Hz modulating signal were applied for obtaining switching frequency for various multicarrier-based PWM strategies.