Reactive Components Research Articles

Shunt active power filtering with reference current generation based on dual second order generalized integrator and LMS algorithm

For reducing the carbon emissions from utility sector, it is important to improve the efficiency of network and electrical loads. Current harmonics are responsible for the degradation of the system as well as load efficiency. The propagation of current harmonics into the grid can be prevented with shunt active power filters (SAPFs). Reference current generation (RCG) is critical for SAPF operation. This paper presents the control of SAPF with RCG based on least mean square (LMS) and dual second order generalized integrator (SOGI). The two SOGIs separately process grid voltage and load current to determine the respective fundamental in-phase component (FPC) and fundamental quadrature component (FQC). FPC and FQC of grid voltage are used to determine the phase angle of fundamental grid voltage. With LMS algorithm the distorted current can be decomposed into fundamental active (FA), fundamental reactive (FR) and harmonic components. However, the dynamic response of LMS based estimation is poor when the same learning rate is used for all components. FQC of load current, estimated with SOGI, can be processed by LMS algorithm to separate FA and FR components. RCG can be implemented with the computed phase angle and FA component. In LMS algorithm, as only two components are to be separated, two different learning rates can be easily specified. This results in faster dynamic response for LMS algorithm and has consequent positive impact on RCG and SAPF operation. Also, the computational complexity is considerably reduced. The performance of SAPF with the proposed extraction algorithm is analyzed for different operating conditions and comparative analysis is carried out.

On the noise performances of fractal‐fractional electrical circuits

AbstractIn this work, the noise performances of the fractal‐fractional electrical circuits have been addressed. The nonlocal fractal calculus has been adopted as our mathematical basis. The fractal time component has also been included for the physical measurability of electrical quantities. The derivations of crucial stochastic parameters of circuit responses, which determine their noise performances, have been performed. Numerical simulations have also been conducted where the influences of Hausdorff dimension of the fractal set, orders of fractal‐fractional reactive components, and other parameters on the noise performances have been studied. Regardless to any specific circuit, we have found that the noise performances can be improved by increasing the orders of fractal‐fractional reactive components. The optimum Hausdorff dimensions, which the best noise performances can be achieved given the orders of fractal‐fractional reactive components, have also been calculated. The results proposed in this work serve as the foundation for understanding noise in fractal‐fractional electrical circuits and can be extensively applied to large‐scaled circuits, for example, the infinite circuit networks and so forth.

Temporal changes in the physical and mechanical properties of beetle elytra during maturation

Changes in physical properties of Tenebrio molitor and Tribolium castaneum elytra (hardened forewings) were studied to understand how the development of microstructure and chemical interactions determine cuticle mechanical properties. Analysis of these properties supports a model in which cuticular material is continuously secreted from epidermal cells to produce an extracellular matrix so that the outermost layers mature first. It is hypothesized that enzymatic crosslinking and pigmentation reactions along with dehydration help to stabilize the protein-chitin network within the initial layers of cuticle shortly after eclosion. Mature layers are proposed to bear most of the mechanical loads. The frequency dependence of the storage modulus and the tan δ values decreased during the beginning of maturation, reaching constant values after 48 h post-eclosion. A decrease of tan δ indicates an increase in crosslinking of the material. The water content declined from 75% to 31%, with a significant portion lost from within the open spaces between the dorsal and ventral cuticular layers. Dehydration had a less significant influence than protein crosslinking on the mechanical properties of the elytron during maturation. When Tribolium cuticular protein TcCP30 expression was decreased by RNAi, the tan δ and frequency dependence of E’ of the elytron did not change during maturation. This indicates that TcCP30 plays a role in the crosslinking process of the beetle's exoskeleton. This study was inspired by previous work on biomimetic multicomponent materials and helps inform future work on creating robust lightweight materials derived from natural sources. Statement of significanceExamination of changes in the physical properties of the elytra (hardened forewings) of two beetle species advanced understanding of how the molecular interactions influence the mechanical properties of the elytra. Physical characterization, including dynamic mechanical analysis, determined that the outer portion of the elytra matured first, while epidermal cells continued to secrete reactive components until the entire structure reached maturation. RNA interference was used to identify the role of a key protein in the elytra. Suppression of its expression reduced the formation of crosslinked polymeric components in the elytra. Identifying the molecular interactions in the matrix of proteins and polysaccharides in the elytra together with their hierarchical architecture provides important design concepts in the development of biomimetic materials.

Maximum Torque Operation of Open-Winding Induction Motor Dual Drives Using a Floating Capacitor Bridge in the Field Weakening Region

A field weakening controller is presented that extends the speed range of a dual inverter drive using a floating capacitor bridge. The controller utilizes the stator current reference frame to decouple the motor demand into active and reactive components. This is used so that the main bridge supplies the real power and the floating bridge supplies the reactive power until the floating bridge reaches its maximum voltage. The main bridge is then used to supply some of the reactive demand, which in turn adds additional voltage boost that is used to extend the drive’s constant power region, improve the motor speed acceleration performance, output power, and torque. It is found that the presented controller can increase the drive speed extension ratio to 9.2 times the base speed compared to 5 when always operating the main bridge at unity power factor. The motor maximum fundamental voltage is 1.82 p.u when compared to that of a single inverter drive. This controller performance is demonstrated experimentally using both transient and steady-state analysis. The controller is also compared with other two field weakening controllers using the same regulator tunings and experimental setup.

Spectral theory of diffusion in partially absorbing media

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position X t and a Brownian functional U t that specifies the amount of time the particle is in contact with a reactive component M . Absorption occurs as soon as U t crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to U t leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption z , where z is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary ∂ M , this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann (D-to-N) operator on ∂ M . In this paper, we develop the analogous construction in the case of a reactive substrate M . In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of D-to-N operators on ∂ M . However, inverting the Laplace transform with respect to z is considerably more involved. We illustrate the theory by considering the D-to-N operators for some simple geometries.

Application of Shunt Capacitor Compensation Technique on Electrical Power Distribution System: A Review

The performance and quality of service of the electrical power distribution system are one of the utmost issues bothering the power system operator. This matter is important in order to fulfil load demands, which increase significantly. The progress in enhancing the efficiency of the system is plagued by high real power losses and poor voltage profile especially in the conventional radial distribution system. Hence, researchers have adopted a variety of different approaches to solve these problems in electrical power distribution system. One of the techniques employed is installation of shunt capacitor (using Capacitor Switching Compensation). Studies have shown that when Capacitor Switching Compensation is incorporated into the distribution system, the system losses can be minimized by reducing the reactive power component. Capacitor Switching Compensation is a widely used technique in electric power distribution system to improve the power system performance. This study therefore, reviews some of the applications of Capacitor Switching Compensation in electrical distribution system based on voltage and reactive power control. Thus, the usage of Capacitor Switching Compensation help to control the reactive power on a distribution system, maintenance of the flat voltage profile, improve the system efficiency and the stability of the electrical power distribution system. Keywords: Electrical Power Distribution System, Reactive Power, Voltage Control, Capacitor Switching Compensation, System Losses, Load Demand. DOI: 10.7176/ISDE/12-5-03 Publication date: August 31 st 2022

Additive manufacturing of inorganic components using a geopolymer and binder jetting

A large volume binder jetting printer was employed to fabricate prism-shaped geopolymer components. A two-parts system was used, comprising: 1) a highly alkaline solution, which was jetted on a powder bed containing aggregates (sand particles), and 2) a reactive solid component (pure metakaolin or metakaolin plus fast setting cement), present in the powder bed. In order to be able to generate appropriate, defect-free powder layers and suitably discharge the powders from the hopper feeding the layer forming system, a granulation approach was employed. The jetted alkaline solution effectively reacted with the metakaolin powders present in the granules, forming a geopolymer. Printed geopolymer parts, fabricated with the addition of 30 wt% metakaolin, possessed a compressive strength of ~20 MPa, even with ~30 vol% of residual porosity, and no significant variation in the compressive strength was observed after leaving the printed parts submerged in water for 1 week.

World Federation of Athletic Training and Therapy World Congress 2022 Peer-Reviewed Track Abstracts, May 5–7, 2022, Winnipeg, Manitoba, Canada

World Federation of Athletic Training and Therapy World Congress 2022 Peer-Reviewed Track Abstracts, May 5–7, 2022, Winnipeg, Manitoba, Canada

Biomass Behavior upon Fast Pyrolysis in Inert and in CO2-Rich Atmospheres: Role of Lignin, Hemicellulose and Cellulose Content

The present work focuses on the quality of char and primary tar produced from fast pyrolysis in N2 and CO2 of lignocellulosic biomasses: walnut shells (lignin-rich), straw (hemicellulose-rich) and pinewood (cellulose-rich). Heat treatments are carried out in a heated strip reactor (HSR) at 1573 and 2073 K for 3 s, with a heating rate of 104 K/s. The equipment allows for quenching the volatiles as soon as they are emitted. Chars are analyzed by thermogravimetric analysis in air. Results are compared with the products obtained from raw lignin, pure cellulose and pure hemicellulose. Cellulose and hemicellulose tars are dominated by anhydrous monosaccharides, which are scarce in straw tar and abundant in walnut shells tar. Polycyclic aromatic hydrocarbons PAHs are present in the primary products, in particular for walnut shells. The most reactive char is the one obtained from straw and the least reactive is the walnut shells char. Severe heat treatment and a CO2 atmosphere generate additional char components with higher and lower reactivity. The more reactive char component may arise from cross-linking reactions involving the monosaccharides (for which the result decreased in tar), whereas the less reactive component arises from thermal annealing and graphitization. Thus, the pyrolytic behavior of biomasses cannot be reconstructed with a mere addition of the lignin/cellulose/hemicellulose contribution, taking into account their content in the biomass.

Glucose boosts protein oxidation/nitration during simulated gastric digestion of myofibrillar proteins by creating a severe pro-oxidative environment

The severe pro-oxidative environment in the stomach promotes oxidation of dietary components. The pro-oxidant molecular mechanisms of reducing sugars on this environment are unknown. To investigate the mechanisms involved in protein oxidation and nitration during a simulated gastric digestion (porcine pepsin, 37 °C, 2 h) of meat proteins, these were exposed to several dietary reactive components namely myoglobin, glucose, glyoxal, myoglobin + glucose and myoglobin + glyoxal. Two versions of each experimental unit were prepared depending on the addition or absence of nitrite. Compared to control (only meat proteins), myoglobin + glucose showed the highest pro-oxidative and pro-nitrosative effect (p < 0.001), likely caused by an increase in ROS derived from the degradation of glucose during assay. Nitrite promoted the occurrence of protein nitration but decreased protein oxidation in myoglobin-added groups (p < 0.001) by, plausibly, stabilizing heme iron. These results indicate the relevant role of glyco-oxidation during digestion of red meat with other dietary components such as reducing sugars.

Influence of thermochemical activation of wood on the physicochemical properties of lignin

The wood matrix is a lignin–carbohydrate nanobiocomposite, thermodynamically quasi-equilibrium heterogeneous system of biopolymers. Changing its thermodynamic equilibrium due to directed chemical and (or) physical impacts opens up new approaches to the study of plant objects. Thermochemical activation, including treatments in sub- (steam explosion) and supercritical conditions (supercritical fluid extraction) having similar mechanisms of action, is one such method. The effect of steam explosion is determined by two components — chemical (the catalytic effect of formed acetic and formic acid) and physical (a sharp adiabatic expansion). The main components of supercritical treatment are increased temperature and pressure in the CO2 medium with cosolvents. The chemical component of this treatment is due to the addition of chemical reagents. Such treatments lead to a change in the thermodynamic state and capillary-porous structure of the lignin–carbohydrate matrix, an increase in its heterogeneity, and the yield of extracted lignin preparations. Lignin is the most reactive component of the wood matrix, and these processes result in changes in its functional nature and reaction properties. Thus, the lignin sample extracted after steam explosion had the greatest increase in the content of phenolic hydroxyl (by 39 rel.%) and carboxyl (by 57 rel.%) groups. Change in the functional composition of lignin leads to a change in its redox state, characterized by the oxidative potential and free energy of oxidation. It was shown that lignin after steam explosion had the highest oxidative potential and the lowest value of the oxidation energy, which indicated the greatest change in its reactivity in redox interactions.

Power Quality Management Strategy for High-Speed Railway Traction Power Supply System Based on MMC-RPC

This paper adopts the Modular Multilevel Converter Type Railway Power Conditioner (MMC-RPC) equipment to effectively manage the power quality of the high-speed railway traction power supply system including the reactive power and negative sequence component. Firstly, the single-phase model of the MMC was established to deduce the working characteristics of the MMC-RPC and its compensation principle for the traction power supply system with the v/v wiring transformer. Secondly, the adaptive VSG control strategy was adopted for the inverter of the MMC-RPC to provide dynamic inertial and damping support for the traction power supply system based on the virtual synchronous generator (VSG) control. Compared with the traditional double closed-loop (DCL) and VSG controls, it has better anti-disturbance and dynamic performance. The root locus analysis of control parameters based on a small signal model shows that VSG control can provide more stability margin. Furthermore, Differential Flatness Control (DFC) was used in the inner-loop controller to ensure the stable control of the inverter and the stability was verified by the Lyapunov stability analysis. For the rectifier of the MMC-RPC, a hierarchical three-level control strategy with system-level control, cluster-group voltage control, and inter-cluster voltage control for keeping the voltage balance was adopted. Finally, simulation results on the Matlab/Simulink platform verified the effectiveness and stability of the joint control applied in the MMC-RPC.

Preclinical Cold Atmospheric Plasma Cancer Treatment.

Simple SummaryCold atmospheric plasma (CAP) is generated in a rapid yet low-energy input streamer-discharge process at atmospheric pressure conditions. CAP is an ionized gas with a low ionization level and plenty of reactive species and radicals. These reactive components, and their near-room temperature nature, make CAP a powerful tool in medical applications, particularly cancer therapy. Here, we summarized the latest development and status of preclinical applications of CAP in cancer therapy, which may guide further clinical studies of CAP-based cancer therapy.CAP is an ionized gas generated under atmospheric pressure conditions. Due to its reactive chemical components and near-room temperature nature, CAP has promising applications in diverse branches of medicine, including microorganism sterilization, biofilm inactivation, wound healing, and cancer therapy. Currently, hundreds of in vitro demonstrations of CAP-based cancer treatments have been reported. However, preclinical studies, particularly in vivo studies, are pivotal to achieving a final clinical application. Here, we comprehensively introduced the research status of the preclinical usage of CAP in cancer treatment, by primarily focusing on the in vivo studies over the past decade. We summarized the primary research strategies in preclinical and clinical studies, including transdermal CAP treatment, post-surgical CAP treatment, CAP-activated solutions treatment, and sensitization treatment to drugs. Finally, the underlying mechanism was discussed based on the latest understanding.

Understanding Immune Responses to Viruses-Do Underlying Th1/Th2 Cell Biases Predict Outcome?

Emerging and re-emerging viral diseases have increased in number and geographical extent during the last decades. Examples include the current COVID-19 pandemic and the recent epidemics of the Chikungunya, Ebola, and Zika viruses. Immune responses to viruses have been well-characterised within the innate and adaptive immunity pathways with the outcome following viral infection predominantly attributed to properties of the virus and circumstances of the infection. Perhaps the belief that the immune system is often considered as a reactive component of host defence, springing into action when a threat is detected, has contributed to a poorer understanding of the inherent differences in an individual’s immune system in the absence of any pathology. In this review, we focus on how these host factors (age, ethnicity, underlying pathologies) may skew the T helper cell response, thereby influencing the outcome following viral infection but also whether we can use these inherent biases to predict patients at risk of a deviant response and apply strategies to avoid or overcome them.

Stable Formulations for the Lithium and Sodium Metal Interfaces in Alkali Metal-Oxygen Batteries

The high reactivity of both positive and negative interfacial regions in metal-oxygen (M-O2) batteries leads to a variety of parasitic degradation reactions that reduce reversibility on charge/discharge and can lead to rapid cell failure. To reversibly access the high theoretical specific energies these chemistries promise (3456 and 1602 Wh·kg-1 for Li-O2 and Na-O2, respectively), reducing charging overpotentials and the design of new electrode and electrolyte materials with improved stabilities are key targets. Considering the M|electrolyte interface, where decomposition reactions and dendrite formation generates severe safety concerns as well as reduced cycling stabilities, surface protection of the alkali metal anode by pre-treatment techniques or additive formulation has been among the more successful methodologies.1 In this work, we present a formulation strategy targeting enhanced cycling stabilities of the metal anode in M-O2 cells. Initially demonstrated in the Li-O2 chemistry, we report on an in-depth investigation into the electrochemical performance and the spectroscopic and diffusional properties of ternary ionic liquid (IL)-molecular solvent blend electrolytes.2 By introduction of the IL and exploring a wide formulation range (Figure 1a), we attain significant enhancements in the stability of practically-relevant electrolyte materials that otherwise fail rapidly at alkali metal anodes (Figure 1b), achieving the highest Coulombic efficiencies for Li plating/stripping in this solvent. The optimized formulations consequently displayed enhanced performances in Li-O2 full cells and ex situ characterization of Li surfaces also revealed the suppression of dendrite formation and important changes in the solid electrolyte interphase as a result of modulating solvent reactivity. Using Raman spectroscopy and diffusional analyses, we relate this closely to the local solvation environments involving the reactive solvent component in optimized formulations and, therefore, elucidate critical solvent/Li-salt ratios for improved stability.By understanding key shifts in Raman spectra relating to solvation effects in concentrated Li formulations, and how this modulates cycling performances, we further demonstrate the applicability of this relationship and formulation strategy to the Na-O2 battery chemistry. Therein, the Na metal interface is comparably more reactive and, therefore, presents greater stability challenges, with decomposition reactions in non-optimized formulations more rapidly causing plating and stripping at the anode to fail. However, we demonstrate the plating/stripping of Na (Figure 1c) and cycle lifetime in Na-O2 cells can be hugely improved by applying the above strategy and understandings of critical solvation interactions to equivalent formulations based on Na-salts. Y. Yu, G. Huang, J.-Z. Wang, K. Li, J.-L. Ma, and X.-B. Zhang, Adv. Mater. (Weinheim, Ger.), 32 (38), 2004157 (2020). A. R. Neale, R. Sharpe, S. R. Yeandel, C.-H. Yen, K. V. Luzyanin, P. Goddard, E. A. Petrucco, and L. J. Hardwick, Adv. Funct. Mater., 31 (27), 2010627 (2021). Figure 1. (a) Ternary plot highlighting the changes in stability of Li/Na metal anode cycling as a function of the studied formulation ranges and example voltage profiles of symmetric (b) Li|Li cells and (c) Na|Na cells with non-optimized (navy/purple) and optimized (orange) electrolyte formulations. Figure 1

Impedance spectroscopy method for testing moistened wheat crops

The authors presented the results of a study of the electrical and dielectric characteristics of wetted wheat grains by measuring their complex electrical resistance (impedance Z) in a wide frequency range (from 1 Hz to 100 MHz). The results of electrical impedance measurements of grains with surface or volumetric moisture content under different experimental conditions can provide useful information on the properties of the biological tissues of grain crops. These results can also be used to develop a new type of impedance sensor for testing grain quality and moisture content. The authors used well-dried wheat grains and grains saturated with moisture and saline as objects of research. A major problem in grain impedance measurements is the selection of a suitable electrode material to be placed on the end surfaces of the samples. The electrodes must ensure reliable contact with the grain and have a minimum transient resistance. The end surfaces of the pressed samples were reinforced with a protective dielectric ring to prevent transverse deformation. These contacts provided a transition resistance between 1-2 ohms. The authors have identified processes of accumulation of electric charges near the surface of metal electrodes at low frequencies and on internal grain structures, leading to an increase in the dielectric permittivity and dissipation factor. The behavior of the active and reactive components of the impedance at higher frequencies is determined by dielectric relaxation processes. The obtained impedance spectra were compared with the spectra of the most suitable equivalent electrical circuits. The radio components of the circuits provide information about the basic mechanisms of alternating electric current flow through the complex inhomogeneous structure of the grain. The authors found that moistening the grain with saline water enhances the process of accumulation of electric charges and affects the dispersion of the real and imaginary components of the impedance.

Improved Third-Harmonic Injection Two-Stage Matrix Converter Topology Based on Decomposition Control of Injection Current

In this article, an improved topology of the third-harmonic injection two-stage matrix converter (3TSMC) is proposed, which not only ensures that the input reactive power control capability is independent of the voltage transfer ratio (VTR) and the load conditions but also achieves high-quality mains current waveforms. To solve the problem of injection current control error in nonunit input power factor operation of 3TSMC, the third-harmonic injection current is decomposed into the active and reactive components, which are, respectively, controlled by the original injection current control bridge arm and an additional bridge arm named reactive power control bridge arm (RB). The maximum current of the inductor of RB is equal to the absolute value of the required input reactive current amplitude and will not increase with the increase of the VTR. The design criteria of the inductor of RB are discussed. To ensure the closed-loop stability under two injection directions, the controller of the injection current reactive component is designed. The effectiveness of the proposed topology and control strategy is verified by the experimental results.

Wireless Electric Vehicle Battery Charging System using PV Array

Abstract: The rapid emergence and evolution of wireless power transfer technology (WPT) have led to the development of various electrical vehicle applications. One of these is the exploitation of the power from a photovoltaic (PV) array. This paper proposes a system that can extract the power from the PV array and recharge the electric vehicle's battery using a Series-Series compensated network. The use of the resonance phenomenon in transferring power efficiently has been widely acknowledged. Due to the presence of various reactive components, a frequency analysis of a series-series compensator is performed. A proposed system for analyzing the frequency of a wireless power transmission system is simulated in MATLAB Simulink software. The results of the study and the simulation are presented in this paper, which helps in validating the proposed system. The proposed system can be used in various climatic conditions to recharge an electric vehicle. In addition, the proposed system can be developed with closed-loop controllers to improve its performance. Keywords: PV array, H-bridge inverter, Rectifier, wireless power transfer, series-series compensation, photovoltaic, Battery, Transmitter, Receiver.

Assessment of Alkali-Silica Reaction Potential in Aggregates from Iran and Australia Using Thin-Section Petrography and Expansion Testing.

The alkali–silica reaction can shorten concrete life due to expansive pressure build-up caused by reaction by-products, resulting in cracking. Understanding the role of the aggregate, as the main reactive component, is essential for understanding the underlying mechanisms of the alkali–silica reaction and thereby reducing, or even preventing, any potential damage. The present study aims to investigate the role of petrographic studies along with accelerated tests in predicting and determining the potential reactivity of aggregates, including granite, rhyodacite, limestone, and dolomite, with different geological characteristics in concrete. This study was performed under accelerated conditions in accordance with the ASTM C1260 and ASTM C1293 test methods. The extent of the alkali–silica reaction was assessed using a range of microanalysis techniques including optical microscopy, scanning electron microscopy, energy-dispersive X-ray analysis, and X-ray powder diffraction. The results showed that a calcium-rich aggregate with only a small quantity of siliceous component but with a higher porosity and water adsorption rate can lead to degradation due to the alkali–silica reaction, while dolomite aggregate, which is commonly considered a reactive aggregate, showed no considerable expansion during the conducted tests. The results also showed that rhyodacite samples, due to their glassy texture, the existence of strained quartz and quartz with undulatory extinction, as well as the presence of weathering minerals, have a higher alkali-reactivity potential than granite samples.

Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform

Wavelet theory has disentangled numerous complexities, including those pertinent to transient and steady-state responses of systems, when Laplace and Fourier transforms face insoluble obstacles. Reactive linear components (e.g. inductors and capacitors) are typically handled in the frequency plane. Non-linear (e.g. diodes) or time-variant components (e.g. switches) are conventionally simulated in the time plane (e.g. a diode via its I–V characteristic) and are considered open or short circuits in AC analyses (e.g. in circuit simulation software). Although translating circuits in an alternative plane, such as the Haar wavelet plane, significantly simplifies the process, a wide integration of wavelets into instruments and education is not yet realised; an underlying reason is the considerate complexity of applying wavelet theory to circuits and signals. The aim of this paper is to bridge this gap, providing a new user-friendly, Laplace-alike approach, utilising measurement-based models and the Haar wavelet. The Haar wavelet transform and a numerical method for the inverse Laplace transform which uses the Haar operational matrix are applied, to calculate the total current of a non-linear, time-variant system, that is the total current of a voltage source which powers a non-linear, time-variant load.