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Full-Text Articles in Engineering

Effect Of Alcohol-Gasoline Blends Optimization On Fuel Properties, Performance And Emissions Of A Si Engine Jan 2015

Effect Of Alcohol-Gasoline Blends Optimization On Fuel Properties, Performance And Emissions Of A Si Engine

Faculty of Engineering University of Malaya

This study, as an observation, put its utmost effort to emphasize on the development of various physicochemical properties using multiple alcohols (C-2 to C-6) at different ratios compared to that of the conventional ethanol gasoline blend. To optimize the properties of multiple alcohol-gasoline blends, properties of each fuel were measured first. An optimization tool of Microsoft Excel "Solver" was used for obtaining the optimum blend. Using optimizing tool, three optimum blend ratios were selected which possessed maximum heating value (MaxH), maximum research octane number (MaxR) and maximum petroleum displacement (MaxD). These blends were used for testing in a four cylinder …


Enhancement Of The Mechanical Properties Of Lightweight Oil Palm Shell Concrete Using Rice Husk Ash And Manufactured Sand Jan 2015

Enhancement Of The Mechanical Properties Of Lightweight Oil Palm Shell Concrete Using Rice Husk Ash And Manufactured Sand

Faculty of Engineering University of Malaya

This study explores the use of rice husk ash (RHA) and manufactured sand (M-sand) as replacements for cement and fine aggregate, respectively, in lightweight oil palm shell concrete (OPSC). In the first stage of this study, the effect of various cement replacement levels, with RHA (5%, 10%, 15%, and 20%) and 100% sand replacement with M-sand and quarry dust (QD), on the compressive strength of OPSC was investigated. The results showed that the highest compressive strength of OPSC of about 51.49 MPa was achieved with the use of 15% RHA and M-sand. In the second stage of the work, the …


Dumbbell Shaped Inline Mach-Zehnder Interferometer For Glucose Detection Jan 2015

Dumbbell Shaped Inline Mach-Zehnder Interferometer For Glucose Detection

Faculty of Engineering University of Malaya

A simple inline Mach Zehnder Interferometer (MZI) with a dumbbell-shaped structure is developed for measuring glucose concentration in distilled water. The MZI is fabricated using an arcing function of a fusion splicer. The sensor consists of two bulges separated by a tapered waist. The MZI generates a good reflected interference spectrum where the dip wavelength is red-shifted with the increase of glucose concentration. This is due to the increase of the surrounding refractive index, which reduces the phase difference between the core and cladding modes. As the glucose concentration increases from 0% to 12%, the dip wavelength increases from 1554.419 …


Eulerian-Lagrangian Analysis Of Solid Particle Distribution In An Internally Heated And Cooled Air-Filled Cavity Jan 2015

Eulerian-Lagrangian Analysis Of Solid Particle Distribution In An Internally Heated And Cooled Air-Filled Cavity

Faculty of Engineering University of Malaya

A parametric study has been conducted to investigate particle deposition on solid surfaces during free convection flow in an internally heated and cooled square cavity filled with air. The cavity walls are insulated while several pairs of heaters and coolers (HACs) inside the cavity lead to free convection flow. The HACs are assumed to be isothermal heat source and sinks with temperatures T-h and T-c (T-h > T-c). The problem is numerically investigated using the Eulerian-Lagrangian method. Two-dimensional Navier-Stokes and energy equations are solved using finite volume discretization method. Applying the Lagrangian approach, 5000 particles, distributed randomly in the enclosure, were …


Evaluation Of N-Butanol As An Oxygenated Additive To Improve Combustion-Emission-Performance Characteristics Of A Diesel Engine Fuelled With A Diesel-Calophyllum Inophyllum Biodiesel Blend Jan 2015

Evaluation Of N-Butanol As An Oxygenated Additive To Improve Combustion-Emission-Performance Characteristics Of A Diesel Engine Fuelled With A Diesel-Calophyllum Inophyllum Biodiesel Blend

Faculty of Engineering University of Malaya

Alexandrian laurel or Calophyllum inophyllum oil is considered as one of the most forthcoming non-edible biodiesel sources in recent years. In the present study, the relative improvement of an Alexandrian laurel biodiesel-diesel blend (AL20) was attempted with the addition of 5-10% n-butanol (by vol), which is often used as an oxygenated cold starting additive. Constant 80 Nm torque at variable engine speed, ranging from 1000 to 3000 rpm was chosen as the operating condition on a 4-cylinder turbocharged, water cooled diesel engine. Brake specific fuel consumption (BSFC), brake specific energy consumption (BSEC) and brake thermal efficiency (BTE) was measured to …


Functionalization Of Amorphous Carbon Nanotubes For Au Nanoparticles Hybridization Jan 2015

Functionalization Of Amorphous Carbon Nanotubes For Au Nanoparticles Hybridization

Faculty of Engineering University of Malaya

Our study focuses on selection of nitric acid, sulfuric acid, citric acid, and hydrochloric acid as the most suitable oxidation agent for a-CNT. Nitric acid functionalized a-CNT has the highest value of zeta potential -142.9 mV, followed by H2SO4, citric acids, and HCl functionalized samples of -60.3 mV, -15.9 mV, and -3.2 mV, respectively. High values of zeta potential represents surface charges, which refers to carboxyl groups present on tubes' bodies. At the same time, auric chloride (AuCl3) solution treatment was applied on citric acid, nitric acid, hydrochloric acid, and sulfuric acid treated a-CNT at the same condition. Nitric acid …


Four-Wave-Mixing-Assisted Brillouin Fiber Laser With Double-Brillouin-Frequency Spacing Jan 2015

Four-Wave-Mixing-Assisted Brillouin Fiber Laser With Double-Brillouin-Frequency Spacing

Faculty of Engineering University of Malaya

The generation of multiwavelength Brillouin fiber laser assisted by four wave mixing has been demonstrated. A maximum of 18 channels of laser Stokes lines are generated at a Brillouin Pump (BP) of 190 mW (similar to 22.5 dBm). The multiple peaks have a wavelength spacing of 0.176 nm (similar to 20 GHz). A tunable optical bandpass filter is incorporated to the design to suppress up to 6 dB of the noise floor hump exhibited at the multiwavelength laser spectrum while limiting the laser peaks attenuation thereby providing a much cleaner and better OSNR. (C) 2014 Elsevier Inc. All rights reserved. …


Impact Analysis On Distance Variation Between Patch Antenna And Metamaterial Jan 2015

Impact Analysis On Distance Variation Between Patch Antenna And Metamaterial

Faculty of Engineering University of Malaya

Metamaterials are artificially engineered material having negative permittivity and permeability. Due to their negative constitutive parameters, metamaterials are capable of focusing incident electromagnetic energy called as beam focusing property. We have made use of beam focusing property of metamaterial to enhance antenna far-field gain. We have also conducted experimental study by varying the distance between patch antenna and metamaterial array to determine optimum distance. The distance is varied in seven steps of 35 mm. The far-field gain of antenna is increased by 4 dB when metamaterial is placed at 95 mm. The beamwidth of antenna reduces when loaded with metamaterial …


Improved Friction And Wear Performance Of Micro Dimpled Ceramic-On-Ceramic Interface For Hip Joint Arthroplasty Jan 2015

Improved Friction And Wear Performance Of Micro Dimpled Ceramic-On-Ceramic Interface For Hip Joint Arthroplasty

Faculty of Engineering University of Malaya

The purpose of this study is to investigate the tribological effect of micro-dimpled surface textures for application in ceramic-on-ceramic hip prostheses. A rectangular array of circular dimples was selected as the texture pattern. A CNC micro drilling machine was used to fabricate these dimples on a flat ceramic substrate. Tribology tests were performed by using a pin-on-disk method with selected hertzian contact pressures and speeds based on normal gait of a hip joint, and results compared with non-dimpled surface. A dimpled surface with large dimple diameters and a high dimple density (phi 400 mu m and density 15%) showed significant …


Interface Stress In Socket/Residual Limb With Transtibial Prosthetic Suspension Systems During Locomotion On Slopes And Stairs Jan 2015

Interface Stress In Socket/Residual Limb With Transtibial Prosthetic Suspension Systems During Locomotion On Slopes And Stairs

Faculty of Engineering University of Malaya

OBJECTIVE: This study aimed to compare the effects of different suspension methods on the interface stress inside the prosthetic sockets of transtibial amputees when negotiating ramps and stairs. DESIGN: Three transtibial prostheses, with a pin/lock system, a Seal-In system, and a magnetic suspension system, were created for the participants in a prospective study. Interface stress was measured as the peak pressure by using the F-socket transducers during stairs and ramp negotiation. RESULTS: Twelve individuals with transtibial amputation managed to complete the experiments. During the stair ascent and descent, the greatest peak pressure was observed in the prosthesis with the Seal-In …


An Improved Particle Swarm Optimization Based Maximum Power Point Tracking Strategy With Variable Sampling Time Jan 2015

An Improved Particle Swarm Optimization Based Maximum Power Point Tracking Strategy With Variable Sampling Time

Faculty of Engineering University of Malaya

This paper presents an improved maximum power point tracking (MPPT) strategy for photovoltaic (PV) systems based on particle swarm optimization (PSO). The capability of the PSO algorithm to cope with partially shaded conditions (PSCs) is the primary motivation of this research. Unlike conventional PSO-based MPPT systems, a variable sampling time strategy (VSTS) based on the investigation of the dynamic behavior of converter current is deployed to increase system tracking time. The performance of the proposed system is evaluated using MATLAB simulation and experimentation, in which a digital signal controller is used to implement the proposed algorithm on a real boost …


Investigating The Surface Tribology Of Roller-Burnished Polymer Using The Fuzzy Rule-Based Approach Jan 2015

Investigating The Surface Tribology Of Roller-Burnished Polymer Using The Fuzzy Rule-Based Approach

Faculty of Engineering University of Malaya

Burnishing is specified as the plastic deformation cold working process applied as surface treatment and smoothing following machining to obtain a superior surface roughness finish. The present experimental study was carried out on roller-burnished polyurethane using a roller burnishing tool. An analysis was done to investigate the effect of burnishing depth, speed, feed rate, and roller width on the surface roughness of the polymer workpiece. Roughness (R-a) prediction was achieved with a fuzzy rule-based system. The results indicate 95% accuracy between the fuzzy predicted roughness values and experimental results. Link to Full-Text Articles : www.tandfonline.com/doi/abs/10.1080/10402004.2014.962205


Mode-Locked Thulium Ytterbium Co-Doped Fiber Laser With Graphene Oxide Paper Saturable Absorber Jan 2015

Mode-Locked Thulium Ytterbium Co-Doped Fiber Laser With Graphene Oxide Paper Saturable Absorber

Faculty of Engineering University of Malaya

A mode-locked thulium ytterbium co-doped fiber laser (TYDFL) is proposed and demonstrated by using a commercial graphene oxide (GO) paper as saturable absorber (SA). The GO paper is sandwiched between two fiber ferrules and incorporates a ring laser cavity to generate soliton pulse train operating at 1942.0 nm at a threshold multimode pump power as low as 1.8 W. The mode-locked TYDFL has a repetition rate of 22.32 MHz and the calculated pulse width of 1.1 ns. Even though the SA has a low damage threshold, the easy fabrication of GO paper should promote its potential application in ultrafast photonics. …


Mechanistic Analysis Of Cavitation Assisted Transesterification On Biodiesel Characteristics Jan 2015

Mechanistic Analysis Of Cavitation Assisted Transesterification On Biodiesel Characteristics

Faculty of Engineering University of Malaya

The influence of sonoluminescence transesterification on biodiesel physicochemical properties was investigated and the results were compared to those of traditional mechanical stirring. This study was conducted to identify the mechanistic features of ultra sonication by coupling statistical analysis of the experiments into the simulation of cavitation bubble. Different combinations of operational variables were employed for alkali-catalysis transesterification of palm oil. The experimental results showed that transesterification with ultrasound irradiation could change the biodiesel density by about 0.3 kg/m(3); the viscosity by 0.12 mm(2)/s; the pour point by about 1-2 degrees C and the flash point by 5 degrees C compared …


Imposed Weighting Factor Optimization Method For Torque Ripple Reduction Of Im Fed By Indirect Matrix Converter With Predictive Control Algorithm Jan 2015

Imposed Weighting Factor Optimization Method For Torque Ripple Reduction Of Im Fed By Indirect Matrix Converter With Predictive Control Algorithm

Faculty of Engineering University of Malaya

This paper proposes a weighting factor optimization method in predictive control algorithm for torque ripple reduction in an induction motor fed by an indirect matrix converter (IMC). In this paper, the torque ripple behavior is analyzed to validate the proposed weighting factor optimization method in the predictive control platform and shows the effectiveness of the system. Therefore, an optimization method is adopted here to calculate the optimum weighting factor corresponds to minimum torque ripple and is compared with the results of conventional weighting factor based predictive control algorithm. The predictive control algorithm selects the optimum switching state that minimizes a …


Modified Robust External Force Control With Disturbance Rejection With Application To Piezoelectric Actuators Jan 2015

Modified Robust External Force Control With Disturbance Rejection With Application To Piezoelectric Actuators

Faculty of Engineering University of Malaya

In micromanipulation applications, controlling the force exerted on the object is of great importance. In such cases, any uncontrolled forces may damage the object or cause system failure. However, the presence of disturbances such as impedance uncertainties and hysteresis can strongly degrade force control performance and even lead to instability. Therefore, accurate force control when internal and external disturbances occur is a significant challenge. Conventional control methods usually have a number of restrictive conditions especially on the disturbance bounds. To rectify those issues, a modified robust disturbance rejection-based force control approach is proposed in this paper. For this purpose, an …


Model Predictive Control Of Bidirectional Ac-Dc Converter For Energy Storage System Jan 2015

Model Predictive Control Of Bidirectional Ac-Dc Converter For Energy Storage System

Faculty of Engineering University of Malaya

Energy storage system has been widely applied in power distribution sectors as well as in renewable energy sources to ensure uninterruptible power supply. This paper presents a model predictive algorithm to control a bidirectional AC-DC converter, which is used in an energy storage system for power transferring between the three-phase AC voltage supply and energy storage devices. This model predictive control (MPC) algorithm utilizes the discrete behavior of the converter and predicts the future variables of the system by defining cost functions for all possible switching states. Subsequently, the switching state that corresponds to the minimum cost function is selected …


Modulation Techniques To Reduce Leakage Current In Three-Phase Transformerless H7 Photovoltaic Inverter Jan 2015

Modulation Techniques To Reduce Leakage Current In Three-Phase Transformerless H7 Photovoltaic Inverter

Faculty of Engineering University of Malaya

Recently, reduced common-mode voltage (CMV) pulsewidth modulation (RCMV-PWM) methods have been proposed to reduce the leakage current in three-phase transformerless photovoltaic (PV) systems. However, most of these studies only focus on leakage current elimination and neglect the overall performance of the PV systems on issues such as cost, voltage linearity, dc-link current ripples, and harmonic distortion. In this paper, a three-phase transformerless inverter, adapted from the single-phase H5 topology, is investigated. Since the H5 topology has been conventionally developed for a single-phase system, its adaptation to the three-phase system requires the development of corresponding three-phase modulation techniques. Hence, modulation techniques …


Nitrogen-Doped Graphene-Silver Nanodendrites For The Non-Enzymatic Detection Of Hydrogen Peroxide Jan 2015

Nitrogen-Doped Graphene-Silver Nanodendrites For The Non-Enzymatic Detection Of Hydrogen Peroxide

Faculty of Engineering University of Malaya

An organic-metal hybrid film based on nitrogen-doped graphene-silver nanodendrites (Ag-NG) was fabricated on an indium tin oxide (ITO) electrode using a simple electrophoretic and electrochemical sequential deposition approach. The microwave-assisted method was utilized for the synthesis of nitrogen-doped graphene. This method involves a three-step process consisting of graphite oxidation, exfoliation, and finally chemical reduction with the use of hydrazine as the reducing agent, which leads to the simultaneous reduction of graphene oxide and production of nitrogen-doped graphene. The morphology and structure of the as-fabricated electrode were determined by X-ray diffraction, field emission electron microscopy and transmission electron microscopy. The as-prepared …


A New Wide-Band Double-Negative Metamaterial For C- And S-Band Applications Jan 2015

A New Wide-Band Double-Negative Metamaterial For C- And S-Band Applications

Faculty of Engineering University of Malaya

A new design and analysis of a wide-band double-negative metamaterial, considering a frequency range of 0.5 to 7 GHz, is presented in this paper. Four different unit cells with varying design parameters are analyzed to evaluate the effects of the unit-cell size on the resonance frequencies of the metamaterial. Moreover, open and interconnected 2 x 2 array structures of unit cells are analyzed. The finite-difference time-domain (FDTD) method, based on the Computer Simulation Technology (CST) Microwave Studio, is utilized in the majority of this investigation. The experimental portion of the study was performed in a semi-anechoic chamber. Good agreement is …


Nitrogen-Doped Graphene-Silver Nanodendrites For The Non-Enzymatic Detection Of Hydrogen Peroxide Jan 2015

Nitrogen-Doped Graphene-Silver Nanodendrites For The Non-Enzymatic Detection Of Hydrogen Peroxide

Faculty of Engineering University of Malaya

An organic-metal hybrid film based on nitrogen-doped graphene-silver nanodendrites (Ag-NG) was fabricated on an indium tin oxide (ITO) electrode using a simple electrophoretic and electrochemical sequential deposition approach. The microwave-assisted method was utilized for the synthesis of nitrogen-doped graphene. This method involves a three-step process consisting of graphite oxidation, exfoliation, and finally chemical reduction with the use of hydrazine as the reducing agent, which leads to the simultaneous reduction of graphene oxide and production of nitrogen-doped graphene. The morphology and structure of the as-fabricated electrode were determined by X-ray diffraction, field emission electron microscopy and transmission electron microscopy. The as-prepared …


Optimizing Cutting Parameters In Inclined End Milling For Minimum Surface Residual Stress - Taguchi Approach Jan 2015

Optimizing Cutting Parameters In Inclined End Milling For Minimum Surface Residual Stress - Taguchi Approach

Faculty of Engineering University of Malaya

End milling is an important and common machining operation because of its versatility and capability to produce various profiles and curved surfaces. Inclined end milling possesses the capability to translate in all 3 axes but can perform the cutting operation in only 2 of the 3 axes at a time. This research work focuses on investigating the effect of machined surface inclination angle, axial depth of cut, spindle speed and feed rate for better surface integrity in inclined end milling process utilizing titanium coated carbide ball end mill. An optimization method known as Taguchi optimization was used in order to …


Potential Application Of Pure Silica Optical Flat Fibers For Radiation Therapy Dosimetry Jan 2015

Potential Application Of Pure Silica Optical Flat Fibers For Radiation Therapy Dosimetry

Faculty of Engineering University of Malaya

Pure silica optical flat fibers (FF) have been proposed as the basis for a novel radiation sensor by the measurement of the thermoluminescence (TL) produced. In this paper the 17, performance of the FFs were studied. Using a linear accelerator (LINAC) delivering doses in the range 0.2-10.0 Gy, the TL dosimetric glow curves of the FFs were studied with respect to 6 MeV electron and 6 MV photon beams. When exposed to 6 MeV electron irradiation, the pure silica FFs displayed a supralinear response starting from 2 Gy up to 10.0 Gy. While for 6 MV photon irradiation, the FFs …


Practical Performance Analysis Of An Industrial-Scale Ultrafiltration Membrane Water Treatment Plant Jan 2015

Practical Performance Analysis Of An Industrial-Scale Ultrafiltration Membrane Water Treatment Plant

Faculty of Engineering University of Malaya

Common design and operational issues to evaluate the performance of an ultrafiltration (UF) membrane water treatment plant are highlighted with a case study on an industrial-scale drinking water treatment plant located in Malaysia. This treatment plant has been in operation since February 2013 using dead-end polyethersulfone UF membrane filtration system to produce up to 14 million litres a day of drinking water to a small township. Literature solutions are compared with the practised solutions and elucidated with the case study. Gaps between literature solutions which are mainly based on lab-scale research and industry practices are identified. Reducing this gap will …


Q-Switched Erbium Doped Fiber Laser Based On Single And Multiple Walled Carbon Nanotubes Embedded In Polyethylene Oxide Film As Saturable Absorber Jan 2015

Q-Switched Erbium Doped Fiber Laser Based On Single And Multiple Walled Carbon Nanotubes Embedded In Polyethylene Oxide Film As Saturable Absorber

Faculty of Engineering University of Malaya

A passive, stable and low cost Q-switched Erbium-doped fiber laser (EDFL) is demonstrated using both single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), which are embedded in polyethylene oxide (PEO) film as a saturable absorber (SA). The film is sandwiched between two FC/PC fiber connectors and integrated into the laser cavity for Q-switching pulse generation operating at wavelength of 1533.6 am. With SWCNTs, the laser produces a stable pulse train with repetition rate and pulse width ranging from 9.52 to 33.33 kHz and 16.8 to 8.0 is while varying the 980 am pump power from 48.5 mW to 100.4 …


Properties Of Zn-Bi Composite Coatings Prepared By Ionic Co-Discharge Deposition Jan 2015

Properties Of Zn-Bi Composite Coatings Prepared By Ionic Co-Discharge Deposition

Faculty of Engineering University of Malaya

Zn-Bi composite was synthesized by ionic co-discharge deposition and its properties were investigated. The results show that the Zn-Bi composite with the incorporation of Bi has a finer grain size than the pure Zn coating and improves the mechanical properties. The microhardness is increased by approximately two times simply by adding a small amount of Bi electrolyte into a Zn bath solution. A lower volume loss of the Zn-Bi composite coating compared with the pure Zn coating also indicates that the Zn-Bi coating has a better wear resistance. Link to Full-Text Articles : http://www.sciencedirect.com/science/article/pii/S1003632615635968


A Review Of Safety, Health And Environmental (She) Issues Of Solar Energy System Jan 2015

A Review Of Safety, Health And Environmental (She) Issues Of Solar Energy System

Faculty of Engineering University of Malaya

Solar energy is one of the cleanest forms of energy sources and considered as a green source of energy. Solar energy benefit ranges from low carbon emission, no fossil fuel requirement, long term solar resources, less payback time and other. However like other power generation sources, solar energy has also some Safety, Health and Environmental (SHE) concerns. This paper presents the overview of solar energy technologies and addresses the SHE impact of solar energy technologies to the sustainability of human activities. This paper will also recommend the possible ways to reduce the effect of potential hazards of widespread use of …


Review Of Improvements In Wire Electrode Properties For Longer Working Time And Utilization In Wire Edm Machining Jan 2015

Review Of Improvements In Wire Electrode Properties For Longer Working Time And Utilization In Wire Edm Machining

Faculty of Engineering University of Malaya

Wire electrical discharge machining (WEDM) is an important technology, which demands high-speed cutting and high-precision machining to realize productivity and improved accuracy for manufacturing hard materials. WEDM has experienced explosive growth and complexity of equipment as well as rising demand for the basic process tool (the wire electrode). Greater taper angles, thicker workpieces, automatic wire threading, and long periods of unattended operation make the selection of the ideal wire a much more critical basis for achieving successful operation. This paper focuses on the evolution of EDM wire electrode technologies from using copper to the widely employed brass wire electrodes and …


Stability And Performance Investigations Of Model Predictive Controlled Active-Front-End (Afe) Rectifiers For Energy Storage Systems Jan 2015

Stability And Performance Investigations Of Model Predictive Controlled Active-Front-End (Afe) Rectifiers For Energy Storage Systems

Faculty of Engineering University of Malaya

This paper investigates the stability and performance of model predictive controlled active-front-end (AFE) rectifiers for energy storage systems, which has been increasingly applied in power distribution sectors and in renewable energy sources to ensure an uninten-uptable power supply. The model predictive control (MPC) algorithm utilizes the discrete behavior of power converters to determine appropriate switching states by defining a cost function. The stability of the MPC algorithm is analyzed with the discrete z-domain response and the nonlinear simulation model. The results confirms that the control method of the active-front-end (AFE) rectifier is stable, and that is operates with an infmite …


Semi-Z-Source Inverter Topology For Grid-Connected Photovoltaic System Jan 2015

Semi-Z-Source Inverter Topology For Grid-Connected Photovoltaic System

Faculty of Engineering University of Malaya

Transformer-less inverters are necessary parts for grid-connected renewable energy resources. Owing to its cost effectiveness, downsize and less weight, great attention has been paid to these inverters development. With these aforementioned advantages, these inverters have limitations like the flow of leakage current through photovoltaic arrays, high total harmonic distortion (THD) at inverter's output and DC current injection to the grid. This study presents coupled inductor-based single-phase transformer-less semi-Z-source inverter topology to lessen those limitations. Since the DC input and AC output voltage share a common ground, the presented inverter system is categorised under doubly grounded topologies. For the purpose of …