Search results for: Photovoltaic processes control

Authors: Hiroaki Sumi, Kiichiro Hayashi

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Now, the use of renewable energy power generation has been advanced. In this paper, we compared the usable amount of resource for photovoltaic power generation which was estimated using the NEDO formula and the expansion support policy of photovoltaic power generation which was researched using Internet in the municipality level in Hokkaido and Aichi Prefecture, Japan. This paper will contribute to grasp the current situation especially about the policy. As a result, there were municipalities which seemed to be no consideration of fitting the amount of resources. We think it would need to consider the suitability between the resources and policies.

Keywords: Photovoltaic power generation, expansion support policy, amount of resources, Japan.

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Authors: J. Levodo, A. Ford, I. Chaer

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Africa enjoys some of the best solar radiation levels in the world averaging between 4-6 kWh/m2/day for most of the year and the global economic and political conditions that tend to make African countries more dependent on their own energy resources have caused growing interest in renewable energy based technologies. However to-date, implementation of modern Energy Technologies in Africa is still very low especially the use of solar conversion technologies. This paper presents literature review and analysis relating to the techno-economic feasibility of solar photovoltaic power generation in Africa. The literature is basically classified into the following four main categories. Techno-economic feasibility of solar photovoltaic power generation, design methods, performance evaluations of various systems and policy of potential future of technological development of photovoltaic (PV) in Africa by exploring the impact of alternative policy instruments and technology cost reductions on the financial viability of investing solar photovoltaic in Africa.

Keywords: Africa Solar Potential, Policy, Photovoltaic, Technologies.

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Authors: Engy A. Mohamed, Yasser G. Hegazy

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This paper presents a novel algorithm for modeling photovoltaic based distributed generators for the purpose of optimal planning of distribution networks. The proposed algorithm utilizes sequential Monte Carlo method in order to accurately consider the stochastic nature of photovoltaic based distributed generators. The proposed algorithm is implemented in MATLAB environment and the results obtained are presented and discussed.

Keywords: Comulative distribution function, distributed generation, Monte Carlo.

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Authors: Horng-Yuan Wu, Chin-Yuan Hsu, Tsair-Fwu Lee

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A novel three-phase active power filter (APF) circuit with photovoltaic (PV) system to improve the quality of service and to reduce the capacity of energy storage capacitor is presented. The energy balance concept and sampling technique were used to simplify the calculation algorithm for the required utility source current and to control the voltage of the energy storage capacitor. The feasibility was verified by using the Pspice simulations and experiments. When the APF mode was used during non-operational period, not only the utilization rate, power factor and power quality could be improved, but also the capacity of energy storage capacitor could sparing. As the results, the advantages of the APF circuit are simplicity of control circuits, low cost, and good transient response.

Keywords: active power filter, sampling, energy-storagecapacitor, harmonic current, energy balance.

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Authors: Sarah Abdourraziq, Rachid El Bachtiri

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The solar power source for pumping water is one of the most promising areas in photovoltaic applications. The implementation of these systems allows to protect the environment and reduce the CO₂ gas emission compared to systems trained by diesel generators. This paper presents a comparative study between the photovoltaic pumping system driven by DC motor, and AC motor to define the optimum design of this application. The studied system consists of PV array, DC-DC Boost Converter, inverter, motor-pump set and storage tank. The comparison was carried out to define the characteristics and the performance of each system. Each subsystem is modeled in order to simulate the whole system in MATLAB/ Simulink. The results show the efficiency of the proposed technique.

Keywords: Photovoltaic water pumping system, DC motor-pump, AC motor-pump, DC-DC boost converter.

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Authors: Mustafa A. Al-Refai

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This paper presents the optimal design and simulation of a grid-connected Photovoltaic (PV) system to supply electric power to meet the energy demand by Electrical Department in University of Tripoli Libya. Solar radiation is the key factor determining electricity produced by photovoltaic (PV) systems. This paper is designed to develop a novel method to calculate the solar photovoltaic generation capacity on the basis of Mean Global Solar Radiation data available for Tripoli Libya and finally develop a system design of possible plant capacity for the available roof area. MatLab/Simulink Programming tools and monthly average solar radiation data are used for this design and simulation. The specifications of equipments are provided based on the availability of the components in the market. Simulation results and analyses are presented to validate the proposed system configuration.

Keywords: Photovoltaic (PV), solar energy, solar irradiation, Simulink.

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Authors: Ivanka Valova

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This paper is aimed at using a multi-agent approach to monitor and diagnose a biotechnological system in order to validate certain control actions depending on the process development and the operating conditions. A multi-agent system is defined as a network of interacting software modules that collectively solve complex tasks. Remote monitoring and control of biotechnological processes is a necessity when automated and reliable systems operating with no interruption of certain activities are required. The advantage of our approach is in its flexibility, modularity and the possibility of improving by acquiring functionalities through the integration of artificial intelligence.

Keywords: Multi-agent approach, artificial intelligence, biotechnological processes, anaerobic biodegradation.

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Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri

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In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, Gaussian processes, robot control learning, tracked vehicles.

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Authors: P. Selvam, S. Senthil Kumar

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Maximum Power Point Tracking (MPPT) has played a vital role to enhance the efficiency of solar photovoltaic (PV) power generation under varying atmospheric temperature and solar irradiation. However, it is hard to track the maximum power point using conventional linear controllers due to the natural inheritance of nonlinear I-V and P-V characteristics of solar PV systems. Fuzzy Logic Controller (FLC) is suitable for nonlinear system control applications and eliminating oscillations, circuit complexities present in the conventional perturb and observation and incremental conductance methods respectively. Hence, in this paper, FLC is proposed for tracking exact MPPT of solar PV power generation system under varying solar irradiation conditions. The effectiveness of the proposed FLC-based MPPT controller is validated through simulation and analysis using MATLAB/Simulink.

Keywords: Fuzzy logic controller, maximum power point tracking, photovoltaic.

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Authors: M.Paroncini, F.Corvaro, G.Nardini, S.Pistolesi

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The development of renewable energies - particularly energy from wind, water, solar power and biomass - is a central aim of the European Commission's energy policy. There are several reasons for this choice: renewable energies are sustainable, nonpolluting, widely available and clean. Increasing the share of renewable energy in the energy balance enhances sustainability. It also helps to improve the security of energy supply by reducing the Community's growing dependence on imported energy sources.In this paper it was studied the possibility to realize three photovoltaic systems in the Italian Natural Park “Gola della Rossa e di Frasassi". The first photovoltaic system is a grid-connected system for Services and Documentation Center of Castelletta with a nominal power of about 6 kWp. The second photovoltaic system is a grid-connected integrated system on the ticket office-s roof with a nominal power of about 4 kWp. The third project is set up by five grid-connected systems integrated on the roofs of the bungalows in Natural Park-s tourist camping with a nominal power of about 10 kWp. The electricity which is generated by all these plants is purchased according to the Italian program called “Conto Energia". Economical analysis and the amount of the avoided CO2 emissions are elaborated for these photovoltaic systems.

Keywords: CO2 emissions, conto energia, photovoltaic systems.

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Authors: Arvind Kumar, Manoj Kumar, Dattatraya H. Nagaraj, Amanpreet Singh, Jayanthi Prattapati

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The purpose of this paper is to study and compare two maximum power point tracking (MPPT) algorithms in a photovoltaic simulation system and also show a simulation study of maximum power point tracking (MPPT) for photovoltaic systems using perturb and observe algorithm and Incremental conductance algorithm. Maximum power point tracking (MPPT) plays an important role in photovoltaic systems because it maximize the power output from a PV system for a given set of conditions, and therefore maximize the array efficiency and minimize the overall system cost. Since the maximum power point (MPP) varies, based on the irradiation and cell temperature, appropriate algorithms must be utilized to track the (MPP) and maintain the operation of the system in it. MATLAB/Simulink is used to establish a model of photovoltaic system with (MPPT) function. This system is developed by combining the models established of solar PV module and DC-DC Boost converter. The system is simulated under different climate conditions. Simulation results show that the photovoltaic simulation system can track the maximum power point accurately.

Keywords: Incremental conductance Algorithm, Perturb and Observe Algorithm, Photovoltaic System and Simulation Results.

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Authors: Florian Mach, Eric Hund, Malte Stonis

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The dismantling of disused industrial facilities such as nuclear power plants or refineries is an enormous challenge for the planning and control of the logistic processes. Existing control models do not meet the requirements for a proper dismantling of industrial plants. Therefore, the paper presents an approach for the control of dismantling and post-processing processes (e.g. decontamination) in plant decommissioning. In contrast to existing approaches, the dismantling sequence and depth are selected depending on the capacity utilization of required post-processing processes by also considering individual characteristics of respective dismantling tasks (e.g. decontamination success rate, uncertainties regarding the process times). The results can be used in the dismantling of industrial plants (e.g. nuclear power plants) to reduce dismantling time and costs by avoiding bottlenecks such as capacity constraints.

Keywords: Dismantling management, logistics planning and control models, nuclear power plant dismantling, reverse logistics.

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Authors: Thorben Kuprat, Julian Becker, Jonas Mayer, Peter Nyhuis

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For years now, it has been recognized that logistic performance capability contributes enormously to a production enterprise’s competitiveness and as such is a critical control lever. In doing so, the orientation on customer wishes (e.g. delivery dates) represents a key parameter not only in the value-adding production but also in product regeneration. Since production and regeneration processes have different characteristics, production planning and control measures cannot be directly transferred to regeneration processes. As part of a special research project, the Institute of Production Systems and Logistics Hannover is focused on increasing the logistic performance capability of regeneration processes for complex capital goods. The aim is to ensure logistic targets are met by implementing a model specifically designed to align the capacities and load in regeneration processes.

Keywords: Capacity planning, complex capital goods, logistic performance, regeneration process.

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Authors: N. Drir, L. Barazane, M. Loudini

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It is well known that photovoltaic (PV) cells are an attractive source of energy. Abundant and ubiquitous, this source is one of the important renewable energy sources that have been increasing worldwide year by year. However, in the V-P characteristic curve of GPV, there is a maximum point called the maximum power point (MPP) which depends closely on the variation of atmospheric conditions and the rotation of the earth. In fact, such characteristics outputs are nonlinear and change with variations of temperature and irradiation, so we need a controller named maximum power point tracker MPPT to extract the maximum power at the terminals of photovoltaic generator. In this context, the authors propose here to study the modeling of a photovoltaic system and to find an appropriate method for optimizing the operation of the PV generator using two intelligent controllers respectively to track this point. The first one is based on artificial neural networks and the second on fuzzy logic. After the conception and the integration of each controller in the global process, the performances are examined and compared through a series of simulation. These two controller have prove by their results good tracking of the MPPT compare with the other method which are proposed up to now.

Keywords: Maximum power point tracking, neural networks, photovoltaic, P&O.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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This paper presents a model predictive control (MPC) of a utility interactive three phase inverter (TPI) for a photovoltaic (PV) system at commercial level. The proposed model uses phase locked loop (PLL) to synchronize the TPI with the power electric grid (PEG) and performs MPC control in a dq reference frame. TPI model consists of a boost converter (BC), maximum power point tracking (MPPT) control, and a three-leg voltage source inverter (VSI). The operational model of VSI is used to synthesize the sinusoidal current and track the reference. The model is validated using a 35.7 kW PV system in Matlab/Simulink. Implementation results show simplicity and accuracy, as well as reliability of the model.

Keywords: Model predictive control, three phase voltage source inverter, PV system, Matlab/Simulink.

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Authors: E. Sok, Y. Zhuo, S. Wang

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A hybrid Photovoltaic/Thermal (PV/T) solar system integrates photovoltaic and solar thermal technologies into one single solar energy device, with dual generation of electricity and heat energy. The aim of the present study is to evaluate the potential for introduction of the PV/T technology into Northern China. For this purpose, outdoor experiments were conducted on a prototype of a PV/T water-heating system. The annual thermal and electrical performances were investigated under the climatic conditions of Beijing. An economic analysis of the system was then carried out, followed by a sensitivity study. The analysis revealed that the hybrid system is not economically attractive with the current market and energy prices. However, considering the continuous commitment of the Chinese government towards policy development in the renewable energy sector, and technological improvements like the increasing cost-effectiveness of PV cells, PV/Thermal technology may become economically viable in the near future.

Keywords: Hybrid Photovoltaic/Thermal (PV/T), Solar energy, Economic analysis

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Authors: Fadia M. A. Ghali

Abstract:

The problem of wastewater treatment in Egypt is a two-fold problem; the first part concerning the existing rural areas, the second one dealing with new industrial/domestic areas. In Egypt several agricultural projects have been initiated by the government and the private sector as well, in order to change its infrastructure. As a reliable energy source, photovoltaic pumping systems have contributed to supply water for local rural communities worldwide; they can also be implemented to solve the problem “wastewater environment pollution". The solution of this problem can be categorised as recycle process. In addition, because of regional conditions past technologies are being reexamined to select a smallscale treatment system requiring low construction and maintenance costs. This paper gives the design guidelines of a Photovoltaic Small- Scale Wastewater Treatment Plant (PVSSWTP) based on technologies that can be transferred.

Keywords: Renewable energy sources, Photovoltaic, small-scale projects, wastewater treatment.

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Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva

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In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.

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Authors: Arvind Kumar, Manoj Kumar, Dattatraya H. Nagaraj, Amanpreet Singh, Jayanthi Prattapati

Abstract:

In recent years, the use of renewable energy resources instead of pollutant fossil fuels and other forms has increased. Photovoltaic generation is becoming increasingly important as a renewable resource since it does not cause in fuel costs, pollution, maintenance, and emitting noise compared with other alternatives used in power applications. In this paper, Perturb and Observe and Incremental Conductance methods are used to improve energy conversion efficiency under different environmental conditions. PI controllers are used to control easily DC-link voltage, active and reactive currents. The whole system is simulated under standard climatic conditions (1000 W/m2, 250C) in MATLAB and the irradiance is varied from 1000 W/m2 to 300 W/m2. The use of PI controller makes it easy to directly control the power of the grid connected PV system. Finally the validity of the system will be verified through the simulations in MATLAB/Simulink environment.

Keywords: Incremental conductance algorithm, modeling of PV panel, perturb and observe algorithm, photovoltaic system and simulation results.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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This paper presents modeling of an Alternating Current (AC) Photovoltaic (PV) module using Matlab/Simulink. The proposed AC-PV module model is simple, realistic, and application oriented. The model is derived on module level as compared to cell level directly from the information provided by the manufacturer data sheet. DC-PV module, MPPT control, BC, VSI and LC filter, all were treated as a single unit. The model accounts for changes in variations of both irradiance and temperature. The AC-PV module proposed model is simulated and the results are compared with the datasheet projected numbers to validate model’s accuracy and effectiveness. Implementation and results demonstrate simplicity and accuracy, as well as reliability of the model.

Keywords: AC PV Module, Datasheet, Matlab/Simulink, PV modeling.

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Authors: Rohit Tripathi, Sumit Tiwari, G. N. Tiwari

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In present study, an approach is adopted where photovoltaic thermal flat plate collector is integrated with compound parabolic concentrator. Analytical expression of temperature dependent electrical efficiency of N number of partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) water collector connected in series has been derived with the help of basic thermal energy balance equations. Analysis has been carried for winter weather condition at Delhi location, India. Energy and exergy performance of N - partially covered Photovoltaic Thermal (PVT) - Compound Parabolic Concentrator (CPC) Water collector system has been compared for two cases: (i) 25% area of water collector covered by PV module, (ii) 75% area of water collector covered by PV module. It is observed that case (i) has been best suited for thermal performance and case (ii) for electrical energy as well as overall exergy.

Keywords: Compound parabolic concentrator, Energy, Photovoltaic thermal, Temperature dependent electrical efficiency.

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Authors: Tisciane Perpetuo e Oliveira, Dante Inga Narvaez, Marcelo Gradella Villalva

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Installations of solar photovoltaic systems have increased considerably in the last decade. Therefore, it has been noticed that monitoring of meteorological data (solar irradiance, air temperature, wind velocity, etc.) is important to predict the potential of a given geographical area in solar energy production. In this sense, the present work compares two computational tools that are capable of estimating the energy generation of a photovoltaic system through correlation analyzes of solar radiation data: PVsyst software and an algorithm based on the PVlib package implemented in MATLAB. In order to achieve the objective, it was necessary to obtain solar radiation data (measured and from a solarimetric database), analyze the decomposition of global solar irradiance in direct normal and horizontal diffuse components, as well as analyze the modeling of the devices of a photovoltaic system (solar modules and inverters) for energy production calculations. Simulated results were compared with experimental data in order to evaluate the performance of the studied methods. Errors in estimation of energy production were less than 30% for the MATLAB algorithm and less than 20% for the PVsyst software.

Keywords: Energy production, meteorological data, irradiance decomposition, solar photovoltaic system.

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Authors: Le Linh, Truong Nguyen Luan Vu, Le Hieu Giang

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In this work, the IMC-PID controller cascaded filter based on Internal Model Control (IMC) scheme is systematically proposed for the simplified decoupling control system. The simplified decoupling is firstly introduced for multivariable processes by using coefficient matching to obtain a stable, proper, and causal simplified decoupler. Accordingly, transfer functions of decoupled apparent processes can be expressed as a set of n equivalent independent processes and then derived as a ratio of the original open-loop transfer function to the diagonal element of the dynamic relative gain array. The IMC-PID controller in series with filter is then directly employed to enhance the overall performance of the decoupling control system while avoiding difficulties arising from properties inherent to simplified decoupling. Some simulation studies are considered to demonstrate the simplicity and effectiveness of the proposed method. Simulations were conducted by tuning various controllers of the multivariate processes with multiple time delays. The results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Keywords: Coefficient matching method, internal model control scheme, PID controller cascaded filter, simplified decoupler.

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Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.

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Authors: S. Ganesh, J. Janani, G. Besliya Angel

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Photovoltaic (PV) energy is one of the most important renewable energy sources. Maximum Power Point Tracking (MPPT) techniques should be used in photovoltaic systems to maximize the PV panel output power by tracking continuously the maximum power point which depends on panel’s temperature and on irradiance conditions. Incremental conductance control method has been used as MPPT algorithm. The methodology is based on connecting a pulse width modulated dc/dc SEPIC converter, which is controlled by a microprocessor based unit. The SEPIC converter is one of the buck-boost converters which maintain the output voltage as constant irrespective of the solar isolation level. By adjusting the switching frequency of the converter the maximum power point has been achieved. The main difference between the method used in the proposed MPPT systems and other technique used in the past is that PV array output power is used to directly control the dc/dc converter thus reducing the complexity of the system. The resulting system has high efficiency, low cost and can be easily modified. The tracking capability has been verified experimentally with a 10 W solar panel under a controlled experimental setup. The SEPIC converter and their control strategies has been analyzed and simulated using Simulink/Matlab software.

Keywords: Maximum Power Point Tracking, Microprocessor, PV Module, SEPIC Converter.

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Authors: Shaharin A. Sulaiman, Haizatul H. Hussain, Nik Siti H. Nik Leh, Mohd S. I. Razali

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Accumulation of dust from the outdoor environment on the panels of solar photovoltaic (PV) system is natural. There were studies that showed that the accumulated dust can reduce the performance of solar panels, but the results were not clearly quantified. The objective of this research was to study the effects of dust accumulation on the performance of solar PV panels. Experiments were conducted using dust particles on solar panels with a constant-power light source, to determine the resulting electrical power generated and efficiency. It was found from the study that the accumulated dust on the surface of photovoltaic solar panel can reduce the system-s efficiency by up to 50%.

Keywords: Dust, Photovoltaic, Solar Energy.

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Authors: Sachin Vrajlal Rajani, Vivek Pandya, Ankit Suvariya

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Green and renewable energy is getting extraordinary consideration today, because of ecological concerns made by blazing of fossil powers. Photovoltaic and wind power generation are the basic decisions for delivering power in this respects. Producing power by the sun based photovoltaic systems is known to the world, yet control makers may get confounded to pick between on-grid and off-grid systems. In this exploration work, an endeavor is made to compare the off-grid (stand-alone) and on-grid (grid-connected) frameworks. The work presents relative examination, between two distinctive PV frameworks situated at V.V.P. Engineering College, Rajkot. The first framework is 100 kW remain solitary and the second is 60 kW network joined. The real-time parameters compared are; output voltage, load current, power in-flow, power output, performance ratio, yield factor, and capacity factor. The voltage changes and the power variances in both frameworks are given exceptional consideration and the examination is made between the two frameworks to judge the focal points and confinements of both the frameworks.

Keywords: Standalone PV systems, grid connected PV systems, comparison, real time data analysis.

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Authors: Myungraee Cha, Jun Seok Kim, Seung Hwan Park, Jun-Geol Baek

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In manufacturing industries, development of measurement leads to increase the number of monitoring variables and eventually the importance of multivariate control comes to the fore. Statistical process control (SPC) is one of the most widely used as multivariate control chart. Nevertheless, SPC is restricted to apply in processes because its assumption of data as following specific distribution. Unfortunately, process data are composed by the mixture of several processes and it is hard to estimate as one certain distribution. To alternative conventional SPC, therefore, nonparametric control chart come into the picture because of the strength of nonparametric control chart, the absence of parameter estimation. SVDD based control chart is one of the nonparametric control charts having the advantage of flexible control boundary. However,basic concept of SVDD has been an oversight to the important of data characteristic, density distribution. Therefore, we proposed DW-SVDD (Density Weighted SVDD) to cover up the weakness of conventional SVDD. DW-SVDD makes a new attempt to consider dense of data as introducing the notion of density Weight. We extend as control chart using new proposed SVDD and a simulation study of various distributional data is conducted to demonstrate the improvement of performance.

Keywords: Density estimation, Multivariate control chart, Oneclass classification, Support vector data description (SVDD)

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Authors: Attila Balogh, Eszter Varga, István Varjasi

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Nowadays in applications of renewable energy sources it is important to develop powerful and energy-saving photovoltaic converters and to keep the prescriptions of the standards. In grid connected PV converters the obvious solution to increase the efficiency is to reduce the switching losses. Our new developed control method reduces the switching losses and keeps the limitations of the harmonic distortion standards. The base idea of the method is the utilization of 3-state control causing discontinuous current mode at low input power. In the following sections the control theory, the realizations and the simulation results are presented.

Keywords: Discontinuous current, high efficiency, PVconverter, control method.

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Authors: N. Pekin Alakoç, A. Apaydın

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Quality control charts indicate out of control conditions if any nonrandom pattern of the points is observed or any point is plotted beyond the control limits. Nonrandom patterns of Shewhart control charts are tested with sensitizing rules. When the processes are defined with fuzzy set theory, traditional sensitizing rules are insufficient for defining all out of control conditions. This is due to the fact that fuzzy numbers increase the number of out of control conditions. The purpose of the study is to develop a set of fuzzy sensitizing rules, which increase the flexibility and sensitivity of fuzzy control charts. Fuzzy sensitizing rules simplify the identification of out of control situations that results in a decrease in the calculation time and number of evaluations in fuzzy control chart approach.

Keywords: Fuzzy set theory, Quality control charts, Run Rules, Unnatural patterns.

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