Search results for: interleaved boost converter

Authors: T. Abdelkrim, K. Ben Seddik, B. Bezza, K. Benamrane, Aeh. Benkhelifa

Abstract:

This paper proposes an implementation of boost converter for a resistive load using photovoltaic energy as a source. The model of photovoltaic cell and operating principle of boost converter are presented. A PIC micro controller is used in the close loop control to generate pulses for controlling the converter circuit. To performance evaluation of boost converter, a variation of output voltage of PV panel is done by shading one and two cells.

Keywords: boost converter, microcontroller, photovoltaic power generation, shading cells

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Authors: Abdar Ali, Rizwan Ullah, Zahid Ullah

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This paper focuses on the study of DC-to-DC converters, which are suitable for low-voltage high-power applications. The output voltages generated by renewable energy sources such as photovoltaic arrays and fuel cell stacks are generally low and required to be increased to high voltage levels. Development of DC-to-DC converters, which provide high step-up voltage conversion ratios with high efficiencies and low voltage stresses is one of the main issues in the development of renewable energy systems. A procedure for three converters-conventional DC-to-DC converter, interleaved boost converter, and isolated flyback based converter, is illustrated for a given set of specifications. The selection among the converters for the given application is based on the voltage conversion ratio, efficiency, and voltage stresses.

Keywords: flyback converter, interleaved boost, photovoltaic array, fuel cell, switch stress, voltage conversion ratio, renewable energy

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Authors: Viji Vijayakumar, R. Divya, A. Vivek

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This paper deals with a quadratic boost converter which belongs to cascade boost family, controlled by sliding mode controller. In the cascade boost family, quadratic boost converter is the best trade-off when circuit complexity and modulator saturation is considered. Sliding mode control being a nonlinear control results in a robust and stable system when applied to switching converters which are inherently variable structured systems. The stability of this system is analyzed through Lyapunov’s approach. Analysis is done for load regulation, line regulation and step response of the system. Also these results are compared with that of PID controller based system.

Keywords: DC-DC converter, quadratic boost converter, sliding mode control, PID control

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Authors: Ismail Aksoy, Haci Bodur, Nihan Altintaş

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This paper introduces a boost converter with a new active snubber cell. In this circuit, all of the semiconductor components in the converter softly turns on and turns off with the help of the active snubber cell. Compared to the other converters, the proposed converter has advantages of size, number of components and cost. The main feature of proposed converter is that the extra voltage stresses do not occur on the main switches and main diodes. Also, the current stress on the main switch is acceptable level. Moreover, the proposed converter can operates under light load conditions and wide input line voltage. In this study, the operating principle of the proposed converter is presented and its operation is verified with the Proteus simulation software for a 1 kW and 100 kHz model.

Keywords: active snubber cell, boost converter, zero current switching, zero voltage switching

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Authors: M. Kaouane, A. Boukhelifa, A. Cheriti

Abstract:

In this paper, a new Buck-Boost DC-DC converter is designed and simulated for photovoltaic energy system. The presented Buck-Boost converter has a double switch. Moreover, its output voltage is regulated to a constant value whatever its input is. In the presented work, the Buck-Boost transfers the produced energy from the photovoltaic generator to an R-L load. The converter is controlled by the pulse width modulation technique in a way to have a suitable output voltage, in the other hand, to carry the generator’s power, and put it close to the maximum possible power that can be generated by introducing the right duty cycle of the pulse width modulation signals that control the switches of the converter; each component and each parameter of the proposed circuit is well calculated using the equations that describe each operating mode of the converter. The proposed configuration of Buck-Boost converter has been simulated in Matlab/Simulink environment; the simulation results show that it is a good choice to take in order to maintain the output voltage constant while ensuring a good energy transfer.

Keywords: Buck-Boost converter, switch, photovoltaic, PWM, power, energy transfer

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Authors: Naim Suleyman Ting, Yakup Sahin, Ismail Aksoy

Abstract:

This paper presents a zero voltage transition-zero current transition (ZVT-ZCT)-PWM DC-DC boost converter with direct power transfer. In this converter, the main switch turns on with ZVT and turns off with ZCT. The auxiliary switch turns on and off with zero current switching (ZCS). The main diode turns on with ZVS and turns off with ZCS. Besides, the additional current or voltage stress does not occur on the main device. The converter has features as simple structure, fast dynamic response and easy control. Also, the proposed converter has direct power transfer feature as well as excellent soft switching techniques. In this study, the operating principle of the converter is presented and its operation is verified for 1 kW and 100 kHz model.

Keywords: direct power transfer, boost converter, zero-voltage transition, zero-current transition

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Authors: Jun Yu, Yat-Hei Lam, Boris Grinberg, Kevin Chai Tshun Chuan

Abstract:

This paper presents a 5-V to 30-V current-mode boost converter for powering the drive circuit of a micro-electro-mechanical sensor. The design of a transconductance amplifier and an integrated current sensing circuit are presented. In addition, essential building blocks for power-on protection such as a soft-start and clamp block and supply and clock ready block are discussed in details. The chip is fabricated in a 0.18-μm CMOS process. Measurement results show that the soft-start and clamp block can effectively limit the inrush current during startup and protect the boost converter from startup failure.

Keywords: boost converter, current sensing, power-on protection, step-up converter, soft-start

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Authors: Seyed Hossein Hosseini, Seyed Majid Hashemzadeh

Abstract:

Solar energy is one of the remarkable renewable energy sources that have particular characteristics such as unlimited, no environmental pollution, and free access. Generally, solar energy can be used in thermal and photovoltaic (PV) types. The cost of installation of the PV system is very high. Additionally, due to dependence on environmental situations such as solar radiation and ambient temperature, electrical power generation of this system is unpredictable and without power electronics devices, there is no guarantee to maximum power delivery at the output of this system. Maximum power point tracking (MPPT) should be used to achieve the maximum power of a PV string. MPPT is one of the essential parts of the PV system which without this section, it would be impossible to reach the maximum amount of the PV string power and high losses are caused in the PV system. One of the noticeable challenges in the problem of MPPT is the partial shading conditions (PSC). In PSC, the output photocurrent of the PV module under the shadow is less than the PV string current. The difference between the mentioned currents passes from the module's internal parallel resistance and creates a large negative voltage across shaded modules. This significant negative voltage damages the PV module under the shadow. This condition is called hot-spot phenomenon. An anti-paralleled diode is inserted across the PV module to prevent the happening of this phenomenon. This diode is known as the bypass diode. Due to the performance of the bypass diode under PSC, the P-V curve of the PV string has several peaks. One of the P-V curve peaks that makes the maximum available power is the global peak. Model-based Global MPPT (GMPPT) methods can estimate the optimal point with higher speed than other GMPPT approaches. Centralized, modular, and interleaved DC-DC converter topologies are the significant structures that can be used for GMPPT at a PV string. there are some problems in the centralized structure such as current mismatch losses at PV sting, loss of power of the shaded modules because of bypassing by bypass diodes under PSC, needing to series connection of many PV modules to reach the desired voltage level. In the modular structure, each PV module is connected to a DC-DC converter. In this structure, by increasing the amount of demanded power from the PV string, the number of DC-DC converters that are used at the PV system will increase. As a result, the cost of the modular structure is very high. We can implement the model-based GMPPT through the multi-input interleaved boost DC-DC converter to increase the power extraction from the PV string and reduce hot-spot and current mismatch error in a PV string under different environmental condition and variable load circumstances. The interleaved boost DC-DC converter has many privileges than other mentioned structures, such as high reliability and efficiency, better regulation of DC voltage at DC link, overcome the notable errors such as module's current mismatch and hot spot phenomenon, and power switches voltage stress reduction.

Keywords: solar energy, photovoltaic systems, interleaved boost converter, maximum power point tracking, model-based method, partial shading conditions

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Authors: Andrés Gomez-Casseres, Rubén Contreras

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In this paper, a bidirectional boost converter operated in Discontinuous Conduction Mode (DCM) is presented as a suitable power conditioning circuit for tuning of kinetic energy harvesters without the need of a battery. A nonlinear control scheme, composed by two linear controllers, is used to control the average value of the input current, enabling the synthesization of complex loads. The converter, along with the control system, is validated through SPICE simulations using the LTspice tool. The converter model and the controller transfer functions are derived. From the simulation results, it was found that the input current distortion increases with the introduced phase shift and that, such distortion, is almost entirely present at the zero-crossing point of the input voltage.

Keywords: average current control, boost converter, electrical tuning, energy harvesting

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Authors: Nidhi Vijay, A. K. Sharma

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Many industrial applications require power from dc source. DC-DC boost converters are now being used all over the world for rapid transit system. Although these provide high efficiency, smooth control, fast response and regeneration, conventional DC-DC boost converters are unable to provide high step up voltage gain due to effect of power switches, rectifier diodes and equivalent series resistance of inductor and capacitor. This paper proposes new transformerless dc-dc converters to achieve high step up voltage gain as compared to the conventional converter without an extremely high duty ratio. Only one power stage is used in this converter. Steady-state analysis of voltage gain is discussed in brief. Finally, a comparative analysis is given in order to verify the results.

Keywords: MATLAB, DC-DC boost converter, voltage gain, voltage stress

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Authors: Mustafa Engin Başoğlu, Bekir Çakır

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The most important component affecting the efficiency of photovoltaic power systems are solar panels. Efficiency of these systems are significantly affected because of being low efficiency of solar panel. Therefore, solar panels should be operated under maximum power point conditions through a power converter. In this study, design boost converter with maximum power point tracking (MPPT) operation has been designed and performed with Incremental Conductance (Inc-Cond) algorithm by using direct duty control. Furthermore, it is shown that performance of boost converter with MPPT operation fails under low load resistance connection.

Keywords: boost converter, incremental conductance (Inc-Cond), MPPT, solar panel

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Authors: Ammar Nimer Natsheh

Abstract:

Chaos control is used to design a controller that is able to eliminate the chaotic behaviour of nonlinear dynamic systems that experience such phenomena. The paper describes the control of the bifurcation behaviour of a parallel-connected DC-DC buck-boost converter used to provide an interface between energy storage batteries and photovoltaic (PV) arrays as renewable energy sources. The paper presents a delayed feedback control scheme in a module converter comprises two identical buck-boost circuits and operates in the continuous-current conduction mode (CCM). MATLAB/SIMULINK simulation results show the effectiveness and robustness of the scheme.

Keywords: chaos, bifurcation, DC-DC Buck-Boost Converter, Delayed Feedback Control

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Authors: Edwina G. Rodrigues, S. J. Bindhu, A. V. Rajesh

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This paper proposes a switched capacitor based driver circuit for high power light emitting diodes with a front end rectifier. LEDs are low-voltage light sources, requiring a constant DC voltage or current to operate optimally. LEDs, therefore, require a device that can convert incoming AC power to the proper DC voltage, and regulate the current flowing through the LED during operation. Proposed topology has a front end converter. It is an AC-DC rectifier that works on bridgeless boost topology which shapes the input current waveform. The front end converter is followed by a DC-DC converter which provides a constant DC voltage across the LEDs. A 12V AC input is given to the input of frontend converter which rectifies and boost the voltage to 24v DC and gives it to the DC-DC converter. The DC-DC converter converts the 24V DC and regulates this constant DC voltage across the LEDs.

Keywords: bridgeless rectifier, power factor correction(PFC), SC converter, total harmonic distortion (THD)

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Authors: Chih-Chiang Hua, Yi-Hsiung Fang, Yuan-Jhen Siao

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A bridgeless boost (BLB) power factor correction (PFC) rectifier with hold-up time extension circuit is proposed in this paper. A full bridge rectifier is widely used in the front end of the ac/dc converter. Since the shortcomings of the full bridge rectifier, the bridgeless rectifier is developed. A BLB rectifier topology is utilized with the hold-up time extension circuit. Unlike the traditional hold-up time extension circuit, the proposed extension scheme uses fewer active switches to achieve a longer hold-up time. Simulation results are presented to verify the converter performance.

Keywords: bridgeless boost (BLB), boost converter, power factor correction (PFC), hold-up time

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Authors: Yakup Sahin, Naim Suleyman Ting, Ismail Aksoy

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In this paper, a single phase soft switched Zero Voltage Transition and Zero Current Transition (ZVT-ZCT) Power Factor Correction (PFC) boost converter is proposed. In the proposed PFC converter, the main switch turns on with ZVT and turns off with ZCT without any additional voltage or current stresses. Auxiliary switch turns on and off with zero current switching (ZCS). Also, the main diode turns on with zero voltage switching (ZVS) and turns off with ZCS. The proposed converter has features like low cost, simple control and structure. The output current and voltage are controlled by the proposed PFC converter in wide line and load range. The theoretical analysis of converter is clarified and the operating steps are given in detail. The simulation results of converter are obtained for 500 W and 100 kHz. It is observed that the semiconductor devices operate with soft switching (SS) perfectly. So, the switching power losses are minimum. Also, the proposed converter has 0.99 power factor with sinusoidal current shape.

Keywords: power factor correction, zero-voltage transition, zero-current transition, soft switching

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Authors: Nagaraju Jarugu, B. R. Narendra

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This paper focused on boost rectification by Single Phase Matrix Converter with fewer numbers of switches. The conventional matrix converter consists of 4 bidirectional switches, i.e. 8 set of IGBT/MOSFET with anti-parallel diodes. In this proposed matrix converter, only six switches are used. The switch commutation arrangements are also carried out in this work. The SPMC topology has many advantages as a minimal passive device use. It is very flexible and it can be used as a lot of converters. The gate pulses to the switches are provided by the PWM techniques. The duty ratio of the switches based on Pulse Width Modulation (PWM) technique was used to produce the output waveform of the circuit, simply by turning ON and OFF the switches. The simulation results using MATLAB/Simulink were provided to validate the feasibility of this proposed method.

Keywords: single phase matrix converter, reduced switches, AC voltage regulators, boost rectifier operation

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Authors: Yakup Sahin, Naim Suleyman Ting, Ismail Aksoy

Abstract:

A 1 kW power factor correction boost converter with an active snubber cell is presented in this paper. In the converter, the main switch turns on under zero voltage transition (ZVT) and turns off under zero current transition (ZCT) without any additional voltage or current stress. The auxiliary switch turns on and off under zero current switching (ZCS). Besides, the main diode turns on under ZVS and turns off under ZCS. The output current and voltage are controlled by the PFC converter in wide line and load range. The simulation results of converter are obtained for 1 kW and 100 kHz. One of the most important feature of the given converter is that it has direct power transfer as well as excellent soft switching techniques. Also, the converter has 0.99 power factor with the sinusoidal input current shape.

Keywords: power factor correction, direct power transfer, zero-voltage transition, zero-current transition, soft switching

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Authors: S. Abdourraziq, M. A. Abdourraziq

Abstract:

One of the most famous and important applications of solar energy systems is water pumping. It is often used for irrigation or to supply water in countryside or private firm. However, the cost and the efficiency are still a concern, especially with a continued variation of solar radiation and temperature throughout the day. Then, the improvement of the efficiency of the system components is one of the different solutions to reducing the cost. In this paper, we will present a detailed definition of each element of a PV pumping system, and we will present the different MPPT algorithm used in the literature. Our system consists of a PV panel, a boost converter, a motor-pump set, and a storage tank.

Keywords: PV cell, converter, MPPT, MPP, PV pumping system

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Authors: Nagesh Vangala, Rayudu Mannam

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Soft switching has attracted the interest of various researchers constantly. Many techniques are in vogue to achieve soft switching (ZVS and/or ZCS) in Boost converters. These techniques utilize an auxiliary switch to incorporate the ZCS/ZVS. Such schemes require additional control circuit and induce complexity in design. This paper proposes an elegant fly back approach which guarantees zero current switching of the main Switch without the need for any additional active device. A simple flyback transformer scheme is implemented which absorbs the initial turn ON energy (or the Reverse recovery energy of Boost diode) and delivers to the output.

Keywords: boost converter, complete energy transfer, flyback, zero current switching

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Authors: Shah Krupa Rajendra, Amit Kumar

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Increasing use of traditional vehicles driven by internal combustion engine is responsible for the environmental pollution. Further, it leads to depletion of limited energy resources. Therefore, it is required to explore alternative energy sources for the transportation. The promising solution is to use electric vehicle. However, it suffers from limited driving range. Regenerative braking increases the range of the electric vehicle to a certain extent. In this paper, a novel methodology utilizing regenerative braking is described. The model comprising of DC machine, feedback based boost converter and micro-controller is proposed. The suggested method is very simple and reliable. The proposed model successfully shows the energy being saved into during regenerative braking process.

Keywords: boost converter, DC machine, electric vehicle, micro-controller, regenerative braking

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Authors: A. Sreedevi, G. Anantaramu

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The present space research organizations are striving towards the development of lighter, smaller, more efficient, low cost, and highly reliable power supply. Switch mode power supplies (SMPS) overcome the demerits of linear power supplies such as low efficiency, difficulties in thermal management, and in boosting the output voltage. Space applications require a constant DC voltage to supply its load. As the load varies, the battery terminal voltage tends to vary accordingly. To avoid this variation in the load terminal voltage, a DC-DC regulator is required. The conventional regulator for space applications is isolated boost topology. The proposed topology uses an interleaved push-pull converter with a current doubler secondary to reduce the EMI issues and increase efficiency. The proposed topology uses a floating technique where the converter derives power from the battery and generates only the voltage that is required to fill the gap between the bus and the battery voltage. The direct voltage sense and current loop provide tight regulation of output and better stability. Converter is designed with 50 kHz switching frequency using UC 1825 PWM controller employing both voltage and peak current mode control. Experimental tests have been carried out on the converter under different input and load conditions to validate the design. The experimental results showed that the efficiency was greater than 91%. Stability analysis is done using venable stability analyzer.

Keywords: push pull converter, current doubler, converter, PWM control

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Authors: Mohamed Amarouayache, Badia Amrouche, Gharbi Akila, Boukadoume Mohamed

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This work is devoted to the modeling of DC-DC converter (boost) used for MPPT applications to set conditions of stability. For this, we establish a linear mathematical model of the DC-DC converter with an average small signal model. This model has allowed us to apply conventional linear methods of automation. A mathematical relationship between the duty cycle and the voltage of the panel has been set up. With this relationship we specify the conditions of the stability in closed-loop depending on the system parameters (the elements of storage capacity and inductance, PWM control).

Keywords: MPPT, PWM, stability, criterion of Routh, average small signal model

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Authors: Sudha Bhutada, S. R. Nigam

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In this paper, a single-phase PV inverter applying a dual boost converter circuit inverter is proposed for photovoltaic (PV) generation system and PV grid connected system. This system is designed to improve integration of a Single phase inverter with Photovoltaic panel. The DC 24V is converted into to 86V DC and then 86V DC to 312V DC. The 312 V DC is then successfully inverted to AC 220V. Hence, solar energy is powerfully converted into electrical energy for fulfilling the necessities of the home load, or to link with the grid. Matlab Simulation software was used for simulation of the circuit and outcome are presented in this paper.

Keywords: H bridge inverter, dual boost converter, PWM, SPWM

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Authors: Fatma Soltani

Abstract:

In power electronics the DC-DC converters or choppers are now employed in large areas, particularly in the field of electricity generation by wind and solar energy conversion. Photovoltaic generators (GPV) can deliver maximum power for a point on the characteristic P = f (Vpv), called maximum power point (MPP), or climatic variations, entraiment fluctuation PPM. To remedy this problem is interposed between the generator and receiver a DC-DC converter. The converter is usually used a simple MOSFET chopper. However, the MOSFET can be applied in the field of low power when you need a high switching frequency but becomes highly dissipative when should block large voltages For PV generators medium and high power, the use of IGBT chopper is by far the most recommended. To reduce stress on semiconductor components using several choppers series connected in parallel is known as interleaved chopper. These choppers lead to rotas.

Keywords: converter DC-DC entrelaced

, photovoltaic generators, IGBT, optimisation

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Authors: Badr M. Alshammari, Mohamed A. Khlifi

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This paper presents the analysis of DC/DC converter including a comparative study of control methods to extract the maximum power and to track the maximum power point (MPP) from photovoltaic (PV) systems under changeable environmental conditions. This paper proposes two methods of maximum power point tracking algorithm for photovoltaic systems, based on the first hand on P&O control and the other hand on the first order IC. The MPPT system ensures that solar cells can deliver the maximum power possible to the load. Different algorithms are used to design it. Here we compare them and simulate the photovoltaic system with two algorithms. The algorithms are used to control the duty cycle of a DC-DC converter in order to boost the output voltage of the PV generator and guarantee the operation of the solar panels in the Maximum Power Point (MPP). Simulation and experimental results show that the proposed algorithms can effectively improve the efficiency of a photovoltaic array output.

Keywords: solar cell, DC/DC boost converter, MPPT, photovoltaic system

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Authors: Fatih Suleyman Taskincan, Ahmet Karaarslan

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In this article, the study and analysis of Single Ended Primary Inductance Converter (SEPIC) are presented for battery charging applications that will be used in military applications. The usage of this kind of converters come from its advantage of non-reverse polarity at outputs. As capacitors charge and discharge through inductance, peak current does not occur on capacitors. Therefore, the efficiency will be high compared to buck-boost converters. In this study, the converter (SEPIC) is designed to be operated with Internal Model Controller (IMC). The traditional controllers like Proportional Integral Controller are not preferred as its linearity behavior. Hence IMC is designed for this converter. This controller is a model-based control and provides more robustness and better set point monitoring. Moreover, it can be used for an unstable process where the conventional controller cannot handle the dynamic operation. Matlab/Simulink environment is used to simulate the converter and its controller, then, the results are shown and discussed.

Keywords: DC/DC converter, single ended primary inductance converter, SEPIC, internal model controller, IMC, switched mode power supply

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Authors: Yasunori Kobori, Li Quan, Shu Wu, Nizam Mohyar, Zachary Nosker, Nobukazu Tsukiji, Nobukazu Takai, Haruo Kobayashi

Abstract:

This paper proposes an electrolytic capacitor-less transformer-less AC-DC LED driver with a current ripple canceller. The proposed LED driver includes a diode bridge, a buck-boost converter, a negative feedback controller and a current ripple cancellation circuit. The current ripple canceller works as a bi-directional current converter using a sub-inductor, a sub-capacitor and two switches for controlling current flow. LED voltage is controlled in order to regulate LED current by the negative feedback controller using a current sense resistor. There are two capacitors which capacitance of 5 uF. We describe circuit topologies, operation principles and simulation results for our proposed circuit. In addition, we show the line regulation for input voltage variation from 85V to 130V. The output voltage ripple is 2V and the LED current ripple is 65 mA which is less than 20% of the typical current of 350 mA. We are now making the proposed circuit on a universal board in order to measure the experimental characteristics.

Keywords: LED driver, electrolytic, capacitor-less, AC-DC converter, buck-boost converter, current ripple canceller

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Authors: Kusum Tharani, Ratna Dahiya

Abstract:

This paper aims to analyze the power flow of a grid connected 100-kW Photovoltaic(PV) array connected to a 25-kV grid via a DC-DC boost converter and a three-phase three-level Voltage Source Converter (VSC). Maximum Power Point Tracking (MPPT) is implemented in the boost converter bymeans of a Simulink model using the 'Perturb & Observe' technique. First, related papers and technological reports were extensively studied and analyzed. Accordingly, the system is tested under various loading conditions. Power flow analysis is done using the Newton-Raphson method in Matlab environment. Finally, the system is subject to Single Line to Ground Fault and Three Phase short circuit. The results are simulated under the grid-connected operating model.

Keywords: grid connected PV Array, Newton-Raphson Method, power flow analysis, three phase fault

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Authors: Sarah Abdourraziq

Abstract:

To improve the efficiency of photovoltaic pumping system, more attention has been paid to their setting up. This paper presents an optimal technique to establish an efficient system under different conditions of irradiance and temperature. The state of place should be carefully studied before stage of installation of the over system: local climate, boreholes, soil, crops and water resources. The studied system consists of a PV panel, a DC-DC boost converter, a DC motor-pump, and storage tank. The concepts shown in this paper presents a support for an optimal installation of each solar pump.

Keywords: photovoltaic pumping system, optimal implementation, boost converter, motor-pump

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Authors: A. Mansouri, F. Krim

Abstract:

This paper discusses the implementation and design of both linear PI and fuzzy controllers for DC-DC boost converters. Design of PI controllers is based on temporal response of closed-loop converters, while fuzzy controllers design is based on heuristic knowledge of boost converters. Linear controller implementation is quite straightforward relying on mathematical models, while fuzzy controller implementation employs one or more artificial intelligences techniques. Comparison between these boost controllers is made in design aspect. Experimental results show that the proposed fuzzy controller system is robust against input voltage and load resistance changing and in respect of start-up transient. Results indicate that fuzzy controller can achieve best control performance concerning faster transient response, steady-state response good stability and accuracy under different operating conditions. Fuzzy controller is more suitable to control boost converters.

Keywords: boost DC-DC converter, fuzzy, PI controllers, power electronics and control system

Procedia PDF Downloads 439