The document discusses modelling of DC-DC converters. It describes:
1) DC-DC converters regulate output voltage by varying the duty cycle of switching signals to transistors and diodes.
2) Buck and boost converters are analyzed, determining equations for inductor current, capacitor voltage, and minimum inductance for continuous mode.
3) Parameters like maximum current, output ripple, and filtering capacitor value are calculated based on duty cycle, switching frequency, and load.
International Journal of Engineering Research and DevelopmentIJERD Editor
This document summarizes a study investigating two soft-switched isolated DC-DC converter topologies for auxiliary power supply in railways. The converters aim to reduce size and weight by using a lightweight medium frequency transformer instead of heavy 50Hz transformers. One proposed topology uses an auxiliary circuit on the secondary side to achieve zero-current switching for the primary inverter switches. Equations are provided to analyze the operating modes and design considerations of this topology, including resonant component sizing, power device ratings, and output voltage characteristics based on input voltage and load current. Analytical expressions are given to determine maximum stresses on the power devices under different operating conditions.
This document discusses Matlab/Simulink implementation for reducing motor derating and torque pulsation of an induction motor using a matrix converter. It provides background on how non-sinusoidal supply from traditional inverters causes harmonic losses and torque pulsation in induction motors. The document summarizes simulation results showing that a matrix converter can provide a pure sinusoidal supply, reducing harmonic losses and torque pulsation. Simulations of a matrix converter driving an induction motor in Matlab/Simulink are presented, showing sinusoidal voltage/current waveforms and reduced torque pulsation at steady state.
The document discusses uncontrolled rectifiers, which provide a fixed DC output voltage from an AC supply using diodes. It describes single-phase half-wave and full-wave uncontrolled rectifiers with resistive and resistive-inductive loads. For a half-wave rectifier with resistive load, the average DC output voltage is half the peak AC input voltage. A full-wave rectifier doubles this output voltage by using two pairs of diodes to conduct during both half-cycles of the AC input. Rectifiers with resistive-inductive loads have more complex non-sinusoidal current waveforms that decay during the negative half-cycles.
Fuzzy Logic Controlled Harmonic Suppressor in Cascaded Multilevel InverterIJPEDS-IAES
This paper presents an investigation of seven level cascaded H-bridge (CHB)
inverter in power system for compensation of harmonics. For power quality
control a Fuzzy Logic Control (FLC) giving comparatively better harmonic
reduction than the conventional controllers. Harmonic distortion is the most
important power quality problem stirring in multilevel inverter; the
harmonics can be eliminated by an optimal selection of switching angles. A
hybrid evaluation technique evaluates the obtained optimal switching angles
that are attained from the fuzzy inference system as well as neural network.
The proposed method will be implemented in MATLAB working platform
and the harmonic elimination performance will be evaluated.
The document discusses regulated DC power supplies and their components. It explains that a regulated DC power supply consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC, the filter smooths the output, and the regulator sets the output to a fixed voltage. It then discusses half-wave and full-wave rectifiers in detail, deriving their key parameters such as DC output voltage and current, ripple factor, and efficiency.
The document summarizes the key components and operation of a regulated DC power supply. It consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC but with variation, the filter smooths the output, and the regulator sets the output to a fixed voltage. Rectifiers are then discussed in more detail, including half-wave and full-wave rectifiers. Key rectifier parameters like DC output voltage and current, ripple factor, and efficiency are defined. Half-wave rectifier operation and analysis is explained through derivations of these parameters.
This document presents a ripple theorem for determining the ripple components in PWM DC-DC converters operating in continuous conduction mode. The theorem shows that the ripple current in a switched inductor can be obtained by replacing the duty ratio control signal d with the AC component of the switching signal p(t)-D in the small-signal control-to-state transfer function. The theorem is then used to determine, for the first time, the actual output ripple current in a zero-ripple coupled Cuk converter as a function of load. Simulation results demonstrate good agreement between the small-signal model and actual circuit.
This document discusses output capacitor selection for low voltage, high current power supplies used in applications like microprocessors. It derives an equation to calculate the minimum number of capacitors needed to meet transient voltage regulation requirements during load current steps. Different capacitor types are compared based on this calculation, including electrolytic, tantalum, ceramic, and polymer capacitors. Simulation and experimental results are presented to verify the theoretical analysis. The analysis shows that the minimum capacitors required depends on factors like equivalent series resistance, capacitance, current step size, and whether the system frequency is higher or lower than the capacitor's zero frequency. This methodology allows engineers to optimize capacitor selection for cost and performance.
International Journal of Engineering Research and DevelopmentIJERD Editor
This document summarizes a study investigating two soft-switched isolated DC-DC converter topologies for auxiliary power supply in railways. The converters aim to reduce size and weight by using a lightweight medium frequency transformer instead of heavy 50Hz transformers. One proposed topology uses an auxiliary circuit on the secondary side to achieve zero-current switching for the primary inverter switches. Equations are provided to analyze the operating modes and design considerations of this topology, including resonant component sizing, power device ratings, and output voltage characteristics based on input voltage and load current. Analytical expressions are given to determine maximum stresses on the power devices under different operating conditions.
This document discusses Matlab/Simulink implementation for reducing motor derating and torque pulsation of an induction motor using a matrix converter. It provides background on how non-sinusoidal supply from traditional inverters causes harmonic losses and torque pulsation in induction motors. The document summarizes simulation results showing that a matrix converter can provide a pure sinusoidal supply, reducing harmonic losses and torque pulsation. Simulations of a matrix converter driving an induction motor in Matlab/Simulink are presented, showing sinusoidal voltage/current waveforms and reduced torque pulsation at steady state.
The document discusses uncontrolled rectifiers, which provide a fixed DC output voltage from an AC supply using diodes. It describes single-phase half-wave and full-wave uncontrolled rectifiers with resistive and resistive-inductive loads. For a half-wave rectifier with resistive load, the average DC output voltage is half the peak AC input voltage. A full-wave rectifier doubles this output voltage by using two pairs of diodes to conduct during both half-cycles of the AC input. Rectifiers with resistive-inductive loads have more complex non-sinusoidal current waveforms that decay during the negative half-cycles.
Fuzzy Logic Controlled Harmonic Suppressor in Cascaded Multilevel InverterIJPEDS-IAES
This paper presents an investigation of seven level cascaded H-bridge (CHB)
inverter in power system for compensation of harmonics. For power quality
control a Fuzzy Logic Control (FLC) giving comparatively better harmonic
reduction than the conventional controllers. Harmonic distortion is the most
important power quality problem stirring in multilevel inverter; the
harmonics can be eliminated by an optimal selection of switching angles. A
hybrid evaluation technique evaluates the obtained optimal switching angles
that are attained from the fuzzy inference system as well as neural network.
The proposed method will be implemented in MATLAB working platform
and the harmonic elimination performance will be evaluated.
The document discusses regulated DC power supplies and their components. It explains that a regulated DC power supply consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC, the filter smooths the output, and the regulator sets the output to a fixed voltage. It then discusses half-wave and full-wave rectifiers in detail, deriving their key parameters such as DC output voltage and current, ripple factor, and efficiency.
The document summarizes the key components and operation of a regulated DC power supply. It consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC but with variation, the filter smooths the output, and the regulator sets the output to a fixed voltage. Rectifiers are then discussed in more detail, including half-wave and full-wave rectifiers. Key rectifier parameters like DC output voltage and current, ripple factor, and efficiency are defined. Half-wave rectifier operation and analysis is explained through derivations of these parameters.
This document presents a ripple theorem for determining the ripple components in PWM DC-DC converters operating in continuous conduction mode. The theorem shows that the ripple current in a switched inductor can be obtained by replacing the duty ratio control signal d with the AC component of the switching signal p(t)-D in the small-signal control-to-state transfer function. The theorem is then used to determine, for the first time, the actual output ripple current in a zero-ripple coupled Cuk converter as a function of load. Simulation results demonstrate good agreement between the small-signal model and actual circuit.
This document discusses output capacitor selection for low voltage, high current power supplies used in applications like microprocessors. It derives an equation to calculate the minimum number of capacitors needed to meet transient voltage regulation requirements during load current steps. Different capacitor types are compared based on this calculation, including electrolytic, tantalum, ceramic, and polymer capacitors. Simulation and experimental results are presented to verify the theoretical analysis. The analysis shows that the minimum capacitors required depends on factors like equivalent series resistance, capacitance, current step size, and whether the system frequency is higher or lower than the capacitor's zero frequency. This methodology allows engineers to optimize capacitor selection for cost and performance.
Variable Voltage Source Equivalent Model of Modular Multilevel ConverterIJRES Journal
The structures of modular multilevel converter module (MMC) are very complex, and the
numerous sub-modules and output level number bring difficulties for the analysis and simulation. In this paper,
assuming the sub-capacitor voltage instantaneous value of a single arm is the same value, the switching
frequency of the switch is much higher than the output voltage frequency, the system harmonics were ignored,
the system state equations are deduced about the intermediate variables as circulation current and the capacitor
voltage between the upper and lower arms. On this basis, a variable voltage source continuous equivalent
model is proposed, which may replace the system physical simulation model with the actual simulation study. At
the same time, the model reflects the relationship between the output voltage and circulation current,which
provide a way to analyze the formation mechanism of circulation and the capacitor voltage fluctuations, and
make system analysis simple and intuitive. The simulation results validate that this continuous model is
rationality and correctness.
This document outlines the design of a 200 Watt, 150 Vrms PWM bipolar inverter with the following key points:
1. The design process includes calculating component values based on design requirements, building the circuit in Multisim software, and analyzing the simulation results.
2. Key calculations include determining the required DC bus voltage to achieve the 150Vrms AC output voltage despite voltage drops, as well as component sizing based on the given power, modulation index, and carrier frequency specifications.
3. Simulation results show the generated PWM switching signals and the final inverter output voltage matching the desired 150Vrms sinusoidal waveform.
This document discusses different inverter topologies including half bridge, full bridge, diode clamped multilevel, and PWM multilevel inverters. It provides circuit diagrams, output voltage waveforms, Fourier analysis to calculate harmonics, methods for computing switching angles, and simulation results comparing the total harmonic distortion for each topology. The conclusion is that PWM inverters have the highest THD but fewest switches, while diode clamped multilevel has the lowest THD but most switches. A PWM multilevel inverter provides a good balance with fewer switches than diode clamped and lower THD than basic PWM.
The document summarizes a seminar presentation on AC-DC converters given by Ankur Mahajan. The presentation covered single phase half wave and full wave converters. It discussed various rectifier types including uncontrolled, half controlled, and fully controlled bridges. It provided calculations for average and RMS voltage values for different converter configurations under resistive and inductive loads. The presentation also covered single phase half controlled and fully controlled bridge converters in both continuous and discontinuous conduction modes.
1. A chopper is a static device that converts a fixed DC input voltage to a variable DC output voltage directly through high-speed switching.
2. It operates by connecting the source to the load and disconnecting the load from the source at a fast rate, producing a chopped output voltage from a constant DC supply.
3. By varying the ON and OFF times of the switching semiconductor, the average output voltage can be controlled and varied as needed.
Equal Switching Distribution Method for Multi-Level Cascaded Inverterijsrd.com
the paper proposes a new method of equal switching distribution that can be applied to cascaded multilevel inverters. This method is based on the fact that in the cascaded multilevel inverters, the output phase voltage is the sum of voltage waveforms produced by all cascaded cells. By periodically exchanging cells' voltage waveforms, the proposed method ensures equal average switching's distribution between all cascaded cells. This method is applied to the 13-level inverter, which consists of three cascaded 5-level H-bridge cells per phase. However, the proposed method can be extended to any desired number of voltage levels and applied to any type of cascaded multilevel inverter. Extensive simulation results of the tested 13- level inverter with the equal switching distribution are presented. Moreover, the proposed method is compared to the standard control approaches and its advantages are shown.
Thyristors require commutation to turn off, which involves reducing the anode current to zero and then applying a reverse voltage for a time. There are natural and forced commutation methods. Forced methods include classes A through F, which use resonant circuits, auxiliary thyristors, or line voltage reversals to commutate the main thyristor. Turn off time has two stages - reverse recovery time to remove outer layer carriers, then gate recovery time for inner layer recombination. Proper commutation circuit design is needed to apply reverse voltage for longer than the thyristor's turn off time.
This document discusses various types of phase controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides equations for the average and RMS output voltage of single-phase converters with resistive and RL loads. It also derives an expression for the average output voltage of a three-phase half wave converter with continuous and constant load current. Key aspects of three-phase half wave, full wave, and dual converters are summarized.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The document contains short questions and answers related to power electronics topics like IGBTs, thyristors, power diodes, power MOSFETs, choppers, inverters, and AC voltage controllers. Some key points covered include:
- IGBT is popular due to lower heat requirements and switching losses compared to other power devices.
- Thyristors can be turned on through various methods including forward voltage, gate, and light triggering.
- Power diodes have higher voltage, current, and power ratings than signal diodes.
- Power devices like IGBT, MOSFET and thyristor are voltage controlled while BJT is current controlled.
- Choppers provide
Soft Switched Resonant Converters with Unsymmetrical ControlIOSR Journals
1) The document describes a half-bridge DC-DC converter with unsymmetrical control that achieves zero-voltage switching (ZVS). By operating one switch with less than 50% duty cycle and the other with greater than 50% duty cycle, soft switching conditions can be achieved using the passive elements.
2) A prototype 5V, 50W half-bridge converter was designed, fabricated, and tested to validate the performance of the converter. Experimental waveforms confirmed ZVS turn-on of the power devices.
3) The converter topology exhibits benefits of both resonant converters like zero switching losses and switched-mode circuits like low conduction losses, due to the unsymmetrical duty ratio control at a constant switching frequency.
- The document describes a cyclo-converter, which converts AC voltage at the supply frequency directly to AC voltage at the load frequency without an intermediate DC stage.
- It discusses the basic principle of operation using an equivalent circuit model and voltage waveforms for loads with different displacement angles.
- The circuit of a single-phase to single-phase cyclo-converter using thyristor bridges is presented. Its operation is explained for resistive and inductive loads in both continuous and discontinuous current modes. Waveforms show how the firing angles are varied to synthesize the output voltage.
- Cyclo-converters allow output frequencies up to about one-third of the supply frequency and operate with loads of any phase angle.
Three Phase Controlled Rectifier Study in Terms of firing angle variationsIDES Editor
This paper introduce topology of three phase
controlled rectifiers and proposed an accurate Statistical
method to calculate their input current harmonic components,
and calculate THD and harmonic currents with accurate
simulation in various firing angles, then investigate influence
of load variations in terms of firing angle variations on
harmonic currents. Finally a harmonic current database of
rectiûers is obtained in terms of firing angle and load
variations.
This paper addresses a novel approach for designing and modeling of the isolated
flyback converter. Modeling is done without parasitic as well as with parasitic components.
A detailed analysis, simulation and different control strategy are conferred for flyback
converter in continuous conduction mode (CCM). To verify the design and modeling at
primary stage, study of the converter is practiced in CCM operation for input AC voltage
230V at 50Hz and output DC voltage of 5V and 50W output power rating using PSIM 6.0
software. Simulation result shows a little ripple in output of the converter in open loop. Finally
in order to evaluate the system as well as response of the controller, flyback converter is
simulated using MATLAB. This work, highlighting the modeling when the system have
transformer and facilitate designers to go for it when they need one or more than one output
for a given application upto 150W
This document provides an overview of single phase fully controlled rectifiers. It begins by explaining the advantages of fully controlled rectifiers over uncontrolled rectifiers, namely the ability to control output voltage/current and allow bidirectional power flow. It then discusses the operation of a single phase fully controlled half-wave rectifier with resistive and resistive-inductive loads. The full bridge configuration is introduced as the most popular topology. Operation in both continuous and discontinuous conduction modes is analyzed for a full bridge supplying an R-L-E load. Key points like conduction periods, voltage waveforms, and the relationship between firing angle and output voltage/current are explained.
This document describes a 6-winding rectifier circuit. It consists of two 3-phase star rectifiers with their neutral points interconnected through an interphase transformer. This configuration produces an output voltage that is the average of the rectified voltages from each 3-phase unit. It also increases the ripple frequency to 6 times the mains frequency, allowing for a smaller filter size. Key performance parameters of the rectifier like efficiency, form factor, and power factor are calculated. Simulations are also presented to validate the theoretical analysis.
Unit-2 Three Phase controlled converter johny renoald
This document discusses three phase controlled rectifiers. It provides equations and diagrams for a three phase half-wave converter with an RL load operating under continuous and constant load current. The average output voltage is derived as one-third the peak phase voltage multiplied by 2/π. Waveforms at different trigger angles are shown. Methods for calculating the maximum, RMS, and normalized average output voltages are also presented.
The document describes the operation of a single phase semi-converter circuit with an R-L load. It has two SCRs and two diodes arranged in a bridge configuration, which allows current to flow in only one direction, making it a single quadrant converter. The operation involves four modes - in modes 1 and 3 current flows from the supply to the load through one of the SCRs, storing energy in the inductive load. In modes 2 and 4, freewheeling occurs through the diodes as the supply voltage changes polarity, maintaining current flow with the stored energy in the inductor.
This chapter provides complete description of two port network parameters. It also provides relationship between different parameters. Also it provides condition for symmetry and reciprocity.
This document presents a soft-switching two-switch resonant AC-DC converter that achieves high power factor and efficiency. The converter integrates a boost power factor correction circuit with a two-switch resonant converter. This allows it to achieve soft-switching, reduce component stress, and recycle energy stored in transformer leakage inductance. Simulation results show the converter achieves a power factor of 0.9 and soft-switching of the main switches and output diodes to reduce losses. The converter provides high efficiency power conversion with a simple control scheme.
State-space averaged modeling and transfer function derivation of DC-DC boost...TELKOMNIKA JOURNAL
This paper presents dynamic analysis of a boost type DC-DC converter for high-brightness LED (HBLED) driving applications. The steady state operation in presence of all system parasitics has been discussed for continuous conduction mode (CCM). The state-space averaging, energy conservation principle and standard linearization are used to derive ac small signal control to inductor current open-loop transfer function of the converter. The derived transfer function can be further used in designing a robust feed-back control network for the system. In the end frequency and transient responses of the derived transfer function are obtained for a given set of component values, hence to provide a useful guide for control design engineers.
Variable Voltage Source Equivalent Model of Modular Multilevel ConverterIJRES Journal
The structures of modular multilevel converter module (MMC) are very complex, and the
numerous sub-modules and output level number bring difficulties for the analysis and simulation. In this paper,
assuming the sub-capacitor voltage instantaneous value of a single arm is the same value, the switching
frequency of the switch is much higher than the output voltage frequency, the system harmonics were ignored,
the system state equations are deduced about the intermediate variables as circulation current and the capacitor
voltage between the upper and lower arms. On this basis, a variable voltage source continuous equivalent
model is proposed, which may replace the system physical simulation model with the actual simulation study. At
the same time, the model reflects the relationship between the output voltage and circulation current,which
provide a way to analyze the formation mechanism of circulation and the capacitor voltage fluctuations, and
make system analysis simple and intuitive. The simulation results validate that this continuous model is
rationality and correctness.
This document outlines the design of a 200 Watt, 150 Vrms PWM bipolar inverter with the following key points:
1. The design process includes calculating component values based on design requirements, building the circuit in Multisim software, and analyzing the simulation results.
2. Key calculations include determining the required DC bus voltage to achieve the 150Vrms AC output voltage despite voltage drops, as well as component sizing based on the given power, modulation index, and carrier frequency specifications.
3. Simulation results show the generated PWM switching signals and the final inverter output voltage matching the desired 150Vrms sinusoidal waveform.
This document discusses different inverter topologies including half bridge, full bridge, diode clamped multilevel, and PWM multilevel inverters. It provides circuit diagrams, output voltage waveforms, Fourier analysis to calculate harmonics, methods for computing switching angles, and simulation results comparing the total harmonic distortion for each topology. The conclusion is that PWM inverters have the highest THD but fewest switches, while diode clamped multilevel has the lowest THD but most switches. A PWM multilevel inverter provides a good balance with fewer switches than diode clamped and lower THD than basic PWM.
The document summarizes a seminar presentation on AC-DC converters given by Ankur Mahajan. The presentation covered single phase half wave and full wave converters. It discussed various rectifier types including uncontrolled, half controlled, and fully controlled bridges. It provided calculations for average and RMS voltage values for different converter configurations under resistive and inductive loads. The presentation also covered single phase half controlled and fully controlled bridge converters in both continuous and discontinuous conduction modes.
1. A chopper is a static device that converts a fixed DC input voltage to a variable DC output voltage directly through high-speed switching.
2. It operates by connecting the source to the load and disconnecting the load from the source at a fast rate, producing a chopped output voltage from a constant DC supply.
3. By varying the ON and OFF times of the switching semiconductor, the average output voltage can be controlled and varied as needed.
Equal Switching Distribution Method for Multi-Level Cascaded Inverterijsrd.com
the paper proposes a new method of equal switching distribution that can be applied to cascaded multilevel inverters. This method is based on the fact that in the cascaded multilevel inverters, the output phase voltage is the sum of voltage waveforms produced by all cascaded cells. By periodically exchanging cells' voltage waveforms, the proposed method ensures equal average switching's distribution between all cascaded cells. This method is applied to the 13-level inverter, which consists of three cascaded 5-level H-bridge cells per phase. However, the proposed method can be extended to any desired number of voltage levels and applied to any type of cascaded multilevel inverter. Extensive simulation results of the tested 13- level inverter with the equal switching distribution are presented. Moreover, the proposed method is compared to the standard control approaches and its advantages are shown.
Thyristors require commutation to turn off, which involves reducing the anode current to zero and then applying a reverse voltage for a time. There are natural and forced commutation methods. Forced methods include classes A through F, which use resonant circuits, auxiliary thyristors, or line voltage reversals to commutate the main thyristor. Turn off time has two stages - reverse recovery time to remove outer layer carriers, then gate recovery time for inner layer recombination. Proper commutation circuit design is needed to apply reverse voltage for longer than the thyristor's turn off time.
This document discusses various types of phase controlled converters including single-phase and three-phase semiconverters, full converters, and dual converters. It provides equations for the average and RMS output voltage of single-phase converters with resistive and RL loads. It also derives an expression for the average output voltage of a three-phase half wave converter with continuous and constant load current. Key aspects of three-phase half wave, full wave, and dual converters are summarized.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The document contains short questions and answers related to power electronics topics like IGBTs, thyristors, power diodes, power MOSFETs, choppers, inverters, and AC voltage controllers. Some key points covered include:
- IGBT is popular due to lower heat requirements and switching losses compared to other power devices.
- Thyristors can be turned on through various methods including forward voltage, gate, and light triggering.
- Power diodes have higher voltage, current, and power ratings than signal diodes.
- Power devices like IGBT, MOSFET and thyristor are voltage controlled while BJT is current controlled.
- Choppers provide
Soft Switched Resonant Converters with Unsymmetrical ControlIOSR Journals
1) The document describes a half-bridge DC-DC converter with unsymmetrical control that achieves zero-voltage switching (ZVS). By operating one switch with less than 50% duty cycle and the other with greater than 50% duty cycle, soft switching conditions can be achieved using the passive elements.
2) A prototype 5V, 50W half-bridge converter was designed, fabricated, and tested to validate the performance of the converter. Experimental waveforms confirmed ZVS turn-on of the power devices.
3) The converter topology exhibits benefits of both resonant converters like zero switching losses and switched-mode circuits like low conduction losses, due to the unsymmetrical duty ratio control at a constant switching frequency.
- The document describes a cyclo-converter, which converts AC voltage at the supply frequency directly to AC voltage at the load frequency without an intermediate DC stage.
- It discusses the basic principle of operation using an equivalent circuit model and voltage waveforms for loads with different displacement angles.
- The circuit of a single-phase to single-phase cyclo-converter using thyristor bridges is presented. Its operation is explained for resistive and inductive loads in both continuous and discontinuous current modes. Waveforms show how the firing angles are varied to synthesize the output voltage.
- Cyclo-converters allow output frequencies up to about one-third of the supply frequency and operate with loads of any phase angle.
Three Phase Controlled Rectifier Study in Terms of firing angle variationsIDES Editor
This paper introduce topology of three phase
controlled rectifiers and proposed an accurate Statistical
method to calculate their input current harmonic components,
and calculate THD and harmonic currents with accurate
simulation in various firing angles, then investigate influence
of load variations in terms of firing angle variations on
harmonic currents. Finally a harmonic current database of
rectiûers is obtained in terms of firing angle and load
variations.
This paper addresses a novel approach for designing and modeling of the isolated
flyback converter. Modeling is done without parasitic as well as with parasitic components.
A detailed analysis, simulation and different control strategy are conferred for flyback
converter in continuous conduction mode (CCM). To verify the design and modeling at
primary stage, study of the converter is practiced in CCM operation for input AC voltage
230V at 50Hz and output DC voltage of 5V and 50W output power rating using PSIM 6.0
software. Simulation result shows a little ripple in output of the converter in open loop. Finally
in order to evaluate the system as well as response of the controller, flyback converter is
simulated using MATLAB. This work, highlighting the modeling when the system have
transformer and facilitate designers to go for it when they need one or more than one output
for a given application upto 150W
This document provides an overview of single phase fully controlled rectifiers. It begins by explaining the advantages of fully controlled rectifiers over uncontrolled rectifiers, namely the ability to control output voltage/current and allow bidirectional power flow. It then discusses the operation of a single phase fully controlled half-wave rectifier with resistive and resistive-inductive loads. The full bridge configuration is introduced as the most popular topology. Operation in both continuous and discontinuous conduction modes is analyzed for a full bridge supplying an R-L-E load. Key points like conduction periods, voltage waveforms, and the relationship between firing angle and output voltage/current are explained.
This document describes a 6-winding rectifier circuit. It consists of two 3-phase star rectifiers with their neutral points interconnected through an interphase transformer. This configuration produces an output voltage that is the average of the rectified voltages from each 3-phase unit. It also increases the ripple frequency to 6 times the mains frequency, allowing for a smaller filter size. Key performance parameters of the rectifier like efficiency, form factor, and power factor are calculated. Simulations are also presented to validate the theoretical analysis.
Unit-2 Three Phase controlled converter johny renoald
This document discusses three phase controlled rectifiers. It provides equations and diagrams for a three phase half-wave converter with an RL load operating under continuous and constant load current. The average output voltage is derived as one-third the peak phase voltage multiplied by 2/π. Waveforms at different trigger angles are shown. Methods for calculating the maximum, RMS, and normalized average output voltages are also presented.
The document describes the operation of a single phase semi-converter circuit with an R-L load. It has two SCRs and two diodes arranged in a bridge configuration, which allows current to flow in only one direction, making it a single quadrant converter. The operation involves four modes - in modes 1 and 3 current flows from the supply to the load through one of the SCRs, storing energy in the inductive load. In modes 2 and 4, freewheeling occurs through the diodes as the supply voltage changes polarity, maintaining current flow with the stored energy in the inductor.
This chapter provides complete description of two port network parameters. It also provides relationship between different parameters. Also it provides condition for symmetry and reciprocity.
This document presents a soft-switching two-switch resonant AC-DC converter that achieves high power factor and efficiency. The converter integrates a boost power factor correction circuit with a two-switch resonant converter. This allows it to achieve soft-switching, reduce component stress, and recycle energy stored in transformer leakage inductance. Simulation results show the converter achieves a power factor of 0.9 and soft-switching of the main switches and output diodes to reduce losses. The converter provides high efficiency power conversion with a simple control scheme.
State-space averaged modeling and transfer function derivation of DC-DC boost...TELKOMNIKA JOURNAL
This paper presents dynamic analysis of a boost type DC-DC converter for high-brightness LED (HBLED) driving applications. The steady state operation in presence of all system parasitics has been discussed for continuous conduction mode (CCM). The state-space averaging, energy conservation principle and standard linearization are used to derive ac small signal control to inductor current open-loop transfer function of the converter. The derived transfer function can be further used in designing a robust feed-back control network for the system. In the end frequency and transient responses of the derived transfer function are obtained for a given set of component values, hence to provide a useful guide for control design engineers.
This document provides an overview of forward-type switched mode power supplies (SMPS). It begins by stating the objectives and introducing the basic topology, which consists of a switching device, transformer, and rectification/filtering circuit. It then explains the principles of operation, including two modes - the powering mode when the switch is on, and the freewheeling mode when it is off. Key points covered include the relationship between input/output voltages and duty cycle, and factors that influence the sizing of filter components like the switching frequency. Practical considerations like non-ideal transformer characteristics necessitate modifications to the basic circuit.
This document presents a high efficient loaded resonant converter with feedback for DC-DC energy conversion. The proposed converter consists of a half-bridge inductor-capacitor-inductor resonant inverter connected to a bridge rectifier and load. Soft switching reduces losses and improves efficiency. Simulation results show the converter achieves up to 85.8% efficiency. Feedback control provides accurate output regulation. Analysis and MATLAB simulation demonstrate the converter's improved performance for DC-DC energy conversion applications.
This document presents a design and simulation of a boost converter with input ripple cancellation for applications like fuel cells. It proposes a boost converter with a tapped inductor and ripple cancellation network (RCN) consisting of a small inductor and capacitor. This helps reduce input current ripples compared to a conventional boost converter. The RCN achieves input ripple cancellation by having its inductor current increase as the main inductor current decreases and vice versa. Simulation results show the proposed converter has lower input current ripple while maintaining output voltage regulation through a closed loop controller.
This project envisages a Buck dc – dc
converter mathematical analysis and simulation. This power
regulator is made up of some vital circuit elements such as
inductor, freewheeling diode, filter capacitor and electronics
power switch. The circuit is analysed based on two modes of
operation namely: continuous current conduction mode and
discontinuous current mode. Ansoft Simplorer software is
used to carry out the circuit simulation under the two modes
of operation which aided in verifying the calculated results.
Both calculated and simulated waveforms are displayed. The
results obtained are very similar.
The document summarizes a proposed non-isolated ZVZCS resonant PWM converter for high step-up and high power applications. The proposed converter uses an interleaved structure of basic cells connected in series and parallel to achieve flexibility in device selection. It allows soft-switching turn-on of switches via zero-voltage switching and turn-off of diodes via zero-current switching through the use of an auxiliary circuit. Simulation results are provided to validate the converter's operation and advantages over conventional hard-switched converters, such as reduced switch voltage and current stresses leading to higher efficiency.
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In this paper, AC modeling and small signal transfer function for DC-DC converters are
represented. The fundamentals governing the formulas are also reviewed. In DC-DC converters, the
output voltage must be kept constant, regardless of changes in the input voltage or in the effective load
resistance. Transfer function is the necessary knowledge to design a proper feedback control such as PID
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converters using standard frequency response techniques based on the small signal model of the
converter.
PID Controller Response to Set-Point Change in DC-DC Converter ControlIAES-IJPEDS
Power converter operations and efficiency is affected by variation in supply
voltage, loads current, circuit elements, ageing and temperature. To meet the
objective of tight voltage regulation, power converters circuit module and the
control unit must be robust to reject disturbances arising from supply, load
variation and changes in circuit elements. PID controller has been the most
widely used in power converter control. This paper presents studies of
robustness of PID controller tuning methods to step changes in the set point
and disturbance rejection in power converter control. A DC-DC boost
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controllers were designed with five different tuning methods. The study
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Single-Input Double Output High Efficient Boost Dc–Dc ConverterIJMER
The aim of this project is to develop a high-efficiency single-input multiple-output (SIMO) dc–dc converter. The proposed converter can boost the voltage of a low-voltage input power source to a controllable high-voltage dc bus and middle-voltage output terminals. The high-voltage dc bus can take as the main power for a high-voltage dc load or the front terminal of a dc–ac inverter.Moreover, middle-voltage output terminals can supply powers for individual middle-voltage dc loads or for charging auxiliary power sources (e.g., battery modules). In this project, a coupled-inductor based dc–dc converter scheme utilizes only one power switch with the properties of voltage clamping and soft switching, and the corresponding device specifications are adequately designed. As a result, the objectives of high-efficiency power conversion, high step up ratio, and various output voltages with different levels can be obtained
A New Single-Stage Multilevel Type Full-Bridge Converter Applied to closed lo...IOSR Journals
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A Novel Approach of Position Estimation and Power Factor Corrector Converter ...IJPEDS-IAES
This paper proposes a Power factor Corrected (PFC) Bridgeless Buck-Boost converter fed BLDC motor drive. The Bridgeless configuration eliminates the Diode Bridge Rectifier in order to reduce the number of components and the conduction loss. The position sensors used in BLDC drives have drawbacks of additional cost, mechanical alignment problems. These bottle necks results in sensorless technique. The Sensorless technique mostly relies on measurement of Back EMF to determine relative positions of stator and rotor for the correct coil energising sequence can be implemented. This paper introduces the offline Finite Element method for sensorless operation. The proposed sensorless scheme estimates the motor position at standstill and running condition. The obtained Power Factor is within the acceptable limits IEC 61000-3-2. The proposed drive is simulated in MATLAB/Simulink the obtained results are validated experimentally on a developed prototype of the drive.
High efficiency zcs single input multiple output simo d.c to dIAEME Publication
This document summarizes a research paper presented at the International Conference on Emerging Trends in Engineering and Management. The paper proposes a new single-input multiple-output DC-DC converter topology that can boost a low voltage input to multiple isolated outputs using only one switch. This converter uses a coupled inductor and fuzzy logic controller to achieve high efficiency and zero current switching. Simulation and experimental results are presented to validate the design and performance of the proposed converter. The converter is well-suited for powering multi-level inverters with multiple isolated inputs.
Closed Loop Analysis of Single-Inductor Dual-Output Buck Converters with Mix-...IOSR Journals
This document presents an analysis of closed loop operation of single-inductor dual-output buck converters. It begins with an overview of these converters and their applications. It then analyzes the circuit operation in both continuous and discontinuous conduction modes, developing equations for voltage gains, duty cycles, and other parameters. Most importantly, it identifies a new "mix-voltage" operation mode where the input voltage can be lower than one output voltage. Experimental results are presented to validate the analytical equations and this new operating mode.
This paper proposed a new sparce matrix converter with Z-source network to provide unity voltage transfer ratio. It is an ac-to-ac converter with diode-IGBT bidirectional switches. The limitations of existing matrix converter like higher current THD and less voltage transfer ratio issues are overcome by this proposed matrix converter by inserting a Z-source. Due to this Z-source current harmonics are totally removed. The simulation is performed for different frequencies. The simulation results are presented to verify the THD and voltage transfer ratio and compared with the existing virtual AC/DC/AC matrix converter. The experimental output voltage amplitude can be varied with the variable frequencies.
International Journal of Engineering Research and DevelopmentIJERD Editor
This document describes a novel bidirectional DC-DC converter that can provide high step-up and step-down voltage gains. It utilizes a coupled inductor with the same number of turns in the primary and secondary windings to achieve these high voltage gains. The steady-state analysis and operating principles of the converter in continuous conduction mode are presented. Simulations in MATLAB are used to verify the performance of the proposed converter and show it can provide constant output voltage when feedback is applied. Compared to a conventional bidirectional DC-DC converter, the proposed design offers higher voltage conversion ratios in both step-up and step-down modes of operation.
International Refereed Journal of Engineering and Science (IRJES)irjes
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Iaetsd analysis of zvs, zcs interleaved boost - converterwith ac driveIaetsd Iaetsd
The document analyzes an interleaved boost converter with zero-voltage switching and zero-current switching for improved efficiency. An interleaved boost converter uses two or more boost converters operating in parallel to reduce ripple and improve efficiency. The proposed design adds an auxiliary circuit to achieve soft switching, reducing switching losses. It can operate with duty cycles greater than or less than 50% and maintains low voltage stress on the main switches. Analysis of the circuit operation shows it achieves zero-voltage turn-on and zero-current turn-off of the main switches through resonant charging and discharging of parasitic capacitances during the switching transitions. Simulations and experimental results demonstrate improved efficiency over 90% across a range of loads.
This paper presents a new single switched inductor-capacitor coupled transformer-less high gain DC-DC converter which can be used in renewable energy sources like PV, fuelcell in which the low DC output voltage is to be converted into high dc output voltage. With the varying low input voltages, the output of DC-DC converter remains same and does not change. A state space model of the converter is also presented in the paper. This constant output voltage is obtained by close loop control of converter using PID controller. High voltage gain of 10 is obtained without use of transformer. All the simulations are done in MATLAB-SIMULINK environment.
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1. Modelling of DC-DC converters 125
X
Modelling of DC-DC converters
Ovidiu Aurel Pop and Serban Lungu
Technical University of Cluj-Napoca
Romania
1. Introduction
The DC-DC converters are electrical circuits that transfer the energy from a DC voltage
source to a load and regulate the output voltage. The energy is transferred via electronic
switches, made with transistors and diodes, to an output filter and than is transferred to the
load.
DC-DC converters are used to convert unregulated dc voltage to regulated or variable dc
voltage at the output. They are widely used in switch-mode dc power supplies and in dc
motor drive applications. In dc motor control applications, they are called chopper-controlled
drives. The input voltage source is usually a battery or derived from an ac power supply
using a diode bridge rectifier. These converters are generally either hard-switched PWM
types or soft-switched resonant-link types.
These converters employ square-wave pulse width modulation to achieve voltage
regulation. The output voltage is regulated varying the duty cycle of the power
semiconductor switch driving signal. The voltage waveform across the switch and at the
input of the filter is square wave in nature and they generally result in higher switching
losses when the switching frequency is increased. Also, the switching stresses are high with
the generation of large electromagnetic interference (EMI), which is difficult to filter.
However, these converters are easy to control, well understood, and have wide load control
range.
These converters operate with a fixed-frequency, variable duty cycle. This type of signal is
called Pulse Width Modulated signal (PWM). Depending on the duty cycle, they can operate
in either continuous current mode (CCM) or discontinuous current mode (DCM). If the
current through the output inductor never reaches zero then the converter operates in CCM;
otherwise DCM occurs.
The output voltage will be equal with the average value on the switching cycle of the
voltage applied at the output filter. Due to the losses on the ON or OFF state of the ideal
transistor are zero, the theoretical efficiency of the switching mode converters is up to 100%.
But, considering the real switches, with parasitic elements, the efficiency will be a little bit
lower, but higher than linear regulators.
Another advantage of switching mode converters consist in the possibility to use the same
components but in other topology in order to obtain different values of the output voltages:
positive or negative, lower or higher than input voltage.
7
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2. Matlab - Modelling, Programming and Simulations
126
There are various analysis methods of DC-DC converters. Throughout the chapter an
extended analysis and modelling for DC-DC power converters is proposed. In this
approach, the differential equations that describe the inductor current and capacitor voltage
are determined and are solved according with the boundary conditions of the switching
periods. The values of currents and voltages at the end of a period become initial conditions
for the next switching period. This method is very accurate and produces a set of equations
that require extensive computation.
In addition, for specified values of converter parameters (inductance and capacitor) we can
calculate the maximum value of transistor and diode current and reverse voltage, in order to
help user to choose the appropriate type of transistor and diode.
2. Buck converter
The buck (or step-down converter), shown in the figure 1, contain a capacitor and an
inductor with role of energy storing, and two complementary switches: when one switch is
closed, the other is open and vice-versa.
Fig. 1. The buck converter diagram
The switches are alternately opened and closed with at a rate of PWM switching frequency.
The output that results is a regulated voltage of smaller magnitude than input voltage. The
converter operation will be analyzed function of switches states.
The first time interval: The transistor is in ON state and diode is OFF.
During this time period, corresponding with duty cycle of PWM driving signal, the
equivalent diagram of the circuit is presented bellow:
Fig. 2. The equivalent circuit during the ON state of transistor and OFF state of diode
www.intechopen.com
3. Modelling of DC-DC converters 127
For this equivalent circuit will write the equations that describe the converter operation:
1
( ) ;
;
o o
L
L o
du u
i
dt R C
di E u
dt L
(1)
The second time period: the transistor is OFF and diode is ON
In the moment when the transistor switch in OFF state, the voltage across the inductor will
change the polarity and the diode will switch in ON state. The equivalent diagram of
converter during this period is shown in the bellow figure:
E
L
C R
i
u
L
C
L
u
uo
iR
i C
Fig. 3. The equivalent circuit for OFF state of transistor and ON state of diode
For this operation period, the output voltage u0 and the current through the inductor iL
satisfy the following equations:
1
;
;
o o
L
L o
du u
i
dt R C
di u
dt L
(2)
The third operation mode: The both transistor and diode are OFF
If the inductor current becomes zero before ending the diode ON period, both transistor and
diode will naturally closed. This operation regime is called discontinuous current mode. The
equivalent diagram of this operation regime is shown bellow.
E
L
C R
u
C
L
u
uo
iR
i C
Fig. 4. The equivalent circuit with transistor and diode in OFF state
www.intechopen.com
4. Matlab - Modelling, Programming and Simulations
128
For this operation period, the output voltage uo and the current through the inductor iL
satisfy the following equations:
1
;
0;
o o
L
du u
dt R C
di
dt
(3)
2.1 CCM inductance
The minimum value of inductance for continuous current mode (CCM) operation is
calculated from output voltage and inductor current equations.
Thus, the output voltage uo and the current through the inductor iL satisfies the following
equations:
........ 0,
............ ,
L
L
u E Uo t D T
u Uo t D T T
(4)
........... 0,
............... ,
L
L
E Uo
i t t D T
L
Uo
i t t D T T
L
(5)
The waveforms of inductor voltage and current on a switching period are shown in the
figure 5:
Fig. 5. The waveforms of output voltage and inductor current
In the steady state regime, the average value of voltage across the inductor is zero. Thus,
E
D
Uo
D
T
Uo
T
D
Uo
E
1 (6)
Based on the inductor current waveform, the following equation can be write:
max min
L L
E Uo
I I D T
L
(7)
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5. Modelling of DC-DC converters 129
The average value of the inductor current is equal with the output current:
max min
2
L L o
o
I I U
I R
R
(8)
From the equations (7) and (8) results the minimum ad the maximum values of inductor
current.
min
2
o o
L
U E U
I D T
R L
(9)
max
2
o o
L
U E U
I D T
R L
(10)
Thus:
max min
o
L L
E U
i I I D T
L
(11)
From the equations (6) and (11) the inductor current ripple can be calculated.
T
L
D
D
E
i
1
(12)
From the condition, min 0
L
I , it results:
2
1
L
D
RT
. (13)
This relation can be used to determine the minimum value of inductance, when the
switching frequency and load value are known.
D
T
R
L
1
2
min
(14)
2.2 The discontinuous current mode
In discontinuous current regime, the waveforms of inductor voltage and current are shown
in the figure bellow:
Fig. 6. The waveforms of voltage and inductor current in DCM
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6. Matlab - Modelling, Programming and Simulations
130
The average value of the input current is equal with the current through the switching
transistor.
max
1
2
iav L
I T D T I
(15)
max
o
L
E U
I D T
L
(16)
From the above equations, it results:
2
2
o
iav
E U
I D T
L
. (17)
Considering that there are no losses in the circuit, the input and the output powers are
equals.
2
o
in out iav
U
P P E I
R
(18)
Thus,
2
2
2
o o
U E U
E D T
R L
(19)
2
2
2
1
2
o o
U RT U
D
L E
E
(20)
Denoting the circuit transfer ratio
E
Us
=M:
2 2
2
0
2 2
R T D R T D
M M
L L
(21)
Denoting a=
L
T
D
R
2
2
, (22)
the solutions of the above equation are :
2
4
2
a a a
M
. (23)
Analyzing those solutions, can be observed that the single valid solution is
2
4
2
a a a
M
(24)
The variation of circuit transfer ratio M function of PWM signal duty-cycle D, for different
values of
2L
RT
parameters is shown in the figure:
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7. Modelling of DC-DC converters 131
Fig. 7. Variation of circuit transfer ratio M function of PWM signal duty-cycle D
2.3 Filtering capacitor
Other important parameter that is important to be determined is the value of the output
capacitor, in order to obtain a specific value of the output voltage ripple.
The capacitor charging current is equal with difference between the inductor current iL and
the output current iO. Considering a constant output current, the electric charge stored in the
capacitor during a switching period is equal with the shade area from the figure bellow:
Fig. 8. The waveforms of inductor current and output voltage
max 1 2
1
( )( )
2
L O
Q u C I I t t
(25)
1 2 1 2 max
max min
1
L O
L L
t t t t I I
DT D T T I I
(26)
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8. Matlab - Modelling, Programming and Simulations
132
Thus, the value of the output capacitor can be calculated with the following formula:
2
2
1
8 8
O
E U DT E D D
C
L u Lf u
(27)
It can be seen in this formula that the capacitor value depends by the switching frequency.
Increasing the switching frequency, the capacitor value will be smaller.
3. Boost Converter
The boost (or step-up converter), shown in the figure 9, contains, like the Buck converter, a
capacitor and an inductor with role of energy storing, and two complementary switches. In
the case of the boost converter, the output voltage is higher than the input voltage.
Fig. 9. The boost converter diagram
The switches are alternately opened and closed with at a rate of PWM switching frequency.
As long as transistor is ON, the diode is OFF, being reversed biased. The input voltage,
applied directly to inductance L, determines a linear rising current. When transistor is OFF,
the load is supplied by both input source and LC filter. The output that results is a regulated
voltage of higher magnitude than input voltage. The converter operation will be analyzed
according with the switches states.
The first time interval: The transistor is in ON state and diode is OFF.
During this time period, corresponding with duty cycle of PWM driving signal, the
equivalent diagram of the circuit is presented bellow. In this time period the inductance L
store energy.
E
L
C
i
u
L
C
L u u
o
iR
R
Fig. 10. The equivalent circuit during the ON state of transistor and OFF state of diode
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9. Modelling of DC-DC converters 133
For this operation period, the output voltage uo and the current through the inductor iL
satisfies the following equations:
;
;
L
o o
di E
dt L
du u
dt R C
(28)
The second time period: the transistor is OFF and diode is ON
In the moment when the transistor switch in OFF state, the voltage across the inductor will
change the polarity and diode will switch in ON state. The equivalent diagram of converter
during this period is shown in the bellow figure:
Fig. 11. The equivalent circuit for OFF state of transistor and ON state of diode
For this operation period, the output voltage uo and the current through the inductor iL
satisfy the following equations:
;
1
;
L o
o o
L
di E u
dt L
du u
i
dt C R
(29)
The third operation mode: The both transistor and diode are OFF
If the inductor current becomes zero before ending the diode conduction period, both the
transistor and the diode will be in OFF state. Due to the diode current becomes zero, the
diode will naturally close, and the output capacitor will discharge on the load. This
operation regime is called discontinuous current mode. The equivalent diagram of this
operation regime is shown bellow.
E
L
C R
u
C
L
u
uo
iR
i C
Fig. 12. The equivalent circuit with transistor and diode in OFF state
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10. Matlab - Modelling, Programming and Simulations
134
For this operation period, the output voltage uo and the current through the inductor iL can
be calculated from the following equations:
0;
;
L
o o
di
dt
du u
dt R C
(30)
3.1 CCM inductance
The minimum value of inductance for continuous current mode (CCM) operation is
calculated from inductor current equation. In the steady state regime, the average value of
voltage across the inductor is zero.
Fig. 13. The waveforms of inductor voltage and current in steady-state regime
Thus, the output voltage u0 and the current through the inductor iL satisfies the following
equations:
D
E
Uo
E
Uo
D
T
T
D
E
1
;
1 (31)
Based on the above waveforms, the maximum value of the inductor current is:
T
D
L
E
i
i L
L
min
max
(32)
The output current is equal with the diode average current:
max min
1
2
L L o
i i U
T D T
R
(33)
Based on the equations (32) and (33), results:
max
1 2
o
L
U E D T
i
R D L
(34)
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11. Modelling of DC-DC converters 135
min
1 2
o
L
U E D T
i
R D L
(35)
Based on the equations (34) and (35), can be determined the inductor current ripple:
E D T
i
L
(36)
From the condition for continuous conduction mode, 0
min
L
i , results:
2
2
1
L
D D
R T
(37)
This condition can be used to determine the minimum inductance value, for a specific
switching period T and a specific load value R.
2
min 1
2
R T
L D D
(38)
3.2 The discontinuous current mode
In discontinuous conduction mode, the waveforms of the inductor voltage and current are
shown in the figure bellow:
Fig. 14. The waveforms of voltage and inductor current in DCM
The average value of the input current is equal with the inductor average current.
1
max
2
1
t
T
D
I
T
I L
iav
(39)
where
L
T
D
E
IL
max
. (40)
Based on the equations (39) and (40), results:
1
2
t
T
D
L
D
E
I av
i
(41)
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12. Matlab - Modelling, Programming and Simulations
136
The average value of the inductor voltage during a switching period is zero.
E
Uo
t
T
D
E
1 ;
E
U
T
D
E
t
0
1 (42)
Replacing equation (42) in the equation (41), and also considering the input and the output
power equals,
av
i
out
in I
E
R
Uo
P
P
2
(43)
it results:
L
R
T
D
E
Uo
E
Uo
2
1
2
. (44)
Denoting the voltage transfer ratio with M=
E
Uo
, the equation (44) becomes:
2
1
2
D T R
M M
L
(45)
The solution of this equation is:
2
4
1 1
2
2
D T R
L
M
(46)
The variation of circuit transfer ratio M function of PWM signal duty-cycle D, for different
values of
2L
RT
parameters is shown in the figure:
Fig. 15. Variation of circuit transfer ratio M function of PWM signal duty-cycle D
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13. Modelling of DC-DC converters 137
3.3 Filtering capacitor
Other important parameter that is important to be determined is the value of the output
capacitor, in order to obtain a specific value of the output voltage ripple.
The capacitor charging current is equal with the difference between the diode current iD and
the output current io. Considering a constant output current, the electric charge stored in the
capacitor during a switching period is equal with the shade area from the figure bellow:
Fig. 16. The waveforms of inductor current and output voltage
max 2
1
( )
2
L o
Q C u I I t
(47)
2 max
max min
(1 )
L o
L L
t I I
T D I I
(48)
Thus, the value of the output capacitor can be calculated with the following formula:
2
max
max min
(1 )
2
L o
L L
I I T D
C
I I
(49)
4. Buck-Boost converter
The buck-boost converter (polarity inverter) is shown in figure 17.
Fig. 17. Buck-Boost converter diagram
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14. Matlab - Modelling, Programming and Simulations
138
The switches are alternately opened and closed with at a rate of PWM switching frequency.
As long as the transistor is ON, the diode is OFF, being reversed biased. The input voltage,
applied directly to inductance L, determines a linear rising current. The capacitor is
discharged on the load circuit. When the transistor is OFF, the load is supplied by LC filter.
The output that results is a regulated voltage of smaller or higher magnitude than input
voltage, depending on the value of duty cycle, but it has a reverse polarity. The converter
operation will be analyzed according with the ON or OFF state of switches.
The first time interval: The transistor is in ON state and diode is OFF.
During this time period, corresponding with duty cycle of PWM driving signal, the
equivalent diagram of the circuit is presented bellow. In this time period the inductance L
stores energy. The load current is assured by the output capacitor.
Fig. 18. The equivalent circuit during the ON state of transistor and OFF state of diode
For this operation period, the output voltage uo and the current through the inductor iL are
given by the following equations system:
L
o o
di
E
dt
du u
dt R C
(50)
The second time period: the transistor is OFF and diode is ON
In the moment when the transistor switch in OFF state, the voltage across the inductor will
change the polarity and diode will switch in ON state. The energy stored in the inductor will
supply the load. The equivalent diagram of converter during this period is shown in the
figure bellow:
Fig. 19. The equivalent circuit during the OFF state of transistor and ON state of diode
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15. Modelling of DC-DC converters 139
For this operation period, the following equations for the output voltage uo and the current
through the inductor iL can be written:
1
L o
o o
L
di u
dt L
du u
i
dt R C
(51)
The third operation mode : The both transistor and diode are OFF
If the inductor current becomes zero before ending the diode ON period, both the transistor
and the diode will be OFF. Due to the diode current becomes zero, the diode will naturally
close, and the output capacitor will discharge on the load. This operation regime is called
discontinuous current mode. The equivalent diagram of this operation regime is shown bellow.
Fig. 20. The equivalent diagram for discontinuous conduction mode operation
For this operation mode, the output voltage uo and the current through the inductor iL can be
calculated from the following differential equations:
0
L
o o
di
dt
du u
dt R C
(52)
4.1 CCM inductance
The minimum value of the inductance for continuous current mode (CCM) operation is
calculated from the the inductor current equations.
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16. Matlab - Modelling, Programming and Simulations
140
Fig. 21. The inductor voltage and current waveforms in steady-state regime
In the steady state regime, the average value of the voltage across the inductor is zero. From
this condition, the output voltage Uo can be determined:
D
D
E
Uo
D
Uo
D
E
D
T
Uo
T
D
E
1
1
1
(53)
Based on the above waveforms:
max min
L L
E
I I D T
L
(54)
Also, the average diode current is equal with the output current.
max min 1
2
L L o
I I U
T D T
R
(55)
Based on the equations (54) and (55), the maximum and the minimum value of the inductor
current will be:
max
1 2
o
L
U E D T
I
R D L
(56)
min
1 2
o
L
U E D T
I
R D L
(57)
Thus, the inductor current ripple is:
E D T
i
L
(58)
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17. Modelling of DC-DC converters 141
From the condition for continuous conduction mode, 0
min
L
i , results:
2
2
1
L
D
RT
(59)
This condition can be used to determine the minimum inductance value, for a specific
switching period T and a specific load value R.
2
1 2
min
D
T
R
L
(60)
4.2 The discontinuous current mode
In discontinuous conduction mode, the waveforms of the inductor voltage and current are
shown in the figure bellow:
Fig. 22. The waveforms of voltage and inductor current in DCM
The average value of the input current is equal with the transistor average current.
max
1
2
av
i L
I T I D T
(61)
where,
max
L
E D T
I
L
(62)
From the above equations results:
2
2
av
i
E D T
I
L
(63)
Neglecting the losses in the circuit, the input power is equal with the output power.
2
av
o
in out i
U
P P E I
R
(64)
2 2 2
2
o
E D T U
L R
(65)
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18. Matlab - Modelling, Programming and Simulations
142
Denoting the voltage transfer ratio
E
Uo
=M , it results:
2
R T
M D
L
(66)
The variation of circuit transfer ratio M function of PWM signal duty-cycle D, for different
values of
2L
RT
parameters is shown in the figure:
Fig. 23. Variation of circuit transfer ratio M function of PWM signal duty-cycle D
4.3 Filtering capacitor
Other important parameter that must be determined is the value of the output capacitor, in
order to obtain a specific value of the output voltage ripple.
The capacitor charging current is equal with difference between the diode current iD and the
output current io. Considering a constant output current, the electric charge stored in the
capacitor during a switching period is equal with the shade area from the bellow figure:
Fig. 24. The waveforms of the inductor current and output voltage
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19. Modelling of DC-DC converters 143
max 2
1
( )
2
L o
Q C u I I t
(67)
2 max
max min
(1 )
L o
L L
t I I
T D I I
(68)
The value of the output capacitor can be calculated with the following formula:
2
max
max min
(1 )
2
L o
L L
I I T D
C
I I
(69)
5. Matlab Modeling of DC-DC Converters
In order to simulate the converters, the equations that describe the converter operation on
each of the three possible operating stages are implemented in Matlab, and solved using
Matlab facilities.
The program structure consists in two files. The first file initializes the default values of
converter parameters: the input voltage E, the inductance value L, the capacitor value C, the
load value R, the switching period T, the duty-cycle D and the number of periods to be
displayed. All the parameters can be changed during the converters simulation. The
structure of this file is:
Listing for initialization of default parameters values
clear all;
close;
E=10; %input voltage value
L=1e-4; %inductor value
C=10e-6; %capacitor value
R=10; %load value
%---------------------
Q=sqrt(L./C)./R;
T0=2.*pi.*sqrt(L.*C);
%------------
T=50e-6; %switching period
D=0.5; %duty-cycle
N=20; %numbers of periods to be displayed
%---------------
p=1; % default plotting regime (transient)
%--------------------
type=1; % default analyzed converter -Buck
%type=2; % Boost
%type=3; % Buck-Boost
%----------------
ed_converter(E,L,C,R,T,D,N,p,type); % function for converters simulation
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20. Matlab - Modelling, Programming and Simulations
144
As it can be seen at the end of the file, the ed_converter(E,L,C,R,T,D,N,p,type) function is
called. This function is implemented in a file with the same name, and had as arguments the
converter parameters. In the first part of the file are created the buttons that allow to change
the values of the converter parameters. Than, are implemented the functions that solve the
differential equations that describe the converter operation and are calculated the critical
values of inductor for continuous conduction mode operation and value of output voltage.
Also, are defined the plots for output voltage and input current.
The structure of this file is presented bellow:
Listing of function file
function ed_converter(E,L,C,R,T,D,N,p,type);
%create a new figure;
Fig=figure('Name',' DC-DC Converters',...
'Numbertitle','off', 'color', [1, 1, 1]);
% creating 7 text buttons B_T;
txt=['E [V] L[ H] C[ F] R[ohm] T[ s] D N '];
for k=1:7
B_T(k)=uicontrol('Style','text', ...
'Units','normalized', ...
'backgroundcolor',[1, 1, 1],...
'Position',[0.91 0.95-0.1.*(k-1) 0.10 0.04], ...
'String',txt((7.*(k-1))+1:7.*k), ...
'Callback','close; ');
end
% Creating 7 Edit buttons B_E ;
var=['E';'L';'C';'R';'T';'D';'N'];
val=[E;L;C;R;T;D;N];
xc= '=str2num(get(gco,''String''));close;ed_converter(E,L,C,R,T,D,N,p,type)';
for i=1:7
B_E= uicontrol('Style','edit',...
'Units','normalized',...
'backgroundcolor',[1, 1, 0],...
'Position',[0.91 0.90-0.1*(i-1) 0.10 0.04],...
'String',val(i),...
'Callback',cat(2,var(i),xc));
end
%Creating the control buttons for selection of converter type: Buck, Boost or Buck-Boost
Buck=uicontrol('Style','pushbutton',...
'Units','normalized',...
'Position',[0.05 0.01 0.17 0.04],...
'String','Buck',...
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21. Modelling of DC-DC converters 145
'backgroundcolor',[0, 1, 0.5],...
'Callback','type=1,close;ed_converter(E,L,C,R,T,D,N,p,type)');
Boost=uicontrol('Style','pushbutton',...
'Units','normalized',...
'Position',[0.25 0.01 0.17 0.04],...
'String','Boost',...
'backgroundcolor',[0, 1, 0.5],...
'Callback','type=2,close;ed_converter(E,L,C,R,T,D,N,p,type)');
Buck_Boost=uicontrol('Style','pushbutton',...
'Units','normalized',...
'Position',[0.45 0.01 0.17 0.04],...
'String','BuckBoost',...
'backgroundcolor',[0, 1, 0.5],...
'Callback','type=3,close;ed_converter(E,L,C,R,T,D,N,p,type)');
%----------------
Bp=uicontrol('Style','pushbutton',...
'Units','normalized',...
'Position',[0.01 0.92 0.19 0.04],...
'String','Steady-State Regime',...
'backgroundcolor',[0, 1, 1],...
'Callback','p=0;close;ed_converter(E,L,C,R,T,D,N,p,type)');
if p==0
set(Bp,'String','Transient Regime');
set(Bp,'Callback','p=1,close;ed_converter(E,L,C,R,T,D,N,p,type)');
end
% When a button is pushed, the callback will call again the function file with the
newer parameters
%Routine for solving the function ec_conv, that describes the converters operation
t=0;
y=[0 0];
for k=1:N
nt=length(t);
t0=(k-1).*T;
tf=t0+D.*T;
ci=y(nt,:);
interval=1;
[t,y]=ode45(@ec_conv,[t0,tf],[ci],[],E,R,L,C,type,interval);
nt=length(t);
%Setting the plots
subplot('Position',[0.10 0.55 0.80 0.35]);
plot(t,y(:,1),'r');grid on;hold on;
subplot('Position',[0.10 0.15 0.80 0.35]);
plot(t,y(:,2),'r');grid on;hold on;
%---------------------interval=2;
t0=(k-1).*T+D.*T;
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22. Matlab - Modelling, Programming and Simulations
146
tf=k.*T;
ci=y(nt,:);
interval=2;
options=odeset('Events',@conv_ev);
[t,y,te,ye,ie]=ode45(@ec_conv,[t0,tf],[ci],[options],E,R,L,C,type,interval);
nt=length(t);
%-----------------------
subplot('Position',[0.10 0.55 0.80 0.35]);
plot(t,y(:,1),'b');grid on;hold on;
subplot('Position',[0.10 0.15 0.80 0.35]);
plot(t,y(:,2),'b');grid on;hold on;
%----------------------------interval=3;
if te>0;
t0=t(nt);
tf=k.*T;
ci=y(nt,:);
interval=3;
[t,y]=ode45(@ec_conv,[t0,tf],[ci],[],E,R,L,C,type,interval);
%-----------------------
subplot('Position',[0.10 0.55 0.80 0.35]);
plot(t,y(:,1),'g');grid on;hold on;
subplot('Position',[0.10 0.15 0.80 0.35]);
plot(t,y(:,2),'g');grid on;hold on;
%---------------------
end
if (p==0)&(j<N-1)
subplot('Position',[0.10 0.55 0.80 0.35]);
hold off;
end
if (p==0)&(j<N-1)
subplot('Position',[0.10 0.15 0.80 0.35]);
hold off;
end
end
%========================================
subplot('Position',[0.10 0.55 0.80 0.35]);
ylabel(['iL [ A ]']);
switch type;
case 1
Lm=R.*T.*(1-D)./2; %Calculating the minimum value of inductance for Buck Converter
if 2.*L./(R.*T)>=1-D
Uo=E.*D; %Calculating the output voltage in Continuous conduction mode
else
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23. Modelling of DC-DC converters 147
z=0.5.*R.*D.^2.*T./L;
v=0.5.*(sqrt(z.^2+4.*z)-z);
Uo=v.*E; %Calculating the output voltage in Discontinuous conduction mode
end
title(['Buck Converter',' Uo = ',num2str(Uo),' [ V ]',' Lm = ',num2str(Lm),' [ H ]']);
case 2
Lm=R.*T.*D.*(1-D).^2./2; %Calculating the minimum value of inductance for
Boost Converter
di=E.*D.*T./L;
if 2.*L./(R.*T)>=D*(1-D).^2
Uo=E./(1-D); %Calculating the output voltage in Continuous conduction mode
else
v=0.5.*(1+sqrt(1+2.*D.^2.*T.*R./L));
Uo=v.*E; %Calculating the output voltage in Discontinuous conduction mode
end
title(['Boost Converter',' Uo = ',num2str(Uo),' [ V ]',' Lm = ',num2str(Lm),' [ H ]']);
case 3
Lm=R.*T.*(1-D).^2./2, %Calculating the minimum value of inductance
for Buck-Boost Converter
if 2.*L./(R.*T)>=(1-D).^2
Uo=E.*D./(1-D); %Calculating the output voltage in Continuous conduction mode
else
v=D.*sqrt(0.5.*T.*R./L);
Uo=v.*E; %Calculating the output voltage in Discontinuous conduction mode
end
title(['Buck-Boost Converter',' Uo = ',num2str(Uo),' [ V ]',' Lm = ',num2str(Lm),' [ H ]']);
end
subplot('Position',[0.10 0.15 0.80 0.35]);
ylabel(['Uo = uC [ V ]']);
xlabel(['t [ s ]']);
%Function that describes the converters operation
function dy=ec_conv(t,y,E,R,L,C,type,interval);
dy=zeros(2,1);
switch type;
case 1
if interval==1
a=1;b=1;c=1;
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24. Matlab - Modelling, Programming and Simulations
148
elseif interval==2
a=0;b=1;c=1;
else
a=0;b=0;c=0;
end
case 2
if interval==1
a=1;b=0;c=0;
elseif interval==2
a=1;b=1;c=1;
else
a=0;b=0;c=0;
end
case 3
if interval==1
a=1;b=0;c=0;
elseif interval==2
a=0;b=1;c=1;
else
a=0;b=0;c=0;
end
end
dy(1)=(a.*E-b.*y(2))./L; % Current equation
dy(2)=(c.*y(1)-y(2)./R)./C; % Voltage equation
%===========================================================
function [value,isterminal,direction] =conv_ev(t,y,E,R,L,C,type,interval);
value = y(1); % detect iL = 0
isterminal = 1; % stop the integration
direction = -1; % negative direction
As it can be seen in the converters description, for all types of converters, the equation that
describes the operation has the same shape. The difference consists in the value of the
coefficients. From this reason, the same equations are used for the simulation of the
converters operation and from each converter only the value of a, b, and c coefficients are
set. The equations system is:
1
( )
L o
o o
L
di a E b u
dt L
du u
c i
dt R C
(70)
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25. Modelling of DC-DC converters 149
The simulation results of the dc-dc converters are presented in the following figure:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10
-3
-1
0
1
2
3
iL
[
A
]
Buck Converter Uo = 5.3759 [ V ] Lm = 0.000125 [ H ]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10
-3
0
2
4
6
8
10
Uo
=
uC
[
V
]
t [ s ]
Fig. 25. The converters simulation results
As can be seen in the figure, from the upper left side button can be chosen the display mode:
transient, when all the simulated periods are plotted or steady state regime when only the
last simulated period is plotted.
From the right site editing buttons, all of the converter parameters can be set. From the
bottom side it can be selected the desired converter: buck, boost or buck-boost. Also, for
each converter type, the program displays the output voltage value and the minimum
inductance value in order to obtain continuous current mode operation.
6. References
Attaway, S (2009). Matlab: A Practical Introduction to Programming and Problem Solving, 480
pages, Butterworth Heinemann, ISBN 978-0-7506-8762-1, USA
Attia, J. (1999). Electronics and Circuits Analysis using Matlab, 378 pages, CRC Press, ISBN 0-
8493-1176-4, USA
Erickson, R.W. & Macksimovic, D. (2001). Fundamentals of Power Electronics, Second ed., 920
pages, Kluver Academic Publisher, ISBN 0-7923-7270-0, USA
Mohan, N. & Undeland, T.M. (2003). Power Electronics: Converters, Applications and Design.
Third Ed., 802 pages, John Wiley & Sons, ISBN 0-4714-2902-2, USA
Lungu, S. & Pop, O.A. (2006). Modelling of Electronics Circuits, 133 pages, Science Books
House, ISBN 978-973-686-975-4, Romania
Schaffer, R. (2007). Fundamentals of Power Electronics with Matlab, 384 pages, Charles River
Media, ISBN 1-58450-853-3, USA
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27. Matlab - Modelling, Programming and Simulations
Edited by Emilson Pereira Leite
ISBN 978-953-307-125-1
Hard cover, 426 pages
Publisher Sciyo
Published online 05, October, 2010
Published in print edition October, 2010
InTech Europe
University Campus STeP Ri
Slavka Krautzeka 83/A
51000 Rijeka, Croatia
Phone: +385 (51) 770 447
Fax: +385 (51) 686 166
www.intechopen.com
InTech China
Unit 405, Office Block, Hotel Equatorial Shanghai
No.65, Yan An Road (West), Shanghai, 200040, China
Phone: +86-21-62489820
Fax: +86-21-62489821
This book is a collection of 19 excellent works presenting different applications of several MATLAB tools that
can be used for educational, scientific and engineering purposes. Chapters include tips and tricks for
programming and developing Graphical User Interfaces (GUIs), power system analysis, control systems
design, system modelling and simulations, parallel processing, optimization, signal and image processing,
finite different solutions, geosciences and portfolio insurance. Thus, readers from a range of professional fields
will benefit from its content.
How to reference
In order to correctly reference this scholarly work, feel free to copy and paste the following:
Ovidiu Pop and Serban Lungu (2010). Modeling of DC-DC Converters, Matlab - Modelling, Programming and
Simulations, Emilson Pereira Leite (Ed.), ISBN: 978-953-307-125-1, InTech, Available from:
http://www.intechopen.com/books/matlab-modelling-programming-and-simulations/modeling-of-dc-dc-
converters-