This chapter discusses the design of inductors and coupled inductors. It presents the key constraints in inductor design including maximum flux density, inductance, winding area, and winding resistance. It then provides a step-by-step design procedure that involves selecting a core, determining the air gap length, number of turns, and wire size. Methods for designing multiple-winding magnetics using the Kg method are also described, including how to allocate window area between windings to minimize copper losses.
Design, Modeling and control of modular multilevel converters (MMC) based hvd...Ghazal Falahi
This document outlines the design, modeling, and control of modular multilevel converter (MMC) based HVDC systems. It begins with background information on MMC technology and discusses state of the art MMC systems using IGBT devices that have higher losses than desired. The document then proposes a design procedure for an MMC-HVDC system using emerging ETO semiconductor devices, which are expected to have lower losses than IGBTs. It provides details on the MMC topology, mathematical modeling, control schemes, modulation methods, and proposes a new 60Hz modulation strategy along with a method to estimate losses for the system.
Mppt and mppt with pi converter based phtovoltic systemMadhu Kundu
This document discusses maximizing power output from a photovoltaic (PV) system using perturb and observe (P&O) and proportional-integral (PI) maximum power point tracking (MPPT) algorithms. It first provides background on solar cells, modules, and arrays. It then presents the mathematical modeling of a solar cell and simulations of equations describing current and voltage. The document shows simulation diagrams of a PV system using P&O and PI controllers, and results comparing the output power of each. It concludes that using PI control improved system performance and increased output power compared to P&O alone.
The presentation discusses the design of inverters used in solar systems. It describes three types of solar inverters: stand-alone inverters that power isolated systems from batteries charged by solar panels; grid-tie inverters that convert DC power from solar panels into AC to feed into the electrical grid; and battery backup inverters that can power loads during grid outages from batteries charged by excess solar energy. The presentation outlines the hardware components of inverters, including MOSFETs, transformers, voltage regulators, and PWM inverter ICs. It explains how solar panels generate DC power from sunlight and how inverters convert this to the AC power used in homes and businesses.
Power Backup Market in India 2018 - 2023 - Snippets of the Market Research Re...Research On Global Markets
The power backup market in India is characterized by the dominant presence of the unorganized sector. Wondering how it will affect the overall growth of the market? Check out the snapshot of our market research report on the Power Backup Market in India.
The document discusses the construction and operating principles of an Insulated Gate Bipolar Transistor (IGBT). It describes how the IGBT was developed from earlier power semiconductor devices like the IGT and COMFET. The IGBT cell contains a parasitic thyristor structure that must be controlled to prevent latch-up. In operation, the IGBT behaves like a MOSFET for gate control and can block high voltages like a BJT. It finds use in medium frequency, high voltage applications like motor drives and power supplies.
This document provides class notes on electromechanical energy conversion. It covers topics like principles of electro-mechanical energy conversion including energy flow diagrams and definitions. It also discusses DC machines including their construction, operation principles, torque and EMF equations. Performance characteristics of DC generators and motors are explained. Starting and speed control methods for DC motors are described. Testing of DC machines and transformers is also summarized.
Berdasarkan simulasi, pemasangan kapasitor 2 MVA dan pembangkit listrik tenaga mikrohidro 2x800 kVA memberikan perbaikan terbaik pada profil tegangan saluran OK-4. Analisis ekonomi menunjukkan bahwa pemasangan kapasitor memiliki masa bayar kembali tercepat yaitu kurang dari satu tahun, sedangkan pembangkit listrik dan penggantian kabel memiliki masa bayar kembali di bawah tiga tahun. Semua alternat
Design, Modeling and control of modular multilevel converters (MMC) based hvd...Ghazal Falahi
This document outlines the design, modeling, and control of modular multilevel converter (MMC) based HVDC systems. It begins with background information on MMC technology and discusses state of the art MMC systems using IGBT devices that have higher losses than desired. The document then proposes a design procedure for an MMC-HVDC system using emerging ETO semiconductor devices, which are expected to have lower losses than IGBTs. It provides details on the MMC topology, mathematical modeling, control schemes, modulation methods, and proposes a new 60Hz modulation strategy along with a method to estimate losses for the system.
Mppt and mppt with pi converter based phtovoltic systemMadhu Kundu
This document discusses maximizing power output from a photovoltaic (PV) system using perturb and observe (P&O) and proportional-integral (PI) maximum power point tracking (MPPT) algorithms. It first provides background on solar cells, modules, and arrays. It then presents the mathematical modeling of a solar cell and simulations of equations describing current and voltage. The document shows simulation diagrams of a PV system using P&O and PI controllers, and results comparing the output power of each. It concludes that using PI control improved system performance and increased output power compared to P&O alone.
The presentation discusses the design of inverters used in solar systems. It describes three types of solar inverters: stand-alone inverters that power isolated systems from batteries charged by solar panels; grid-tie inverters that convert DC power from solar panels into AC to feed into the electrical grid; and battery backup inverters that can power loads during grid outages from batteries charged by excess solar energy. The presentation outlines the hardware components of inverters, including MOSFETs, transformers, voltage regulators, and PWM inverter ICs. It explains how solar panels generate DC power from sunlight and how inverters convert this to the AC power used in homes and businesses.
Power Backup Market in India 2018 - 2023 - Snippets of the Market Research Re...Research On Global Markets
The power backup market in India is characterized by the dominant presence of the unorganized sector. Wondering how it will affect the overall growth of the market? Check out the snapshot of our market research report on the Power Backup Market in India.
The document discusses the construction and operating principles of an Insulated Gate Bipolar Transistor (IGBT). It describes how the IGBT was developed from earlier power semiconductor devices like the IGT and COMFET. The IGBT cell contains a parasitic thyristor structure that must be controlled to prevent latch-up. In operation, the IGBT behaves like a MOSFET for gate control and can block high voltages like a BJT. It finds use in medium frequency, high voltage applications like motor drives and power supplies.
This document provides class notes on electromechanical energy conversion. It covers topics like principles of electro-mechanical energy conversion including energy flow diagrams and definitions. It also discusses DC machines including their construction, operation principles, torque and EMF equations. Performance characteristics of DC generators and motors are explained. Starting and speed control methods for DC motors are described. Testing of DC machines and transformers is also summarized.
Berdasarkan simulasi, pemasangan kapasitor 2 MVA dan pembangkit listrik tenaga mikrohidro 2x800 kVA memberikan perbaikan terbaik pada profil tegangan saluran OK-4. Analisis ekonomi menunjukkan bahwa pemasangan kapasitor memiliki masa bayar kembali tercepat yaitu kurang dari satu tahun, sedangkan pembangkit listrik dan penggantian kabel memiliki masa bayar kembali di bawah tiga tahun. Semua alternat
This document discusses the design and construction of a 33/11 kV power line and substation. It provides details on the survey, layout, equipment, and sequence of construction. Key points include:
1. A survey is conducted to determine the optimal route for the power line, avoiding difficult terrain and areas of development.
2. Construction of the line involves digging poles, concreting, stringing conductors, and installing safety signs. The substation is built using equipment like transformers, circuit breakers, isolators, and busbars to transfer electricity between voltages.
3. Proper spacing must be maintained between the power line and other underground utilities or communication lines according to regulations.
This document describes an automatic power factor corrector system. It begins with an introduction to power factor, different types of power factor correction including static capacitors and synchronous condensers. It then discusses the importance of power factor correction including reduced utility charges and system losses. The document outlines the principles, sections, advantages of an automatic power factor correction system. It shows results for inductive and resistive loads before and after correction. It concludes that automatic power factor correction provides an efficient way to improve power factor through static capacitors.
The document describes modeling and simulation of a dynamic voltage restorer (DVR) for mitigating voltage sags and swells. A DVR is proposed as a cost-effective solution to protect sensitive loads from voltage fluctuations. The operation and equivalent circuit of a DVR are presented. Simulation results show that the DVR can satisfactorily compensate for both balanced and unbalanced voltage sags and swells, maintaining the load voltage at its nominal value.
Proteksi sistem tenaga listrik adalah sistem proteksi yang dipasang pada peralatan-peralatan listrik suatu sistem tenaga listrik, misalnya generator, transformator, jaringan dan lain-lain, terhadap kondisi abnormal operasi sistem itu sendiri. Kondisi abnormal itu dapat berupa antara lain: hubung singkat, tegangan lebih, beban lebih, frekuensi sistem rendah, asinkron dan lain-lain.
The document discusses converter configurations and analyzes a 12 pulse converter. It begins by explaining pulse number and valve/switch types in converters. It then discusses how converter configuration is selected based on pulse number to maximize valve and transformer utilization. It provides equations for peak inverse voltage, utilization factor, and transformer rating calculations. Finally, it analyzes a 12 pulse converter, explaining how two transformers connected in star-star and star-delta configurations produce 12 pulses of output with each pulse having a 30 degree duration.
Power electronic converters use components like IGBTs to control and convert electric power for end users. A modular multilevel converter (MMC) is a power electronic converter topology that has several advantages over traditional converters. The MMC consists of submodules that each contain a half-bridge and capacitor. The submodules are arranged in an arm configuration with inductors to handle voltage differences and limit fault currents. Multicarrier pulse width modulation techniques are used to generate switching signals for the submodules to produce a stepped voltage waveform and perform power conversion while distributing energy across the capacitors.
This document discusses different types of rectifier circuits used to convert alternating current (AC) to direct current (DC). It describes single phase half-wave and full-wave rectifiers using one or two diodes, as well as a four diode full-wave bridge rectifier. The final circuit discussed is a three phase full-wave rectifier used for applications requiring large amounts of DC power.
CMOS ring oscillator delay cell performance: a comparative studyIJECEIAES
A common voltage-controlled oscillator (VCO) architecture used in the phase locked loop (PLL) is the ring oscillator (RO). RO consist of number of inverters cascaded together as the input of the first stage connected to the output of the last stage. It is important to design the RO to be work at desired frequency depend on application with low power consumption. This paper presents a review the performance evaluation of different delay cell topologies the implemented in the ring oscillator. The various topologies analyzed includes current starved delay cell, differential delay cell and current follower cell. Performance evaluation includes frequency range, frequency stability, phase noise and power consumption had been reviewed and comparison of different topologies has been discussed. It is observed that starved current delay cell have lower power consumption and the different of the frequency range is small as compared to other type of delay cell.
Listrik adalah bentuk energi sekunder yang paling praktis penggunaanya oleh manusia, Kebutuhan listrik di masyarakat semakin meningkat seiring dengan meningkatnya pemanfaatan tenaga listrik. Sistem tenaga listrik yang baik adalah sistem tenaga yang dapat melayani beban secara kontinyu, tegangan dan frekwensi yang konstan, fluktuasi tegangan dan frekuensi yang terjadi harus berada pada batas toleransi yang diizinkan agar peralatan listrik konsumen dapat bekerja dengan baik dan aman
Untuk keperluan penyediaan tenaga listrik bagi para pelangggan, berbagai peralatan listrik ini dihubungkan satu sama lain dan secara keseluruhan membentuk suatu sistem tenaga listrik. Oleh karena itu dibutuhkan stabilitas pada operasi sistem tenaga listrik agar para pelanggan bisa menikmati tenaga listrik tanpa ada gangguan.
A solar charge controller regulates voltage and current from solar panels to batteries to prevent overcharging. It uses op-amps, MOSFETs, diodes and other components. Solar panels produce more than 12 volts, so the controller ensures batteries charge to 14-14.5 volts. It also protects against overcharging, deep discharge, and undervoltage. Charge controllers are used in solar home systems, street lights, hybrid power systems, and water pumps to store solar energy in batteries.
The document provides a third quarter report on the creation of a custom PSCAD library component for renewable energy systems. Key accomplishments include successfully designing wind, solar, and battery storage models and integrating them into a custom library. Future work identified is improving the battery control system. The custom library allows users to easily design renewable energy systems in PSCAD.
Dokumen tersebut membahas tiga faktor penting dalam penyaluran listrik yaitu kualitas, ekonomis, dan keandalan. Dokumen juga menjelaskan sistem SCADA yang digunakan untuk pengawasan dan pengendalian peralatan listrik dari jarak jauh dengan tingkat keandalan dan kualitas yang tinggi serta tetap menjaga faktor ekonomis. Sistem SCADA terdiri dari Master Station, Remote Terminal Unit, dan saluran komunikasi untuk menghubungkan keduanya.
Sistem distribusi listrik berguna untuk menyalurkan listrik dari sumber daya besar ke konsumen. Rugi tegangan atau drop voltage terjadi karena hambatan pada saluran distribusi dan menyebabkan tegangan yang diterima konsumen lebih rendah dari tegangan sumber. Faktor yang mempengaruhi besarnya rugi tegangan antara lain panjang saluran, luas penampang kawat, dan besarnya beban listrik.
This document provides an overview of DC to DC converters (choppers). It discusses:
1) Choppers are static devices that are used to obtain a variable DC output voltage from a constant DC source. They offer benefits like greater efficiency and smoother control.
2) The output voltage can be controlled through pulse width modulation or variable frequency control. Pulse width modulation varies the ON time while keeping frequency constant. Variable frequency control varies the chopping frequency.
3) There are different types of choppers - buck, boost, buck-boost, Cuk - that can step up or step down the voltage. The boost converter operates by storing energy in an inductor during the ON state and releasing it during
This document discusses various control strategies for power sharing in AC microgrids, including droop control approaches. It provides details on several types of droop control methods and their advantages and drawbacks. Specifically, it describes conventional droop control based on frequency-power (P/f) and voltage-reactive power (Q/V) drooping characteristics. It also discusses voltage-power droop and frequency-reactive power boosting control for microgrids with resistive lines, as well as complex line impedance-based droop control methods.
A flyback converter is a type of switch mode power supply that uses a transformer to transfer energy from the input to the output. It operates by storing energy in the transformer during the on-time of the primary switch, and releasing this energy to the output during the off-time when a diode is conducting. Flyback converters provide galvanic isolation between the input and output through the use of the transformer. They can operate in discontinuous conduction mode where the transformer fully demagnetizes during each switching cycle.
Dokumen tersebut membahas tentang gardu induk sebagai pusat pembagi daya listrik ke konsumen. Ia menjelaskan pengertian gardu induk, jenis-jenisnya, fasilitas dan peralatan yang ada seperti transformator, pemutus daya, dan peralatan lainnya. Dokumen ini juga membahas perancangan gardu induk yang mempertimbangkan kapasitas sistem, sifat gardu induk, dan kondisi setempat.
The document describes the process of constructing steady-state equivalent circuit models for DC-DC power converters. Key steps include:
1) Deriving loop and node equations from circuit analyses during switching intervals.
2) Representing the equations as equivalent circuits using dependent sources and transformers.
3) Solving the equivalent circuit to obtain output characteristics like voltage conversion ratio and efficiency.
Losses from resistances and semiconductor voltages can be included to make the model more accurate. The equivalent circuit approach provides a time-invariant model of the converter under steady-state conditions.
This document provides an introduction to power electronics. It discusses various power electronic applications including power supplies, motor drives, and utility transmission systems. It also covers common power electronic components like switches, capacitors, inductors, and semiconductor devices. The document outlines the topics that will be covered in the course, including converter circuit operation, control systems, magnetics design, rectifiers, and resonant converters.
This document discusses the design and construction of a 33/11 kV power line and substation. It provides details on the survey, layout, equipment, and sequence of construction. Key points include:
1. A survey is conducted to determine the optimal route for the power line, avoiding difficult terrain and areas of development.
2. Construction of the line involves digging poles, concreting, stringing conductors, and installing safety signs. The substation is built using equipment like transformers, circuit breakers, isolators, and busbars to transfer electricity between voltages.
3. Proper spacing must be maintained between the power line and other underground utilities or communication lines according to regulations.
This document describes an automatic power factor corrector system. It begins with an introduction to power factor, different types of power factor correction including static capacitors and synchronous condensers. It then discusses the importance of power factor correction including reduced utility charges and system losses. The document outlines the principles, sections, advantages of an automatic power factor correction system. It shows results for inductive and resistive loads before and after correction. It concludes that automatic power factor correction provides an efficient way to improve power factor through static capacitors.
The document describes modeling and simulation of a dynamic voltage restorer (DVR) for mitigating voltage sags and swells. A DVR is proposed as a cost-effective solution to protect sensitive loads from voltage fluctuations. The operation and equivalent circuit of a DVR are presented. Simulation results show that the DVR can satisfactorily compensate for both balanced and unbalanced voltage sags and swells, maintaining the load voltage at its nominal value.
Proteksi sistem tenaga listrik adalah sistem proteksi yang dipasang pada peralatan-peralatan listrik suatu sistem tenaga listrik, misalnya generator, transformator, jaringan dan lain-lain, terhadap kondisi abnormal operasi sistem itu sendiri. Kondisi abnormal itu dapat berupa antara lain: hubung singkat, tegangan lebih, beban lebih, frekuensi sistem rendah, asinkron dan lain-lain.
The document discusses converter configurations and analyzes a 12 pulse converter. It begins by explaining pulse number and valve/switch types in converters. It then discusses how converter configuration is selected based on pulse number to maximize valve and transformer utilization. It provides equations for peak inverse voltage, utilization factor, and transformer rating calculations. Finally, it analyzes a 12 pulse converter, explaining how two transformers connected in star-star and star-delta configurations produce 12 pulses of output with each pulse having a 30 degree duration.
Power electronic converters use components like IGBTs to control and convert electric power for end users. A modular multilevel converter (MMC) is a power electronic converter topology that has several advantages over traditional converters. The MMC consists of submodules that each contain a half-bridge and capacitor. The submodules are arranged in an arm configuration with inductors to handle voltage differences and limit fault currents. Multicarrier pulse width modulation techniques are used to generate switching signals for the submodules to produce a stepped voltage waveform and perform power conversion while distributing energy across the capacitors.
This document discusses different types of rectifier circuits used to convert alternating current (AC) to direct current (DC). It describes single phase half-wave and full-wave rectifiers using one or two diodes, as well as a four diode full-wave bridge rectifier. The final circuit discussed is a three phase full-wave rectifier used for applications requiring large amounts of DC power.
CMOS ring oscillator delay cell performance: a comparative studyIJECEIAES
A common voltage-controlled oscillator (VCO) architecture used in the phase locked loop (PLL) is the ring oscillator (RO). RO consist of number of inverters cascaded together as the input of the first stage connected to the output of the last stage. It is important to design the RO to be work at desired frequency depend on application with low power consumption. This paper presents a review the performance evaluation of different delay cell topologies the implemented in the ring oscillator. The various topologies analyzed includes current starved delay cell, differential delay cell and current follower cell. Performance evaluation includes frequency range, frequency stability, phase noise and power consumption had been reviewed and comparison of different topologies has been discussed. It is observed that starved current delay cell have lower power consumption and the different of the frequency range is small as compared to other type of delay cell.
Listrik adalah bentuk energi sekunder yang paling praktis penggunaanya oleh manusia, Kebutuhan listrik di masyarakat semakin meningkat seiring dengan meningkatnya pemanfaatan tenaga listrik. Sistem tenaga listrik yang baik adalah sistem tenaga yang dapat melayani beban secara kontinyu, tegangan dan frekwensi yang konstan, fluktuasi tegangan dan frekuensi yang terjadi harus berada pada batas toleransi yang diizinkan agar peralatan listrik konsumen dapat bekerja dengan baik dan aman
Untuk keperluan penyediaan tenaga listrik bagi para pelangggan, berbagai peralatan listrik ini dihubungkan satu sama lain dan secara keseluruhan membentuk suatu sistem tenaga listrik. Oleh karena itu dibutuhkan stabilitas pada operasi sistem tenaga listrik agar para pelanggan bisa menikmati tenaga listrik tanpa ada gangguan.
A solar charge controller regulates voltage and current from solar panels to batteries to prevent overcharging. It uses op-amps, MOSFETs, diodes and other components. Solar panels produce more than 12 volts, so the controller ensures batteries charge to 14-14.5 volts. It also protects against overcharging, deep discharge, and undervoltage. Charge controllers are used in solar home systems, street lights, hybrid power systems, and water pumps to store solar energy in batteries.
The document provides a third quarter report on the creation of a custom PSCAD library component for renewable energy systems. Key accomplishments include successfully designing wind, solar, and battery storage models and integrating them into a custom library. Future work identified is improving the battery control system. The custom library allows users to easily design renewable energy systems in PSCAD.
Dokumen tersebut membahas tiga faktor penting dalam penyaluran listrik yaitu kualitas, ekonomis, dan keandalan. Dokumen juga menjelaskan sistem SCADA yang digunakan untuk pengawasan dan pengendalian peralatan listrik dari jarak jauh dengan tingkat keandalan dan kualitas yang tinggi serta tetap menjaga faktor ekonomis. Sistem SCADA terdiri dari Master Station, Remote Terminal Unit, dan saluran komunikasi untuk menghubungkan keduanya.
Sistem distribusi listrik berguna untuk menyalurkan listrik dari sumber daya besar ke konsumen. Rugi tegangan atau drop voltage terjadi karena hambatan pada saluran distribusi dan menyebabkan tegangan yang diterima konsumen lebih rendah dari tegangan sumber. Faktor yang mempengaruhi besarnya rugi tegangan antara lain panjang saluran, luas penampang kawat, dan besarnya beban listrik.
This document provides an overview of DC to DC converters (choppers). It discusses:
1) Choppers are static devices that are used to obtain a variable DC output voltage from a constant DC source. They offer benefits like greater efficiency and smoother control.
2) The output voltage can be controlled through pulse width modulation or variable frequency control. Pulse width modulation varies the ON time while keeping frequency constant. Variable frequency control varies the chopping frequency.
3) There are different types of choppers - buck, boost, buck-boost, Cuk - that can step up or step down the voltage. The boost converter operates by storing energy in an inductor during the ON state and releasing it during
This document discusses various control strategies for power sharing in AC microgrids, including droop control approaches. It provides details on several types of droop control methods and their advantages and drawbacks. Specifically, it describes conventional droop control based on frequency-power (P/f) and voltage-reactive power (Q/V) drooping characteristics. It also discusses voltage-power droop and frequency-reactive power boosting control for microgrids with resistive lines, as well as complex line impedance-based droop control methods.
A flyback converter is a type of switch mode power supply that uses a transformer to transfer energy from the input to the output. It operates by storing energy in the transformer during the on-time of the primary switch, and releasing this energy to the output during the off-time when a diode is conducting. Flyback converters provide galvanic isolation between the input and output through the use of the transformer. They can operate in discontinuous conduction mode where the transformer fully demagnetizes during each switching cycle.
Dokumen tersebut membahas tentang gardu induk sebagai pusat pembagi daya listrik ke konsumen. Ia menjelaskan pengertian gardu induk, jenis-jenisnya, fasilitas dan peralatan yang ada seperti transformator, pemutus daya, dan peralatan lainnya. Dokumen ini juga membahas perancangan gardu induk yang mempertimbangkan kapasitas sistem, sifat gardu induk, dan kondisi setempat.
The document describes the process of constructing steady-state equivalent circuit models for DC-DC power converters. Key steps include:
1) Deriving loop and node equations from circuit analyses during switching intervals.
2) Representing the equations as equivalent circuits using dependent sources and transformers.
3) Solving the equivalent circuit to obtain output characteristics like voltage conversion ratio and efficiency.
Losses from resistances and semiconductor voltages can be included to make the model more accurate. The equivalent circuit approach provides a time-invariant model of the converter under steady-state conditions.
This document provides an introduction to power electronics. It discusses various power electronic applications including power supplies, motor drives, and utility transmission systems. It also covers common power electronic components like switches, capacitors, inductors, and semiconductor devices. The document outlines the topics that will be covered in the course, including converter circuit operation, control systems, magnetics design, rectifiers, and resonant converters.
This chapter discusses principles of steady-state analysis of DC-DC power converters. It introduces inductor volt-second balance and capacitor charge balance, which relate the average inductor voltage and capacitor current to be zero during steady-state. A small ripple approximation is used to simplify analysis by ignoring output voltage ripple. Examples of steady-state analysis of the buck and boost converters are presented using these principles to determine output voltage, inductor current, and capacitor sizing for given ripple levels.
This chapter discusses discontinuous conduction mode (DCM) in power electronics. DCM occurs when inductor current or capacitor voltage ripple causes the applied switch current or voltage to reverse polarity. Analysis techniques for DCM include inductor volt-second balance and capacitor charge balance. The chapter provides an example analysis of a buck converter in DCM and derives the mode boundary and conversion ratio equations.
This document discusses transformer design. It covers selecting an appropriate core size based on constraints like core loss and copper loss. It presents a step-by-step design procedure that involves determining the core size, flux density, turns ratios, wire sizes and other parameters. The effects of switching frequency on transformer size are also considered, with higher frequencies generally allowing for smaller core sizes. Two examples applying the design procedure are provided.
This chapter discusses power and harmonics in nonsinusoidal systems. It covers average power calculation using Fourier series, RMS value calculation, power factor, and harmonic distortion. Power factor is defined as the ratio of average power to apparent power. Harmonics always increase RMS values but do not necessarily increase average power. Harmonics reduce the power factor for nonlinear loads fed by sinusoidal voltages. Three-phase systems can experience overloading of neutral conductors and capacitors due to harmonic currents.
Steady-state Analysis for Switched Electronic Systems Trough ComplementarityGianluca Angelone
A synthesis of my Ph.D. defense. It's about modeling and steady state analysis of switched electronic power converters, both in open and closed loop, by using the complementarity framework. Application examples: Buck, Boost, Resonant and Modular Multilevel Converters
Two single-phase motors are connected in parallel to a 240V, 50Hz power supply. One motor draws 12A at a power factor of 0.4, while the other draws 16A at a power factor of 0.8. Given these parameters, the document calculates the total current drawn, total power factor, and refers to a textbook for more information on power factor calculations for motors in parallel.
This document provides an overview of various analysis tools available in EWB software for circuit simulation and analysis. It describes the following analysis types: DC operating point analysis, AC frequency analysis, transient analysis, Fourier analysis, noise analysis, distortion analysis, DC sweep analysis, sensitivity analysis, parameter sweep analysis, temperature sweep analysis, transfer function analysis, worst case analysis, pole zero analysis, and Monte Carlo analysis. For each analysis type, it provides a brief description of the analysis and an example circuit to demonstrate how to set up and interpret the results of that analysis.
This document introduces phasors and their graphical representation. It discusses that a phasor can represent the magnitude and angular position of a sinusoidal quantity. It also describes that a phasor diagram can show the relative relationship of sine waves of the same frequency. The document outlines different forms to represent a phasor including rectangular, trigonometric, exponential and polar forms. It discusses operations that can be performed on phasors such as addition, subtraction, multiplication and division in both rectangular and polar forms. Finally, it describes how phasors can be graphically added and subtracted on a phasor diagram.
This document summarizes Chapter 17 of the textbook "Fundamentals of Power Electronics" which covers line-commutated rectifiers. It discusses single-phase and three-phase full-wave rectifiers in both continuous and discontinuous conduction modes. It also describes phase control of rectifiers, harmonic trap filters used to reduce harmonics, and different transformer connections that can shift voltages and currents to cancel harmonics. The chapter provides analysis of rectifier circuits including harmonic content, power factor, and efficiency over a range of operating conditions.
The document discusses AC circuits using phasors to represent voltages and currents. It introduces the concepts of resistive reactance (R), capacitive reactance (XC), and inductive reactance (XL). R causes voltage to be in phase with current, while XC causes voltage to lag current by 90° and XL causes voltage to lead current by 90°. Together, R, XC and XL determine the impedance (Z) and phase angle (φ) of the circuit. The document uses an example of an L-C circuit to show how to calculate the frequency where XC and XL are equal.
The document discusses quasi-resonant converters and the half-wave zero-current-switching quasi-resonant switch cell. The switch cell uses a small resonant inductor and capacitor to achieve zero-current switching of the transistor. It operates in four subintervals per switching period: 1) transistor on, 2) resonant ringing, 3) capacitor discharging, 4) diode on. Mathematical analysis determines the waveforms and durations of each subinterval. Averaging the switch cell currents and voltages gives the conversion ratio, allowing the cell to be analyzed and incorporated into converter circuits.
In an electrical circuit the impedance of a component is defined as the ratio of the voltage phasor v, across the component over the current phasor I , through the component.
This document discusses power electronics and provides an overview of key concepts:
1. Power electronics refers to controlling and converting electrical power using power semiconductor devices like SCRs. Main applications include rectification, inversion, DC-DC conversion, and AC-AC conversion.
2. Rectification can be uncontrolled using diodes or controlled using SCRs. Common rectifier configurations include single and three-phase bridge rectifiers. Inversion converts DC to AC using devices like SCRs, IGBTs, and MOSFETs.
3. DC-DC conversion is commonly done using switch-mode power supplies with devices like BJTs and MOSFETs. AC-AC conversion using cycloconverters
This document provides an overview of power electronics and drives, focusing on modeling and simulation. It discusses power electronic systems and converters used in electrical drives, including DC and AC drives. It also covers modeling and control of electrical drives, specifically current controlled converters, modeling of power converters, and scalar control of induction motors. The document is intended to support a problem-based and project-oriented learning approach to the topics of power electronics, modeling, and drives.
We looked at the data. Here’s a breakdown of some key statistics about the nation’s incoming presidents’ addresses, how long they spoke, how well, and more.
The document discusses the design of filter inductors for power electronics applications. It covers various types of magnetic devices and their operating principles. The key constraints in inductor design are discussed as maximizing flux density without saturation, achieving the required inductance value, fitting the winding within the core window, and meeting the target winding resistance. A step-by-step procedure is outlined that involves selecting a suitable core based on its geometrical constant and calculating the necessary air gap length.
This document summarizes the key steps in designing a transformer, including:
1. Selecting an appropriate core size based on specifications and material properties to minimize total power loss.
2. Calculating the optimum operating flux density based on voltage, current, and core geometry.
3. Determining the required number of turns for each winding based on voltage and flux density.
4. Sizing the wire gauges for each winding based on current and available winding area.
The procedure is then demonstrated through an example design of a transformer for a Cuk converter.
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power electronics FiringCkt.pdf.crdownload.pptxdivakarrvl
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Part of Lecture series on EE321N, Power Electronics-I delivered by me during Fifth Semester of B.Tech. Electrical Engg., 2012
Z H College of Engg. & Technology, Aligarh Muslim University, Aligarh
Please comment and feel free to ask anything related. Thanks!
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2. An example is worked through for a buck converter with diode reverse recovery, constructing waveforms and deriving equations for inductor voltage, capacitor current, and input current.
3. The equations are used to build an equivalent circuit model with independent current sources representing switching loss, allowing calculation of efficiency degradation.
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Chapter 14
1. Fundamentals of Power Electronics Chapter 14: Inductor design1
Chapter 14 Inductor Design
14.1 Filter inductor design constraints
14.2 A step-by-step design procedure
14.3 Multiple-winding magnetics design using the
Kg method
14.4 Examples
14.5 Summary of key points
2. Fundamentals of Power Electronics Chapter 14: Inductor design2
14.1 Filter inductor design constraints
Pcu = Irms
2
R
Objective:
Design inductor having a given inductance L,
which carries worst-case current Imax without saturating,
and which has a given winding resistance R, or, equivalently,
exhibits a worst-case copper loss of
L
R
i(t)
+
–
L
i(t)
i(t)
t0 DTs
Ts
I ∆iL
Example: filter inductor in CCM buck converter
3. Fundamentals of Power Electronics Chapter 14: Inductor design3
Assumed filter inductor geometry
Solve magnetic circuit:
Air gap
reluctance
Rg
n
turns
i(t)
Φ
Core reluctance Rc
+
v(t)
– +
–
ni(t) Φ(t)
Rc
Rg
Fc
+ –
Rc =
lc
µcAc
Rg =
lg
µ0Ac
ni = Φ Rc + Rg
ni ≈ ΦRg
Usually Rc < Rg and hence
4. Fundamentals of Power Electronics Chapter 14: Inductor design4
14.1.1 Constraint: maximum flux density
Given a peak winding current Imax, it is desired to operate the core flux
density at a peak value Bmax. The value of Bmax is chosen to be less
than the worst-case saturation flux density Bsat of the core material.
From solution of magnetic circuit:
Let I = Imax and B = Bmax :
This is constraint #1. The turns ratio n and air gap length lg are
unknown.
ni = BAcRg
nImax = Bmax Ac Rg = Bmax
lg
µ0
5. Fundamentals of Power Electronics Chapter 14: Inductor design5
14.1.2 Constraint: inductance
Must obtain specified inductance L. We know that the inductance is
This is constraint #2. The turns ratio n, core area Ac, and air gap length
lg are unknown.
L = n2
Rg
=
µ0Ac n2
lg
6. Fundamentals of Power Electronics Chapter 14: Inductor design6
14.1.3 Constraint: winding area
core window
area WA
wire bare area
AW
core
Wire must fit through core window (i.e., hole in center of core)
nAW
Total area of
copper in window:
KuWA
Area available for winding
conductors:
Third design constraint:
KuWA ≥ nAW
7. Fundamentals of Power Electronics Chapter 14: Inductor design7
The window utilization factor Ku
also called the “fill factor”
Ku is the fraction of the core window area that is filled by copper
Mechanisms that cause Ku to be less than 1:
• Round wire does not pack perfectly, which reduces Ku by a
factor of 0.7 to 0.55 depending on winding technique
• Insulation reduces Ku by a factor of 0.95 to 0.65, depending on
wire size and type of insulation
• Bobbin uses some window area
• Additional insulation may be required between windings
Typical values of Ku :
0.5 for simple low-voltage inductor
0.25 to 0.3 for off-line transformer
0.05 to 0.2 for high-voltage transformer (multiple kV)
0.65 for low-voltage foil-winding inductor
8. Fundamentals of Power Electronics Chapter 14: Inductor design8
14.1.4 Winding resistance
The resistance of the winding is
where is the resistivity of the conductor material, lb is the length of
the wire, and AW is the wire bare area. The resistivity of copper at
room temperature is 1.724 10–6 -cm. The length of the wire comprising
an n-turn winding can be expressed as
where (MLT) is the mean-length-per-turn of the winding. The mean-
length-per-turn is a function of the core geometry. The above
equations can be combined to obtain the fourth constraint:
R = ρ
n (MLT)
AW
R = ρ
lb
AW
lb = n(MLT)
9. Fundamentals of Power Electronics Chapter 14: Inductor design9
14.1.5 The core geometrical constant Kg
The four constraints:
R = ρ
n (MLT)
AW
KuWA ≥ nAW
These equations involve the quantities
Ac, WA, and MLT, which are functions of the core geometry,
Imax, Bmax , µ0, L, Ku, R, and , which are given specifications or
other known quantities, and
n, lg, and AW, which are unknowns.
Eliminate the three unknowns, leading to a single equation involving
the remaining quantities.
nImax = Bmax Ac Rg = Bmax
lg
µ0
L = n2
Rg
=
µ0Ac n2
lg
10. Fundamentals of Power Electronics Chapter 14: Inductor design10
Core geometrical constant Kg
Ac
2
WA
(MLT)
≥
ρL2
Imax
2
Bmax
2
RKu
Elimination of n, lg, and AW leads to
• Right-hand side: specifications or other known quantities
• Left-hand side: function of only core geometry
So we must choose a core whose geometry satisfies the above
equation.
The core geometrical constant Kg is defined as
Kg =
Ac
2
WA
(MLT)
11. Fundamentals of Power Electronics Chapter 14: Inductor design11
Discussion
Kg =
Ac
2
WA
(MLT)
≥
ρL2
Imax
2
Bmax
2
RKu
Kg is a figure-of-merit that describes the effective electrical size of magnetic
cores, in applications where the following quantities are specified:
• Copper loss
• Maximum flux density
How specifications affect the core size:
A smaller core can be used by increasing
Bmax use core material having higher Bsat
R allow more copper loss
How the core geometry affects electrical capabilities:
A larger Kg can be obtained by increase of
Ac more iron core material, or
WA larger window and more copper
12. Fundamentals of Power Electronics Chapter 14: Inductor design12
14.2 A step-by-step procedure
The following quantities are specified, using the units noted:
Wire resistivity ( -cm)
Peak winding current Imax (A)
Inductance L (H)
Winding resistance R ( )
Winding fill factor Ku
Core maximum flux density Bmax (T)
The core dimensions are expressed in cm:
Core cross-sectional area Ac (cm2)
Core window area WA (cm2)
Mean length per turn MLT (cm)
The use of centimeters rather than meters requires that appropriate
factors be added to the design equations.
13. Fundamentals of Power Electronics Chapter 14: Inductor design13
Determine core size
Kg ≥
ρL2
Imax
2
Bmax
2
RKu
108
(cm5
)
Choose a core which is large enough to satisfy this inequality
(see Appendix D for magnetics design tables).
Note the values of Ac, WA, and MLT for this core.
14. Fundamentals of Power Electronics Chapter 14: Inductor design14
Determine air gap length
with Ac expressed in cm2. µ0 = 4 10–7 H/m.
The air gap length is given in meters.
The value expressed above is approximate, and neglects fringing flux
and other nonidealities.
lg =
µ0LImax
2
Bmax
2
Ac
104
(m)
15. Fundamentals of Power Electronics Chapter 14: Inductor design15
AL
Core manufacturers sell gapped cores. Rather than specifying the air
gap length, the equivalent quantity AL is used.
AL is equal to the inductance, in mH, obtained with a winding of 1000
turns.
When AL is specified, it is the core manufacturer’s responsibility to
obtain the correct gap length.
The required AL is given by:
AL =
10Bmax
2
Ac
2
LImax
2 (mH/1000 turns)
L = AL n2
10– 9
(Henries)
Units:
Ac cm2,
L Henries,
Bmax Tesla.
16. Fundamentals of Power Electronics Chapter 14: Inductor design16
Determine number of turns n
n =
LImax
Bmax Ac
104
17. Fundamentals of Power Electronics Chapter 14: Inductor design17
Evaluate wire size
AW ≤
KuWA
n
(cm2
)
Select wire with bare copper area AW less than or equal to this value.
An American Wire Gauge table is included in Appendix D.
As a check, the winding resistance can be computed:
R =
ρn (MLT)
Aw
(Ω)
18. Fundamentals of Power Electronics Chapter 14: Inductor design18
14.3 Multiple-winding magnetics design
using the Kg method
The Kg design method can be extended to multiple-
winding magnetic elements such as transformers and
coupled inductors.
This method is applicable when
– Copper loss dominates the total loss (i.e. core loss is
ignored), or
– The maximum flux density Bmax is a specification rather than
a quantity to be optimized
To do this, we must
– Find how to allocate the window area between the windings
– Generalize the step-by-step design procedure
19. Fundamentals of Power Electronics Chapter 14: Inductor design19
14.3.1 Window area allocation
n1 : n2
: nk
rms current
I1
rms current
I2
rms current
Ik
v1(t)
n1
=
v2(t)
n2
= =
vk(t)
nk
Core
Window area WA
Core mean length
per turn (MLT)
Wire resistivity ρ
Fill factor Ku
Given: application with k windings
having known rms currents and
desired turns ratios
Q: how should the window
area WA be allocated among
the windings?
20. Fundamentals of Power Electronics Chapter 14: Inductor design20
Allocation of winding area
Total window
area WA
Winding 1 allocation
α1WA
Winding 2 allocation
α2
WA
etc.
{
{
0 < αj < 1
α1 + α2 + + αk = 1
21. Fundamentals of Power Electronics Chapter 14: Inductor design21
Copper loss in winding j
Copper loss (not accounting for proximity loss) is
Pcu,j = I j
2
Rj
Resistance of winding j is
with
AW,j =
WAKuαj
nj
length of wire, winding j
wire area, winding j
Hence
Rj = ρ
l j
AW,j
l j = nj (MLT)
Rj = ρ
n j
2
(MLT)
WAKuα j
Pcu,j =
n j
2
i j
2
ρ(MLT)
WAKuα j
22. Fundamentals of Power Electronics Chapter 14: Inductor design22
Total copper loss of transformer
Sum previous expression over all windings:
Pcu,tot = Pcu,1 + Pcu,2 + + Pcu,k =
ρ (MLT)
WAKu
nj
2
I j
2
αj
Σj = 1
k
Need to select values for 1, 2, …, k such that the total copper loss
is minimized
23. Fundamentals of Power Electronics Chapter 14: Inductor design23
Variation of copper losses with 1
For 1 = 0: wire of
winding 1 has zero area.
Pcu,1 tends to infinity
For 1 = 1: wires of
remaining windings have
zero area. Their copper
losses tend to infinity
There is a choice of 1
that minimizes the total
copper lossα1
Copper
loss
0 1
Pcu,tot
Pcu,1
P cu,2+
P
cu,3+...+P
cu,k
24. Fundamentals of Power Electronics Chapter 14: Inductor design24
Method of Lagrange multipliers
to minimize total copper loss
Pcu,tot = Pcu,1 + Pcu,2 + + Pcu,k =
ρ (MLT)
WAKu
nj
2
I j
2
αj
Σj = 1
k
subject to the constraint
α1 + α2 + + αk = 1
Define the function
f(α1, α2, , αk, ξ) = Pcu,tot(α1, α2, , αk) + ξ g(α1, α2, , αk)
Minimize the function
where
g(α1, α2, , αk) = 1 – αjΣj = 1
k
is the constraint that must equal zero
and is the Lagrange multiplier
25. Fundamentals of Power Electronics Chapter 14: Inductor design25
Lagrange multipliers
continued
Optimum point is solution of
the system of equations
∂ f(α1, α2, , αk,ξ)
∂α1
= 0
∂ f(α1, α2, , αk,ξ)
∂α2
= 0
∂ f(α1, α2, , αk,ξ)
∂αk
= 0
∂ f(α1, α2, , αk,ξ)
∂ξ
= 0
Result:
ξ =
ρ (MLT)
WAKu
njIjΣj = 1
k 2
= Pcu,tot
αm =
nmIm
njIjΣn = 1
∞
An alternate form:
αm =
VmIm
VjIjΣn = 1
∞
26. Fundamentals of Power Electronics Chapter 14: Inductor design26
Interpretation of result
αm =
VmIm
VjIjΣn = 1
∞
Apparent power in winding j is
Vj Ij
where Vj is the rms or peak applied voltage
Ij is the rms current
Window area should be allocated according to the apparent powers of
the windings
27. Fundamentals of Power Electronics Chapter 14: Inductor design27
Ii1(t)
n1
turns {
}n2 turns
}n2 turns
i2(t)
i3(t)
Example
PWM full-bridge transformer
• Note that waveshapes
(and hence rms values)
of the primary and
secondary currents are
different
• Treat as a three-
winding transformer
–
n2
n1
I
t
i1(t)
0 0
n2
n1
I
i2(t)
I
0.5I 0.5I
0
i3(t)
I
0.5I 0.5I
0
0 DTs Ts 2TsTs +DTs
28. Fundamentals of Power Electronics Chapter 14: Inductor design28
Expressions for RMS winding currents
I1 = 1
2Ts
i1
2
(t)dt
0
2Ts
=
n2
n1
I D
I2 = I3 = 1
2Ts
i2
2
(t)dt
0
2Ts
= 1
2
I 1 + D
see Appendix A
–
n2
n1
I
t
i1(t)
0 0
n2
n1
I
i2(t)
I
0.5I 0.5I
0
i3(t)
I
0.5I 0.5I
0
0 DTs Ts 2TsTs +DTs
29. Fundamentals of Power Electronics Chapter 14: Inductor design29
Allocation of window area: αm =
VmIm
VjIjΣn = 1
∞
α1 = 1
1 + 1 + D
D
α2 = α3 = 1
2
1
1 + D
1 + D
Plug in rms current expressions. Result:
Fraction of window area
allocated to primary
winding
Fraction of window area
allocated to each
secondary winding
30. Fundamentals of Power Electronics Chapter 14: Inductor design30
Numerical example
Suppose that we decide to optimize the transformer design at the
worst-case operating point D = 0.75. Then we obtain
α1 = 0.396
α2 = 0.302
α3 = 0.302
The total copper loss is then given by
Pcu,tot =
ρ(MLT)
WAKu
njIjΣj = 1
3 2
=
ρ(MLT)n2
2
I2
WAKu
1 + 2D + 2 D(1 + D)
31. Fundamentals of Power Electronics Chapter 14: Inductor design31
14.3.2 Coupled inductor design constraints
n1 : n2
: nk
R1 R2
Rk
+
v1(t)
–
+
v2(t)
–
+
vk(t)
–
i1(t) i2(t)
ik(t)
LM
iM(t)
+
–n1iM(t) Φ(t)
Rc
Rg
Consider now the design of a coupled inductor having k windings. We want
to obtain a specified value of magnetizing inductance, with specified turns
ratios and total copper loss.
Magnetic circuit model:
32. Fundamentals of Power Electronics Chapter 14: Inductor design32
Relationship between magnetizing
current and winding currents
n1 : n2
: nk
R1 R2
Rk
+
v1(t)
–
+
v2(t)
–
+
vk(t)
–
i1(t) i2(t)
ik(t)
LM
iM(t)
iM(t) = i1(t) +
n2
n1
i2(t) + +
nk
n1
ik(t)
Solution of circuit model, or by use of
Ampere’s Law:
33. Fundamentals of Power Electronics Chapter 14: Inductor design33
Solution of magnetic circuit model:
Obtain desired maximum flux density
+
–n1iM(t) Φ(t)
Rc
Rg
n1iM(t) = B(t)AcRg
Assume that gap reluctance is much
larger than core reluctance:
Design so that the maximum flux density Bmax is equal to a specified value
(that is less than the saturation flux density Bsat ). Bmax is related to the
maximum magnetizing current according to
n1IM,max = BmaxAcRg = Bmax
lg
µ0
34. Fundamentals of Power Electronics Chapter 14: Inductor design34
Obtain specified magnetizing inductance
LM =
n1
2
Rg
= n1
2 µ0 Ac
lg
By the usual methods, we can solve for the value of the magnetizing
inductance LM (referred to the primary winding):
35. Fundamentals of Power Electronics Chapter 14: Inductor design35
Copper loss
Allocate window area as described in Section 14.3.1. As shown in that
section, the total copper loss is then given by
Pcu =
ρ(MLT)n1
2
Itot
2
WAKu
Itot =
nj
n1
I jΣj = 1
k
with
36. Fundamentals of Power Electronics Chapter 14: Inductor design36
Eliminate unknowns and solve for Kg
Pcu =
ρ(MLT)LM
2
Itot
2
IM,max
2
Bmax
2
Ac
2
WAKu
Eliminate the unknowns lg and n1:
Rearrange equation so that terms that involve core geometry are on
RHS while specifications are on LHS:
Ac
2
WA
(MLT)
=
ρLM
2
Itot
2
IM,max
2
Bmax
2
KuPcu
The left-hand side is the same Kg as in single-winding inductor design.
Must select a core that satisfies
Kg ≥
ρLM
2
Itot
2
IM,max
2
Bmax
2
KuPcu
37. Fundamentals of Power Electronics Chapter 14: Inductor design37
14.3.3 Step-by-step design procedure:
Coupled inductor
The following quantities are specified, using the units noted:
Wire resistivity ( -cm)
Total rms winding currents (A) (referred to winding 1)
Peak magnetizing current IM, max (A) (referred to winding 1)
Desired turns ratios n2/n1. n3/n2. etc.
Magnetizing inductance LM (H) (referred to winding 1)
Allowed copper loss Pcu (W)
Winding fill factor Ku
Core maximum flux density Bmax (T)
The core dimensions are expressed in cm:
Core cross-sectional area Ac (cm2)
Core window area WA (cm2)
Mean length per turn MLT (cm)
The use of centimeters rather than meters requires that appropriate factors be added to the design equations.
Itot =
nj
n1
I jΣj = 1
k
38. Fundamentals of Power Electronics Chapter 14: Inductor design38
1. Determine core size
Kg ≥
ρLM
2
Itot
2
IM,max
2
Bmax
2
Pcu Ku
108
(cm5)
Choose a core that satisfies this inequality. Note the values of Ac, WA,
and MLT for this core.
The resistivity of copper wire is 1.724 · 10–6 cm at room
temperature, and 2.3 · 10–6 cm at 100˚C.
39. Fundamentals of Power Electronics Chapter 14: Inductor design39
2. Determine air gap length
lg =
µ0LM IM,max
2
Bmax
2
Ac
104
(m)
(value neglects fringing flux, and a longer gap may be required)
The permeability of free space is µ0 = 4 · 10–7 H/m
40. Fundamentals of Power Electronics Chapter 14: Inductor design40
3. Determine number of turns
For winding 1:
n1 =
LM IM,max
BmaxAc
104
For other windings, use the desired turns ratios:
n2 =
n2
n1
n1
n3 =
n3
n1
n1
41. Fundamentals of Power Electronics Chapter 14: Inductor design41
4. Evaluate fraction of window area
allocated to each winding
α1 =
n1I1
n1Itot
α2 =
n2I2
n1Itot
αk =
nkIk
n1Itot
Total window
area WA
Winding 1 allocation
α1WA
Winding 2 allocation
α2WA
etc.
{
{
0 < αj < 1
α1 + α2 + + αk = 1
42. Fundamentals of Power Electronics Chapter 14: Inductor design42
5. Evaluate wire sizes
Aw1 ≤
α1KuWA
n1
Aw2 ≤
α2KuWA
n2
See American Wire Gauge (AWG) table at end of Appendix D.
43. Fundamentals of Power Electronics Chapter 14: Inductor design43
14.4 Examples
14.4.1 Coupled Inductor for a Two-Output Forward
Converter
14.4.2 CCM Flyback Transformer
44. Fundamentals of Power Electronics Chapter 14: Inductor design44
14.4.1 Coupled Inductor for a Two-Output
Forward Converter
n1
+
v1
–
n2
turns
i1
+
v2
–
i2
+
–vg
Output 1
28 V
4 A
Output 2
12 V
2 Afs = 200 kHz
The two filter inductors can share the same core because their applied
voltage waveforms are proportional. Select turns ratio n2/n1
approximately equal to v2/v1 = 12/28.
45. Fundamentals of Power Electronics Chapter 14: Inductor design45
Coupled inductor model and waveforms
n1:n2
+
v1
–
i1
+
v2
–
i2
LM
iM
Coupled
inductor
model
vM
+ –
iM(t)
vM(t)
IM
0
0
– V1
∆iM
D′Ts
Secondary-side circuit, with coupled
inductor model
Magnetizing current and voltage
waveforms. iM(t) is the sum of
the winding currents i1(t) + i2(t).
46. Fundamentals of Power Electronics Chapter 14: Inductor design46
Nominal full-load operating point
n1
+
v1
–
n2
turns
i1
+
v2
–
i2
+
–vg
Output 1
28 V
4 A
Output 2
12 V
2 Afs = 200 kHz
Design for CCM
operation with
D = 0.35
iM = 20% of IM
fs = 200 kHz
DC component of magnetizing current is
IM = I1 +
n2
n1
I2
= (4 A) + 12
28
(2 A)
= 4.86 A
47. Fundamentals of Power Electronics Chapter 14: Inductor design47
Magnetizing current ripple
iM(t)
vM(t)
IM
0
0
– V1
∆iM
D′Ts
∆iM =
V1D′Ts
2LM
To obtain
iM = 20% of IM
choose
LM =
V1D′Ts
2∆iM
=
(28 V)(1 – 0.35)(5 µs)
2(4.86 A)(20%)
= 47 µH
This leads to a peak magnetizing
current (referred to winding 1) of
IM,max = IM + ∆iM = 5.83 A
48. Fundamentals of Power Electronics Chapter 14: Inductor design48
RMS winding currents
Since the winding current ripples are small, the rms values of the
winding currents are nearly equal to their dc comonents:
I1 = 4 A I2 = 2 A
Hence the sum of the rms winding currents, referred to the primary, is
Itot = I1 +
n2
n1
I2 = 4.86 A
49. Fundamentals of Power Electronics Chapter 14: Inductor design49
Evaluate Kg
The following engineering choices are made:
– Allow 0.75 W of total copper loss (a small core having
thermal resistance of less than 40 ˚C/W then would have a
temperature rise of less than 30 ˚C)
– Operate the core at Bmax = 0.25 T (which is less than the
ferrite saturation flux density of 0.3 ot 0.5 T)
– Use fill factor Ku = 0.4 (a reasonable estimate for a low-
voltage inductor with multiple windings)
Evaluate Kg:
Kg ≥
(1.724 ⋅ 10– 6
Ω – cm)(47 µH)2
(4.86 A)2
(5.83 A)2
(0.25 T)2
(0.75 W)(0.4)
108
= 16 ⋅ 10– 3
cm5
50. Fundamentals of Power Electronics Chapter 14: Inductor design50
Select core
A1
2D
It is decided to use a ferrite PQ core. From
Appendix D, the smallest PQ core having
Kg 16 · 10–3 cm5 is the PQ 20/16, with Kg =
22.4 · 10–3 cm5 . The data for this core are:
Ac = 0.62 cm2
WA = 0.256 cm2
MLT = 4.4 cm
51. Fundamentals of Power Electronics Chapter 14: Inductor design51
Air gap length
lg =
µ0LM IM,max
2
Bmax
2
Ac
104
=
(4π ⋅ 10– 7
H/m)(47 µH)(5.83 A)2
(0.25 T)2
(0.62 cm2)
104
= 0.52 mm
52. Fundamentals of Power Electronics Chapter 14: Inductor design52
Turns
n1 =
LM IM,max
BmaxAc
104
=
(47 µH)(5.83 A)
(0.25 T)(0.62 cm2)
104
= 17.6 turns
n2 =
n2
n1
n1
=
12
28
(17.6)
= 7.54 turns
Let’s round off to
n1 = 17 n2 = 7
53. Fundamentals of Power Electronics Chapter 14: Inductor design53
Wire sizes
Allocation of window area:
α1 =
n1I1
n1Itot
=
(17)(4 A)
(17)(4.86 A)
= 0.8235
α2 =
n2I2
n1Itot
=
(7)(2 A)
(17)(4.86 A)
= 0.1695
Aw1 ≤
α1KuWA
n1
=
(0.8235)(0.4)(0.256cm2)
(17)
= 4.96 ⋅ 10– 3
cm2
use AWG #21
Aw2 ≤
α2KuWA
n2
=
(0.1695)(0.4)(0.256cm2)
(7)
= 2.48 ⋅ 10– 3
cm2
use AWG #24
Determination of wire areas and AWG (from table at end of Appendix D):
54. Fundamentals of Power Electronics Chapter 14: Inductor design54
14.4.2 Example 2: CCM flyback transformer
+
–
LM
+
V
–
Vg
Q1
D1
n1 : n2
C
Transformer model
iM
i1
R
+
vM
–
i2
vM(t)
0
Vg
DTs
iM(t)
IM
0
∆iM
i1(t)
IM
0
i2(t)
IM
0
n1
n2
55. Fundamentals of Power Electronics Chapter 14: Inductor design55
Specifications
Input voltage Vg = 200V
Output (full load) 20 V at 5 A
Switching frequency 150 kHz
Magnetizing current ripple 20% of dc magnetizing current
Duty cycle D = 0.4
Turns ratio n2/n1 = 0.15
Copper loss 1.5 W
Fill factor Ku = 0.3
Maximum flux density Bmax = 0.25 T
56. Fundamentals of Power Electronics Chapter 14: Inductor design56
Basic converter calculations
IM =
n2
n1
1
D′
V
R
= 1.25 A
∆iM = 20% IM = 0.25 A
IM,max = IM + ∆iM = 1.5 A
Components of magnetizing
current, referred to primary:
Choose magnetizing inductance:
LM =
Vg DTs
2∆iM
= 1.07 mH
RMS winding currents:
I1 = IM D 1 + 1
3
∆iM
IM
2
= 0.796 A
I2 =
n1
n2
IM D′ 1 + 1
3
∆iM
IM
2
= 6.50 A
Itot = I1 +
n2
n1
I2 = 1.77 A
57. Fundamentals of Power Electronics Chapter 14: Inductor design57
Choose core size
Kg ≥
ρLM
2
Itot
2
IM,max
2
Bmax
2
Pcu Ku
108
=
1.724 ⋅ 10– 6
Ω-cm 1.07 ⋅ 10– 3
H
2
1.77 A
2
1.5 A
2
0.25 T
2
1.5 W 0.3
108
= 0.049 cm5
The smallest EE core that satisfies
this inequality (Appendix D) is the
EE30.
A
58. Fundamentals of Power Electronics Chapter 14: Inductor design58
Choose air gap and turns
lg =
µ0LM IM,max
2
Bmax
2
Ac
104
=
4π ⋅ 10– 7
H/m 1.07 ⋅ 10– 3
H 1.5 A
2
0.25 T
2
1.09 cm2
104
= 0.44 mm
n1 =
LM IM,max
BmaxAc
104
=
1.07 ⋅ 10– 3
H 1.5 A
0.25 T 1.09 cm2
104
= 58.7 turns
n1 = 59Round to
n2 =
n2
n1
n1
= 0.15 59
= 8.81
n2 = 9
59. Fundamentals of Power Electronics Chapter 14: Inductor design59
Wire gauges
α1 =
I1
Itot
=
0.796 A
1.77 A
= 0.45
α2 =
n2I2
n1Itot
=
9 6.5 A
59 1.77 A
= 0.55
AW1 ≤
α1KuWA
n1
= 1.09 ⋅ 10– 3
cm2 — use #28 AWG
AW2 ≤
α2KuWA
n2
= 8.88 ⋅ 10– 3
cm2 — use #19 AWG
60. Fundamentals of Power Electronics Chapter 14: Inductor design60
Core loss
CCM flyback example
dB(t)
dt
=
vM (t)
n1Ac
dB(t)
dt
=
Vg
n1Ac
B(t)
Hc(t)
Minor B–H loop,
CCM flyback
example
B–H loop,
large excitation
Bsat
∆BBmax
vM(t)
0
Vg
DTs
B(t)
Bmax
0
∆B
Vg
n1Ac
B-H loop for this application: The relevant waveforms:
B(t) vs. applied voltage,
from Faraday’s law:
For the first
subinterval:
61. Fundamentals of Power Electronics Chapter 14: Inductor design61
Calculation of ac flux density
and core loss
Solve for B:
∆B =
Vg
n1Ac
DTs
Plug in values for flyback
example:
∆B =
200 V 0.4 6.67 µs
2 59 1.09 cm2
104
= 0.041 T
∆B, Tesla
0.01 0.1 0.3
Powerlossdensity,
Watts/cm3
0.01
0.1
1
20kHz
50kHz
100kHz
200kHz
400kHz
150kHz
0.04
W/cm3
0.041
From manufacturer’s plot of core
loss (at left), the power loss density
is 0.04 W/cm3. Hence core loss is
Pfe = 0.04 W/cm3 Ac lm
= 0.04 W/cm3 1.09 cm2 5.77 cm
= 0.25 W
62. Fundamentals of Power Electronics Chapter 14: Inductor design62
Comparison of core and copper loss
• Copper loss is 1.5 W
– does not include proximity losses, which could substantially increase
total copper loss
• Core loss is 0.25 W
– Core loss is small because ripple and B are small
– It is not a bad approximation to ignore core losses for ferrite in CCM
filter inductors
– Could consider use of a less expensive core material having higher
core loss
– Neglecting core loss is a reasonable approximation for this
application
• Design is dominated by copper loss
– The dominant constraint on flux density is saturation of the core,
rather than core loss
63. Fundamentals of Power Electronics Chapter 14: Inductor design63
14.5 Summary of key points
1. A variety of magnetic devices are commonly used in switching
converters. These devices differ in their core flux density
variations, as well as in the magnitudes of the ac winding
currents. When the flux density variations are small, core loss can
be neglected. Alternatively, a low-frequency material can be used,
having higher saturation flux density.
2. The core geometrical constant Kg is a measure of the magnetic
size of a core, for applications in which copper loss is dominant.
In the Kg design method, flux density and total copper loss are
specified.