Simulation Of Power Electronics Circuits Using Simulink

      


                         

                    

  

             

               

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Simulation of Power Electronics Circuits using SIMULINK

by

Hadeed Ahmed Sher Department of Electrical Engineering, King Saud University, Riyadh, Kingdom of Saudi Arabia

Dedicated to my Wife and my family

Preface Power electronics is a core field in automation and industrial world. It forms the life lines of industrial revolution in the present era. A lot of books on power electronics are available in market. These books, in general, cover the theoretical aspects of power electronics. Presently software based simulation has gained a lot of attention and is considered most effective tool for research and development in engineering. MATLAB is one of the most powerful tools for analyzing the hypothesis and ideas of engineers. Within MATLAB is SIMULINK, that provides us a modular approach to solve problems. The prime aim of this book is to facilitate students in an elegant manner about using SIMULINK in general and SIM POWER SYSTEMS in particular. A very basic approach is adopted as each and every step is depicted to facilitate the students in getting grip of this powerful tool. The book has six chapters. First chapter explains the importance of modeling and simulation and i have tried my best to explain the very basics of modeling a physical system and above all why simulation is required. This section also highlights the choice of using SIMULINK mainly when a variety of powerful softwares are available. Chapter two and three covers the rectifiers with a difference that chapter three is about the SCR based controlled rectifiers. Inverters are discussed in chapter 4. Variety of different inverters including single phase, quasi wave and three phase with induction motor as load are presented in it. AC-AC conversion is covered in chapter 5 with a title of cycloconverters. Here only single phase to single phase and three phase to single phase step down cycloconverter are simulated. Chapter 6 covers basic types of DC-DC converters and along with them full bridge converters are simulated using unipolar and bipolar PWM switching. The focus of this book is simulating power electronics circuits using SIMULINK, therefore detailed theory is not presented. Readers are advised to consult the standard text books for theoretical explanation of these circuits. The simulation results in this book are verified using the famous power electronic books by renowned authors. The experiments in this book are written keeping in view the undergraduate course of power / industrial electronics in almost all universities and technological institutes of region, however it can be considered as a useful quick reference guide for the students of graduate classes. I am greatly thankful to my family, colleagues and friends for providing support in accomplishing this task. Any comments and suggestions regarding this book are greatly welcomed and should be sent to the hadeedsher[at]gmail[dot]com. Hadeed Ahmed Sher KSU, Riyadh, Saudi Arabia

Page II

Contents 1 Introduction to Modeling and Simulation 1.1 Importance of Simulation . . . . . . . 1.2 Why Simulink . . . . . . . . . . . . . . 1.3 SIMPOWER SYSTEM . . . . . . . . 1.4 Architecture of book . . . . . . . . . .

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1 1 3 4 5

2 Uncontrolled Rectifiers 2.1 Introduction . . . . . . . . . . . . . . . . . 2.2 Single phase half wave rectifier . . . . . . 2.2.1 Without freewheeling diode . . . . 2.2.2 With freewheeling diode . . . . . . 2.3 Single phase full wave center tap rectifier 2.3.1 Without freewheeling diode . . . . 2.3.2 With freewheeling diode . . . . . . 2.4 Single phase full wave bridge rectifier . . . 2.4.1 Without free wheeling diode . . . . 2.4.2 With free wheeling diode . . . . . 2.5 Three phase full wave rectifier . . . . . . . 2.5.1 Without freewheeling diode . . . . 2.6 Twelve pulse rectifier . . . . . . . . . . . . 2.6.1 Simulation Procedure . . . . . . . 2.6.2 Results . . . . . . . . . . . . . . .

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6 6 6 6 19 20 20 23 23 24 25 27 27 29 29 32

3 Controlled Rectifiers/Converters 3.1 Introduction . . . . . . . . . . . . . . . . . . . . 3.2 Single phase half wave controlled converter . . 3.2.1 Simulation Procedure . . . . . . . . . . 3.2.2 Results . . . . . . . . . . . . . . . . . . 3.3 Single phase full wave half controlled converter 3.3.1 Simulation Procedure . . . . . . . . . . 3.3.2 Results . . . . . . . . . . . . . . . . . . 3.4 Single phase full wave full controlled converter 3.4.1 Simulation Procedure . . . . . . . . . . 3.4.2 Results . . . . . . . . . . . . . . . . . . 3.5 Three phase full controlled bridge converter . . 3.5.1 Simulation Procedure . . . . . . . . . .

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Page III

Contents 3.5.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 DC-AC Inverters 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Pulse Width Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Single phase half bridge inverter . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Single phase PWM inverter with bipolar voltage switching . . . . . . . . . 4.4.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Single phase PWM inverter with Unipolar voltage switching . . . . . . . . 4.5.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Quasi square wave single phase Inverter . . . . . . . . . . . . . . . . . . . 4.6.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Single phase inverter with hysteresis band current controlled PWM . . . . 4.7.1 Simulation Procedure for PWM . . . . . . . . . . . . . . . . . . . . 4.7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 PWM based DC-AC 3 phase Inverter . . . . . . . . . . . . . . . . . . . . . 4.8.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 SPWM based 3 phase inverter with 3 phase Asynchronous motor as load . 4.9.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46 46 47 50 52 52 54 54 54 55 58 58 58 60 60 61 63 64 65 67 67 68 72 72 73 76

5 Cycloconverters 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Single phase to Single phase Step down Cycloconverter 5.2.1 Simulation Procedure . . . . . . . . . . . . . . 5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . 5.3 Three phase to Single phase Step down Cycloconverter 5.3.1 Simulation Procedure . . . . . . . . . . . . . . 5.3.2 Results . . . . . . . . . . . . . . . . . . . . . .

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6 DC-DC Converters 6.1 Introduction . . . . . . . . . . 6.2 DC-DC Buck Converter . . . 6.2.1 Simulation Procedure 6.2.2 Results . . . . . . . .

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Page IV

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Contents 6.3

6.4

6.5

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DC-DC Boost Converter . . . . . . . . . . 6.3.1 Simulation Procedure . . . . . . . 6.3.2 Results . . . . . . . . . . . . . . . DC-DC Buck / Boost Converter . . . . . 6.4.1 Simulation Procedure . . . . . . . 6.4.2 Results . . . . . . . . . . . . . . . ` K DC-DC Converter . . . . . . . . . . CU 6.5.1 Simulation procedure . . . . . . . 6.5.2 Results . . . . . . . . . . . . . . . Full Bridge DC DC Converter . . . . . . . 6.6.1 Full Bridge DC DC Converter with 6.6.2 Full Bridge DC DC Converter with

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93 94 95 95 95 97 99 100 101 101 102 105

Page V

List of Figures 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35

Page VI

1 φ half wave rectifier with RL load . . . . . . . . . . . . . . . . . . . . Reaching simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Creating a new model . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adding a block in the model . . . . . . . . . . . . . . . . . . . . . . . . . Construction of a model . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adjusting the oscilloscope . . . . . . . . . . . . . . . . . . . . . . . . . . Adjusting the oscilloscope parameters . . . . . . . . . . . . . . . . . . . Getting towards the simulation parameters . . . . . . . . . . . . . . . . Adjusting the simulation parameters . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FFT analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Half wave rectifier with free wheeling diode . . . . . . . . . . . . . . . . Output waveforms with free wheeling diode . . . . . . . . . . . . . . . . FFT of the rectifier with free wheeling diode . . . . . . . . . . . . . . . Circuit arrangement for single phase full wave center tap rectifier . . . . Adjusting the transformer parameters . . . . . . . . . . . . . . . . . . . Output waveform of center tapped full wave rectifier . . . . . . . . . . . Center tapped full wave rectifier with free wheeling diode . . . . . . . . Output waveform of center tapped full wave rectifier with free wheeling diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full wave bridge rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . Full wave bridge rectifier without freewheeling diode . . . . . . . . . . . Output of full wave bridge rectifier without freewheeling diode . . . . . Full wave bridge rectifier with freewheeling diode . . . . . . . . . . . . . Full wave bridge rectifier with freewheeling diode . . . . . . . . . . . . . Three phase full wave bridge rectifier . . . . . . . . . . . . . . . . . . . . Simulation setup for three phase full wave rectifier . . . . . . . . . . . . Three phase balanced input . . . . . . . . . . . . . . . . . . . . . . . . . Three phase balanced input . . . . . . . . . . . . . . . . . . . . . . . . . Output of three phase full wave bridge rectifier . . . . . . . . . . . . . . Simulation setup for twelve pulse rectifier . . . . . . . . . . . . . . . . . Three phase three winding transformer block parameters . . . . . . . . . Waveforms for twelve pulse rectifier . . . . . . . . . . . . . . . . . . . . . FFT of primary current of transformer for phase A . . . . . . . . . . . .

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23 24 24 25 25 26 27 28 29 30 30 31 32 33 33

List of Figures 3.1 3.2 3.3 3.4 3.5 3.6

35 36 36 37 37

3.14 3.15

Single phase half wave controlled rectifier . . . . . . . . . . . . . . . . . . Simulation setup for single phase half wave controlled rectifier . . . . . . . Waveforms for single phase half wave controlled rectifier . . . . . . . . . . Single phase full wave semi-controlled rectifier . . . . . . . . . . . . . . . . Single phase full wave semi-controlled rectifier with improved configuration Simulation setup for two topologies of single phase full bridge half controlled converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation results for two topologies of single phase full bridge half controlled converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single phase full wave Full-controlled converter . . . . . . . . . . . . . . . Simulation setup for 1Φ full wave full-controlled converter . . . . . . . . . Simulation results for 1Φ full wave full-controlled converter . . . . . . . . Input parameters waveforms for single phase full bridge full controlled converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three phase SCR based full wave full controlled converter . . . . . . . . . Simulation setup for three phase SCR based full wave full controlled converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Output voltage of 3Φ full wave full-controlled converter . . . . . . . . . . Input current analysis of 3Φ full wave full-controlled converter . . . . . .

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24

Typical three phase inverter [4] . . . . . . . . . . . . . . . . . . . . . Pulse Width Modulation . . . . . . . . . . . . . . . . . . . . . . . . . Three phase sinusoidal PWM [5] . . . . . . . . . . . . . . . . . . . . Generation of triangular waveform . . . . . . . . . . . . . . . . . . . Triangular waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . PWM generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of PWM with different value of constant. . . . . . . . . . . . Single phase SinePWM . . . . . . . . . . . . . . . . . . . . . . . . . . Results of three phase SPWM. . . . . . . . . . . . . . . . . . . . . . Simulation setup of single phase half bridge inverter . . . . . . . . . Subsystem for PWM generation of single phase half bridge inverter . Results of Half bridge Inverter with Resistive load. . . . . . . . . . . Results of Half bridge Inverter with Inductive load. . . . . . . . . . . Simulation setup of single phase inverter with bipolar switching . . . Single phase asynchronous motor . . . . . . . . . . . . . . . . . . . . Waveforms for Single phase inverter with bipolar switching . . . . . Simulation setup of single phase inverter with unipolar switching . . Output waveforms of single phase inverter with unipolar switching . FFT of output of single phase inverter with unipolar switching . . . Simulation setup for quasi square wave single phase inverter . . . . . Subsystem for quasi square wave single phase inverter . . . . . . . . Results of quasi square wave inverter. . . . . . . . . . . . . . . . . . Block diagram for simulation of hysteresis band 3 phase inverter [6] . Conceptual explanation of hysteresis band single phase inverter [6] .

47 48 49 50 51 51 52 53 53 55 55 57 57 58 59 60 61 62 63 64 64 65 65 66

3.7 3.8 3.9 3.10 3.11 3.12 3.13

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Page VII

List of Figures 4.25 4.26 4.27 4.28 4.29 4.30 4.31 4.32 4.33 4.34 4.35 4.36 4.37 4.38

Simulation setup of hysteresis band inverter . . . . . . . . . . . . . . . . Results of PWM inverter using hysteresis band method. . . . . . . . . . Modeling of leg of an inverter [1] . . . . . . . . . . . . . . . . . . . . . . Modeling of output voltages of inverter [1] . . . . . . . . . . . . . . . . . Complete model of an inverter [1] . . . . . . . . . . . . . . . . . . . . . . Results three phase Inverter. . . . . . . . . . . . . . . . . . . . . . . . . FFT of inverter waveform . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation setup for 3 phase inverter with 3 phase asynchronous motor as load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parameter adjustment of universal bridge . . . . . . . . . . . . . . . . . Asynchronous motor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement selection of bus selector . . . . . . . . . . . . . . . . . . . Parameter adjustment of STEP input . . . . . . . . . . . . . . . . . . . Output of motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminal voltages and three phase stator currents . . . . . . . . . . . . .

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13

General diagram of a cycloconverter [3] . . . . . . . . . . . General diagram of a cycloconverter [6] . . . . . . . . . . . Output waveform of a cycloconverter [3] . . . . . . . . . . . Simulation setup of a single phase to single phase step down Selection of measurements . . . . . . . . . . . . . . . . . . . Plotting of measurements . . . . . . . . . . . . . . . . . . . Plotting of measurements . . . . . . . . . . . . . . . . . . . Plotting of measurements . . . . . . . . . . . . . . . . . . . Three phase to single phase cycloconverter [3] . . . . . . . Simulation setup for 3 phase to 1 phase cycloconverter . . . Timing diagram of pulses . . . . . . . . . . . . . . . . . . . Output without filter . . . . . . . . . . . . . . . . . . . . . . Output with filter . . . . . . . . . . . . . . . . . . . . . . .

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6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14

DC-DC buck converter . . . . . . . . . . . . . . . DC-DC buck converter simulation setup . . . . . DC-DC buck converter simulation results . . . . DC-DC boost converter . . . . . . . . . . . . . . DC-DC boost converter simulation setup . . . . DC-DC boost converter output current . . . . . DC-DC boost converter simulation results . . . DC-DC buck / boost converter . . . . . . . . . . DC-DC buck / boost converter simulation setup Simulation results with 25% duty cycle . . . . . Simulation results with 50% duty cycle . . . . . Simulation results with 75% duty cycle . . . . . . ` K DC-DC converter . . . . . . . . . . . . . . CU ` K DC-DC converter . . . Simulation setup of CU

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Page VIII

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List of Figures 6.15 6.16 6.17 6.18 6.19 6.20 6.21 6.22 6.23

` K converter. . . . . . . . . . . . . . . . . . . Simulation results of CU Full Bridge DC DC converter [6] . . . . . . . . . . . . . . . . . . . . Bipolar voltage switching [6] . . . . . . . . . . . . . . . . . . . . . . . Simulation setup for bridge converter with bipolar voltage switching Subsystem for bipolar voltage switching . . . . . . . . . . . . . . . . Simulation results of bridge converter with bipolar voltage switching Voltage waveforms for unipolar voltage switching [6] . . . . . . . . . Subsystem for unipolar voltage switching . . . . . . . . . . . . . . . Simulation results for unipolar voltage switching . . . . . . . . . . .

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101 102 103 104 104 105 106 107 108

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1 Introduction to Modeling and Simulation 1.1 Importance of Simulation Circuit performance is a key factor in designing a system in electrical engineering. Each and every component contributes towards the overall performance of a system. In high power electronics known as power electronics we need to be very focused towards the evaluation of system. Not only the components but the junction capacitances and noise also affect the output waveforms. In this modern world power electronics engineers are assisted by control engineers that providing them very useful control chips for signal generation and circuit operation. But these control ICs are also very complex and therefore it is desired to analyze them using software based tools. Circuit simulation is fast becoming an alternative to prototyping. Software based simulation is now considered as an optional aid in learning power electronics. Simulation is an art of converting a circuit design into a software model and then testing it using input stimuli and output monitoring. It can be used to evaluate the performance of new circuits for enhancement of knowledge. The flaws in any circuit can be corrected at early design stage with the help of simulation. Novel techniques can be tested using simulation based packages that saves cost, time and any potential hazard that can arise from short circuit across power components. Apart from its wide use in academia, industrial users gains benefit from simulation by verifying their process performance. Simulation in the past received critics as it adds another step in design cycle but with on going work based on simulation it has been now proved that, as a product progresses through the design cycle, errors become more and more costly to correct. It is best for conducting studies for destructive nature of tests of electric machines. Simulation is an excellent way to reveal logic and/or timing errors in a circuit before continuing for the prototyping. With simulation we can do a variety of operations including the following [3, 6] ˆ Waveforms at various points of circuit ˆ Circuit performance in transient and steady state condition that may be very difficult in hardware prototype. ˆ Assessment of performance improvement / degradations ˆ Measurement of noise and distortion at any node / point of circuit without using expensive network signal analyzers ˆ Voltage and current ratings by examining the waveforms ˆ Calculation of tolerance level for various components that leads to sensitivity analysis.

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1.1 Importance of Simulation ˆ Harmonics analysis without using any expensive equipment ˆ Evaluate the effects of non linear elements on circuit performance ˆ Optimize the design of electronic circuits in terms of circuit parameters ˆ Measurement of power losses for various components including the power switches and diodes. ˆ Development of temperature versus losses curves for circuit elements

Simulation in the field of power electronics is somewhat different then other fields of electrical engineering due to its interdisciplinary nature. Almost every circuit of power electronics exhibits an extremely non linear behavior that makes it difficult to accurately model circuit elements. The simulation time is not constant i.e it may be possible that an inverter with some electrical load at the output may require less time for simulation then an inverter driving a motor. It is because the inverter has a time constant in microseconds whereas a motor can not respond so quick so it has a response time in seconds. So for accurate simulation it is mandatory to keep the step size much smaller that has a side effect of longer simulation time. Further in power electronics we have to essentially deal with power switches like MOSFETs, IGBTs, SCRs and diodes. Unfortunately no accurate model is available therefore that makes it difficult to model them. Specific requirements can be met only with careful objective based simulation. Since, power electronics needs a controller therefore sophisticated controllers are modeled along with to verify the exact system response. Inductors and capacitors used in power electronics circuits may have some initial states that can hamper the swiftness of simulation. Therefore what we need is to carefully analyze what to achieve from a simulation.Sometimes we may not need all the responses from a circuit. A good simulation can be defined as following [6] “The best simulation is the simplest possible simulation that meets the immediate objective” Therefore we need to specify the system objectives before simulation. For a detailed system design following steps are followed [6] ˆ Low level simulation or large signal simulation ˆ Small signal model and controller design ˆ High level simulation or large signal system behavior

Usually for initial testing of new system and for choosing the circuit topology controller is not included in initial level simulation. Predefined signals are given to the system to observe the response. The observations from such low level simulation is then tested with analytical calculations. This gives an idea about the component ratings and circuit topology. Normally we need not to use detailed models for devices used at such low level simulation. Ideal components are used to get a bird eye view of system performance.

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1 Introduction to Modeling and Simulation After deciding the type of circuit the next step is to include the design of controller. Component values are also specified to create a linear model. Controller design may include Proportional (P), Proportional Integral (PI) or Proportional Integral Derivative (PID) control and may be strengthened by use of Fuzzy Logic (FL), or Artificial Neural Network (ANN). The complete design of controller makes it sure to proceed for the high level simulation where it is combined with the circuit to verify the performance of the designed system. At this stage the power losses, heat curves and non linear behavior is also studied in detail. The details of voltage stress on switching devices, the effect of stray capacitances and leakage inductances are also incorporated in this stage to get a response closer to the real world. At this stage ideal models are not used , rather we use detailed models to show the system nonlinearities explicitly. The bottom line here is “Simulation makes it easier to find design problems early in the design cycle.”

1.2 Why Simulink SIMULINK is available with MATLAB installation and unlike MATLAB it is a model based software, i.e. it models the system with the help of building blocks and small elements and then simulates for the analysis of the model. It is so simple that making a system is not more than plug and play. You put your desired building blocks on the blank model page, fix their values and connect the output to a scope to see the effect. Various kinds of building blocks are available within SIMULINK ranging from the simple to advanced one based on artificial intelligence techniques. Both linear and non linear systems can be modeled in it with the same ease. The analysis could be of dynamic system and can be of any level. The main idea behind every simulation is to model the system. It can perform mathematical modeling as well as real component based modeling. The ongoing research in the field of engineering has proved that the SIMULINK results are very promising and resembles too close with the real system provided that the modeling is accurately accomplished. The models can be made in accordance with the simulation guidelines given in section 1.1. The model once made can be modified with real values of components. It can be used for the simulation of following systems ˆ Continuous timed model ˆ Sampled timed model ˆ Hybrid system with both continuous and sample time modeling ˆ Linear system ˆ Non-linear system

With the time, SIMULINK has become so mature in its work that now a very large portion of research work is based on the simulation results of SIMULINK. Since the main computational engine used is MATLAB therefore SIMULINK allows you to use the

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1.3 SIMPOWER SYSTEM MATLAB functions to work in parallel with the SIMULINK model. Even the MATLAB function can be made as part of the SIMULINK model. Engineers and scientists are using this to testify their theoretical hypothesis and novel techniques and its outcome is saving a lot of time and money. SIMULINK is widely used in the following areas [2] ˆ Aerospace and defense ˆ Automotive ˆ Power system analysis ˆ Power electronics and renewable energy system simulation ˆ Artificial intelligence based systems ˆ Communications ˆ Electronics and signal processing ˆ Medical instrumentation

As this book is on the simulation of power electronics therefore we will focus on one of the functionaries of SIMULINK known as SIMPOWER system.

1.3 SIMPOWER SYSTEM SimPower Systems software is a very useful tool for the analysis of power system problems. It has produced a lot of ease for engineers and researchers for in depth analysis of power system using its user friendly interface. As discussed above the work of SIMULINK is merely a plug and play operation therefore SimPower Systems is easy to use and models can be developed using simple click and drag procedures. SIMULINK is used for variety of systems and SimPower Systems being an integral part of SIMULINK provides and opportunity to develop a whole industrial environment with thermal, mechanical and control blocks connected with the electrical system. In SimPower Systems software the electrical components are present that can be adjusted to model a specific device. For example transformer has built in data that can be modified for the input and output values by simple clicking and editing the value. Besides the transformer SimPower Systems has other components like transmission lines, electrical machines, wind generation, HVDC and electric drives. For simulation of power electronics systems a semiconductor based library lies within the SimPower Systems. Measurement library allows the researcher to measure various parameters like current, voltages, power, THD, RMS, and impedance for single and three phase systems. Input can be selected by a mix library of input sources that includes the AC and DC voltage and current sources. Very interestingly the POWERGUI block makes it fun calculating the FFT of the waveform at any instant and any particular point. By selecting the fundamental frequency and the limit for harmonic analysis one can see details of harmonic pollution within a model in both graphical and tabular form. People have spent years on the research and development

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1 Introduction to Modeling and Simulation of these components therefore, these models are proven and are tested in reputed laboratories including Power Systems Testing and Simulation Laboratory of Hydro-Qubec, a large North American utility located in Canada, and also on the experience of cole de Technologie Suprieure and Universit Laval [2]. The capabilities of SimPower Systems software for modeling a power electronics system are presented in this book with a lot of graphical illustrations.

1.4 Architecture of book Power electronic is a science of power conversion. There are four types of power conversion within the domain of power electronic conversion. These include ˆ AC-DC conversion (Rectifiers) ˆ AC-AC conversion (Cycloconverter) ˆ DC-AC conversion (Inverter) ˆ DC-DC conversion (Switch Mode Power Supplies)

In this book the topic of rectifiers has been divided into two parts with simulation of controlled and uncontrolled rectifiers. Different topologies for single and three phase rectifiers are simulated using free wheeling diode and without using freewheeling diode. A little theory has also been given for each circuit assuming that the reader know well about the working of these circuits. Chapter on cycloconverter has two simulations for single phase to single phase and single phase to three phase cycloconverter with step down feature. We have tried to cover inverters with detail especially the single phase, three phase, quasi square wave and SPWM inverters. Last chapter is about DC -DC converters. All the basic types are simulated and in addition to them the concept of unipolar and bipolar output has been elaborated using simulation of full bridge DC-DC converter.

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2 Uncontrolled Rectifiers 2.1 Introduction Most of the power electronic devices converts the incoming AC voltage of fixed frequency and fixed voltage into DC of fixed value. The objective here is to obtain useful DC supply from grid side. Diode based rectifiers are used commonly for such purpose. They are also known as uncontrolled rectifiers. In these type of rectifiers the power can only flow from AC side to the DC side hence, we do not have any control on the power flow. The output is entirely dependent on circuit topology and the biasing condition of diodes. As soon as the applied voltage exceeds the diode depletion layer potential (typically 1-2 V for a power diode and 0.7V for ordinary Si diode and 0.3V for ordinary Ge diode) it starts conducting and keeps on conducting unless and until the voltages becomes less then the required threshold voltage. Since, everything that happens in this entire process is automatic and no external parameter can control the power flow therefore such rectifiers are called uncontrolled rectifiers. These kind of power electronic devices are also known as linear power supply and suffer from their large size and low efficiency. However, these type of rectifiers are widely used in single and three phase domestic applications. In this chapter we are presenting the simulation for both single phase and three phase rectifiers with various configurations.

2.2 Single phase half wave rectifier Single phase half wave rectifiers are the most basic form of rectifier. A rectifier without having any control on power flow is based on diodes. These diodes turn on and off according to the voltages available on their terminals. They cannot be controlled through some external signal. The term half wave is originated from the fact that these rectifiers only allow half wave to appear across the load. Half of the cycle always drops across the diode. They have the least number of diodes in their topology that results in poor power quality, increased voltage drop and less power utilization. They typically have an efficiency of 41 % and a ripple factor of 121 %, therefore such type of rectifiers are not used in practical applications. Since this kind of rectifier is a basic building block for the theoretical advancement in diode based rectifiers it is simulated for RL load.

2.2.1 Without freewheeling diode The single phase half wave rectifier is shown in Fig.2.1. It has only one diode that allows to pass only one half cycle of input AC voltage and blocks the other half. The part of cycle it blocks depends on the connectivity of diode with input supply. These kind of

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2 Uncontrolled Rectifiers converters have a fixed output and a low efficiency due to the wastage of half the supply voltage.

Figure 2.1: 1 φ half wave rectifier with RL load

Simulation Procedure We will now simulate this circuit using the following values of circuit components ˆ Resistance = 0.5 Ω ˆ Inductance = 6.5 mH ˆ Vin =220 Vrms at 50Hz (312Vp )

Open MATLAB and click on the icon for SIMULINK as shown in fig.2.2. Alternatively you can open SIMULINK by writing SIMULINK in the command window. Another way is to adopt the way through START icon of MATLAB Start ⇒ Simulink ⇒ Librarybrowser. Click on NEW MODEL or go to F ILE ⇒ N EW ⇒ M ODEL and a new blank model is created as shown in Fig.2.3. You can also reach this point directly by adopting this route M AT LAB ⇒ F ile ⇒ N ew ⇒ M odel. However, after creating a blank model you need to open the SIMULINK component storeroom by going to V iew ⇒ LibraryBrowser. Select SIMPOWER SYSTEMS then select Power Electronics library and by right clicking on diode and click on add to untitled will add the diode in the blank model. Alternatively you can drag the component directly in the model page as shown in Fig.2.4. Similarly go to ELECTRICAL SOU RCES ⇒ AC Voltage Source and add it to untitled. Select Elements and select SERIES RLC BRANCH and add it to untitled. Simulink do not perform simulation unless and until a measurement block is present in a system. Since we need to measure the instantaneous input and output voltages and the load current we need to have 3 instruments (2 voltmeters and 1 ammeter). To add them select Measurement in SIMPOWER SYSTEMS and then

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2.2 Single phase half wave rectifier

Figure 2.2: Reaching simulink

add current measurement and voltage measurement blocks to untitled. Oscilloscope is not included in SIMPOWER SYSTEMS and is present in the top most block of the left column that is SIM U LIN K ⇒ Sinks ⇒ Scope. We can join various blocks by clicking on their edges and then drag the wire till the other connection terminal. Construct the circuit by joining them together in the form as given in Fig. 2.5

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2 Uncontrolled Rectifiers

Figure 2.3: Creating a new model

Figure 2.4: Adding a block in the model

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2.2 Single phase half wave rectifier

Figure 2.5: Construction of a model

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2 Uncontrolled Rectifiers

Figure 2.6: Voltage block

Now double click the voltage block to set the values of voltage and frequency. A dialog box will appear as shown in Fig.2.6. Inside it various parameters can be set that are ˆ Peak amplitude of the generated voltage, in volts (V)

Set it to 312 V (Default is 100V)(. ˆ Phase in degrees (deg).

Set it to zero (0) degrees. ˆ Frequency in hertz (Hz).

Set it to 50Hz (Default is 60Hz) ˆ Sample time in seconds (s). The default is 0, corresponding to a continuous source.

Let it remain as it is ˆ Measurements

Set it to none because we are not using multi meter (Use of multi meter is discussed in comming simulations). Double click on diode and you can set various parameters for DIODE according to the specific data sheet. Double click on series RLC branch and set the values for R and L

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2.2 Single phase half wave rectifier as given in the start of the problem. Select the Branch type as RL as shown in Fig.2.7. It should be noted that for writing the values of L we have to use e-6 for micro and e-3 for milli etc. In the Scope menu “>” is shown which can only be connected to the inverse icon “<” in the measurement blocks. It has only 1 input terminal. When we need to observe the waveforms we use scope and if the resultant waveforms are more than one then there are several methods to display all the three waveforms as given below ˆ Use separate scopes for all the measurements. ˆ Use MUX before the scope. ˆ Adjust the number of axes of scope.

We will adopt the third method. Double click on SCOPE and then click on parameter icon as shown in Fig.2.8. Make the number of axes equal to 3. Now you can observe that we have 3 axes that can be used for the three plots as required in problem statement. Before simulation also adjust the data history of scope by following the Fig.2.9. By checking the save data to history we can perform the fourier analysis of the waveforms. You can also remove the “limit data points....” by unchecking it.

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2 Uncontrolled Rectifiers

Figure 2.7: Load selection

Figure 2.8: Adjusting the oscilloscope

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2.2 Single phase half wave rectifier

Figure 2.9: Adjusting the oscilloscope parameters

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2 Uncontrolled Rectifiers Before running the simulation we have to configure the parameters. Go to Simulation ⇒ Conf igurationparameters as shown in Fig.2.10. Various kind of solvers are available for simulation. Each solver uses different techniques for solving the system based on stiff and non stiff problems. Among the available solvers given below first four are considered good for non-stiff problems. Rest all are for stiff problems [5, 7], ˆ ODE45

It is based on Dormand-Prince which is explicit, one step Runge-Kutta recommended as a first try method. ˆ ODE23

It uses Bogacki-Shampine that is also explicit, one step Runge-Kutta. May be more efficient than ODE45 when tolerances are wide. ˆ ODE113

It is multi step, variable order Adams-Bashforth-Moulton PECE solver.When function evaluation is time consuming and tolerances are tight it is recommended ˆ ODE23t

It is used for moderately stiff problems if you need a solution without numerical damping. ˆ ODE15

Multi step variable order solver based on backward differentiation formula ˆ ODE23s

One step solver based on Rosenbrock formula of order two. It has the A stability property. ˆ ODE23tb

It is also for stiff problem and can be used for using curde error tolerances to solve stiff systems Select the ode23tb (Stiff/TR-BDF2) or ode15s (Stiff/NDS) or any suitable solver as shown in Fig. 2.11. ode15s (Stiff/NDS) is used for simulating this circuit. Start the simulation by either clicking on Start Simulation icon as shown in Fig. 2.4 or by going to Simulation ⇒ Start.

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2.2 Single phase half wave rectifier

Figure 2.10: Getting towards the simulation parameters

Figure 2.11: Adjusting the simulation parameters

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2 Uncontrolled Rectifiers Results Double click on scope and observe the three graphs as shown in Fig. 2.12. Left click on any graph and drag to make a rectangle to get the waveforms for a small period of time. This actually zoom the waveforms within a specified interval of time. Right click on each graph and select the axes properties and label each graph. As shown in Fig.2.5 double click on power GUI and click on FFT analysis. Figure 2.13 shows the FFT window. Set fundamental frequency as 50 Hz and click on display. The results can also be obtained in term of tabular form by selecting the display style in FFT window. Save the file as half wave. It should be noted that simulink do not allow to save files with spaces therefore usually is included in between two words.

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2.3 Single phase full wave center tap rectifier

Figure 2.16: FFT of the rectifier with free wheeling diode

2.3 Single phase full wave center tap rectifier 2.3.1 Without freewheeling diode Full wave rectifiers are a refined form of the basic rectifiers and are widely used for low power applications like battery chargers, DC power supplies and computer power supplies. They are also uncontrolled hence the quantity of the output cannot be controlled. The center tap rectifier uses a center tapped transformer and it has only two diodes to conduct in alternate paths. Figure 2.17 shows the schematic of a center tapped rectifier. The transformer used is center tapped and have two secondary windings with their center tapped. The central end is connected to ground and the other two ends are connected through each other via diode D1 and D2. The diode D1 conducts when there is a positive voltage at the transformer secondary winding. However while D1 conducts there is a negative voltage at the anode of D2 so it acts as an open circuit. D2 conducts when it gets a positive voltage at the anode. When it conducts then at that time D1 will act as an open circuit. So in this way it rectifies both the portions of input cycle. In this method the transformer is used and only two diodes are used for the rectification. We will now present the simulation of this circuit using an RL load. Simulation Procedure Create a blank page and add the following blocks

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2 Uncontrolled Rectifiers

Figure 2.17: Circuit arrangement for single phase full wave center tap rectifier

ˆ SimPower Systems⇒Electrical sources ⇒ AC voltage source ˆ SimPower Systems⇒Elements ⇒ Linear transformer ˆ SimPower Systems⇒Power electronics ⇒ Diode ˆ SimPower Systems⇒ Elements ⇒ Series RLC branch

Arrange the circuit as shown in fig 2.17. The center tapped transformer here is used as a step down transformer with 12 volts set at the secondary. For having teo secondaries check the “Three winding transformer” option given in transformer parameter dialog box. To set the parameters of this transformer double click on it and enter the value of input voltage and frequency as shown in Fig. 2.18. The rest of the circuit is very simple and can be completed by following the rules mentioned in the previous topic. Results The waveforms for the above circuit are given in Fig.2.19 and it is very visible that both the positive and the negative half cycles are rectified using this circuit.

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2.5 Three phase full wave rectifier

Figure 2.28: Simulation setup for three phase full wave rectifier

ˆ Voltmeter (Simulink ⇒ Sim Power system ⇒ Measurements ⇒ Voltmeter) ˆ Diode ( Simulink ⇒ Sim Power system ⇒ Power electronics ⇒ Diode) ˆ Ground (Simulink ⇒ Sim Power system ⇒ Elements ⇒ Ground) ˆ Multimeter Block (Simulink ⇒ Sim Power System ⇒ Measurement ⇒ Multimeter ) ˆ Mux (Simulink ⇒ Commonly used blocks ⇒ Mux)

Assemble the circuit as shown in Fig. 2.28. Double click power GUI and click on configure parameters. Select simulation type as discrete with sample time of 50e-6. Open the scope and go to parameters. Select sampling as sample time and make it similar to the value selected in GUI block (50e-6). To make a three phase supply join the three AC voltage source as shown in Fig. 2.28 and enter 0,120 and 240 (or -120) in phase tab of each source respectively. The resultant 3 phase waveforms are shown in Fig.2.29. Connect the negative terminal to ground. In order to get the line voltage use voltmeter and connect them to get Vab , Vbc and Vca . It should be noted that Vab = Va − Vb , Vbc = Vb − Vc and Vca =Vc − Va . Set the value of RLC series branch as RL load with R = 1 ohm and L = 1e−3 H. Also select the branch voltage and current in measurement tab. Before running the circuit make sure the following ˆ Set the solver as ode23tb (stiff/TR-BDF2) ˆ Max. step size as 0.001

Double click on multimeter and within the dialog box that will appear, the list on left side contains the available measurements. Select them and add them in selected measurement as shown in Fig. 2.30. It should be noted that if we uncheck the measurement tab in RLC series branch then there will be no available measurement in multimeter.

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2 Uncontrolled Rectifiers

Figure 2.29: Three phase balanced input

Results Run the simulation for 0.5 sec time Fig. 2.31 shows the output where it can be seen that current and voltage across the load have phase difference.

2.6 Twelve pulse rectifier So far we have simulated those rectifiers that are most suitable for off line domestic applications. The most powerful among these rectifiers is the three phase full wave rectifier that is also referred as six pulse rectifier. These rectifiers have high THD for inrush current and if we need to use them for very high power applications they are considered inappropriate. This is specifically evident in case of HVDC systems, where we need to keep the THD of input current as low as possible and on the other side the DC link ripple as minimum as possible. For such high power applications,one method is to use a combination of two six pulse rectifiers connected in delta-wye ( − Y ) and delta-delta( − ) connection. The use of  and Y at the secondary of transformer gives a delay of 30◦ at the secondary. For coping with the high power requirement the secondary can be connected in series or parallel for high voltage and high current applications respectively. The main advantage is revealed in the fourier analysis of input line current that states that the lowest order harmonic that appear are 11th and 13th [6].

2.6.1 Simulation Procedure For simulation place the following components as shown in Fig. 2.32. ˆ AC voltage source ˆ Three phase transformer, three windings (SIMULINK ⇒ SIM POWERSYSTEMS ⇒ Elements ⇒ Three phase transformer, three windings) ˆ Diodes ˆ Series RLC branch

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3 Controlled Rectifiers/Converters 3.1 Introduction Controlled rectifiers are kind of rectifiers that employee thyristors or SCRs. By using these generic devices the output can be controlled by varying the firing angle. These type of rectifiers provide us some degree of freedom depending on the circuit topology. Following are the different types of controlled rectifiers ˆ Half controlled rectifiers ˆ Full controlled rectifiers

These type of rectifiers are applicable for both single and three phase applications. They form the basis for the four quadrant operation. With it we can design flexile power electronic systems for electric drives and other applications. In the coming sections we will simulate various types of controlled rectifiers.

3.2 Single phase half wave controlled converter Single phase half wave rectifier is the most basic kind of controlled rectifier using only one SCR. Only positive half cycle is used hence the power utilization is minimum. The ripple voltage contains high harmonics and for such harmonics the current drawn by the load inductance L will be less. Since the output voltage should not be rich in harmonics therefore this kind of controlled rectifier is seldom used practically and is given in text books for understanding of basic concepts. Figure 3.1 shows the architecture of this simple controlled rectifier. Here the point where current goes to zero or where SCR stop conduction is not in our control so we do not know the output ripple across inductance. Since we have negative conduction here so we should get rid of the negative conduction portion due after π. Also in case of a highly inductive circuit the inductance L will not allow the current to change instantaneously. So if we want to have eq.3.1 valid here we have to remove the negative side. Vo =

Vm (1 + cosα) 2π

(3.1)

Therefore we need another part to be installed and there comes the concept of free wheeling.

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3 Controlled Rectifiers/Converters If the gate pulses are applied at zero degree then this circuit is similar in operation to a three phase diode bridge rectifier. The output voltage obtained is a difference of the voltage at positive and negative rail. The supply current is a rectangular waveform with only non triplen odd harmonics present in them. It should be noted that if we replace the lower side SCRs i.e T2, T4 and T6 with diodes then the circuit works as a three phase full wave semi controlled converter. Its simulation is left as an option for the reader.

3.5.1 Simulation Procedure Place the following components as shown in fig. 3.13. ˆ Thyristors ˆ Pulse generator ˆ AC voltage source ˆ Current measurement ˆ Voltage measurement ˆ Series RLC branch ˆ Scope ˆ Connection port(Simulink ⇒ SIMPOWER systems ⇒ Elements⇒ Connection port)

Here three phase input is created by making a subsystem and the output of the subsystem is connected with the bridge. Three pulse generators are used for firing of all six SCRs. They are fired at 45◦ with an additional phase delay of 120◦ and 240◦ for phase B and C respectively. The load is taken as highly inductive with R=50Ω and L=650mH.

3.5.2 Results For this circuit the waveforms for output voltage, the line current for phase A and the FFT of the input current are drawn. Figure 3.14 shows the output voltage at α = 45◦ . Whereas Fig.3.15 shows the line current for phase A and its FFT. It can be seen that only non triplen odd harmonics are present here.

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4 DC-AC Inverters 4.1 Introduction DC-AC inverters are used mostly in applications where we need to have a variable frequency with either DC or AC input voltage. Typical examples of inverter use are motor drive applications, Uninterrupted Power Supply (UPS), Renewable energy systems (Solar PV and Wind) and HVDC link, where the desired task is to generate the frequency of user choice. Inverters are available in a variety of topologies for three phase and single phase applications. Figure 4.1 shows the general schematic of a 3 phase inverter1 . It is fed by a DC source that can either be supplied by rectifying the offline power supply of utility or by other means like using a DC battery as in case of hybrid vehicles or the output of a solar array in case of a solar system. For single phase inverters there are four switches for a full bridge inverter and six switches in a 3 phase inverter. The output voltage waveform for a voltage source inverter and output current waveform of current source inverter are stepped waveforms and their quality depends on the switching scheme of Pulse Width Modulation (PWM). Generally sinusoidal PWM is used for periodic switching of the inverter switches. For analysis in almost every text book the DC link is divided into two capacitors each holding half of the DC link voltage such that their mid point becomes at zero potential as shown in Fig 4.1. The power flow in each phase is controlled by the ON/OFF ratio or duty cycle of the respective switches. In the operation of inverter some important relations are Vao = Van + Vno

(4.1)

Vbo = Vbn + Vno

(4.2)

Vco = Vcn + Vno

(4.3)

Van + Vbn + Vcn = 0

(4.4)

3Vno + 0 = Vao + Vbo + Vco

(4.5)

1 Vno = (Vao + Vbo + Vco ) 3

(4.6)

For balanced load phase voltages

Adding these equations, we get

1

PROJECT  SPACE VECTOR PWM INVERTER by JIN-WOO JUNG Ohio State University, USA

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4 DC-AC Inverters

Figure 4.1: Typical three phase inverter [4]

Putting the value of Vno in Vao , Vbo and Vco we get 2 1 1 Van = Vao − Vbo − Vco 3 3 3

(4.7)

2 1 1 Vbn = Vbo − Vco − Vao (4.8) 3 3 3 2 1 1 Vcn = Vco − Vao − Vbo (4.9) 3 3 3 Since,most of the times inverters are used against the inductive load, in order to keep the transistors safe, diodes are used in antiparallel direction for dissipating the energy stored in the load inductance. Furthermore, the transistors connected in same leg should never be turned on simultaneously so as to avoid any short circuit of dc bus bar. In this chapter different types of single phase and three phase inverters are simulated. As PWM is an essential ingredient of inverters the first simulation is dedicated to the refinement of the concepts of PWM.

4.2 Pulse Width Modulation PWM is one of the most widely used technique in power electronics switching. It is a process of producing pulse trains with variable widths that control the flow of power through power electronic switches. Various kinds of PWM techniques are available in literature, from simplest to specialized one like Selected harmonic Elimination (SHE). Figure 4.2 very clearly shows the simplest PWM scheme in which a triangular wave is compared with a DC voltage. The amplitude of DC voltage is directly responsible for the production of pulses with variable width. The output will be high if amplitude of DC is greater then the amplitude of triangle waveform at any instant.It is obvious from the the related figures that decreasing the amplitude of DC is actually generating pulses with narrow pulse width and vice versa. It should be noted that the frequency of waveform is independent of the amplitude of DC value. Mostly such kind of PWM is employed in DC DC Converters where the DC is fetched from the output via a voltage divider

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4 DC-AC Inverters

Figure 4.3: Three phase sinusoidal PWM [5]

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4.2 Pulse Width Modulation

Figure 4.4: Generation of triangular waveform

4.2.1 Simulation Procedure We have to generate PWM using SIMULINK.Open the SIMULINK and create new page and place the following blocks on the model page. ˆ Constant ˆ Integrator ˆ Scope ˆ User defined function f(n) ˆ MUX

We have to first generate the triangular waveform. To generate this following setup is required as shown in Fig. 4.4. In Fig. 4.4 we have to write an M file and write the value of “ωe” or alternatively we can enter its value equal to the desired value. The MUX can have many inputs. In SIMULINK each input is designated as U1, U2, U3 up to Un. So in our case the input from integrator is U1 and that of constant1 block is U2. In order to produce a triangular waveform we have to take reminder in order to compare the ever going ramp as shown in Fig. 4.5 .One more interesting block in this simple model is the user defined function Fcn. Open Fcn block and write the following function Rem(u(1),u(2)) It is evident from the Fig. 4.5 that using this function we can generate triangular waveform. Next step is to compare this triangle waveform with a DC wave to generate variable widths PWM pulses. Figure 4.6 shows the complete structure of simulation setup for this simple PWM scheme. Comparing the triangular waveform with an AC waveform gives us what is called Sinusoidal PWM.

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4.4 Single phase PWM inverter with bipolar voltage switching

4.3.1 Simulation procedure To perform the simulation assemble the circuit as shown below in figure 4.10 using the following components ˆ DC voltage source (Enter any desirable value) ˆ Multimeter ˆ Series RLC branch ˆ Sine wave source ˆ Mosfet ˆ Trignometric function ˆ Gain ˆ Rational Operator ˆ Out port(Simulink ⇒ Sinks ⇒ Out 1)

It should be noted that a small resistance Rs is connected in series with the voltage source Vdc . This is to take care of a simulink error that arises when we connect a capacitor in shunt with the dc voltage source. For switching the power MOSFETs sinusoidal PWM is used. It has two reference sine waves with 180◦ phase difference. Figure 4.11 shows the subsystem for PWM generation. The resultant PWM are feeded to the gates of corresponding MOSFETs

4.3.2 Results Figure 4.12 shows the output voltage and the FFT of the waveform for resistive load and Fig.4.13 shows the output voltage and FFT of the waveform for highly inductive load. It should be noted that 21 Vdc is available at the output and since it is an odd symmetry therefore the even harmonics are clearly negligible in fourier spectrum.

4.4 Single phase PWM inverter with bipolar voltage switching Single phase inverters has two legs of switches that are connected in parallel with each other. It is similar to the bridge rectifier with the basic difference of switches in place of diodes. The switches are turned ON and OFF at specified pattern to produce AC output. PWM used here works in such a way that we get bipolar switching voltage that is the output voltage obtained is between +Vdc and −Vdc .

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4 DC-AC Inverters

Figure 4.10: Simulation setup of single phase half bridge inverter

4.4.1 Simulation Procedure We have to simulate a single phase inverter with bipolar switching with single phase Asynchronous motor as load and to plot the waveforms for output voltage, the fundamental component of output voltage, the current for the asynchronous motor and dc link current. Open SIMULINK and create a new model and place the following components according to the diagram shown in figure 4.14 ˆ Discrete PWM generator ˆ Series RLC branch

Figure 4.11: Subsystem for PWM generation of single phase half bridge inverter

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4.4 Single phase PWM inverter with bipolar voltage switching ˆ DC voltage source ˆ MOSFETs ˆ Voltmeter, Ammeter ans scope ˆ Discrete second order filter ˆ Demux

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4.5 Single phase PWM inverter with Unipolar voltage switching

Figure 4.14: Simulation setup of single phase inverter with bipolar switching

It is chosen to work here as a bandpass filter with cutoff frequency of 52Hz and damping factor and the sample time are left as default. The output of the filter is merged with the output voltage of inverter using a MUX and is fed to the scope. The motor used here is an asynchronous motor with 14 hp,110V and 60Hz ratings. Figure 4.15 shows the parameter adjustment window of an asynchronous motor. Note that for power the value entered is 0.25*746 that is the desired value.

4.4.2 Results Figure 4.16 shows the waveforms for output voltage, the fundamental component of output voltage, the motor armature current and the DC link current.

4.5 Single phase PWM inverter with Unipolar voltage switching With a little modification of control logic the circuit used for bipolar switching inverter can be used to get unipolar output. In this technique the output goes from +Vdc to zero for positive half cycle and then from zero to -Vdc for the negative half cycle. That is why it is called Unipolar voltage switching PWM. Thus the two legs on inverter are controlled separately. Therefore, two control signals are to be used that must be 180 degree out of phase with each other. The advantage of this kind of PWM is that the harmonics appeared are at side bands of twice the switching frequency.

4.5.1 Simulation procedure We have to simulate a single phase full bridge inverter using unipolar voltage switching PWM and plot the waveforms for Van , Vbn , Vab and FFT of the Vab . Crete a new page and place the following components according to fig.4.17

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4 DC-AC Inverters

Figure 4.15: Single phase asynchronous motor

ˆ Discrete PWM Generator ˆ Series RLC branch ˆ DC voltage source ˆ MOSFETs ˆ Voltmeter ˆ Goto ˆ From ˆ Scope ˆ Discrete second order filter ˆ Demux

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4.8 PWM based DC-AC 3 phase Inverter also known as tripplen harmonics. However, the fundamental components are summed to zero provided that the operation is symmetric i.e. V1ao + V1bo + V1co = 0

(4.14)

where 1 stands for the fundamental component There are topologies that do not have neutral to get rid of tripplen harmonics. We have to plot the waveforms for eq.4.7, 4.8 and 4.9 for Fig.4.1. A good model is presented in B.K.Bose and we are using that model with little bit modification in this experiment. Furthermore it is desired to perform the Fourier analysis of these waveforms. It is also required to plot the current waveform in each phase for Inductive load of 6.5 mH.

4.8.1 Simulation Procedure Open the SIMULINK and create new page. Place the following blocks on the model page. ˆ Three phase SPWM (refer to section4.2) ˆ Switch ˆ Scope ˆ Gain ˆ DEMUX ˆ Integrator ˆ Sum

In section4.2 we have successfully generated the three phase SPWM (also known as Sub oscillation method) . Place it in the new model for this experiment. In order to model the three legs of inverter we use the switch. For example consider leg A of Figure 4.1 with S1 and S4. We have to turn them ON in such a way that S1 and S4 can not turn on simultaneously (What’s the reason?). Therefore it is evident that leg A can have only one state at a time. Either it can provide positive Vdc to output or it can pass negative Vdc to output. The switch we are using has three ports. It gives the output based on the information given at the center input port. Figure 4.27 shows the model for three legs of inverter with +500 Vdc and a -500 Vdc [1]. In this figure Pulse A , Pulse B and Pulse C are the waveforms we generated in section4.2. In each phase leg top input is connected to +500 Vdc and bottom input with -500 Vdc . The output of each phase leg is Vao , Vbo and Vco for phase A, B and C respectively. Next we have to implement the equations for Van , Vbn and Vcn . For this we need gain blocks and a sum block. For an instance consider the following equation reproduced here for clarity 2 1 1 Van = Vao − Vbo − Vco 3 3 3

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(4.15)

4 DC-AC Inverters We have to multiply Vao with 23 and Vbo and Vco with 13 . Then using sum block (double click and then you can adjust the shape and list of signs which in our case is +–) we add them by giving 23 Vao to +ve and rest two to negative terminal. The output will be the Van as desired in the problem statement. Since the load is inductive as stated in the simulation procedure so we know that the relationship for current though the inductor is given by  1 V dt (4.16) iL = L

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4.8 PWM based DC-AC 3 phase Inverter

Figure 4.27: Modeling of leg of an inverter [1]

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4.9 SPWM based 3 phase inverter with 3 phase Asynchronous motor as load

Figure 4.29: Complete model of an inverter [1]

Therefore for getting  the current waveform across an inductive load we have to integrate the voltages by L1 V dt. Figure 4.28 shows the model for implementation of Van , Vbn and Vcn . Figure 4.29 shows the complete model of the inverter that is a modified form of model presented in the book “Modern Power Electronics and AC drives by B.K. Bose”.

4.8.2 Results Figure 4.30 shows the voltage and current waveforms for all the three phases respectively. It should be noted that current comes to steady state after some time and all the three waveforms are 120◦ displaced with each other. In the first 60◦ Vbo andVco are opposite so they cancel each other. Only 32 Vao is available at the output. It should also be noted that there is a change every 60◦ so it is also known as six step inverter. There are 5th , 7th and11th harmonics but no tripplen harmonic component is present. Figure 4.31 shows the FFT of the said system

4.9 SPWM based 3 phase inverter with 3 phase Asynchronous motor as load Sinusoidal PWM based inverter can be used for the controlled operation of an asynchronous motor. The model developed in the last experiment can be used to run a three phase motor with little modification however in this section we will be using real components to model a three phase inverter. Apart from this a built in block for diode rectifier is also used to convert the incoming three phase AC into DC. We will plot the waveforms

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5 Cycloconverters 5.1 Introduction A cycloconverter is a type of power electronic converter that converts the input frequency at different frequencies without using a dual stage (AC-DC-AC) conversion process. It is widely used in high power industrial applications. SCRs as well as IGBT can be used in the implementation of cycloconverter. Today multi-megawatt, thyristors based cycloconverter are widely used for driving asynchronous motors (up to 15,000kW) at low speed typically from 0Hz to 20Hz [3]. They have been successfully utilized for the operation of industrial drives specially in cement industry. They are also used in aircraft for producing variable speed and constant frequency power generation. They can be used to replace AC-DC-AC systems where the operation is a variable speed at fixed frequency. Here the input AC is converted into high frequency using a step up cycloconverter and before feeding it to the load that high frequency link is connected to a step down cycloconverter that convert it according to the load requirements. In case of a DC input the step up cycloconverter, which is responsible for high frequency generation, is replaced with an inverter that is designed to generate high frequency. The load side part however, remains same [1]. Contrary to the dual stage conversion process (AC-DC-AC) this works without a DC link thus nullifying the requirement of bulky DC link capacitors. Cycloconverter can be designed using a bridge topology or by using center tapped transformer. Two full wave fully controlled single phase bridge circuits are connected in anti parallel direction. One act as a positive converter and one as a negative converter so that we can control the voltage and current of both polarities in the load. It should be noted that both of the converters are fed by the same source. Figure 5.1 shows a single phase cycloconverter in bridge configuration and Fig. 5.2 in center tapped configuration. Whereas Fig. 5.3 shows the waveforms of the cycloconverter. Cycloconverter can control output voltage and frequency up to a certain extent. So it can be used as an electric drive with constant V/f ratio in a small range. By controlling the switching of the P and N converter (Fig.5.1) we can change the output frequency and by changing the firing angle we can control the output voltages. Hence it can somehow make the torque constant in a specified degree of freedom. However the firing pulses in both the P and N converter should be at the same angle to produce symmetric output. There must be a delay in switching the P and N converters, switching them simultaneously will create a dead short circuit. Therefore when one converter is switching the other must be inhabited. In literature such kind of operation is referred as circulating current free mode. In this chapter our main aim is to describe some brief methods of simulating the basic cycloconverters. We will stick to the basic type of cycloconverters such that on those basis the advance type of cycloconverters can be

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5 Cycloconverters

5.2 Single phase to Single phase Step down Cycloconverter In these type of cycloconverters the input and output both are single phase and the output has less frequency then the input hence called step down cycloconverters. Figure 5.1 and 5.2 shows the general connection scheme of single phase to single phase cycloconverter. It can be seen that they are merely just the connection of two single phase controlled converter connected in antiparallel direction so as to utilize both the cycles of input waveform. Each converter in Fig.5.1 is designated as P and N that tells that positive and negative output can be obtained by their stand alone operation, i.e we get positive output if only P is fired and negative output if we fire only N. Similarly as shown in Fig.5.2 the correct firing of pairs gives positive and negative outputs. By sequential switching of converter pairs we can get low frequency at the output. So if the total time is To then the output frequency is T1o if and only if the pairs of switches or the P and N converters are turned on for T2O . The output of both positive and negative converter are equal in magnitude and opposite in polarity. Referring to Fig.5.1 the triggering pulses for the SCRs are given such that during the positive half cycle of input the P converter is turned on and if we need a voltage control then T1 and T2 are fired at α and the remaining two switches in P converter (T3 and T4) are fired at π + α. For the negative half cycle of input P converter is isolated and the negative converter works to give the output. The voltage control should be achieved for same firing angle α to get symmetrical output as discussed above. Here T1’ and T2’ are fired at π − α and T3’ and T4’ are turned on at 2π − α.

5.2.1 Simulation Procedure We have to generate a frequency of 5 Hz from 50 Hz power supply with the help of cycloconverter keeping the voltage level constant. Then plot the waveform for voltage and current for a resistive load. Open the SIMULINK and create new page. Place the following components as shown in Fig. 5.4 ˆ Ideal switches ˆ Thyristors ˆ Series RLC branch ˆ Multimeter ˆ Pulse generator ˆ NOT gate ˆ Goto (Simulink ⇒ Signal Routing ⇒ Goto) ˆ From (Simulink ⇒ Signal Routing ⇒ From) ˆ Scope

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5.2 Single phase to Single phase Step down Cycloconverter

Figure 5.4: Simulation setup of a single phase to single phase step down cycloconverter

There are two bridges that are connected to load through 4 ideal switches (IGBTs in practical scenario). The two clock sources are used in firing the thyristors. In order to get the same output voltage we have to switch all the thyristors at 0 degree i.e all the thyristors will act as diode. The change in frequency is generated by the switching of ideal switches. The clock feeding the pulses to ideal switches is set at 1 V, frequency of 5.15 Hz and duty cycle of 50% (S1 and S3). The output is 180 degree phase shifted (S2 and S4) to avoid short circuit. The clock for T1, T4, T5 and T8 have an amplitude of 1 V and a frequency of 50 Hz. With pulse width 5%. Same clock properties are provided to thyristors designated as T2,T3, T6 and T7. Using the Goto and From blocks we can get rid of the nasty routing. Select the Goto block and connect it with the signal generator. Double click the“Goto” and tag it as you like .e.g. let it be A1. Now in order to route its signals we will use the block From . Attach the From blocks to the gates of switching devices (T1, T4, T5 and T8) and tag it with the same name as A1. In this way all the signals are sent to their destinations. It should be noted that if there is a subsystem in the model then you have to modify the GOTO and FROM properties. In that case we have to select global visibility. Connect all the clock signals to respected switching devices using these blocks. For measurement we are using Multimeter. Place a Multimeter and connect it with scope. Now in order to measure the branch voltage and current of load double click on load (RLC series branch in this case). A dialogue box will appear as shown in Fig. 5.5. Since we want to measure the branch voltage and current so we will select it. Now we will double click the Multimeter and you will see the available measurements . Select all the desired measurements and add them. In order to view the plot of measurements we have to check the “Plot selected Measurement” as shown in figure 5.6. The input voltage is set at 100 V 50 Hz.

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5 Cycloconverters

Figure 5.5: Selection of measurements

Figure 5.6: Plotting of measurements

5.2.2 Results Figure 5.7 shows the branch voltages and Fig. 5.8 shows the branch current. It can be viewed that the output frequency is 5 Hz.

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5.2 Single phase to Single phase Step down Cycloconverter

Figure 5.7: Plotting of measurements

Figure 5.8: Plotting of measurements

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5 Cycloconverters

5.3 Three phase to Single phase Step down Cycloconverter Three phase to single phase cycloconverter is same in working as that of the single phase to single phase cycloconverter discussed in section 5.2 with the only difference of multiple phases in the input. The point of interest here is to generate the pulses for three phase converter. The load is connected at the point of common coupling of P and N converter with other side connected to ground. Figure 5.9 below shows the general schematic of this converter. The simplest cycloconverter is the envelope cycloconverter whose output is made up of whole number of half cycles of supply waveform. By controlling the point on wave at which the individual phases are switched we get an output voltage waveform in which the fundamental is emphasized. Remember, by increasing the pulse number of the cycloconverter the output can be made much more closer to the sine wave. The peak output voltage that a cycloconverter can provide depends on the DC bus voltage that each converter can produce. For a cycloconverter of an “n“ number of pulses and ignoring overlap π n o (5.1) = sin Vpeakin Cosα Vpeak π n The firing angle of individual thyristors in the cycloconverter is determined by reference to the instantaneous value of output voltage required. Firing angle can then be calculated. Three phase to single phase cycloconverter are superior in performance then the single phase to single phase cycloconverters. They can deliver more power to load and have less ripple.

5.3.1 Simulation Procedure We have to generate a frequency of 10 Hz from input power supply of 50Hz with the help of cycloconverter. Then plot the waveform for voltage and current for a resistive load. Open the SIMULINK and create new page. Place the following components as shown in Fig. 5.10 ˆ Ideal switches ˆ Thyristors ˆ Series RLC branch ˆ Multimeter ˆ Pulse generator ˆ NOT gate ˆ Goto ˆ From ˆ 2nd order filter(Sim power System ⇒ Extra Library ⇒ Control blocks ⇒ 2nd order filter)

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5 Cycloconverters

Figure 5.10: Simulation setup for 3 phase to 1 phase cycloconverter

Figure 5.11: Timing diagram of pulses

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5.3 Three phase to Single phase Step down Cycloconverter

Figure 5.12: Output without filter

Figure 5.13: Output with filter

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6 DC-DC Converters 6.1 Introduction DC DC converters are also known as switch mode power supplies and are widely used in power electronics based systems due to their superior performance in term of efficiency, as compared to the linear power supplies. They are capable of step up/down the input DC voltages. They are also capable of generating multiple output dc voltages. Moreover the output can be isolated from input. Power transistors used in SMPS are operated in the most efficient mode that is in saturation and cut off region. Switching frequency is very high as compared to the linear supplies (power frequencies) thus, decreasing the size of the output filter capacitor. The magnetic and capacitive elements are much smaller then linear power supplies. However they are complex in designing and considerable high attention in required to get rid of the high frequency noise. Basic topologies are of three types. ˆ One which step down the input DC voltages ( Buck Converter) ˆ One that steps up the input DC voltages (Boost Converter) ˆ One that ca step up and step down the DC voltages ( Buck/Boost Converter)

The ingredients of designing the most basic circuit for the three kinds of converter are ˆ Power Transistor ˆ Diode ˆ Inductor ˆ Capacitor

The output can either be stepped up or down by different combinations of the above components.

6.2 DC-DC Buck Converter Figure 6.1 below shows the basic buck converter. Buck converter steps down the DC voltage. Here when the transistor is turned on the input voltage is applied to the inductor and diode act as open circuit. When the transistor is turned off the inductor reverses its polarity and makes the diode forward biased thus making a loop of current. The voltage transfer ratio is dependent on the duty cycle and can be max to 1 as evident

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6 DC-DC Converters

Figure 6.2: DC-DC buck converter simulation setup

6.3 DC-DC Boost Converter Figure 6.4 shows the basic boost converter. Boost converter is also known as ringing choke converter. It is called boost converter since it steps up the input DC voltages. Here when the diode is reversed biased the inductor stores energy from input. With transistor T off the inductor changes its polarity to keep the current flowing in the same direction thus making the total voltage across the Transistor Vin + Vl , thus according to equation 6.2 (6.2) Vo = V in + Vl Where ˆ Vo = Output voltage ˆ Vin = Input voltage ˆ Vl = Voltage across inductor

Equation 6.2 clearly shows that the output voltage is always greater then the input voltage. Inductor stores energy during the ON time of transistor. Whereas, during the ON time output capacitor supplies energy to the output circuit. In terms of the duty cycle the voltage transformation ratio is given by 1 Vo = V in 1−D

(6.3)

Where, ˆ 0 ≤D ≤ 1

Equation 6.3 depicts that the output is solely dependent on duty cycle and will theoretically tends to infinity with D equals to 1. However, practically there is always some conduction losses in real components.

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6 DC-DC Converters

Figure 6.5: DC-DC boost converter simulation setup

6.3.2 Results Figure 6.6 shows the output current while Fig. 6.7 shows the input and output voltages. It is visible that the output voltage is greater than the input voltage

6.4 DC-DC Buck / Boost Converter One type of DC-DC converter can either buck or boost the input voltages. It is called buck/boost converter. It is also known as polarity inverting converter and is use in applications up to 200 watt. It is used where we need to reverse the polarity. Figure 6.8 shows the basic structure of buck/boost converter. When T is ON the input voltage is applied to inductor L and capacitor C supplies power to load. When T is OFF the inductor reverses its polarity and forward bias the diode D and will supply the energy to output. The duty cycle decides the operation as buck or boost. When ˆ For D = 0 to 0.5 operation is of buck converter ˆ For D = 0.5 to 1.0 operation is of boost converter

Theoretically at 1 the output must be infinity, but in practical it is limited by the losses due to switching and circuit components. At a duty cycle of 50 % theoretically, the output is equal to input.

6.4.1 Simulation Procedure We have to simulate a buck/boost converter capable of buck/boost 10V input. Plot the waveforms for input and output voltages at duty cycle of 25%, 50% and 75%. Open the SIMULINK and create new page. Place the following components as shown in Fig. 6.9

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6.4 DC-DC Buck / Boost Converter

Figure 6.6: DC-DC boost converter output current

Figure 6.7: DC-DC boost converter simulation results

ˆ Mosfet ˆ Series RLC branch ˆ Voltmeter ˆ Pulse generator ˆ Scope

Adjust the values of L as 500 mH and C as 2500 μF. Load resistance is taken as 100Ω. Switching time can be set through the pulse generator and it is set as 0.009sec.

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6.4 DC-DC Buck / Boost Converter

Figure 6.10: Simulation results with 25% duty cycle

Figure 6.11: Simulation results with 50% duty cycle

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6.6 Full Bridge DC DC Converter

Figure 6.23: Simulation results for unipolar voltage switching

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Bibliography [1] B.K.Bose. Modern Power Electronics and AC drives. Pearson Education, 2006. [2] Simulink Help. Simulink help as given within the software. [3] H.Rashid. Power Electronics Circutis Devices and Applications. Prentice Hall Int. Ed., 1993. [4] Jin-Woo Jung. Project Space Vector PWM inverter. [5] Matlab. www.mathworks.com/help/techdoc/ref/oder23.html. [6] T. Undeland N.Mohan and W.P.Robbins. Power Electronics Converters, Applications and Design. Wiley India, 2006. [7] Chee-Mon ONG. Dynamic Simulation of Electric Machinery using MATLAB/SIMULINK. Prentice Hall, 1998.

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