DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING BUET

Transcription

1 DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER By MD. MAIDUL ISLAM MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING BUET DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET) SEPTEMBER 2014

2 DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER By MD. MAIDUL ISLAM A thesis submitted to the Department of Electrical and Electronic Engineering in partial fulfillment for the degree of Master of Science in Electrical and Electronic Engineering DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

3 The thesis titled DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER, submitted by Md.Maidul Islam, Roll No: , Session : October 2009 has been accepted as satisfactory in partial fulfillment of the requirement for the degree of master of science in electrical and electronic engineering on September 27, Board of Examiners Dr. Mohammad Ali Choudhury Professor Department of Electrical and Electronic Engineering, BUET Chairperson (Supervisor) Dr. Taifur Ahmed Chowdhury Professor and Head Department of Electrical and Electronic Engineering, BUET Member (Ex-Officio) Dr. Mohammad Jahangir Alam Professor Department of Electrical and Electronic Engineering, BUET Member Dr. Md. Ashraful Haque Professor Department of Electrical and Electronic Engineering, IUT, Gazipur Member (External)

4 Candidate s Declaration I hereby declare that this thesis has been prepared in partial fulfillment of the requirement for the degree of Master of Science in Electrical and Electronic Engineering at the Bangladesh University of Engineering and Technology (BUET), Dhaka and has not been submitted anywhere else for any other degree. Signature of Candidate Md. Maidul Islam Student No EEE,BUET,Dhaka

5 Dedicated to My parents

6 Abbreviations V in = The input voltage V a = The average output voltage V st = peak of the saw tooth waveform V =The voltage of repetitive waveform repetitive V control = peak of the control waveform T ON = Turn on time. T OFF = Turn off time. T = T ON + T OFF.= Time period D = Duty cycle = T ON / T. i o = The load current I LB =Average inductor current f = Switching frequency L = Inductor C = Filter capacitance vi

7 Acknowledgement All praises goes to Allah for blessing me with the knowledge and ability to do the present study. My indebt gratitude must be to the most benevolent and merciful for everything what I have from Him. It is the greatest pleasure to acknowledge my deepest gratitude to my supervisor Dr. Mohammad Ali Choudhury, Professor, Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka, for his continuous guidance, cooperation, valuable suggestions and encouragement at all stage of this work. I would like to express my sincere thanks and regards to all faculty members of the department especially the thesis examination committee members for valuable suggestions to improvement of the thesis. I wish to convey my sincere thanks to all of my well wishers for their constant encouragement, sympathetic co-operation and mental support as well as backing at all stages of my thesis work. Heartfelt appreciation goes to my family. My family is the crypt of my all muse, ethics and values. My little effort to this study is just a reflection of that. Finally, I express my thanks to the librarian and all staffs of the Department of Electrical and Electronic Engineering, BUET, for their cordial help and assistance. vii

8 Abstract In this thesis, a new topology of four quadrant DC-DC sepic converter has been developed to provide four quadrant operation of a high frequency dc-dc converter having one supply source and proper control of the converter. The investigation started with modifying single quadrant dc-dc SEPIC converter circuit for two quadrant operation. This required a dc-dc SEPIC converter with two switches. Two quadrant dc-dc SEPIC converter has been investigated with variable duty cycle operation for verifying the buck-boost gain characteristics of the voltage and also the circuit has been investigated with input/output dc sources for two quadrant operation as the duty cycle is varied from near zero to near one. One quadrant SEPIC dc-dc converter is similar to a buck-boost converter, but it has advantages of having non-inverted output and continuous input current. Connecting a switch across the diode of the one quadrant SEPIC dc-dc converter in parallel has made the converter operate in two quadrants. Proper differential connection of two 2Q SEPIC dc-dc converter has resulted in a four quadrant dc-dc converter with buckboost gain characteristics having positive output voltage. The result is a single source topology switched by conventional ON/OFF duty cycle control as used in other high power chopper circuits. The combined topology has been analyzed and studied by spice simulation. Conversion efficiency and gain data has been taken from simulation result and the performance has been analyzed and studied by Tecplot10 Software. viii

9 Chapter-One Introduction 1.1 Introduction Development in the field of power electronics has constituted one of the great success stories of the 20 th century. As manufacturing technology has improved, the cost of the semiconductor devices has decreased. It is often said that solid-state electronics brought in the first electronics revolution, whereas solid-state power electronics is the second electronics revolution. It is interesting to note that power electronics blends the mechanical, electrical and electronic era [1]. A high level productivity of the industries and product quality enhancement is not possible by using non power electronic systems. Today, power electronics is an indispensable tool in any country s industrial economy [2]. It is necessary that some converters are to be used to improve the quality of power supply. Power semiconductor devices are making it possible for utilities to use a variety of power control equipment to raise power quality level and enhance performance and efficiency. The DC DC converter, also known as chopper, is a converter which transforms a D.C. to another D.C. The average value of a chopper s output voltage can be modified between zero and the full voltage. This can be done using the Pulse Width Modulation (PWM) principle of constant frequency pulses. There are schemes of chopper operating in one to four quadrants. The H bridge converters are widely utilized in adjustable electrical drives with d.c. motors. An arm of this bridge is obtained by series connection of two controllable power switches. Each switch has an anti-parallel diode, called freewheeling diode. The two switches of an arm structure work in anti-phase. 1

10 1.2 Overview of DC Choppers Silicon control rectifier (Thyristor, SCR) based DC Choppers were introduced in the early 1960 s. SCRs were constrained to operate at low chopping frequencies. The advent of power MOSFET s and IGBT s allow power switches to operate at high frequency [3]. Conventional switch mode dc-dc converters (SMPS) operate either in single quadrant or in two quadrants [4-5]. A switch mode DC-DC power supply is switched at very high frequency. Conversion of both step down and step up dc with small filter size having facility of feedback regulation is possible in an SMPS. The output voltage in DC-DC converters is generally controlled by using a switching concept, as illustrated in Figure 1.1. Early DC-DC converters were known as choppers with silicon-controlled rectifiers (SCRs) used as the switching device. Modern DC-DC converters classified as switch mode power supplies (SMPS) employ insulated gate bipolar transistors (IGBTs) and metal oxide silicon field effect transistors (MOSFETs). The switch mode power supply has several functions [6]: 1. Step down an unregulated DC input voltage to produce a regulated DC output voltage using a buck or step-down converter, 2. Step up an unregulated DC input supply to produce a regulated DC output voltage using a step-up converter, 3. Step down and then step up an unregulated DC input voltage to produce a regulated DC output voltage using a buck boost converter, 2

11 Figure 1.1 Basic DC-DC converter. Figure 1.2 DC-DC converter voltage waveform. 3

12 Figure 1.3 Pulse width modulation concept. 4. Invert the DC input voltage if necessary and 5. Produce multiple DC outputs using a combination of SMPS topologies and multiple transformer secondary operating at high frequency The regulation of the average output voltage in a DC-DC converter is a function of the on-time Ton of the switch, the pulse width, and the switching frequency fs as illustrated in Figure 1.2. Pulse width modulation (PWM) is the most widely used method of controlling the output voltage. The PWM concept is illustrated in Figure 1.3. The output voltage control depends on the duty ratio D. The duty ratio is defined as, T D T ON s V V control repetitive 1.1 based on the on-time ton of the switch and the switching period T s. PWM switching involves comparing the level of a control voltage V control to the level of a repetitive waveform as illustrated in Figure 1.3. The on-time of the switch is defined as the portion of the switching period, where, the value of the repetitive waveform is less than the control voltage. The switching period (switching frequency) remains constant while the control voltage level is adjusted to change the on-time and therefore the duty ratio of the switch. The switching frequency is usually chosen above 20 khz so the noise is outside 4

13 the audio range [7]. DC-DC converters operate in one of two modes depending on the the characteristics of the inductor current: 1. Continuous conduction and 2. Discontinuous conduction The continuous-conduction mode is defined by continuous inductor current (greater than zero) over the entire switching period, whereas the discontinuous conduction mode is defined by discontinuous inductor current, zero during any portion of the switching period There are two main designs for the DC power supplies: 1. Linear Power Supply and 2. Switching Power Supply. The traditional linear power supplies are typically heavy, durable, and have low noise across low and high frequencies. For this reason they are mostly suitable for lower power applications, where, the weight does not pose a problem. The switching power supplies are light weight, efficient and durable. The switching power supplies are not suitable for audio frequency and high power applications. The two types are swappable for various applications, and they cost about the same. Linear regulator is used to maintain a steady voltage across the load. The resistance of a linear regulator varies in accordance with the load resulting in a constant output voltage. The regulating device is made to act like a variable resistor, continuously adjusting a voltage divider network to maintain a constant output voltage dissipating power due to the difference between the input and regulated voltages as waste heat. By contrast, a switching regulator uses an active device that switches on and off to maintain an average value of output. Because the regulated voltage of a linear regulator must always be lower than input voltage, efficiency is limited and the input voltage must be high enough to always allow the active device to drop voltage across the device. Linear regulator may be 5

14 preferred for light loads or where the desired output voltage approaches the source voltage. In such cases, the linear regulator may dissipate less power than a switcher. The linear regulator also has the advantage of not requiring inductors. Linear regulators are simple to design and implement than switch mode dc-dc converters. Linear regulators using only transistors, diodes and resistors. They are easy to fabricate into an integrated circuit and on PCBs. When the output regulated voltage must be higher than the available input voltage, linear regulator will not work. In this situation, a switching regulator of the "boost" type may be used. A conventional DC-DC SMPS consists of a rectifier fed directly from line voltage, a filter and a static switch. The SMPS is switched by control circuitry at high frequency to step down or step up dc voltage by on/off ratio (duty cycle) control. The filter and the feedback circuit are the other components of a DC-DC SMPS. Figure-1.4 shows the block diagram of a DC-DC SMPS. Main components of a dc-dc SMPS are: 1. Power circuit 2. Control circuit 3. Magnetic circuit. The control circuit of an SMPS generates high frequency gate pulses for the switching device to control the dc. Switching is performed in multiple pulse width modulation (PWM) according to feedback error signal from the load to serve two purposes, 1. Produce high frequency switching signal, 2. Control ON/OFF period of switching signal to maintain constant voltage across the load. 6

15 Power circuit 3. Input Input filter Switch Output Output filter Gating Signal generator Reference Feedback control circuit Controller Unit Figure 1.4: Block Diagram of SMPS. High frequency switching reduces filter size at the input/output sides of the converter. Simplest PWM control uses multiple pulse modulations generated by comparing a dc with a high frequency carrier triangular wave. 7

16 BJT + _ Vin Diode Vout R V Vin Vout t t Figure 1.5: Switch mode (non dissipative) power conversion circuit. The circuit of Figure 1.5 illustrates the basic principle of a dc-dc switch mode power conversion. The controlling device is a switch. By controlling the ratio of the time intervals spent in on and off positions (defined as duty ratio), the power flow to the load can be controlled in an efficient way. Ideally this method is 100% efficient. In practice, the efficiency is reduced as the switch is non-ideal and losses occur in power circuits. The dc voltage to the load can be controlled by controlling the duty cycle of the rectangular waveform supplied to the base or gate of the switching device. When the switch is fully on, it has only a small saturation voltage across it. In the off condition the current through the device is zero. The output of the switch mode power conversion control (Figure 1.5) is not pure dc. This type of output is applicable in cases such as oven heating without proper filtration. If constant dc is required, then output of an SMPS has to be smoothed out by the addition of a low-pass filter. Switches are required as basic components for efficient electric power conversion and control. Inductors and capacitors are used to smooth the pulsating dc originating from the switching action. V Vin + _ Vin Diode C Vout R Vout Figure 1.6: Typical switch mode power conversion circuit. t 8

17 Although the conversion would be 100% efficient in the ideal case of lossless components (Figure 1.6), in practice all components are lossy. Thus, efficiency is reduced. Hence, one of the objectives in switch mode power conversion is to realize conversion with the least number of components to have better efficiency and reliability. The purpose of a DC-DC converter is to supply a stepped-down or stepped-up regulated DC output voltage to a load from a DC input voltage. In many cases the DC input voltage is obtained by rectifying a line voltage that changes in magnitude. DC-DC converters are commonly used in applications requiring regulated DC power, such as in computers, medical instrumentation, communication devices, television receivers and battery chargers [7, 8]. DC-DC converters are also used to provide a regulated variable DC voltage for DC motor speed control applications. 1.3 Specific aims and possible outcomes The objective of the thesis is to propose and investigate a high frequency switching four quadrant dc-dc converter with improved performance. A single topology that can provide Buck-Boost operation with positive output having four quadrant operation is not available in literature. Luo [7-10] has proposed incorporation of voltage lift techniques in conventional switch mode circuits to obtain better voltage gain and higher efficiency in wide range of duty cycle variation. Luo also suggested four quadrant operation of switching dc-dc converter using two separate circuits. None of the Luo converters operate in single source circuit configuration in all four quadrants. Single source circuit configuration combining two separate circuits by differential connection of the load at the output fed by same source has been proposed in reference [11]. The proposed circuit of [11] used Buck-Boost topology for the purpose. The new topology is developed out of switching dc-dc converters based on SEPIC topology (modified Ĉuk topology having positive output) with improved performance. Its operational range is wide at high conversion efficiency, whereas, the present four quadrant switching dc-dc converters conversion efficiency decreases around the 9

18 operation of a particular duty cycle. It is expected that this study will yield an effective design strategy of a four quadrant switching dc-dc converter and higher efficiency which can be fabricated economically making it commercially viable. 1.4 Thesis Outline This thesis consists of three chapters. Chapter-1 is the introduction chopper with brief overview of DC-DC Converter. It also describes the objective and goal of the thesis.chapter-2 deals with introduction to DC Choppers, review of DC Choppers. Chapter-3 includes the study of Four Quadrant DC-DC converters based on SEPIC topology. In reference [12] two separate switch mode dc-dc converters with voltage lift circuits, one working in two quadrant forward mode and the other working in two quadrant reverse mode have been switched by complex gate pulses to obtain the four quadrant dc-dc operation. Two sources are necessary for such circuit. Combining the two circuits to have single source topology would result in mal-operation due to overlapping switches. In this research investigation have been started with modifying single quadrant dc-dc SEPIC converter circuit for two quadrant operation. This has introduced a dc-dc SEPIC converter with two switches. Two quadrant dc-dc SEPIC converter has been investigated with variable duty cycle operation for verifying the buck-boost gain characteristics of the voltage and also the circuit has been investigated with input/output dc sources for two quadrant operation as the duty cycle is varied from 0 to near one. Connecting a switch across the diode of the one quadrant SEPIC dc-dc converter in parallel makes the converter operate in two quadrants. Proper differential connection of two 2Q SEPIC dc-dc converter has resulted in a four quadrant dc-dc converter with buckboost gain characteristics having positive output voltage. Chapter-4 concludes the thesis with summary, achievements and suggestion on future works. 10

19 Chapter-Two DC-DC Converter 2.1 Choppers Choppers are DC-DC converters that are used for transferring electrical energy from a DC source to another DC source or to a load. These converters are widely used in regulated switching power supplies and DC motor drive applications. DC-DC converters that are discussed in this section are one-quadrant, two-quadrant, and four-quadrant choppers. Step-down (buck) converter and step-up (boost) converters are basic onequadrant converter topologies. The two-quadrant chopper, which is a current reversible converter, is the combination of the two dc-dc basic topologies. The full-bridge converter four quadrant is derived from two quadrant boost and the step-down buck converter. One-Quadrant Choppers In one-quadrant choppers, the average DC output voltage is usually kept at a desired level, as there are changes in input voltage and output load. These choppers operate in first quadrant of v i plane, where output and input voltages and currents are always positive. Therefore, these converters are called one-quadrant choppers. One method of controlling the output voltage employs switching at a constant frequency, i.e., a constant switching time period (T= t ON + t OFF ), and adjusting the on-duration of the switch to control the average output voltage. In this method, which is called pulse-width modulation (PWM), the switch duty ratio is defined as the ratio of the on-duration to the switching time period. t d T ON 2.1 In the other control method, both the switching frequency and the on-duration of the 11

20 switch are varied. Choppers can have two distinct modes of operation, which have significantly different characteristics: continuous-conduction and discontinuousconduction modes. In practice, a converter may operate in both modes. Therefore, converter control should be designed for both modes of operation. 2.2 Buck Converters The buck or step-down converter regulates the average DC output voltage at a level lower than the input or source voltage. The buck converter is used to provide a variable DC voltage to the armature of a DC motor for variable speed drive applications. This is accomplished through controlled switching where the DC input voltage is turned on and off periodically, resulting in a lower average output voltage. The buck converter is commonly used in regulated DC power supplies like those in computers and instrumentation Ideal Buck Circuit The circuit that models the basic operation of the buck converter with an ideal switch and a purely resistive load is shown in Figure 2.1. The output voltage equals the input voltage when the switch is in position 1 and the output voltage is zero when the switch is in position 2. The average output voltage level is varied by adjusting the time the switch is in position 1 and 2 or the duty ratio. The resulting average output voltage Vo is given in terms of the duty ratio and the input voltage Vi by Eq. (2.2) [13]. Vo DV i 2.2 Where, D is the duty cycle = T ON T. T ON is the on time of the rectangular base/gate pulse, whereas the T is the period of switch pulse. The rectangular wave output voltage for the ideal circuit of the buck converter contains an undesirable amount of voltage ripple. The circuit is modified by adding an inductor L in series and a capacitor C in parallel with the load resistor as shown in Figure 2.2. The inductor reduces the ripple in the current through the load resistor, while the capacitor directly reduces the ripple in the output 12

21 voltage. Since the current through the load resistor is the same as that of the inductor, the voltage across the load resistor (output voltage) contains less ripple. The current through the inductor increases with the switch in position 1. The current through the inductor increases with the switch in position 1. As the current through the inductor increases, the energy stored in the inductor increases. When the switch changes to position 2, the current through the load resistor decreases as the energy stored in the inductor decreases Figure 2.1 Ideal buck converter. Figure 2.2 Buck converter with LC filter. 13

22 Figure 2.3 Rise and fall of load current in buck converter. Figure 2.4 Buck converter with practical switch. The rise and fall of current through the load resistor is linear if the time constant due to the LR combination is relatively large compared with the on- and off-time of the switch as shown in Figure 2.3 [14]. A capacitor is added in parallel with the load resistor to reduce the ripple content in the output voltage. The combination of the inductor and capacitor reduces the output voltage ripple to low levels. The circuit in Figure 2.2 is ideal. A practical realization of the switch is designed using a diode and power semiconductor switch as shown in Figure 2.4. A freewheeling diode is used with the switch in position 2 since the inductor current freewheels through the switch. The switch is controlled by a scheme such as pulse width modulation. 14

23 2.2.2 Continuous-Conduction Mode The continuous-conduction mode of operation occurs when the current through the inductor in the circuit of Figure 2.2 is continuous. This means that the inductor current is always greater than zero. The average output voltage in the continuous-conduction mode is the same as that shown in Eq. (2.2) for the ideal circuit. As the conduction of current through the inductor occurs during the entire switching period, the average output voltage is the product of the duty ratio and the DC input voltage. The operation of this circuit resembles a DC transformer according to Eq. (2.3) based on the time-integral of the inductor voltage equal to zero over one switching period. Figure 2.5 Buck converter switch states: (a) switch in position 1; (b) switch in position 2. Figure 2.6 Inductor voltage and current for continuous mode of buck converter. 15

24 V V o D = i I I i o 2.3 The operation of the circuit in steady state consists of two states as illustrated in Figure 2.5 [14]. The first state with the switch in position 1 has the diode reverse-biased and current flows through the inductor from the voltage source to the load. The switch changes to position 2 at the end of the on-time and the inductor current then freewheels through the diode. The process starts again at the end of the switching period with the switch returning to position 1. A representative set of inductor voltage and current waveforms for the continuous-conduction mode is shown in Figure Discontinuous-Conduction Mode The discontinuous mode of operation occurs when the value of the load current is less than or equal to zero at the end of a given switching period. Assuming a linear rise and fall of current through the inductor, the boundary point between continuous- and discontinuous-current conduction occurs when the average inductor current over one switching period is half of the peak value, as illustrated in Figure 2.7. The average inductor current at the boundary point is calculated using Eq. (2.4). I LB 1 i 2 L DTS (peak) ( Vi Vo ) 2L

25 Figure 2.7 Inductor current at boundary point for discontinuous mode of buck converter. The input voltage or output voltage is kept constant depending on the application. If the input voltage remains constant, then the average inductor current at the boundary is calculated by replacing the output voltage in Eq. (2.4) with Eq. (2.2), which yields the expression in Eq. (2.5) [15]. I LB DT 2L S ( V i )(1 D) The voltage ratio is now defined according to Eq. (2.6): 2.5 V V O i D 2 2 D 1 ( 4 I I O LB (max) ) 2.6 If the output voltage remains constant, then the average inductor current at the boundary is calculated by replacing the input voltage in Eq. (2.4) with Eq. (2.2), which yields the expression in Eq. (2.7) [15]: I LB TS ( 2L V o 2.7 )(1 D) 17

26 The duty ratio is defined according to Eq. (2.8) by manipulating Eq. (2.6) [13]: D V V O i ( I O I V 1 ( V LB (max) O i ) ) Boost Converters A boost converter regulates the average output voltage at a level higher than the input or source voltage. The boost converter is referred to as a step-up converter or regulator. The DC input voltage is in series with an inductor acting as a current source. A switch in parallel with the current source and the output is turned off periodically, providing energy from the inductor and the source to increase the average output voltage. The boost converter is commonly used in regulated DC power supplies and regenerative braking of DC motors Ideal Boost Circuit The circuit that models the basic operation of the boost converter is shown in Figure 2.8 [15]. The ideal boost converter uses the same components as the buck converter with different placement. The input voltage in series with the inductor acts as a current source. The energy stored in the inductor builds up when the switch is closed. When the switch is opened, current continues to flow through the inductor to the load. Since the source and the discharging inductor are both providing energy with the switch open, the effect is to boost the voltage across the load. The load is in resistor in parallel with a filter capacitor. The capacitor voltage is larger than the input voltage. The capacitor is large to hold output voltage and acts to reduce the ripple in the output voltage. 18

27 2.3.2 Continuous Conduction Mode The continuous-conduction mode of operation occurs when the current through the inductor in the circuit of Figure 2.8 is continuous with the inductor current always greater than zero. The operation of the circuit in steady state consists of two states, as illustrated in Figure 2.9 [15]. The first state with the switch closed has current charging the inductor from the voltage source. The switch opens at the end of the on-time and the inductor discharges current to the load with the input voltage source still connected. This results in an output voltage across the capacitor larger than the input voltage. Figure 2.8 Basic boost converter. Figure 2.9 Basic boost converter switch states: (a) switch closed; (b) switch open. 19

28 Figure 2.10 Inductor voltage and current waveforms for continuous mode of boost converter. The output voltage remains constant if the RC time constant is significantly larger than the on-time of the switch. A representative set of inductor voltage and current waveforms for the continuous conduction mode is shown in Figure 2.10 [15]. The voltage ratio for a boost converter is derived based on the time-integral of the inductor voltage equal to zero over one switching period. The voltage ratio is equivalent to the ratio of the switching period to the off-time of the switch as illustrated by Eq. (2.9) [13]. V I T T T 2.9 D = o i s s V I t Ts t 1 D i o off off The current ratio is derived from the voltage ratio assuming that the input power is equal to the output power, as with ideal transformer analysis. 20

29 Figure 2.11 Inductor current at boundary point for discontinuous mode of boost converter Discontinuous-Conduction Mode The discontinuous mode of operation of boost dc-dc converter occurs when the value of the inductor current is less than or equal to zero at the end of a given switching period. Assuming a linear rise and fall of current through the inductor, the boundary point between continuous- and discontinuous-current conduction occurs when the average inductor current over one switching period is half the peak value, as illustrated in Figure 2.11 [15]. The average inductor current at the boundary point is calculated using Eq. (2.10) [15]. I LB 1 il(peak) 2 DVOTs ( D)(1 D) 2L

30 The output current at the boundary condition is derived by using the current ratio of Eq. (2.9) in Eq. (2.10) with the inductor current equal to the input current. This results in Eq. (2.11) [13]: I V Ts 2L o 2 OB ( D)(1 D) 2.11 For the boost converter in discontinuous mode, the output voltage Vo is generally kept constant while the duty ratio D varies in response to changes in the input voltage Vi. The duty ratio is defined as a function of the output current for various values of the voltage ratio according to Eq. (2.12) [15]: D [ 4 27 V V O i V ( V O i 1) I I O i 1 ] / Ĉuk Converter The Ĉuk converter is a dc-dc converter named after the inventor Dr. Slobodan Ĉuk. The basic non-isolated Ĉuk converter shown in Figure 2.12 is designed based on the principle of using buck and boost converters to provide an inverted DC output voltage [16]. The advantage of the basic non-isolated Ĉuk converter over the standard buck boost converter is to provide regulated DC output voltage at higher efficiency with identical components due to an integrated magnetic structure, reduced ripple currents, and reduced switching losses [17, 18]. The integrated magnetic structure of an isolated Ĉuk converter consists of the isolation transformer and the two inductors in a single core. As a result, the ripple currents in the inductors are driven into the primary and secondary windings of the isolation transformer. Also, the single core results in reduced flux paths, which improve the overall efficiency of the converter. 22

31 2.4.1 Non isolated Operation The basic non-isolated Ĉuk converter is a switching power supply with two inductors, two capacitors, a diode, and a transistor switch as illustrated in Figure 2.12 [16, 17]. The transfer capacitor Ct stores and transfers energy from the input to the output. The average value of the inductor voltage for steady-state operation is zero. As a result, the voltage across the transfer capacitor is assumed to be the average value in steady state and is the sum of the input and output voltages. The inductor currents are assumed to be continuous. Figure 2.12 Non-isolated Ĉuk converter. Figure 2.13 Ĉuk converter switch states: (a) switch open; (b) switch closed. 23

32 Figure 2.14 Inductor 1, voltage and current waveforms for Ĉuk converter. The operation of the basic non isolated Ĉuk converter in the steady state consists of two transistor states, as illustrated in Figure 2.13 [16, 17]. In the first state when the transistor is off, the inductor currents flow through the diode and energy is stored in the transfer capacitor from the input and the inductor L 1. The energy stored in the inductor L 2 is transferred to the output. As a result, both of the inductor currents are linearly decreasing in the off-state. In the second state when the transistor is on, the inductor currents flow through the transistor and the transfer capacitor discharges while energy is stored in the inductor L 1. As the transfer capacitor discharges through the transistor, energy is stored in the inductor L 2. Consequently, both of the inductor currents are linearly increasing in the on-state. A representative set of inductor voltage and current waveforms for the non isolated Ĉuk converter are shown in Figures 2.14 and 2.15 [16]. The voltage and current ratio for the non isolated Ĉuk converter can be derived by assuming the inductor currents, which correspond to the input current and output current, are ripple-free [16]. This results in an equal charging and discharging of the transfer capacitor during the off-state and the on-state. The charging and discharging are defined in Eq. (2.13) in terms of the product of current and time [16]. I L toff I L2ton

33 The resulting current ratio is expressed in Eq. (2.14) by substituting I L = I I, I L2 = I o, t off = (1 -D) s T, and t on = DT s into Eq. (2.13) [16]. Figure 2.15 Inductor 2, voltage and current waveforms for Ĉuk converter. I I o i D D If the input power is equal to the output power for the ideal case, the voltage ratio in Eq. (2.15) is determined as the inverse of the current ratio using the analysis of an ideal transformer. V V o i D D 2.5 Buck Boost Converter A schematic of the buck boost converter circuit is shown below in Figure 2.16.The main power switch is shown to be a bipolar transistor, but it could be a power MOSFET, or any other self commuted switching device that could be turned on in a controlled fashion. This converter processes the power from a DC-biased source to a DC output.the DC output voltage value can be chosen to be higher or lower than the input DC voltage. This circuit processes power from input to output with square wave technology, that is, the 25

34 circuit produces waveforms that have sharp edges (such as those shown in Figure 2.17). The waveforms in Figure 2.17 have a square-wave (or semi-square-wave) appearance and are indicative of current waveforms in a typical DC-DC converter. The i L waveform is of similar shape as that of inductor (L) current in the buck boost converter of Figure 2.16, i D represents the diode current and i C, the capacitor current. The operation of this converter is nonlinear and discrete; however, it can be represented by a cyclic change of power stage topologies. The three modes for this converter, the equations for those topologies, and the small-signal transfer functions are presented in this section. Figure 2.16 Buck boost converter 26

35 Figure 2.17 Typical current waveforms in a buck boost converter Continuous-Conduction Mode Figure 2.17 illustrates the topology, where the main power switch is on and the diode is reverse-biased; thus, it is off. For the purpose of illustration the semiconductor devices are assumed to be ideal. There are two independent state variables that contain the information describing the operation of this circuit: the inductor current, i L, and the capacitor voltage, v c. Two differential equations in terms of these variables, the output voltage, v o, and the source voltage, v S, for the designated mode 1 are shown below. dil dt vs L 2.16 dvc dt R v L o C

36 The inductor gets energy from the source and charges up. The capacitor discharges into the output load, R L and output voltage falls. Figure 2.19 shows the change in topology when the main power switch turns off. The inductor maintains current flow in the same direction so that the diode is forward-biased. The differential Figure 2.18 Topology 1 for the buck boost converter. Figure 2.19 Mode 2 for the buck boost converter. equations for the designated mode 2 are shown below. The inductor transfers energy it has obtained from the source into the capacitor. The capacitor charges up as the inductor is discharged, and the output voltage rises. 28

37 di L dt vc L 2.18 dv dt c il vo C R C Another mode change will occur if the inductor has transferred all of its energy out into the capacitor. In that case the inductor current will fall to zero. Initially the inductor current is assumed to be nonzero. The power stage analysis is linear for each interval. However, for the complete operational cycle, it becomes a piecewise linear problem. The on-time or off-time of the main power switch may vary from cycle to cycle. Various modeling schemes have been proposed using nonlinear techniques that would in essence combine these equations. Basically there are two approaches: numerical and analytical techniques. In analytical technique, a closed-form expression representing the operation of the converter is obtained, enabling a qualitative analysis to be performed [19]. The numerical technique uses various algorithms to produce accurate quantitative results. Simple relations among the system parameters are not easily obtainable. Analytical techniques can be divided into two different system descriptions, discrete and continuous. The discrete system description makes no assumption on the basis of converter application. This description could be used in any application, where, the linearization of a periodically changing structure is sought. This method is accurate, but very complicated. The derived expressions are complex, which impedes its practical usefulness, and physical insight into the system operation is not easily obtainable. An important continuous analytical technique is the averaging technique proposed by Wester and Middlebrook [20]. It is easy to implement and gives physical insight into the operation of a buck boost converter. Through circuit manipulation, analytical expressions were derived to determine the appropriate expressions. Middlebrook and Ĉuk[21] modified the technique to average the state space descriptions (variables) over a complete cycle. Shortt and Lee [22 24] used a discrete sample of the average state space L

38 representation to develop a modeling technique that would enable a judicious control selection to be made. Vorpérian et al. [25] developed an equivalent circuit model for a pulse width modulation (PWM) switch that can be used in the analysis of this converter. For the averaging technique each interval in the cycle is described by its state space representation (differential equation). Figure 2.20 shows the waveform of the continuous, instantaneous inductor current (that is, Figure 2.20 Continuous inductor current. i L does not equal zero at any point in time) and the average inductor current for the buck boost converter (Figure 2.18). The instantaneous current is cyclic with a time period equal to TP s; the main power switch is on for T ON s and off for T OFF s. The equations are averaged to give a single period representation, as shown below: i L v vc vs d d L L c il vo d C R C L To study the small signal behavior, the time-varying system described in Eqs. (2.20) and (2.21) can be linearized using small signal perturbation techniques. By using these techniques, the inputs are assumed to vary around a steady-state operating point. Taking a first-order Fourier series approximation, the inputs are represented by the sum of a DC or steady-state term and an AC variation or sinusoidal term. Introducing variations in the line voltage and duty cycle by the following substitutions 30

39 v V vˆs, d D dˆ, d D dˆ S S cause perturbations in the state and output, as shown below. In the above and following equations the variables in capital letters represent the DC or steady-state term; and the variables with the symbol above them represent the AC variation or sinusoidal term. il = I L + i L, il = IL +iˆl, vc = V C +vcˆ Figure 2.21 shows the type of change that is being modeled for an inductor current perturbation of Figure Note the TON and TOFF slowly change from cycle to cycle, which produces a slight change in the inductor current from cycle to cycle. The derivative of a DC term is zero, so the above equations can be simplified to the following: i L = ilˆ, il =IL +iˆl, vc =VC +v ˆc, Substituting these equations into (2.27) and (2.28), separating the DC (steady-state) terms and the AC (sinusoidal) terms results in the following: Figure 2.21 Inductor current perturbation. DC terms: D V L C DV L s D L V 2.23 L O 0 C R C L 31

40 AC terms (neglecting the higher-order terms): îl D vˆ C Dvˆ S VS VC dˆ 2.24 L L L vˆ C D iˆ vˆ L o I L dˆ 2.25 C R C C L The equation Vc Vs D D is derived from Eq. (2.22). From Figure 2.16, putting V C = V O and substituting this into the previous equation results in: V V O s D D 2.26 Equation (2.26) states that the ratio of the DC output voltage to the DC input voltage is equal to the ratio of the power switch on-time to the power switch off-time. The expression for the DC inductor current term is i L VO D R Equations (2.24) and (2.25) constitute the small signal model of a buck boost converter. Another method that is utilized to extract the small signal model is to realize an equivalent circuit model from Eqs. (2.20) and (2.21). Figure 2.22 is the average circuit model of the buck boost converter. L

41 Figure 2.22 Average circuit model of the buck boost converter. Figure 2.23 The small signal circuit model. Figure 2.24 Discontinuous inductor current. 33

42 Figure 2.25 Topology 3 for the buck boost converter (discontinuous inductor current). Introducing perturbations into the state and output, removing the DC conditions, neglecting the small nonlinear terms, and simplifying the structure, results in Figure Discontinuous-Conduction Mode Figure 2.26 shows the waveform of the discontinuous inductor current for the buck boost converter (Figure 2.18 where, inductor current is equal to zero for TF2s. An additional (third) mode change is shown in Figure Since the inductor current is zero for this portion of the switching cycle, there is only one state equation that can be determined. dv dt c vo R C L This equation indicates that the capacitor discharges its energy into the load resistor, and the while output voltage falls R L, 34

43 Figure 2.26 General form of discontinuous inductor current. In the discontinuous conduction mode, the inductor current does not behave as a true state variable, since d i L /dt = 0, thereby reducing the system order by one. Figure 2.26 illustrates the general form of the inductor current. The equations for the Ton time interval are the same as Eqs. (2.16) and (2.17), except i L = i R + i L, where i R represents the DC level at which the inductor current begins and, the value of the time-varying inductor current. The equations for the TOFF interval are the same as Eqs. (2.18) and (2.24) except i = i + i, where L R L i L represents the value of the time-varying inductor current. By combining these sets of equations with Eq. (2.24) by the averaging technique, the equations listed below are obtained. dil dt 1 T p Ton Vs 1 dt L T 0 p Ton TOFF v ( L ) dt 0 For the buck boost converter case I R = 0; also, from Figure 2.26, ton c 2.29 Ton TOFF i L ton * dt 1 ( 2 vs T L ON ) T OFF i AV T OFF 2.30 The variable i AV is the average value of the inductor during the T ON + T OFF time, but not for the whole cycle. Substituting into Eqs. (2.29) and (2.30) results in the following: 35

44 dvc dt TonVc TpR L C T OFF T P i C AV T T OFF P R v L C C T T F 2 p R v L C C 2.31 Let d 1 T T on p T off d 2, T p T F d 2 3 T, p and substitute into the above equation. v C d 2 iav C vc R C L 2.32 Figure 2.27 Buck boost converter small signal model for the discontinuous mode. Where d1+ d2 + d3 =1 and i AV 1 vs T 2 L on 2.33 At this point, the same perturbation techniques, as presented previously, are used to obtain the small signal model. Introducing variations in the line voltage and duty cycle produce perturbations in the state and output; separating the DC and AC terms and simplifying results in 36

45 v c vˆ c R C L T OFF V 2 LC S dˆ T V 2 LC ON S 1 d 2 ˆ T T ON P T OFF 2 LC vˆ s 2.34 Where T ON V V S 2LT R L p 2.35 T OFF 2LT R L p 2.36 V V C S D D A circuit model (Figure 2.27) can be realized from the above equations. The above small signal model is used to derive them. 2.6 Two-Quadrant Choppers A two-quadrant chopper has the ability to operate in two quadrants of the (v i) plane. Therefore, input and output voltages are positive; however, input and output currents can be positive or negative. Thus, these converters are also named current reversible choppers. They are composed of two basic chopper circuits. Figure 2.28 A current reversible chopper. 37

46 Figure 2.29 Output current of a two-quadrant chopper. Usually, a two-quadrant DC-DC converter is achieved by a combination of two basic chopper circuits, a step-down chopper and a step-up chopper, as is shown in Figure The step-down chopper is composed of S1 and D1, electric energy is supplied to the load. The step-up chopper is composed of S2 and D2; electric energy is fed back to the source. Reversible current choppers can transfer from operating in the power mode to operating in the regenerative mode smoothly by changing the control signals for S1 and S2, without using any mechanical contacts. Figure 2.29 depicts the output current of a two-quadrant chopper. d 1 and d 2 = 1 d1 are the duty ratios of step-down and step-up converters, respectively. By changing d1 and d 2, not only the amplitude of the average of the output current changes, but it can also be positive and negative, leading to two-quadrant operation. Figure 2.30 (vo, ave./vin, ave.)- io, shows the characteristic of a two-quadrant converter in continuous- and discontinuous-conduction modes of operation. As is shown in Figure 2.30, for changing the operating mode both from step-down to step-up operation and in the opposite direction, 38

47 Figure 2.30 (, / -i o, ave ) characteristic of a two-quadrant converter. v o ave vin, ave Figure 2.31 A full-bridge four-quadrant chopper. By applying d 2 = 1 d1, the operating point will never move into the discontinuousconduction region of the two basic converters. In Figure 2.30, the broken lines indicate passage from step-down operation to step-up operation, and vice versa. Because of specific command the relation between the two duty ratios the converter operating point always stays in the continuous-conduction mode. 39

48 2.7 Four-Quadrant Choppers In four-quadrant choppers, not only can the output current be positive and negative, but the output voltage also can be positive and negative. These choppers are full-bridge DC- DC converters, as shown in Figure The main advantage of these converters is that the average of the output voltage can be controlled in magnitude as well as in polarity. A four-quadrant chopper is a combination of 2 two quadrant choppers in order to achieve negative average output voltage and/or negative average output current. The fourquadrant operation of the full-bridge DC-DC converter, as shown in Figure 2.32, for the first two quadrants of the (v i) plane is achieved by switching S1 and S2 and considering D1 and D2 like a two-quadrant chopper. For the other two quadrants of the (v i) plane, the operation is achieved by switching S3 and S4 and considering D3 and D4 as another two-quadrant chopper, which is connected to the load in the opposite direction of the first two-quadrant chopper. Figure 2.32 Four-quadrant operation of a full-bridge chopper. 40

49 Chapter Three Four Quadrant SEPIC Converter 3.1 One Quadrant SEPIC converter [26-27] Single-ended primary-inductor converter (SEPIC) is a type of DC-DC converter allows the electrical potential (voltage) at its output to be greater than, less than, or equal to that at its input. The output of a SEPIC dc-dc converter can be controlled by the duty cycle of the semiconductor switch used with converter. A SEPIC converter has gain characteristics similar to a traditional buck-boost converter. It has advantages of having non-inverted output (the output has the same voltage polarity as the input) and use of a series capacitor for energy transfer from the input to the output. SEPIC converters are useful in applications in which a source voltage can be above and below that of the regulator's intended output. Figure 3.1: Schematic Circuit diagram of SEPIC converter. 41

50 Circuit operation The schematic circuit diagram of a basic SEPIC dc-dc converter is shown in Figure 3.1. Like other dc-dc converter, the SEPIC converter exchanges energy between the capacitors and inductors in order to convert voltage and current. The amount of energy exchanged is controlled by switch S1, which is typically a semiconductor switch such as a MOSFET. MOSFETs offer high input impedance and lower voltage drop than bipolar junction transistors (BJTs). BJTs require current drive whereas MOSFET switching is controlled by gate source voltage differences. A SEPIC dc-dc converter is in continuous-conduction mode ("continuous mode") if the current through the inductor L 1 does not fall to zero. During a SEPIC's steady-state operation, the average voltage across capacitor C 1 (V C1 ) is equal to the input voltage (V in ). Because the capacitor C 1 blocks the direct current (DC), the average current across it (I C1 ) is zero, making inductor L 2 the only source of load current. Therefore, the average current through inductor L 2 (I L2 ) is the same as the average load current and hence independent of the input voltage. Looking at average voltages, the following can be written: 3.1 Because the average voltage of V C1 is equal to V IN, V L1 = V L2. The two inductors can be wound on the same core. Since the voltages are the same in magnitude, their effects of the mutual inductance will be zero. Also, since the voltages are the same in magnitude, the ripple currents from the two inductors will be equal in magnitude. The average currents can be summed as follows: 42

51 When switch S1 is turned on, current I L1 increases and the current I L2 increases in the negative direction. (Mathematically, it decreases). The energy to increase the current I L1 comes from the input source. Since S1 is a short while closed, and the instantaneous voltage V C1 is approximately V IN, the voltage V L2 is approximately V IN. Therefore, the capacitor C 1 supplies the energy to increase the magnitude of the current in I L2 and thus increase the energy stored in L 2. The easiest way to visualize this is to consider the voltages of the circuit in a d.c. state, then close S1. Figure 3.2: With S1 closed current increases through L 1 (green) and C 1 discharges increasing current in L 2 (red) When switch S1 is turned off, the current I C1 becomes the same as the current I L1. The current I L2 will continue in the negative direction. It can be seen from the diagram that a negative I L2 will add to the current I L1 to increase the current delivered to the load. Using Kirchhoff's Current Law, it can be shown that I D1 = I C1 - I L2. It can then be concluded, that while S1 is off, power is delivered to the load from both L 2 and L 1. C 1, however is being charged by L 1 during this off cycle, and will in turn recharge L 2 during the on cycle. 43

52 Figure 3.3: With S1 open current through L 1 (green) and current through L 2 (red) produce current through the load The potential (voltage) across capacitor C 1 may reverse direction every cycle. A nonpolarized capacitor should therefore be used. The capacitor C IN is required to reduce the effects of the parasitic inductance and internal resistance of the power supply. The boost/buck capabilities of the SEPIC are possible because of capacitor C 1 and inductor L 2. Inductor L 1 and switch S1 create a standard boost converter, which generates a voltage (V S1 ) that is higher than V IN, whose magnitude is determined by the duty cycle of the switch S1. Since the average voltage across C 1 is V IN, the output voltage (V O ) is V S1 - V IN. If V S1 is less than 2V IN, then the output voltage will be less than the input voltage. If V S1 is greater than 2V IN, then the output voltage will be greater than the input voltage. Ideal Voltage and Current Gain Equations of 1Q SEPIC DC-DC converter: The one quadrant SEPIC DC-DC converter in switch ON and switch OFF states are shown in Figures 3.2 and 3.3. In these figures following volt-sec balance for each switching cycle may be carried out to yield ideal voltage and current gain equation of the converter. 44

53 For inductor L 1, Vin DT ( Vin Vc Vo)(1 D) T Which yield, V And Vin 3.3 C VO 1 I C D D 1 I 3.4 O I in For inductor L 2, VC DT VO ( 1 D) T Which yields, V And C I VO V D C O O O 3.6 DI I 3.7 From equations (3.3) and (3.6) Vin V 1 d Or, V O O VO V D O D 3.8 Vin 1 D And from equation(3.4) and (3.7) 45

54 1 D I I in I I O in O DI O I O D D Equations (3.8) and (3.9) indicates that ideal SEPIC DC-DC converter has Buck-Boost voltage and current gain relationship Simulation Results of One Quadrant SEPIC DC-DC Converter Initially a 1-Q SEPIC DC-DC converter as shown Figure 2.4 which is controlled by a pulse waveform as shown in Figure 2.5 is studied for input voltage 24V and load resistance 20 ohm. APT30G100BN R12 L1 C1 D mH 20u MR2406F V+ R13 V1 gate1 Z1 D139 MR2406F.001 C2 20u R Vdc L2 gnd1 5mH V- R3 1meg SEPIC CONVERTER(QUADRANT ONE MODE) 0 Figure 3.4 One Quadrant SEPIC Chopper Typical waveforms of an One Quadrant SEPIC Chopper of Figure 3.4 with resistive load for gate pulse of Figure 3.5 are shown in Figures Figures show typical waveforms of circuit of Figure 3.4, both Load Current and voltage are positive with changing duty cycle. 46

55 Figure 3.5 Gate Signal of the one quadrant SEPIC dc-dc converter. 47

56 Figure 3.6: Load Current and voltage are positive of circuit of Figure 3.4 for gate signal at DC level 3V (Quadrant-I). 48

57 Figure 3.7: Load Current and voltage are positive of circuit of Figure 3.4 for gate signal at DC level 6V (Quadrant-I). 49

58 3.1.2 Typical Result of Duty cycle variation of 1-Q SEPIC DC-DC converter The duty cycle variation of control pulse of the switch of 1-Q SEPIC DC-DC converter of Figure 3.4 has been carried out for D=.10 to.98 and the values of voltage gain and efficiency of the converter has been obtained as tabulated in Table 3.1 and 3.2.These results are graphically shown Figure 3.8 and 3.9 respectively. Table 3.1: The Value of Voltage with changing Duty Cycle for 1-Q SEPIC DC-DC converter of the Circuit of Figure 3.4 Duty Cycle(%) Input Voltage(Vin),V Output Voltage(Vo),V Voltage Gain(Vo/Vin)

59 Table 3.2: The Value of Power with changing Duty Cycle for One quadrant Chopper of Circuit of the Figure 3.4 Duty Cycle Input Voltage(Vin) Input Power(Pin) Output Power(Po) Efficency(%)

60 Figure 3.8 Characteristics Curve Gain Vs Duty Cycle for One quadrant Chopper for the Data Table

61 Figure 3.9 Characteristics Curve Efficiency Vs Duty Cycle for One quadrant Chopper for the Data Table

62 The simulation results tabulated in table 3.1 and 3.2, and graphically represented in Figures 3.8 and 3.9 indicate, i) Voltage gain(vo/vin) of the converter increases with duty cycle increase. The voltage gain peaks to 6.3 at duty cycle.89 as equation for output voltage, V D 1 D O V in increases with duty cycle ii) After the peak is reached, the voltage gain decreases with increase of duty cycle Results i) and ii) above are expected of practical dc-dc converter, whereas efficiency of ideal dc-dc converter are 100% or unity and for SEPIC converter the voltage gain less than 1 for duty cycle D<.5 and higher than 1upto infinity for D>.5 54

63 3.2 Two Quadrant SEPIC converter The 1-Q SEPIC converter shown Figure 3.4 has been extended to a 2-Q SEPIC dc-dc converter in the quest for development of a 4Q SEPIC dc-dc converter. The Circuit used for 2-Q SEPIC dc-dc converter which has been derived from 1-Q SEPIC dc-dc converter is shown in Figure 3.10(a). The Circuit has an extra switch across output diode and an anti parallel diode across switch. Figure 3.10(a) Two Quadrant SEPIC Chopper 55

64 The operation of the 2-QSEPIC converter in the forward direction is the same as the circuit of Figure 3.4 which is shown in Figure 3.10(b). Figure 3.10(b) Two Quadrant SEPIC converter in forward direction (left to right). The operation of the 2-Q SEPIC converter of Figure 3.10(a) in the reverse direction can be understood from Figure 3.10(c)-(d). 56

65 Figure 3.10(c): Two Quadrant SEPIC converter in Reverse direction (right to left) Figure 3.10(d) Two quadrant SEPIC converter in Reverse direction (right to left) as combination of a Buck-Boost (right box part) and lift circuit (left box part) 57

66 The operation in the reverse direction does not use the switch 1 and diode 1(as shown dotted) as shown in Figure 3.10(c). The Circuit of Figure 3.10(c) can be identified as an Buck-Boost converter of the right box of Figure 3.10(d) with the output at the capacitor as shown. The left box part of circuit acts as a lift circuit that transfers the capacitor charge to appear as +ve voltage at the output at the left side as in SEPIC converter. In simulation the converter is switched by two pulse as shown in Figure 3.11 Figure 3.11: Gate pulse of switches of Circuit of Figure 3.10(a). Typical waveforms of Two Quadrant SEPIC Chopper connected (+ve) EMF of circuit of Figure 3.10(a) are shown in Figures Figures show typical waveforms of circuit of Figure 3.10(a), Load Current changes positive to Negative with changing duty cycle. 58

67 3.2.1 Simulation Result two Quadrant SEPIC DC-DC Converter If we choose for gate signal at DC level 5V than duty cycle of S1 will be greater than duty cycle of S2, Energy transfer in Forward direction (from A side to B side) that is shown in Figure 3.12 Figure 3.12: Current is Positive at B side for Positive output of circuit of figure 3.10 for gate signal at DC level 5V (Quadrant-I) 59

68 If we choose for gate signal at DC level 2V than duty cycle of S2 will be greater than duty cycle of S1, Energy transfer in Reverse direction (from B side to A side) that is shown in Figure 3.13 Figure 3.13: Current is Negative at B side for Positive Voltage of circuit of figure 3.10(a) for gate signal at DC level 2V (Quadrant-II). 60

69 3.2.2 Typical Result of Duty cycle variation of 2-Q SEPIC DC-DC converter The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter of Figure 3.10(a) has been carried out for D=.10 to.90 and the values of voltage gain and efficiency of the converter has been obtained as tabulated in Table 3.3. These results are graphically shown Figure 3.14 and Table 3.3: The Value of Power with changing Duty Cycle for Two quadrant Chopper of the Circuit of Figure 3.10(a) Duty Cycle Voltage(Va) Power(Watt)AT A side Power(Watt) at B side

70 Figure 3.14 Characteristics Curve of Power at A side Vs Duty Cycle for Two quadrant Chopper for the Data Table 3.3 Figure 3.14 show that the value of Power at A side changes positive to negative at near 36% duty cycle. Before duty cycle 36%, Power at A side is positive means power is supplied from B side to A and after 36% duty cycle, Power at A side is negative means power is supplied from A side to B. 62

71 Figure 3.15 Characteristics Curve of Power at B side Vs Duty Cycle for Two quadrant Chopper for the Data Table 3.3 Figure 3.15 show that the value of Power at A side changes positive to negative at near 37% duty cycle. Before duty cycle 37%, Power at B side is negative means power is supplied from B side to A and after 37% duty cycle, Power at B side is positive means power is supplied from A side to B. 63

72 From above discussion about Circuit figure 3.10(a), that Converter has bi-directional energy transfer (Energy is transferred from A side to B side and also B to A side). So, Our assumption is justified that it is 2-Q SEPIC dc-dc converter. The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter of Figure 3.10(a) has been carried out for duty cycle above 37% to 90% than Energy is transferred into forward direction (From A to B side) and the values of power and efficiency of the converter has been obtained as tabulated in Table 3.4. These results are graphically shown Figure Table 3.4: Efficiency with changing Duty Cycle for Two quadrant Chopper of the Circuit of Figure 3.10(a)(Forward operation) Duty Cycle Voltage(Va) Power(Watt) at A side Power(Watt) at B side Efficiency(%)

73 Figure 3.16 Characteristics Curve of Efficiency Vs Duty Cycle for Two quadrant Chopper for the Data Table

74 The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter of Figure 3.10(a) has been carried out for duty cycle above 10% to 35% than Energy is transferred into reverse direction (From B to A side) and the values of power and efficiency of the converter has been obtained as tabulated in Table 3.5. These results are graphically shown Figure Table 3.5: Efficiency with changing Duty Cycle for Two quadrant Chopper of the Circuit of Figure 3.10 (Reverse operation) Duty Cycle Voltage(Va) Power(Watt)AT A side Power(Watt) at B side Efficiency(%)

75 Figure 3.17 Characteristics Curve of Efficiency Vs Duty Cycle for Two quadrant Chopper for the Data Table 3.5. The simulation results tabulated in table 3.4 and 3.5, and graphically represented in Figures 3.16 and 3.17 indicate, i) Duty cycle from above.37 to.90 (Energy transfer in forward direction), Efficiency of the converter decreases with duty cycle increase. The efficiency peaks to 78% at duty cycle.50 and ii) Duty cycle from above 0 to.37 (Energy transfer in reverse direction), Efficiency of the converter increases with duty cycle increase. The efficiency peaks to 81% at duty cycle.34 67

76 3.3 Four Quadrant SEPIC converter The 2-Q SEPIC converter shown Figure 3.10(a) has been extended to a 4-Q SEPIC dc-dc. The Circuit used for 4-Q SEPIC dc-dc converter which has been derived from 2-Q SEPIC dc-dc converter is shown in Figure Two 2-Q SEPIC converter dc-dc converter has been connected with differential connection to obtain 4-Q SEPIC dc-dc converter shown Figure 3.22.Here A indicates input side and B indicates output side. Figure 3.18: Four Quadrant SEPIC Chopper 68

77 In simulation among four gate pulses, using gate1, gate11 same signal and gate2, gate22 same signal for the converter of circuit figure 3.20 is switched shown in Figure 3.19 Figure 3.19 Typical Gate pulses of four quadrant SEPIC dc-dc Converter. Voltage and Current Gain Equations of Four Quadrant SEPIC DC-DC converter: The ideal voltage and current Gain Equations of Four Quadrant SEPIC DC-DC converter may be obtained from the difference of 2Q DC-DC converter and current gain expressions where one side converter operates at D and the other side converter operates at 1-D Hence, V O V V O1 O2 69

78 70 in in in in in in V D D D D D V D D D D V D D V D D V D D V D D ) (1 ) 2 (1 ) (1 ) (1 1 1 ) ( O V in D D D V ) ( Similarly, O I in D D D I 1 2 ) (1 3.11

79 3.3.1 Simulation Result of 4-Q SEPIC Converter switching by rectangular wave signal Four Quadrant SEPIC Chopper with output positive DC voltage shown Figure 3.20 at B side a 30V DC voltage source is a differential connected load. Typical waveforms of four Quadrant SEPIC Chopper connected (+ve) EMF of circuit of Figure 3.20 are shown in Figures Figures show typical waveforms of circuit of Figure 3.20, Current at B side changes positive to Negative with changing duty cycle from.10 to.90. Figure 3.20: Four Quadrant SEPIC Chopper with output positive DC voltage. 71

80 72

81 Figure 3.22: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.04ms. 73

82 Figure 3.23: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.06ms. 74

83 Figure 3.24: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.08ms. 75

84 Figure 3.25: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.10ms. 76

85 Figure 3.26: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.12ms. 77

86 Figure 3.27: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.14ms. 78

87 Figure 3.28: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.16ms. 79

88 Figure 3.29: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width.18ms. 80

89 Four Quadrant SEPIC Chopper with output negative DC voltage shown Figure 3.34 at B side a 30V DC voltage source is a differential connected load. Typical waveforms of four Quadrant SEPIC Chopper connected (-ve) EMF of circuit of Figure 3.34 are shown in Figures Figures show typical waveforms of circuit of Figure 3.34, Current at B side changes positive to Negative with changing duty cycle from.10 to.90. Figure 3.30: Four Quadrant SEPIC Chopper with output negative DC voltage. 81

90 Figure 3.31: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.02ms. 82

91 Figure 3.32: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.04ms. 83

92 Figure 3.33: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.06ms 84

93 Figure 3.34: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.08ms. 85

94 Figure 3.35: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.10ms 86

95 Figure 3.36: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.12ms 87

96 Figure 3.37: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.14ms 88

97 Figure 3.38: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.16ms 89

98 Figure 3.39: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width.18ms 90

99 3.3.2 Typical Result of Duty cycle variation of 4-Q SEPIC DC-DC Converter The duty cycle variation of control pulse of the switch of 4-Q SEPIC DC-DC Converter of Figure 3.20 and Figure 3.30 has been carried out for D=.10 to.90.the control pulse of Gate1, 11 and Gate2, 22 are opposite pulse. So if Duty Cycle of control pulse of Gate1, 11 is decreases Duty Cycle of control pulse of Gate2, 22 is increases. The value of output current with direction of current flow has been obtained from output Figure 3.21 to 3.29 for the circuit of Figure 3.24 as tabulated in Table 3.6 and from output Figure 3.31 to 3.39 for the circuit of Figure 3.30 as tabulated in Table 3.6 and 3.7. Table 3.6: The value output current changing with Duty Cycle for four quadrant Chopper of the Circuit of Figure 3.20 Sl no. Simulated Figure No. Duty Cycle (Gate 1,11) Duty Cycle (Gate2,22) Output Voltage (+30V) Output Current(B side)(a) Quadrant 01 Figure I 02 Figure I 03 Figure I 04 Figure I 05 Figure I 06 Figure I 07 Figure II 08 Figure II 09 Figure II 91

100 The simulation results for the Four Quadrant SEPIC converter of circuit figure 3.20 with positive output voltage source from Figure 3.21 to 3.29 tabulated as in Table 3.6 indicate, i) Output voltage is always positive, the output current changes positive to negative with duty cycle changing. ii) When Duty cycle for gate pulse 1, 11 >Duty cycle for gate pulse 2, 22 output current always positive so our four Quadrant SEPIC converter working as Quadrant-I operation iii) When Duty cycle for gate pulse 1, 11 <Duty cycle for gate pulse 2, 22 output current always negative so our four Quadrant SEPIC converter working as Quadrant-II operation So, Four Quadrant SEPIC converter of circuit Figure 3.20 is justified as Two Quadrant DC-DC Converter (as working Quadrant-I and Quadrant-II). 92

101 Table 3.7: The value output current changing with Duty Cycle for four quadrant Chopper of the Circuit of Figure 3.30 Sl no. Simulated Figure No. Duty Cycle (Gate 1,11) Duty Cycle (Gate2,22) Output Voltage (-30V) Output Current(B side)(a) Quadrant 01 Figure IV 02 Figure IV 03 Figure IV 04 Figure III 05 Figure III 06 Figure III 07 Figure III 08 Figure III 09 Figure III The simulation results for the Four Quadrant SEPIC converter of circuit figure 3.30 with positive output voltage source from Figure 3.31 to 3.39 tabulated as in Table 3.7 indicate, i) Output voltage is always of four Quadrant SEPIC converter negative, the output current changes positive to negative with duty cycle changing. ii) When Duty cycle for gate pulse 1, 11 >Duty cycle for gate pulse 2, 22 output current always positive so our four Quadrant SEPIC converter working as Quadrant-IV operation. 93

102 iii) When Duty cycle for gate pulse 1, 11 <Duty cycle for gate pulse 2, 22 output current always negative so our four Quadrant SEPIC converter working as Quadrant-III operation. So, Four Quadrant SEPIC converter of circuit Figure 3.30 is justified as Two Quadrant DC-DC Converter (as working Quadrant-IV and Quadrant-III). From above discussion, Proposed circuit of Figure 3.18 is justified as FOUR QUADRANT DC-DC CONVERTER. 94

103 3.3.3 Simulation Result of Four Quadrant SEPIC Converter switched by sine PWM wave Figure 3.40: Four Quadrant SEPIC Chopper with differentially connected R-L load. Four quadrant chopper circuits perform dc-dc conversion. With inductive load, inverter output voltage and load current clearly demonstrate four quadrant operation for R-L, R- L-EMF and R-L-C loads. The SEPIC converter developed in this investigation has been studied with sine PWM gate pulse to operate the inverter(dc-ac conversion) mode. The SEPIC 4Q dc-dc converter is shown in Figure 3.40.Typical sine PWM gate pulse for switching the converter is shown in Figure

104 Figure 3.41: Typical PWM gate pulses of Four Quadrant SEPIC DC-DC converter Typical waveforms of the Four Quadrant SEPIC Chopper connected to an R-L load circuit of Figure 3.40 are shown in Figure Figure 3.42 shows that the value of output voltage amplitude and current are alternating (periodic with average=0). Also it is seen in the Figure 3.42 that while the output voltage is +ve, both +ve and ve load current are present when the output voltage is ve, load current is both +ve and ve are available. 96

105 Figure 3.42: Load Current and voltage at B side in forward and reverse direction operation of circuit of figure 3.40 with (R=50ohm,L=100mh) 97

106 The investigation is replaced for Four Quadrant SEPIC Converter of circuit Figure 3.18 using Pulse Width Modulation switching Scheme. Interchanging between R-L load and voltage source, R-L load is differentially connected at the Four Quadrant SEPIC Chopper at input side A and voltage source is now connected to output B side shown in Figure Figure 3.43: Four Quadrant SEPIC Chopper with differentially connected R-L load at input side. Typical waveforms of Four Quadrant SEPIC Chopper connected R-L load of circuit of Figure 3.43 are shown in Figure Figure 3.44 shows that the value of Output Voltage amplitude and current are alternating. 98

107 Figure 3.44: Load Current and voltage at B side in forward and reverse direction operation of circuit of Figure 3.40 with (R=50ohm, L=100mh) 99

108 From the above investigation it is evident that the 4Q SEPIC dc-dc converter works as a dc-dc converter and with R-L or R-L-emf load it clearly demonstrate 4-Quadrant operation (For positive output voltage the load current may be either positive or negative, and for negative output voltage the load current may be either negative or positive). Also the reversible operation of the proposed circuit is clearly demonstrate by the fact that the circuit works in four quadrants even if the source and load position are interchanged Typical Result of Modulation index variation of 4-Q SEPIC DC-DC Converter The modulation index variation of control pulse of the switch of 4-Q SEPIC DC-DC Converter of Figure 3.43 has been carried out for M=.10 to.90.the control pulse of Gate1, 11 and Gate2, 22 are opposite PWM pulse. The value of output current and power has been obtained from 4-Q SEPIC DC-DC Converter of the circuit of Figure 3.43 as tabulated in Table 3.8 and graphically shown in Figure 3.45 and

109 Table 3.8: Value of Output Power and Voltage with changing Modulation Index of Four Quadrant SEPIC Chopper of Figure 3.43 Modu lation index Output Voltage(V) Output Power(W) Input Voltage( V) Input Power(W) Voltage Gain Efficiency

110 Figure 3.45 Characteristics Curve of Voltage Gain Vs Modulation Index of the Four quadrant SEPIC Chopper for the circuit Figure The simulation result tabulated in Table 3.8 and graphically shown in Figure 3.45 indicate, i) Voltage gain of the converter increases with modulation index increases. ii) Voltage gain less than 1 for modulation index<.50 and higher than 1 for modulation index >.50 Above two results i) and ii) are expected for DC-DC SEPIC Converter 102

111 Figure 3.46 Characteristics Curve of Efficiency Vs Modulation Index for Four quadrant SEPIC Chopper for the circuit Figure 3.43 The simulation result tabulated in Table 3.8 and graphically shown in Figure 3.46 indicate, the variation of the efficiency with modulation index. Efficiency of the converter increases with modulation index and peaks 76% when Modulation index is.49. After approximate.5 modulation index the efficiency of the 4Q SEPIC converter operating as a PWM inverter (dc-ac) decreases. 103