A Dc–Dc Converter with High-Voltage Step-Up Ratio and Reduced- Voltage Stress for Renewable Energy Generation Systems

Home , Direct current, Voltage controller

A DC–DC CONVERTER WITH HIGH-VOLTAGE STEP-UP RATIO AND REDUCED- VOLTAGE STRESS FOR RENEWABLE ENERGY GENERATION SYSTEMS

A Dissertation by

Satya Veera Pavan Kumar Maddukuri

Master of Science, University of Greenwich, UK, 2012

Bachelor of Technology, Jawaharlal Nehru Technology University Kakinada, India, 2010

Submitted to the Department of Electrical Engineering and Computer Science and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

December 2018

1 A DC–DC CONVERTER WITH HIGH-VOLTAGE STEP-UP RATIO AND REDUCED- VOLTAGE STRESS FOR RENEWABLE ENERGY GENERATION SYSTEMS

The following faculty members have examined the final copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirement for the degree of Doctor of Philosophy with a major in Electrical Engineering and Computer Science.

______Aravinthan Visvakumar, Committee Chair

______M. Edwin Sawan, Committee Member

______Ward T. Jewell, Committee Member

______Chengzong Pang, Committee Member

______Thomas K. Delillo, Committee Member

Accepted for the College of Engineering

______Steven Skinner, Interim Dean

Accepted for the Graduate School

______Dennis Livesay, Dean

iii DEDICATION

To my parents, my wife, my in-laws, my teachers, and my dear friends

iv ACKNOWLEDGMENTS

Firstly, I would like to express my sincere gratitude to my advisor

Dr. Aravinthan Visvakumar for the continuous support of my PhD study and related research, for his thoughtful patience, motivation, and immense knowledge. His guidance helped me in all the time of research and writing of this dissertation. I could not have imagined having a better advisor and mentor for my PhD study. Thanks, are also due to Dr. M. Edwin Sawan, Dr. Ward T. Jewell,

Dr. Chengzong Pang, Dr. Thomas K. Delillo for their insightful comments, encouragement, and for the hard question which incented me to widen my research from various perspectives.

My sincere thanks also go to Dr. John Watkins, Dr. Parlekar Tamtam, Dr. Richard Seals, and Dr. Yuri B. Shtessel, for their moral support. Thanks to WSU graduate school and NSF I-corps for providing the funds to develop and test the prototype.

I am also grateful to the following university staff: Nathan Smith and Tom McGuire for their unfailing support and assistance in developing and testing the prototype circuit.

I thank my fellow power quality lab mates in for the stimulating discussions, for the sleepless nights we were working together before deadlines, and for all the fun we have had in the last three years. Also, I thank my friends in the PDS group whom I consider as my extended family.

And finally, last but by no means least, I would like to thank my parents, my wife and brother-in- law for supporting me spiritually throughout my PhD education and my life in general.

Thanks for all your encouragement!

v ABSTRACT

This research work presents a high gain direct current–direct current (DC–DC) converter which is derived from a traditional boost converter. Electrical power systems are changing from a centralized generation model to a hybrid model with distributed generation. Distributed renewable energy sources such as photovoltaic (PV) modules, wind and fuel cells are becoming possible alternatives. However, to connect these systems to the grid, reliable DC–DC boost converters with high voltage gain is becoming a requirement. Firstly, a new open-loop DC–DC boost converter with superior performance in terms of voltage step-up ratio and reduced voltage stress on the switches, compared to other existing high gain DC–DC boost converter counterparts is proposed.

Along with analyzing the operation principle of the proposed converter, design procedure and component selection procedures are presented in this report. Experimental results along with simulation results are provided to validate the fundamentals of the open-loop proposed converter.

This converter can easily achieve a gain of 20 while benefiting from the continuous input current.

Secondly, to effectively maintain the voltage output at the required level, closed loop dc-dc converter with Proportional–Integral-Differential (PID) controller was proposed and simulated.

Thirdly a multi-loop with Proportional–Integral (PI) was proposed and simulated. Later, a charge controller was designed and operated along with closed loop dc-dc converter to supply load with two different voltage requirements. Simulation results are presented and analyzed to validate the theoretical results of the closed loop converter. Based on the simulation results the proposed controller can maintain the output voltage at the required level with respect to the changes in load.

vi TABLE OF CONTENTS

Chapter Page

1. INTRODUCTION ...... 1

2. LITERATURE REVIEW ...... 4

2.1 DC–DC Boost Converters...... 4 2.2 Controller for DC–DC Boost Converter ...... 8

3. MOTIVATION AND PROPOSED WORK ...... 12

4. METHODOLOGY ...... 17

4.1 Modeling of Proposed Converter ...... 17 4.2.1 Mode-I...... 19 4.2.2 Mode-II ...... 19 4.2 Modified Proposed Converter ...... 21 4.2.1 Mode-I...... 22 4.2.2 Mode-II ...... 23 4.3 Analysis of the Proposed Converter ...... 24 4.3.1 Steady-State Conditions of Converter ...... 25 4.3.3 Topologies Comparison ...... 27 4.4 Single loop controller ...... 30 4.5 Pulse Width Modulation Generator with Saturation limiter ...... 33 4.6 Single loop DC–DC boost converter with change in reference voltage ...... 34 4.7 Multi-loop controller ...... 35 4.8 Full bridge DC-AC Converter ...... 41

5. RESULTS ...... 43

5.1 Component Selection ...... 43 5.1.1 Inductor Selection ...... 43 5.1.2 Capacitor Selection ...... 44 5.1.3 MOSFET Selection ...... 45 5.2 Simulation Validation ...... 48 5.2.1 Open-loop Simulation Results ...... 48 5.2.2 Single-loop Simulation Results...... 50 5.2.3 Single-Loop with Charge Controller Simulation Results ...... 54 5.2.4 Multi-loop Controller Simulation Results ...... 55 5.2.5 Multiloop Controlled DC-DC Converter Response with Respect to Change in Input ...... 57 5.2.6 Output Voltage from the DC-AC Converter ...... 58 5.3 Experimental Validation ...... 59

vii TABLE OF CONTENTS (continued)

Chapter Page

5.3.1 PCB Design ...... 60 5.3.1 System Test Results ...... 64

6. CONCLUSION ...... 67

7. REFERENCES ...... 69

viii LIST OF FIGURES

Figure Page

1. General applications of DC–DC boost converters...... 1

2. Isolated DC–DC boost converter (a) with two controlled switches (b) with voltage doubling rectifier...... 4

3. Non-isolated DC–DC (a) elementary boost converter (b) double boost circuit (c) three- stage boost circuit (d) elementary multiple boost circuit...... 5

4. Nom-isolated DC–DC boost converter with coupled inductors (a) flyback topology (b) interleaved cross-winding topology (c) wide input wide output (WIWO) topology (d) interleaved topology ...... 6

5. Non-isolated (a) switched capacitor convertor (b) Hybrid step-up converter with switching structure DC–DC boost converter (c) Quadratic boost converter (d) SEPIC converter ...... 7

6. Isolated and Non-isolated DC–DC boost converters ...... 7

7. Block diagram of closed-loop converter in distributed generation systems...... 13

8. Block diagram of the energy management system with charge controller and closed loop DC–DC boost converter inside the RSC-EV ...... 14

9. Proposed DC–DC boost converter...... 17

10. Topological stages for the proposed converter in Figure 9: (a) controlled switches S − ON topology, and (b) controlled switches S − OFF topology...... 18

11. Equivalent inductor current waveforms for converter shown in Figure 9 in continuous conduction mode...... 20

12. Modified proposed DC–DC boost converter...... 21

13. Topological stages for the modified proposed converter in Figure 12: (a) controlled switches S1 − ON, S2 − OFF topology, and (b) controlled switches S1 − OFF, S2 − ON topology...... 22

14. Figure 14. Equivalent inductor current waveforms for converter shown in Figure 12 in continuous conduction mode...... 27

ix LIST OF FIGURES (continued)

Figure ...... Page

15. Figure 15. Averaged circuit model for converter shown in Figure 12...... 29 16. CCM characteristics for proposed converter and other boost converter counterparts: (a) voltage conversion ratio M as function of duty cycle D, and (b) normalized switch voltage 푀푠 as a function of duty cycle D...... 29

17. Schematic of proposed converter with closed-loop PID-based PWM control...... 30

18. Schematic of the closed loop converter with inbuilt charge controller ...... 34

19. Schematic of the proposed single loop converter with inbuilt controller for roof top solar panel electric vehicle ...... 35

20. Schematic of the closed loop converter with inbuilt charge controller ...... 37

21. Frequency response of (a) is(s)/ds for different values of gain N (b) Vo(s)/ds for different values of gain N ...... 40

22. Schematic of the SPWM driven dc-ac converter ...... 41

23. Safe operating area for STP5NK100Z N- Channel MOSFET...... 47

24. Open-loop output waveforms: (a) output voltage, and (b) output current...... 49

25. Simulation waveforms of output voltage for DC–DC proposed boost converter (PBC), conventional quadratic boost converter (QBC), and traditional boost converter (BC) with duty cycle D = 0.8 and input voltage 푉푖푛 = 10 V. 50

26. Output waveforms of proposed converter under closed-loop operation: (a) voltage, (b) settled output voltage, and (c) zoom of voltage ...... 52

27. Figure 27. Output DC waveform from the proposed converter with change in load: (a) with enough generation, and (b) with no-enough generation ...... 554

28. Output DC waveform from the proposed converter with change in load: (a) with enough generation (b) with no-enough generation...... 56

29. Response of the proposed dc-dc converter with respect to changes (a) in input at time period of 1.3 seconds (b) in input at time period of 1.4 seconds (c) in input at time period of 1.2 seconds (d) in input at time period of 1.1 seconds ...... 57

x LIST OF FIGURES (continued)

Figure ...... Page

30. Output RMS-AC waveform from the DC-AC converter with change in load (a) AC waveform for the whole operation of load (b) Zoomed output voltage for one millisecond showing the 50 HZ frequency ...... 58

31. Schematic of the proposed open-loop converter developed in Proteus software ...... 61

32. PCB of the proposed open-loop converter developed in Proteus software ...... 61

33. 3-dmentional image of the PCB ...... 62

34. Pulse width modulation signal from Arduino microcontroller ...... 63

35. Photograph of the prototype and the measuring setup ...... 65

36. Change in output with respect to change in duty cycle from experimental setup...... 65

37. Simulation and experimental waveforms of voltage stress on uncontrolled switches: (a) across diode D1, (b) across diode D2, (c) across diode D3, and (d) across diode D4...... 66

xi LIST OF TABLES

Table Page

1. Performance Comparison of Boost Converters ...... 28

2. Controller Parameters for Ziegler-Nichols method ...... 33

3. Reference voltage set by charge controller based on 푉푇 and 푉푖푛 ...... 36

4. Switching States of the Full Bridge VSI ...... 42

5. Parameters for Proposed Converter ...... 48

6. Parameters for Closed-Loop Controller ...... 51

7. Key Parameters for Proposed Open-Loop Converter ...... 64

xii LIST OF ABBREVIATIONS/NOMENCLATURE

AC Alternating Current DC Direct Current DG Distributed Generation PV Photovoltaic PWM Pulse-Width-Modulation ESR Equivalent Series Resistance SMC Sliding Mode Control PID Proportional Integral and Derivate PI Proportional and Integral DCM Discontinuous Conduction Mode CCM Continuous Conduction Mode VM Voltage Multiplier EV Electric Vehicle RSA Roof mounted Solar Array RMS Root Mean Square MOSFET Metal-Oxide-Semiconductor Field-Effect Transistor PV Photovoltaic WSU Wichita State University

xiii CHAPTER I

INTRODUCTION

Direct Current–Direct Current (DC–DC) boost converters are widely used in power, industrial, and consumer products as shown in Figure 1. Renewable energy sources can be an appropriate alternative for the fossil fuels due to their advantage of inexhaustible resources, fuel diversification, and environmental friendliness. To connect these systems to the network, DC–DC boost converters with wide dc conversion ratios are needed [1]. The basic DC–DC boost converters are not suitable for this application due to the need of operating at extreme duty ratios, hence alternative topologies need to be considered [1]. The main objective of such a system is to maximize energy yield and minimize maintenance.

Figure 1. General applications of DC–DC boost converters.

1 To achieve the above objective, the converters should be able to produce the required output from the minimum input with high conversion efficiency at low cost, and size [2] – [3]. A good DC–DC boost converter should satisfy the following three types of requirements:

1. Economic requirements:

The circuit should be energy efficient, small in size, light in weight, and low in

cost.

2. Steady-state performance requirements:

The output voltage, output current, and AC ripple should be within the specified

range.

3. Dynamic performance requirements:

The circuit should be stable, and the output voltage should be kept within the

specified range under small disturbances at the source voltage and the load.

(i.e. the converter should have good line and load regulation).

In admission to the above, one of the major challenges faced by designers of today’s DC–

DC boost converter’s is to optimize the converters design based on contradictory constraints: low cost and increased life. A solution to improve the life and efficiency of DC–DC boost converters is by reducing the voltage stress on the switches. The future converters should also reduce the issue of voltage fluctuations occurring due to the intermittent nature of renewable energy sources.

There are two main types of DC–DC boost converters: linear and switch-mode. In general, linear DC–DC boost converters are not energy efficient and are very large, while switch-mode

DC–DC boost converters can meet the three requirements previously mentioned. In switching converters, lossless elements such as efficient switches, inductors, and capacitors are used to store energy temporarily and transmit it to the load. By properly choosing the switching frequency,

2 inductance, and capacitance values, the converter can be of small size and light weight and can filter out large alternating current (AC) ripples, so that the steady-state performance requirements are met. Despite all the advantages of switches, they also make the circuits nonlinear and difficult to analyze.

Switched DC–DC boost converters can be classified into two categories, pulse width modulation (PWM) converters and soft switching converters, which are also called resonant converters. In soft-switching converters the increased peak currents for the same output voltage is a major disadvantage. Using PWM technique, there is an efficient regulation over a wide range of voltage inputs and outputs. The only disadvantage with this method is small loss of power during switching because of the finite values of voltage and current during the switching transient.

Analysis, control, and stabilization are the main issues in switching converters. Along with novel design, the converter needs to be properly analyzed. To facilitate the analysis and design of these converters, a good analysis method is also needed. The most popular step-up DC–DC boost converters till date are discussed in the following section.

3 CHAPTER II

LITERATURE REVIEW

DC–DC conversion technology is a major subject area in the field of electrical power engineering and is widely used in industrial applications and computer hardware circuits. The

DC–DC conversion technique was established in the 1920s. A simple voltage conversion, the simplest DC–DC boost converter is a voltage divider, but it only converts output voltage lower than the input voltage with poor efficiency [5]. The multi-quadrant chopper is the second step in

DC–DC conversion. Much time has been spent trying to find the equipment to convert the DC energy source of one voltage to another DC actuator with another voltage, as does a transformer employed in AC–AC conversion [6].

2.1 DC–DC Boost Converters

In 1940s, the buck converter was derived from the “A” type chopper [6] and later boost converter was derived from “B” type chopper [8]. From then different topologies for DC–DC boost converters have been presented in the literature. Recent converters in this area are studied and analyzed as follows. There are numerous isolated DC–DC boost converter topologies presented in the literature, in which the voltage is raised by increasing the transformer ratio [8] – [11].

a b

Figure 2. Isolated DC–DC boost converter (a) with two controlled switches (b) with voltage doubling rectifier.

4 A model topology is shown in Figure 2. Even though it can achieve the high voltage there are many disadvantages. For instance, size, costs, and voltage spikes across the power systems due to leakage inductance [12].

In applications where galvanic insulation is not a must, non-isolated DC–DC converters can be used to achieve voltage step-up or step-down, with consequent reduction of size, weight and volume associated to the increase of efficiency because of the lack of a high-frequency transformer[12]. The converters with cascaded topologies in [13] can achieve high step-up voltage gain with relatively high efficiency. The elementary boost converter with cascaded connection topologies is shown in Figure 3. However, connecting two or more converters to form a single converter results in increased complexity and cost. In addition, the two converters need to be synchronized to avoid beat frequencies [14].

a b

c d

Figure 3. Non-isolated DC–DC (a) elementary boost converter (b) double boost circuit (c) three-stage boost circuit (d) elementary multiple boost circuit.

5 The coupled inductor converters as shown in Figure 4 (a), (c), are used to meet the requirements of high output voltage gains [15]–[17]. The major drawbacks of this topologies are voltage spikes across the switches due to leakage inductance. Moreover, the leakage inductance increases with a rise in voltage gains, because it requires a higher number of winding turns. To compensate for these spikes, isolated topologies with improved active clamping and soft switching are presented in [18]–[22]. The model topologies are shown in Figure 4 (b), (d). However, the inclusion of clam stage has increased the component count and design complexity and added losses at the clamp stage. A topology with improved clamping presented in [23] overcame the aforementioned glitches, but at the cost of resonating currents from both the power switch and the magnetizing inductance.

a b

c d

Figure 4. Non-isolated DC–DC boost converter with coupled inductors (a) fly-back topology (b) interleaved cross-winding topology (c) wide input wide output (WIWO) topology (d) interleaved topology

a b

c d

Figure 5. Non-isolated (a) switched capacitor convertor (b) Hybrid step-up converter with switching structure DC–DC boost converter (c) Quadratic boost converter (d) SEPIC converter

Figure 6. Isolated and Non-isolated DC–DC boost converters

7 The main objective here is to reach a high output voltage gain, high efficiency, and low- cost topology with simple structures. One possible solution for this problem is the use of a capacitor-diode voltage multiplier, popularly known as a hybrid switched capacitor, which can eliminate the abovementioned drawbacks such as, high size, cost, and low efficiency [24]–[30].

The model topologies with switched capacitors is shown in Figure 5. The ladder showing the different types of isolated and non-isolated DC–DC boost converters is shown in Figure 6.

In this research work, a newly configured DC–DC boost converter with high step up ratio is proposed. First, the proposed converter under open loop mode, shows improvement in the voltage step-up ratio, compared to the existing single-switch boost converters under the same duty ratio. Second, along with high output, the proposed structure shows a remarkable reduction in voltage stress on switches over existing single-switch converters.

2.2 Controller for DC–DC Boost Converter

Analysis, control, and stabilization are the main issues in switching DC–DC boost converters. To facilitate the stabilization of these converters, a good analysis method is needed.

The conventional small signal-based pulse width modulation (PWM) controllers are often used although they operate optimally only for specific operating points [31]– [34]. The in-depth studies have been applied to various nonlinear controls for DC–DC converters [35] – [36]. They are feedback state linearization, input–output linearization, flatness, passivity-based control, dynamic feedback control by input–output linearization, exact tracking, error passivity feedback, and boundary control. Implementations of them require PWM modulators. Five recent techniques from hybrid and optimal controls are evaluated on buck and boost converters [37]. These methods display high performances, while respecting circuit constraints. One-cycle control is applied to

Cuk Converter [38]. Synergetic control is applied to buck and boost converters with an incomplete

8 analysis of the closed-loop system stability [39]. As a primitive-control method for variable structure systems, hysteresis control is still popular for converters. A hysteretic current-mode control is applied to a buck converter with low-voltage microprocessor loads [40]. A simple, self- adjusting analog prediction of the hysteresis band is added to the phase-locked-loop control to ensure constant switching frequency of three-phase voltage-source inverters [41]. Hysteresis and delta-modulation controls are implemented for a buck converter by using sensor-less current mode, reporting voltage-source characteristics, excellent open-loop tracking, and near-ideal source rejection [42].

The researchers have made efforts to improve dynamic response, transients, and voltage ripples for DC–DC converters. Song and Chung [43] claim that boundary control can improve fast dynamic response. Through sensitivity analysis, they conclude that the steady state switching frequency decreases, or the hysteresis band increases as the equivalent series resistance (ESR) for the capacitor increases. Sliding-mode control (SMC) has gained popularity in converters in recent years [44]. The indirect control of the current on a switching manifold is used for output voltage regulation. Unfortunately, open-loop SMC lacks robustness against system uncertainties and disturbances. In [45], a PWM based sliding-mode voltage controller is designed for basic DC–DC converters in continuous conduction mode. It is limited to a lower bandwidth application. In [46] and [47], sliding mode controllers with dynamic sliding manifolds allow direct control of the voltages of buck, boost, and buck–boost converters. However, the output voltage tracking error must converge to zero asymptotically in sliding mode. In [48], sliding mode control is applied for quadratic boost converter. But, it is difficult to extend this method to more complicated converters or converters with other modeling methods.

9 As a practical control method with a deep industrial root, proportional integral and derivate

(PID) control is widely applied to converters or inverters either in conventional manner or in combination with the other control methods discussed above. Closed-loop analysis of such systems with a resultant guideline for selecting PID gains has a demand from practicing engineers and corporations [49]. In [50], generalized proportional integral (PI) controllers are applied to buck, boost, and buck–boost converters based on integral re-constructors of the unmeasured observable state variables. However, the system robustness with respect to input voltage variation or disturbances is not studied, and extremely large load variation renders loss of feedback for the controller [51].

The controller of a converter should first guarantee that the system is stable under all operating conditions, and secondly robust to maintain the desired operational performance when a disturbance occurs in the circuit. For a single-loop feedback DC–DC boost converter operating under discontinuous conduction mode (DCM), the stability and dynamic performance can be guaranteed through increasing the loop gain as large as possible with a high crossover frequency and an adequate gain and phase margins. Whereas, the right half plane zeros for the DC–DC boost converters in the continuous conduction mode (CCM) severely restricts crossover frequency of the open loop gain, which results in poor dynamic performance if single loop feedback control is adopted [52]–[55]. On the other hand, linear multi-loop control has become widely applied

[56]–[60] due to its simplicity and a long history of proved efficiency and dynamic performance.

In this research work, a proportional-integral-differential (PID) based single and proportional-integral (PI) based multi-loop controllers are used for the closed-loop control. In multiloop, the inner current loop is designed to maximize the bandwidth of closed loop system and an external voltage loop is used for the regulation task. First the proposed DC–DC boost converter

10 with closed loop controller has minimized the fluctuations in the input voltage. Second the use of the PI-based PWM control has the added advantage of easy programming and robustness.

11 CHAPTER III

MOTIVATION AND PROPOSED WORK

A novel DC–DC converter that address the issues stated in literature review is proposed in this research work. The proposed converter is inspired from the charge pump voltage converter

[61]. Initially, by integrating the diode-capacitor voltage multiplier (VM) stages along with inductors to the boost converter a newly configured non-isolated DC–DC boost converter is proposed. This has the higher overall voltage gain and reduced voltage stress. The operation of the proposed converter is comparable to its pulse-width-modulation (PWM) counterparts but possesses several essential performance advantages:

• Higher step-up voltage with lower operating duty cycle.

• Lower voltage stress on the semiconductor devices.

• Simple control due to use of complementary controlled switches

• Continuous input and output current.

Furthermore, the absence of both transformer and extreme duty cycle in the proposed converter allows it to operate at high switching frequencies, thereby resulting in higher efficiency, reduced size, weight, simple structure and control. This will help in connecting the standalone renewable generating units to the distribution systems [62] effectively.

One of the critical requirements of future distribution systems in the presence of distributed generation is active power management. It is critical to ensure the output AC voltage maintain within the standard limits by sensing the sudden solar ramping and automatically varying the output voltage of the DC-AC converter (inverter). But rather than controlling the inverter, controlling the DC–DC boost converter exhibits several advantages, the most important of which is easy control and quality of the output voltage sine wave that have been often mentioned in the

12 literature [63], [64]. To automatically achieve and maintain the desired output voltage by comparing it with the reference voltage, a closed loop control is designed for the proposed converter. The closed-loop is formed with PI based pulse width modulation (PWM) controller is shown in Figure 7. The error between the reference voltage and output voltage determines the PI controller action. The PWM block then varies the duty cycle in accordance with the PI output voltage signal.

Battery Closed-loop Distributed 퐷퐶 − 퐷퐶 Generation 푙표푤 ℎ𝑖푔ℎ Converter DC-AC AC Converter Appliances

Figure 7. Block diagram of closed-loop converter in distributed generation systems.

In addition to micro-grid applications, the proposed converter is modified to use for electric vehicles (EV). EV’s are growing at a rapid pace in the internal combustion engine dominated transportation sector and bring environmental and economic benefits to society. Use of roof mounted solar array (RSA) systems to generate the energy required for operating a thermoelectric system and the compressors for maintaining the car cabin temperature helps to extend the cruising range of electric vehicles [65]. In such systems, managing and maintaining the output voltage is crucial. So, the proposed DC–DC boost converter needs a robust controller. The controller of a converter should guarantee first that the system is stable under all operating conditions, and second that the system is robust enough to maintain the desired operational performance when a circuit disturbance occurs. For a single-loop feedback DC–DC boost converter operating under discontinuous conduction mode (DCM), the stability and dynamic performance can be guaranteed

13 by increasing the loop gain as large as possible with a high crossover frequency and adequate gain and phase margins. Whereas the right half plane zeros for the DC–DC boost converters in the continuous conduction mode (CCM) severely restricts the crossover frequency of the open-loop gain, which results in poor dynamic performance if single-loop feedback control is adopted. On the other hand, linear multi-loop control has become widely applied due to its simplicity and a long history of proven efficiency and dynamic performance. Hence, a multi-loop controller is designed for the proposed converter [66].

Along with this, an inbuilt charge controller is built to manage the output voltage depending on the load and solar array power output. The multi-loop-controlled DC–DC boost converter along with the charge controller is shown in Figure 8. In these vehicles, the solar panel’s generated energy is primarily used to run the cabin temperature control unit when needed and to charge the batteries otherwise. To run the cabin temperature control unit, the generated dc voltage from the

RSC should be boosted to around dc voltage of 156 푉 by means of proposed converter and invert it to ac voltage of 110 푉 (RMS), 60Hz using an inverter circuit [67]. The generated voltage need

Figure 8. Block diagram of the energy management system with charge controller and closed loop DC–DC boost converter inside the RSC-EV

14 to be boosted to 500 푉푑푐 for charging the batteries. The charge controller plays a prominent role in controlling the output voltage from the DC–DC converter as per the changes in load.

Below is the summary of the proposed work:

• An in-depth literature review of existing DC–DC boost converters and their control

systems.

• Study of Renewable energy generation systems

• Propose a novel high voltage step-up gain and low voltage stress DC–DC boost converter

for distributed generating systems

• Simulation and experimental validation of the proposed DC–DC boost converter.

• Develop a closed loop control system to the said converter, such that the small disturbances

at the source voltage are mitigated.

• Develop a PWM generator that changes the duty cycle with respect to the data from

controller.

• Determine the range of input disturbances that the proposed closed loop DC–DC boost

converter can mitigate.

• Propose an intelligent controller that sense the changes in the load and vary the reference

voltage for the closed loop.

• Design a control system that provides the required PWM signal for the controlled switch/s

sensing the error between the output and the reference voltages.

• Enhance the proposed intelligent controller capability to sense the changes in the input

voltage along with load changes and there by vary the reference voltage for the closed loop.

• Develop an advanced closed loop controller that produces the required output mitigating

the high disturbances in the input.

15 • Analyze the input voltage mitigation capacity of the closed loop controller.

The rest of this document is organized in the following way. Preliminary results, including the design of proposed converter, mathematical analysis and controller design is given in section

IV. The modelling and analysis of the converter along with simulation and experimental results are explained in this section V. Conclusion along with the future work is given in section VI.

16 CHAPTER IV

METHODOLOGY

The modelling of the proposed DC–DC boost converter along with mathematical analysis is discussed in this section.

4.1 Modeling of Proposed Converter

A novel DC–DC converter with high voltage step-up ratio is formed by integrating the

Diode-capacitor voltage multiplier (VM) stages along with inductors to a single-switch DC–DC boost converters, as shown in Figure 9. The proposed converter utilizes a single controllable switch, hence enabling an easy driver circuit. For theoretical analysis, the proposed converter is considered to operate under a steady-state, continuous-conduction mode (CCM) based on the following assumptions. Assumptions for a single-switching cycle 푇푆 are as follows:

• All components are ideal.

• The switching frequency is much higher than the natural frequency, which in turn considers

inductor currents 푖퐿1, 푖퐿2, 푎푛푑 푖퐿3 and capacitor voltages 푉퐶1, 푉퐶2, 푎푛푑 푉퐶0 as constants

with relatively small ripples [68].

Figure 9. Proposed DC–DC boost converter.

17 Normal operation of the proposed converter involves two modes, as shown in Figure 10(a) and 10(b). The active switch (MOSFET) is represented by 푆; passive switches (diodes) are represented by 퐷1, 퐷2, 퐷3 푎푛푑 퐷표; and the nominal duty cycle is represented by 퐷. The key to the analysis for determining the output voltage 푉0 is to examine the inductor current during switch

푆 ON and OFF periods.

Figure 10. Topological stages for the proposed converter in Figure 9: (a) controlled switches 푆 − 푂푁 topology, and (b) controlled switches 푆 − 푂퐹퐹 topology.

18 4.1.1 Mode-I

In mode I, when the control switches 푆 is ON, and the diodes 퐷2, 퐷3 are forward-biased and the diodes 퐷1, 퐷표 are reverse-biased as shown in Figure 10(a). The inductor 퐿1 is charged form input source 푉𝑖푛, whereas inductors 퐿2, 퐿3 are charged from capacitors 퐶1, 퐶2 respectively.

The current in the inductors rise linearly as shown in Figure 11 during ON period. The change in inductor current is represented by ∆푖퐿.

Based on the above discussion, the following relationships are developed:

푑𝑖퐿 퐿 1 = 푉 1 푑푡 𝑖푛 (1a)

푑𝑖 퐿 퐿2 = 푉 2 푑푡 퐶1 (1b)

푑𝑖퐿 퐿 3 = 푉 − 푉 3 푑푡 퐶1 퐶2 (1c)

푑푉퐶 퐶 1 = −푖 1 푑푡 퐿2 (1d)

푑푉퐶 퐶 2 = −푖 2 푑푡 표 (1e)

푑푉 퐶 퐶0 = 푖 + 푖 − 푖 0 푑푡 퐿1 퐿2 퐿3 (1f)

4.1.2 Mode-II

In mode II, when the control switches 푆 is OFF, the diodes 퐷2, 퐷3 are reverse-biased as shown in Figure 10(b). Diodes 퐷1, 퐷표 are forward-biased, providing a path for the inductors

퐿1, 퐿2, 푎푛푑 퐿3 to deliver stored energy to capacitors 퐶1, 퐶2, and 퐶0, respectively. Accordingly, during OFF period the current in the inductors drops linearly as shown in Figure 11.

푑𝑖 퐿 퐿1 = 푉 − 푉 1 푑푡 𝑖푛 퐶1 (2a)

푑𝑖 퐿 퐿2 = (푉 + 푉 ) − 푉 2 푑푡 퐶1 퐶0 표 (2b)

푑𝑖 (퐿 − 퐿 ) 퐿3 = 푉 3 2 푑푡 퐶0 (2c)

19 푑푉 퐶 퐶1 = 푖 − 푖 − 푖 1 푑푡 퐿1 퐿2 퐿3 (2d)

푑푉 퐶 퐶2 = 푖 + 푖 − 푖 2 푑푡 퐿2 퐿3 표 (2e)

푑푉 퐶 퐶0 = 푖 0 푑푡 퐿2 (2f)

Figure 11. Equivalent inductor current waveforms for converter shown in Figure 9 in continuous conduction mode.

20 4.2 Modified Proposed Converter

In the proposed converter, the diode 퐷3 is turned ON in both mode I and II as shown in

Figure 10. This results in more stress on the diode, hence to avoid this a modified converter is proposed as shown in Figure 12. In addition to existing controlled switch 푆1, an additional controlled switch 푆2 is added.

Figure 12. Modified proposed DC–DC boost converter.

Normal operation of the modified proposed converter involves two modes as shown in

Figs. 13(a), (b). The complimentary controlled active switches (MOSFET) are represented by 푆1, 푆2; passive switches (diodes) are represented by퐷1, 퐷2, 퐷3 푎푛푑 퐷표; and the nominal duty cycle is represented by 퐷. The key to the analysis for determining the output voltage 푉0 is to examine the voltage second balance in inductors.

Figure 13. Topological stages for the modified proposed converter in Figure 12: (a) controlled switches 푆1 − 푂푁, 푆2 − 푂퐹퐹 topology, and (b) controlled switches 푆1 − 푂퐹퐹, 푆2 − 푂푁 topology. 4.2.1 Mode-I

In mode I, when the control switches 푆1 is ON, 푆2 is OFF, the diodes 퐷2, 퐷3 are forward- biased and the diodes 퐷1, 퐷표 are reverse-biased as shown in Figure 13(a). The inductor 퐿1 is charged form input source 푉𝑖푛, whereas inductors 퐿2, 퐿3 are charged from capacitors 퐶1, 퐶2

22 respectively. The current in the inductors rise linearly as shown in Figure 14 during ON period.

The change in inductor current is represented by ∆푖퐿.

Based on the above discussion, the following relationships are developed:

푑𝑖퐿 퐿 1 = 푉 1 푑푡 𝑖푛 (3a)

푑𝑖 퐿 퐿2 = 푉 2 푑푡 퐶1 (3b)

푑𝑖퐿 퐿 3 = 푉 − 푉 3 푑푡 퐶1 퐶2 (3c)

푑푉퐶 퐶 1 = −푖 − 푖 1 푑푡 퐿2 퐿3 (3d)

푑푉퐶 퐶 2 = 푖 2 푑푡 퐿3 (3e)

푑푉 퐶 퐶0 = −푖 0 푑푡 0 (3f)

4.2.2 Mode-II

In mode II, when the control switches 푆1 is OFF, 푆2 is ON, the diodes 퐷2, 퐷3 are reverse- biased as shown in Figure 13(b). Diodes 퐷1, 퐷표 are forward-biased, providing a path for the inductors 퐿1, 퐿2, 푎푛푑 퐿3 to deliver stored energy to capacitors 퐶1, 퐶2, and 퐶0, respectively.

Accordingly, during OFF period the current in the inductors drops linearly as shown in Figure 14.

푑𝑖 퐿 퐿1 = 푉 − 푉 1 푑푡 𝑖푛 퐶1 (4a)

푑𝑖 퐿 퐿2 = (푉 + 푉 ) − 푉 2 푑푡 퐶1 퐶2 표 (4b)

푑𝑖 퐿 퐿3 = 푉 3 푑푡 퐶1 (4c)

푑푉 퐶 퐶1 = 푖 − 푖 − 푖 1 푑푡 퐿1 퐿2 퐿3 (4d)

푑푉 퐶 퐶2 = −푖 2 푑푡 퐿2 (4e)

푑푉 퐶 퐶0 = 푖 − 푖 0 푑푡 퐿2 0 (4f)

23 Analyzing the (1a – 1f), (2a – 2f), (3a – 3f) & (4a – 4f), the operation of the proposed and modified converter is same except the additional controlled witch 푆2. Hence for steady-state analysis, either of these equations can be used.

Figure 14. Equivalent inductor current waveforms for converter shown in Figure 12 in continuous conduction mode.

4.3 Analysis of the Proposed Converter

This section presents the steady-state analysis and switching voltage stress analysis.

24 4.3.1 Steady-State Conditions of Converter

A steady-state operation requires that the inductor current at the end of the switching cycle is the same as that at the beginning, meaning that the net change in inductor current over one period is zero. Therefore, as can be seen in Figure 14, the volt-second balance of inductor 퐿1 is

푉푖푛푇푂푁 (푉퐶1−푉푖푛)(푇−푇푂푁) 퐿1: = 퐿1 퐿1

⇒ 푉𝑖푛 = 푉퐶1(1 − 퐷) (5)

where 퐷 is the switching duty cycle for switch 푆1, 푇푂푁 is the time for which the switch 푆1 is ON, 푇푂퐹퐹 is the time for which the switch 푆1 is OFF and 푇 (푇푂푁 + 푇푂퐹퐹) is the switching period.

Similarly, the volt-second balance of inductors 퐿2 and 퐿3 is

푉퐶1푇푂푁 [푉표−(푉퐶1+푉퐶2)](푇−푇푂푁) 퐿2: = 퐿2 퐿2

⇒ 푉퐶1 = (1 − 퐷)[푉표 − 푉퐶2] (6)

(푉퐶1−푉퐶2)푇푂푁 −푉퐶1(푇−푇푂푁) 퐿3: = 퐿3 퐿3

1 ⇒ 푉 = 푉 퐷 ⇒ 푉 = [ ] 푉 퐶1 퐶2 퐶2 퐷(1−퐷) 𝑖푛 (7)

By solving (5) – (7), the step-up ratio M is determined as

푉표 1 푀 = = 2 (8) 푉푖푛 퐷(1−퐷)

The state equations of the proposed converter given by rewriting the (1) ─ (7):

푑𝑖 푉 푉 −푉 퐿1 = 푖푛 푢 + 푖푛 퐶1 (1 − 푢) (9a) 푑푡 퐿1 퐿1

푑𝑖 푉 (푉 +푉 )−푉 퐿2 = 퐶1 푢 + 퐶1 퐶2 퐶표 (1 − 푢) (9b) 푑푡 퐿2 퐿2

푑𝑖 푉 −푉 푉 퐿3 = 퐶1 퐶2 푢 + 퐶1 (1 − 푢) (9c) 푑푡 퐿3 퐿3

25 푑푉 −𝑖퐿 −푖 𝑖 −𝑖 −𝑖 퐶1 = 2 퐿3 푢 + 퐿1 퐿2 퐿3 (1 − 푢) (9d) 푑푡 퐶1 퐶1

푑푉 𝑖 𝑖 퐶2 = 퐿3 푢 − 퐿2 (1 − 푢) (9e) 푑푡 퐶2 퐶2

푑푉 −푉 𝑖 −(푉 /푅) 퐶0 = 퐶2 푢 + 퐿2 퐶2 (1 − 푢) (9f) 푑푡 푅퐶0 퐶0

Where 푢 = 1 when the control switch 푆1 is ON, and 푢 = 0 when the control switch 푆1 is OFF.

The behavior of the proposed converter can be described through a state-space model by means of state-space equations of the resulting current flow during modes I and II. The state-space variables are identified as three inductor currents and three capac1-itor voltages. Thus, the resultant equation is given by

−(1−푢) 0 0 0 0 0 퐿1 푖퐿̇1 1 (1−푢) −(1−푢) 푖 1 0 0 0 퐿1 퐿2 퐿2 퐿2 퐿 푖퐿̇2 푖 1 1 푢 퐿2 푖 ̇ 0 0 0 0 0 퐿3 퐿 퐿 푖퐿 = 3 3 3 + 0 푉 푉 ̇ (1−푢) −1 −1 푉 𝑖푛 (10) 퐶1 0 0 0 퐶1 0 퐶1 퐶1 퐶1 푉 ̇ 푉퐶 퐶2 −(1−푢) 푢 2 0 0 0 0 0 ̇ 퐶 퐶 [푉퐶표] [0] [푉퐶표] 2 2 (1−푢) 1 0 0 0 − 0 [ 퐶표 푅퐶0 ]

The model in (10) is non-linear, because the steady state matrix depends on the switching function 푢(푡) with a binary value of 1 when switch 푆1 is turned ON, and 0 when switch 푆1 is turned

OFF.

4.3.2 Voltage stress on the switches

One of the major factors in designing a controller is the stress created during switching operations. The voltage stress on switch and diodes is calculated by rewriting (1)─(7) as follows:

26 Switch 푆1: 푉푆1−푠푡푟푒푠푠 = 퐷푉푂 (11)

Switch 푆2: 푉푆2−푠푡푟푒푠푠 = (1 − 퐷)푉푂 (12)

Diode 퐷1: 푉퐷1−푠푡푟푒푠푠 = 퐷(1 − 퐷)푉푂 (13)

2 Diode 퐷2: 푉퐷2−푠푡푟푒푠푠 = 퐷 푉푂 (14)

Diode 퐷3: 푉퐷3−푠푡푟푒푠푠 = 푉푂 (15)

Diode 퐷0: 푉퐷0−푠푡푟푒푠푠 = (1 − 퐷)푉푂 (16)

The voltage stress on the switch 푆1 of the proposed converter is given in (11), and its performance is compared with the other traditional converters in section E.

4.3.3 Topologies Comparison

The averaged circuit model for the proposed converter, shown in Figure 15 is used to measure the voltage conversion ratio and semiconductor normalized peak voltage. The voltage gain ratio 푀 and the normalized switch stress 푀푠 for the proposed converter and other traditional boost converters are listed in Table 1

Figure 15. Averaged circuit model for converter shown in Figure 12.

27 The relations of Table 1 are graphically illustrated as shown in Figure 16. The voltage gain of the proposed converters is higher than their equivalent counterparts, shown in Figure 16 (a) for the same duty cycle. At lower duty cycles the proposed converter has similar performance with traditional converters but for 퐷 > 0.3 the voltage gain has great change. The proposed converter normalized voltage stress on active and passive switches is compared as shown in Figure 16 (b) with the traditional boost converter counterparts. It can be interpreted from the graph, for the same voltage gain ratio, the proposed converter is subjected to low voltage stress on the switches.

Table 1. Performance Comparison of Boost Converters

푽풐 푽푺 Converter 푴 = 푴푺 = 푽풊풏 푽풐

1 Proposed Converter 퐷 퐷(1 − 퐷)2

1 Conventional Boost Converter 1 1 − 퐷

Conventional Quadratic Boost 1 1 (1 − 퐷)2 Converter

퐷 1 Conventional Cuk Converter (1 − 퐷) 퐷

2 − 퐷 1 Self-Lift DC/DC Converter 1 − 퐷 2 − 퐷

Figure 16. CCM characteristics for proposed converter and other boost converter counterparts: (a) voltage conversion ratio M as function of duty cycle D, and (b) normalized switch voltage 푀푠 as a function of duty cycle D.

29 4.4 Single loop controller

One of the critical requirements of future distribution systems in the presence of distributed generation is active power management. It is critical to ensure that the AC voltage varies with sudden solar ramping, which requires the controller to follow the reference voltage through output feedback. The circuit diagram of the closed-loop proportional integral derivative (PID) based

PWM controller is shown in Figure 17. For controlling, it is vital to select the appropriate variable from the view point of performance and implementation. In this converter, the natural state variables are inductor currents and capacitor voltages. The use of output capacitor voltage for the feedback is a common practice in voltage-programmed control [69].

Figure 17. Schematic of proposed converter with closed-loop PID-based PWM control.

30 The steady-state operating conditions obtained from (1) – (7) are as follows:

푉 푉 = 푖푛 From equation 5, 퐶1 1−퐷 (15a)

푉 푉 = 푖푛 From equation 7, 퐶2 퐷(1−퐷) (15b)

푉 푉 = 푖푛 From equation 8, 퐶표 퐷(1−퐷)2 (15c)

퐼푑푒푎푙푙푦, 푃𝑖푛 = 푃표푢푡

2 푉푖푛 푉2 [ 2] 푉 퐼 = 표 ⇒ 푉 퐼 = 퐷(1−퐷) 𝑖푛 퐿1 푅 𝑖푛 퐿1 푅

푉 퐼 = 푖푛 퐿1 푅퐷2(1−퐷)4 (15d)

From figure 13 (a),

푉 퐼 (1 − 퐷) = 퐼 ⇒ 퐼 = 푖푛 . (1 − 퐷) 퐿1 퐿2 퐿2 푅퐷2(1−퐷)4

푉 퐼 = 푖푛 퐿2 푅퐷2(1−퐷)3 (15e)

From figure 13 (a), 퐼퐿3 = −퐼퐿2

−푉 퐼 = 푖푛 퐿3 푅퐷2(1−퐷)3 (15f)

The similar methodology used by the authors in [70]–[72] for linearizing the chopper circuit is used in this model. First, the perturbations are added, thus breaking down the duty ratio and input voltage, respectively, as

푈(푡) = 푈 + 푢̃(푡) (16a)

푉𝑖푛(푡) = 푉𝑖푛 + 푣̃𝑖푛(푡) (16b)

where the nominal operation points are represented by uppercase characters and the perturbations are represented by ~. When (15a)–(15f) and (16a)–(16b) are substituted into expression (10), and assuming the perturbations are sufficiently small such that non-linear terms

31 can be neglected, a linear model in (17) is obtained. The derived linear model can be used for analysis and controller design under different control strategies.

−(1−푈) 푉 1 0 0 0 0 0 푖푛 퐿1 (1−푈)퐿1 퐿1 1 (1−푈) −(1−푈) 푖퐿̇1 푉푖푛 0 0 0 푖퐿1 2 0 푖 ̇ 퐿2 퐿2 퐿2 (1−푈) 퐿2 퐿2 푖퐿 1 푈 2 −푉푖푛 푖 ̇ 0 0 0 0 0 퐿3 퐿 퐿 푖퐿 푈(1−푈)퐿 푢̃(푡) = 3 3 3 + 3 [ ] (17) 푉 ̇ (1−푈) −1 −1 푉 −푉푖푛 ( ) 퐶1 0 0 0 퐶1 0 푣̃𝑖푛 푡 2( )4 ̇ 퐶1 퐶1 퐶1 푈 1−푈 푅퐶1 푉퐶 푉퐶2 2 −(1−푈) 푈 2푉푖푛 0 0 0 0 푉 2 3 0 ̇ 퐶 퐶 [ 퐶표] 푈 (1−푈) 푅퐶2 [푉퐶표] 2 2 푉 (1−푈) −1 푖푛 0 0 0 0 0 [푈2(1−푈)3푅퐶 ] [ 퐶표 푅퐶표 ] 0

Without loss of generality, the above expression is generalized as

푥(푡̇ ) = 퐴 푥(푡) + 퐵 푢(푡) where 푒̃(푡) = [푑̃(푡) 푢̃(푡)]푇 ∈ ℝ2 is the input vector, 푨 ∈ ℝ6×6 & 푩 ∈ ℝ6 are constant matrices

̇ ̇ ̇ ̇ ̇ ̇ ̇ 푇 6 푖̃ 푖̃ 푖̃ 푣̃ 푣̃ 푣̃ 푇 6 푥̃(푡) = [푖퐿̃ 1 푖퐿̃ 2 푖̃퐿3 푣̃퐶1 푣̃퐶2 푣̃퐶0] ∈ ℝ , ̃푥(푡) = [ 퐿1 퐿2 퐿3 퐶1 퐶2 퐶0] ∈ ℝ is the state vector.

The error between the reference voltage and output voltage determines the PID controller action. The PWM block then varies the duty cycle in accordance with the PID output voltage signal. The PID controller is an economical and robust controller that is commonly used in industry applications. Since RSC electric vehicle requires an effective and economical control device, the

PID controller is used in this work. Tuning of PID controller involves designing the controller constants 퐾푝, 퐾𝑖, 푎푛푑 퐾푑 per performance requirements. Several methods are available in the literature to design these parameters. The ultimate cycling method given by Ziegler-Nichols rules

[73] is used in this work. The output of the PID controller is equal to 푢(푡), which is given by

푑푒(푡) 푢(푡) = 퐾 푒(푡) + 퐾 ∫ 푒(푡)푑푡 + 퐾 (18) 푃 𝑖 푑 푑푡

32 where e(t) is the error between the reference signal and the system output. The generated error signal was fed through the circuit, thus generating the output voltage, which was then fed to the

PWM generator through the saturation block.

Table 2. Controller Parameters for Ziegler-Nichols method

Controller 푲풑 푻풊 푻풅

PID 0.6 푃푢 푃푢/2 푃푢/2

To meet the required performance in terms of steady-state error and settling time, direct adjustment of control parameters was used in this work. To determine the necessary parameters,

PID controller was connected to the base system, and tuned as follows

• The input was increased manually, and it was determined that the resulting steady-state

value of the process output was increasing, which confined the proportional control gain

as positive.

• The PID controller was turned into a proportional (P) controller by setting 푇𝑖 = ∞, 푇푑 =

0. The proportional gain 퐾푝 was increased from zero until sustained periodic oscillation in

the output was observed.

• Once the system started to oscillate, critical values of the period 푃푢 of the sustained

oscillations were noted.

• The controller parameters were calculated using Table 2.

4.5 Pulse Width Modulation Generator with Saturation limiter

The PWM generator was used to fire the forced commutated device used in the proposed circuit. Pulses were generated by comparing a reference modulating signal generated by the PID block explained in section IV-A to a triangular career waveform of switching frequency chosen as

100 KHz.

33 The maximum and minimum values of the duty cycle were enforced to ensure that switching operations are within safe limits. To limit the duty cycle, upper and lower bounds for the control signal were applied through a saturation limiter. The output of the PID controller was connected to the PWM controller through a saturation limiter, as shown in Figures 17, 18. The output exactly matched the input within the hard limits; however, if the voltage variation is too high, then the controller will try to operate at the boundary conditions. This is a very important safety measure in practical applications.

4.6 Single loop DC–DC boost converter with change in reference voltage

The DC–DC boost converter with the single loop controller is shown in Figure 18. The charge controller regulates the reference voltage depending on the load. The error between the output and reference voltages is used to generate the PWM signal. The generated PWM signal is used to control the switches 푆1, 푆2. The charge controller acts as the smart system that regulates the reference voltage for the DC–DC boost converter depending on the load. The load status is taken as one input and energy generated by the solar cells is taken as other input.

Figure 18. Schematic of the closed loop converter with inbuilt charge controller

34 The proposed single loop DC–DC boost converter with inbuilt controller is shown in

Figure 19. The energy generated from solar photo-voltaic (PV) cells is used to charge the battery.

The generated solar PV voltage needs to step-up in-order to charge the battery and therefore DC–

DC boost converter plays a prominent role in stepping up the generated voltage. The charge controller sets the reference voltage by comparing the voltage between the battery and the generated solar energy. With enough generation from solar PV cells, the voltage is stepped up and used to charge the battery.

Closed Loop DC–DC Roof Top Converter with Solar PV Cells Inbuild Controller

Figure 19. Schematic of the proposed single loop converter with inbuilt controller for roof top solar panel electric vehicle

4.7 Multi-loop controller

The block diagram of the electric vehicle with closed-loop DC–DC boost converter used to control the car cabin temperature is shown in Figure 20. These days, for better utilization of energy, the cabin temperature is controlled by using the thermoelectric systems based individualized heating/cooling car seats. Due to the unique advantage of thermoelectric systems for this application, car seats in the front and rear cabin can be individually heated or cooled based on the occupant’s preference. As the individual controls the temperature selection switch, airflow is directed through a thermoelectric heat pump which adjusts the temperature. The seat application,

35 often considered a green-energy application, has the potential to reduce the total energy consumption by enabling the smaller compressors to be used for the main cabin.

The input voltage and the cabin temperatures are measured and send to the charge controller.

The charge controller does the following:

• Converts the measured cabin temperature 푇푐푎푏𝑖푛 to the voltage signal 푉푇.

• Sets the reference voltage 푉푟푒푓 by comparing the voltages 푉푇 and 푉𝑖푛 as shown in

Table 3.

Table 3. Reference voltage set by charge controller based on 푉푇 and 푉𝑖푛

Thermoelectric Roof Top Solar Input Load 푽풓풆풇 System Panel Output

Thermoelectric 16 V > 푉𝑖푛< 28 V Solar Panels 325 V System ON Thermoelectric 푉𝑖푛< 16 V Battery 325 V System

푉𝑖푛>16 V Solar panels Battery 500 V OFF 푉𝑖푛< 16 V - - -

The output voltage is compared with the reference and the resulting error signal is used to generate the PWM signal required to turn on the switch S. The derived models using averaging techniques describe the behavior of the converter up to half the switching frequency. These models are only valid in CCM. As stated in section II, the CCM assumes the peak inductor current ripple is always smaller than the dc component in the inductor current. This means, when the switch 푆 is

푂퐹퐹, the total inductor current is always positive and hence the diodes are forced to turn on. The

36 derived linear model is used for the controller design under different control tactics. The selection of variables plays a prominent role in the controller’s operation and performance.

In this DC–DC boost converter the inductor currents 푖̃퐿1, 푖퐿̃ 2, 푖퐿̃ 3 and capacitor voltages

푣̃퐶1, 푣̃퐶2, 푣̃퐶0 corresponds to natural state variables and switch currents 푖푠̃ is the derived state

variable. This current corresponds to 푖푠̃ = 푖퐿̃ 1 + 푖퐿̃ 2 + 푖퐿̃ 3, when the switch 푆 is 푂푁 and 푖̃푠 = 0 when switch 푆 is 푂퐹퐹. The output voltage constitutes to the first loop and the switch current creates the second loop as shown in Figure 20. The use of switch current is a common practice in current feedback control [74], [75]. In this converter, the use of inductor current is considered for this control. It is valid under the following assumptions (푖) magnitude of the inductor ripple is small

(푖푖) artificial ramp waveform is small.

Figure 20. Schematic of the closed loop converter with inbuilt charge controller

37 The reason for choosing the inductor currents for the feedback control is as follows. Like

푖̃ (푠) 푖̃ (푠) 푣̃ (푠) 푣̃ (푠) 푣̃ (푠) 퐿2 , 퐿3 , 퐶1 , 퐶2 , 퐶0 traditional boost converter, all the transfer functions 푑̃(푠) 푑̃(푠) 푑̃(푠) 푑̃(푠) 푑̃(푠) except

푖̃ (푠) 퐿1 푅푒(푠) > 0 푑̃(푠) are stable and in non-minimum phase, that is, the zeros with . The transfer

푖̃퐿1(푠) 푖̃푠(푠) function 푑̃(푠) is stable and is in minimum phase. For typical values, the transfer function 푑̃(푠) is also stable and is in minimum phase. Hence, use of this as feedback is advantageous.

The switch current along with gain 푁 constitutes to the current loop and output voltage along with gain 푁 constitutes to the voltage loop. The current loop is used as inner loop, because the variations are comparatively small to the outer voltage loop. In [76], the output voltage-to-duty ratio is second order, with the addition of second loop the dynamic behavior is changed to dominant first order. This has drastically simplified the output voltage loop design. In the voltage loop the output voltage is amplified with a gain 푁 and then compared with the reference voltage 푉푟푒푓. The resultant error signal is fed to the modulator block. Similarly, the measured current signal is fed to the modulator block after amplifying with a gain 푁. The gains 푁 adds the damping to the resonant peaks, which results in single dominant pole transfer function. The

푖̃ (푠) 푣̃ (푠) 푠 퐶2 frequency response of 푑̃(푠) and 푑̃(푠) for different values of gains are shown in Figure 21 (a), (b) respectively. The gains 푁 are selected such that the resonant peak of the high frequency response is below 0 푑푏. From the Figure 21 the value of 푁 = 9.

Once the voltage and current loops are realized the conventional controller is designed in the modulator. The PI controller is an economical and robust controller that is commonly used in industry applications. Since RSC electric vehicle requires an effective and economical control device, the PI controller is used in this work. Tuning of PI controller involves designing the controller constants 퐾푝, 푎푛푑 퐾𝑖 as per performance requirements. Several methods are available

38 in the literature to design these parameters. The ultimate cycling method given by Ziegler-Nichols rules is used in this work. The output of the PI controller is equal to u(t), which is given by

푢(푡) = 퐾푃푒(푡) + 퐾𝑖 ∫ 푒(푡)푑푡 (19)

Where 푒(푡), is the error between the signals fed into the modulator. The generated error signal was fed through the circuit, thus generating the output voltage, which was then fed to the

PWM generator through the saturation block.

To meet the required performance in terms of steady-state error and settling time, direct adjustment of control parameters was used in this work. To determine the necessary parameters,

PI controller was connected to the base system, and tuned as follows

• The input was increased manually, and it was determined that the resulting steady-state

value of the process output was increasing, which confined the proportional control gain

as positive.

• The PI controller was turned into a proportional (P) controller by setting 푇𝑖 = ∞, 푇푑 = 0.

The proportional gain 퐾푝 was increased from zero until sustained periodic oscillation in

the output was observed.

• Once the system started to oscillate, critical values of the period 푃푢 of the sustained

oscillations was noted.

• The controller parameters are selected as 퐾푝 푖푠 10 푎푛푑 퐾𝑖 푖푠 1.

̃ Figure 21. Frequency response of (a) 푖̃푠(푠)/푑(푠) for different values of gain 푁 ̃ (b) 푉̃표(푠)/푑(푠) for different values of gain 푁

4.8 Full bridge DC-AC Converter

The ac output is synthesized from a dc input by using a sinusoidal pulse width modulation

(SPWM) driven full bridge voltage source inverter (VSI) proposed by Maddukuri et. al [77].

SPWM signal is generated by PIC18F1320 microcontroller and the VSI topology is formed with four IRF740 MOSFET switches. The four MOSFET’s are labeled as 푄1+, 푄1−, 푄2+, and 푄2− as shown in Figure 22. Switching states of the inverter are shown in the Table 4. To generate the states, a carrier-based bipolar PWM technique [78] is used. The ac output voltage waveform in a

SPWM driven full-bridge VSI is basically a fluctuated sine waveform. It is filtered with RLC filter circuit. The maximum amplitude of the fundamental phase voltage in the linear region (푚푎 ≤ 1) is 푣𝑖 /2, the maximum amplitude of the fundamental ac output line voltage is

푣 푣̂ = 푚 √3 푖푛−푑푐 , 0 ≤ 푚 ≤ 1 0−푎푐 푎 2 푎 (20) where, 푣𝑖푛−푑푐 is the output from the boost converter and 푚푎 is modulation index

푄1+ 푄2+

푉𝑖푛−푑푐 + - 푉표−푎푐 (Output of DC– 푄1− 푄2− DC Boost Converter)

PIC18f1320 Microcontroller

Figure 22. Schematic of the SPWM driven dc-ac converter

41 Table 4. Switching States of the Full Bridge VSI

State Number State 푽풐−풂풄 Components Conducting

푄1+, 푄2− are ON 1 +푉𝑖푛−푑푐 푄1+, 푄2− If 푖0 > 0 푄1−, 푄2+ are OFF

푄1−, 푄2+ are ON 2 −푉𝑖푛−푑푐 푄1−, 푄2+ If 푖0 < 0 푄1+, 푄2− are OFF

42 CHAPTER V

RESULTS

This section includes the component selection and simulation validation of the proposed

converter.

5.1 Component Selection

5.1.1 Inductor Selection

To validate the preceding analysis, the converter needs to operate under a steady-state,

continuous conduction mode. The minimum value of inductors to generate the continuous current

is computed as follows:

For 퐿1:

2 푉표 푃 = 푃 ⟹ 푉 퐼 = 𝑖푛 표푢푡 𝑖푛 퐿1 푅

푉𝑖푛 △ 푖퐿1 푉𝑖푛퐷푇 퐼퐿1 = 2 4 & = 푅퐷 (1 − 퐷) 2 2퐿1

△𝑖 퐷3(1−퐷)4푅 퐼 = 퐼 − 퐿1 ≥ 0 ⟹ 퐿 ≥ 퐿1(min) 퐿1 2 1(min) 2푓 (19)

Similarly,

푉𝑖푛 △ 푖퐿2 푉𝑖푛퐷푇 퐼퐿2 = 2 3 & = 푅퐷 (1 − 퐷) 2 2퐿2

△𝑖 퐷3(1−퐷)2푅 퐼 = 퐼 − 퐿2 ≥ 0 ⟹ 퐿 ≥ 퐿2(min) 퐿2 2 2(min) 2푓 (20)

−푉𝑖푛 △ 푖퐿3 −푉𝑖푛퐷푇 퐼퐿3 = 2 3 & = 푅퐷 (1 − 퐷) 2 2퐿3(1 − 퐷)

퐷3(1−퐷)2푅 퐿 ≥ 3(min) 2푓 (21)

43 The peak value of inductor currents is given by solving (4a) ─ (4f)

For 퐿3: Solving (4e) and (4f)

−푉푖푛 1−퐷 −푉푖푛 퐼 = × ⟹ 퐼 = 퐿3, 푝푘 푅퐷2(1−퐷)3 퐷 퐿3 퐷3(1−퐷)2푅 (22)

For 퐿2: Solving (4b), (4e) and (4f)

푉푖푛 퐼 = 퐿2, 푝푘 퐷3(1−퐷)2푅 (23)

For 퐿1: Solving (4b), (4d), (4e) and (4f)

퐼퐿2, 푝푘 푉𝑖푛 −푉𝑖푛 퐼 = + 퐼 ⇒ 퐼 = + 퐿1, 푝푘 (1 − 퐷) 퐿3, 푝푘 퐿1, 푝푘 푅퐷3(1 − 퐷)3 푅퐷3(1 − 퐷)2

푉푖푛 ⟹ 퐼 = 퐿1, 푝푘 퐷2(1−퐷)3푅 (24)

5.1.2 Capacitor Selection

The minimum value of output capacitor to maintain the continuous output voltage is as

follows:

푉 푉 퐶 |∆푄| = 표 퐷푇 ⟹ |퐶 ∆푉 | = 표 퐷푇 For output capacitor 푂: 푅 표 표 푅

푉 퐶 ∆푉 ≥ 표 퐷푇 표 (min) 표 푅

퐷 퐶표 (min) ≥ ∆푉 (25) 푅 ( 표)푓 푉표

The peak value of capacitor voltage is given by solving (4a) ─ (4c)

푉 퐶 : 푉 = 푖푛 (26) For 1 퐶1 1−퐷

푉 푉 푉 .(1+퐷) 퐶 : 푖푛 + 푖푛 = 푉 (1 − 퐷) ⟹ 푉 = 푖푛 (27) For 2 1−퐷 퐷(1−퐷) 퐶2 퐶2 퐷(1−퐷)2

푉퐶 푉 퐶 : 푉 = 1 ⟹ 푉 = 푖푛 (28) For 0 퐶0 퐷 (1−퐷) 퐶0 퐷(1−퐷)2

44 5.1.3 MOSFET Selection

Metal-oxide semiconductor field-effect transistors are heavily used in a most of the

electronics we use every day. When looking at it from a sheer numbers’ perspective, the clear

majority are contained within what is known as an integrated circuit. These parts can contain

anywhere from hundreds to billions of the devices on a single chip and perform a myriad of

different functions.

The basic function of a MOSFET is to act like a switch, making or breaking a connection

with an electronic circuit. MOSFET’s are analogous to a switch on a wall, but instead of using a

mechanical means to turn it on, MOSFETs are turned on with an electrical signal. Their

applications range from controlling small lights and LED’s all the way up to large industrial

motors.

Selecting the right MOSFET for a design can be a daunting task, as there are several

parameters which manufacturers publish that are inherent to the parts design and construction.

Below is a list of the key parameters to keep in mind when choosing a part:

▪ Channel Type (N channel or P Channel)

▪ Max Drain to Source Voltage (푉푑푠푠)

▪ Drain to Source Resistance (푅푑푠표푛)

▪ Maximum DC Drain Current

▪ Gate Threshold Voltage (푉푡ℎ)

• Gate Charge (푄푔)

• Package/Case

45 5.1.3.1. Channel Type

It refers to the construction of the silicon inside the device. N channel MOSFETs will turn on with a positive voltage on the gate relative to the source where P-channel MOSFETs will turn on with a negative voltage on the gate relative to the source. Depending on where the device is used in the circuit and what voltage will be applied to the gate can help decide which part to be used. Here the Arduino micro controller, whose PWM signal has a positive magnitude voltage is used to turn on the MOSFET. Hence, N-channel MOSFET was chosen.

5.1.3.2. Max Drain to Source Voltage (푽풅풔풔)

It is the rating given to the parts ability to block voltage applied to it when it is off. A good rule of thumb is to choose a part whose voltage rating is twice that of the expected voltage applied to the drain. Reasoning behind this is that short voltage spikes well above the input voltage are common in electrical systems where switching MOSFETs are present. The expected output voltage for the prototype is 450V, hence twice the expected voltage, i.e. 푉푑푠푠 = 900푉 rated MOSFET is required.

5.1.3.3. Drain to Source Resistance (푹풅풔풐풏)

It is an important parameter as it will dictate how much heat is being generated by the device while it is conducting. One critical thing to keep in mind is that the 푅푑푠표푛 in the datasheet is specified at a certain gate to source voltage and temperature, so differences in either of these will result in different 푅푑푠표푛 values. To dissipate less heat and reduce the power drop it is preferred to use a MOSFET with low 푅푑푠표푛.

5.1.3.4. Gate Threshold Voltage (푽풕풉)

It is the voltage at which the device will begin to conduct. This parameter is important depending on what voltage is available from the MCU or gate driver. In the prototype the Arduino

46 microcontroller is used. The PWM voltage magnitude from the microcontroller is 5V and hence the MOSFET with 푉푡ℎ < 5푉 is preferred.

5.1.3.5. Maximum DC Drain Current

This quantifies the maximum current a device can withstand indefinitely given adequate cooling. This rating can be a bit deceiving as it isn't always a guarantee of device reliability.

Depending on the 푉푑푠, the device may only be able to conduct a small fraction of this current before failure. The only way to be sure the device can withstand the desired current is to refer to the safe operating area curve in the device’s datasheet. From the above discussion the STP5NK100Z,

푉푑푠 = 1000 푉, 푅푑푠표푛 = 3Ω. From Figure 23 it can be interpreted that, for 450 V and DC drain current of 0.25A, this MOSFET can bare the drain current up to 10msec without damage.

Figure 23. Safe operating area for STP5NK100Z N- Channel MOSFET

47 5.2 Simulation Validation

Circuit simulations were performed for the proposed converter using the MATLAB and

PSpice software to validate the theoretical results from section III. Based on the (19) ─ (26), the

values of inductors and capacitors is chosen and listed in Table 5.

Table 5. Key Circuit Parameters for Proposed Converter

Component Rating

Capacitor C1 100 휇퐹

Capacitor C2 100 휇퐹

Capacitor C0 100 휇퐹

Inductor L1 180 휇퐻

Inductor L2 900 휇퐻

Inductor L3 100 휇퐻

5.2.1 Open-loop Simulation Results

The simulated output voltage and current waveforms for the proposed converter with

resistive load are shown in Figs. 23(a), (b), respectively. It is clear from Figure 24 that the output

voltage acquired from the simulation results for an input voltage of 15V and duty-cycle 0.8 is

430 V, which is 93% of the theoretical output voltage given in (29).

푉표 1 1 = 2 = 2 = 31 푉𝑖푛 퐷(1 − 퐷) 0.8(1 − 0.8)

⟹ 푉표 = 31 ∗ 15 = 465 푉 (29)

This proves that the proposed converter can achieve the high step-up voltages within the

safe duty cycles.

Figure 24. Open-loop output waveforms: (a) output voltage, and (b) output current.

Figure 25. Simulation waveforms of output voltage for DC–DC proposed boost converter (PBC), conventional quadratic boost converter (QBC), and traditional boost converter (BC) with duty cycle D = 0.8 and input voltage Vin = 10 V.

In Figure 25, with input voltage of 10 V and duty cycle of 0.8., the simulation output

voltage of the proposed converter is compared with the other boost converter counterparts. From

the figure, it can be interpreted that the proposed converter has clearly provided a higher output,

which is a beneficial support for applications that need high step-up voltage.

5.2.2 Single-loop Simulation Results

The ability of the proposed controller to minimize changes in the input voltage is evaluated

using the circuit shown in Figure 26. The input voltage was recorded on a typical sunny day on

March 17, 2016, using solar panels mounted in the campus. The parameters used in the closed-loop

analysis are shown in Table 6. The output voltage across the resistive load for the proposed

converter with input voltage of 24V and reference voltage of 480 V are shown in Figure 26. The

50 waveform of the constant output voltage 푉표 is shown in Figure 26 (a). It was observed that the settling time was about three seconds; the settled output voltage is shown in Figure 26 (b).

Overshoot was observed due to disturbances in the designed controller, and once the output achieved the settled constant voltage, the input disturbances were able to be mitigated when the input was within the range of ±2%. A zoomed view of the output voltage waveform of the proposed

DC–DC boost converter is shown in Figure 26 (c) to indicate the harmonic distortion in the output

DC voltage, which was found to be ± 0.8%, within the standard limits [79].

Table 6. Parameters for Closed-Loop Controller

Rated Input of Solar Panel 24 V DC Voltage

Range of Input Voltage 16–28 V DC due to Intermittency

0.2–0.8, controlled by PI-based PWM Varying Duty Cycle controller

325 V with Thermoelectric control systems ON Constant Output 500 V with Thermoelectric control systems Reference Voltage OFF (battery charging mode)

Figure 26. Output waveforms of proposed converter under closed-loop operation: (a) voltage, (b) settled output voltage, and (c) zoom of voltage

Figure 26. (continued)

Efficiency of the proposed converter

푃표푢푡 휂 = 푃𝑖푛

푃표푢푡 = 푃𝑖푛 − 푃푙표푠푠

푃푙표푠푠 = 푃푠푤𝑖푡푐ℎ + 푃𝑖푛푑푢푐푡표푟푠 + 푃푐푎푝푎푐𝑖푡표푟푠

⇒ 푃푙표푠푠 = 푃푠푤𝑖푡푐ℎ + 푃퐿1 + 푃퐿2 + 푃퐿3 + 푃퐶1 + 푃퐶2 + 푃퐶3

2 2 2 2 2 2 ⇒ 푃푙표푠푠 = 푖푠푤𝑖푡푐ℎ푅푂푁 + 푖퐿1푟퐿1−푒푠푟 + 푖퐿2푟퐿2−푒푠푟 + 푖퐿3푟퐿3−푒푠푟 + 푖퐶1푟퐶1−푒푠푟 + 푖퐶2푟퐶2−푒푠푟 2 + 푖퐶3푟퐶3−푒푠푟

퐹표푟 퐷 = 0.8, 푓 = 100푘퐻푧, 푅 = 3.2푘Ω

푉𝑖푛 15 퐼 = = = 0.916 퐴 퐿1, 푝푘 퐷2(1 − 퐷)3푅 0.82 ∗ 0.23 ∗ 3.2푘

푉𝑖푛 15 퐼 = = = 0.239 퐴 퐿2, 푝푘 퐷3(1 − 퐷)2푅 0.83 ∗ 0.22 ∗ 3.2푘

푉𝑖푛 15 퐼 = = = 0.239 퐴 퐿3, 푝푘 퐷3(1 − 퐷)2푅 0.83 ∗ 0.22 ∗ 3.2푘

2 2 2 2 2 2 ⇒ 푃푙표푠푠 = 0.45 ∗ 3 + 0.0005 ∗ 3 + 0.91 ∗ 48푚 + 0.24 ∗ 175푚 + 0.24 ∗ 9푚 + (2.7 + 0.32 + 0.452) ∗ 20푚 = 0.809 푊 푃𝑖푛 = 푃표푢푡 + 푃푙표푠푠 푃표푢푡 50 %휂 = ∗ 100 = ∗ 100 = 98.4 % 푃표푢푡 + 푃푙표푠푠 50 + 0.809

53 5.2.3 Single-Loop with Charge Controller Simulation Results

The ability of the proposed converter to produce the required output was tested using the

simulations. The waveform of the constant output voltage V0 with reference voltage as 325 V and

500 V respectively for the proposed DC–DC converter with input voltage of 24 V is shown in

Figure 27. The harmonic distortion in the output DC voltage, which was found to be ± 0.4%, within

the standard limits [79]. It is observed that the settling time is about 0.1 seconds, which proves that

the PID gain is adjusted properly and once output achieved the settled constant voltage, input

disturbances could be mitigated.

The output DC voltage from the proposed converter when there is enough and without

enough generated electric energy is showing Figure 27 (a), (b) respectively. As explained in

section 4, the charge controller plays a prominent role in regulating the output voltage from the

DC–DC boost converter. As stated in the introduction, the proposed converter is capable to give the

constant output dc voltage when the input is varying within the specified limits of ±2%, which helps

to improve the battery life by reducing the charging discharging cycles.

Figure 27. Output DC waveform from the proposed converter with change in load: (a) with enough generation, and (b) with no-enough generation

Figure 27. (continued)

5.2.4 Multi-loop Controller Simulation Results

The waveform of the constant output voltage 푉표 with reference voltage of 325 V and 500 V

respectively for the controlled DC–DC boost converter with varying input voltage is shown in

Figure 28. The output ac voltage with varying input voltage is shown in Figure 29. The harmonic

distortion in the output DC voltage, which was found to be ±0.4%, within the standard limits. It is

observed that the settling time is about 0.1 seconds, which proves that the PI gain is adjusted

properly and once output achieved the settled constant voltage, input disturbances could be

mitigated.

As explained in section III, the charge controller plays a prominent role in regulating the

output voltage from the DC–DC boost converter. As stated in the introduction, the proposed

converter is capable to minimize the varying input voltage when is within the specified limits, which

helps to improve the battery life by reducing the charging discharging cycles.

Figure 28. Output DC waveform from the proposed converter with change in load: (a) with enough generation (b) with no-enough generation

56 5.2.5 Multiloop Controlled DC-DC Converter Response with Respect to Change in Input

As stated in the introduction, the proposed converter can minimize the varying input voltage

when it is within the specified limits (rated voltage ± 10% V), which in-turn gives a constant input

voltage for the load and batteries. Thereby improves the battery life by reducing the charging-

discharging cycles. The simulated response of the dc-dc converter with respect to changes in input

voltage is shown in Figure 29. When the input voltage is within the specified limits, for instance

here a 24V rated solar array is used hence the accepted input range is between 16-28V. When the

voltage is changing between this ranges, the controller took 1.3 seconds to mitigate the changes in

the input voltage. This is within the range of 2 seconds as per IEEE 1453-2004 standard and can be

considered as constant output voltage.

a b

c d

Figure 29. Response of the proposed dc-dc converter with respect to changes (a) in input at time period of 1.3 seconds (b) in input at time period of 1.4 seconds (c) in input at time period of 1.2 seconds (d) in input at time period of 1.1 seconds

5.2.6 Output Voltage from the DC-AC Converter

The constant dc voltage of 325V is shown in Figure 28 is given as an input to the inverter

circuit shown in Figure 22. The inverter circuit produces the alternating voltage of 230V (RMS)

with 50 Hz frequency, as shown in Figure 30. This energy is used to drive the thermoelectric

systems and the compressors.

Figure 30. Output RMS-AC waveform from the DC-AC converter with change in load (a) AC waveform for the whole operation of load (b) Zoomed output voltage for one millisecond showing the 50 HZ frequency

58 From Figures 28 and 29, the following were observed:

• When thermoelectric system is ON

o With enough generation from solar cells, the intelligent DC–DC boost converter

could produce a high step-up dc voltage of 325V from a low input voltage with a

quick settling time, which is converted to ac by inverter and fed to the

thermoelectric system.

o When the generation is less than the limit the charge, controller supplies the energy

to the load from the battery.

• When thermoelectric system is OFF

o With enough generation from solar cells, the intelligent DC–DC boost converter

produces a high step-up dc voltage of 500V and charge the battery.

• The use of a complimentary controlled switches has made the controller easy to design and

operate.

The huge fluctuating nature in input voltage was handled with the intelligent DC–DC boost converter, which provided a constant output voltage and advantageous in RSC–EV.

5.3 Experimental Validation

A 45-W high-voltage converter was constructed and tested to demonstrate its feasibility.

First the circuit was designed and tested in PSpice software, upon the successful simulation, printed circuit board (PCB) was developed and printed in the lab. The experimental setup is shown in Figure 31. This section explains the process in detailed.

59 5.3.1 PCB Design

5.3.1.1 Schematic Design

The schematic of the proposed DC–DC boost converter with Arduino Uno microcontroller

was designed in Proteus software as shown in Figure 31. DC–DC boost converters with faster

switching frequencies are becoming popular due to their ability to decrease the size of the output

capacitor and inductor to save board space. A DC–DC boost converter switching at 1 or 2 MHz

sounds like a great idea, but there is more to understand about the impact to the power supply

system than size and efficiency. Several design examples will be shown in the literature [80]

revealing the benefits and obstacles when switching at faster frequencies. Here the pulse width

modulation (PWM) signal was generated using the microcontroller operating at a switching

frequency of 100 푘퐻푧. After successful simulation, the PCB was developed as shown in Figure

32 in Proteus ARES software. In this converter only through hole components were chosen, so

single-sided PCB was a cheaper option. In addition, it also helps in keeping the noise level low.

The 3-dimentional image of the PCB was shown in Figure 33. This helps in fixing the mistakes

during prototyping than at design level.

Figure 31. Schematic of the proposed open-loop converter developed in Proteus software

Figure 32. PCB of the proposed open-loop converter developed in Proteus software

Figure 33. 3-dmentional image of the PCB

5.3.1.2 PWM Signal Generation

PWM, is a technique for getting analog results with digital means. A digital signal switched

between on and off to create a square wave. This ON-OFF pattern can simulate voltages in between

full on (5 Volts) and off (0 Volts) by changing the portion of the time the signal spends on versus

the time that the signal spends off. The duration of "on time" is called the pulse width.

In Figure 34, the green lines represent a regular time-period. This period is the inverse of

the PWM frequency. In other words, with Arduino's PWM frequency at about 1 MHz, the green

lines would measure 1 microsecond each. A call to analogWrite () is on a scale of 0 - 255, such

that

• analogWrite (0) requests a 0% duty cycle (always off),

• analogWrite (127) is a 50% duty cycle (on half the time), and

• analogWrite (255) is a 100% duty cycle (always on).

Figure 34. Pulse width modulation signal from Arduino microcontroller

5.3.1.3 Continuity Test Results

This test was performed to check if there were any bridge connections in the soldered

components.

Because of this test two errors were identified:

 The first was, in the combined PCB, as the track sizes chosen were T30 and T60, which

was big compared to the size of the PCB, resulted in the introduction of noise into the

system. To eliminate the noise, few connections were removed and reconnected using the

extra wire.

 The second was the negative terminals of the bridge rectifier IC and the output from the

RC filter were connected to a common pin.

 The switch S2 was not connected

63 The above three errors were eliminated by making the following changes in the PCB:

✓ The ground pin of the Arduino was not properly grounded due to the presence of noise in

those tracks. Hence, with the help of external wires those connections were formed.

✓ The second error was eliminated by introducing two separate vero-pins. The vero- pins

were connected using the wire.

✓ The third error was eliminated by manually connecting the MOSFET with wires.

5.3.2 System Test Results

A prototype circuit of the proposed DC–DC boost converter is shown in Figure 35. The

converter is switched at 100 kHz with the circuit parameters as shown in Table 7. One

STP5NK100Z N-Channel MOSFET and four 1N4007RLG diodes are selected as the switch 푄 and

diodes 퐷1, 퐷2, 퐷3, 퐷4 respectively.

Table 7. Key Circuit Parameters of the Prototype Circuit

Component Identification Component Name Component Value (Manufacture Number) Capacitor 퐶1 150 RMI 100 휇퐹, 퐸푆푅 20 푚Ω

Capacitor 퐶2 R60EW61005000K 100 휇퐹, 퐸푆푅 20 푚Ω

Capacitor 퐶표 R60EW61005000K 100 휇퐹, 퐸푆푅 20 푚Ω

Inductor L1 PCV 2 VT Power Chock 180 휇퐻, 퐸푆푅 48 푚Ω

Inductor L2 1540 M22 900 휇퐻, 퐸푆푅 175 푚Ω

Inductor L3 7447231101 100 휇퐻, 퐸푆푅 9 푚Ω

Arduino Uno Mega ATmega328P 2560

Figure 35. Photograph of the prototype and the measuring setup

An input of 15V DC was supplied to the prototype connected with a 3.2 kΩ resistor.

Initially the duty cycle was chosen as 0.2 and increased to 0.8 in steps of 0.1. The graphs shown in Figure 36, illustrates the outputs from the proposed converter setup.

Figure 36. Change in output with respect to change in duty cycle from experimental setup.

65 Referring to Figure 36, the measured DC output voltage from the experimental setup is

418 V. This is 90% of theoretically measured value, thus the voltage gains in (6) is fulfilled.

Voltage across the uncontrolled switches for the proposed DC–DC boost converters for the typical values of input of 15 V and output of 50 V are shown in Figure 37. The values are in close approximation to (12) – (15). The measured full-load efficiency of this converter is about 92.8%.

The converter efficiency can be further improved by using a MOSFET of 푅퐷푆−푂푁 and capacitors of lower equivalent series resistance. However, the experimental results are in good agreement with the theoretical analysis.

Simulation Experimental Simulation Experiment 20 30 15 20 10 10 5 Voltage (V) Voltage Voltage (V) Voltage 0 0 0 1 Time (S) 2 3 0 1 Time (S) 2 3

a b

30 Simulation Experiment 40 Simulation Experiment

20 30 20 10

Voltage (V) Voltage 10 Voltage (V) Voltage 0 0 0 1 Time (S) 2 3 0 1 Time (S) 2 3

c d

Figure 37. Simulation and experimental waveforms of voltage stress on uncontrolled switches: (a) across diode D1, (b) across diode D2, (c) across diode D3, and (d) across diode D4.

66 CHAPTER VI

CONCLUSION

A new DC–DC boost converter with a high voltage step-up ratio is presented in this paper, which consists of two active switches, four passive switches and three LC filters. By increasing the passive inductor-capacitor cells, the voltage gain of the system is improved. The operation and voltage transfer function of the proposed converter is derived under continuous conduction mode.

In comparison with other dc-dc boost converter counterparts, the proposed converter has improved characteristics in terms of high voltage step-up ratio and reduced voltage stress on the active and passive switches. The high voltage gain at low duty cycles results in the reduction of conduction losses. Use of a complimentary controlled active switch resulted in stress-free control system. The analysis and performance have been fully validated experimentally on a 15V input, 418V output hardware prototype. Experimental results demonstrate that the proposed converter is an excellent candidate for high step-up voltage gain applications

A simple yet robust closed-loop-controlled DC–DC converter with built-in charge controller for the RSA-EV is later proposed and analyzed. The charge controller played a prominent role in controlling the output voltage from the proposed converter according to changes in load and energy from the solar array. The charge controller could switch between the battery and the RSA, depending on the energy requirements. Initially single-loop PID converter is designed and analyzed. Use of the PID-based PWM control has the added advantage of easy programming and robustness. The simulation results presented clearly demonstrate validity of the theoretical analysis. But the right half plane zeros for the DC–DC converters in CCM severely restricted the crossover frequency of the open-loop gain, which resulted in poor dynamic performance if single-loop feedback control is adopted. Later a multi-loop control is proposed.

67 This has resulted in changing the output voltage-to-duty ratio to dominant first order thereby drastically simplified the output voltage loop design. The proposed controller gave a constant output voltage from a variable input (rated ± 10%). This helps in operating the thermostat systems more effectively and increases the life of the battery, because the charging-discharging cycles are reduced, due to the use of energy from the RSA. Use of the PI-based PWM control has the added advantage of easy programming and robustness. The simulation results presented here clearly demonstrate the fundamentals of the proposed multi-loop-controlled DC–DC converter.

REFERENCES

69 REFERENCES

[1] Li W., and He X., Review of nonisolated high-step-up DC/DC converters in photovoltaic grid-connected applications, IEEE Transactions on Industrial Electronics, 2011, 58(4), pp. 1239–1250 .

[2] Ismail E.H., Al-Saffar M.A., Sabzali A.J., and Fardoun A.A., A family of single-switch PWM converters with high step-up conversion ratio, IEEE Transactions on Circuits and System I: Regular Papers, 2008, 55(4), pp. 1159–1171.

[3] Chen S.M., Liang T.J., Yang L.S. and Chen J.F., A cascaded high step-up DC–DC converter with single switch for microsource applications, IEEE Transactions on Power Electronics, 2011, 26(4), pp. 1146–1153.

[4] Adam G.P., Gowaid I.A., Finney S.J., Holliday D., and Williams B.W., Review of DC– DC converters for multi-terminal HVdc transmission networks, IET Power Electronics, 2016, 9(2), pp. 281–296.

[5] Coates Leonard, and William Fenemore Ronald, Voltage divider, U.S. Patent 2,784,369, issued March 5, 1957.

[6] Luo Fang Lin, and Hong Ye., Advanced dc/dc converters. CRC Press, 2016.

[7] Slobodan Cuk, R. Middlebrook, A general unified approach to modelling switching DC- to-DC converters in discontinuous conduction mode, IEEE Power Electronics Specialists conference, 1977, pp. 36–57.

[8] Chaplin G. B. B., and A. R. Owens, A transistor high-gain chopper-type dc amplifier," Proceedings of the IEEE-Part B: Radio and Electronic Engineering, 1958, 105 (21), pp. 258–272.

[9] Jang Y., and Jovanovic M.M., Isolated boost converters, IEEE Applied Power Electronics Conference and Exposition, 2006, pp. 7–14.

[10] Mi C., Bai H., Wang C., and Gargies S., Operation, design and control of dual H-bridge- based isolated bidirectional DC–DC converter, IET Power Electronics, 2008, 1(4), pp. 507–517.

[11] Nymand M., and Andersen M.A., High-efficiency isolated boost DC–DC converter for high-power low-voltage fuel-cell applications, IEEE Transactions on Industrial Electronics, 2010, 57(2), pp. 505–514.

[12] Tofoli F.L., de Castro Pereira D., de Paula W.J., and Júnior D.D.S.O., Survey on non- isolated high-voltage step-up DC–DC topologies based on the boost converter, IET power Electronics, 2015, 8(10), pp. 2044–2057.

70 [13] Luo F. L., and Ye H., Positive output cascade boost converters, IEE Proceedings—Electric Power Applications, 2004, 151(5), pp. 590–606.

[14] Feng X., Liu J., and Lee F. C., Impedance specifications for stable DC distributed power systems, IEEE Transactions on Power Electronics, 2002, 17(2), pp. 157–162.

[15] Wu T. F., Lai Y. S., Hung J. C., and Chen Y. M., Boost converter with coupled inductors and buck–boost type of active clamp, IEEE Transactions on Industrial Electronics, 2008, 55(1), pp. 154–162.

[16] Changchien S. K., Liang T. J., Chen J. F., and Yang L. S., Step-up Dc-dc boost converter by coupled inductor and voltage-lift technique, IET power electronics, 2010, 3(3), pp. 369–378.

[17] Cheng H., Smedley K. M., and Abramovitz A., A wide-input–wide-output (WIWO) Dc- dc boost converter, IEEE Transactions on Power Electronics, 2010, 25(2), pp. 280–289.

[18] Li W., and He X., A family of isolated interleaved boost and buck converters with winding- cross-coupled inductors, IEEE Transactions on Power Electronics, 2008, 23(6), pp. 3164–3173.

[19] Lin B. R., Chiang H. K., and Cheng C. Y., Analysis and implementation of an interleaved ZVS bi-fly back converter, IET Power Electronics, 2010, 3(2), pp. 259–268.

[20] Lin B. R., and Dong J. Y., Analysis and implementation of an active clamping zero-voltage turn-on/zero-current turn-off switching converter, IET Power Electronics, 2010, 3(3), pp. 429–437.

[21] Jabbari M., and Farzanehfard H., Family of soft-switching resonant Dc-dc boost converters, IET Power Electronics, 2009, 2(2), pp. 113–124.

[22] Li W., and He X., High step-up soft switching interleaved boost converters with cross- winding-coupled inductors and reduced auxiliary switch number, IET Power Electronics, 2009, 2(2), pp. 125–133.

[23] Hiroyuki K., McNeal S., Jordan B., Scofield J., Ray B., and Turgut Z. Coupled inductor characterization for a high-performance interleaved boost converter, IEEE Transactions on Magnetics, 2009, 45(10), pp. 4812–4815.

[24] Axelrod B., Berkovich Y., and Ioinovici A., Switched-capacitor/switched-inductor structures for getting transformer less hybrid DC–DC PWM converters, IEEE Transactions on Circuits and Systems I: Regular Papers, 2008, 55(2), pp. 687–696.

[25] Lee Y. S., and Ko Y. P., Switched-capacitor bi-directional converter performance comparison with and without quasi-resonant zero-current switching, IET Power Electronics, 2010, 3(2), pp. 269–278.

71 [26] Zhao Q., Tao F., and Lee F. C., High-efficiency, high step-up Dc-dc boost converters, IEEE Transactions on Power Electronics, 2003, 18 (1), pp. 65–73.

[27] Yang P., Xu J., Zhou G., and Zhang S., A new quadratic boost converter with high voltage step-up ratio and reduced voltage stress, 7th International Power Electronics and Motion Control Conference, 2012, 2, pp. 1164–1168.

[28] Williams R. K., High-efficiency DC/DC voltage converter including capacitive switching pre-converter and up inductive switching post-regulator, Advanced Analogic Technologies Inc., 2010. U.S. Patent 7,812,579.

[29] Makowski M. S., and Maksimovic D., Performance limits of switched-capacitor Dc-dc boost converters, IEEE Power Electronics Specialists Conference, 1995, 2, pp. 1215–1221.

[30] M. H. Taghvaee, M. A. M. Radzi, S. M. Moosavain, H. Hizam, and M. H. Marhaban, “A current and future study on non-isolated Dc-dc boost converters for photovoltaic applications,” Renewable and Sustainable Energy Reviews, 2013, 17, pp. 216–227.

[31] Erickson R. W. and Maksimovic D., Fundamentals of Power Electronics. Boston, USA: Kluwer Academic Publishers, 2004.

[32] Xu D., Zhao C., and Fan H., A PWMplus phase shift control bidirectional DC–DC boost converter, IEEE Trans. Power Electronics, 2004, 19(13), pp. 666–675.

[33] Mitchell D.M., DC–DC Switching Regulator Analysis. NewYork, USA: McGraw-Hill, 1998.

[34] Forsyth A. J. and Mollow S. V, Modeling and control of DC–DC boost converters, Power Eng. Journal, 1998, 12 (5), pp. 229–236.

[35] Sira-Ramirez H. and Silva-Origoza R., Control Design Techniques in Power Electronics Devices, New Mexico City, USA: Springer, 2006.

[36] Chu G., Tse C. K., Wong S. C., and Tan S. X., A unified approach for the derivation of robust control for boost PFC converters, IEEE Trans. Power Electronics, 2009, 24(1), pp. 2531–2544.

[37] Mariethoz S., Almer S., Beja M., Comparison of hybrid control techniques for buck and boost Dc-dc boost converters, IEEE Trans. Control Syst. Technology, 2010, 18 (5), pp. 1126–1145.

[38] Smedley K. M. and Cuk S., One-cycle control of switching converters, IEEE Trans. Power Electronics, 1995, 10(6), pp. 625–633.

[39] Jiang T. Y., and Dougal R., Synergetic control of power converters for pulse current charging of advanced batteries from a fuel cell power source, IEEE Trans. Power Electronics, 2004, 19(4), pp. 1140–1150.

72 [40] Arbetter B. and Maksimovic D., Dc-dc boost converter with fast transient response and high efficiency for low-voltage microprocessor loads, Proc. IEEE Appl. Power Electronics, 1998, 1, pp. 156–162.

[41] Malesani L., Mattavelli P., and Tomasin P., Improved constant-frequency hysteresis current control of VSI inverters with simple feedforward bandwidth prediction, IEEE Trans. Ind. Appl., 1997, 33(5), pp. 1194–1202.

[42] Kimball J. W., Krein P. T., and Chen Y. X., Hysteresis and delta modulation control of converters using sensorless current mode, IEEE Trans. Power Electronics, 2003, 21 (4), pp. 1154–1158.

[43] Song T. T. and Chung H. S., Boundary control of boost converters using state-energy plane, IEEE Trans. Power Electronics, 2008, 23 (2), pp. 551–563.

[44] Utkin V. I., Guldner J., and Shi J. X., Sliding Mode Control in Electromechanical Systems, London, UK: Taylor & Francis, 2008.

[45] Tan S. C., Lai Y. M., and Tse C. K., A unified approach to the design of PWM-based sliding-mode voltage controllers for basic Dc-dc boost converters in continuous conduction mode, IEEE Trans.Circuits Syst., 2006, 53(8), pp. 1816–1827.

[46] Yuri B. S., Zinober A. S. I., and Shkolnikov I. A., Boost and buckboost power converters control via sliding modes using dynamic sliding manifold, Proc. 41st IEEE Conf. Decis. Control, 2002, 3, pp. 2456–2461.

[47] Baev S., and Sheessel Y., Causal output tracking in nonminimum phase boost DC/DC converter using sliding mode techniques, Proc. Amer. Control Conf., 2009, pp. 77–82.

[48] Satya Veera Pavan Kumar M., Yuri B. Stessel, Robust Sliding Mode Control design for a Quadratic Boost Converter, International Journal of Electrical & Electronics Engineering, 2016, 4(5), pp. 386–391.

[49] Visioli A., Practical PID Control. London, UK: Springer, 2006.

[50] Sira-Ramirez H., On the generalized PI sliding mode control of DC–DC power converters: A tutorial, Int. J. Control, 2003, 76(9/10), pp. 1018–1033.

[51] Tan S. C., Lai Y. M., and Tse C. K., Indirect sliding mode control of power converters via double integral sliding surface, IEEE Trans. Power Electronics, 2008, 23(2), pp. 600–611.

[52] Carbajal-Gutie´rrez E.E., and Leyva-Ramos J., Modeling of switch-mode DC–DC cascade converters, IEEE Trans. Aerosp. Electron. Syst., 2002, 38(1), pp. 295–299.

[53] Carbajal-Gutie´rrez E.E., Morales-Saldana J.A., and Leyva-Ramos J, Modeling of a single- switch quadratic buck converter, IEEE Trans. Aerosp. Electron. Syst., 2004, 41(4), pp. 1451–1457.

73 [54] Yan Zhu J., and Lehman B., Control loop design for two-stage Dc-dc boost converters with low voltage/high current output, IEEE Trans. Power Electron., 2005, 20(1), pp. 44–45.

[55] Carbajal-Gutie´rrez E.E., Morales-Saldana J.A., and Leyva-Ramos J., Average current- mode control for a quadratic buck converter, Proc. of IEEE Power Electronics Specialists Conf., 2007, pp. 2652–2657.

[56] Lee F. C., High-frequency quasi-resonant converter technologies, Proc. IEEE, 1988, 76, pp. 377–390.

[57] Baha B., The control of quasi-resonant converters, Proc. Power Electronic Appl. Eur. Conf., 1993, pp. 304–309.

[58] Cervantes Ilse, David García, and Daniel Noriega, Linear multiloop control of quasi- resonant converters, IEEE Transactions on Power Electronics, 2005, 18(5), pp. 1194–1201.

[59] Sun Xiao, Yim-Shu Lee, and Dehong Xu, Modeling, analysis, and implementation of parallel multi-inverter systems with instantaneous average-current-sharing scheme, IEEE Transactions on Power Electronics, 2003, 18(3), pp.844–856.

[60] Morales-Saldana J.A., Galarza-Quirino R., and Leyva-Ramos J., Multiloop controller design for a quadratic boost converter, IET Electric Power Applications, 2007, 1(3), pp.362–367.

[61] Dickson, John F. On-chip high-voltage generation in MNOS integrated circuits using an improved voltage multiplier technique, IEEE Journal of solid-state circuits,1976, 11(3), pp. 374–378.

[62] Satya Veera Pavan Kumar M., Aravinthan V., and Ward T. Jewell., Analysis and Implementation of High Step-Up Non-Isolated DC–DC Boost Converter for Distributed Generation Systems, IET Transactions on Power Electronics, Unpublished manuscript.

[63] Cáceres R. O., and Barbi I., A Boost dc–ac converter: analysis, design and experimentation, IEEE Trans. Power Electronics, 1999, 14 (1), pp.134–141.

[64] Kazimierczuk M. K., Synthesis of phase-modulated dc/ac inverters and dc/dc converters, Proc. Inst. Elect. Eng., 1992, 139, pp. 387–394.

[65] Ehsani M., Gao Y., and Emandi A., Modern Electric Hybrid electric and Fuel Cell Vehicle Fundamentals, 2nd edision, New York, USA, CRC Press, 2010.

[66] Satya Veera Pavan Kumar M., Aravinthan V., Multi Loop Single-Switch High Gain DC/DC Converter for Electric Vehicles, IET Renewable Power Generation, Unpublished manuscript.

74 [67] Satya Veera Pavan Kumar M., Sashivardhan P. Intilligent Inverter Using Aurdino for Solar Power Applications, International Journal of Innovate Research and Development, 2014, 2(8), pp.72–77.

[68] Sizkoohi H. M., Milimonfared J., Taheri M., and Salehi S., High step-up soft-switched dual-boost coupled-inductor-based converter integrating multipurpose coupled inductors with capacitor-diode stages, IET Power Electronics, 2015, 8(9), pp. 1786–1797.

[69] Mummadi V., Design of robust digital PID controller for H-bridge soft-switching boost converter, IEEE Transactions on Industrial Electronics, 2011, 58(7), pp. 2883–2897.

[70] Vlad C., Rodriguez-Ayerbe P., Godoy E., and Lefranc P., Advanced control laws of Dc-dc boost converters based on piecewise affine modelling application to a stepdown converter, IET Power Electronics, 2014, 7(6), pp. 1482–1498.

[71] Boglietti A., Griva G., Pastorelli M., Profumo F., and Adam T., Different PWM modulation techniques indexes performance evaluation, IEEE International Symposium on Industrial Electronics Conference Proceedings, 1993, pp. 193–199.

[72] Lopez-Santos O., Martinez-Salamero L., Garcia G., Valderrama-Blavi H., and Sierra- Polanco T., Robust sliding-mode control design for a voltage regulated quadratic boost converter, IEEE Transactions on Power Electronics, 2015, 30(4), pp. 2313–2327.

[73] Astrom K. J. and Hagglund T., Revisiting the Ziegler-Nichols step response method for PID control, J. Process Control., 2004, 14, pp. 635–650.

[74] Redl R., and Sokal N.O., Current-mode control, five different types, used with the three basic classes of power converters: small-signal ac and large-signal dc characterization, stability requirements, and implementation of practical circuits, IEEE Power Electronics Specialists Conference, 1985, pp. 771–785.

[75] Ridley R.B., Cho B.H., and Lee F.C., Analysis and interpretation of loop gains of multiloop-controlled switching regulators, IEEE Trans. Power Electron., 1988, 3, pp. 489– 498.

[76] Satya Veera Pavan Kumar M., Aravinthan V., and Uday Kishan R., An intelligent closed loop single-switch DC/DC converter with high voltage step-up ratio for roof-mounted solar cells electric vehicle, IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 2016, pp. 1–6.

[77] Satya Veera Pavan Kumar M., Ippili, G. and Reddy, V.L., Supply Voltage Optimisation using power electronic devices and pic microcontroller, International Journal of Innovative Research and Development, 2013, 2(8), pp. 81–89.

[78] Floyd M. D., and Stump J. D., Voltage multiplying and inverting charge pump, U.S. Patent 4,807,104, issued February 21, 1989.

75 [79] Xiong Y., Cheng X.; Shen Z. J.; Mi C.; Wu H.; Garg V. K., Prognostic and warning system for power-electronic modules in electric, hybrid electric, and fuel-cell vehicles, IEEE Trans. Ind. Electron., 2008, 55(6), pp.2268–2276.

[80] Richard N., and King B., Design How-To Choosing the optimum switching frequency of your DC/DC converter, Texas Instruments Inc, 25 10 2006. [Online]. Available: https://www.eetimes.com/document.asp?doc_id=1272335. [Accessed 10 05 2016]