CONVERTER DESIGN for Nuna Maximum Power Point Tracker

Farnaz Nassiri Nia Aarnoud Tjerk Sluimer

TU Delft Faculty of EEMCS July 2, 2012 2 Abstract

he world is rapidly moving towards a greener future, a mainstay of which is solar energy. Hence, maximum power point trackers, or T MPPTs for short, are an indispensable component, since these devices provide one with the capability to fully maximize the achievable power from solar cells in a system. A symbol of the greener world that is evolving around us is the biannual World Solar Challenge, where state-of-the-art solar powered cars race against one another through the deserts of Australia. This thesis forms the link between these two elements: to design an MPPT optimally suited towards the requirements of the Nuna Solar Car. Commercially available MPPTs are not particularly well suited for the specific demands of such a bleeding edge race. They are mostly designed for high power or low voltage systems. The MPPT designed during this thesis is optimized for high efficiency and other requests stated by the Nuon Solar Team members. The design of the MPPT has been split into several parts. This thesis is focused on the converter within the MPPT. It presents the result of research, design exploration, simulation and testing. The results obtained with the prototype that has been built show the designs correctness and conformance to the requirements, with an efficiency of up to 98,5%.

3 4 Preface

s part of the Bachelor program Electrical Engineering at the EEMCS faculty of Delft University of Technology, a research project has been A performed for the course Bachelor Afstudeer Project, or BAP for short. The subject of the thesis report is to design a Maximum Power Point Tracker for the Nuon Solar Team. This report is a summary of the work that has been done. Our dissertation would not have been possible without the guidance and the assistance of several individuals who in diﬀerent ways contributed and put their precious time in the preparation and completion of this study. Special thanks to:

• Jelena Popovic for being our supervisor during the project.

• The Nuon Solar Team for making this project possible

• Willem Zwetsloot and Javier Sint Jago for being our contacts within the Nuon Solar Team.

• Milos Acanski for giving advice during the project.

• Kasper Zwetsloot for helping us with building the prototype

• And last but not least we would like to thank our supportive family for making this all possible, friends for their feedback and anyone who spent time reading this thesis.

Delft, July 2, 2012 Farnaz Nassiri Nia (1544179) Tjerk Aarnoud Sluimer (1518712)

5 6 Contents

Preface 5

List of Figures 10

List of Tables 11

Glossary 13

1 Introduction 15 1.1 Thesis Structure ...... 16

2 Problem Deﬁnition: The Maximum Power Point Tracker 17 2.1 Problem Description ...... 17 2.2 Brief of Requirements ...... 18

3 Literature Study on MPPT Hardware 21 3.1 Introduction to MPPT Hardware ...... 21 3.2 Diﬀerent Converter Topologies ...... 24 3.3 Possible Switching Elements ...... 26 3.4 Possible Rectiﬁer Diodes ...... 27 3.5 Converter Output Capacitor ...... 28 3.6 Converter Inductor ...... 31

4 Converter Design 39 4.1 Topology Decision ...... 39 4.2 Boost Converter Principles ...... 40 4.3 Assembling Converter Inputs ...... 42 4.4 Choosing the Rectiﬁer Diode ...... 48 4.5 Choosing the Capacitor ...... 49 4.6 Inductor Design ...... 49

5 Concept Design of the MPPT 55 5.1 Concept Simulation ...... 55

6 Evaluation of the Prototype 59 6.1 Building Process of the MPPT ...... 59 6.2 Test Setup of the Prototype ...... 61 6.3 Test Results of the Prototype ...... 62 6.4 Proof of Principle ...... 64

7 Conclusion and Recommendations 69

7 Appendix 75 A. Matlab and Simulink Code & Files ...... 75 B. Brief of Requirements ...... 79 C. Measurements on the System ...... 82 D. Inductor Core Dimension and Calculation ...... 88

8 List of Figures

1 I-V and P-V characteristics of solar panels [1] ...... 17 2 Classification of power supply technologies ( [2], pp. 2) . . . . 21 3 PWM regulator topologies ( [2], pp.3) ...... 22 4 Hard switching versus resonant switching ( [3], pp. 2) . . . . . 23 5 A basic schematic of a boost converter ...... 24 6 A basic buck-boost converter schematic ...... 25 7 Circuit of a flyback converter ...... 26 8 Preferred operating regions for MOSFET and IGBT [4] . . . . 27 9 Voltage versus capacitance for different types of dielectrics ( [5], pp.5-2) ...... 30 10 Core loss versus frequency for different types of magnetics ( [5], pp.6-5) ...... 32 11 Saturation flux density versus temperature for different types of magnetics ( [5], pp.6-5) ...... 33 12 B-H characteristic of a transformer core having hysteresis and hence magnetic losses ...... 34 13 Temperature dependence of core loss ( [6], pp.9) ...... 36 14 Magnetization curve of the core ( [6], pp.6) ...... 37 15 Dimensioned diagram of (a) a double-E core (b) bobbin, and (c) assembled core with winding ( [7], pp.750) ...... 37 16 A basic schematic of a boost converter ...... 40 17 Equivalent circuit while the MOSFET is on ...... 41 18 Equivalent circuit while the MOSFET is off ...... 41 19 Waveform of the voltage over and current trough the inductor 42 20 Efficiency of the boost converter according to the switching frequency ...... 45 21 Voltage over the inductor and current through the inductor . . 47 22 Specified power loss as a function of flux density with frequency as a parameter ...... 52 23 Simulink model used for testing the boost converter ...... 57 24 Output voltage steady state of the boost converter ...... 58 25 Output voltage of the boost converter including initialization . 58 26 Total setup of the prototype ...... 60 27 Boost converter of the prototype ...... 61 28 Final setup for testing ...... 62 29 Setup for measuring the efficiency of the converter ...... 63 30 Measured efficiency against input power ...... 64 31 Inductor current ...... 65 32 Output voltage and current of the boost converter ...... 66

9 33 Voltage ripple at 60V input ...... 67 34 Core dimensions 1 ...... 88 35 Core dimensions 2 ...... 89 36 Core dimension calculations ...... 90 37 Ferrite speciﬁcations ...... 91

10 List of Tables

1 Overview of diﬀerent capacitor choices ...... 29 2 Capacitor application measurements ...... 29 3 Converter electrical speciﬁcations ...... 43 4 Database of core characteristics needed for inductor design . . 50

11 12 Glossary

Q Charge [C] DC Direct Current AC Alternating Current I Current [A] V Voltage [V] CCM Continuous Conduction Mode DCM Discontinuous Conduction Mode EMF Electromotive Force EMI Electromagnetic Interference ESR Equivalent Series Resistance [Ω] f Frequency [Hz] Il Inductor Current [A] LC Inductor-Capacitor IGBT Insulated Gate Bipolar Transistor ◦ Tj Junction Temperature [ C] RL Load Resistance [Ω] MPP Maximum Power Point MPPT Maximum Power Point Tracking MOSFET Metal-Oxide-Semiconductor Field-Eﬀect Transistor RDS(on) Mosfet on-state resistance [Ω] Voff Oﬀ-state Voltage [V] CO Output Capacitance [F] Vout Output Voltage [V] Ipeak Peak Current Rating [A] PV Photovoltaic P Power [W] PWM Pulse Width Modulation SiC Silicon Carbide fs Switching Frequency [Hz] SMPS Switch-Mode Power Supply t time [s] ZCS Zero Current Switching ZVS Zero Voltage Switching

13 14 1 Introduction

he World Solar Challenge is a biannual event where solar-powered cars race 3000km straight through the Australian desert. Participating T teams come from all over the world, most of them fielded by university teams or companies. The goal of the race is to be the first one to arrive at the finish line, given only a limited amount of stored energy. The rest of the needed energy has to be obtained from solar power. A high efficiency is therefore key in finishing first. The Nuon solar team (Nuna) is a team, formed by TU Delft students, that participates in this competition. They have an impressive track record of four successive wins, and of achieving second place during the last event. The chase to reclaim the title is on. One of the improvements planned for the next car is to design a custom-made MPPT that is built specifically for this application. Previous Nuna cars utilized commercially available, off-the- shelf, MPPTs. However, using an MPPT that is optimized for the Nuna solar car allows for a faster, lighter, and thus better, car than previous models. Tracking the maximum power point of solar panels can be used to greatly improve their efficiency. This is especially desirable in implementations where maximum efficiency is critical like in the Nuna Solar Car, built by the Nuon Solar Team. This report covers the design of a maximum power point tracker that is specifically designed to suit the needs of the next version of the Nuna. In order to cope with the complexity of the subject, the design of the MPPT is split in several smaller parts. Each of these different parts is described, fleshed out and simulated in a separate thesis. The titles of the three theses are:

• ”Maximum Power Point Tracking: Algorithm & Software Develop- ment”, describing a high speed algorithm that tracks the maximum power point,

• ”Maximum Power Point Tracking Topology, Sensor and Switch De- sign”, an interface between the hardware and software,

• ”Converter Design for Nuna Maximum Power Point Tracker”, a converter to transform the output voltage to the desired level.

This thesis concentrates on the design of the power stage of the MPPT and the design of the converter is explored and simulated. The converter design can be broken down further into choosing a suitable topology, calculating the values for the required components, and designing the customized components. After the design process, simulations have been performed to

15 evaluate the eﬃciency of these parts. Besides the theoretical part, a prototype of the MPPT has been built and tested to verify that the requirements are reached.

1.1 Thesis Structure The functions and requirements for the MMPT are covered in Chapter 2. This is followed by a literature study on Maximum Power Point Trackers in chapter 3. Chapter 4 is dedicated to design procedure of the converter used in the MPPT. Chapter 5 covers the theoretical performance measurements, made by simulations. The construction and testing of the prototype is docu- mented in chapter 6. The ﬁnal chapter is a conclusion on the whole project, governing the test results, the building process and possible improvements.

16 2 Problem Deﬁnition: The Maximum Power Point Tracker

n this chapter, the requirements of the maximum power point tracker for I the Nuna are presented. In 2.1, a description of the assignment is given. In 2.2, the requirements from the Nuna Solar Power Team are broken down in three categories: must-have, wanted and would-be-nice.

2.1 Problem Description Distinct from most other power sources, the maximum power point of a solar generator is time variant. For example, if the irradiation intensity decreases, or the ambient temperature rises, the generated power level drops. The battery level or even motor voltage level also changes depending on its charge state. An MPPT continuously observes the voltage transmission factor of the input power and multiple other points on the power curve. At some point, the voltage transmission factor changes, corresponding to an eventual new global maximum power point at one of these neighboring points. These points are shown in Figure 1.

Figure 1: I-V and P-V characteristics of solar panels [1]

A high conversion eﬃciency is crucial for Nuna, since all energy available will be needed to be victorious during the World Solar Challenge. The MPPT that is currently used in Nuna is built for multiple solar arrays, that are combined together in series. In such systems, the same current ﬂows

17 through all panels in the string. Due to manufacturing tolerance, partial shading or other possible reasons, different panels have different I-V curves, and therefore different maximum power points. It means that some panels perform below their maximum power point, which results in the loss of energy. Placing the peak power point converters into individual panels allows each solar panel to operate at its peak efficiency, disregarding uneven shading or other mismatches. [8,9] To achieve maximal efficiency, the Nuna team requested an MPPT that is specifically designed for their car. The car will need five MPPTs instead of one for the whole array. Each MPPT must have a working range between 20 and 100 watts and a maximum power of 200 watts. The target efficiency needs to be above 95%. Such MPPTs are not commercially available. There- fore, a unique design is needed, specific to the Nuna requirements.

2.2 Brief of Requirements The following conditions are a short summary of the total requirements that together form the design criteria. The detailed Brief of Requirements can found in appendix B.

Must-Have Requirements • The MPPT must have an efficiency of above 95%. • The MPPT has to be installed in fivefold in the Nuna solar car, resulting in a nominal input power between 20W and 100W and an absolute maximum of 200W. • The MPPT accepts input voltage between 60V and 120V and provides an output voltage between 120V and 160V. • The MPPT provides plug-and-play connectivity, thus every team member of Nuna can install it. • The MPPT needs to work independently, but must be able to react to externally given commands. • The MPPT is maintenance-free during operation. • The MPPT will work under the conditions present in Australia during the World Solar Challange. • All the used components meet the specifications as provided by Veolia World Solar Challenge.

18 Wanted Requirements • The MPPT needs to communicate with the car using CAN-bus communication on a send-only basis, providing additional information on at least:

– Power in [W] – Power out [W] – Input voltage [V] – Output voltage [V] – Output current [A]

• An external reset switch is needed for resetting the MPPT during an inﬁnite loop or error.

• Extra safety systems, such as fuses to prevent overcharging or limit short circuit damage, are applied to the design.

• Input and output and other high-voltage connections need to be properly shielded.

Would-Be-Nice Requirements • The status of the MPPT can be inspected visually using multiple LEDs.

• The design is robust, light and compact.

• The case and connections are dust-sealed and are shock and vibration proof.

19 20 3 Literature Study on MPPT Hardware

ection 3.1 contains the results of the research performed on the current state of the art in MPPT designs. In 3.2, converter topologies for S MPPTs are discussed. Sections 3.3, 3.4, 3.5, and 3.6 describe the individual components of the converter and their eﬀect on the overall system.

3.1 Introduction to MPPT Hardware The Nuna Solar Racing car operates 6m2 of PV panels that output a certain DC voltage. The engine and battery system of the car operate at another, higher, voltage. Furthermore, to operate the PV panels efficiently, they need to be kept at a specific voltage and current, using a Maximum Power Point Tracking (MPPT) algorithm. To achieve the goal of setting PV panels at their maximum power point and to provide the engine and batteries with the required voltage, a power conversion device is needed. In order to minimize the effects of partial shading and differences in solar incident angle, the total PV area is divided into several smaller segments. Each segment will be equipped with its own tracking unit and power converter, rated at 100W. Power converters exist in several forms, and are ultimately derived from a general form of power supply. An overview of power supply technology is given in Figure 2.

Figure 2: Classiﬁcation of power supply technologies ( [2], pp. 2)

To maintain a constant voltage level under varying load and input conditions, a regulator is used. Figure 2 shows that two classes of regulators exist: linear and switching regulators. Although linear regulators have ex- cellent characteristics when it comes to bandwidth and noise, they can only step-down a voltage, making their output voltage lower than their input voltage [2], and thus rendering them useless for the given application, where an increase in voltage is needed. The eﬃciency will also drop greatly when the diﬀerence between the input and output voltage is large. Switching regulators

21 come in three forms: switched-capacitor regulators, pulse width modulation (PWM) regulators, and resonant regulators. Switched capacitor regulators, or charge-pumps, can be used to step-up a voltage without the need for inductors and with relative simple circuit topologies [10]. However, they are not suited for medium or high-power applications due to limitations on the capacitors [11]. PWM regulators regulate their output voltage by hard switching a transistor between the on and oﬀ states, whereby the duty cycle of the switch control signal determines the output voltage. A magnetic ﬁeld in an inductive element is used to store and release energy, which also allows some types of PWM regulators to step-up the input voltage [2]. PWM regulators come in various forms, either isolated, using a transformer, or non-isolated. The most important PWM topologies are summarized in Figure 3.

Figure 3: PWM regulator topologies ( [2], pp.3)

PWM regulators can work either in continuous conduction mode (CCM) or discontinuous conduction mode (DCM), depending on the shape of the current in the inductive element [12]. In CCM, the current in the inductive element ﬂows during the whole cycle, whereas in DCM it is zero for some time in the cycle. The boundary between the CCM and DCM regions is called critical conduction mode. Hard switching causes signiﬁcant electromagnetic interference (EMI), leads to switching losses in the switch elements and high device stresses. Switching losses are directly proportional to the switching

22 frequency. These losses are thus limiting the useful switching frequency of PWM converters and are generally a very signiﬁcant factor in power loss in converters [13–15]. However, PWM converters are relatively simple to build, easy to control and cheap to implement. Resonant regulators are a special kind of topology related to PWM regulators. Using resonant LC networks to achieve zero-voltage or zero-current switching (ZVS or ZCS) is a good option, as they reduce switching losses and electromagnetic interference problems [12, 15]. The resonant circuits shape the voltage across, or the current through the transistor, to enable switching with zero-voltage or zero-current (zero crossing) [16,17]. Figure 4 illustrates the diﬀerence between hard and resonant switching.

Figure 4: Hard switching versus resonant switching ( [3], pp. 2)

Due to the elimination or reduction of switching losses, resonant converters can utilize a higher switching frequency then regular PWM converters [15]. This increase in frequency leads to smaller, cheaper components and thus a lighter product. For comparison, a commonly used high-power insulated-gate bipolar transistor (IGBT) has a maximum switching frequency of about 30 kHz in hard-switching mode, whereas the same IGBT can be operated at up to 70 kHz when a switching loss reducing soft-switching technique is used [18,19]. Disadvantages of resonant converters include higher component count, which in some cases can oﬀset the decrease in device size due to higher operating frequency, increased complexity in design and operation, the requirement of matching the operating frequency to the resonant tank network and the higher conduction losses due to circulating currents [15,20]. Apart from resonant networks, other methods exist for improving converter performance relative to hard-switched PWM regulators. In recent years, several other soft-switching techniques have been developed for DC/DC conversion aiming to reduce the switching losses. Besides the already mentioned resonant converters [3,16,17], there are also other systems that aim to overcome the limitations of resonant converters by implementing other soft- switching techniques. At the same time, they provide better performance than hard-switched PWM regulators [21–25].

23 These alternative soft-switching techniques use either passive or active methods to make sure that the ZVS or ZCS conditions are met. Active soft- switching has the disadvantage that extra switches require complex control circuitry, while the passive methods require a lot of extra components and/or auxiliary circuits [20].

3.2 Diﬀerent Converter Topologies In this section, three converter topologies will be discussed. Due to time considerations, we are only able to investigate those topologies whose complexity allows them to be designed and implemented within the time available for the thesis. Perhaps one of the more complex topologies could result in a higher eﬃciency. Given more time, it would be an interesting option to investigate these possibilities further. In this subsection, a number of commonly used converter topologies will be reviewed. The choice of topology is based on its simplicity and suitability for the design.

Boost Converter The boost converter is a converter that steps up the input voltage. It is a suitable option for this application, since it does exactly what is needed. The system is a quite simple system, but it will not give a steady output voltage. There is also no isolation between the input and the output of the system since they have a common ground. The basic boost converter is shown in Figure 5 [26].

Figure 5: A basic schematic of a boost converter

While the switch is turned on, the inductor stores energy and the capacitor will be discharged. There will be no current flowing through the diode. The circuit will have two current flow loops. The first is the current IL, which flows from the source through the inductor. The second flow is from the capacitor through the load and then back to the capacitor. If the switch is turned off, the inductor will charge the capacitor. During this time there will be a current flowing from the source through the inductor,

24 diode and then the current will be divided over the load and the capacitor.

Buck-boost Converter The buck-boost converter is a combination of the buck and boost converter. It is able to give both a lower and a higher voltage at the output compared to the input voltage. Therefore, it is another suitable option for the problem. A basic buck-boost converter is shown in Figure 6 [2].

Figure 6: A basic buck-boost converter schematic

Since this converter is a combination of a buck and a boost converter, it is to be expected that the used components are similar, but need to have higher ratings compared to the separate designs. Note that the output voltage is inverted due to the diode. It is wise to keep in mind that because of the inversion, the input and output do not have a common ground, which can lead to problems with usage of the converter [27]. This also leads to the drawback that the gate of the transistor has to be configured on a floating level, making it harder to have accurate control on the switching frequency. In this configuration the capacitor will be used intensely, which will have negative effects on the lifetime of the capacitor [28]. When the switch is turned on, the inductor will be charged and the output voltage will be equal to the voltage of the (discharging) capacitor. When the switch is turned off the inductor tries to keep the current flow and thus will raise the voltage. During that time the capacitor will be charged and the inductor will be discharged.

Flyback Converter The flyback converter is a variation of a buck-boost converter. The inductor placed in the buck-boost converter is replaced with a transformer, which leads to a converter with electrical isolation. A basic schematic of a flyback converter is shown in Figure 7 [29]. Due to the fact that the transformer is not ideal, there are leakage induc- tances and losses. This results in the need for snubbers in the implementation. The usage of snubbers will make the topology more complex than the previously discussed converters. The major benefit of this converter is that it is capable to work with a wide variation of input voltages. Drawbacks are

25 Figure 7: Circuit of a flyback converter that, as earlier stated, it is hard to control the magnetic fields caused by the transformer and the transformer will take a lot of space which is problematic considered the limited space available [28]. When the switch is turned on, there will be a current flowing from the source through the inductor and the capacitor will be discharged over the load resistance. If the switch is turned off the current will flow from the inductor through the diode and it will be divided over the capacitor and the resistor. During this time, the capacitor will be charged for the period that the switch will be turned on.

Other Converter Topologies The other converter topologies are too complicated to implement in the small time window given for the bachelor thesis. Therefore, we will not discuss them any further in the literature study.

3.3 Possible Switching Elements The switch is one of the most important elements in all the topologies discussed above. There are many possible choices for any of the converters. Two will be examined here: the Power MOSFET and the IGBT. The choice between a MOSFET and an IGBT is based on the rated output power, voltage and operating frequency. According to [2]: ”IGBTs are good devices for low-frequency, high-voltage, high-power applications.” In general, the limit between low and high-power applications is put at 500W [4]. Most IGBTs can be operated with a frequency up to 50 kHz, thus making them unsuitable for high frequency converters. Figure 8 shows the diﬀerent operating regions of IGBT and MOSFET switches, but it does not take the operating power into account. For the MPPT to be built, the maximum power is 200W and the output voltage will not be above 160V. Combining this information and Figure 8, the decision to choose for a MOSFET is obvious.

26 Figure 8: Preferred operating regions for MOSFET and IGBT [4]

3.4 Possible Rectifier Diodes The switching behavior of a Switch Mode Power Supply, or SMPS, has a large effect on power loss and frequency. As soon as the switch turns off, the inductor voltage increases rapidly to maintain the flow of current. Spikes occur on the drain of the switch when the diode reacts too slow to the change in voltage. These spikes can harm and even destroy the switch [30]. Different approaches exist to solve this problem: soft-switching techniques and hard-switching techniques. Soft-switching methods turn the power on and off gradually. This way, device switching losses are reduced and switching frequencies increased by constraining the switching of power devices to periods when the voltage or current through the device is almost zero. A drawback however is that soft-switching devices require additional passive components. The higher the switching frequency in a hard-switching device, the higher the losses are. Therefore, using hard-switching techniques makes the design frequency limited, even though they are much simpler to implement than soft- switching techniques. MOSFETs and other unipolar devices are encroaching on the territory of bipolar devices. The biggest reason is that parasitic capac- itances in unipolar devices are very small, which is the result of the absence of stored carriers. Hence, ”on-to-off” and ”off-to-on” transition times of the power MOSFET switches are decreased, thus minimizing switching losses. Silicon Schottky devices have very low forward drops and reduced forward and reverse recovery characteristics and therefore function better than ultra-fast power diodes. The disadvantage of Schottky devices is that they have a low breakdown voltage, which limits them to low-voltage applications. The Silicon Carbide Schottky diode improves upon this with improved

27 characteristics, making it easily usable in high voltage applications. it is a high-performance diode with high blocking voltage capabilities, a three times higher band gap than silicon, a breakdown ﬁeld ten times higher than silicon, and thermal conductivity comparable to copper. A combination of power MOSFETs and SiC Schottky diodes results in hard-switching circuits with the highest eﬃciency, resulting in much higher switching frequencies. Hence, for this design, this is the combination that has been used [31–34].

3.5 Converter Output Capacitor The converter output capacitor should keep the output voltage nearly constant. The ripple caused by the discharging and charging of the output capacitor while the inductor is charging is dictated by the equation below: [35]

dv i = C (1) c dt

where ic is the capacitor current in Amps; C is the output capacitance dv in Farads; dt is the change in output voltage with time; dt is the on-time period of the capacitor. There is a wide range of capacitor types that could be used for the converter. All available technologies are classified into different groups. This classification is based on the dielectrics they use. The most used capacitor technologies are ceramic, metal film and electrolyte. Capacitors from different technologies are distinct in capacitance, voltage range, operating frequency and thermal behavior. Figure 9 makes the comparison realization easier. The most popular capacitors are T a−P olymer, T a−MnO2 (single), NbO −MnO2 , T a−MnO2 (multi), MLCC, and AluminiumEl. They have very different characteristics. A comparison of different capacitors is given in Table 1 and 2. Tantalum capacitors can only be used for low power applications because of limited range of capacitance and voltage levels. Multi layer ceramic capacitors are available in capacitance up to approximately 10µF. Their rect- angular shapes makes them suitable for integration with other components on the board. They are also designed to work at very high temperature, up to 200 ◦C and are desirable for automotive applications. Single layer ceramic capacitors are suitable for high voltage applications, up to several tenths of kV. Dielectrics are also available in metal film capacitors. Most used category of those is the super metallized polypropylene film. These capacitors are designed for capacitance up to a few thousands of µF and are able to work

28 Table 1: Overview of diﬀerent capacitor choices Capacitor Tech- Level of Capacitance Capacitance ESR stabil- nology the ESR at stability vs stability vs ity vs tem- fsw=300kHz tempera- DC voltage perature ture bias Ta-Polymer ++ + + ++ Ta-MnO2 (single) + ++ ++ + NbO-MnO2 + + + + Ta-MnO2 (multi) ++ ++ ++ + MLCC - (too low) 0 - ++ Aluminium El. - (too high) - ++ - Explanation: ++ very good, + good, 0 neutral, - poor

Table 2: Capacitor application measurements Capacitor Technol- AC Vrms at 25 Vrms stability Case size ogy ◦C vs temperature Ta-Polymer + ++ ++ Ta-MnO2 (single) + + + NbO-MnO2 0 0 + Ta-MnO2 (multi) ++ ++ 0 MLCC - - + Aluminium El. - - - Explanation: ++ very good, + good, 0 neutral, - poor with voltage up to a few kV, which gives them the possibility to operate properly at very high current applications. Low output ripple voltage for the DC/DC converter can be achieved using output capacitors with low ESR (Eﬀective Series Resistance) at the switching frequency. The rate of decrease of the actual capacitance with frequency in relation to the resonance frequency is also important. With external com- pensation, equations 2 and 3 can be used to adjust the output capacitor values for a desired output voltage ripple:

R ic dt ∆Q tcharge Cout(min) = = (2) ∆Vout ∆Vout

29 Figure 9: Voltage versus capacitance for diﬀerent types of dielectrics ( [5], pp.5-2)

With Cout(min) = minimum output capacitance

Ic = output current of the application

tcharge = the time the capacitor is charged

∆Vout = desired output voltage ripple

The ESR of the output capacitor adds more ripple, given with Equation 3:

∆Uout(ESR) = ESR ∗ Icrms (3)

With Uout(ESR) = additional output voltage ripple due to capacitor ESR ESR = equivalent series resistance of the used output capacitor

Icrms = the rms value of the current through the capacitor

30 3.6 Converter Inductor The performance of the converter is critically aﬀected by the inductor, because inductor regulates the output voltage of the converter, the rising time and the energy consumption during. Therefore, inductors are an indispensable part of most power electronic converters. However, they are not commercially available in a wide range of properties, but are usually custom designed and constructed for the particular application. The design procedure in which the inductor is contrived and built shows that the size and the rating of an inductor is dominated by the electrical loss in the component.

Inductor Construction and Core Material (Iron Alloys and Fer- rites) The inductor is constructed of a coil which is made of conducting material, copper wire, wrapped around a magnetic core. Inductor construction is based on a copper wire wrapped around a bobbin which makes the space available for the magnetic core to be inserted. Often used materials for magnetic cores of the inductors are iron alloys material and ferrite materials. Iron alloys often consist of small iron particles electrically isolated from each other. Hysteresis loss and eddy current loss come along while using iron alloy materials. Due to their eddy current loss characteristic, they are only usable for low-frequencies less than 2 kHz. Ferrite materials are made of oxide of iron and other magnetic elements. They have much lower saturation flux density, about 0.3 T, than iron alloy materials but very large electrical resistivity. Therefore, they don’t bear the eddy current loss. Thus, only hysteresis loss (explained below) is present. Ferrites are then the material of choice for cores that operate at high frequencies greater than 10 kHz because of the low eddy current loss. [36–38] Figure 10 presents the core loss versus frequency for different types of magnetics and figure 11 shows the saturation flux density versus temperature for different types of magnetics.

Hysteresis Loss A material that undergoes a non reversible energy cycle, such as a magnetic material, loses some of its energy in what is called hysteresis loss. If a system can start and end its cycle at the same point without gaining any energy it is said to have a reversible cycle. Figure 12 shows a typical B-H charesteristic (B-H loop).

31 Figure 10: Core loss versus frequency for diﬀerent types of magnetics ( [5], pp.6-5)

The field applied performs work on the material which is represented by the area inside the B-H loop. This work dissipates in the material and causes a raise in temperature of the material. With increasing ac flux density B, and increased operating or switching frequency f, the hysteresis loss of the core materials are raised. The specific loss (or loss per unit volume), Pm,sp is shown by equation 4:

a d Pm,sp = Kf Bac (4) where k, a, and d are constants that vary depending on the material characteristics. After choosing the appropriate core, k, a and d can be found in the data sheets belonging to that specific core. The range of frequency and flux density whereby this equation applies differs depending on the specific material The peak value of the ac waveform represents the flux density B. [7,39]

Winding Loss Due to DC Resistance of Windings Electrical currents in the inductor windings introduce losses caused by heat production. These losses are called copper losses, for the currents ﬂow

32 Figure 11: Saturation flux density versus temperature for different types of magnetics ( [5], pp.6-5) through the copper conductor of the inductor. Since they are losses they are undesired in a design for high efficiency. The currents also induce un- wanted currents in adjacent components. According to Joule’s First Law, copper losses are a result from Joule heating and are also referred as ”Ohmic losses”. The energy lost will increase in proportion to the current flowing through the windings and to the electrical resistance of the used conductor. This relation is given in equation 5.

Copper loss = RI2 (5) where I is the current flowing in the conductor and R the resistance of the conductor. With high-frequency currents, winding losses are not calculated as easily. The reason is that winding losses are additionally affected by skin and proximity effects. [40]

Skin Effect and Eddy Current in an Inductor Inside the inductor, due to an alternating magnetic field, an alternating current is induced in the conductor. The AC-current generates an alternating magnetic field around the conductor, leading to changes according to the change of the current intensity.

33 Figure 12: B-H characteristic of a transformer core having hysteresis and hence magnetic losses

The change in the magnetic field generates an electric field, which is in opposite direction to the changes caused by the current intensity. The opposite directed electric field is called counter-electromotive force (counter-EMF). It is strongest at the center of the conductor and therefore the conducting electrons are pushed to the outside of the conductor. In other words, change in the magnetic field intensity causes another current to flow, called eddy current.

Based on Lenz’s law, the direction of eddy current causes its magnetic field to oppose the magnetic field that caused the current flow. Hence, eddy currents develop a flux that partly cancels the external flux, resulting the current density to decline. This phenomenon is known as skin effect. The skin depth is a value of the depth at which the current density falls to 1/e of its value near the surface. It is given by the Equation 6:

r 2 δ = (6) ωµσ Where f = ω/2π is the frequency (in hertz) of the applied magnetic field, σ is the magnetic permeability of the core material, and µ is the conductivity of the magnetic material [7]. In short, the skin effect is due to the circulating eddy currents, arising from a changing H-field, canceling the current flow in the center of a conductor and reinforcing it in the skin. In order to minimize the skin effect in

34 the conductor, Litz wire is designed. It consists of many thin wire strands, individually insulated and twisted or woven together. Litz wire reduces the impact of the skin eﬀect and the proximity eﬀect. [7,41]

Proximity Effect In the coil winding used in an inductor two wires carrying the same alternating current lie parallel to each other. The magnetic field of one wire induces eddy currents in the adjacent wire. This induced current is lengthwise and is directed in such a way that the eddy current fortifies the main current on the side facing away from the first wire, and opposes the main current on the side facing the first wire. This leads the current to be focused in the areas of the conductor furthest away from nearby conductors carrying current in the same direction. As the resistivity of the wire, caused current is inversely proportional to the effective cross section of the wire, when the current is concentrated into a smaller area of the wire, the resistance is raised. Accord- ingly, the effective resistance of the circuit is also increased and results in more power loss. [42]

Thermal Considerations Temperature variation has big impact on the winding and core material performance. With an invariable current density, raise in temperature results in the winding loss of the conductor and the core loss of the magnetic material. Core loss stars to raise significantly for temperatures above 100 ◦C, consid- ering the frequency and flux density to stay constant. This can be seen in figure 13. Figure 14 shows the flux density behavior of the core vs. temperature: Hereupon, flux saturation level is inversely proportional with the temperature. For any inductor design minimizing the core temperature within the allowable maximum is essential. Components situated closely together transfer their heat via radiation and convection. Therefore, the steady-state of all the components approach one value. In that case, overall maximum temperature of the system is set to the temperature of the component with lowest maximum allowable temperature.

Internal and Surface Temperature of an Inductor In general, it is assumed that the internal and surface temperature of an inductor are almost equal. The rationale behind this assumption is as follows: the thermal conductivity of the materials are relatively large, and the power dissipation will be approximately the same throughout the cores and winding. Therefore,

35 Figure 13: Temperature dependence of core loss ( [6], pp.9)

the surface-to-ambient thermal resistance Rsa is the main thermal resistance that determines the inductor or transformer temperature.

Core Shapes and Optimum Dimensions Cores are available in a wide variety of shapes and sizes to suit the given application. For example, ferrite cores are available as toroids, pot cores, U, E, and I shapes. A double E-core is generally accepted for this kind of design (it is shown in Figure 15). Once a core such as double E-core is selected, the combination of dimensions d, ha , and b, should be optimized. The bobbin dimensions h, and b, are made to be as close as possible to the core dimensions ha and b. In this design the criteria for the optimization is considered to be the lowest total volume or weight and the least loss possible. [7]

36 Figure 14: Magnetization curve of the core ( [6], pp.6)

Figure 15: Dimensioned diagram of (a) a double-E core (b) bobbin, and (c) assembled core with winding ( [7], pp.750)

37 38 4 Converter Design

aximum Power Point Tracker is based on a simple boost converter. Therefore, the output voltage must never drop below the input volt- M age level. Within the speciﬁed I/O voltages, any voltage conversion factor is feasible. This chapter contains the calculations and component choices for the converter to arrive at the desired design. In section 4.1, the topology of the converter will be decided. Section 4.3 contains the calculations for the base values required for the design, including a basic power loss model. Section 4.3, 4.4, and 4.5 present the result of the calculations for the values of the components in the converter. Finally, section 4.6 shows the step-by-step procedure of the inductor and its power loss calculations to arrive at the inductor design.

4.1 Topology Decision As shown in section 3.1, there are different topologies for making a converter for MPPT. A few were not discussed due to the short time window given for the assignment. The converters investigated were the boost converter, the buck-boost converter and the fly-back converter. In this section, arguments are made to lead us to the right converter choice. The flyback converter is a variation of a buck-boost converter and therefore it is a good option to look at. Because of the transformer in the topology, it is usable for a wide range of input voltages, which could be useful since the PV cells do not always give maximum output voltage. However, there are some major drawbacks to the implementation as well. The transformer introduces a huge magnetic field and for good efficiency, a high magnetic coupling is needed [40]. This is hard to accomplish and will lead to larger components. A second drawback is the need for a snubber circuit to get an efficient system. This results in a more complicated system which takes more time to design. Hence, this topology will not be used. The buck-boost converter is able to convert to a lower and higher voltage at the output of the system. The topology is not very complicated and it could be useful in our design. However, this topology also has certain drawbacks. The main drawback is that the input and output do not have a common ground, since the input and the output are inverted [28]. The lack of a common ground results in difficult configuration of the MOSFET used for switching. Another drawback of this topology is the usage of the diode and the capacitor. They will be used intensely, which will have negative effects on the longevity for these components. The last topology discussed is the boost converter. A boost converter

39 steps up the input voltage and can perform with up to 99% eﬃciency . Therefore, it’s suitable choice for this design. The design of the converter is also relatively simple which is good for the current time window. Once the boost converter is chosen for the design, topologies must be thought of. Since the load of the MPPT will be batteries and the motor of Nuna, the ripple in the output voltage will not be a major issue. The buck-boost converter was also a good alternative, but a step-down converter like a buck converter will never be used. Therefore, if we were to choose the buck-boost converter, functionality would be included in the system that would never be used.

4.2 Boost Converter Principles As already discussed in section 3.2 the boost converter converts the input voltages to a higher output voltage. This is done by combining the inductor and capacitor in the circuit. Charging these components is done by switching a MOSFET on and oﬀ resulting in two equivalent circuits. Both circuits will be brieﬂy discussed in this section. A basic schematic of a boost converter is shown in Figure 16. [26]

Figure 16: A basic schematic of a boost converter

When the MOSFET is turned on, the inductor will be charged and the capacitor will be discharged, for the diode will block currents flowing from the capacitor to the inductor. This will result in the following equivalent circuit given in Figure 17. The first current IL flows from the source to the inductor and through the MOSFET. The second current flow is from the capacitor to the load.

If the MOSFET is turned oﬀ, the inductor will be discharged and the capacitor will be charged, since the MOSFET can be seen as an open connection. The equivalent circuit during this state is shown in Figure 18.

40 Figure 17: Equivalent circuit while the MOSFET is on

In this state there is only one current ﬂowing in the circuit. It goes from the source to the inductor, through the diode and it will then be devided over the capacitor and the load.

Figure 18: Equivalent circuit while the MOSFET is oﬀ

Both the equivalent circuits are highly dependent on the current through and the voltage over the inductor. To get a better impression on how a boost converter works these waveforms are given in Figure 19. In Figure 19, T is the time used for one periode, ton the time when the MOSFET is turned on and toff the time when the MOSFET is turned oﬀ. The charging and discharging of the inductor is clearly visible in the waveform of the current. The waveform of the current through the capacitor will be inverted to the waveform of the current through the inductor. This is because the capacitor charges when the inductor dicharges and will be discharged when the inductor is being charged. From the wave forms given in Figure 19, eq. 7 can be derived. This equation is important for it gives the relation between the input and output voltage of the converter.

Vin · ton + (Vin − Vout)toff = 0 (7)

By writing eq. 7 in a diﬀerent way, the following equation for the relation

41 Figure 19: Waveform of the voltage over and current trough the inductor between the input and output voltage can be derived. V T 1 out = = (8) Vin toff 1 − D Eq. 8 introduces the duty-cycle. This is a parameter normally used in calcutions on the circuit. It is equal to the time the MOSFET is turned on (ton). The duty-cycle will be further calculated in section 4.3.

4.3 Assembling Converter Inputs The values of capacitance and inductance are important for the converter operation since they determine the voltage and current ripple in the converter. For calculating the inductor and capacitor values needed for the design, several other values are needed. They are shown in Table 3 below. In the calculations, the worst case scenario will be considered. In that scenario, the input voltage will be minimal and the output voltage will be

42 Table 3: Converter electrical speciﬁcations Data Value Vout 160 [V] Vout,min 120 [V] Vin,min 60 [V] Vin,max 120 [V] Pout,max 200 [W] the desired maximum voltage, 160V. In this case, the components will be slightly overdesigned, but that will also be an extra safety margin calculated in the models and designs.

Powerloss Model The efficiency of the total system is an important requirement given in chapter 2. The efficiency needs to be higher than 95%, otherwise the benefit of a low power MPPT is lost. For the losses in the components some general equations are used from [2,43,44].

First all the losses for the components are calculated independently. After all the separate losses are calculated they are summed and a total efficiency will be calculated. The losses in the doide are during two different stages. The fist stage is the losses according to the voltage drop and the second is the losses according to the resistance of the diode.

2 PD,res = Rf · IDrms (9) with Rf being calculated according to [45] with a temperature T equal to 40◦C. −3 Rf = 0.14 + T · 1.13 · 10 (10) and IDrms is equal to. r 1 − D I = I · (11) Drms ripple 3 where D is the duty-cycle, which is in this calculation the worst case scenario of Vin minimal and Vout maximum. and Iripple is the ripple current measured from peak to peak in the worst case scenario.

43 The power loss caused by the forward voltage drop of the diode is equal to: Vf PD,f = · Pout (12) Vout

With Vf is the forward voltage drop over the diode, which is 1, 7V according to [45], Vout and Pout are the stated output voltage and rated maximum power output accordingly. The total powerloss caused by the diode is equal to the sum of equations. 9 and 12. PDiode = PD,res + PD,f (13) The losses caused by the MOSFET are divided into two states as well. The calculations are made according to [43,44]. The ﬁrst loss approximation is for the losses in the MOSFET during conduction mode.

2 P M, cm = Rds · IDrms (14) with Rds as the drain source resistance of the MOSFET given in the data sheet, which will be further discussed in [44]. The other loss is caused by the switching of the MOSFET. This is the highest loss in components and is also related to the switching frequency fs in the circuit. 1 P = · V · I · f · (t + t ) (15) M,sw 2 out d s on off In this Id is the maximum current through the switch calculated by:

Id = Iout + Iripple (16) ton the turn on time and toff the turn oﬀ time of the MOSFET as speciﬁed in the datasheet and fs the switching frequency of the system. The total power loss of the MOSFET is equal to the sum of both calculated losses. PM = PM,cm + PM,sw (17) The last losses taken into calculation are the copper losses caused by the inductor. To make a reasonable approximation of the losses the internal resistance of the inductor must be approximated, this is done by:

RL = rL · L (18)

To get the constant rL, the resistance for one calculated inductor value is used. The series resistance for an inductor value of 112µH is equal to 0.09018Ω. For the constant eq. 19 is used:

rLcalculated 0.09018 rL = = −6 ≈ 800[Ω/H] (19) Lcalculated 112 · 10

44 2 PL,R = RL · Iripple (20) Eq. 20 is only a really rough approximation, but it will give an idea of the losses caused by the inductor L. For the total powerloss and the efficiency the following equations are used, with Pin the maximum power provided by the panel at the input of the converter. Ptotalloss = PDiode + PM + PL,R (21) P P − P efficiency = out = in totalloss (22) Pin Pin With these calculations a Matlab file is used to calculate the efficiency for different switching frequencies. In that file an array of frequencies is given in an input, the efficiency is an output and it will be plotted against the frequency. The matlab file is given in the appendix. The results are zoomed to the maximum point of efficiency resulting in Figure 20.

Figure 20: Eﬃciency of the boost converter according to the switching frequency

In respect to Figure 20 the maximum efficiency would be at 74kHz and would be 97,37%. The frequency is still chosen at 100kHz because the size of the inductor will be smaller at that frequency and the efficiency difference is less than 0.1%. The efficiency of the design of the boost converters according to this rough approximation 97,3%, which is good enough in respect to the requirements.

45 Calculating the Duty Cycle

The duty-cycle is gives the maximum duty-cycle (D) needed in the system. The other components need to be designed for this calculated cycle. The duty-cycle can be calculated according to Equation 23.

V D = 1 − in,min (23) Vout Using the values stated in Table 3, the maximum duty-cycle is 0.6288 for the system. This is the duty-cycle in the worst case senario of the lowest input voltage and the highest output voltage.

The Maximum Output Current

The maximum output current and ripple current are two values that are also needed for the calculation of the capacitor and inductor value. The output current is quite easy to calculate using Equation 24, which results in Iout,max = 1,67 A.

Pout,max Iout,max = (24) Vout,min

Deriving the Ripple Current

The ripple current is the change in the current caused by the inductor charging and discharging. Figure 21 shows a basic drawing of the ripple current in the system. To get the minimum input current, the maximum supplied voltage and power are needed. As given in the the brief of requirements, the maximum input voltage is 120V and the maximum power is 200W. This results in the following equation for the minimum input current.

Pmax 200 Iin,min = = = 1, 67A (25) Vin,max 120

This will be the absolute minimum average input given by our source. The ripple current may thus have a maximum of:

∆I = 2 · Iin,min = 3.33A (26)

46 Figure 21: Voltage over the inductor and current through the inductor

Calculating the Capacitor Value The value of the capacitor has a large eﬀect on the output ripple voltage of the converter. This is also shown in Equation 27 where ∆Vout is the output voltage ripple of the whole system.

I · D C = out,max (27) fs∆Vout As discussed before, it is not good to design an MPPT with an output voltage ripple that is greater than 2% of the desired output voltage. To get a good estimated value of the output ripple the voltage ripple, the capacitor’s output voltage ripple caused by the equivalent series resistance needs to be calculated as well. This can be done by using Equation 28.

I ∆I ∆V = ESR · ( out,max + L ) (28) out 1 − D 2

When choosing an ESR of 125 mΩ, which is a relatively high value, ∆VC is 0.6167 V. To calculate the total output ripple, an acceptable standard

47 voltage ripple is also needed. This is set to 1 V in these calculations, a result that is not too large and will also keep the size of the capacitor within an acceptable range. The total estimated voltage ripple ∆Vout is then 1.6167 V. This is a ripple that is 1.01% of the desired output voltage, an acceptable value for the system. Applying the above values in Equation 27, the value of the capacitor is 6.48 µF.

Calculating the Inductor Value The ripple current and the inductor value are directly related. This can also be seen by the following equation:

D · V ∆I = in (29) L · fsw In the rest of the calculations, the lowest input voltage (60V) will be used, since it would set the design to the worst case scenario. The duty cycle D is 0.625, as calculated previously in this section. The frequency fsw is stated at 100 kHz. Taking all the above into account the value of the inductor is:

D · V 0.625 · 60 L = in = = 1, 125 · 10−4 = 112, 5µH (30) ∆I · fsw 3, 33 · 100000 This is a value that results in an inductor that is acceptable in size and guarantees a good safety margin for the boost converter and thus the MPPT.

4.4 Choosing the Rectifier Diode Schottky diodes reduce the losses of the system, since the voltage drop over the diode is lower than other compatible diodes. With choosing the diode, the forward current rating of the diode needs to be equal to the maximum output current. That is, the sum of Iout and ∆IL, which gives a maximum output current of 5 A. On the data sheets of the diodes that are chosen, the average forward current is given. To have safety margins on the diode, the forward current of the diodes will be higher (5 A and 6 A). This will probably make the whole system a bit slower, but it will provide higher safety. All the ordered diodes need to be SiC Schottky diodes, since those are the only diodes that can work with the high voltage and are fast enough to not destroy the MOSFET. There is also an other benefit to these diodes, namely the diodes have very high efficiency and low switching costs. [45]

48 4.5 Choosing the Capacitor The capacitor needed has an ESR value of 0.125 Ω according to section 4.3, but there are no capacitors with a capacitance of 6.48 µF available to buy. The capacitor with a value closest to it is rated at 6.8 µF, which is a bit higher. Since a smaller ripple current is ﬁne, a capacitor rated at 6.8 µF will be used. It is also needed to order components designed for high voltages, i.e. above 200 V DC and preferably a bit higher. This will also be relevant to the longevity of the components as requested in section 2.2.

4.6 Inductor Design For designing the inductor of the MPPT, the procedure below is used, which is based on limiting the inductor temperature to a maximum value that it could reach while rated voltages and currents are applied. The ambient temperature is considered to be at the maximum and it is distinct from the surface temperature. This surface-to-ambient thermal diﬀerence leads to a surface-to-ambient thermal resistance. This resistance includes convection and radiation and relates the maximum surface temperature to the maximum allowable power dissipation in the inductor. The power dissipation is substantiated in terms of allowable current density through the winding and allowable ﬂux density in the core of the inductor. The basis of the design is formed by these relationships and the procedure step-by-step is described below:

Step 1: Assembling Design Inputs The design inputs consist of the following parameters:

• Inductance value L = 112 µH

• Inductor ripple current Iac = 3.3 A

• Rated dc current Idc = maximum output current from solar panels = Pmax,out,panels = 200W = 3.33 Vmin,out,panel 60V ˆ • Rated peak current I = Idc + Iac = 6.6 A

2 2 Idc+Iac 0.5 • Rated rms current Irms = ( 3 ) = 3.811 A • Operating frequency f = 100 kHz

49 • The maximum surface temperature of the inductor Ts is set to a gen- ◦ erally accepted value of Ts, 100 C, and for the maximum ambient tem- ◦ perature Ta 60 C is chosen, based on the brief of requirements.

ˆ Step 2: Computation of Stored Energy Value LIIrms The second ˆ ˆ step is using the design inputs to compute LIIrms. I is the maximum peak value of the current and Irms is the maximum rms value of the current:

ˆ LIIrms = 2.82mJ (31)

Step 3: Choosing the Core Material, Shape, and Size The conductor may be composed of a single round wire or it may be a special multi-stranded conductor, such as Litz wire, in which each strand has a diameter in the order of a few hundred microns or less. In this design, Litz wire is used to avoid problems with the skin effect and proximity effect. A value of 0.3 for the fill factor is considered to be practical for Litz wire. Since the operating frequency is 100 kHz, a Ferrite material will be used for the core. Based on comparisons made in the literature study, the 3C94 core material is selected, as it appears to have the best performance factor. A double-E core is chosen as the core shape. The core size is picked based on ˆ ˆ the value of LIIrms as computed in Step 2. The value of kCuJrmsBAwAcore for different cores can be calculated according to the databases belonging to different cores. Core number E41/17/12 seems to be the best option with having the value equal to 4.408mJ. See Appendix D. It has the smallest value ˆ ˆ of kCuJrmsBcoreAwAcore larger than LIIrms. Some of the core characteristics are listed in the table 4. Core dimensions are to be found in the appendix ˆ D. This is an iterative procedure, therefore, Bcore is calculated in steps 4, 5 and 6 using the values of K, a and d given in the database of the material. Jrms is calculated in the latter steps as well.

Core No. Material AwAcore Bsat mm4 mT E41/17/12 3C94 21569.68 330

Table 4: Database of core characteristics needed for inductor design

kCu is approximately 0.3 for Litz wire.

Step 4: Find Rθ and Psp The surface-to-ambient thermal resistance Rθsa of the combined core and winding is the next item to be found. This thermal resistance is the result of two heat transfer processes operating in parallel,

50 convection and radiation. This item could be given in the data sheet of the material or calculated as follows: Convection heat transfer: 1 d R = ( vert )1/4 (32) θ,conv 1.34A ∆T

Where A is the total surface area of the inductor and equals to 6121.7mm2. dvert indicates the vertical height of the inductor in meters. Core dimensions and the calculations needed to obtain the related parameters are attached in appendix D. Radiation heat transfer is formulated as: ∆T Rθ,rad = (33) Ts 4 Ta 4 5.1A(( 100 ) · ( 100 ) ) These two heat transfer processes operate in parallel. Therefore, the equivalent thermal resistance can be calculated by:

Rθ,radRθ,conv ◦ Rθ,sa = = 21.8 C/W (34) Rθ,rad + Rθ,conv

The allowable speciﬁc power density, Psp, which can be dissipated in the core and the winding, is calculated using:

Ts − Ta mW kW Psp = Pcore,sp = Pw,sp = = 80.4 3 = 80.4 3 (35) Rθsa(Vcore + Vw) cm m

Step 5: Speciﬁcation of the AC Core Flux Density From the literature study, we know the general form of the loss per unit volume Pm,sp is:

a d Pm,sp = Kf Bac (36) Core manufacturers provide detailed information about core loss, usually coming in the form of graphs of specific loss Pm,sp as a function of flux density B, with frequency given as a parameter. Such a graph for the 3C94 core is shown in Figure 15. Bac can be found using the allowable value of specific power density dissipation, Psp, estimated in Step 4 in conjunction with Figure 15, which is provided by the core manufacturer or by inverting Equation 36. Constants a, d and K of the core are specified using the best line estimation method or are provided in the data sheet of the core material. For 3C94, values of a, b and K are 1.6, 2.7 and 1.53·10−7 respectively.

51 Figure 22: Speciﬁed power loss as a function of ﬂux density with frequency as a parameter

Pcore 1 d Bac = ( a ) = 97.6mT (37) KC f

Step 6: Calculation of the Peak Core Flux Density Bˆ The flux density in the inductor core is proportional to the current in the inductor. The application dictates the peak current Î, and the inductor core must be ˆ ˆ chosen so that the peak current I generates a peak flux density B < Bsat. If ˆ the peak current has both a dc value Idc, and an ac value I − Idc, then the ratio below holds.

Iˆ− I B Iˆ dc = ac , Bˆ = B = 195.3mT (38) ˆ ˆ core ac ˆ I Bcore I − Idc ˆ The suitability of Bac is proven as it leads to a value for Bcore, which is ˆ smaller than Bsat. Otherwise Bac must be reduced until Bcore < Bsat. In this case, the core ﬂux is not loss limited [7].

Step 7: Speciﬁcation of Winding Parameters (Jrms, ACu, N) The allowable current density is estimated regarding winding loss due to resistance

52 of the winding. The power Pcu,sp dissipated per unit of copper volume in a copper winding due to its dc resistance is given by the following equation [7]:

2 Pcu,sp = ρcu(Jrms) (39)

It is favorable to express Pcu,sp as power dissipated per unit of winding volume, Pw,sp. Vcu is the total volume of the copper and equals to kcuVw, here, V is the total winding volume. Therefore, PwSpy can be expressed as:

2 Pw,sp = kcuρcu(Jrms) (40) Knowing that the resistivity of copper at 100◦C is 2.2·10−8 Ωm, we obtain:

2 3 Pw,sp = 22kcu(Jrms) (mW/cm ) (41)

Hereupon, Jrms has the value of 3.5A. Irms based on the initial calculations is equal to 3.811A. The required area of the copper conductor Acu is then given as: Irms 3 Acu = = 1.09(mm ) (42) Jrms The required number of turns N is then found from the equation derived from the copper ﬁll factor property:

NmaxAcu kcu = (43) Aw Solving the equation above for number of turns N results in maximum turns Nmax = 38.4 needed to reach the maximum inductance value. The maximum achievable inductance with the speciﬁed core is given by

ˆ NmaxAcoreBcore Lmax = = 222.7µH (44) Iˆ Hereupon, it is proven that the calculated inductance value is suitable for the design and the procedure has been followed properly, as Lmax is greater than the design value of inductance. The number of turns is proportional to the inductance of the inductor.

N L L = ,N = Nmax = 24.5 (45) Nmax Lmax Lmax

Thus, number of turns required to achieve the desired inductance is equal to 24.5 .

53 Step 8: Specification of the Air-Gap Length Excessive flux produced by a high level of current in the winding is not desired. This problem is solved by implementing an air gap. To realize this, Magnetomotive force, or MMF, is introduced. MMF can be thought of as the magnetic equivalent of electromotive force (EMF) generated from the magnetic field of the core. It can be calculated as: Fm = IN Ampere turns. The task of the air-gap is to increase the reluctance of the core so that less flux flows for any given level of MMF. The virtue of the air-gap is that, because it is free from ferromagnetic material, it does not suffer any change of reluctance with flux level. Its reluctance depends only on its length, lg, and cross sectional area, Ae; and both of those parameters can be made very stable [46]. The air-gap length P g is the last dimension to be found in an inductor ˆ design. The air-gap must be selected in such a way that the value of Bcore appears when the inductor current is Iˆ. Distributed air-gap is indicated by the symbol Pg. N and g correspond to the number of gaps and gap length. For the double-E core, the total length Pg of the gap is given by

X NIˆ g = µ A = 1.25mm (46) 0 g ˆ AcoreBcore This value corresponds to one centered air gap. In the E-core, inductor air-gap is destributed into two parts. Therefore, the value of each air-gap length is equal to: g = 1.25/2 = 0.625mm (47)

54 5 Concept Design of the MPPT

ithin this chapter, the design of the MPPT made in chapter 4 is examined by means of simulations. In section 5.1, the simulation W of the design is presented, the simulation model in simulink that has been used is discussed and the simulation results are given and reviewed.

5.1 Concept Simulation Simulation Model of the Boost Converter For simulating the design as calculated in chapter 4, Simulink is used. The basic design is that of a boost converter, with additional measurement blocks to allow an internal analysis of the system. For an overview of the system, the measured values are put inside a scope-block. The boost converter model is shown in Figure 23. The average load of the batteries and the motor of the Nuna car is considered to be 100 Ω. Therefore a 100 Ω resistance is set as the output load for the design. The source is implemented by a dc-source at 60 V and a small resistor of 0.1 Ω. It supplies a static voltage, as it is just used for testing the converter, not the whole MPPT design. The values for inductor and capacitor are the same as calculated in section 4.3. Not all components are available at the exact calculated value. Hence, simulations are performed to verify if the errors made by ordering components with slightly different values results in large deviations from the theory. If the differences appear to be within acceptable limits and in agreement with the requirements, the components can be used without affecting the overall performance of the system.

Simulation Results When simulating the values calculated in section 4.3, the output voltage is very close to the desired 160 V. Figure 24 shows similar result. In this ﬁgure, only a short period of the simulation time is shown, corresponding to the steady state behavior of the system. The output voltage of the system ripples between 157,1V and 158,7V as plotted in Figure 24. This is a acceptable ripple value and it is close to the desired value of 160 V. The voltage can be altered by ﬁne-tuning the duty cycle. This way, the output voltage will be around 160V. Figure 25 gives an overall view of the output voltage, including the time needed for initialization. It also clearly states that the output voltage is not yet exactly 160 V, but keeps very close to it.

55 The simulation implies that the converter will work according to the spec- iﬁcations given for Nuna. Also, the diﬀerence between the calculated capacitor value and the capacitor value available to purchase is lower than 0.01V, this can be neglected for it is unnoticeable. The relation between simulation, theory and practice will be reviewed in chapter 6, in which the test results and the proof of principles are discussed.

56 Figure 23: Simulink model used for testing the boost converter

57 Figure 24: Output voltage steady state of the boost converter

Figure 25: Output voltage of the boost converter including initialization

58 6 Evaluation of the Prototype

he following chapter contains results of tests performed on the prototype. First, in section 6.1, the building process of the MPPT using T the designed boost converter is presented. Section 6.2 contains information on the devices used for measurements. In section 6.3, the test results of the prototype will be presented. Finally, the proof of principle is discussed in 6.4.

6.1 Building Process of the MPPT For building the prototype, the high and low voltage circuits are build on separate boards. The low voltage and also low power subsystem is built on bread boards, since this makes eventual rebuilding or replacing components easier. The converter, which,operates at high voltage and high power, is build on a separate prototyping board where all the components are soldered on. The setup used with subsystems on different boards provides better safety, since both circuits are almost stand-alone and because high voltages are concentrated in one subsystem. An overview of the total prototype is shown in Figure 26. In this setup, the boost converter is the high power (sub)system of the prototype. It is better visible in Figure 27. The converter has an extra capacitor at the input of the system to smoothen the input, if the input would proof to be unstable. Also without the input capacitor, the current supplied by the solar panels would drop every time the MOSFET switches, resulting in a suboptimal efficiency and possibly damage the panels. The other components not discussed in chapter 4 are the shunt resistors, used for measuring the currents flowing through the system. This is discussed in detail in [44].

Building the Inductor The ﬁrst step in building an inductor is to choose a suitable core. Based on the calculations performed in section 4.6, the ideal core number is E41/17/12 3C94. However, due to restrictions in the components that were available to order, an ETD39/20/13 3C90 core was ordered. This core has the nearest value of energy level to the ideal. Suitable bobbins and clips corresponding to this core type were ordered as well. To create the inductor, 24.5 turns of Litz wire were spun around the bobbin. The Litz wire has a cross section of 1.1mm2, based on the calculations. Then, the E-cores were inserted into the bobbin and the band-gaps were

59 Figure 26: Total setup of the prototype adjusted. Fixing everything together with clips was the ﬁnal step for the building process of the inductor. After the inductor was completed, the inductance was measured at 100 kHz and 3.3 A. The result was an inductance of 111.6 µH. The impedance was 0.5 Ω, which is half of the maximum value deemed acceptable from simulations.

Initial Modiﬁcations

During the first test runs problems occurred, caused by the length of the cables connecting all the separate circuits. The cables caused a lot of interference on the signal going to and coming from the gate driver. This resulted in short circuits of the converter system caused by the MOSFET. To solve this problem, the gate driver had been relocated to the same board as the micro-controller. Also, all the connection cables were made as short as possible. This resolved the interference problem, but also resulted in a slightly different setup for the prototype of the MPPT. The final setup

60 Figure 27: Boost converter of the prototype used for testing is shown in Figure 28.

6.2 Test Setup of the Prototype In order to perform measurements on the system, the following devices were used:

• Fluke 189 True RMS Multimeter

• Asyc II Advance safety concept TRMS IP67 Mulitmeter

• Yokogawa DLM2034 Mixed signal oscilloscope

• Delta Elektronika Power Supply EST 150

• Delta Elektronika Power Supply SM 70 - 22

• M.L. A368 Variable resistance maximum 238Ω 2A

61 Figure 28: Final setup for testing

During the ﬁrst tests the eﬃciency of the system was measured. These measurements were done with the setup shown in Figure 29. The reason for using multimeters instead of an oscilloscope is because of their better resolution compared to the scope. The results of these measurements are available in appendix C. Other samples of the waveforms have been obtained by using a scope, resulting in measurements with slightly more deviation. However, these results will still give an adequate impression on the system’s behavior.

6.3 Test Results of the Prototype The results given in appendix C, show that the measured efficiency is between 96% and 98,5%. This is at the desired voltage range, but at a higher maximum input power for some high voltages. The maximum efficiency measured is 98,5% at an input voltage of 100V and a duty-cycle of 20%. An overview of all the measured efficiencies for different input power, with a load of 100 Ω, is given in Figure 30.

62 Figure 29: Setup for measuring the eﬃciency of the converter

Note that the power, supplied by the separate power source for the low voltage system, is not yet subtracted from the total output power. This will result in a slightly lower efficiency for the actual MPPT design. When the input voltage is at the desired range, measured efficiencies were above 96,5%. Hence, it can be concluded that the boost converter design has potential to satisfy the design requirements, which is a good starting point to get the whole MPPT to work at a high efficiency.

The measured current through the inductor is shown in Figure 31 and was done with an input voltage at 60 V, a load of 200 Ω, and the duty-cycle at 0.6. It shows that the inductor behaves as expected, since the waveform is similar to Figure 21. The main diﬀerence is the noise caused by switching the MOSFET. Therefore, it can be concluded that the inductor is designed and build accordance with the requirements and calculated design value. Figure 32 shows the output at a duty-cycle of 0.5, an input voltage of 70V and the input current equal to 2.8A. This implies that the converter is working according to the designed speciﬁcations. In Figure 32 the yellow line

63 Figure 30: Measured eﬃciency against input power is the output voltage, the green line represents the output current and the red line is the product of the voltage and the current. The spikes that can be seen in Figure 32 are caused by the MOSFET switching. A steady state ripple on the voltage and current is also visible in Figure 32. Figure 33 gives a clearer picture of the voltage ripple. This picture is made while using a voltage of 60 V, since in that case, results are better to compare with the simulation results. The steady state voltage ripple is best visible at the left part of the ﬁgure where the line is nearly constant. The other (bigger) spike is caused by the MOSFET and is used for triggering the signal. A closer look at the measured value given in Figure 33 shows the output voltage ripple to be roughly 5V peak to peak, which is more than 4% of the total output voltage. The output ripple is quite high and could be lowered by using an extra capacitor that further smooths the output voltage.

6.4 Proof of Principle From section 6.3, the conclusion can be drawn that the design of a high ef- ﬁciency boost converter at a relatively low power range is possible. At the beginning the whole desired range of the converter could not be tested, since the power supply available was limited up to 70V. However, later by using a solar simulator and a power supply with a higher voltage range, measure-

64 Figure 31: Inductor current ments for the complete required range were possible. The results obtained from all the measurements seem promising and imply that the design for the converter meets the requirements. Except for the noise caused by switching the MOSFET, all the results were in accordance to the ones simulated in Simulink.

Summarizing, it can be concluded that a high efficiency boost converter, and thus a high efficiency MPPT, has been made. Using the full voltage range power supply, gives a favorable steady-state output voltage and it is expected to obtain the same result while implementing it on the car. However, it is likely that solar panels would have less ideal characteristics. The reason is that power generators create a steady-state voltage and the solar panel output voltage is less stable and varies over time. This could be investigated and probably fixed by adding an extra smoothing capacitor at the input of the system.

65 Figure 32: Output voltage and current of the boost converter

66 Figure 33: Voltage ripple at 60V input

67 68 7 Conclusion and Recommendations

ollowing the design steps described earlier in this thesis a suitable boost converter for an MPPT, requested by Nuon solar team, was F designed and implemented. Throughout the design of this MPPT the specific use-cases for the Nuna car have always been taken into consideration, resulting in a potential for robust and lightweight design, that meets all the regulations of the Veolia World Solar Challenge. The MPPT was specifically designed to efficiently provide a maximum output power of 200W at required input voltages of 60V to 120V.

After the design phase, a Simulink model of this MPPT was made for optimization. Final simulations showed a very promising theoretical eﬃciency up to 97,3%. Based on this design, a prototype was constructed. The prototype MPPT operated successfully with an eﬃciency between 96% and 98.5% for the required input power range of 60 to 200W .

For the ﬁnal design of the MPPT some practical aspects need to be considered. Firstly the mentioned use of a custom designed PCB to reduce the total footprint of the design. The high frequency signals should be shielded and connections to the neighboring components in the Nuna car should be considered allowing for easy installation and servicing of the car. The MPPT can be enclosed in a lightweight carbon-ﬁber casing that secures it against shocks, vibrations and moisture.

Final considerations to further increase the efficiency of the MPPT, are the use of diodes with a smaller voltage drop, and a more efficient MOSFET. Implementing techniques as soft switching could increase the efficiency up to 99% or more while making the system faster as well. This would result in an MPPT that could outperform any similar available MPPT.

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74 Appendix

A. Matlab and Simulink Codes & Files

75 Matlab code for calculations:

%kHz (minimum switching frequency) fs = 100e3

%V (Disired output voltage) Vout = 160

%V (minimum output voltage Voutm = 120

%V (minimum input voltage) Vin = 60

% (rendement of our converter) n = 0.95

% (duty cycle of the system) D = 1-(Vin*n/Vout)

%W (maximum output power) Pout = 200

%A (maximum output current) Iout = Pout/Voutm

%A (estimated inductor riple current) dIl = 3.33

%ohm (equvalent series resistance of the output capacitor) ESR = 0.125

%A (maximum)switch current through the MOSFET I_switch = (Iout/(1-D)+dIl/2)

%V (additional voltage ripple caused by capacitor) dUout = ESR*(Iout/(1-D)+dIl/2)

%V output voltage ripple (its now 1V + ripple of capacitor) dVout = 1+dUout percV = dVout/Vout

76 %F (Calculated output capacitor value) given in the TI-sheet and in Ned Mohan C = (Iout*D)/(fs*dVout)

%H (calculated inductor value) TI-sheet L = (Vin*(Vout-Vin))/(dIl*fs*Vout)

Calcutations power loss model

%kHz (minimum switching frequency) fs = (0:500e3);

%V (Desired output voltage) Vout = 160

%V (minimum output voltage Voutm = 120

%V (minimum input voltage) Vin = 60

% (duty cycle of the system, worst case) D = 1-(Vin/Vout)

%W (maximum output power) Pout = 200

%A (maximum output current) Iout = Pout/Voutm

%A ripplecurrent peak to peak dIl = 3.33

L = (Vin*(Vout-Vin))*(dIl*fs*Vout).^(-1) Mvdc = Vout/Vin

%diode D1 = 1-D

% IDrms = il*sqrt(D1/3) IDrms = dIl*sqrt(D1/3)

77 %junction temp Tj = 40

%ceed datasheet Rf = 0.14+(Tj*1.13e-3) PDrf = Rf*IDrms^2 Vf = 1.7 PDvf = Vf/Vout*Pout

%W (losses of the Diode) PDiode = PDrf+PDvf

%MOSFET Rds = 0.0637 ton = 22.4e-9 toff = 25.4e-9 Id = Iout+dIl Pcm = Rds*IDrms^2 Psw = 1/2*Vout*Id*fs*(ton+toff)

%W (losses of the MOSFET) Pmosfet = Pcm+Psw

%inductor rl = 800*L %estimation for the internal resistance

%W (losses Caused by the ESR of L) PLr = rl*(D+D1)*dIl^2%/3

%total losses %W (total losses) P_loss = PDiode+Pmosfet+PLr efficiency = (Pout-P_loss)/Pout plot(efficiency)

78 B. Brief of Requirements A maximum power point tracker with power converter (MPPT) will be developed for use in the Nuna solar racing vehicles. This will be a new system developed for the professional solar racing market.

Requirements related to product usage • The MPPT will maximize the output power of a connected solar cell under all conditions speciﬁed in the Usage Characteristics.

• The MPPT will be installed ﬁvefold in the Nuna 6 solar racing vehicle; this will be called the system.

• The system can be installed, removed and operated by any Nuna team member, without requiring prior knowledge of its inner workings.

• The MPPT provides plug-and-play connectivity.

• Each MPPT has an external reset switch.

• The system will communicate with the vehicle.

• Each MPPTs operating status can be visually inspected.

• The system will be robust, stable and safe.

• The system will be constructed as light and compact as possible.

• The system can be easily integrated into Nuna 6 and its future succes- sors.

• Each MPPT will have a life expectancy under normal operating conditions of at least three years.

• The MPPT is maintenance free during its expected life.

B. Requirements on the ecological situation of the system • The system wastes as little energy as possible.

• The production process has minimal environmental impact.

• All components are RoHS compliant.

79 Requirements on the system Section 1: Usage Characteristics

• A total of ﬁve onboard MPPTs will provide Nuna 6 with more power under equal conditions than the current power point tracking system.

• A fault in one of the MPPTs will not lead to loss of power to Nuna 6, other than the power controlled by the faulty MPPT itself.

• The MPPT accepts input voltages between 60 V and 120 V.

• The MPPT connects to the Nuna 6 power bus, providing an output voltage between 120 V and 160 V.

• Should the output voltage rise above 160 V, indicating a full battery on the Nuna vehicle, the system will stop tracking to prevent overcharging.

• The systems nominal input power is between 20W and 100W, with an absolute maximum of 200W.

• The average eﬃciency of each MPPT will be greater than 95%.

• The system operates without malfunction with environmental temperatures ranging between -10 ◦C and 60 ◦C.

• The system operates without malfunction with environmental humidity ranging between 5% and 95%.

• Each MPPT communicates with the vehicle via the vehicles CAN-bus on a send-only basis, providing, next to all communication necessary for safe and reliable CAN-bus operation, at least: Power in [W], Power out [W], Input Voltage [V], Output Voltage [V], Output Current [A].

• The MPPT has at least four status LEDs, showing operating status and/or possible error codes.

• The software needs to run independent of external users, but must also be able to interact with signals given from an extern computer.

• The MPPT provides In-System Programming (ISP) using a JTAG interface.

80 Section 2: Safety Requirements

• All components meet the speciﬁcations as provided by Veolia World Solar Challenge.

• High-voltage connections must be properly shielded.

• All critical high-power connections contain correctly dimensioned fuses.

• Casings and enclosures must be constructed properly and provide adequate sealing, strength and durability to protect enclosed components.

• All connections will be dust-sealed, shock and vibration proof.

Section 3: Production and Installation Requirements

• The MPPT and all its components are integrated in an enclosure for easy mounting in the Nuna 6.

• Installation of the system is possible using standard tools available to the Nuna team.

• Each enclosure has a label for identiﬁcation purposes.

• External connections provide standard connectors for easy installation in the vehicle: for Power bus connectors: Green Power Connector PC 4 HV/4-STF-7.62 Phoenix; for CAN-bus connectors: Orange CAN Con- nector BL 3,5/4 Weidmller.

Section 4: Requirements on Product End-of-Life

• The MPPT complies with EU WEEE guidelines for electronic waste disposal.

• The system must be removable from the vehicle.

• Any batteries in the system must be easy to remove to be processed separately.

Section 5: Strategic and Marketing Requirements

• The system is sold business-to-business.

81 C. Measurements Input Power vs Output Power

Measurements done on the boost conveter, with the IRF4620 MOSFET. The losses in the driver are 0,2W and are not yet substracted.

D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,44 64,20 0,32 200,6 21,85 20,54 1,31 94,02% 55,00 0,48 70,70 0,35 202,0 26,40 24,75 1,66 93,73% 60,00 0,52 77,00 0,38 202,6 31,32 29,26 2,06 93,42% 65,00 0,57 83,40 0,42 198,6 36,79 35,03 1,76 95,21% 70,00 0,61 89,80 0,44 204,1 42,56 39,51 3,05 92,84% 30% 50,00 0,60 75,20 0,36 208,9 30,15 27,07 3,08 89,79% 55,00 0,66 82,50 0,41 201,2 36,41 33,83 2,59 92,90% 60,00 0,72 90,00 0,45 200,0 43,20 40,50 2,70 93,75% 65,00 0,78 97,50 0,49 199,0 50,57 47,78 2,80 94,47% 70,00 0,84 105,00 0,53 198,1 58,66 55,65 3,01 94,87% 40% 50,00 0,87 90,20 0,46 196,1 43,50 41,49 2,01 95,38% 55,00 0,95 99,20 0,51 194,5 52,25 50,59 1,66 96,83% 60,00 1,03 108,10 0,55 196,5 61,80 59,46 2,35 96,21% 65,00 1,12 116,90 0,61 191,6 72,61 71,31 1,30 98,21% 70,00 1,20 125,80 0,65 193,5 83,93 81,77 2,16 97,43% 50% 50,00 1,06 100,20 0,49 204,5 53,00 49,10 3,90 92,64% 55,00 1,17 110,20 0,54 204,1 64,35 59,51 4,84 92,48% 60,00 1,28 120,50 0,61 197,5 76,50 73,51 3,00 96,08% 65,00 1,38 130,50 0,65 200,8 89,70 84,83 4,87 94,57% 70,00 1,49 140,70 0,70 201,0 104,30 98,49 5,81 94,43% 60% 50,00 1,62 124,30 0,62 200,5 80,85 77,07 3,78 95,32% 55,00 1,78 136,90 0,69 198,4 97,96 94,46 3,49 96,43% 60,00 1,94 149,40 0,75 199,7 116,64 111,75 4,89 95,81% 65,00 2,10 161,80 0,81 199,8 136,50 131,06 5,44 96,01% 70,00 2,27 174,50 0,87 200,6 158,90 151,82 7,09 95,54% 70% 50,00 2,86 165,80 0,83 199,8 142,95 137,61 5,34 96,27% 55,00 3,15 182,60 0,91 200,7 173,25 166,17 7,08 95,91%

82 D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,80 61,80 0,63 98,4 40,23 38,81 1,42 96,47% 55,00 0,88 68,05 0,69 98,3 48,65 47,09 1,55 96,80% 60,00 0,96 74,30 0,76 98,3 57,90 56,17 1,73 97,01% 65,00 1,04 80,54 0,82 98,3 67,97 65,96 2,00 97,05% 70,00 1,12 86,83 0,88 98,3 78,84 76,67 2,17 97,25% 30% 50,00 1,05 70,68 0,72 98,2 52,75 50,89 1,86 96,47% 55,00 1,16 77,82 0,79 98,5 63,83 61,48 2,35 96,32% 60,00 1,26 84,92 0,86 98,7 75,90 73,03 2,87 96,22% 65,00 1,37 92,13 0,94 98,3 89,35 86,33 3,02 96,62% 70,00 1,47 99,27 1,01 98,3 103,48 100,26 3,22 96,89% 40% 50,00 1,43 82,51 0,84 98,2 71,85 69,31 2,54 96,46% 55,00 1,58 90,87 0,93 98,2 86,98 84,05 2,93 96,64% 60,00 1,72 99,18 1,00 99,2 103,50 99,18 4,32 95,83% 65,00 1,87 107,61 1,10 98,1 121,79 118,05 3,74 96,93% 70,00 2,01 115,85 1,18 98,2 141,28 136,70 4,58 96,76% 50% 50,00 2,06 99,18 1,01 98,5 103,20 99,87 3,33 96,78% 55,00 2,27 109,20 1,11 98,5 124,99 121,10 3,88 96,89% 60,00 2,48 119,17 1,21 98,4 148,86 144,31 4,55 96,95% 65,00 2,68 129,07 1,31 98,4 174,50 169,34 5,16 97,04% 70,00 2,90 139,03 1,42 98,0 203,30 197,28 6,02 97,04% 60% 50,00 3,20 123,90 1,26 98,3 160,45 156,24 4,21 97,37%

83 D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,80 61,80 0,63 98,4 40,23 38,81 1,42 96,47% 55,00 0,88 68,05 0,69 98,3 48,65 47,09 1,55 96,80% 60,00 0,96 74,30 0,76 98,3 57,90 56,17 1,73 97,01% 65,00 1,04 80,54 0,82 98,3 67,97 65,96 2,00 97,05% 70,00 1,12 86,83 0,88 98,3 78,84 76,67 2,17 97,25% 80,00 1,30 98,70 1,03 95,5 104,32 102,00 2,32 97,77% 90,00 1,46 111,10 1,16 96,1 131,40 128,39 3,01 97,71% 100,00 1,63 123,80 1,30 95,5 163,00 160,57 2,43 98,51% 110,00 1,81 136,20 1,43 95,2 198,55 194,90 3,65 98,16% 120,00 1,97 148,50 1,57 94,9 236,88 232,40 4,48 98,11% 30% 50,00 1,05 70,68 0,72 98,2 52,75 50,89 1,86 96,47% 55,00 1,16 77,82 0,79 98,5 63,83 61,48 2,35 96,32% 60,00 1,26 84,92 0,86 98,7 75,90 73,03 2,87 96,22% 65,00 1,37 92,13 0,94 98,3 89,35 86,33 3,02 96,62% 70,00 1,47 99,27 1,01 98,3 103,48 100,26 3,22 96,89% 80,00 1,73 113,30 1,19 95,1 138,40 135,05 3,35 97,58% 90,00 1,95 127,70 1,34 95,4 175,32 170,99 4,33 97,53% 100,00 2,16 141,90 1,49 95,2 216,17 211,43 4,74 97,81% 110,00 2,39 156,40 1,65 95,1 262,35 257,28 5,07 98,07% 120,00 2,61 170,90 1,80 95,0 312,96 307,45 5,51 98,24% 40% 50,00 1,43 82,51 0,84 98,2 71,85 69,31 2,54 96,46% 55,00 1,58 90,87 0,93 98,2 86,98 84,05 2,93 96,64% 60,00 1,72 99,18 1,00 99,2 103,50 99,18 4,32 95,83% 65,00 1,87 107,61 1,10 98,1 121,79 118,05 3,74 96,93% 70,00 2,01 115,85 1,18 98,2 141,28 136,70 4,58 96,76% 80,00 2,35 132,00 1,39 95,0 187,76 183,35 4,41 97,65% 90,00 2,64 148,40 1,56 95,0 237,69 231,80 5,89 97,52%

84 Measurements done with the STF20NF20 MOSFET D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,80 61,30 0,62 98,7 39,75 38,07 1,68 95,77% 55,00 0,87 67,20 0,68 98,4 48,02 45,90 2,12 95,59% 60,00 0,94 72,60 0,74 98,8 56,34 53,36 2,98 94,71% 65,00 1,04 80,00 0,81 98,9 67,28 64,72 2,55 96,20% 70,00 1,12 86,30 0,87 98,9 78,05 75,34 2,71 96,53% 30% 50,00 1,06 70,60 0,72 98,6 52,95 50,55 2,40 95,47% 55,00 1,17 77,80 0,79 98,8 64,08 61,29 2,78 95,65% 60,00 1,27 84,90 0,86 98,6 76,38 73,10 3,28 95,70% 65,00 1,38 92,20 0,93 98,7 89,70 86,11 3,59 96,00% 70,00 1,49 99,20 1,01 98,6 104,09 99,80 4,29 95,87% 40% 50,00 1,47 83,42 0,85 98,3 73,30 70,78 2,52 96,56% 55,00 1,61 91,65 0,93 98,3 88,77 85,42 3,35 96,22% 60,00 1,76 100,00 1,02 98,3 105,54 101,78 3,76 96,44% 65,00 1,91 108,49 1,10 98,2 124,09 119,85 4,24 96,59% 70,00 2,06 116,75 1,19 98,1 143,92 138,93 4,99 96,53% 50% 50,00 2,10 100,11 1,02 98,4 104,80 101,81 2,99 97,15% 55,00 2,30 110,03 1,12 98,3 126,67 123,12 3,54 97,20% 60,00 2,51 119,92 1,22 98,4 150,66 146,18 4,48 97,03% 65,00 2,73 129,86 1,32 98,1 177,19 171,93 5,26 97,03% 70,00 2,94 139,70 1,43 97,9 205,66 199,35 6,31 96,93% 60% 50,00 3,29 124,29 1,27 98,0 164,60 157,60 7,00 95,75%

85 D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,80 61,30 0,62 98,7 39,75 38,07 1,68 95,77% 55,00 0,87 67,20 0,68 98,4 48,02 45,90 2,12 95,59% 60,00 0,94 72,60 0,74 98,8 56,34 53,36 2,98 94,71% 65,00 1,04 80,00 0,81 98,9 67,28 64,72 2,55 96,20% 70,00 1,12 86,30 0,87 98,9 78,05 75,34 2,71 96,53% 80,00 1,31 99,00 1,03 96,1 104,88 101,97 2,91 97,23% 90,00 1,47 111,20 1,17 95,3 132,57 129,77 2,80 97,89% 100,00 1,64 123,70 1,30 95,4 163,70 160,44 3,26 98,01% 110,00 1,80 136,30 1,43 95,3 198,44 194,91 3,53 98,22% 120,00 1,97 148,70 1,56 95,3 236,40 231,97 4,43 98,13% 30% 50,00 1,06 70,60 0,72 98,6 52,95 50,55 2,40 95,47% 55,00 1,17 77,80 0,79 98,8 64,08 61,29 2,78 95,65% 60,00 1,27 84,90 0,86 98,6 76,38 73,10 3,28 95,70% 65,00 1,38 92,20 0,93 98,7 89,70 86,11 3,59 96,00% 70,00 1,49 99,20 1,01 98,6 104,09 99,80 4,29 95,87% 80,00 1,73 113,40 1,19 95,3 138,45 134,95 3,50 97,47% 90,00 1,95 128,00 1,34 95,2 175,86 172,03 3,83 97,82% 100,00 2,17 142,20 1,49 95,2 216,90 212,30 4,60 97,88% 110,00 2,39 156,70 1,65 95,1 263,23 258,08 5,15 98,05% 120,00 2,61 170,50 1,80 95,0 313,08 306,05 7,03 97,75% 40% 50,00 1,47 83,42 0,85 98,3 73,30 70,78 2,52 96,56% 55,00 1,61 91,65 0,93 98,3 88,77 85,42 3,35 96,22% 60,00 1,76 100,00 1,02 98,3 105,54 101,78 3,76 96,44% 65,00 1,91 108,49 1,10 98,2 124,09 119,85 4,24 96,59% 70,00 2,06 116,75 1,19 98,1 143,92 138,93 4,99 96,53% 80,00 2,40 133,40 1,40 95,3 191,84 186,76 5,08 97,35% 90,00 2,70 150,10 1,58 95,1 242,91 236,86 6,05 97,51%

86 Measurements done with the IRFU220NPBF MOSFET D Vin Iin Vout Iout Rload Pin Pout Ploss η 20% 50,00 0,79 61,10 0,62 99,0 39,40 37,70 1,70 95,68% 55,00 0,87 67,30 0,68 98,8 47,74 45,83 1,91 96,00% 60,00 0,95 73,50 0,74 98,9 56,88 54,61 2,27 96,01% 65,00 1,03 79,70 0,81 99,0 66,76 64,16 2,60 96,11% 70,00 1,11 85,90 0,87 99,0 77,49 74,56 2,93 96,22% 30% 50,00 1,04 69,40 0,71 98,3 51,80 49,00 2,80 94,59% 55,00 1,14 76,80 0,78 98,8 62,65 59,67 2,97 95,26% 60,00 1,25 84,00 0,85 98,9 74,70 71,32 3,38 95,47% 65,00 1,35 91,00 0,92 99,0 87,62 83,63 3,99 95,45% 70,00 1,45 98,10 0,99 99,0 101,71 97,22 4,49 95,58% 40% 50,00 1,41 80,70 0,82 98,3 70,40 66,25 4,15 94,11% 55,00 1,55 89,50 0,91 98,9 85,31 81,00 4,31 94,95% 60,00 1,69 97,80 0,99 99,0 101,64 96,63 5,01 95,07% 65,00 1,84 105,90 1,07 98,9 119,28 113,42 5,86 95,09% 70,00 1,98 114,00 1,15 98,9 138,32 131,44 6,88 95,03% 50% 50,00 2,03 97,53 0,99 98,3 101,45 96,75 4,70 95,37% 55,00 2,23 106,85 1,09 98,3 122,38 116,18 6,20 94,94% 60,00 2,42 115,97 1,18 98,3 145,08 136,84 8,24 94,32% 65,00 2,60 124,16 1,27 98,0 169,07 157,31 11,75 93,05% 70,00 2,79 133,04 1,36 97,8 195,51 180,93 14,58 92,54%

87 D. Inductor Core Dimension and Calculation

Figure 34: Core dimensions 1

88 Figure 35: Core dimensions 2

89 Figure 36: Core dimension calculations

90 Figure 37: Ferrite speciﬁcations