Design and analysis of an IPT wireless system for electric vehicles

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POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell'Informazione

Corso di Laurea Magistrale in Ingegneria Elettrica

Design and Analysis of an IPT Wireless System

for Electric Vehicles

Relatore: Prof.ssa Maria Stefania Carmeli

Tesi di Laurea Magistrale di:

Anno Accademico 2016-2017

Massimo Pedretti

Isacco Simonini

Matr. n. 854333

Matr. n. 853924

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Summary

ABSTRACT (IT) ... 1

ABSTRACT (EN)... 2

INTRODUCTION ... 3

CHAPTER 1 - CAR RECHARGE ... 4

1.1 PLUG-IN RECHARGE ... 4

1.2 BATTERY SWAP ... 9

1.3 STATE OF THE ART ... 10

1.3.1 GENERAL CONFIGURATION ... 12

1.3.2 V2G ... 15

1.3.3 STATIC OR DYNAMIC ... 16

1.4 COMPARISON BETWEEN WIRELESS AND CABLE RECHARGE OF EVs .. 16

1.5 APPLICATIONS IN REAL WORLD ... 20

CHAPTER 2 - CONFIGURATION ANALYSIS ... 24

2.1 FULL DIODE BRIDGE RECTIFIER ... 25

2.2 GENERAL CASES ... 31

2.2.1 FINAL CONSIDERATIONS ... 63

CHAPTER 3 - APPLICATION ANALYSIS ... 64

3.1 PAD DESIGN ... 67

3.2 APPLICATION ... 70

3.3 FROM MAXWELL TO SIMULINK ... 77

3.4 RESULTS ... 87

CHAPTER 4 - INVERTER LOSSES... 93

4.1 CONDUCTION LOSSES ... 94

4.1.1 VALIDATION OF CONDUCTION LOSSES MODEL ... 96

4.2 SWITCHING LOSSES ... 105

4.2.1 VALIDATION OF SWITCHING LOSSES MODEL ... 110

CONCLUSIONS ... 128

Annex A ... 130

Annex B ... 132

Annex C ... 145

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A

BSTRACT (IT)

Lo scopo del lavoro di tesi è quello di presentare l’analisi e lo studio di un sistema di ricarica wireless per veicoli elettrici. L’aspetto innovativo risiede nel fatto che: non solo verrà analizzata una condizione di ricarica statica ma anche quasi dinamica, con l’obiettivo di liberare così gli automobilisti dalle lunghe soste dovute dalla completa scarica della batteria del veicolo. Dopo un breve capitolo introduttivo relativo allo stato dell’arte delle diverse tecniche di ricarica, il progetto di tesi si divide in tre principali cardini. In primo luogo, nel secondo capitolo, vengono presentate diverse configurazioni che descrivono applicazioni studiate in diverse pubblicazioni scientifiche per la ricarica statica caratterizzate da un ampio range di frequenza e potenza. Successivamente, il terzo capitolo si concentra sulla creazione e sullo studio di un sistema di controllo in ambiente Matlab per la ricarica quasi statica e rappresenta il vero cuore del lavoro svolto. La maggior parte delle configurazioni descritte in precedenza sono risultate essere di difficile realizzazione e modellizzazione di conseguenza una sola è stata analizzata con maggiore dettaglio. Il sistema implementato è caratterizzato da un livello di potenza media contenuto, attorno a 4 kW trasmessi al carico. Infine un’attenzione particolare è stata posta, nel quarto capitolo, al calcolo delle perdite nell’inverter presente all’interno del sistema di ricarica, validando tali valori con differenti metodologie, incluso l’uso di simulazioni Simulink Simscape.

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A

BSTRACT (EN)

The aim of the thesis is to present the analysis and the study of a wireless recharge system for electric vehicles. The innovative aspect lies in the fact that: not only a static recharging procedure is described but also a quasi-dynamic one, with the goal of releasing the drivers from the long stops due to complete discharge of the vehicle battery. After a brief introduction about the state of the art for charging techniques, the project is divided into three main topics. Firstly, in the second chapter, several static recharge configurations, coming from scientific publications, are described. They are characterized by a wide frequency and power range. The second part, developed in the third chapter, is focused on the creation and study of a Matlab control system for a quasi-dynamic recharge, this is the real core of the realized work. Most of the previously described configurations resulted to be unfeasible and difficult to model, consequently only a reference arrangement has been developed in deeper details. The implemented system is characterized by a contained mean power level, around 4 kW delivered to the load. In the end, particular care has been given to the computation of the recharging system inverter losses, validating each value with different methods, including Simulink Simscape simulations.

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I

NTRODUCTION

The electricity demand is continuously growing around the world thanks to the evolution of technologies and the huge diffusion of electronic components in household environments in the last decades.

Moreover, thanks to an increasing consideration of public opinion, also allowed by the possibility of reaching information easily using modern mass media such as internet, the problem concerning environmental pollution has been put into the foreground.

Increased awareness for our planet’s issues, decreased costs of electronic components and European commission incentives to fulfill goals as 20-20-20 targets led to realizing projects involving electric mobility. The main goal in these ventures was to reduce the emissions of CO2 and NOx in the atmosphere, achieving ideally a zero-emission transport. Moreover

there is a significant economical convenience in using electricity instead of fuel whose price is very unstable.

As a result, different car manufacturers started an important set of researches in the field. One of the leaders at present times in this field is Tesla Motors with its Model S, followed closely in the last years also by the biggest manufacturers around the globe, such as Renault, BMW and Volkswagen.

However, Italy is in some way in delay with respect to many other developed European countries and the diffusion of electric vehicles is slower even if still growing. One of the major reasons is the complexity of our regulation which does not provide a suitable way to define an installation plan of charging spots in a homogenous way all over the country. Private investors have to face the “zone a fallimento di mercato”, characterized by a low density of electric vehicles that won’t be able to generate any profit. This generates a vicious cycle where the low number of chargers does not incentivize the diffusion of electric vehicles and private investors will not repay their investments and therefore won’t feel incentivized to install new charging stations.

The increasing number of electric vehicles, the continuous seeking for more advanced technologies that can improve people lifestyle and create a better world for future generations, as well as the need to make available new businesses to increase profits, define the scenario in which this thesis is going to be developed.

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Chapter

1

C

AR RECHARGE

Electric vehicles need to be recharged once the battery is empty just like it happens with traditional cars with gasoline in their tanks. There are different ways to reach this target, some more high-tech than others.

1.1 PLUG-IN RECHARGE

For what concerns the technology nowadays applied in recharging electric vehicles it is possible to notice that the most widespread is the plug-in mode. In this application users are required to park in the proximity of the recharger and connect a cable to the car in a way as for filling the oil tank in traditional vehicles.

In Europe, four different models of recharger have been defined by standard IEC 61851-1.  Mode 1: it refers to a slow recharging method operated with an alternate current of 16 A. It takes around 6 to 8 hours for a complete charge. This type of recharging is allowed only in domestic areas and performed through a domestic socket or eventually an industrial one.

 Mode 2: it refers to a slow charging method operated with an alternate current of 16 A. It takes around 6 to 8 hours for a complete charging cycle. It can be performed either in public or private areas making use of industrial sockets. Differently to Model 1, on the charging cable a control device named Control Box is present. Its purpose is to ensure a correct operation during the charging phase.  Mode 3: it refers to both slow charging method operated with an alternate current

of 16 A, that takes 6 to 8 hours, and fast charging method operated with an alternate current of 63 A and voltage of 400 V, that takes 30min to 1h for a complete charging. This type of recharging can be performed in both public and private areas with the constraint that specific connectors must be used.

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 Mode 4: it refers to a very fast recharging method that takes between 5 and 10 minutes. Differently from the previous three modes it makes use of a 200 A DC current, with a voltage level of 400 V. This type of recharging can be applied only in public areas and the battery charger is designed to be necessarily outside the vehicle, generally inside a dedicated recharging tower.

The standards distinguish also specific cable designs that may be used for the recharging operation. It is possible to identify:

 Type A: the cable is permanently connected to the vehicle;

 Type B: the cable is connected neither to the vehicle nor to the charger;  Type C: the cable is permanently connected to the charger.

For what concerns connectors’ designs, it is necessary to refer to standards, in this case the most relevant is IEC 62196. It identifies four different types of plugs:

1. Type 1 (Yazaki connector, North America)

Fig. 1.1 – Type 1 recharge plug

It is based on SAE J1772 automotive plug specification and then standardized for charging with single phase AC. It is characterized by a round housing and five pins for the two AC wires, earth, and two signal pins [Fig. 1.1].

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2. Type 2 (Mennekes connector, Europe)

It is based on

VDE-AR-E 2623-2-2

plug specification and then standardized as single and three phase vehicle coupler [Fig. 1.2].

3. Type 3

It reflects the

EV Plug Alliance

proposal. It is possible to distinguish between two different configurations of connectors: type 3a [Fig. 1.3] and type 3b [Fig. 1.4].

 Type 3a

Fig. 1.3 – Type 3a recharge plug

It has been standardized as single phase coupler. It operates with an alternate voltage of 250 V and with a current of 16 A. It is designed with four pins for the two AC wires, the ground, and one signal pin [1].

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 Type 3b

Fig. 1.4 – Type 3b recharge plug

It has been standardized as both single and three phase coupler. In single phase operation it performs the recharge with alternate voltage of 250 V and current of 16 A. In three phase operation it has been designed for alternate voltage of 480 V and 63 A of current. It is characterized by seven pins: the three phases, the neutral, the ground and two signal pins [2].

4. Type 4

It is based on Japan Electric Vehicle Standard (JEVS) G105-1993 specifications. It has been standardized as direct current coupler first and then used for DC Fast Charging operation. It is designed to manage voltage levels up to 500 V DC and currents around 125 A [Fig. 1.5].

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 Type 4bis – Supercharger

In the last years, improvements were made for what concerns DC charging [Fig. 1.6]. Tesla Motors has introduced in 2012 a 90 kW DC charging system called Supercharger [3].

Fig. 1.6 – Type 4bis recharge system, Tesla solution

The system has been upgraded in 2013 reaching 120 kW of DC power. Moreover, Tesla makes use of modified type 2 plugs. This modified connector allows for deeper insertion and longer conductor pins, allowing greater currents. There is no need for additional DC pins because DC current can flow using the same pins as AC current.

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1.2 BATTERY SWAP

It is possible to recognize in the previous lines one of the greatest disadvantages of EVs: the recharging procedure can take up to hours to be completed. An alternative approach in order to speed up the “refueling” is called “battery swap” [Fig. 1.7] and consists of a physical substitution of the discharged battery with a fully charged one in a dedicated station [4]. This action can obviously eliminate the delay related to the waiting for the vehicle’s battery to be fully charged.

Fig. 1.7 – Instance of battery swap mechanism developed by Picchio Spa

Battery Swapping introduces different advantages to the electric vehicle sector. The main ones are:

 Fast battery swapping operation, it takes less than five minutes;

 Problems of limited driving range are solved where battery switch stations are available;

 Drivers do not get out the car during the replacement of the battery;

 Drivers do not own the battery and costs related to its management are transferred to the station company;

 Contract with battery switch company can subsidize the electric vehicle at a price lower than equivalent petrol cars;

 Spare batteries at swap stations could participate to grid services, enhancing the evolution towards smart grids.

However also severe drawbacks should be considered. The major issue is represented by the huge costs of the components needed to obtain an efficient switching station. Moreover, in order to perform battery swap it is necessary to have suitably designed cars since

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interoperability in battery swap technology is not assured in terms of battery access, attachment, dimension, location or type.

The first study involving battery swapping has been performed around 1896. However, the first application available for electric trucks was proposed by Hartford Electric Light Company through the General Vehicle Company (GeVeCo) battery service, between 1910 and 1924 .

In recent years the study had been picked up again by “Better Place” that has implemented the first modern application for battery swap, allowing a battery exchange in five minutes and opening this type of service also to private vehicles. However due to the enormous costs in charging and swapping infrastructure, the company failed in 2013. In June 2013, Tesla has announced that it is under research a new type of super-recharger that will allow an exchange of battery in 90 seconds, that is half of the time required to refill the tank of a traditional car. Focusing on the Italian scenario, it is important to mention “Picchio Spa” that in 2015 has developed a battery switching station characterized by low costs, able to manage 12 batteries and to perform a replacement in around 2 minutes.

1.3 STATE OF THE ART

The first objective is to find a way to replace the traditional conductive charging method already quite widespread in developed countries with a contactless station. Many are the advantages that can be underlined in switching from one technology to the other and they are going to be explained later on.

This need for innovation in transferring energy without plugs started in other fields, especially driven by sectors such as small technology and healthcare, even if military applications have been in the background all along. It came in the public automotive sector at the end of the XIX century with vehicles performing heavy duty cycles at first, through lighter duty cycle machines.

For the sake of knowledge, it is important to underline that speaking of Wireless Power Transfer (WPT) is somewhat generic since there is a number of different technologiesthat allow to transfer power contactless. They are classified in terms of distance between receiver and transmitter, keeping always a reasonable efficiency and amount of energy transferred per unit of time [5].

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Energy-carrying

medium

Technology Power Range Efficiency Comments

Electromagnetic field Near-field IPT Traditional

IPT High Low High

Range is too small for EV application. Magnetic Resonant IPT

High Medium High

Capable for EV charging.

Far-field

Laser,

Microwave High High High

Needs direct line-of-sight transmission path, large antennas and complex tracking mechanisms. Radio

wave High High Low

Efficiency is too low for EV charging.

Electric field Capacitive power

transfer Low Low High

Both power and range are too small for EV application. Mechanical

force Magnetic gear High Medium High

Capable for EV charging. Tab. 1.1 – Classification of WPT technologies

Since the goal of this study is to describe the application of WPT in recharging EVs, it is clear that laser, microwave, radio wave and capacitive power transfer are equally not feasible for different reasons. Taking into account the three remaining, it can be easily said that traditional Inductive Power Transfer (IPT) is not the solution of interest because of its reduced admitted range. Between Magnetic Gear and Magnetic Resonant IPT, the latter one results to be the preferred choice of manufacturers in this kind of application and will be also the main focus of this work. For the sake of clarity, if not explicitly specified otherwise, referring to WPT will be actually considered as referring to Magnetic Resonant IPT.

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1.3.1 GENERAL CONFIGURATION

The standard configuration of Magnetic Resonant IPT Systems, common to the potentially wide range of applications in terms of target vehicles, is a set of three main components arranged in different ways: supplying unit, transmitting unit and receiving unit [Fig. 1.8]. All of them are strictly regulated by a number of different control systems in order to provide the best performances of the overall system.

Fig. 1.8 – General configuration of a coupled magnetic resonant WPT system Let us now describe them some more in details [6].

SUPPLYING UNIT

There is a number of possible combinations but the constant among them is that the point of withdrawal is directly connected to the utility through a power rectifier which is then connected to an inverter. The reason to perform these two counter-actions is that the transmitting unit must work at a frequency that is very much different from the mains’. Not only the frequency, but also the voltage level required at DC bus might need to be changed from the value given as rectifier output. In such case an additional component, a DC/DC converter, is needed.

Actually, considering that rectifier and converter are on the ground and are well known technologies, it is not purpose of this paper to investigate about their behavior, therefore it is going to be considered the supply unit made of only the ideal DC voltage source and the inverter.

As already mentioned, the inverter output is characterized by very high frequency with respect to the mains, that is ranging from about 11 kHz to almost 100 kHz according to [7],

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[8], [9], [10]. Frequency also represents one of the greatest challenges in designing the inverter since it strongly influences the device’s power losses. In the following chapters detailed analysis of this issue will be carried on.

TRANSMITTING UNIT

Fig. 1.9 – Pads structure and position

The transmitting unit is basically composed of two pads which are two magnetically coupled coils, characterized by inductance (both self and mutual) and conductor resistance. In other words, it is a transformer with very low magnetic permeability of the core since the core itself is made of air. They are distinguished by their function: transmitter pad, known as track, and receiver pad, known as pick-up. As one can imagine, the track is placed on the ground and the pick-up on the vehicle [Fig. 1.9].

Concerning the coils, one must remember that traditional copper cables’ resistance characteristic is strongly influenced by variations of frequency. These power transmission applications deal with frequencies up to thousands of Hertz, therefore simple copper cables are surely not the proper choice. Such particular working conditions require the implementation of an advanced technology of cables called Litz wire [11]. The main issues in high frequency applications are the skin effect and the proximity effect, in order to reduce their impact, the conductor is divided into a number of thinner wire strands that are singularly insulated and twisted in predefined patterns.

The values of inductance are defined when the shape of the pads is decided. They are the result of a number of simulations performed with adequate simulating tools that provide the best trade-off between material costs and inductance values. To be considered the fact that track and pick-up may or may not be identical depending on the target range of consumers, that is, only light duty cycle vehicles (they are identical) or heavy-duty cycle vehicles as well (track must accommodate pick-ups of larger sizes as well).

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In the WPT described in this analysis, unlike it happens in traditional IPT technologies, both track and pick-up are supported by capacitors specifically designed to compensate the pads’ inductance. According to the position of these capacitors, they are going to affect differently the overall system. Also in this case, there will be a dedicated chapter for a detailed description.

The design of these pads is a major challenge in having the highest transmitting efficiency since cable resistance and compensation can limit the power throughput [12]. Resistance can be limited by increasing the cable section composing the coils, but also in that case it is to be considered the increase in size, weight and costs. Available space in the cockpit is very much restricted, therefore a trade-off is the best choice.

In describing the transmission of energy, of utmost importance is the fact that also physical characteristics regarding the relative position of the two pads influences the output power. In particular, misalignment and air-gap between pads are the main characteristics, even if a minor role is played also by the achieved parallelism between the surfaces. In terms of mutual coupling, it strongly worsens when these parameters increase. Less relevant but still worth mentioning, the shields’ thickness positioned behind each pad has negligible impact on the overall performance of the transmission unit even if it plays a major role in protecting nearby devices and living beings from the potentially very powerful magnetic field generated.

RECEIVING UNIT

This is the side of the system that is completely on board which includes the rectifier and the battery pack. Based on the considerations expressed before, one should remember that the receiving unit must fulfill some requirements of size, weight and shape compatible with the available space and payload in the vehicle.

The rectifier may be configured in multiple ways, even if the space constraint limits the wide range of possibilities at designers’ disposal. The goal of radically increasing the exchanged power is an issue in this device since it must be properly designed to support such power exchange. Of course, increasing the rated power means also to increase the size, which leads again to the same issue.

However, the most critical characteristic on this side is the battery pack. It represents one of the heaviest and most expensive components on the vehicle and with very specific technical requirements.

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1.3.2 V2G

Fig. 1.10 – V2G concept

In future applications, the idea is to achieve the implementation of a Vehicle-to-Grid (V2G) control system as well in order to provide services to the grid [13]. In that case, two main challenges can be identified [Fig. 1.10]:

 Implementing a communication technology which for sure carries some challenges, in order to make it compatible with the WPT technology, not influencing with its magnetic field all nearby signals;

 Designing a bidirectional receiver instead of a purely passive receiver, which increases the complexity of the system and consequently costs.

It is not the purpose of the thesis to describe it in deeper details, future works will be specifically dedicated to the subject.

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1.3.3 STATIC OR DYNAMIC

Fig. 1.11 – Dynamic and static WPTs, instances of application

Once the general configuration is clear, it is important to underline how WPT systems can be classified in terms of recharging condition [Fig. 1.11]. In particular, there have been studies describing the possibility to perform the recharge when the vehicle is either stationary or moving [14]. They both introduce researchers to major issues. Especially, it is easy to understand that the dynamic flavor is very challenging from the technical and cost points of view. As well as some great issues, also some quite important advantages can be pointed out.

To describe the most important advantages and disadvantages of these two types of resonant wireless power transfer there is going to be a dedicated section in this analysis in the following pages.

1.4 COMPARISON BETWEEN WIRELESS AND

CABLE RECHARGE OF EVs

Electric vehicles were reintroduced in the last few decades as a reaction to the environmental sensibility that we, as humans, developed. Moreover, the volatility of fuel prices and reduction of electricity bills made investments in this field more interesting. At the beginning, designers had to find a way to recharge the on-board batteries in a manner that could be comparable to the way we already fill the tanks of traditional cars or somehow even better. That was and still is a challenging target since at present, no EV storage can be charged as quickly as any internal combustion vehicle tank filling. The mean through

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which the recharging operation is performed consists of cables even if the industry is moving towards new technologies for a number of reasons. Let us describe the reasons why the Magnetic Resonance method will replace little by little cables, even considering its drawbacks.

It is possible to classify the reasons to perform the charging operation in innovative ways in two classes of issues: cable related dangers and battery related drawbacks.

First of all, considering cable related dangers, they can be intended either as technical or discomfort issues.

Concerning technical issues, they can be discussed:

 Electrical danger represented by insulation breakdown due to aging of the component, fulguration is a real possibility;

 The same security is endangered also by external events that could put at stake safety of the charging operation;

 Interoperability is not ensured in most of the cases, car manufacturers developed proprietary plugs;

 The electrical pins must be thoroughly cleaned from dust and debris in order to perform an optimal connection between car and recharging tower.

On the other hand, from an amenity point of view it can be said:  The cable is not aesthetic;

 It requires some manual actions that make it not very functional.

Considering the battery related issues, to be underlined is the fact that the specific energy of batteries, even the most technologically advanced once, as lithium-ion batteries are, is rather low with respect to gasoline, that is 0.3 MJ/kg against 47.5 MJ/kg respectively [15]. Moreover, they are characterized by higher cost, weight and size as well as slower charging time compared to the equivalent fuel tanks. For this reason, if developers were able to reduce the need for large battery packs, users would obtain great advantages from a number of viewpoints. The problem at this point would be that the reduction in size determines a reduction of driving hours available, sometimes to unfeasible levels.

To address both issues, it has been proposed the concept of WPT. As already mentioned two are the flavors of WPT: dynamic WPT and static WPT.

For the sake of knowledge, it shall be specified that dynamic WPT addresses both of the issues listed above. On the opposite, the stationary WPT only addresses cable related drawbacks since the recharging procedure is the same as in cable based operations, therefore large battery packs are still needed. Avoiding the use of a cable is anyway a

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fundamental step towards a more desirable EV integration in the future. Some great advantages can be underlined indeed:

 There is no more electrical exposure, now the transmitting mean is air and all electrical components are galvanically isolated. During a rainy day, the pins of a socket may get wet and discharge, putting at stake people safety. Pads and equipment are always well protected from the external environment;

 The driver is not required to perform any action in order to begin the recharge but stopping on a dedicated spot, therefore no specific physical skills are needed. It may happen that the driver is in a hurry, he won’t need to spend any time connecting cables or anything;

 The aging of transmitting mean is not a concern anymore. It is well proven that rubber, especially if subjected to harsh conditions such as a roadway under the sun and the rain, ages quickly, which means that the conductor may be exposed;  Interoperability can be ensured in most of the cases, but manufacturers must be

willing to participate.

Such technology is also characterized by some drawbacks:

 Low transmission efficiency. From theory, one may remember that transmission efficiency in transformers is quite high thanks to the ferrite cores that concentrate the magnetic flux. In this application, air replaces ferrite material, which has much higher magnetic permeability, thus much higher magnetic coupling between sides;  Fast worsening of charging efficiency in case the car is not perfectly positioned on

the charging spot. There is not a linear decrease of efficiency furthering from the optimal position of the track, it decreases according to a faster characteristic;  System complexity is increased and therefore costs are increased. As explained in

the previous paragraphs, there is a number of needed components in this transmission system as well as an effective control mechanism. Their design requires suitable technical skills and funding;

 It has limited flexibility. When the charging conditions vary, even by little, a radical upgrade of the system is required. For example, the compensating elements are designed for a specific condition, changing the inductance introduces some major issues;

 Some EMC concerns are to be considered that could affect both nearby devices and living beings. It is proven the fact that human exposures to strong magnetic fluxes has some relevant effects of its wellbeing as well as effects on the good operation of electronic devices.

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In any case, this thesis will focus on static or quasi-dynamic WPT systems, letting future works be concerned about dynamic WPT, also knowing that most of the considerations made here are valid for all flavors of WPT.

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1.5 APPLICATIONS IN REAL WORLD

It is necessary to specify that WPT recharge system for EVs is not simply a dream for the future but it is present reality. Many are the well-developed applications all over the world. The reader is now introduced to some examples of WPT already implemented both as prototypes and actual applications [5]. The first instances of this technology are listed below, they are mostly prototypes that go back in time.

Institute / corporation

Year of

Installation Location Project Type

Vehicle Type Power Air Gap Efficiency Auckland University & Conductix-Wampfler 1997 Auckland Public Demonstration (Stationary) 5 Golf buses 20kW 50mm 90-91% 2002-2003 Italy 8-23 mini buses 60kW 30mm - Auckland University & Qualcomm Halo

2010 Auckland Evaluation kits (Stationary) Private vehicles 3kW 180mm 85% 2012 UK Public Demonstration (Stationary/ Dynamic) - - - - ORNL 2010 US Prototype (Dynamic) - 4.2kW 254mm 92% (coil-to-coil) 2012 US Prototype (Stationary) - 7.7kW 200mm 93% (coil-to-coil) 2012 US Prototype (Stationary/ Dynamic) GEM EV 2kW 75mm 91% (coil-to-coil) KAIST 2009 Korea Prototype (Dynamic) Golf Bus 3kW 10mm 80% Bus 6kW 170mm 72% SUV 17kW 170mm 71% 2010 Korea Public Demonstration (Dynamic) Tram 62kW 130mm 74% 2012 Korea Bus 100kW 200mm 75% MIT WiTricity & Delphi 2010 US Commercial kits (Stationary) Private vehicles 3.3kW 180mm 90% Evatran 2010 US Commercial Product (Stationary) Private vehicles 3.3kW 100mm 90% Tab. 1.2 – Former applications of WPT systems and their characteristics

If not satisfied by the older applications to demonstrate that this is most likely to be the future way to recharge vehicles, some other examples can be produced in more details.

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PLUGLESS POWER, US

It is an American start-up in the energy business from 2012 with experience built in power transformers for industrial applications. Quoting the company itself, this is the reason why they succeeded in developing this wireless technology: “We come from the power business, not the car business. Wireless EV charging is all about power transfer.”

Plugless-enabled EVs have over 1 millionwireless charging hours with actual EV drivers under the belt [Fig. 1.12]. This firm doesn’t work on its own, it is involved in the development of wireless charging stations in the international scenario with Tesla Motors at the head of its partnerships [16].

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Not only new vehicles can be equipped with the technology required to perform wireless recharge, but also former vehicles can receive the upgrade. Such procedure has been undertaken for the Model S manufactured by Tesla Motors. In fact, Plugless is able to install the wireless equipment on Model S cars that were born at first without them in about 2 hours. This additional installation allows to have both cable and wireless recharge on-board at the same time [Fig. 1.13].

Fig. 1.13 – Plugless device installed on Tesla Model S

BUS WIRELESS CHARGING, Torino

Fig. 1.14 – WPT bus public transport in Torino

In order to face the problem of pollution and then to achieve an improvement of the air quality in the historical part of the city center, Torino has defined a ZTL zone where only authorized vehicles can circulate [Fig. 1.14]. In order to facilitate the transfer towards important points in the center, a public electric transport service has been introduced. This is a very important achievement since what usually happens is that municipalities don’t

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even consider the opportunity to undertake such projects with electric busses due to the wrong idea that prohibitive expenses are to be faced. For what concerns the viability of the project, it is of main importance an American study which compared the acquisition and energy costs of electric and diesel propulsion public vehicles for over 10 years, showing that the cost of an electric bus pays off in one to four years of operation. Moreover, the noise produced by an electric vehicle is sensibly less than a combustion engine one, as well as the vibrations, that are much reduced, not to mention emissions.

In Torino, STAR 1 line has been established in 2003 and in 2007 the service has been improved with the addition of a further line called STAR 2 line.

One problem already described before could be related to the limited autonomy of batteries. The issue has been addressed adding wireless charging points along bus routes. The wireless recharging process is based on IPT magnetic resonance coupling technology. Two charging points are placed at the end of each line and are able to charge the on-board batteries within 10-12 minutes allowing an operation from 7 am to 8 pm. However, the profitability of electric busses is increased by means of frequent charging cycles during the service. This allows to save money since smaller batteries can be adopted and designing lighter vehicles is possible. [17]

IHI Corp, Japan

This Japanese company advertises the availability of wireless charging stations as early as 2019. The product, developed jointly with US firm WiTricity Corp, is expected to recharge the battery of an EV as fast as a traditional charger does [18].

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Chapter 2

C

ONFIGURATION ANALYSIS

The Wireless Power Transfer (WPT) can be designed in different configurations

characterized by different performance and parameters.

The essential elements are the two coils that by means of magnetic field exchange

power [19], as shown in Figure 2.1.

Fig. 2.1 – Pad circuital structure

The consequent mutual coupling can be expressed as:

𝑀 =

𝑘

√𝐿

1

∙ 𝐿

2

(2.1)

 𝑘, coupling coefficient;

 𝐿

₁

, inductance of primary coil;

 𝐿

2

, inductance of secondary coil.

As already mentioned before, WPT systems are characterized by high frequency

switching power supply, full-bridge diode rectifier, full-bridge IGBT inverter,

transmission coils and load.

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2.1 FULL DIODE BRIDGE RECTIFIER

The full bridge diode rectifier is a power electronic device composed of four diodes with the goal of converting a sinusoidal input into an ideally constant output. Of course, one must face real world non-idealities.

In the configuration implemented in this kind of applications, a battery is connected to the output side. Such battery can be modeled using multiple equivalent circuits, in this analysis they have been considered two cases which are equally important for different reasons. They are either a simple resistor [Fig. 2.2], assuming a purely passive load, or a capacitor in parallel with a resistor [Fig. 2.5]. The Ideal AC Voltage source is instead representative of the transmitting unit up to the receiving pad.

Let’s analyze the behavior of these circuits in the following paragraphs.

PURE RESISTOR

Fig. 2.2 – Purely resistive load diode bridge rectifier

The input voltage is characterized by a sinusoidal voltage source that can be expressed as:

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The current is going to be sinusoidal accordingly and shown in Figure 2.3.

Fig. 2.3 – Voltage and current at AC side

To be noted from the load viewpoint the second half of the sinusoidal waveform is mirrored, as in Figure 2.4.

Fig. 2.4 – Rectified voltage and current, load side The output quantities of interest are:

 𝑖_𝑟 , resistor current (rectified current);  𝑣𝑜 , resistor voltage (load voltage).

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One can readily observe that the rectified current and voltage are far from constant, that is why the purely resistive model is very simple to implement but also not very attractive from the storage point of view.

Let’s consider different steps of operation of the rectifier using as reference the time, always greater than 0.

 For the range 0 < 𝜔𝑡 < 180° or, analogously, for 0 < 𝑡 <𝑇₂:

o Diodes 1 and 4 are directly polarized, therefore they are able to conduct, unlike it happens for diodes 2 and 3 that are reverse-biased.

o The load voltage follows the source: 𝑣_𝑜 = 𝑣_𝑠

o The current flowing through the resistance can be simply defined as: 𝑖𝑟 =

𝑣_𝑜 𝑅_𝑙 =

√2 ∙ 𝑉𝑠

𝑅_𝑙 𝑠𝑖𝑛(𝜔𝑡)

o At ωt = 90°, the voltage 𝑣_𝑜 results to be equal to the maximum value of 𝑣_𝑠:

𝑣_𝑜= √2 ∙ 𝑉𝑠  For 𝜔𝑡 > 180° or for 𝑇

2< 𝑡 < 𝑇:

o The two diodes that were conducting before now result to be reverse-biased and the current flowing through results to be null. The other two diodes (2 and 3) are conducting:

𝑖_𝐷1= 𝑖_𝐷4= 0 𝑖_𝐷2= 𝑖_𝐷3> 0

o Since the two conducting diodes are diodes 2 and 3, voltage at load side is reversed with respect to the source, hence:

𝑣_𝑜= −𝑣_𝑠

o Accordingly, the current flowing through the resistance results to be equal to:

𝑖_𝑟 =𝑣𝑜 𝑅𝑙 =

−𝑣𝑠

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But since the direction is opposite to what it was in the previous situation, at load side both voltage and current waveforms are inverted as shown in Figure 2.4.

 After 𝜔𝑡 > 360°, the cycle starts again.

CAPACITOR AND RESISTOR

Fig. 2.5 – Resistive and capacitive load

As said, the input voltage is characterized by a sinusoidal voltage source that can be expressed as (2.2).

The current is going to follow the characteristic depicted in Figure 2.6.

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To be noted, from the load viewpoint the second half of the sinusoidal waveform is mirrored, as in Figure 2.7.

Fig. 2.7 – Rectified voltage and current, load side The output quantities of interest are:

 𝑖𝑟 , Resistor current;

 𝑖𝑐 , capacitor current;

 𝑖_{𝑟𝑒𝑐𝑡} , rectified current;  𝑣𝑜 , load voltage.

Let’s consider different steps of operation of the rectifier using as reference the time, always greater than 0.

 For the range 0 < 𝜔𝑡 < 90° or for 0 < 𝑡 < 𝑡₁: o The capacitor is charging and the result is:

𝑣𝑜= 𝑣𝑠

o The current flowing through the capacitor can be derived as: 𝑖_𝑐= 𝐶𝑑𝑣𝑜

𝑑𝑡 = 𝐶√2 ∙ 𝑉𝑠∙ 𝜔 𝑐𝑜𝑠(𝜔𝑡)

o The current flowing through the resistance can be simply defined as: 𝑖_𝑟 =𝑣𝑜

𝑅_𝑙 = √2 ∙ 𝑉𝑠

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o The rectified current 𝑖𝑟𝑒𝑐𝑡 can be obtained by the sum of the previous two

currents:

𝑖_{𝑟𝑒𝑐𝑡} = 𝑖_𝑐+ 𝑖_𝑟

 At the instant 𝜔𝑡 = 90° or for 𝑡 = 𝑡₁ :

o The voltage 𝑣_𝑜 will result to be equal to the maximum value of 𝑣_𝑠: 𝑣_𝑜= √2 ∙ 𝑉𝑠

 For 𝜔𝑡 > 90° or for 𝑡₁< 𝑡 < 𝑡₂:

o The capacitor is charged and the voltage 𝑣_𝑑 will result to be higher than 𝑣_𝑠: 𝑣_𝑜> 𝑣_𝑠

o The diodes result to be reverse-biased and the current 𝑖𝑟𝑒𝑐𝑡 results to be

null since the diodes will conduct only if directly polarized: 𝑖_{𝑟𝑒𝑐𝑡}= 0

o The charged capacitor will discharge through the parallel resistance and the voltage 𝑣_𝑜 results to be:

𝑣_{𝑜(𝑡>𝑡}₁₎= √2 ∙ 𝑉𝑠∙ 𝑒−𝑡−𝑡1𝜏

With τ, time constant, equal to:

𝜏 = 𝑅 ∙ 𝐶

o The current flowing through the resistance results to be equal to: 𝑖𝑟 =

𝑣_𝑜 𝑅_𝑙

o As already said, the capacitor is discharging through the resistance and then the current results to be:

𝑖_𝑐= −𝑖_𝑟  At point 𝑡 = 𝑡₂:

|𝑣_𝑠(𝑡₂)| = 𝑣_𝑜(𝑡₂) For this reason, the capacitor is charged again.

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o The current flowing through the capacitor can be defined by: 𝑖_𝑐= 𝐶𝑑𝑣𝑜

𝑑𝑡 o The current flowing through the resistance is:

𝑖_𝑟 =𝑣𝑜 𝑅𝑙

o The rectified current is defined as the sum of the previous two currents: 𝑖_{𝑟𝑒𝑐𝑡} = 𝑖_𝑐+ 𝑖_𝑟

Another important system element is the full bridge inverter. The description of this device is not reckoned necessary right now since it is given more space to its operation in the following chapter. On the opposite, the full bridge diode rectifier won’t be analyzed any further.

2.2 GENERAL CASES

Several parameters may impact on the transfer of power, such as: 1) the size, the shape and the distance between coils; 2) the resonant frequency; 3) the final load; 4) the type of connection in the two resonators.

In order to reduce the leakage inductances and maximize the transfer of power: capacitors are applied both on primary and secondary side and the operating frequency is chosen equal to the resonant frequency, defined the same for both primary and secondary sides. Compensation can achieve two main goals: compensation of the primary winding, allowing to minimize the VA rating of the supply and switching losses; compensation of the secondary winding, allowing to enhance the power transfer capability.

With these precautions, the current flowing on the transmitting coil will reach high values and a massive electromagnetic field is generated around the transmitting coil, the two coils will generate strong magnetic coupling resonance, delivering energy to the load with high efficiency.

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For what concerns the compensations that can be designed, it is possible to identify four main configurations according to the different compensation topology of transmission coils [8]:

1. Series-series (SS); 2. Series-parallel (SP); 3. Parallel-Series (PS); 4. Parallel-Parallel (PP).

The configuration structures are depicted below:

Fig. 2.8 – Circuit topologies Considering the following two main assumptions:

 Frequency remains constant, equal to nominal resonant frequency;

 The primary current is constant, which is normally the case in Magnetic Resonant IPT designs.

For each different configuration, it is possible to identify different features:

 A series-compensated primary is required to reduce the primary voltage to manageable levels for long track applications;

 A parallel-compensated primary is usually used to give a large primary current;  The series-compensated secondary can be represented by a voltage source [8] and

achieves no reflected reactance at the secondary resonant frequency;

 The parallel-compensated secondary is equivalent a current source [8], however it reflects a capacitive reactance at the secondary resonant frequency, that can be tuned out because it is independent of the load.

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Some problems in these configurations may arise in case of frequency or phase shift with changing load. In case of frequency shift, the system will not operate at nominal resonant frequency. In case of phase shift the desired primary current is not available when the required VA rating exceeds the capability of the selected power supply. Both these problems will not allow to deliver the required power at load side.

In order to improve the operation of the system, reducing problems associated with frequency variation or phase shift and in order to make the input voltage and current in phase at certain coupling and load conditions the idea is to achieve the primary Zero Phase Angle (ZPA). The basic operation is to define the primary capacitance in order to set to zero the imaginary component of the load impedance at secondary resonant frequency, compensating then both the primary inductance and the existing reflected impedance in series with the primary winding.

A key role in the design of this capacitance is then given by the selected primary and secondary compensation topology:

 The series-compensated secondary, as previously said, reflects no reactance at nominal frequency. To be noted that in a SS configuration the primary inductance can be tuned out by a series primary capacitance that is independent of either the magnetic coupling or the load, unlike it happens with PS configuration [8];  The parallel-compensated secondary reflects a load-independent capacitive

reactance at the nominal resonant frequency. On the primary side, the series tuning is dependent on the magnetic coupling but not the load, while the parallel primary tuning is dependent on both the magnetic coupling and the load [8].

From these considerations it is possible to identify SS as the best topology regarding primary resonance design since the primary capacitance results to be independent of both magnetic coupling and load.

However, the other compensation topologies must be taken into account for other reasons. In particular the SP compensation can be used to realize a double-sided LCC that could result not affected by load changing and mutual coupling, achieving ZVS and resulting a good solution for high power applications.

In the following part a few configurations are described. They represent the state of the art for WPT, as a matter of fact they derive from a bibliographical research performed on scientific documents. Taking in mind these general considerations they will be implemented in Simulink Simscape with the aim to validate the static wireless power recharging structures able to transfer higher power with respect to the present technologies.

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CONFIGURATION N. 1

Fig. 2.9 – Configuration Scheme

A Double Sided LCC [Fig. 2.9] is developed here [9] and it is characterized by the following settings:

General Parameters

DC Bus Voltage [V] 420

Frequency [Hz] 79000

IGBT Duty Cycle [%] 50

Primary Series Inductance [μH] 26.82 Primary Parallel capacitance [nF] 151.3 Primary Series capacitance [nF] 12.18 Secondary Parallel capacitance [nF] 151.3 Secondary Series capacitance [nF] 12.44 Secondary Series Inductance [μH] 26.82

Load parameters

Filter inductance L0 [μH] 10

Filter Capacitance C0 [μF] 10

Battery Nominal Voltage [V] 450

Transformer

Primary Leakage Inductance [mH] 0.2448 Secondary Leakage Inductance [mH] 0.2448

Mutual Inductance [mH] 0.1152

Tab. 2.1 – Configuration settings

As already explained in the previous paragraphs, in order to maximize the efficiency of transmission is important to achieve resonant conditions making use of series and parallel capacitors to compensate leakage and mutual inductances respectively.

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An important advantage of the LCC compensation is that the resonant frequency is almost independent from load and coupling coefficient. With this configuration a nearly unit power factor can be achieved for both the primary and the secondary converters in the whole range of coupling and load conditions and also high efficiency for the overall system can be achieved.

It has been implemented a compensation on the primary side composed by 𝐿𝑓1, 𝐶𝑓1 and 𝐶1;

and a compensation on the secondary side composed in the same way by 𝐿_𝑓2, 𝐶_𝑓2 and 𝐶₂.

Here the LCC parameters are defined as follows:

 𝐿

_𝑓1

∙ 𝐶

_𝑓1

=

_𝜔1 1 2

;

 𝐿

_𝑓2

∙ 𝐶

_𝑓2

=

_𝜔1 2 2

;

 𝐿

1

− 𝐿

𝑓1

=

_𝜔1 1 2_𝐶 1

;

 𝐿

₂

− 𝐿

_𝑓2

=

_𝜔1 22𝐶2

.

Where 𝜔1 and 𝜔2 represent the angular resonant frequency and they are equal to the

angular frequency 𝜔₀.

One of the main problems for what concerns WPT power transfer is represented by the losses. In order to minimize them, the idea is to achieve a Zero Voltage Switching (ZVS) for the primary side switching.

The primary side inverter is designed with 4 IGBTs. The parasitic output capacitance of the IGBTs will hold the voltage at zero during the turn-off phase. Then it is possible to identify that the losses during the switching off are very small. For what concerns the turn-on phase, it is necessary to take into account two main losses: 1) related to the diode reverse recovery; 2) related to the stored energy in the parasitic capacitances. In order to achieve ZVS, reducing losses, the system must be designed in a way that the body diode will conduct before the IGBTs, the IGBTs must be activated by a negative current. In other words, the full bridge converter must see an inductive impedance. To guarantee ZVS the turn off current must be large enough to discharge the junction capacitors within a certain dead-time, or analytically speaking:

𝐼_𝑜𝑓𝑓 ≥4 ∙ 𝐶𝑜𝑠𝑠∙ 𝑈𝐴𝐵,𝑚𝑎𝑥

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It is possible to identify:

 𝐶_𝑜𝑠𝑠 , junction capacitance;  𝑡𝑑 , dead-time;

 𝑈_𝐴𝐵,max , maximum input voltage.

Achieving this constraint, the current will result to be sufficiently high to charge the parasitic capacitances of IGBT1 and IGBT4 and discharge the ones of IGBT2 and IGBT3. In this way when IGBT2 and IGBT3 are turned-on after the dead-time, their cross-voltage will result to be zero.

In order to obtain this condition however a variation to capacitance 𝐶₂ must be performed with reference to the equation obtained before, in accordance to the process presented in [9].

Simulating the circuit, in accordance with the computed parameters, the following results are obtained [Fig. 2.10], [Fig. 2.11], [Fig. 2.12], [Fig. 2.13].

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Fig. 2.11 – Output Current and Voltage

Fig. 2.12 – Output Power

As it is possible to notice from the previous graphs and from literature, the rectifier device, as well the inverter device, is characterized by very high efficiency.

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Fig. 2.13 – Mean Output Power

The results obtained show that with this configuration it is possible to achieve a transmission of high amount of power, reaching a mean value around 50 kW and peaks close to 80 kW.

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CONFIGURAZIONE N.2

It is shown an LCL configuration [Fig. 2.14] characterized as follows:

Frequency [Hz] 25 740

Series Inductance [μH] 50

Series Resistance [mΩ] 30

Primary Parallel Capacitance [mF] 2 Secondary Parallel Capacitance [mF] 0.23

Load Resistance [Ω] 20

Transformer

Primary Self-inductance [μH] 31.6 Secondary Self-inductance [μH] 270 Coupling Coefficient [-] 0.216523

The Series-Parallel LC on the primary [Fig. 2.15] can be briefly described from a theoretical point of view [21].

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This type of configuration is used typically for induction heating and IPT applications. However, with only two compensating elements the LC configuration does not provide enough degrees of freedom in order to minimize switching losses and converter VA rating. Additionally, having such a limited freedom doesn’t allow a control of the track current that must result in an independent load as well as in a delivery of constant power to the pick-up side.

In more advanced applications it is possible to implement also the so called LCL- Compensation Double-Sided [22].

Fig. 2.16 – LCL double-sided scheme

A second coil is added in series on both primary and secondary sides [Fig. 2.16]. The choice of the inductance has the aim to reduce the inverter current harmonics. In this configuration the goal is to make the system work at unitary power factor. In order to obtain constant primary current operation, the idea is to design the filter inductances in order to resonate at the same resonant frequency of the wireless system.

As it is clear, this configuration is composed of more passive components than the others; on the other hand, it achieves a constant current operation, high efficiency at light loads and harmonics filtering capabilities. Additionally, the system can operate without current controller and it is not sensitive to misalignment, unlike LC-series topology.

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Inputs and outputs of the abovementioned circuit are listed [Fig. 2.17], [Fig. 2.18], [Fig. 2.19], [Fig. 2.20].

Fig. 2.17 – Input voltage and current

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Fig. 2.19 – Output power

Fig. 2.20 – Mean output power

As it can be deduced from the previous graphs, peak power output results to be about 15 kW during transient conditions and 12 kW in steady state. Speaking of mean power output, the circuit is dealing with more than 7 kW at steady state.

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CONFIGURATION N. 3

Fig. 2.21 – Circuit configuration

A SS configuration [Fig. 2.21] is here represented [23], characterized as follows:

Primary Series Resistor [mΩ] 132 Secondary Series Resistor [mΩ] 179 Primary Series Capacitance [mF] 0.097 Secondary Series Capacitance [mF] 0.365

Transformer

Primary Self-inductance [μH] 603 Secondary Self-inductance [μH] 160

Coupling Coefficient [-] 0.14

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Fig. 2.22 - SS input voltage and current

As it is possible to recognize, voltage and current waves after the inverter are in phase and Zero Current Switching is achieved thanks to the series capacitances whose purpose is to compensate the effect of the transmitting and receiving pads’ leakage inductances.

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Fig. 2.24 - SS output power

Fig. 2.25 - SS mean power output

Here, the steady-state condition provides a peak power output of almost 25 kW and, after a reasonable time quite less than 12 kW as mean value.

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CONFIGURATION N. 4

Fig. 2.26 – Circuit configuration

As Figure 2.26 shows, in this configuration the compensation capacitors are placed in parallel in both the primary and secondary sides. As already mentioned, a drawback of this choice is related to the presence of a low overall efficiency, low power factor due to the large harmonics level in the inverter’s currents arising because huge current spikes are generated during the commutation period [8].

A solution to this problem could be to add a L-filter to the inverter output, damping the spikes and consequently reducing the level of harmonics.

The PP configuration is characterized as follows:

Series Inductance [μH] 18

Primary Parallel Capacitance [mF] 2.28 Secondary Parallel Capacitance [mF] 2.42

Transformer

Primary Self-inductance [μH] 29.6 Secondary Self-inductance [μH] 26.9

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Fig. 2.27 – PP input voltage and current

As it is displayed in these graphs, voltage and current values after the inverter are in phase and Zero Current Switching is achieved thanks to the series capacitances that perform a compensation of the transmitting and receiving pads’ leakage inductances. However, differently from the previous configuration, these parameters are characterized by important spikes due to the presence of only parallel capacitors.

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Fig. 2.29 – PP power output

Fig. 2.30 – PP mean power output

In this case the previous graphs show peak power output of almost 35 kW during transient conditions and 30 kW in steady state.

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CONFIGURATION N. 5

In this configuration [Fig. 2.31], it has been implemented another Series-Series (SS) compensation [7]. The advantages of such choice have been expressed in the previous paragraph.

This compensation configuration is one of the most used, as a matter of fact, it allows to achieve a condition in which resonant frequency is almost independent of load and coupling coefficient. This will increase efficiency for all the possible load rate that will be applied. The setting parameters are defined as follows:

Primary Series capacitance [μF] 0.7121 Secondary Series capacitance [μF] 1.5429

Load Resistance [Ω] 1.25

Transformer

Primary Inductance [μH] 109

Secondary Inductance [μH] 50.7

Coupling Coefficient [-] 0.1598 Tab. 2.5 – Configuration settings

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The results obtained are reported in Figure 2.32, Figure 2.33, Figure 2.34, Figure 2.35 and Figure 2.36.

Fig. 2.32 – Input Current and Voltage

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Fig. 2.34 – Output Voltage and Current

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Fig. 2.36 – Mean Power Output

As it is possible to see the system is able to deliver a mean power around 160 kW, reaching instantaneous power peaks of 350 kW.

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CONFIGURATION N. 6

In this configuration [Fig. 2.37], it has been implemented a Series-parallel (SP) compensation [7]. The advantages and disadvantages of such choice have been expressed at the beginning of the chapter.

The settings parameters are defined as follow:

Primary Series capacitance [μF] 0.5842 Secondary Parallel capacitance [μF] 25.7 Primary Series Resistance [mΩ] 55 Secondary Series Resistance [μΩ] 60

Load Resistance [Ω] 1.25

Transformer

Primary Inductance [μH] 145.5

Secondary Inductance [μH] 3.22

Coupling Coefficient [-] 0.15985 Tab. 2.6 – Configuration settings

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The results obtained are reported in Figure 2.38, Figure 2.39, Figure 2.40, Figure 2.41 and Figure 2.42.

Fig. 2.38 – Voltage and Current Input

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Fig. 2.40 – Voltage and Current Output

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As it is possible to see the system is able to deliver a mean power around 160 kW, reaching peaks as high as 300 kW.

However important losses are suffered by the system. Not only conduction losses but also the inverter is characterized by high switching losses and, of course, the transmission step is accountable for a huge power drop.

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CONFIGURATION N. 7

Fig. 2.43 – Configuration circuit

The same circuit as in the previous case can be considered in a PS configuration [Fig. 2.43], characterized as follows [7]:

Primary Series Resistor [mΩ] 5 Secondary Series Resistor [mΩ] 600 Primary Parallel Capacitance [mF] 66.7 Secondary Series Capacitance [mF] 1.927

Load Resistance [Ω] 1.25

Transformer

Primary Self-inductance [μH] 3 Secondary Self-inductance [μH] 106.8

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Fig. 2.44 – Voltage and Current Input

The current in this solution is extremely high, which is one of the reasons the pure fashion of PS configuration is rarely implemented. Current spikes of 500 kA are unacceptable for any power electronics device.

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Fig. 2.46 – Power Output

Just as the previous case, the resulting peak power output of is about 400 kW and the mean power output is slightly more than 200 kW.

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CONFIGURATION N. 8

Fig. 2.48 – Configuration circuit

In Figure 2.48 a PP configuration is displayed again [7], characterized as follows:

Primary Series Resistor [mΩ] 14 Secondary Series Resistor [mΩ] 12 Primary Parallel Capacitance [mF] 59.2 Secondary Parallel Capacitance [mF] 58.3

Load Resistance [Ω] 1.25

Transformer

Primary Self-inductance [μH] 2.99 Secondary Self-inductance [μH] 3.02 Coupling Coefficient [-] 0.1631