**2. Specific economic indicators for the Central and Eastern Europe states**

On 1 May 2004, a total of eight applicant countries positioned in Central and Eastern Europe became full members of the EU. These were the Czech Republic, Slovakia, Slovenia, Hungary, Poland, Lithuania, Latvia and Estonia. In 2007, from 1 January, it was the time for Romania and Bulgaria to become new EU members and in 2013 Croatia gained the right to full mem‐ bership. Thus, an objective was achieved aiming to eliminate the principles of division between European countries imposed by historical agreements between great powers. The EU enlarge‐ ment eastwards followed important objectives regarding political stability in the region, maintaining democracy and peace, but also on the economic plan aimed to extend the common market among members. Thus, the EU economy has become the strongest economy in the world based on the most developed intra-community common market. At the moment of accession, the new member states are bringing their own contribution to the EU in terms of surface area and population, as shown in statistical data values presented in Table 1 (according to European Union, 2015), which includes information on the Central and Eastern Europe countries, values for the total surface area, number of inhabitants and Gross Domestic Product (GDP) recorded in 2014 [16].

**Table 1.** Statistical data regarding the countries of Central and Eastern Europe [1]

agglomerations. To perform an interdisciplinary analysis of rural areas in the EU, an overview is needed of what represents today this interstate union. It must be taken into account both political and economic criteria as well as the social impact achieved with the development programs realized and intended for these specific areas. The current stage was reached after several extensions by adopting new union members at different times. Thus, in 1973, the expanding included the U.K., Ireland and Denmark, and in 1981 Greece and Spain, with Portugal in 1986. In 1995, three European countries decided to enter the EU, these being Austria, Finland and Sweden. In 2004, it was registered the largest EU enlargement with the accession of 10 new members: Cyprus, Estonia, Latvia, Lithuania, Malta, Poland, Slovakia, Slovenia and Hungary which had at the date of accession a population of over 100 million inhabitants, according to European Union, 2015. The EU enlargement in 2004 increased the land area by approximately 23% and the number of inhabitants by about 20%. In 2007, from January 1, Bulgaria and Romania joined the EU, and in 2013 Croatia became the newest member state. By joining the EU, countries in Central and Eastern European continent opted for access in a community in which they have the opportunity of sustainable development for their economy. This development is possible through enhanced trade relations between union members, investments launch in key areas of the economy, creating new jobs and opportunity of labour movement within the EU to those countries that have opted to accept workers from Eastern countries. Significant funding were allocated from the EU budget for agriculture in order to enable farmers from Eastern countries to obtain better agricultural harvests on the cultivated areas and to improve the endowment with efficient equipment that could reduce working time, fuel consumption per surface unit and emitted pollutants into the environment. Farmers in the rural areas of Eastern European countries now have the opportunity to sell their products directly on the European market, thereby ensuring an improvement in their income levels and living standard. Therefore, joining the EU accounted for the countries of Central and Eastern Europe a unique opportunity, which ensured them the accelerated development of their economies and hence an increase of living standards for the population based on results in the economic branches. The political barriers between member states were eliminated, while assuring sustainable economic development that can ensure social benefits for the residents

Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

**2. Specific economic indicators for the Central and Eastern Europe states**

On 1 May 2004, a total of eight applicant countries positioned in Central and Eastern Europe became full members of the EU. These were the Czech Republic, Slovakia, Slovenia, Hungary, Poland, Lithuania, Latvia and Estonia. In 2007, from 1 January, it was the time for Romania and Bulgaria to become new EU members and in 2013 Croatia gained the right to full mem‐ bership. Thus, an objective was achieved aiming to eliminate the principles of division between European countries imposed by historical agreements between great powers. The EU enlarge‐ ment eastwards followed important objectives regarding political stability in the region, maintaining democracy and peace, but also on the economic plan aimed to extend the common market among members. Thus, the EU economy has become the strongest economy in the

of these areas [13, 17].

in the Knowledge Society

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In Figure 1 plotted dots show the situation of EU countries in Central and Eastern Europe by area.

**Figure 1.** The EU countries of Central and Eastern Europe surface [1].

**Figure 2.** The population of the EU countries of Central and Eastern Europe [1].

**Figure 3.** Values of GDP in 2000–2010 for Central and Eastern Europe countries [1]. (a) GDP in 2000. (b) GDP in 2004. (c) GDP in 2007. (d) GDP in 2010.

In Figure 2 are presented information about the population number, while Figure 3 shows the comparative GDP results recorded for the Eastern European countries in 2000, 2004, 2007, 2010 and 2014. Progressive growth of the GDP value can be observed for the majority of Eastern European countries in the years following EU accession compared to 2000 and even 2004. GDP regarded as a macroeconomic indicator provides information on the economic situation of the new EU member countries. Total amounts of GDP are presented in Figure 4 on each economy in part, from where it can be seen that Poland has the first position being the country with the largest economy in the region, followed by the Czech Republic, Romania and Hungary for top positions.

**Figure 4.** The 2014 GDP of the EU countries of Central and Eastern Europe [1].

**Figure 2.** The population of the EU countries of Central and Eastern Europe [1].

(c) GDP in 2007. (d) GDP in 2010.

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(a) (b)

Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

(c) (d)

**Figure 3.** Values of GDP in 2000–2010 for Central and Eastern Europe countries [1]. (a) GDP in 2000. (b) GDP in 2004.

In Figure 2 are presented information about the population number, while Figure 3 shows the comparative GDP results recorded for the Eastern European countries in 2000, 2004, 2007, 2010 and 2014. Progressive growth of the GDP value can be observed for the majority of Eastern European countries in the years following EU accession compared to 2000 and even 2004. GDP The values of exports and imports were also analysed as a percentage of GDP for each Eastern European economies in the period of 2000–2009 (Figure 5 and 6) to observe possible differences in these characteristics between EU pre-accession and post-accession of the Eastern economies. On graphical representations can be observed the values for each year where most countries have registered exports values close to 40%, except Slovakia, Hungary, the Czech Republic, Slovenia and Estonia who have approached or even exceeded the 80% threshold of GDP for exports.

**Figure 5.** Total values calculated for exports as a percentage of GDP (2000-2009) [1].

For the percentage values of imports achieved can be noticed as an average value of over 50% of GDP value over the analysed years, and some countries such as Slovakia, Estonia, Hungary,

**Figure 6.** Total values calculated for imports as a percentage of GDP (2000-2009) [1].

the Czech Republic and Bulgaria are close or even exceed the 80% of the GDP value. Also, using an important macroeconomic indicator, represented by gross national income (GNI), information can be obtained regarding the total income earned by residents of analysed countries and based on the obtained values a comparison can be accomplished regarding the purchasing power with direct implications for living standards in a particular country. Thus, GNI per inhabitant for the Eastern European countries was calculated, EU Members, for the period 2000–2009 and the results are shown in Figure 7. Visible differences between countries depending on the economy level of development can be observed, but the trend is upward for all 11 analysed countries since 2000, continuing with the EU accession years 2004 and 2007 and continuing until 2009.

**Figure 7.** Values calculated for GNI per inhabitant of Central and Eastern countries (2000–2009) [1].

Undoubtedly, the upward trend of GNI per each economy has been achieved as a result of the reforms carried out by each country as a result of the EU accession process, which has generated positive effects in their own economic branches.


**1. Introduction**

#### **1.1 History, main features, advantages and future of sodium-cooled fast reactors**

Since the very beginning of its commercial operation, immediately after the end of the Second World War, nuclear energy has been getting a significant and often increasing part in the production of safe, secure, and economic low carbon electricity.

Innovation has always been - and still is nowadays - a powerful engine for progress in the fields of regulation (also including the trans-national aspects of the emergency management), safety (with a specific care and attention paid to severe accident prevention and mitigation, e.g. through inherent and passive safety features), reliability and efficiency in design and operation (including reliability and independence of control systems), incineration of long-life by-products of the fission-conversion-breeding process, non-proliferation (uselessness of fuel materials for weapon production), environmental impact (to the air, the soil and the water, both in normal operation and in emergency), management of high and low activity wastes, and also in the very sensitive domain of the public-awareness and acceptance, which are the key-issues for the civil nuclear future [1, 2].

This trend has been even more reinforced after the Fukushima events, also accounting for the wide stress test campaign conducted worldwide, as well as the large effort for public information, participation, and inclusion carried-out by International Bodies, Governments, Constructors, Operators, Academia and Research Organizations [3].

Safety has undergone a continuous improvement effort and has been a relevant driving force for progress, improvement as well as research and development in different fields of endeavor for the current GEN III (Generation III) and GEN III+ (Generation III plus) reactor designs, but also for the advanced concept-designs both inside the GIF (Generation IV International Forum) framework and outside, and in complement to it, e.g. with the ever growing interest for the SMRs (Small Modular Reactors), small compact elementary modules, generally sizing from 10MWe to 300MWe, which are designed and engineered along with a modular construction approach enabling to combine them and incrementally extend the power capacity of the overall plant thus offering economy of scale and reducing both capital costs and construction time [4]. Designs with power outputs smaller than 10MWe, often designed for semiautonomous operation, have been referred to as Micro Modular Reactors (MMRs).

Today, facing the high investment needs and the ever increasing costs, the large delays in the licensing process and the construction, the highly expensive financing modes as well as the low public acceptance and sometimes even the fierce opposition of a majority of the population, some developed countries (mainly in the Western Europe, even if Europe in a whole lasts hosting the largest nuclear capacity of the world), have decided to either step out or phase out nuclear energy in a short-medium term.

Nevertheless, nuclear energy still enjoys an increasing and dynamic trend. The Year 2018 has even been a hit as for the installed new nuclear capacity, mainly because the interest for nuclear reactors has widely moved from developed to emergent - developing countries. This trend is to continue and even expand as, according

**243**

Japan (see **Figure 1**).

*International Benchmark Activity in the Field of Sodium Fast Reactors*

to the activity of the spent fuel for thousands of years.

to current estimations, the installed nuclear capacity should double in the emergent economies within the next 20years. Relying upon a robust industrial capacity, the Russian Federation is today by far the larger exporter/provider of nuclear technology worldwide, and the People Republic of China is on the way to become a future

In order to allow nuclear power contribute effectively to the solution of the global warming challenge in the future, it shall be necessary: to continuously up-date and improve regulations; to enhance the safety under the guidance of proactive, transparent and independent Safety Authorities; to establish suitable roadmaps providing all the actors in the nuclear field with a medium - long term clear vision, and to reduce overall costs through continuous improvement, harmonization of practices and standardization. But, mostly, it will be worth addressing and providing a longlasting and sustainable solution to the crucial problem of the long-lived wastes.

Today, the installed nuclear capacity is by far from GEN III reactors, only a few of them belonging to the GEN III+ generation (which includes, e.g., French EPR, American AP-1000, Russian VVER-1000 …), and even less to other concepts. During their operation, such reactors produce, as by-products of the fission-conversion-breeding process, a large quantity of long-lived isotopes, quoted as Actinides and/or Minor Actinides, depending on their features and nature, which contribute

The build-up of such by-products turns-out a major challenge both from the non-proliferation and the waste management viewpoint. Their recycling in the reactor fuel as well as their incineration through suitable strategies will contribute to "close the cycle", i.e., at least theoretically, to bring the spent fuel activity back to a level comparable to the natural earth radiation. The acceptance of the public of further installations of nuclear power plants will strongly depend in the future on

Fast reactors closed fuel cycle can efficiently and effectively contribute to the solution of the problem decreasing the burden of nuclear waste and supporting long-term nuclear power development as part of the world's future energy mix [5]. Global interest in fast reactors has been growing since their inception in 1960's because they can provide efficient, safe and sustainable energy. In addition to the current fast reactor construction projects underway, several countries are engaged in intense research and development programs for the development of innovative, Gen IV, fast reactor concepts, as proposed by the GIF. They include three fast neutrons concepts: the SFR - Sodium Fast Reactor -, the LFR - Lead (or Lead-Bismuth) Fast Reactor - and the GFR (Gas Fast Reactor), as well as the MSR (Molten Salt Reactor) which can be declined both in a thermal and a fast neutrons version.

Moreover, current developments of SMRs include, among the more than 100 versions under study, development and/or licensing, several fast neutrons concepts, even though the most mature ones are undoubtedly based on LWR (Light Water Reactor) technology. The fast SMRs, in addition to their efficient use of the fuel, are flexible because they can operate either as breeders, to produce fissile material, or as burners of Plutonium and/or long-lived Minor Actinides. Combining this capability with the benefits in terms of power generation flexibility, SMRs could turn-out quite attracting. The SFR is, by far, the fast reactor technology most widely spread-out worldwide. It enjoys an acknowledged maturity due to the numerous constructions and because it underwent many years of operation in several countries, from the late '60 prototypes up to the development and deployment of the industrial French fleet (including RAPSODIE, Phénix and Superphénix - the biggest fast reactor ever built, now decommissioned -, and the project ASTRID, now delayed), and other reactors now either in operation or under construction in Russia, India, China and

*DOI: http://dx.doi.org/10.5772/intechopen.97812*

leader in the nuclear field.

this crucial problem.

#### *International Benchmark Activity in the Field of Sodium Fast Reactors DOI: http://dx.doi.org/10.5772/intechopen.97812*

*Recent Advances in Numerical Simulations*

**1. Introduction**

electricity.

Research Organizations [3].

as Micro Modular Reactors (MMRs).

and emphasize how the application of developed procedures allows to validate the

**1.1 History, main features, advantages and future of sodium-cooled fast reactors**

Since the very beginning of its commercial operation, immediately after the end of the Second World War, nuclear energy has been getting a significant and often increasing part in the production of safe, secure, and economic low carbon

Innovation has always been - and still is nowadays - a powerful engine for progress in the fields of regulation (also including the trans-national aspects of the emergency management), safety (with a specific care and attention paid to severe accident prevention and mitigation, e.g. through inherent and passive safety features), reliability and efficiency in design and operation (including reliability and independence of control systems), incineration of long-life by-products of the fission-conversion-breeding process, non-proliferation (uselessness of fuel materials for weapon production), environmental impact (to the air, the soil and the water, both in normal operation and in emergency), management of high and low activity wastes, and also in the very sensitive domain of the public-awareness and

acceptance, which are the key-issues for the civil nuclear future [1, 2].

This trend has been even more reinforced after the Fukushima events, also accounting for the wide stress test campaign conducted worldwide, as well as the large effort for public information, participation, and inclusion carried-out by International Bodies, Governments, Constructors, Operators, Academia and

Safety has undergone a continuous improvement effort and has been a relevant driving force for progress, improvement as well as research and development in different fields of endeavor for the current GEN III (Generation III) and GEN III+ (Generation III plus) reactor designs, but also for the advanced concept-designs both inside the GIF (Generation IV International Forum) framework and outside, and in complement to it, e.g. with the ever growing interest for the SMRs (Small Modular Reactors), small compact elementary modules, generally sizing from 10MWe to 300MWe, which are designed and engineered along with a modular construction approach enabling to combine them and incrementally extend the power capacity of the overall plant thus offering economy of scale and reducing both capital costs and construction time [4]. Designs with power outputs smaller than 10MWe, often designed for semiautonomous operation, have been referred to

Today, facing the high investment needs and the ever increasing costs, the large delays in the licensing process and the construction, the highly expensive financing modes as well as the low public acceptance and sometimes even the fierce opposition of a majority of the population, some developed countries (mainly in the Western Europe, even if Europe in a whole lasts hosting the largest nuclear capacity of the world), have decided to either step out or phase out nuclear energy in a short-medium term. Nevertheless, nuclear energy still enjoys an increasing and dynamic trend. The Year 2018 has even been a hit as for the installed new nuclear capacity, mainly because the interest for nuclear reactors has widely moved from developed to emergent - developing countries. This trend is to continue and even expand as, according

SM results and validate the computer codes against experimental data.

**Keywords:** SFR, Benchmark, EBR-II, FFTF, CEFR, M&S tools

**242**

to current estimations, the installed nuclear capacity should double in the emergent economies within the next 20years. Relying upon a robust industrial capacity, the Russian Federation is today by far the larger exporter/provider of nuclear technology worldwide, and the People Republic of China is on the way to become a future leader in the nuclear field.

In order to allow nuclear power contribute effectively to the solution of the global warming challenge in the future, it shall be necessary: to continuously up-date and improve regulations; to enhance the safety under the guidance of proactive, transparent and independent Safety Authorities; to establish suitable roadmaps providing all the actors in the nuclear field with a medium - long term clear vision, and to reduce overall costs through continuous improvement, harmonization of practices and standardization. But, mostly, it will be worth addressing and providing a longlasting and sustainable solution to the crucial problem of the long-lived wastes.

Today, the installed nuclear capacity is by far from GEN III reactors, only a few of them belonging to the GEN III+ generation (which includes, e.g., French EPR, American AP-1000, Russian VVER-1000 …), and even less to other concepts. During their operation, such reactors produce, as by-products of the fission-conversion-breeding process, a large quantity of long-lived isotopes, quoted as Actinides and/or Minor Actinides, depending on their features and nature, which contribute to the activity of the spent fuel for thousands of years.

The build-up of such by-products turns-out a major challenge both from the non-proliferation and the waste management viewpoint. Their recycling in the reactor fuel as well as their incineration through suitable strategies will contribute to "close the cycle", i.e., at least theoretically, to bring the spent fuel activity back to a level comparable to the natural earth radiation. The acceptance of the public of further installations of nuclear power plants will strongly depend in the future on this crucial problem.

Fast reactors closed fuel cycle can efficiently and effectively contribute to the solution of the problem decreasing the burden of nuclear waste and supporting long-term nuclear power development as part of the world's future energy mix [5].

Global interest in fast reactors has been growing since their inception in 1960's because they can provide efficient, safe and sustainable energy. In addition to the current fast reactor construction projects underway, several countries are engaged in intense research and development programs for the development of innovative, Gen IV, fast reactor concepts, as proposed by the GIF. They include three fast neutrons concepts: the SFR - Sodium Fast Reactor -, the LFR - Lead (or Lead-Bismuth) Fast Reactor - and the GFR (Gas Fast Reactor), as well as the MSR (Molten Salt Reactor) which can be declined both in a thermal and a fast neutrons version.

Moreover, current developments of SMRs include, among the more than 100 versions under study, development and/or licensing, several fast neutrons concepts, even though the most mature ones are undoubtedly based on LWR (Light Water Reactor) technology. The fast SMRs, in addition to their efficient use of the fuel, are flexible because they can operate either as breeders, to produce fissile material, or as burners of Plutonium and/or long-lived Minor Actinides. Combining this capability with the benefits in terms of power generation flexibility, SMRs could turn-out quite attracting.

The SFR is, by far, the fast reactor technology most widely spread-out worldwide. It enjoys an acknowledged maturity due to the numerous constructions and because it underwent many years of operation in several countries, from the late '60 prototypes up to the development and deployment of the industrial French fleet (including RAPSODIE, Phénix and Superphénix - the biggest fast reactor ever built, now decommissioned -, and the project ASTRID, now delayed), and other reactors now either in operation or under construction in Russia, India, China and Japan (see **Figure 1**).

**Figure 1.** *World Sodium Fast Reactor Status.*

Design and operation of such reactors are demanding extended computation capacity, to assess their safety, security, and economics [6], which justifies the organization under IAEA's umbrella of Coordinated Research Projects (CRPs) aimed at improving Member States' fast reactor analytical simulation capabilities and international qualification through code-to-code comparison, as well as experimental validation on mock-up experiment results of codes currently employed in the field of fast reactors. NINE is very actively participating in these exercises, and sometimes conducting them.

The present chapter summarizes the results and discusses the main outcomes of the above-mentioned benchmark exercises, in the aim at underlying the wide convergence among the computational tools adopted by the participants, as well as detecting the main discrepancies and seeking for their common origin and trend, whether and whenever existing. That should enable defining a mid-term vision for further development of the computer codes in the field of fast reactors, whatever their features and nature, and identifying new needs for their extended validation against either available or expected experimental data.

#### **1.2 NINE involvement/interest in sodium-cooled fast reactors**

Starting from the considerations above regarding the deployment of fast reactors and the maturity gained by the SFR, NINE joints the effort of International community to assess the actual computational capabilities in modeling SFRs features. Taking advantage of reactor data gathered in full scale reactor demonstrators, NINE participated, and is still doing, in several International benchmarks aiming at demonstrating the applicability of its modeling methodology to Fast Reactor design and, in particular, to SFRs; to evaluate the level of assessment of computer codes available at NINE in respect to SFR specific features; to check the applicability of the NINE Validation Process – which is part of the more general framework of NEMM (NINE Evaluation Model Methodology)1 - with particular focus on the quantification of accuracies of the Thermal–Hydraulic (TH) simulations by means of Fast Fourier Transform Based Method (FFTBM) and finally to perform independent validation of the Serpent code.

All the analysis presented hereafter have been performed following a best estimate approach which requires, among the other things, a high-fidelity Simulation

**245**

*International Benchmark Activity in the Field of Sodium Fast Reactors*

**2. Analysis and validation of EBR-II SHRT-17**

Department of Energy at the Argonne-West site.

**2.1 The NEMM validation process**

*2.1.1 Overview of SCCRED methodology*

Best Estimate and Uncertainty applications.

of the performed code calculation;

input development;

Argonne's Experimental Breeder Reactor II (EBR-II) in the 1980's.

Model (SM), i.e., a SM that represents with a high level of detail the hardware subject of the analysis to avoid the introduction of inaccuracies due to rough

The IAEA CRP "Benchmark Analyses of EBR-II Shutdown Heat Removal Tests" was initiated in 2012 [7] with the objective of improving the state-of-the-art SFR codes by extending their validation to include comparisons against whole-plant data recorded during landmark Shutdown Heat Removal Tests (SHRT) conducted at

The EBR-II plant was a uranium metal-alloy-fuelled liquid-metal-cooled fast reactor designed and operated by Argonne National Laboratory (ANL) for the U.S.

Several loss of flow tests were conducted in the facility between 1984 and 1986, as a part of SHRT series [8]. SHRT-17, protected loss of flow transient, was one of the mentioned tests to demonstrate the inherent safety of LMR type reactors. At the beginning of the test, the primary pumps were tripped and at the same time a scram was actuated through a full control rod insertion. The effectiveness of natural circulation cooling capability of the reactor, which makes them inherently safe under described accident conditions, was successfully demonstrated by this test.

A key feature of the activities performed in the field of nuclear reactor safety is the need to demonstrate the validation level of each tool adopted within an assigned process and of each step of the concerned process. Therefore, the validation of best estimate codes, models, "best modeling practices" and uncertainty methods must be considered of great importance to ensure the validity of performed Best Estimate and Uncertainty analysis. A consistent code assessment supported by a qualified experimental database is an important step for developing a solid ground for the uncertainty evaluation in the frame of Best Estimate and Uncertainty approach. Thus, the SCCRED (Standardized and Consolidated Calculated & Reference Experimental Database) methodology [9], embedded in NEMM [10], has been developed to generate a series of documents and tools to set up a qualified experimental and calculated database for Verification and Validation (V&V) purposes of

**Figure 2** depicts the SCCRED diagram: the information contained in the experimental reports together with the code input nodalization are the sources to be elaborated in a systematic way by a qualified database made up of the following documents:

• The Reference Data Set for the selected facility or test (RDS-facility and RDStest) containing the information (geometrical data of the facility and boundary and initial conditions of the selected test, respectively) needed for the code

• The Validation Report (VR), which collects the results of the Validation Process

• The Engineering Handbook (EH), that describes the code input file and provides the engineering justifications of the code-user choices.

*DOI: http://dx.doi.org/10.5772/intechopen.97812*

approximations and assumptions.

<sup>1</sup> Within the NEMM (NINE Evaluation Model Methodology), NINE adopts the conventional and internationally acknowledged process to achieve the validation of computation tools and define the inherent uncertainties. It includes three steps: the analytical compliance test - the verification -, the qualification through code-to-code comparisons and benchmarks, the actual validation – supported by scaling analysis – on experimental data originating from mock-up experiments and the outcomes of the operating experience, including downgraded operation and emergency.

*Recent Advances in Numerical Simulations*

sometimes conducting them.

*World Sodium Fast Reactor Status.*

**Figure 1.**

Model Methodology)1

against either available or expected experimental data.

**1.2 NINE involvement/interest in sodium-cooled fast reactors**

Design and operation of such reactors are demanding extended computation capacity, to assess their safety, security, and economics [6], which justifies the organization under IAEA's umbrella of Coordinated Research Projects (CRPs) aimed at improving Member States' fast reactor analytical simulation capabilities and international qualification through code-to-code comparison, as well as experimental validation on mock-up experiment results of codes currently employed in the field of fast reactors. NINE is very actively participating in these exercises, and

The present chapter summarizes the results and discusses the main outcomes of the above-mentioned benchmark exercises, in the aim at underlying the wide convergence among the computational tools adopted by the participants, as well as detecting the main discrepancies and seeking for their common origin and trend, whether and whenever existing. That should enable defining a mid-term vision for further development of the computer codes in the field of fast reactors, whatever their features and nature, and identifying new needs for their extended validation

Starting from the considerations above regarding the deployment of fast reactors and the maturity gained by the SFR, NINE joints the effort of International community to assess the actual computational capabilities in modeling SFRs features. Taking advantage of reactor data gathered in full scale reactor demonstrators, NINE participated, and is still doing, in several International benchmarks aiming at demonstrating the applicability of its modeling methodology to Fast Reactor design and, in particular, to SFRs; to evaluate the level of assessment of computer codes available at NINE in respect to SFR specific features; to check the applicability of the NINE Validation Process – which is part of the more general framework of NEMM (NINE Evaluation

the Thermal–Hydraulic (TH) simulations by means of Fast Fourier Transform Based Method (FFTBM) and finally to perform independent validation of the Serpent code. All the analysis presented hereafter have been performed following a best estimate approach which requires, among the other things, a high-fidelity Simulation

<sup>1</sup> Within the NEMM (NINE Evaluation Model Methodology), NINE adopts the conventional and internationally acknowledged process to achieve the validation of computation tools and define the inherent uncertainties. It includes three steps: the analytical compliance test - the verification -, the qualification through code-to-code comparisons and benchmarks, the actual validation – supported by scaling analysis – on experimental data originating from mock-up experiments and the outcomes of the

operating experience, including downgraded operation and emergency.

**244**

Model (SM), i.e., a SM that represents with a high level of detail the hardware subject of the analysis to avoid the introduction of inaccuracies due to rough approximations and assumptions.


**1. Introduction**

Capacitive power transfer (CPT) is an alternative approach to wireless power transfer (WPT). Rather than using a magnetic field, CPT uses a quasi-static electric field (EF) to deliver power from the primary side to the secondary side through a capacitor formed by electrodes belonging to physically separate devices [1–3]. Murata Electronics Europe adopted this method, and it has become popular because of good galvanic isolation, low cost, and the potential for operation at a higher frequency rating than that of the magnetic core [4,5]. The CPT system has been widely used in previous applications, such as electric vehicle (EV) charging [6–10], drones [11–13], variable message displays [14], and others. Previous research on low-power [11,15] and high-power [16] applications of CPT has been conducted with a reported efficiency of more than 90%. The CPT system offers advantages in lightweight, contactless, and electromagnetic interference (EMI) reduction. These advantages allow the CPT system to compromise a suitability-integrated system for available EV charging, such as in-vehicle grid interaction [17,18] and the grid-tied plug-in EV charging system [19,20]. In the study by [17,19], the potential of the CPT system can be used to replace the cable between the grid-connected EV Supply Equipment (EVSE)-Plug-in EV (PEV) (EVSE-PEV) and the EV itself.

Furthermore, much research has been conducted on reducing EF emissions using techniques, such as the single-wire system [14,21,22] and the six-plate coupling-interface method [23]. In the study by [23], the coupler has a thickness of 1.9 cm and a gap of 15 cm. The efficiency of the system was reported as 91.6% when delivering power of 1.97 kW, whereas the safety range of EF emissions was

>0.4 m from the coupler. However, the method of calculating the resonant and component parameters was too complex. The concept of shielded-CPT was introduced in EV charging applications [24,25], using two extra plates to cover the coupler on each side.

This paper proposes a deep analysis of scaling-factor and design guidelines to achieve a compact shielded-CPT system that meets design requirements and safety considerations. The contributions of this paper are as follows.

#### **2. Scaling Model and Analysis**

The proposed shielded-CPT structure is constructed as a conventional CPT coupling-plate interface with two additional plates behind each side. The coupling structure builds a six-plate CPT system consisting of a power transfer part and a shielding part as seen in Figure 1. With this configuration, the circuit parameter is optimized to the required power and e fficiency, the size and distance of the coupling in consideration to the safety level of air breakdown voltage and the stray of EF. By introducing the extra plates, the EF-emission characteristic was observed through field-simulation and hardware experiments [23,24]. In these studies, the six-plate CPT system shows that the EF emission has been reduced significantly compared to the four-plate systems [26].

**Figure 1.** Structure of shielded-capacitive power transfer (CPT) coupling-interface system.

The circuit model of the complete shielded-CPT system is shown in Figure 2. Four parts of the circuit model comprise a WPT system with a capacitive coupling interface. A switch network can be implemented by a single-ended Class-E power amplifier, half-bridge, or full-bridge inverter system [27–30]. A 50 Ω coaxial cable is used in the proposed system, and a balanced-to-unbalanced (Balun) transformer is coupled to the resonant inductors, providing a balanced condition of the voltage waveform and a stable ground reference to the coupling system [31]. For simplicity of modeling, these two parts will be omitted in the scaling-factor analysis.

**Figure 2.** Circuit model of the complete shielded-CPT system.

#### *2.1. Circuit Model Analysis of the Shielded-CPT System*

Figure 3 presents the analysis of the coupling interface of the proposed shielded-CPT system. The input-voltage source, *V*0, produces a sinewave alternate current (AC) voltage that is applied to the input terminal of the shielded-CPT circuit. Accordingly, the resonant frequency is tuned by the value of the series-resonant inductor, *Lr*, coupling capacitance, *CC*, and parasitic capacitance, *CP*, on the primary and secondary sides. The load resistance, *RLoad*, is connected through the resonant inductors in the secondary side. As an assumption, the circuit topology involves of symmetry parameters for both placement and size.

**Figure 3.** Circuit model for S-CPT-coupling-capacitance analysis.

The shielded-CPT circuit can be analyzed through three approximations. First, the primary (transmitter)-side impedance can be calculated under the assumption that all components on the primary side are modeled by a single parallel resistance, *RL*, if a resonant condition occurs between them. Next, the secondary (receiver)-side impedance was assumed to be in a resonant condition with the receiver side; thus, the circuit is modeled by a single parallel resistance, *RL*. The last approximation is a combination of the previous two, namely, the primary and secondary impedances match. Secondary-side-impedance-matched analysis is used for this paper. Figure 4 illustrates the simplified circuit model for the process of analyzing the coupling capacitance, *CC*. It consists of a single input-voltage source, *V*0, with frequency *f*, connected to the series-resonant inductor, *L*, with equivalent series resistance (ESR), *RS*. The circuit is coupled with the parasitic capacitance, *CP*, in parallel with the coupling capacitance, *CC*. here we assume that the secondary side has a resonant condition. The load resistance *RLoad* and the L-matching circuit can be simplified as the load, *RL*.

**Figure 4.** Simplified circuit model for system analysis.

Using the circuit diagram in Figure 4, Equation (1) is obtained based on the sinusoidal approximation for the *I*1 current loop with angular frequency, ω, using Kirchhoff laws (KCL):

$$V\_0 = (j\omega L + R\_S)I\_1 + \frac{1}{j\omega C\_p}(I\_1 - I\_2) \tag{1}$$

In addition, applying KCL to the *I*2 loop yields the relationship:

$$0 = -\frac{1}{j\omega \mathbb{C}\_p} I\_1 + \left(\frac{1}{j\omega \mathbb{C}\_p} + \frac{1}{j\omega \mathbb{C}\_\mathbb{C}} + R'\_L\right) I\_2 \tag{2}$$

From (1) and (2), *I*2 is

$$I\_2 = \frac{j\omega \mathbf{C\_C}}{\left\{1 - \omega^2 \left(L\mathbf{C\_C} + L\mathbf{C\_p} + \mathbf{C\_C}\mathbf{C\_p}\mathbf{R\_S}\right)\right\} + j\omega \left(\mathbf{C\_C}\mathbf{R\_L} - \omega^2 L\mathbf{C\_C}\mathbf{C\_p}\mathbf{R\_L} + \mathbf{C\_C}\mathbf{R\_S} + \mathbf{C\_p}\mathbf{R\_S}\right)} V\_0 \tag{3}$$

By substituting this term into (1), *I*1 is

$$I\_{1} = \frac{\left(\frac{\text{C}\_{\text{C}} + \text{C}\_{p}}{\text{C}\_{\text{C}}} + j\omega\text{C}\_{p}R\_{L}\right)}{\left(\frac{\text{C}\_{\text{C}} + \text{C}\_{p}}{\text{C}\_{\text{C}}}R\_{S} - \omega^{2}L\text{C}\_{p}R\_{L} + R\_{L}\right) + j\left\{\omega\text{C}\_{p}R\_{S}R\_{L} + \omega L\frac{\text{C}\_{\text{C}} + \text{C}\_{p}}{\text{C}\_{\text{C}}} - \frac{1}{\omega\text{C}\_{\text{C}}}\right\}}V\_{0} \tag{4}$$

Under the resonant condition, the corresponding impedance will be purely resistive. Thus, the imaginary part of the total impedance of the circuit equals zero and the resonant inductance *L* of the circuit can be calculated as

$$L = \frac{\mathbb{C}\_p \mathbb{R}\_L^{-2} + \frac{\mathbb{C}\_\mathbb{C} + \mathbb{C}\_p}{\omega^2 \mathbb{C}\_\mathbb{C} \mathbb{Z}^2}}{\omega^2 \mathbb{C}\_p \mathbb{R}^2 \mathbb{R}\_L^{-2} + \left(\frac{\mathbb{C}\_\mathbb{C} + \mathbb{C}\_p}{\mathbb{C}\_\mathbb{C}}\right)^2} \tag{5}$$

From Figure 3, the stress voltage *V*1 across the shield plate is found as

$$V\_1 = V\_0 - (R\_S + j\omega L)I\_1 \tag{6}$$

where *V*0 is the input voltage, *RS* is the ESR, *j*ω*L* is the inductor reactance, and *I*1 is the current. Using (4), *V*1 becomes

$$V\_1 = \frac{R\_L - j\frac{1}{a\mathcal{C}\_C}}{\left(\frac{\mathcal{C}\_C + \mathcal{C}\_p}{\mathcal{C}\_C} R\_S - a\omega^2 L \mathcal{C}\_p R\_L + R\_L\right) + j\left\{a\mathcal{C}\_p R\_S R\_L + aL\frac{\mathcal{C}\_C + \mathcal{C}\_p}{\mathcal{C}\_C} - \frac{1}{a\mathcal{C}\_C}\right\}} V\_0 \tag{7}$$

#### *2.2. Optimization for Minimal Loss by Impedance Matching*

The complete system topology of Figure 3 is rearranged with *R*0 as the internal characteristic resistance of the power source in Figure 5. An AC-input voltage is applied to the resonant-circuit input. In this analysis, we assume that the total impedance of the coupling interface and the secondary side

of the shielded-CPT are matched to *RL'.* To attain a maximum power transfer, the total reflected output impedance must equal the input impedance of the circuit [32]. This relationship is shown in (8):

$$R\_0 = j\omega L + \frac{R\_L'}{j\omega CR\_L' + 1} \tag{8}$$

**Figure 5.** Circuit model for impedance analysis.

By multiplying both the numerator and the denominator by (1 − *j*ω*CRL*), we have

$$R\_0 = \frac{R\_L'}{1 + \omega^2 \mathcal{C}^2 R\_L'^2} + j\omega \left(L - \frac{\mathcal{C} R\_L'^2}{1 + \omega^2 \mathcal{C}^2 R\_L'^2}\right) \tag{9}$$

The reactive part of the circuit will be cancelled when it is in the resonant condition. Thus, the matching impedance state can be acquired as

$$R\_0 = \frac{R\_L'}{1 + \omega^2 \mathcal{C}^2 R\_L'^2} \tag{10}$$

While the values of capacitance *C* and inductance *L* can be acquired from the quality factor *Q* of the components

$$C = \frac{1}{\omega R\_L'} \sqrt{\frac{R\_L'}{R\_0} - 1} = \frac{Q}{\omega R\_L'} \tag{11}$$

$$L = \frac{CR\_L^{\prime 2}}{1 + \omega^2 C^2 R\_L^{\prime 2}} = \frac{R\_0 Q}{\omega} \tag{12}$$

The maximum value can be obtained using a derivative method. Therefore, the response to the load resistance *RL* from (11) can be calculated by

$$\frac{d\mathbb{C}}{dR'\_L} = \frac{1}{\omega} \left( \frac{1}{R\_L \prime^2} \sqrt{\frac{R\_L \prime}{R\_0} - 1} - \frac{1}{R'\_L} \frac{1}{2R\_0 \sqrt{\frac{R\_L \prime}{R\_0} - 1}} \right) \tag{13}$$

$$\frac{d\mathbf{C}}{dR\_L'} = \frac{1}{\alpha} \frac{1}{R\_L'^2} \sqrt{\frac{R\_L'}{R\_0} - 1} \left(1 - \frac{R\_L'}{2R\_L' - 2R\_0}\right) \tag{14}$$

$$\frac{d\mathbb{C}}{d\mathbb{R}\_L'} = 0 \tag{15}$$

From (14) and (15), the relationship between the load resistance, *RL*', and the internal characteristic resistance, *R*0, can then be obtained as

$$R\_L' = 2R\_0 \tag{16}$$

Thus, the optimum impedance-matching condition can be obtained when the load resistance, *RL*', is twice the internal characteristic resistance, *R*0. Using the KCL method, the gain of the circuit in Figure 5 can be defined as

$$\frac{V\_L}{V\_0} = \frac{\frac{R\_L'}{j\omega CR\_L' + 1}}{R\_0 + j\omega L + \frac{R\_L'}{j\omega CR\_L + 1}}\tag{17}$$

Substituting (11) and (16) into (17), we obtain

$$\frac{V\_L}{V\_0} = \frac{1}{2} \frac{R\_L'}{R\_0 + jR\_0Q} \tag{18}$$

$$\left|\frac{V\_L}{V\_0}\right| = \frac{1}{2}\sqrt{\frac{R\_L'^2}{R\_0r^2 + R\_0r^2Q^2}} = \frac{1}{2}\sqrt{\frac{R\_L'}{R\_0}}\tag{19}$$

For analysis, the parameter of the circuit model is then defined to obtain a correlation in the capacitance, inductance, and circuit gain to the various load values. A square plate 10 cm in height and width achieves a coupling capacitance of 8.9 pF within 1 cm of the gap (see Table 1). The behaviors of the capacitance, inductance, and the circuit gain under various values of impedance are illustrated in Figures 6 and 7.

**Table 1.** Circuit parameters for ratio-of-resistance analysis.

**Figure 6.** Capacitance and inductance behaviors under various impedance values.

**Figure 7.** Voltage and current behaviors under various impedance values.

In Figure 6, the shield parasitic capacitance *CP* becomes large to obtain a thin coupler unit. However, to develop a large ratio between the load resistance and the internal series resistance, *RL'*/*R0*, the shield capacitance *CP* should be small. Thus, there is a trade-off relationship between the unit thickness and output voltage (Figure 7). With the increase of the load resistance, the load voltage, *VL*, increases by a gradient of 1. By contrast, the load current decreases by gradient of −1. On the other hand, a large capacitance requires a small *RL*' and the shield capacitance value is limited to 2 for *RL'*/*R0*. A double-*LC*-resonant-matching system (*LCLC* circuit) may solve this problem.

Figure 8 shows the relationship between the resistance ratio and power loss of the inductor. With increasing *RL*', *RS* rises because the inductor value increases, but *IL* decreases. Thus, the loss in the inductor, *PS*, decreases with increasing *RL*' because *PS* is given by *IL*2*RS* and the gradients in the log-log plot are roughly 1/2 and −1 for *RS* and *IL*, respectively. Therefore, *PS* decreases with increasing *RL*' with a gradient of −3/2 in log-log plot (see Figure 9).

**Figure 8.** Current and equivalent series resistance (ESR) responses under various impedance values.

**Figure 9.** Power loss of the inductor under various impedance values.

#### *2.3. Resonant Inductor Optimization for Minimal Loss*

In this subsection, the ESR value of the inductor is investigated. Inductors can be constructed using many types of core materials; one is an air-core-type inductor that uses any non-magnetic material as its core to reduce core losses, i.e., eddy current & stray losses, especially when the operating frequency is very high. However, the use of a non-magnetic core also reduces inductance. Another type is a toroidal-core inductor, the core of which is made from a ferromagnetic material. The advantage of this circular core is that the magnetic field contains extremely low magnetic-flux leaks inside the core. The magnetic field at the core is higher because of a low leakage flow; hence, a toroidal-core inductor will have a higher inductance than a rod or bar-shaped core of the same material [32,33]. Figure 10 shows the dimensions and parameters of a toroidal-core inductor.

**Figure 10.** Inductor dimension.

The core inductance can be acquired as

$$L = \frac{N^2 \mu S}{l} = \frac{N^2 \mu \left(\pi r^2\right)}{2\pi R} = \frac{N^2 \mu r^2}{2R} \tag{20}$$

where *N* is the number of turns, μ is the core-material permeability, *S* is the core thickness, *l* is the wire length, *R* and *r* represent the core radius and core thickness radius, respectively. The series resistance in the inductor is

$$R\_S = \frac{\rho l\_w}{S\_w} = \frac{\rho \left(2\pi r N\right)}{\pi \left(\phi/2\right)^2} = \frac{8\rho r N}{\phi^2} \tag{21}$$

$$L\_S = \frac{N^2 \mu r^2}{2R} \left(\frac{\phi^4}{64\rho^2 r^2 N^2} R\_S^{-2}\right) = \frac{\mu \phi^4}{128\rho^2 R} R\_S^{-2} \tag{22}$$

Thus, the series resistance *RS* can be written as

$$R\_S = \frac{8\rho}{\phi^2} \sqrt{\frac{2RL\_S}{\mu}}\tag{23}$$

where φ and ρ represent the thickness and resistivity of the wire, respectively. The series inductance is

$$L\_{\mathbb{S}} = \frac{1}{\omega \mathbb{C}\_{2\mathbb{C}}}\tag{24}$$

Because the current flows through an inductor, its ESR consumes some power. Figure 11 shows the circuit model used to analyze the power loss in a resonant inductor without considering parasitic capacitance, CP. An AC voltage source is connected in series with the ESR RS, the inductance *LS*, the coupling capacitance *CC*, and the load resistance *RL*.

**Figure 11.** Circuit model for ESR-effect analysis.

The power loss of the impedance-matching inductor, *PS*, is defined by

$$P\_S = \frac{R\_S}{R\_L + R\_S} P\_{\rm in} \tag{25}$$

by substituting *RS* from (23) and (24) into (25), *PS* can be calculated as

$$P\_S = \frac{1}{\frac{\omega \mathbb{R}\_L \phi^2}{8\sqrt{2}\rho} \sqrt{\frac{\mathbb{C}\_C \mu}{\mathbb{R}}} + 1} P\_{\text{in}} \tag{26}$$

From (26), the relationship between the coupling capacitance, *CC*, and the power loss of the matching inductor, *PS*, is illustrated in Figure 12. Amplification of the coupling capacitance results in inductance drops. In addition, the ESR reduces and corresponds to the end product of (26), which is that the power loss decreases. However, because the distance between the couplers is fixed, the capacitance value is limited to a small number. Furthermore, the parasitic capacitance, *CP*, will introduce a large value of capacitance that can affect the reduction of ESR, *RS*.

**Figure 12.** Inductance power loss as a function of coupling capacitance.

The effect of the parasitic capacitance, *CP*, can be analyzed using (5). The increase of *CP* occurs as the inductance value declines. From (23), the series inductor *LS* proportionally influences the ESR, *RS*, value. Its behavior is illustrated in Figure 13.

**Figure 13.** Series resistance of the resonant inductor with the change of the parasitic capacitance.

The relationship between power and efficiency with a frequency response is shown in Figure 14. It can be seen that, by having a lower ESR value (here below 1 Ω, see Figure 14a), less power is lost in the inductor, resulting in more power being delivered. The system may achieve an efficiency of over 95%. On the contrary, when the series resistance of the inductor is greater, it consumes some power, impacting the output power delivered to the load. From Figure 14b, the overall efficiency can be understood to drop. Thus, to minimize the loss caused by the resonant inductor, lower values of ESR result in higher efficiencies. One way to reduce ESR is by implementing a litz wire.

(**a**)

 **Figure 14.** Frequency responses of power and efficiency: (**a**) Lower ESR value; (**b**) Higher ESR value.

#### *2.4. Scaling Design for Various Loads*

This subsection analyzes the behavior of power and efficiency under the variation of the load resistance. The resonant-inductance parameters used in this analysis are presented in Table 2. The ESR of the inductor, *RS*, was calculated using (23). The value of inductance, *L*, changes due to parasitic capacitance, *CP*. Furthermore, *RS* depends on its value. The parameters of the circuit model for power and efficiency analysis are listed in Table 3.

**Table 2.** Parameters of the inductance model for power and efficiency analysis.

**Table 3.** Parameters of circuit model for power and e fficiency analysis.

The behavior of the load resistance to the output power for various values of parasitic capacitance is illustrated in Figure 15a, while Figure 15b draws the load-resistance behavior to the e fficiency with the shield parasitic-capacitance variations. The escalation in the load resistance *RL* from 1 Ω to 125 Ω (which amplifies *CP* from 1 pF to 1 nF) results in power increases. Increasing load resistance is determined to decrease power loss in the inductor.

**Figure 15.** Effects of parasitic capacitance and load-resistance variations upon: (**a**) power behavior; (**b**) e fficiency behavior.

#### *2.5. Scaling Design for Various Parasitic Capacitances on the Shield-Coupler Stress Voltage*

To acquire a thinner module of the shielded-CPT, the space gap between the shield plate and the coupler plate should be as short as possible. By decreasing the gap, the parasitic capacitance *CP* increases. Assuming no stray capacitance on the edges of the plate, it can be estimated as

$$\mathcal{C}\_P = \frac{\varepsilon\_F \varepsilon\_0 S\_P}{d\_{SC}} \tag{27}$$

where *dSC* and *SP* are the gap distance between the shield-coupler plates and shield plate area, respectively. From (7), let us assume that *CC* is much smaller than *CP*; the stress voltage behavior is inversely proportional to the amount of parasitic capacitance (see (27)). While the gap is smaller, the parasitic capacitance will become greater. Here, increasing *CP* will increase the stress voltage *V*1. The EF value between the shield-coupler plates, *ESC*, can be calculated as follows:

$$E\_{SC} = \frac{V\_1}{d\_{SC}}\tag{28}$$

From (28), the EF level is amplified in proportion to the increase in stress voltage. As we know, the EF in air has a breakdown voltage *EMAX* above 30 kV/cm [34], which is essential for system scaling. From this point, the EF strength between the shield-coupler plates should have a value under *EMAX*. The effect of parasitic capacitance upon the stress voltage is shown in Figure 16. With decrease in *dSC*, the capacitance *CP* increases. The stress voltage over shield-coupler plates increased, which increased the EF between them proportionally.

**Figure 16.** Stress voltage and EF level behavior over parasitic capacitance and gap variations.

#### **3. Design Guidelines and Optimization of the Shielded-CPT System**

The following example will demonstrate the design process of shielded-CPT to find optimum scaling and design values. The design step will rely upon the analytical approaches in the previous section. The scaling-factor of the shielded-CPT system will be described under the optimal condition. Several factors must be considered before the hardware is developed. A design guideline for scaling the system such that it meets constraints is shown in Figure 17. The individual unidentified-element values for this design example are *L*, *RS*, and *CP*. From (23), *RS* is influenced by the *L* value. How *L* itself will vary depends on the parasitic capacitance *CP.* At this point, we investigate *CP* variations as describe in Section 2.5. With variation of *CP, L* can be obtained using (5).

**Figure 17.** Design guidelines for optimizing the shielded-CPT system.

In this study, the shielded-CPT coupling interface need to transfer the power through the capacitive link at a frequency of 13.56 MHz. The frequency selection is decided by three factors. Firstly, the WPT systems for the high-power applications, requires not only to provide a high power through short-range of distance, but also a compact coupling interface that small enough to be integrated in the EV. The volume and weight of the resonant components are inversely proportional to the frequency. Thus, increasing the frequency by 10 s of MHz leads to weight lessening and power density enhancement [35]. Secondly, for the CPT system, the value of inductance is inversely proportional to the angular frequency in which the high frequency gives a low value of inductance, based on Equation (24). Thus, the inductor will become smaller for higher frequencies, offering an advantage to obtain a compact, lightweight, and small size CPT system. Thirdly, the limitation of the industrial, scientific, and medical (ISM) band for a MHz WPT. A fixed 6.78 MHz frequency as the lowest ISM band frequency is preferred. The international telecommunication union radio (ITU-R) communications sector currently recommends this single frequency on WPT for consumer devices because it has little or no negative impact on other licensed bands. A higher operating frequency in the ISM band, such as 13.56 MHz or 27.12 MHz, could further improve local freedom.

The shielded-CPT is connected to a 50 Ω resistive load. The capacitances of the coupling interface are separated by a distance of over 18 cm, which is the EV body-to-ground clearance requirement, with a plate are of 250 cm2 corresponding to a main-coupling capacitance of approximately 1.11 pF. Let us assume that ρ = 1.0 × 10−4, where ρ > ρ (Cu), φ = 0.15 cm, and the radius of the air core *R* = 2.5 cm for the resonant inductor parameter. The designated parameters are listed in Table 4.

**Table 4.** Parameters of the shielded-CPT system for the design example.

The exemplary design results provide several options for the shielded-CPT parameter. Figure 18 shows *L* and *RS* as functions of *CP*. The inductance decreases in value (i.e., decreases its size) as the parasitic capacitance increases. Furthermore, the resistance value decreases. To obtain a small and compact module of the shielded-CPT, increasing the capacitance to a higher value is required. Furthermore, this increases power transfer through the couplers since a larger EF occurs.

**Figure 18.** Inductance and series resistance characteristic for various parasitic-capacitance values.

On the contrary, more power transfer does not necessarily mean greater e fficiency. Figure 19 illustrates the relationship among the parasitic capacitance to the power input, the power loss in the inductor, and the power output of the shielded-CPT. The e fficiency decreases along with the gap between the plates. This occurs due to the increase in the current flowing through the primary-side components, meaning more input power is needed by the system. Thus, its e fficiency is inversely proportionate to the compactness of the shielded-CPT module.

**Figure 19.** Power and e fficiency characteristics for various parasitic-capacitance values.

The EF injected into the shield-coupler plates was limited to the breakdown voltage of air (30 kV/cm), as seen in Figure 20. In this example, at the limit point of 30 kV/cm, the parasitic-capacitance value for safety considerations must be below 2.78 pF. This condition can be obtained when the gap between the shield-coupler plates is much greater than 2.66 cm.

**Figure 20.** Gap and EF levels for various parasitic-capacitance values.

The minimum gap allowed in this design is shown in Figure 20. With a resonant frequency of 13.56 MHz and a coupler distance of 18 cm, the shielded-CPT coupling structure can be acquired for a gap of 2.92 cm, providing 7.59 pF of parasitic capacitance. 15.6 μH is needed as the total inductance works for resonance-circuit operation. For these parameters, the system is predicted to have an efficiency over 92%. The parameters of the shielded-CPT system in this example are listed in Table 5.

**Table 5.** Parameters of the shielded-CPT system for the design example.

#### **4. Hardware Implementation**

The parameters obtained in the previous section are used in the hardware implementation. A single-layer PCB FR4 was used to create the coupling interface; the series-resonant inductors were fabricated manually and measured using an impedance network analyzer. The coupling interface of the shielded-CPT-system implementation is shown in Figure 21. The structure of the coupling capacitance follows the designated and optimized configuration.

**Figure 21.** Hardware implementation of the shielded-CPT system.

Table 6 presents the hardware parameters of the shielded-CPT system for the design example. These were acquired from actual measurement of the system. In this implementation, the gap between the shield-coupler plates is about 3 cm. The resonant inductors are divided into four sections: upper and lower sides of the primary and secondary coupling interfaces. Some parameters exhibit differences from their calculated values due to manual production.

**Table 6.** Hardware parameters of the shielded-CPT system for the design example.

The efficiency of the coupling capacitance of the shielded-CPT system was measured using vector network analyzer. The coupling was connected to the measurement unit via a 50 Ω coaxial cable on both the transmitter and receiver sides. The measured S-parameter of the coupling is shown in Figure 22. The curve S [2,1] presents the power delivered from the transmitter to the receiver. Meanwhile, the curve S [1,1] presents the reflected power through the transmitter. At 13.56 MHz, the shielded-CPT in the hardware implementation has a delivered power above 0.86, equal to an efficiency above 86%.

**Figure 22.** The gain of the hardware implementation of the shielded-CPT system.

A comparison between the design guidelines and the hardware implementation is presented in Table 7. The efficiencies of the design guidelines and the hardware implementation agree to within 93%. Since the implementation has a different parameter value, it affects the precision of the designated system.

**Table 7.** Comparison of results between the design guidelines and the hardware implementation.

Figure 23 illustrates the EF emission that is analyzed using QuickField™ software. Most of the radiated EF appears between the coupling and shield plates over 20 kV/m. This condition deals with the calculated value of EF in Section 3 (Figure 20). However, the EF emission behind the shield plate is between 0 and 2 kV/m.

**Figure 23.** The EF emission of shielded-CPT system.

The highest EF denoted by red shows the value of 20 kV/m. Meanwhile, the lowest emission is shown by dark blue with an EF value between 0 and 2 kV/m. The ICNIRP guidelines and IEEE standards [36,37] mention 48.4 V/m and 60.75 V/m as the safety level of EF radiation for general public exposure limit under the operating frequency of 13.56 MHz. Figure 24 shows the EF emissions of the shielded-CPT system with a distance increase from (a) beside the coupling interface and (b) behind the shield plate. The emissions besides the coupling interface are measured over 1 kV/m. Its emissions are decreased to over 100 V/m when the distance is approximately 7.5 cm beside the coupler. Moreover, increasing the distance over 10 cm obtains a lower EF emission. However, the proposed shielded-CPT successfully reduced the emission behind the shield plate to below 10 V/m when the distance is less than 35 cm, which is reduced to below 1 V/m, meeting the ICNIRP and IEEE regulations.

**Figure 24.** The EF emission of shielded-CPT system: (**a**) beside the coupling interface, (**b**) behind the shield plate.

(**b**)