[pt] A estimação dos fluxos de potência e perdas técnicas nos sistemas de subtransmissão é um grande desafio para as distribuidoras pela importância no planejamento e operação do sistema. Por isso, surge a necessidade de contar com modelos que permitam simular estas grandezas, para o adequado planejamento do sistema. Neste trabalho é proposto e implementado um modelo de estimação de fluxos de potência e perdas técnicas em um sistema de subtransmissão baseado na desagregação de potência da demanda importada da rede de transmissão. A metodologia envolve a determinação de fatores de desagregação por barra associados à importação total de potência, estimação dos fluxos de potência DC usando a matriz de sensibilidade ramo-barra caraterística da rede elétrica e, finalmente, a estimação das perdas elétricas. O sistema IEEE 24 barras foi utilizado para o caso de estudo. Neste caso, a rede elétrica de 230 kV foi tratada como a rede de transmissão e a rede de 138 kV como a rede de subtransmissão. Dados de geração e carga realistas, com base horária e ao longo de um ano, foram utilizados para estimar os parâmetros dos modelos. Para avaliar os resultados, foram utilizadas métricas estatísticas e os resultados foram comparados com um modelo puramente estatístico, que correlaciona a importação total com as potências injetadas em cada barra, os fluxos nas linhas e as perdas totais. Os resultados obtidos indicaram que o modelo proposto ganha importância quando é possível controlar algumas injeções da rede elétrica, tornando-o mais dependente da rede elétrica. / [en] The estimation of the power flows and technical losses in the subtransmission systems is a great challenge for electricity distribution companies because of their importance in the planning and operation of the system. Therefore, there is the increasing need to have models that allow to simulate these variables for the proper planning of the system. In this work, a model of estimation of power flows and technical losses in a subtransmission system is proposed and implemented; this model is based on the power disaggregation of the imported demand from the transmission network. The methodology involves the determination of buses disaggregation factors associated with total power import, estimation of DC power flows using the bus-branch sensitivity matrix of the network and finally the estimation of the electrical losses. The IEEE 24 bus system was used for this study case. In this case, the 230 kV power grid was treated as the transmission network and the 138 kV network as the subtransmission network. Realistic generation and loading data, based on hourly time and over the span of a year, were used to estimate the parameters of the models. In order to evaluate the results, statistical metrics were used and the results were compared with a purely statistical model, which correlates the total imports with the injected power in each bus, line flows and total losses. The obtained results indicate that the proposed model gains importance when it is possible to control some of the injections into the power grid, turning it more dependent of the power grid.

Este trabalho apresenta proposta de modelo matemático para o problema de expansão do sistema de transmissão baseado no fluxo de carga CC considerando a utilização de links CC e FACTS resolvido através de metodologia de solução que considera a primeira e a segunda lei de Kirchhoff em processo enumerativo de branch-and-bound adaptado. A abordagem possui dois pontos em destaque: i) apresenta uma proposta de modelo matemático com possibilidade da utilização direta em problemas de expansão de linhas de transmissão que possuem tanto linhas de transmissão CA, transformadores, links CC e dispositivos FACTS e ii) é um método exato de solução do problema que garante a otimalidade da resposta e traz uma contribuição ao tradicional método branch-and-bound por incluir relaxações adicionais. O método aplicado aos sistemas de 6 barras de Garver e sistema Sul sudeste Brasileiro de 46 barras apresenta respostas adequadas e o modelo matemático testado em um sistema Garver modificado apresenta novas configurações possíveis com redução do custo total do investimento. / This work proposes a mathematical model to the transmission expansion system problem based on the DC power flow model considering the use of DC links and FACTS that is solved using a solution method considering the first and second Kirchhoff’s Law in an enumerative adapted branch-and-bound process. It is possible to highlight two key aspects of the proposed approach: i) presents a mathematical model that can be directly used on expansion transmission systems problems that have AC transmission lines, transformers, DC links and FACTS and ii) is an exact solution method that guarantees the optimum problems’s solutions and contributes to the traditional branch-and-bound method bringing additional relaxations. The solution method applied to Garver’s six-bus network and southeast Brazilian 46 bus network provides correct answers and the mathematical model tested on a modified Garver’s six-bus network presents new possible configurations that enables overall cost reduction to the problem.

DC power systems have a constant DC-link voltage, as well as the advantages such as high stability, high efficiency, small size and light weight; therefore, they are widely used in stand-alone power systems, e.g. the power systems in aircrafts and automobiles, isolated wind power generation systems, etc. Permanent-Magnet Synchronous Generators (PMSGs) possess the advantages including high power density, high efficiency, and high control precision, and have obtained great attention and have been widely used in military, inductry, and daily life. Pulse Width Modulation (PWM) rectifier has been one of the main power conversion topologies thanks to its full controllability. The key point in the dissertation is to study the DC power system consisting of a PMSG to be the main power input device and a PWM rectifier to be the main power conversion topology. The objective of control is to output a constant DC-link voltage in a wide PMSG speed range. Since the PM-excited flux linkage is constant, when the PMSG is working at a high speed, field-weakening is needed to stabilize the stator voltage, further to stabilize the DC-link voltage. Hybrid excitation may be used to realize the field-weakening, but it has complex structure; no auxiliary devices are needed in the field regulation with the armature current, and can be easily realized with the PWM recifier and field-regulation control strategies. In this dissertation, the typical applications of the DC power systems are first introduced, with a comprehensive analysis and elaboration on the relevant research throughout the world. The research work is focused on the DC power system and its stabilization control, which is composed of a PMSG and a PWM rectifier. The involved research content in this dissertation includes the following aspects: 1. DC power system design with a wide-speed-range PMSGAs for the common DC power systems, PMSG with high power density, high efficiency is selected to the system power input device, usually with a variable-speed prime mover. The PWM rectifier with fully controlled switches is chosen to be the power conversion topology, which converts the AC power generated by PMSG into DC power, and supplies the DC load after the DC filter. The matching between the system requirements and the generator parameters are determined. Through finite-element analysis (FEA), a PMSG with strong field-weakening ability and suitable for wide-speed-range operation has been designed and manufactured, and the system test bench has been built based on dSPACE. 2. Study, analysis, optimization and experimental verification of the traditional control strategiesAccording to the PMSG designed in part 1, the DC-link model has been built, as well as the control model of the traditional control strategies, e.g. field-oriented control (FOC), direct torque control (DTC), and the effectiveness of the DC-link voltage stabilization control has been verified in a wide speed range. The theory of active damping has been proposed and analyzed, and has been utilized in the DC-link voltage control. When the load on the DC-link changes, the dynamic response of the DC-link voltage has been greatly accelerated, and it recovers quickly to its reference value. In the meantime, the performance influence of the prime mover speed on the actual system test bench should be considered. Finally, the performance of FOC and DTC has been compared and analyzed. 3. Analysis and experimental verification of the direct voltage control (DVC), and the comparative study of all the studied control strategiesThe derivation process of DVC has been theoretically analyzed: the inner current loops in FOC have been eliminated to obtain the direct voltage field-oriented control (DVFOC); the reference value of d-axis voltage in DVFOC has been replaced by the product of the stator voltage calculated by the speed and the load condition, and the sine value of load angle generated by the DC-link voltage PI controller, in order to form the DVC-1. Further, the DC-link voltage PI controller directly outputs the reference value of load angle and it becomes DVC-2. Finally, the comparative study has been carried out among all the studied control strategies. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

La diode Schottky SiC est un composant qui peut potentiellement remplacer la diode PiN Si dans les applications de puissance. Effectivement, la tenue en tension élevée, la faible résistivité, ainsi que l’indépendance de la température du courant de recouvrement rendent cette diode idéale pour les convertis- seurs de puissance DC/DC. Cependant, face à l’abondance des composants Si sur le marché, la diode Schottky rencontre une certaine réticence. Malgré les nombreuses démonstrations de systèmes électroniques de puissance réalisés, la fiabilité de cette technologie n’arrive pas à convaincre. Cette étude porte sur la caractérisation en régime statique sur une large gamme de températures et l’évaluation de la fiabilité en surcharge des diodes Schottky et JBS SiC-4H. La caractérisation en température a permis de proposer des modèles de la carac- téristique directe et inverse sur une gamme étendue de températures. Les tests en surcharge ont permis de comparer la fiabilité de diodes expérimentales et commerciales à fin de montrer la maturité de cette technologie. / The SiC Schottky diode can potentially replace the PiN diode in power appli- cations. As a matter of fact, high blocking voltage, low resistivity as well as temperature independence of the reverse recovery current make this diode ideal for DC/DC power converters. Nevertheless, Schottky diodes meet some reluc- tance before the abundance of PiN Si diodes. Despite the numerous demons- trations of power electronics systems, there are still some reliability aspects to improve. This study focuses on static characteristic in a large temperature range and reliability assessment of repetitive surge test of Schottky and JBS diodes. The measurements of forward and reverse characteristics yielded new models in a wide temperature range. Repetitive surge tests enabled us to com- pare the reliability of experimental and commercial diodes in order to prove the maturity of this technology.

Thesis Abstract Current Nuclear Power Plant (NPP) design does not account for Beyond Design Basis Events (BDBEs) and thus lack the provisions to effectively mitigates complete loss of AC power and total loss of heat sink. Furthermore, parametric models used in PRA studies to assess Nuclear Power Plant’s safety risk for BDBE and External Events (EE) have significant limitations and proved ineffective to provide solutions on how to mitigate in BDBE or EEs situations. The Fukushima accident is a good example where PRA assessments did not provide the necessary means to cool or contain the reactors effectively. In this thesis, Emergency Mitigation Preparedness (EMP) model and assessment is proposed. The EMP model is objective and practical in evaluating NPP’s mitigation readiness in BDBE and EEs situations and provide a practical NPP Vulnerability indicator gauge which can potentially be used in risk-informed decisions. This will aid further in the NPP to improve in areas of emergency planning, enhance site and reactor design and improve workers safety and readiness to execute effective mitigation procedures and emergency plans. / Thesis / Master of Engineering (ME)

With the development of solar energy, power conversion systems responsible for energy delivering from photovoltaic (PV) modules to ac or dc grid attract wide attentions and have significantly increased installations worldwide. Modular power conversion system has the highest efficiency of maximum power point tacking (MPPT), which can transfer more solar power to electricity. However, this system suffers the drawbacks of low power conversion efficiency and high cost due to a large number of power electronics converters. High-power density can provide potentials to reduce cost through the reduction of components and potting materials. Nowadays, the power electronics converters with the conventional silicon (Si) based power semiconductor devices are developed maturely and have limited improvements regarding in power conversion efficiency and power density. With the availability of wide bandgap devices, the power electronics converters have extended opportunities to achieve higher efficiency and higher power density due to the desirable features of wide bandgap devices, such as low on-state resistance, small junction capacitance and high switching speed. This dissertation focuses on the application of wide bandgap devices to the dc-dc power conversion for the modular PV applications in an effort to improve the power conversion efficiency and power density. Firstly, the structure of gallium-nitride (GaN) device is studied theoretically and characteristics of GaN device are evaluated under testing with both hard-switching and soft-switching conditions. The device performance during steady-state and transitions are explored under different power level conditions and compared with Si based devices. Secondly, an isolated high-efficiency GaN-based dc-dc converter with capability of wide range regulation is proposed for modular PV applications. The circuit configuration of secondary side is a proposed active-boost-rectifier, which merges a Boost circuit and a voltage-doubler rectifier. With implementation of the proposed double-pulse duty cycle modulation method, the active-boost-rectifier can not only serve for synchronous rectification but also achieve the voltage boost function. The proposed converter can achieve zero-voltage-switching (ZVS) of primary side switches and zero-current-switching (ZCS) of secondary side switches regardless of the input voltages or output power levels. Therefore, the proposed converter not only keeps the benefits of highly-efficient series resonant converter (SRC) but also achieves a higher voltage gain than SRC and a wide range regulation ability without adding additional switches while operating under the fixed-frequency condition. GaN devices are utilized in both primary and secondary sides. A 300-W hardware prototype is built to achieve a peak efficiency of 98.9% and a California Energy Commission (CEC) weighted efficiency of 98.7% under nominal input voltage condition. Finally, the proposed converter is designed and optimized at 1-MHz switching frequency to pursue the feature of high-power density. Considering the ac effects under high frequency, the magnetic components and PCB structure are optimized with finite element method (FEM) simulations. Compared with 140-kHz design, the volume of 1-MHz design can reduce more than 70%, while the CEC efficiency only drops 0.8% at nominal input voltage condition. There are also key findings on circuit design techniques to reduce parasitic effects. The parasitic inductances induced from PCB layout of primary side circuit can cause the unbalanced resonant current between positive and negative half cycles if the power loops of two half cycles have asymmetrical parasitic inductances. Moreover, these parasitic inductances reflecting to secondary side should be considered into the design of resonant inductance. The parasitic capacitances of secondary side could affect ZVS transitions and increase the required magnetizing current. Because of large parasitic capacitances, the dead-time period occupies a large percentage of entire switching period in MHz operations, which should be taken into consideration when designing the resonant frequency of resonant network. / Doctor of Philosophy / Solar energy is one of the most promising renewable energies to replace the conventional fossils. Power electronics converters are necessary to transfer power from solar panels to dc or ac grid. Since the output of solar panel is low voltage with a wide range and the grid side is high voltage, this power converter should meet the basic requirements of high step up and wide range regulation. Additionally, high power conversion efficiency is an important design purpose in order to save energy. The existing solutions have limitations of narrow regulating range, low efficiency or complicated circuit structure. Recently, the third-generation power semiconductors attract more and more attentions who can help to reduce the power loss. They are named as wide band gap devices. This dissertation proposed a wide band gap devices based power converter with ability of wide regulating range, high power conversion efficiency and simple circuit structure. Moreover, this proposed converter is further designed for high power density, which reduces more than 70% of volume. In this way, small power converter can merge into the junction box of solar panel, which can reduce cost and be convenient for installations.

Growing concerns about climate change have led to the world experiencing an unprecedented push towards renewable energy. Economic drivers and government policies mean that small, distributed forms of generation, like solar photovoltaics, will play a large role in our transition to a clean energy future. In this thesis, a novel DC-DC converter known as the Coupled Inductors Combined Cuk-SEPIC' (CI-CCS) converter is explored, which is particularly attractive for these photovoltaic applications. A topological modification is investigated which provides several benefits, including increased power density, efficiency, and operational advantages for solar energy conversion. The converter, which is based on the combination of the Cuk and SEPIC converters, provides a bipolar output (i.e. both positive and negative voltages). This converter also offers both step-up and step-down capabilities with a continuous input current, and uses only a single, ground-referenced switching device. A significant enhancement to this converter is proposed: magnetic coupling of the converter's three inductors. This can substantially reduce the CI-CCS converter's input current ripple - an important benefit for maximum power point tracking (MPPT) in photovoltaic applications. The effect of this coupling is examined theoretically, and optimisations are performed - both analytically and in simulations - to inform the design of a 4 kW prototype CI-CCS converter, switched at a high frequency (100 kHz) with a silicon carbide (SiC) MOSFET. Simulation and experimental results are then presented to demonstrate the CI-CCS converter's operation and highlight the benefits of coupling its inductors. An efficiency analysis is also undertaken and its sources of losses are quantified. The converter is subsequently integrated into a domestic photovoltaic system to provide a practical demonstration of its suitability for such applications. MPPT is integrated into the CI-CCS DC-DC converter, and a combined half bridge/T-type converter is developed and paired with the CI-CCS converter to form an entirely transformerless single-phase solar energy conversion system. The combination of the CI-CCS converter's bipolar DC output with the combined half bridge/T-type converter's bipolar DC input allows grounding at both the photovoltaic panels and the AC grid's neutral point. This eliminates high frequency common mode voltages from the PV array, which in turn prevents leakage currents. The entire system can be operated in grid-connected mode - where the objective is to maximise power extracted from the photovoltaic system, and is demonstrated in stand-alone mode - where the objective is to match solar generation with the load's power demands.

Actuellement la nécessité des systèmes d’alimentation d’énergie, capables d’assurer un fonctionnement stable dans des domaines de fonctionnement assez larges avec des bonnes performances dynamiques (rapidité du système, variations limitées de la tension de sortie en réponse aux perturbations de charge ou de tension d’alimentation), devient de plus en plus importante. De ce fait, cette thèse est orientée sur la commande des convertisseurs de puissance DC-DC représentés par des modèles hybrides.En tenant compte de la structure variable de ces systèmes à commutation, un modèle hybride permet de décrire plus précisément le comportement dynamique d’un convertisseur dans son domaine de fonctionnement. Dans cette optique, l’approximation PWA est utilisée afin de modéliser les convertisseurs DC-DC. A partir des modèles hybrides développés, on s’est intéressé à la stabilisation des convertisseurs au moyen des correcteurs à gains commutés élaborés sur la base de fonctions de Lyapunov PWQ, et à l’implantation d’une commande prédictive explicite, en considérant des contraintes sur l’entrée de commande. La méthode de modélisation et les stratégies de commande proposées ont été appliquées sur deux topologies : un convertisseur buck, afin de mieux maîtriser le réglage des correcteurs et un convertisseur flyback avec filtre d’entrée. Cette dernière topologie nous a permis de répondre aux difficultés du point de vue de la commande (comportement à déphasage non-minimal) rencontrées dans la majorité des convertisseurs DC-DC. Les performances des commandes élaborées ont été validées en simulation sur les topologies considérées et expérimentalement sur une maquette du convertisseur buck. / Lately, power supply systems, guaranteeing the global stability for large enough operation ranges with good dynamic performances (small settling time, bounded overshoot of the output voltage in the presence of load or supply voltage variations), are strongly needed. Therefore, this thesis deals with control problems of DC-DC power converters represented by hybrid models.Considering the variable structure of these switched systems, a hybrid model describes more precisely the converter’s dynamics in its operating domain. From this perspective, a PWA (piecewise affine) approximation is used in order to model the DC-DC converters. Based on the developed hybrid models, first we have designed a stable piecewise linear state-feedback controller using piecewise quadratic (PWQ) Lyapunov functions, and secondly, we have implemented an explicit predictive control law taking into account constraints on the control input. The hybrid modeling technique and the proposed control strategies were applied on two different topologies of converters: a buck converter, in order to have a thorough knowledge of the controllers’ tuning, and a flyback converter with an input filter. This last topology, allowed us to manage different control problems (non-minimum phase behavior) encountered in the majority of topologies of DC-DC power converters. The controllers’ performances were validated in simulation on both considered topologies and also experimentally on buck converter.

L'intérêt pour les véhicules électriques ne cesse de croitre au sein de la société contemporaine compte tenu de ses nombreuses interrogations sur l’environnement et la dépendance énergétique. Dans ce travail de thèse, nous essayons d’améliorer l’acceptabtabilité sociétale du véhicule électrique en essayant de faire avancer la recherche sur le diagnostique des défauts d’une chaine de traction électrique. Les résultats escomptés devraient permettre à terme d’améliorer la fiabilité et la durabilité de ces systèmes.Nous commençons par une revue des problèmes des défauts déjà apparus dans les véhicules hybrides séries qui disposent de l’architecture la plus proche du véhicule électrique. Une étude approfondie sur le diagnostic des défauts d’un convertisseur de puissance statique (AC-DC) ainsi que celle du moteur synchrone à aimants permanents est menée. Quatre types de défauts majeurs ont été répertoriés concernant le moteur (court-circuit au stator, démagnétisation, excentricité du rotor et défaut des roulements). Au niveau du convertisseur, nous avons considéré le défaut d’ouverture des interrupteurs. Afin d’être dans les mêmes conditions d’utilisation réelle, nous avons effectué des tests expérimentaux à vitesse et charge variables. Ce travail est basé aussi bien sur l’expérimentation que sur la modélisation. Comme par exemple, la méthode des éléments finis pour l’étude de la démagnétisation de la machine. De même, l’essai en court-circuit du stator du moteur en présence d’un contrôle vectoriel.Afin de réaliser un diagnostic en ligne des défauts, nous avons développé un modèle basé sur les réseaux de neurones. L’apprentissage de ce réseau de neurone a été effectué sur la base des résultats expérimentaux et de simulations, que nous avons réalisées. Le réseau de neurones est capable d'assimiler beaucoup de données. Ceci nous permet de classifier les défauts en termes de sévérité et de les localiser. Il permet ainsi d'évaluer le degré de performance de la chaine de traction électrique en ligne en présence des défauts et nous renseigner ainsi sur l'état de santé du système. Ces résultats devraient aboutir à l’élaboration d’une stratégie de contrôle tolérant aux défauts auto-reconfigurable pour prendre en compte les modes dégradés permettant une continuité de service du véhicule ce qui améliorera sa disponibilité. / The interest in the electric vehicles rose recently due both to environmental questions and to energetic dependence of the contemporary society. Accordingly, it is necessary to study and implement in these vehicle fault diagnosis systems which enable them to be more reliable and safe enhancing its sustainability. In this work after a review on problem of faults in the drivetrain of series hybrid electric vehicles (SHEV), a deep investigation on fault diagnosis of AC-DC power converter and permanent magnet synchronous motor (PMSM) have been done as two important parts of traction chains in SHEVs. In other major part of this work, four types of faults (stator winding inter turn short circuit, demagnetization, eccentricity ant bearing faults) of a PMSM have been studied. Inter turn short circuit of stator winding of PMSM in different speeds and loads has been considered to identify fault feature in all operation aspects, as it is expected by electric vehicle application. Experimental results aiming short circuits, bearing and eccentricity fault detection has been presented. Analytical and finite element method (FEM) aiming demagnetization fault investigation has been developed. The AC-DC converter switches are generally exposed to the possibility of outbreak open phase faults because of troubles of the switching devices. This work proposes a robust and efficient identification method for data acquisition selection aiming fault analysis and detection. Two new patterns under AC-DC converter failure are identified and presented. To achieve this goal, four different level of switches fault are considered on the basis of both simulation and experimental results. For accuracy needs of the identified pattern for SHEV application, several parameters have been considered namely: capacitor size changes, load and speed variations. On the basis of the developed fault sensitive models above, an ANN based fault detection, diagnosis strategy and the related algorithm have been developed to show the way of using the identified patterns in the supervision and the diagnosis of the PMSM drivetrain of SHEVs. ANN method have been used to develop three diagnosis based models for : the vector controlled PMSM under inter turn short circuit, the AC/DC power converter under an open phase fault and also the PMSM under unbalanced voltage caused by open phase DC/AC inverter. These models allow supervising the main components of the PMSM drivetrains used to propel the SHEV. The ANN advantages of ability to include a lot of data mad possible to classify the faults in terms of their type and severity. This allows estimating the performance degree of that drivetrains during faulty conditions through the parameter state of health (SOH). The latter can be used in a global control strategy of PMSM control in degraded mode in which the control is auto-adjusted when a defect occurs on the system. The goal is to ensure a continuity of service of the SHEV in faulty conditions to improve its reliability.

Ces travaux de thèse s’inscrivent dans la problématique de développement de transformateurs planar pour l’intégration de puissance, dans le contexte de l’avion plus électrique (More Electric Aircraft – MEA) où les contraintes de volume et de poids sont primordiales. Les composants magnétiques restent en effet un frein à l’intégration des systèmes d’Electronique de Puissance et les composants planar (transformateurs et inductances) offrent une alternative intéressante aux composants bobinés pour la réduction de la taille des convertisseurs.Dans ce manuscrit, des méthodes, un outil de dimensionnement et des prototypes de transformateurs planar (2 et 3 enroulements) en technologie feuillard et PCB sont développés pour des applications de convertisseur DC/DC aéronautique. Dans un premier temps, les modèles permettant le calcul des pertes, l'estimation de l'élévation de température et le calcul de l’inductance de fuite sont présentés et comparés afin de concevoir des outils de calculs pour la conception. Dans un deuxième temps, il est montré que la modification de la forme des angles des spires rectangulaires permet de réduire significativement les pertes cuivre HF. Sur la base de ces outils et résultats, des prototypes de transformateurs planar à 3 enroulements en PCB multicouches sont développés. De nombreux prototypes sont caractérisés et valident les modèles de dimensionnement proposés. Enfin, l’un de ces prototypes est intégré et testé dans un convertisseur de puissance DC/DC de 3.75kW mettant en évidence les gains obtenus. / These thesis works deal with the issue of the planar transformers development for power integration, in the context of the More Electric Aircraft (MEA), where the constraints of volume and weight are paramount. Magnetic components remain a hindrance to the integration of Power Electronics systems and planar components (transformers and inductors) offer an interesting alternative to wound components for reducing the size of converters.In these works, methods, a sizing tool and prototypes of planar transformers (2 and 3 windings) in strip and PCB technology are developed for aeronautical DC / DC converter applications. Firstly, the models allowing the calculation of the losses, the estimation of the temperature rise and the calculation of the leakage inductance are presented and compared in order to design calculation tools for engineers. In a second step, it is shown that the modification of the shape of the angles of rectangular turns makes it possible to significantly reduce the HF copper losses.Based on these tools and results, prototypes of 3-windings planar transformers in multilayer PCBs are developed. Many prototypes are characterized and validate the proposed designing models. Finally, one of these prototypes is integrated and tested in a DC / DC power converter of 3.75kW highlighting the gains obtained.