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A fast and accurate model of the transformer leakage inductance is crucial for optimization-based design of galvanically isolated converters. Analytical models are fastly executable, and therefore, especially suitable for such optimizations. This article compares several analytical leakage inductance per unit length models with respect to the accuracy and computational effort. The considered models are applicable to E-Core and U-Core transformers. 2D FEM simulations are used as a benchmark to evaluate the model accuracy, whereas the computation time is extracted as an indicator for computational effort. Six different transformer prototypes provide the geometries for the comparison. Based on the conducted comparisons, Roth's model is the most accurate. Rogowski's model is the fastest low-error model. Margueron's model is the most versatile as it takes the finite permeability of the core into account. The conducted comparisons lay the foundation for accurate and fast Double-2D modeling of the transformer leakage inductance as it is executed for the two main cross sections of E-core and U-core transformers: inside the transformer window, and outside the transformer window. This article is accompanied by a supplementary document summarizing the equations of Roth's and Margueron's model. ISSN:0885-8993 ISSN:1941-0107

Due to the increasing integration of renewable energies into the distribution grid, a deterioration of the grid power quality is expected. Consisting of a low-frequency transformer and a fractionally rated power electronic converter, hybrid transformers (HTs) can be applied to ensure a high power quality by controlling voltage, active and reactive power dynamically. For the application in conventional grids, HTs have to withstand considerable overvoltages and overcurrents during voltage surges or short circuits. Although HTs recently gained increasing research interest, protection requirements and protection concepts have not been discussed yet. These aspects are, however, essential to evaluate the practical potential of HTs. In this article, protection requirements are derived and a protection concept is developed and verified by simulations and experiments for a 100-kVA hybrid distribution transformer. Although the protection concept has a considerable impact on the design and performance of the converter, it increases the total losses and volume of the HT only insignificantly. An efficiency of 98.48% is achievable for an HT including protection, which is only slightly lower than the efficiency of 98.64% for a comparable conventional transformer. This renders the HT a promising solution for today's and future ac grids.

IEEE Transactions on Circuits and Systems I: Regular Papers, 67 (3), ISSN:1549-8328, ISSN:1057-7122, ISSN:1558-0806

Accurate and fast models of the equivalent circuit elements of gapped multiwinding inductors are essential to design galvanically isolated converters such as the Flyback converter and the LLC-converter. This paper derives equivalent circuit parameters of gapped multiwinding inductors from 2D magnetic field models proposed in this paper. It is shown and quantitatively examined that frequency affects resistance and inductance values of magnetically coupled windings by several effects. Especially eddy currents in windings induced by the air gap field play a significant role besides the well known skin- & proximity effect. The proposed model accurately takes into account all these effects in foil- and round wire conductors. The model is verified with FEM simulations and measurements., 2022 International Power Electronics Conference (IPEC-Himeji 2022- ECCE Asia), ISBN:978-4-8868-6425-3, ISBN:978-1-6654-1631-3

A model for estimating the total eddy current losses in ring ferrite cores is proposed, which is based on a microstructure model of the electrical parameters of the material (conductivity and permittivity) and on the solution of the wave equations in the core. The presented model, combined with state-of-the-art estimation of the hysteresis losses, gives good agreement with the core loss measurements, over a wide range of frequencies (10–700 kHz)., IEEE Transactions on Magnetics, 58 (2), ISSN:0018-9464, ISSN:1941-0069

A magneto-optical current measurement system based on the Faraday effect is evaluated for measuring fast pulse currents in high power applications. The current measurement system is based on the interaction of the magnetic field, generated by the current, and a beam of light propagating through magneto-optical material which is in close proximity to the current conductor. A high local magnetic field per ampère current inside the optical path is required to improve the accuracy and the sensitivity of the optical current measurement sensor.In this paper, the relation between the conductor geometry and the local magnetic field distribution is analytically modelled resulting in the geometry factor Kg. The analytical model enables an optimisation of the busbar geometry to increase the overall probe sensitivity and the accuracy of the optical current measurement system., 2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe), ISBN:978-1-6654-3384-6, ISBN:978-9-0758-1537-5

Modern wide-bandgap devices, such as SiC- or GaN-based devices, feature significantly reduced switching losses, and the question arises if soft-switching operating modes are still beneficial. For most of the semiconductor devices, only limited information is available to estimate the switching losses. Especially, if a wide operating range is desired, excessive measurements have to be performed to determine the switching losses for arbitrary operating points. Therefore, in this paper, a fast calculation method to determine the switching losses based on the charge equivalent approximation of the mosfet capacitances, relying only on datasheet parameters, is presented. In addition, the turn- off losses at high switching currents are investigated, and an analytical expression to estimate the maximum current range for which the mosfet can be turned off with negligible switching losses is proposed.

The transformer leakage inductance is one of the limiting factors for pulse shape quality in high voltage pulsed power (HVPP) applications such as cancer treatment, particle accelerators, and free electron lasers. Cone winding matrix (CWM) transformers are commonly used in HVPP applications as they offer low leakage inductance, low parasitic capacitance, high power density, and high insulation distance. This paper proposes an analytical Triple-2D leakage inductance model for CWM transformers. The model is based on a 2D model applicable to tilted cone windings which is derived by analytically integrating the magnetic potential. The Triple-2D modelling concept enables high accuracy and versatility. The model is verified with 2D FEM simulations and measurements on an existing pulse transformer for the compact linear collider at CERN. The analytical model is not only accurate and generally applicable but also rapidly executable enabling its time-efficient integration in optimisations., 2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe), ISBN:978-1-6654-3384-6, ISBN:978-9-0758-1537-5

For modelling and optimizing gapped high-frequency inductors, the calculation of eddy current losses in foil windings due to the two-dimensional fringing field caused by air gaps in the core is important. The winding loss models must offer a high accuracy when calculating the 2D field distribution and must be computationally efficient in order to enable several thousand calculations required during the optimization. This article proposes an analytical model based on the magnetic vector potential formulation that can predict the eddy current losses in foil windings due to the fringing field of an arbitrary number of air gaps. The analytical model is combined into a closed-form loss formula and verified by FEA simulations., 2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe), ISBN:978-1-6654-3384-6, ISBN:978-9-0758-1537-5

A bottleneck in optimization procedures of magnetic components is the calculation of the electric field strength (e.g. for an optimized insulation design) since this is based either on a slow numerical field simulation or on rough approximations. Hence, a fast and accurate method for the electric field calculation in the winding window is crucial for a fast optimization process. This paper presents a novel electric field calculation method that combines a variable potential function with a Schwarz-Christoffel (SC) mapping. This leads to accurate results, that match Finite Element Method (FEM) simulations as close as 5 %. The proposed method is more than 200 times faster than FEM and robust against parameter changes., 2021 IEEE Design Methodologies Conference (DMC), ISBN:978-1-6654-3140-8, ISBN:978-1-6654-0301-6

In this paper, the efficiency of the CLIC solid-state pulse modulator developed for the CERN research center and the long-pulse modulator system built for the ESS facility is investigated in detail. The analysis shows the current efficiency status of the modulators and how their performance could be improved by using SiC devices., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

Using GaN HEMTs in high current applications, such as pulsed power modulators for particle accelerator systems, requires the parallelization of multiple devices. In order to achieve a dynamically balanced current distribution between the parallel devices, synchronized gate voltages are crucial. Furthermore, the high switching speeds, which are often required in pulsed power systems, requires a high driving current capability and fast rise/fall times of the gate driver. Therefore, this paper presents a gate driver, based on a low voltage GaN HEMT half bridge, for driving four paralleled 650 V e-mode GaN HEMTs in a low inductive switching cell design., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

Stacked Polyphase Bridge Converters (SPB-C) are well suited for integrated motor drives, i.e. for systems that combine an electric motor with its supplying power electronic converter in one compact unit. A SPB-C requires a motor with multiple 3-phase winding systems. In the literature, the SPB-C is typically combined with motors whose winding systems are phase-aligned. This type of winding is magnetically equivalent to a 3-phase winding (with parallel branches). In this paper, the SPB-C with either 2, 3, or 4 modules is combined with a motor that has non-phase-aligned winding systems what results in a 6-, a 9-, or a 12-phase system, respectively. These multiphase systems are compared to 3-phase systems with the same number of modules with regard to efficiency, power density, and the possible degree of modularity and the benefits of the multiphase systems are evaluated., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

Fast and accurate transformer leakage inductance models are crucial for optimisation-based design of galvanically isolated converters. Analytical models are rapidly executable and therefore specially suitable for such optimisations. These analytical leakage inductance models typically consist of two steps: First, acquire the leakage inductance per unit length and second, scale this value with a suitable length. In this paper, the term leakage length is introduced for the scaling length. It is shown that the leakage length depends on the magnetic energy distribution and the most influential factors are determined. Furthermore, two accurate and fast leakage length models for E-core and U-core transformers with concentric windings are proposed: The Empirically Corrected Axial Flux (ECAF) model is based on a compact modification of the known axial flux formula. The cut line (CL) model pursues a semi-analytical approach and achieves high accuracy at the cost of higher computational effort. The models are verified with more than 6000 FEM simulations and the error of both models is significantly lower than the error of the known axial flux formula., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

In hybrid DC circuit breakers with current-injection, the arc in the mechanical switch is extinguished with a current pulse. After the arc extinction, the voltage increase across the mechanical switch must be limited in order to avoid an arc reignition. The voltage across the MS is usually assumed to be equal to the voltage across the capacitor CCI in the current-injection circuit, which increases slowly due to slow charging of the capacitor by the fault current. However, in reality the voltage across capacitor CCI is usually not zero at the point in time of the arc extinction. This results in high transient voltages across the mechanical switch, the so called so-called initial transient interruption voltage (ITIV) after the arc extinguishes. However, a fast increasing ITIV can lead to a thermal reignition of the arc. Therefore, it is crucial for the design of a DC-CB to understand, which effects contribute to a high ITIV. In this paper, these causes and the influence of the ITIV are investigated. Furthermore, the beneficial influence of grading capacitors parallel to the MS is investigated. Finally, an optimization of a DC-CB including the ITIV and its results are presented for a typical implementation of a current-injection DC-CB., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

For small scale roof-top systems, there is a trend towards module-integrated electronics. Module integrated ac inverters (ac modules) connect each photovoltaic (PV) module separately to the single-phase grid. They feature not only increased yield due to module-level maximum power point (MPP) tracking, but also further advantages such as reduced installation cost. This work investigates the concept of subpanel-level MPP tracking for ac modules, which allows us to increase yield thanks to reduced mismatching losses. Topology concepts to realize such a converter are systematically investigated and categorized. A topology comparison identifies two promising system concepts: first a single-stage converter with a three-port power balancer and second a two-stage topology with three paralleled dc–dc converters and a pulse width modulation full bridge. The later features the advantage of a small power-decoupling capacitor and is therefore further investigated. A model-based optimization of the investigated multi-input ac module is performed, applying high performing Gallium Nitride (GaN) devices and nanocrystalline core materials to increase efficiency. The built prototype confirms the accuracy of the model-based optimization. The performed efficiency study reveals an achievable efficiency of $\eta _{\text{EU}}$ = 94.5%. In order to compete with single-input ac modules, achieving typically an efficiency of 95.5%, the efficiency of multi-input ac modules must improve beyond the level achieved with the investigated two-stage ac-module topology. Given this result, the alternative system concept with a three-port power balancer in combination with a single-stage converter seems to be more promising, as it is conceptually similar to the high efficient single-input ac modules and may achieve the same high efficiency.

Litz wire (LW) is essential for reducing HF winding losses in medium frequency transformers and inductors. In order to predict the losses and optimise the parameters of LW, several analytical loss models have been presented. However, a detailed comparison of the models and the accuracy is missing. Therefore, this paper presents a comprehensive comparison of four loss models with respect to general mathematical approach, computational effort, as well as the impact of different parameters on the accuracy of the different models. Guidelines and insights for choosing the most suitable model are also provided., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

This paper presents a novel real-time implementation of linear model predictive control (MPC) schemes based on region-less explicit MPC (RL-EMPC). RL-EMPC is a recently proposed explicit MPC solution for achieving a low memory footprint compared to other explicit MPC methods. Thus RL-EMPC can effectively handle systems with high sampling rates even for large-size MPC problems, i.e. systems with many states and/or constraints. An architecture for an implementation on an FPGA device is presented and validated with two application examples (buck-boost converter, modular multilevel converter). Simulation results on FPGA hardware-level demonstrate that long-horizon linear MPC can be implemented on low-cost FPGAs with the proposed architecture for various power electronic systems., IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society, ISBN:978-1-7281-5414-5, ISBN:978-1-7281-5413-8, ISBN:978-1-7281-5415-2

The required module capacitance value is a driving factor of the volume and cost of modular multilevel converters (MMC). In order to minimize the required capacitance value, an optimal circulating current and common mode (CM) voltage injection strategy which keeps the conduction losses and die CM voltage as low as possible is proposed in this paper. Unlike previous methods from literature that only focus on minimizing the amplitude of energy fluctuation in the arm capacitors, the proposed optimization procedure is based on the optimal shaping of both the arm voltages and energies. As a result, the proposed optimization scheme achieves a further reduction in the required capacitance value of up to 42% compared to existing methods. The procedure is validated with closed loop simulation results covering the full operating range of an exemplary MMC., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

In this paper, a novel feedback controller concept for grid-connected Modular Multilevel Converters (MMC) is proposed. The controller is based on the Linear Quadratic Regulator (LQR) method and shows outstanding control performance since it is a multi-input multi-output (MIMO) controller. The proposed controller achieves efficient energy balancing control with high bandwidth, such that the required margin for the module capacitance value for dynamic control is reduced and an excellent transient behavior can be accomplished. Alternatively, compact MMC designs can be realized with a reduced capacitance value by sacrificing some transient performance. The implementation requires a relatively low computational effort, and the simple control structure enables a straightforward tuning and time-delay compensation., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

Advanced high voltage (3.3-15kV) SiC MOSFETs have been developed for future medium voltage converters over the past decade due to their superior performance. In order to better understand the operation limits and potential of these devices, this paper evaluates the I max -f sw -dv/dt trade-off (maximal current-handling capability at a specific switching frequency and at a defined switching speed) for high voltage SiC MOSFETs based on a proposed linearized analytical switching loss model. There, high voltage SiC MOSFETs manufactured by Cree combined with data from literature for scaling are used as reference.

Birefringence and optical losses in the optical sensor head of a Faraday effect based, high accuracy and high bandwidth current measurement system lead to changes of the polarisation state and orientation. These changes, if not properly determined and calibrated, lead to systematic measurement errors. Therefore, a calibration method for the optical current measurement system focusing on pulse current applications is proposed. The procedure is based on a zero-current measurement and a full (Stokes) polarimeter. It determines the full polarisation state and orientation of a beam propagating through the optical system. The calibration method then allows to determine the parasitic linear birefringence caused by any subsequent optical element in the system. Eventually, an error analysis characterising the potential error reduction by the proposed calibration method is conducted. Further, the additionally introduced error sources caused by the full polarimeter approach are characterised., 2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), ISBN:978-9-0758-1536-8, ISBN:978-1-7281-9807-1

Excellent control performance is a prerequisite to operate compact modular multilevel converter (MMC) designs that employ very small module capacitance values. This paper presents a novel model predictive control (MPC) scheme featuring a linear and accurate prediction model to overcome the drawbacks of comparable control schemes. The MPC is based on a modulator that determines the switching states of the individual modules to guarantee scalability of the algorithm also for MMCs with a high number of modules. The control performance of the proposed MPC scheme is evaluated with simulations and compared to a classic cascaded PI-controller scheme., IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, ISBN:978-1-7281-4878-6, ISBN:978-1-7281-4879-3

Low switching energies render GaN semiconductor switches a promising technology for hard-switched inverters. For high current applications, the parallel connection of multiple GaN devices makes the PCB and gate drive design challenging. Furthermore, the SMD packages of currently available GaN devices exacerbate a mechanically robust and at the same time thermally and electrically highly conductive integration of the switches into the overall converter. This paper quantifies the performance improvements of GaN FETs over Si MOSFETs and investigates implications of paralleling GaN on the gate drive design. Based on a low voltage high current GaN half-bridge cell, $\frac{{{\text{d}}v}}{{{\text{d}}t}}$-induced turn-on and oscillations of parallel switches are evaluated theoretically and experimentally. Design recommendations for the gate drive and the integration of such a cell into the overall converter are presented.

This paper presents the design of the optical system of a current sensor with a wide bandwidth and a high accuracy. The principle is based on the Faraday effect, which describes the effect of magnetic fields on linearly polarized light in magneto-optical material. To identify suitable materials for the optical system the main requirements and specification are determined. A theoretical description of the optical system shows a maximal applicable magnetic field frequency due to the finite velocity of light inside the material. Hence, the theoretical characterisation of the system implies practical boundaries on the optical material and its specifications. Finally, two different magneto-optical crystals, Terbium Gallium Garnet and Cadmium Manganese Telluride, are investigated, assembled and put into an optical system prototype.

Circuit breakers with current injection enable fast interruption of fault currents in DC grids. Independent of the topology, a high number of semiconductors and capacitors is required. The minimum required number of semiconductors and capacitors depend mainly on the system voltage and the maximum fault current. However, also the MS characteristics have considerable influence on the required number of semiconductors and capacitors. Therefore, in this paper the influence of the MS characteristics on the arc extinction and the influence of the arc voltage on the DC-CB design is presented. In addition, optimization procedures for current injection circuit breaker are presented, which include the MS characteristics and four different possibilities to include the arc voltage. Finally, three DC-CB topologies are compared in terms of number of semiconductors and capacitors., 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe), ISBN:978-9-0758-1531-3, ISBN:978-9-0758-1530-6, ISBN:978-1-7281-2361-5

This paper introduces a special session on results of the Swiss competence center on energy research FURIES that has been established in coordination with the Swiss Energy strategy 2050 with the specific aim to develop, promote and deploy power grid-related innovative solutions toward the implementation of the Swiss Energy Strategy 2050. This contribution will report on activities within WP 3, “AC/DC multi-terminal grids and power electronics”. This WP includes three subtasks with contributions from the major Swiss technical universities: Multi-terminal HVDC system design, fault detection and clearing in multi-terminal HVDC, enabling component and converter technologies and applications. The spectrum of the center's activities is briefly introduced and as an illustrative example, the contributions of the SCCER FURIES in relation with HVDC grids are summarized. These contributions include: new high power DC testing methods and laboratories, new DC breaker principles and fault location techniques, AC/DC grid resonance analysis and novel converter technologies.

The growing need for higher efficiency in converter systems and in power electronic systems in general has led to the implementation of more complex and sophisticated control algorithms. Often, the controller unit is separated from the sensors and the data has to be transmitted via an isolated channel. Plastic optical fibers are utilized for this task due to their low cost, high robustness and easy handling. In order to reduce the number of fibers, intensity modulation can be used to transmit multiple signals over a single optical fiber. A recently introduced modulation scheme with an additional intensity level indicating the clock allows a simple clock recovery at the receiver. In this paper, three receiver concepts based on this modulation scheme are presented for medium data rates in the range of 20 - 50 Mbps which is sufficient for most power electronic applications. The low complexity and small footprint of the proposed concepts facilitate the system integration. Furthermore, a more compact system can be designed due to the lower number of necessary fibers and corresponding transmitter and receiver circuits., 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe), ISBN:978-9-0758-1531-3, ISBN:978-9-0758-1530-6, ISBN:978-1-7281-2361-5

Hardware-in-the-Loop tests of components for high-voltage dc transmission grids, for example circuit breakers, require converter systems capable of generating a high output current with fast transients of the output signal at different output voltages. In this paper, a three-level buck converter (N3L) employing three different supply voltages to enable a wide voltage operation range is presented. The modulation of the converter is investigated in detail with special focus on ripple cancellation, the startup of the interleaved converter and the level shifting between different converter output voltages. A prototype system is designed and constructed, optimized for pulsed power operation and compared to a two level and to a neutral point clamped converter design. The system has been simulated numerically and the design boundaries are validated by measurements on the prototype system.

IEEE Transactions on Industrial Electronics, 66 (3), ISSN:0278-0046, ISSN:1557-9948

IEEJ Transactions on Industry Applications, 8 (2), ISSN:1348-8163, ISSN:0913-6339

Hybrid transformers (HT) are a promising concept to increase the grid flexibility. In the past, only HT with bidirectional auxiliary converter have been investigated. In this paper, HT with unidirectional auxiliary converter, which are advantageous in terms of reliability, cost and complexity, are investigated and their operational limits are derived., 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe), ISBN:978-9-0758-1531-3, ISBN:978-9-0758-1530-6, ISBN:978-1-7281-2361-5

2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), ISBN:978-4-88686-405-5, ISBN:978-4-88686-403-1, ISBN:978-1-5386-4190-3

2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), ISBN:978-4-88686-405-5, ISBN:978-4-88686-403-1, ISBN:978-1-5386-4190-3

The double-star chopper-cell (DSCC) and the double-star bridge-cell (DSBC) modular multilevel converters (MMCs) may be designed with a reduced number of modules when higher grid currents and an increased volume of the passive components are acceptable. The full-bridge modules in the DSBC even allow for designs with increased power conversion efficiency at the expense of additional modules. This paper presents an integrated optimal design methodology that exploits these additional degrees of freedom while at the same time maximizing power density and power conversion efficiency. To demonstrate the effectiveness of the proposed approach, a short-circuit-proof 250kW, 35kVDC bidirectional active rectifier prototype system is presented that has been designed with emphasis on reduced realization effort.

2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), ISBN:978-4-88686-405-5, ISBN:978-4-88686-403-1, ISBN:978-1-5386-4190-3

2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), ISBN:978-4-88686-405-5, ISBN:978-4-88686-403-1, ISBN:978-1-5386-4190-3

The calculation of eddy current losses in foil windings exposed to a 2-D fringing field is a complex task because of the current displacement along the height of the foil. For model-based optimization of magnetic components, loss calculation with 2-D finite element method simulation is not an option because of the high computational effort. The existing alternative calculation methods with low computational effort, rely on approximations applicable only to a certain geometrical arrangement of the windings and the air gap. Therefore, in this study, a new semi-numerical method was developed to overcome these limitations. The method is based on the mirroring method and is applicable to arbitrary air gaps and winding arrangements. The accuracy of the new method was verified by measurements, and the deviation of the model results from the measured losses was found to be below 15%.