Richard Schlesinger

Last Name

Schlesinger

First Name

Richard

ORCID

0000-0002-2143-185X

Organisational unit

03889 - Biela, Jürgen / Biela, Jürgen

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Publications1 - 10 of 10

Modelling and Design Optimisation of a High Bandwidth and High Precision Optical Current Sensor Based on the Faraday Effect
Rietmann, Stefan; Schlesinger, Richard; Biela, Jürgen (2021)
2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe)
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.
Leakage Inductance Modelling of Transformers: Accurate and Fast Models to Scale the Leakage Inductance Per Unit Length
Schlesinger, Richard; Biela, Jürgen (2020)
2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe)
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.
Analytical Transformer Leakage Inductance Modelling
Schlesinger, Richard (2023)
Photovoltaics, railway systems, cancer treatment, and particle accelerators are only a few examples of applications that include a power electronic converter. Many of these converter topologies are galvanically isolated, i.e. they contain a transformer as key element. The transformer leakage inductance significantly affects the converter's operation as it represents a series inductance caused by the imperfection of the magnetic coupling of the windings. Hence, leakage inductance and other converter parameters are best determined in an optimisation before the converter is built to achieve maximum efficiency and power density. Such optimisations require models of the converter's operating parameters to evaluate the virtual prototype's performance. Since these optimisations can require several thousands (and more) feasible designs, it is imperative that the models are both accurate and rapidly executable to deliver significant results within a reasonable amount of time. Analytical models are well-suited for this purpose as they are accurate independent of the geometrical dimensions & aspect ratios and typically have low calculation times. This thesis provides a comprehensive analytical modelling approach of transformer leakage inductance. The transformer as three-dimensional object is split up into winding sections with constant cross section. Leakage inductance contributions of these winding sections are calculated and summed up to obtain the total leakage inductance. Common assumptions in leakage inductance calculations are discussed and evaluated. Existing leakage inductance models are investigated and compared. Furthermore, models are developed for cases that literature does not provide a solution for. The hybrid Quasi-3D (HQ3D) model is presented as the standard model for E/U-core transformers with conventional windings. The model calculates the leakage inductance contribution of curved winding sections directly using an analytical derivation based on Roth's expression for the magnetic vector potential. For straight winding sections, previously existing models are carefully selected based on their performance regarding accuracy and computational effort. The HQ3D model is applicable to arbitrary winding positions as long as the windings are wound on the main core leg. The analytical nature of all used models inherently guarantees high accuracy independent of the geometrical dimensions & aspect ratios. The HQ3D model is verified with measurements and the finite element method (FEM) simulations and is in the accuracy range of geometrical uncertainties, which is the maximum accuracy that models can achieve. For matrix transformers with cone-shaped windings, the improved Triple-2D (iT2D) model is introduced as standard model. The main part of the iT2D model is an analytical antiderivative that enables the analytical integration of the magnetic energy to calculate the leakage inductance between cone-shaped and regular windings. The iT2D model is also characterised by taking a third basic cross section into account for which a solution is derived analytically. The iT2D model is also verified experimentally and with FEM simulations. Both, the HQ3D and the iT2D model are rapidly executable as well as accurate, making them well-suited candidates in optimisations. The accuracy of both models shows that splitting up the three-dimensional transformer geometry into several two-dimensional field problems is an effective way that allows analytically calculating leakage inductance. Ultimately, more accurate and computationally efficient analytical models enable to increase the performance of optimised converters.
Improved Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers
Schlesinger, Richard; Biela, Jürgen (2023)
IEEE Open Journal of Power Electronics
The transformer leakage inductance is one of the limiting factors for pulse shape quality in high voltage pulsed power (HVPP) converters that are essential in applications such as cancer treatment, particle accelerators, and free electron lasers. Cone winding matrix (CWM) transformers are commonly used in HVPP converters as they offer low leakage inductance and high insulation distance. This paper proposes an improved Triple-2D (iT2D) leakage inductance model for CWM transformers. The iT2D model identifies three basic cross sections of CWM transformers and calculates their associated leakage inductance contributions. The paper proposes an accurate and compact analytical formula of the leakage inductance contribution resulting from the magnetic energy stored in between the magnetic cores. For cross sections with cone windings, an expression is presented that computes the leakage inductance per unit length of non-parallel windings. The iT2D model is verified with measurements and finite element simulations of three transformer prototypes. The analytical solutions used in the iT2D model ensure applicability to arbitrary geometric aspect ratios and designs. Furthermore, the iT2D model is rapidly executable enabling its time-efficient integration in converter optimisations.
Frequency-Dependent Equivalent Circuit Parameter Calculation of Gapped Multiwinding Inductors
Ewald, Thomas; Schlesinger, Richard; Agner, Jan; et al. (2022)
2022 International Power Electronics Conference (IPEC-Himeji 2022- ECCE Asia)
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.
Comparison of Analytical Transformer Leakage Inductance Models: Accuracy vs. Computational Effort
Schlesinger, Richard; Biela, Jürgen (2019)
2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe)
Fast and accurate models of design and operating parameters are crucial for optimisation-based design of power electronic converters. The leakage inductance of transformers is one of these design parameters. This paper compares various analytical 1D and 2D leakage inductance models, and assesses them with respect to a trade-off between accuracy vs. computational effort. The computed leakage inductance per length values are compared to 2D FEM simulation results to determine the model accuracy, whereas the calculation times are extracted as indicator of each model's computational effort. The considered models are applied to six existing transformer geometries and compared to measurements. Roth's model is the most accurate of the considered models, Rogowski's model is the fastest model, and Margueron's model is the most versatile as it takes the magnetic permeability of the core into account.
Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers
Schlesinger, Richard; Biela, Jürgen (2021)
2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe)
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.
Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model
Schlesinger, Richard; Ewald, Thomas; Biela, Jürgen (2023)
IEEE Transactions on Power Electronics
Fast and accurate models of the transformer leakage inductance are crucial for optimisation-based design of isolated converters. This paper proposes an analytical Hybrid Quasi-3D (HQ3D) model for E/U/ER/UR-core type transformers that combines the best-suited submodels for each winding section of the transformer. A submodel is developed that directly calculates the leakage inductance contribution of curved winding sections based on the integration of the radially weighted magnetic energy density. The HQ3D model can describe arbitrary winding positions and its fully analytical nature guarantees optimal geometrical scalability. The only restriction is that the windings need to be parallel to the core edges. The HQ3D model is in the accuracy range of 3D FEM and verified with measurements on nine transformer prototypes with significantly different geometry ranges. The HQ3D model is rapidly executable and therefore well-suited for optimisations of galvanically isolated converters.
Equivalent Circuit Element Calculation of Gapped Multiwinding Inductors
Ewald, Thomas; Schlesinger, Richard; Agner, Jan P.; et al. (2023)
IEEJ Journal of Industry Applications
Accurate and fast models of the equivalent circuit (EC) elements of gapped multiwinding inductors are essential for the design of galvanically isolated converters, such as Flyback and LLC converters. Typically, the EC elements are acquired from measurements or time-consuming FEM simulations, both of which are disadvantageous for optimizing the design of the magnetic device. This paper proposes a multiwinding magnetic device EC that exclusively uses the impedance matrix elements, i.e., self- and mutual impedances. The advantage of the impedance matrix equivalent circuit (IMEC) is that self- and mutual impedances are directly measurable. Furthermore, the paper presents an analytical 2D magnetic field model to calculate the EC elements. It is quantitatively confirmed that frequency significantly affects the resistances and the inductances of magnetically coupled windings. In particular, eddy currents in windings induced by the fringing field of the air gap play a role besides the well known skin and proximity effect. The proposed model accurately considers all these effects in foil, Litz, and round wire conductors. The model is verified using FEM simulations and measurements.
Comparison of Analytical Models of Transformer Leakage Inductance: Accuracy vs. Computational Effort
Schlesinger, Richard; Biela, Jürgen (2021)
IEEE Transactions on Power Electronics
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.

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Richard Schlesinger

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