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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Transformer Leakage Inductance Design Methodology

The leakage inductance exhibited by a transformer depends on its winding geometry, which generally involves the selection of several key design parameters in addition to the winding structure and the interleaving configuration. With few resources explaining the effects of these design choices on the observed leakage inductance, numerous trial-and-error iterations become necessary to realize the desired leakage inductance. This paper explores more than a hundred winding geometries feasible in a 2-winding transformer comprising the same magnetic core, number of turns, and wire gauge, and finds the leakage inductance for each unique design using 2-D finite element method (FEM) simulations in association with the semi-analytical double- 2-D model. These leakage inductances are plotted and further analyzed to understand the effects of different design parameters on the effective leakage inductance. The results presented herein and the conclusions drawn from this research can serve as a valuable resource for future design practitioners from both industry and academia.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

New Hybrid Model for Evaluating the Frequency-Dependent Leakage Inductance of a Variable Inductance Transformer (VIT)

Skin and proximity effects can cause a significant drop in the effective leakage inductance of a transformer when the operating frequency is increased. Although the magnetic image method-based double-2-D model can calculate the lowfrequency leakage inductance with sufficient accuracy, it is inherently a frequency-independent model. While Dowell’s 1-D model uses frequency-dependent relations to account for both skin and proximity effects, its accuracy is severely affected by the assumed winding geometry. In this paper, a hybrid model is proposed that uses superposition to combine a modified Dowell’s model with the double-2-D model. The proposed model is investigated on a variable inductance transformer (VIT)—a partially-filled transformer whose leakage inductance can be varied by moving one of the windings mechanically. The frequency-dependent leakage inductances of the VIT evaluated using the hybrid model are in excellent agreement with the corresponding finite element method (FEM) simulated and experimentally measured values, thereby validating the proposed hybrid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Hybrid model to evaluate the frequency-dependent leakage inductance of partially-filled transformers

The leakage inductance of a transformer designed for a power electronic converter can drop significantly as the switching frequency is increased due to skin and proximity effects. Although the magnetic image method-based double-2-D model can predict the low-frequency leakage inductance of a partially-filled transformer with sufficient accuracy, it is inherently a frequency-independent model. While Dowell’s 1-D model uses frequency-dependent relations to account for both skin and proximity effects, its accuracy is severely affected by the assumed winding geometry. In this paper, a semianalytical hybrid model is proposed that uses superposition to combine a modified Dowell’s model with the double-2-D model to predict the true leakage inductance of partially-filled transformers at any given frequency. All three conductor types—round, foil, and litz wire—are modeled and analyzed. The quasi-2-D model is further investigated on a variable inductance transformer (VIT) whose winding geometry can be modified mechanically to vary its leakage inductance. With less than 5 % error throughout, the semi-analytically evaluated leakage inductances are in excellent agreement with the finite element method (FEM) simulated and experimentally measured leakage inductances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

New Modulation and Impact of Transformer Leakage Inductance on Current-Source Solid-State Transformer

This article presents a novel modulation scheme for device voltage stress mitigation and comprehensive analysis of the impact of transformer leakage inductance in a current-source solid-state transformer (SST). Different from dual active bridge (DAB) SST, the operation of the current-source SST is similar to that of a flyback converter. The device bridge on only one side of the transformer is active to store energy into or release energy from the magnetizing inductance which acts as a current-source dc link. Such flyback operation with reverse-blocking switches can lead to additional device voltage stress and incomplete zero-voltage switching (ZVS) on the current-source soft-switching solid-state transformer (S4T) under conventional modulation. A new modulation scheme is proposed to address this issue. Moreover, different from the DAB, the leakage inductance of the medium-frequency transformer (MFT) in the S4T is a parasitic element similar to that in a matrix SST and can cause additional device voltage stress. Though the resonant capacitors, originally added to achieve ZVS, can absorb and recycle the leakage energy in the S4T, these capacitors need to be increased with larger leakage inductances to limit the voltage stress. However, large resonant capacitors can result in more lost duty cycles and reduced efficiency. The impact of such leakage inductance on device voltage stress is analyzed comprehensively, which is critical to guide future research and design of the S4T. Experimental results from S4T prototypes for DC-DC, multiport AC-DC, and AC-AC conversion with 1:1 and 4:1 MFT comprehensively verify the proposed concepts. Lastly, a case study of a three-phase AC-AC S4T over a power range from 1 kVA to 100 kVA each module reveals that the MFT leakage inductance should be less than 1% of the magnetizing inductance for safe operation.

14 SOLAR ENERGY↗
NASA NTRS1985

Rotary transformer design with fixed magnetizing and/or leakage inductances

A design algorithm is considered for transformers that must transfer electric power across a rotating interface. Among other features, this procedure allows the designer to minimize either weight or losses for either a fixed magnetizing inductance or a fixed leakage inductance. Numerical results are included to indicate the design trade-offs between various parameters.

Stuart, T. A.↗
DOE OSTI2021

Planar Transformer With Asymmetric Integrated Leakage Inductance Using Horizontal Air Gap

This article presents a novel planar-based transformer winding and core structure with controllable leakage inductance generation for integrated magnetics applications. As a result of limitations in integrated magnetics from the literature, a new approach is proposed utilizing semi-interleaved windings and controllable leakage via a leakage flux core leg featuring a horizontal air gap. Here, the proposed transformer design is analyzed via detailed reluctance modeling to determine closed-form equations for the magnetizing and asymmetrically distributed leakage inductances. Next, a genetic-algorithm-based multiobjective design optimization problem is developed, seeking to minimize the core and winding losses of the proposed transformer subject to a set of parametric and geometric constraints in a dc-ac dual-active-bridge topology for microinverter applications. The optimization was extended to include other integrated magnetic structures from the literature, where it is determined that the proposed transformer is superior from the perspectives of efficiency, footprint area, and parasitic capacitance. Based on the results of the optimization analysis, two designs with theoretical transformer California Energy Commission (CEC) efficiency drops (i.e., CEC efficiency reduction specifically due to the transformer loss mechanisms) of 1.19% and 0.83% were fabricated and evaluated for electrical and thermal performance in the proposed 40 V, 400 W microinverter.

42 ENGINEERING↗
NASA NTRS2022

Calculation of Transformer Leakage Inductance by Simplified Flux Path Geometries

Series inductance is a critical energy storage element in isolated power converters. Many have explored methods of estimating the total leakage inductance of transformers as an integrated series inductance without external inductors. However, this poses challenges with medium frequency converters and magnetic ribbon-based cores, e.g., metal amorphous nanocrystalline. The material’s relatively high conductivity allows eddy currents to develop when magnetic flux intersects wide surfaces. These eddy currents result in significant additional losses that increase with increasing power flow. This paper presents a simplified and accurate method of estimating leakage flux while identifying separate leakage flux paths that correlate with the magnetic material surfaces. This enables an understanding the proportion of leakage flux that will contribute to extra losses. The methods presented are applicable to both leakage and fringing (around heterogeneous material interfaces) fluxes. This paper includes detailed FEA studies and 3D flux vector measurements matching the presented analytical models.

transformer↗
DOE OSTI2026

A Unified Design Theory for Multi-Port Polyphase Transformers Enabling Scalable Power-Multiplexed EV Fleet Charging Systems

This paper presents a unified analytical design theory for multi-port polyphase transformers, targeting scalable and isolated high-power Electric Vehicle (EV) fleet charging systems with power multiplexing capability. As fleet electrification accelerates, conventional one-to-one charger architectures face significant challenges in infrastructure cost, peak power demand, and low utilization of installed power electronics. Power-multiplexed charging architectures, which dynamically distribute power from a shared pool of converter modules across multiple vehicles, have emerged as a promising solution. However, such architectures require scalable, isolated multi-port power interfaces capable of routing energy among multiple inputs and outputs, whose design remains complex and dependent on iterative modeling. To address this gap, the proposed theory provides closed-form expressions for self-inductance, leakage inductance, and mutual coupling terms for arbitrary multi-phase, multi-port transformer structures. The formulation enables direct synthesis of isolated multi-input and multi-output resonant converter systems without reliance on geometry-specific finite-element analysis or extensive parameter extraction. This capability is particularly critical for power-multiplexed systems, where modular converter structures must interface with multiple vehicles while maintaining galvanic isolation and flexible power allocation. The effectiveness of the proposed framework is demonstrated through the design of a 360 kW multi-phase system operating over a 700–900 VDC input and 400–1250 VDC output range. PLECS simulation results confirm accurate prediction of system behavior and validate the applicability of the approach to multi-port, power-multiplexed charging scenarios. The proposed method significantly reduces design complexity while enabling scalable, cost-effective, and fully utilized EV fleet charging infrastructure.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗
DOE OSTI2021

Novel Transformer with Variable Leakage and Magnetizing Inductances

This paper introduces the concept of a novel variable inductance transformer (VIT) whose leakage and magnetizing inductances can be varied dynamically and independently to aid the advancement of research in isolated power electronic converters. In this transformer, the leakage inductance can be varied by varying the length of overlap between the primary and secondary windings, while the magnetizing inductance can be varied by varying the air gap between the core legs. Individual controls for the two inductances ensure that one can be varied independent of the other, as needed to satisfy different power conversion objectives. In this paper, the analytical models of the variable leakage and magnetizing inductances are presented. Analytical results are compared with those obtained from Finite Element Method (FEM) and an experimental prototype of a VIT. Analytical solutions of the variable leakage inductance present an error of less than 2.35 % when compared to FEM solutions, while the analytical solutions of the variable magnetizing inductance present a maximum error of 1.82 % when compared to experimental measurements.

image method, leakage inductance, magnetizing indu↗
NASA NTRS1991

On modeling the common mode inductor

The common mode inductor is the corner stone of filter design. One of the most important parameters of performance is leakage inductance. The role of leakage inductance in filter performance and current handling is discussed. It is demonstrated that leakage inductance is, in fact, desirable. Underlying physics of operation for the common mode inductor is reviewed. A model is presented which enables the designer to predict the leakage inductance of the common mode choke.

Nave, Mark J.↗
NASA NTRS1983

Development of a rotary power transformer and inverter drive for spacecraft

Many future satellites and spacecraft with spun and despun configurations will require the transfer of power across rotating interfaces in lieu of slip-rings and/or flexures. This is particularly true of spacecraft that have to demonstrate a long life expectancy. The rotary transformer has the desirable characteristics of high reliability and low noise, which qualify it as a potential replacement for slip rings. Development of a rotary power transformer follows the successful completion of a task to develop rotary signal-level transformers for the Galileo Spacecraft Project. The physical configuration of a rotary power transformer has a significant effect on its magnetic and electrical characteristics and therefore impacts the design of the dc/ac inverter driver. Important characteristics addressed during this development effort include: operating frequency, efficiency, transformer gap size, leakage inductance, and leakage flux. A breadboard inverter and rotary transformer were designed, fabricated and tested.

Mclyman, W. T.↗
DOE OSTI2020

Design Optimization of Medium-Frequency Transformer for DAB Converters With DC Bias Capacity

Medium-frequency transformer (MFT) dc bias is critical for the safe operation of dual-active-bridge (DAB) converters. To analyze the dc bias, expressions of dc bias are derived for SiC MOSFET DAB converters. It shows that the dc bias is a current source in steady state; thus, a dc bias current capacity is defined and used as a design constraint in the optimization of MFT. The dc bias current capacity is related to core materials, geometric parameters, and flux density, which is analyzed with analytical expression. Optimization equations with geometric variables are derived, which can be solved theoretically or numerically for both interleaved winding (IW) and separated winding (SW) MFT without and/or with leakage inductance design. Based on the optimization equations, different MFT designs for a 150-kW SiC MOSFET DAB converter are compared on the aspects of core materials, winding structures, and without/with leakage inductance design. The combination of IW structure MFT with auxiliary phase shift inductors is chosen, and the assembled prototype is tested with the 150-kW DAB converter. Here, the designed dc bias capacity, temperature rise, and efficiency are verified.

42 ENGINEERING↗
NASA NTRS1991

High reliability megawatt transformer/rectifier

The goal of the two phase program is to develop the technology and design and fabricate ultralightweight high reliability DC to DC converters for space power applications. The converters will operate from a 5000 V dc source and deliver 1 MW of power at 100 kV dc. The power weight density goal is 0.1 kg/kW. The cycle to cycle voltage stability goals was + or - 1 percent RMS. The converter is to operate at an ambient temperature of -40 C with 16 minute power pulses and one hour off time. The uniqueness of the design in Phase 1 resided in the dc switching array which operates the converter at 20 kHz using Hollotron plasma switches along with a specially designed low loss, low leakage inductance and a light weight high voltage transformer. This approach reduced considerably the number of components in the converter thereby increasing the system reliability. To achieve an optimum transformer for this application, the design uses four 25 kV secondary windings to produce the 100 kV dc output, thus reducing the transformer leakage inductance, and the ac voltage stresses. A specially designed insulation system improves the high voltage dielectric withstanding ability and reduces the insulation path thickness thereby reducing the component weight. Tradeoff studies and tests conducted on scaled-down model circuits and using representative coil insulation paths have verified the calculated transformer wave shape parameters and the insulation system safety. In Phase 1 of the program a converter design approach was developed and a preliminary transformer design was completed. A fault control circuit was designed and a thermal profile of the converter was also developed.

Zwass, Samuel↗
DOE OSTI2020

Investigation of Various Transformer Topologies for HF Isolation Applications

High-frequency (HF) transformers are an essential part of many power electronic devices. The performance and behavior of HF transformers can greatly affect the efficiency and performance of all systems, particularly, from a parasitic parameter point of view. In this article, HF transformers' parasitic parameters, such as leakage inductances and parasitic capacitances, are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements of different structures and winding arrangements. Also, the magnetic field, electric field, electric displacement field, and electric potential distribution within the transformers are simulated and analyzed. Four different HF transformers with E and U cores with different windings are designed and analyzed. Investigation outcomes help to classify structures according to the trade-off between leakage inductances and series parasitic capacitances. This information can later be used for the optimal selection and design of transformers as a function of their operating frequency for any power rating and voltage level. Moreover, 3-D FEM and experimental results validate the proposed methodology to be used for designing HF transformers in high-voltage/power applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

High temperature co-axial winding transformers

The analysis and design of co-axial winding transformers is presented. The design equations are derived and the different design approaches are discussed. One of the most important features of co-axial winding transformers is the fact that the leakage inductance is well controlled and can be made low. This is not the case in conventional winding transformers. In addition, the power density of co-axial winding transformers is higher than conventional ones. Hence, using co-axial winding transformers in a certain converter topology improves the power density of the converter. The design methodology used in meeting the proposed specifications of the co-axial winding transformer specifications are presented and discussed. The final transformer design was constructed in the lab. Co-axial winding transformers proved to be a good choice for high power density and high frequency applications. They have a more predictable performance compared with conventional transformers. In addition, the leakage inductance of the transformer can be controlled easily to suit a specific application. For space applications, one major concern is the extraction of heat from power apparatus to prevent excessive heating and hence damaging of these units. Because of the vacuum environment, the only way to extract heat is by using a cold plate. One advantage of co-axial winding transformers is that the surface area available to extract heat from is very large compared to conventional transformers. This stems from the unique structure of the co-axial transformer where the whole core surface area is exposed and can be utilized for cooling effectively. This is a crucial issue here since most of the losses are core losses.

Divan, Deepakraj M.↗
DOE OSTI2020

Design Optimization for Weighted Conduction Loss Minimization in a Dual-Active-Bridge-Based PV Microinverter

This manuscript presents a harmonic-superposition based frequency-domain approach for analysis and optimal design of a single-stage DAB-based DC-AC converter used in low-voltage DC to high voltage AC applications, such as PV microinverter. Specifically, two topological variations and correspondingly different modulation strategies involving up to four control variables (three phase shifts and switching frequency) are analyzed. Optimal trajectories of control variables are determined that result in minimized transformer RMS current at a given average power, while enforcing near-uniform ZVS. To make the design process holistic, an outer optimization loop is used to determine optimal values for the power transfer inductance (integrated as the transformer’s leakage inductance) and turns ratio, which minimize the weighted-average conduction loss contribution to the microinverter’s CEC efficiency. Based on the optimization analyses, a 400 W microinverter prototype is built and experimental results at one operating point are presented, achieving a measured efficiency of 92.8%.

14 SOLAR ENERGY↗