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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↗
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↗
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↗
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↗
DOE OSTI2021

Impact of the Transformer Magnetizing Inductance on the Performance of the Dual-Active Bridge Converter

The magnetizing inductance of the high-frequency transformer in the dual-active bridge (DAB) converter is usually assumed to be much larger than its leakage inductance, thereby the magnetizing current can be negligible. However, ignoring the magnetizing current will lead to an error in the DAB converter design process. This paper analyzes the operation and performance of the DAB converter for a general case in which the transformer magnetizing inductance is taken into consideration. The analysis shows that the magnetizing inductance impacts the soft-switching region, the power transfer capability, and the leakage inductor current. A simulation case study is provided to verify the analysis. A DAB converter prototype is built to experimentally validate the analysis as well.

Yin, Shiyuan↗
DOE OSTI2020

Soft-Switching Solid-State Transformer With Reduced Conduction Loss

Solid-state transformers (SSTs) are a promising solution photovoltaic (PV), wind, traction, data center, battery energy storage system (BESS), and fast charging electric vehicle (EV) applications. The traditional SSTs are typically three-stage, i.e., hard-switching cascaded multilevel rectifiers and inverters with dual active bridge (DAB) converters, which leads to bulky passives, low efficiency, and high electromagnetic interference (EMI). This article proposes a new soft-switching solid-state transformer (S4T). The S4T has full-range zero-voltage switching (ZVS), electrolytic capacitor-less dc link, and controlled dv/dt, which reduces EMI. The S4T comprises two reverse-blocking current-source inverter (CSI) bridges, auxiliary branches for ZVS, and transformer magnetizing inductor as a reduced dc link with 60% ripple. Compared with the prior S4T, an effective change on the leakage inductance diode is made to reduce the number of the devices on the main power path by 20% for significant conduction loss saving and retain the same functionality of damping the resonance between the leakage and resonant capacitors and recycling trapped leakage energy. The conduction loss saving is crucial, being the dominating loss mechanism in SSTs. Importantly, the proposed single-stage SST not only holds the potential for high power density and high efficiency but also has full functionality, e.g., multiport dc loads integration, voltage regulation, and reactive power compensation, unlike the traditional single-stage matrix SST. The S4T can achieve single-stage isolated bidirectional dc–dc, ac–dc, dc–ac, or ac–ac conversion. It can also be configured input-series output-parallel (ISOP) in a modular way for medium-voltage (MV) grids. Hence, the S4T is a promising candidate for the SST. The full functionality, e.g., voltage buck–boost, multiport, etc., and the universality of the S4T for the dc–dc, dc–ac, and ac–ac conversion are verified through the simulations and experiments of two-port and three-port MV prototypes based on 3.3 kV SiC MOSFETs in dc–dc, dc–ac, and ac–ac modes at 2 kV.

14 SOLAR ENERGY↗
DOE OSTI2022

7.2 kV Three-Port SiC Single-Stage Current-Source Solid-State Transformer With 90 kV Lightning Protection

This article proposes a multiport modular single-stage current-source solid-state transformer (SST) for applications like photovoltaic, energy storage integration, electric vehicle fast charging, data center, etc. The 7.2 kV 50 kVA current-source SST consists of five input-series output-parallel modules, each based on 3.3 kV SiC reverse-blocking MOSFET-plus-diode modules. The proposed SST has some unique features. First, compared to the voltage-source or matrix converter-based SSTs, the current-source SST has a unique advantage of single-stage isolated AC/DC or AC/AC conversion with an inductive DC link, but no medium-voltage (MV) AC experiments have been reported. This article for the first time demonstrates MV AC current-source SST up to 7.5 kV peak. Second, the multiport SST has a buffer port for active power decoupling (APD) or energy storage integration. The double-line-frequency power ripple from single-phase AC grid normally results in a large capacitor size in MV SSTs. The APD scheme is proposed in MV applications for the first time to enable a reduced DC link and the electrolytic capacitor-less SST with high reliability. Third, as a direct grid-connected converter without line-frequency transformer, insulation and protection are critical. A medium-frequency transformer design passes 55 kV basic-insulation level (BIL) and 60 kV high potential dielectrics withstand test with only 0.09% leakage inductance. Importantly, a lightning protection scheme is presented to protect the SST itself from 90 kV BIL impulse. Fourth, the proposed current-source SST topology is a modular soft-switching solid-state transformer (M-S4T) with full-range zero-voltage switching and controlled dv/dt for low electromagnetic interference. Furthermore, these concepts are verified in a three-port M-S4T prototype with forced oil cooling under single-module, stacked-module, steady-state, and dynamic operations.

14 SOLAR ENERGY↗
DOE OSTI2026

A Novel Low-Profile High-Efficiency Three-Phase Matrix Transformer

High step-down isolated DC-DC conversion from an 800 V DC bus to low-voltage, high-current outputs is required in automotive auxiliary converters and data center power supplies. In such applications, conventional transformer-based converters require large turns ratios, which increase winding resistance, leakage inductance, and magnetic height. This paper proposes a novel low-profile three-phase matrix transformer that realizes a large effective voltage ratio through flux division among multiple secondary legs, without increasing the physical turns count of each winding. As a result, the proposed structure reduces copper usage and transformer height while preserving the voltage conversion capability of a conventional three-phase transformer. Finite element analysis shows that the proposed design reduces magnetic height by 27%, ferrite volume by 34%, and copper volume by 28%. Circuit-level simulations of an 800 V/12 V,3 kW CLLLC dual-active-bridge converter further show that the lower winding resistance reduces total system loss by 91% and increases DC-DC efficiency from 82.6% to 97.6% at 3 kW output.

Inoue, Shuntaro [ORNL] (ORCID:0000000262637627)↗
DOE OSTI2021

Design and Optimization of a 200-kW Medium-Frequency Transformer for Medium-Voltage SiC PV Inverters

This paper presents a design and optimization methodology for a 200-kW medium-frequency transformer (MFT) based on low-loss magnetic core (FINEMET FT-3TL). The proposed optimal design methodology consists of predesign, preliminary design, and optimal design. In the preliminary design, the parallel-concentric winding structure is selected to increase the current carrying capability and reduce the leakage inductance. Based on the parallel-concentric winding concept, a novel cooing and insulation structure with 3-D printed bobbins are proposed. The optimal designed MFT prototype achieves a power density higher than 19.23 kW/L. The electrical insulation system is tested at 12 kV ac peak voltage. In addition, the partial discharge (PD) test is conducted at 7.5 kV ac peak voltage to ensure the PD-free design. The high-frequency bipolar pulsewidth modulation voltage insulation (PD) test is the first time applied in MFT design and test process. Finally, the transformer is applied in a dual-active-bridge (DAB) converter with 200 kW rated power. The peak efficiency of the DAB converter is 99.53%, and the efficiency at 200 kW is 98.85%. The peak efficiency of MFT is 99.844%, and the efficiency at 200 kW is 99.842%.

42 ENGINEERING↗
DOE OSTI2021

SiC-Based 5-kV Universal Modular Soft-Switching Solid-State Transformer (M-S4T) for Medium-Voltage DC Microgrids and Distribution Grids

Medium-voltage DC (MVDC) grids are attractive for electric aircraft and ship power systems, battery energy storage system (BESS), fast charging electric vehicle (EV), etc. Such EV or BESS applications need isolated bidirectional MVDC to LVDC or LVAC converters. However, the existing Si-based solutions cannot fulfill the requirements of a high-efficiency and robust converter for MVDC grids. This paper presents a 5 kV SiC-based universal modular solid-state transformer (SST). This universal current-source SST can interface either a LVAC or LVDC grid with a MVDC grid in single-stage power conversion, while the conventional dual active bridge (DAB) converter needs an additional inverter. The proposed SST module using 3.3 kV SiC MOSFETs and diodes is bidirectional and can serve as a building block in series or parallel for higher-voltage higher-power systems. The topology of each module is based on the soft-switching solid-state transformer (S4T) with reduced conduction loss, which features reduced EMI through controlled dv/dt, and high efficiency with full-range ZVS for main devices and ZCS for auxiliary devices. Operation principle of the modular S4T (M-S4T), capacitor voltage balancing control between the cascaded modules, design of components including a medium-voltage (MV) medium-frequency transformer (MFT) to realize a 50 kVA 5 kV DC to 600 V DC or 480 V AC M-S4T are presented. Importantly, the MV MFT prototype achieves very low leakage inductance (0.13%) and 15 kV insulation with coaxial cables and nanocrystalline cores. Here, the proposed universal modular SST is compared against the DAB solution and verified with DC-DC and DC-AC simulation and 4 kV experimental results. Significantly, the MV experimental results of a modular DC transformer with each module at MVDC are rarely covered in the literature and reported for the first time.

14 SOLAR ENERGY↗
DOE OSTI2022

A Tri-Port Current-Source Soft-Switching Medium-Voltage String Inverter for Large-Scale Solar-Plus-Storage Farms

This article presents a tri-port current-source soft-switching medium-voltage string inverter (TMVSI) to reduce the Levelized cost of energy (LCOE) of large-scale solar-plus-storage (SPS) farms. Throughout this work, the topology, operating principle, circuit simulation, control, and hardware design of the TMVSI are introduced. In addition, three key challenges compromising the performance of the TMVSI are addressed in this article. First, a new feed-forward compensation for model predictive control of the TMVSI is proposed to compensate for sampling and computational delay and high dc-link ripple with low computational cost and high scalability. Second, the use of laminated permanent magnets is proposed to reduce the losses of the MV medium-frequency transformer (MFT) in the TMVSI while increasing its saturation current. Finally, an improved U-shape winding pattern is proposed to decrease the leakage inductance of the MV MFT and reduce the voltage stress across semiconductor switches without adding cost or complexity. Here, the effectiveness of the TMVSI is validated by experiments at up to 20kW/500V in different test cases with custom-built prototypes. The contributions of this work make the TMVSI a viable solution to SPS farms and unleash its potential for LCOE reduction.

14 SOLAR ENERGY↗
DOE OSTI2026

Optimal Hairpin Winding Configuration for EV Traction Motors to Enhance Active CMV Cancellation Capability of NPL.X Inverter

Active common-mode voltage (CMV) cancellation in neutral-point-less (NPL.X) inverter is an effective approach for reducing common-mode electromagnetic interference and alleviating voltage stress associated with high-speed switching in EV traction drives. However, the existing hairpin winding configuration often exhibits impedance imbalance due to slot leakage inductance and manufacturing constraints, limiting the effectiveness of active CMV cancellation. This paper investigates symmetric hairpin winding configurations for a dual-three-phase EV traction machine to improve impedance symmetry. Considering the manufacturing constraints of six-layer hairpin windings, four feasible symmetric winding configurations are analyzed. Two-dimensional finite-element analysis is performed to extract the impedance parameters of each configuration. The extracted impedance parameters are used to quantify the impedance mismatch between complementary phase pairs and evaluate its influence on active CMV cancellation. The results show that the fully interleaved winding configuration achieves perfectly balanced phase impedances with 0 % mismatch, whereas the mismatch in the other configurations ranges from approximately 2.4 % to 0.8 %. Consequently, the resulting total CMV overshoot is significantly suppressed to near zero voltage under high-voltage and high switching frequency operating conditions, demonstrating the importance of winding symmetry for maximizing the active CMV cancellation capability of the NPL.X inverter.

Lee, Kangbeen [Purdue Univ., West Lafayette, IN (U↗