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This paper presents an accurate analytical method for calculating the leakage inductance of shell-type E-core transformers with rectangular windings. For this purpose, first, an expression for calculating the leakage inductance per unit length inside the core window considering the core walls as the flux-normal boundary condition is derived. Then, a new accurate method for determining the Mean Length of Turns (MLT) based on the total stored energy is presented. The MLT is needed for the leakage inductance calculation using 2-D methods. By dividing the MLT into three partial lengths and calculating the corresponding leakage inductances using three different core window arrangements, the effect of core structure on the total leakage inductance is considered. The method is verified by 3-D FEM simulations as well as the leakage inductance measurements on two different fabricated transformer prototypes. The superiority of the method is also confirmed by comparisons with the previous analytical approaches. The proposed method enables the leakage inductance calculation with an error less than 1%, compared to the 3-D FEM results. Using the presented method, the leakage inductance calculations can be performed rapidly and accurately in the design stage without the need for time-consuming 3-D FEM simulations.

An active-clamp resonant power factor correction converter with output ripple suppression is proposed and analyzed. It combines a buck power factor correction (PFC) unit and a resonant dc-dc unit by sharing one active switch. With another active-clamp switch, a recycling path is built to recover the leakage inductance energy of transformer, which improves the efficiency and the voltage stress of active switch. The effect of voltage ripple of dc link on output can be suppressed by fast voltage mode control loop. Therefore, low output current or voltage ripple can be achieved. With small voltage ripple across output of buck unit, the turn on time of active switch is almost constant in a half line cycle. Therefore, power factor correction can be achieved with inductor current of buck unit operating in discontinuous conduction mode (DCM). Finally, a 65W high power factor (PF) converter prototype for LED driver application with 91.08% peak efficiency and low output current ripple is built to verify the analytical results.

In this paper, an integrated transformer design methodology for dual-active-bridge (DAB) converters, which basically utilize leakage inductance so as to substitute a cumbersome inductor in the conventional DAB converters, is newly proposed. The proposed integrated transformer with integrated leakage inductance inherently includes leakage inductance and magnetizing inductance, whose values can be appropriately selected by modulating the number of turns and the center-core air-gap. Based on the theoretical analysis of the DAB converters, the major parameters, i.e., primary and secondary current levels and its phase difference, can be derived, and these values are utilized for magnetic analysis of the proposed integrated transformer. Considering core loss and copper loss of the proposed integrated transformer in the DAB converters, optimal values of the center-core air-gap $l_{g}$ and the optimal number of turns $N_{\mathrm {1,}op} ~\&~ N_{\mathrm {2,}op}$ can be determined so that high power efficiency is achieved at a normal operating point of the DAB converters. The 20W prototypes of the DAB converter with EER2834 and EER3019 of the ferrite cores were fabricated and verified by simulation and experiment. The design results showed that the optimal number of turns at $l_{g} =2.0$ mm are found to be 11 and 10, for the EER2834 and EER3019, respectively. Compared to 94.5% and 96.3% of AC efficiencies for the conventional transformer and inductor set, the proposed integrated transformer achieved 95.8% and 96.9% of AC efficiencies at maximum power transfer point of $\theta _{p} = \pi $ /2 for EER2834 and EER3019, respectively.

This paper proposes a non-isolated three-port converter which integrates the input port, battery port, and load port into one converter for renewable energy applications. The coupled inductor and switched capacitor are used to achieve high voltage gain and three power switches can be utilized to realize the power flows between the sources, the battery, and the load. The energy stored in the leakage inductance is recycled to reduce the voltage stress of the power switch. In addition, various operating stages are analyzed and design considerations are presented. Compared to the relevant converters, the proposed converter can realize power flows and achieve high voltage gain by using few components. Finally, a laboratory prototype of the proposed converter with input port voltage 24 V, battery port voltage 48 V, and output voltage 400 V with 200 W rated power is implemented to validate the feasibility and effectiveness of the theoretical analyses.

LLC resonant converter has the advantages of high frequency and high efficiency, and has been developed rapidly and widely used in recent years. However, due to the presence of multiple magnetic components in the circuit, the improvement of power density is limited. To solve this problem, integrated magnetic transformer is usually designed to replace the discrete magnetics. While, the leakage inductance of the transformer cannot be controlled, the loss of the converter increases. In this paper, a magnetic integrated LLC resonant converter with independent inductance winding is proposed. The resonant inductance and magnetizing inductance are integrated with the transformer in the same magnetic core by using the decoupling integration method. Compared with the existing solution of magnetic integrated LLC resonant converter, this method can reduce the leakage inductance between the transformer windings and decrease the magnetic saturation of the integrated magnetics, thereby reducing the magnetic core loss and improving the efficiency of the converter. Compared with the discrete magnetics, the volume and weight of the magnetic components are reduced by 25.68% and 43.82% respectively, making the power density of the converter effectively improved. Finally, an experimental prototype of integrated magnetic LLC resonant converter with operating frequency of 350kHz and output power of 400W is built. The experimental results verify the correctness of the design scheme.

The magnetic field of end windings affects the leakage reactance of end windings and the eddy current losses of end structures in the large electrical machine. With the rising of single-machine capacity, such effect becomes more obvious. However, due to the complexity of end structures of large electrical machine, it will cause difficulty in meshing and long calculation time to calculate the magnetic field of end windings by using 3-D finite element method (FEM). In order to calculate the magnetic field of end windings quickly and accurately, an improved analytical algorithm (IAA) is proposed based on the mirror image principle, which takes into account the influence of stator back core and air-gap on the magnetic field of end windings by adding the fictitious boundary current and air-gap current, respectively. Taking a 300Mvar synchronous condenser (SC) as an example, the boundary current, air-gap current and magnetic field of end windings are calculated. Then, the influence of stator back core and stator involute segment current on the magnetic field of end windings are analyzed, which provides a theoretical support for the design and optimization of SC. To validate the accuracy of IAA, the calculation result is compared with 3-D FEM.

Funding Information: This work was supported by FinElib, Finland, through the FinELib consortium's agreement with IEEE. Publisher Copyright: © 2013 IEEE. In this paper, a new family of ultra-high step-up DC-DC converters based on a center-tapped coupled inductor (CI) is proposed. These single-switch converters employ different inductive and capacitive power transfer techniques by utilizing multi-winding CIs, intermediate capacitor links and simple switched-capacitors to improve the transferred power rate, harvest magnetizing and leakage inductance energies, and enhance power density. Achieving high voltage gain in low duty cycle values enables the proposed converters to operate under wide output voltage ranges; meanwhile, distributing the output voltage on two or three output ports alleviates the voltage stress on output terminal components. Low input current ripple, simple pulse width modulation control, low switch voltage stress and operation without circulating current can be listed as other features. In this paper, the proposed family is introduced, theoretically analyzed and compared with other state-of-the-art researches. Finally, the accuracy of analyses are evaluated with some experimental tests of a 1.25 kW experimental prototype.

Recent studies on compact and lightweight electronic devices have demonstrated that the LLC resonant converter (LRC) can facilitate achieving high efficiency and high power density. Moreover, employing a planar transformer can further improve the overall system power density. Although the planar transformer can assist in reducing the size of the converter, its high magnetic coupling makes the leakage inductance too small for a resonant inductor in the LRC. Therefore, an extra inductor must be employed separately, leading a considerable decrease in the power density. From this reason, significant research on integrated magnetics has been conducted to combine a transformer and external inductor into a single core. However, they require additional wires or magnetic sheets, and their structures are complex and costly. To overcome these limitations, the integrated magnetics planar transformer (IMPT) for a high power density LRC is proposed in this paper. In the proposed approach, since the primary wire is split into each side leg of the EE-type magnetic core and each operates as a transformer and a resonant inductor alternatively, an external inductor or additional wires are unnecessary. In addition, since the magnetic flux density of the IMPT is approximately equivalent to that of conventional transformer, the core size and the number of turns are almost the same. Therefore, the proposed IMPT features higher efficiency and power density without additional size and costs. To confirm the validity of the proposed IMPT, the operational principles, theoretical analysis, design considerations, and experimental results from a 350 W prototype are presented.

This paper proposes a high-performance isolated single-ended primary inductor converter (SEPIC) that is integrated with a non-dissipative snubber for a light-emitting diode (LED) driver. The proposed LED driver employs the snubber circuit to minimize any switching overvoltage caused by parasitic leakage inductance of the high-frequency transformer in the isolated SEPIC converter. This paper also presents a detail theoretical analysis of the proposed LED driver including its operating modes and design calculation. The experimental results of the proposed LED driver at the rated power of 18 W shows that it has a high-power factor, low harmonics, employs non-electrolytic capacitors, low switching stress, high reliability and high efficiency.

In this paper, a non-isolated high step-up interleaved DC-DC converter for distributed generation applications such as solar cells and fuel cells. The proposed converter mixes the benefits of magnetic coupling, voltage multiplier, and voltage lift techniques to conventional interleaved schemes. The proposed converter's voltage lift technique can increase the voltage gain while guaranteeing low voltage stress of the switches. And the magnetic coupling method can combine the switched capacitor of the voltage multiplier technique with the lossless clamp circuit to achieve high voltage gain and reuse the leakage inductance energy to the output terminal. In addition, this leakage inductance energy can achieve zero current switching turn on soft switching performance and mitigate the output diode reverse recovery problem. The proposed converter avoids the extreme duty cycles that cause conduction losses in power devices and can give very low voltage stresses. Therefore, the use of low voltage rated MOSFETs and diodes not only reduces switching losses and costs, but also improves efficiency.

In this paper, a high-efficiency DC/DC converter with low voltage stress is designed for green power applications. The proposed non-isolated high step-up DC/DC converter combines the advantages of switched capacitors, coupling inductors, and voltage multiplier techniques. Adding the cells of the switched capacitor not only increases the voltage gain but reduces the voltage stress of the semiconductor devices. High voltage gain can be achieved by adding a coupled inductor method to adjust the turns ratio. When these are combined with a voltage multiplier circuit, the leakage energy of the coupled inductor is recirculated to the output terminal with lossless passive clamping performance. The leakage inductance of the coupled inductor controls the current dropping rate of the output diode turn OFF so that the reverse-recovery problem is mitigated. The proposed converter integrates these three techniques to achieve high voltage gain without operating at maximum duty cycle. In addition, switching loss reduction is realized through zero current switching turn ON soft switching performance with low voltage stress of semiconductor devices. Finally, this paper verifies the performance of the proposed converter for theoretical analysis by using a $35\sim 45\text{V}$ input, 380V output, and 1kW power prototype circuit.

A high frequency planar transformer with integrated leakage inductance and half-turn secondary windings is proposed for LLC isolated DC-DC converters. The primary windings are wound on both the center leg and the sides leg of an EI planar ferrite core to integrate the leakage inductance. With the proposed method, the magnetizing inductance is constant while adjusting the leakage inductance, thus the design of the magnetizing inductance and the leakage inductance can be decoupled. To adapt the high voltage transform ratio from 380V to 12V, the number of turns of the secondary windings is designed to be 0.5. The output voltage ripple of the LLC converter equipped with the proposed transformer is analyzed and its output filter is designed. The characteristics of the proposed transformer are simulated by ANSYS Maxwell and Simplorer. Finally, a 360V~400V input, regulated 12V output, 750W LLC resonant converter with silicon carbide (SiC) devices was built with the proposed transformer. The evaluated converter realized a power density of 23.1W/cm3 and a peak efficiency of 97% with all the auxiliary power and control circuit included.

Multiphase machines have attracted significant attention in both academic and industrial sectors as candidates for high-power safety-critical applications as well as wind energy conversion systems. Undoubtedly, this interest has been fueled by the rapid development in semiconductor devices. Due to the lack of available standard stator frames suitable for constructing multiphase machines of any phase order, machines with multiple three-phase winding sets seem to be the standard topology in many industrial applications. Recent literature has demonstrated a simple generalized technique to rewind a standard three-phase stator frame with a generic prime-phase order stator winding. However, based on the selected slot/pole combination, this technique yields a small unbalance component in the stator phase currents due to the stator leakage inductance mismatch among different phases. This paper further investigates the optimal slot/pole choices, for a given phase-order, that minimize the unbalance in the stator leakage components between phases to ensure comparable performance to standard symmetrical n -phase machines. The analysis is presented for the well-known phase orders employed in literature, namely, 5-phase, 7-phase, and 11-phase windings. The effect of winding asymmetry on mathematical modeling and, hence, the dynamic response is also investigated. A 1kW prototype machine equipped with a five-phase winding is used to experimentally verify the theoretical findings. - 2013 IEEE. Scopus

It is well-known that the deformation of transformer winding can produce detectable changes to the frequency response spectrum compared with a referenced past measurement. To interpret such changes for diagnostic purposes, main causes of the trace deviation need to be recognized precisely. In addition, it is useful that the interpretation of transformer frequency response is classified in a way that IoT-based techniques can be developed in the near future to analyze the transformer mechanical integrity. This paper has specifically concentrated on the inductance and capacitance variation due to the axial and radial disk deformation of transformer winding. Analytical analyses on self- and mutual-inductance variations are discussed and capacitance variation is studied in detail for symmetrical and asymmetrical transformer disk deformations. A numerical example is provided to establish the analytical approach and compare inductance and capacitance variation. The analytical approach is finally examined through the experimental study of disk deformation in a 66 kV transformer winding.

Fractional slot concentrated winding machines (FSCWMs) with the low operation speed and large diameter usually have a large number of poles and slots; thus, numerous pole/slot combinations are feasible. The common practice to choose pole/slot combinations by multiplying the basic combinations may neglect some competitive candidates. Taking 36-slot FSCWMs as examples, this paper investigates the influence of pole numbers on torque density and flux-weakening ability, the two most vital performances of wheel-hub machine. It is shown that the machines with pole number slightly less than the slot number have the highest torque densities. Each component of synchronous inductance is separately analyzed, and its variation against pole numbers shows obvious regularity. Machines with pole numbers larger than the slot numbers have an excellent flux-weakening ability due to the large inductance and small permanent magnet flux linkage. The measurements together with the finite element analysis results confirm that the stator leakage inductance contributes the most to the superior flux-weakening ability. The identical analysis is also performed on 54-slot and 81-slot FSCWMs, with similar regularities observed.

To meet the requirements of high voltage boosting and high efficiency, a novel high step-up zero voltage transition (ZVT) DC/DC converter based on active switched-inductor (ASL) is proposed. This converter combines ASL and coupled inductor structure, thus can reduce the voltage and current stress of power switch, and the active clamping technology provides zero voltage transition (ZVT) for all switches. The coupled inductors can realize relatively high voltage gain with appropriate turns ratio while all magnetic components can be integrated in one core. In addition, thanks to the leakage inductance, the reverse recovery problem of diodes is resolved. The working principle of the proposed converter is analyzed in detail, also the characteristics including voltage gain, the condition of ZVT is discussed. Then, a family of derived converters are listed and compared to each other. According to the proposed converter, a 500W prototype with 100kHz switching frequency is established in the lab, and the experimental results are given to verify the analysis.