Modeling and optimization of an inductive magnetic harvester considering nonlinear effects

The high-frequency transformer (HFT) is an important component of dual active bridge (DAB) converters to achieve galvanic isolation and bidirectional power transmission, which is widely utilized in renewable energy, distribution grids, railway traction and electric ships. However, the real characteristics of the HFT such as magnetic inductance, leakage inductance and stray capacitance would influence the operation conditions of power converters. This paper analyzes the inductance characteristics of the HFT, focusing on the variation of the leakage inductance. To evaluate the magnitude of the leakage inductance, HFT samples wounded by nanocrystalline cores under 600 V/10 kW with various winding structures and air gap positions are simulated by finite element analysis (FEA) and tested by experimental measurements. The results show that the leakage inductance with the concentric windings is negligibly small, whereas the leakage inductance with the separate windings is so much larger that is even within the range of the phase-shift inductance required in DAB converters. On the other hand, the influence of air gaps on the leakage inductance is not evident not only in the concentric windings but also in the separate windings. A DAB prototype of 600 V/10 kW is designed and established, where the HFT with the separate windings has a leakage inductance adjusted to the magnitude of the phase-shift inductance required. The measurement results validate the feasibility that the phase-shift inductance could be substituted by the leakage inductance of the HFT.

Cathodic protection (CP) anode bed grounding resistance calculating formulae, given by CP standards, are reviewed firstly. Underground assumptions and limitations of these grounding calculating formulae are analyzed, which means formula method may encounter problems when designing anode beds in high soil resistivity area. Based on finite element analysis (FEA) method, a new grounding resistance calculation method is suggested, which is can be treated as more suitable and flexible for anode bed grounding resistance calculation in high soil resistivity condition. The main steps of FEA method, geometric model building, meshing, boundary condition and solver setting, and grounding resistance calculating according to Ohmic law, are clearly presented. In order to introduce the FEA method in detail, a realistic anode bed design program for Northwestern China area, where soil resistivity is always very high, is demonstrated. Based field soil resistivity survey data by Wenner 4-pin method, the candidate anode bed site, named Station A, is regarded as optimal site, and Barnes’ soil layer analysis method is used to predict soil resistivity distribution in depth direction. Both formula method and FEA method are used to calculate grounding resistance. The following comparison results show that formulae from COR-GS-023, GB21448-2008, РД 153-39.4-039-99 standards and FEA method give out almost the same grounding resistance results under the assumption of uniform soil resistivity, which also, from another angle, verifies the correctness of FEA method. But for FEA method, designers can include realistic soil resistivity distribution function and any anode rod layout plan in calculation model. So, FEA method can be treated as a more flexible tool to calculate CP anode bed grounding resistance.

This paper presents a general approach to compute the leakage inductances of power transformers with turn-to-turn winding faults. The leakage inductances are obtained by using well-known conventional formulas, adapted to the asymmetrical conditions produced by the interturn fault in the leakage flux distribution. Two methods for calculating the leakage inductances are presented: the first requires detailed information about the geometry of the windings whereas the second uses simplifying assumptions, allowing to express the leakage inductances as a function of the nameplate short-circuit inductance, the number of turns, and core dimensions. A leakage inductance model of the transformer with faulty turns is also proposed, which is based on the three-winding transformer theory. This leakage inductance equivalent circuit can be easily integrated into other electromagnetic transient simulators. The results obtained from the application of the analytical methods and the equivalent circuit are validated using data obtained from finite-element analysis and experimental short-circuit tests.

While designing a high-frequency transformer, its parasitic components should be modeled with caution as it influences the performance of the transformer. In many converter topologies, a transformer with specific parasitic components could be needed. For example, in the phase-shifted full-bridge converter, bidirectional dual active bridge converter dc-dc converters, or LLC resonant converters, the leakage inductance of the transformer needs to be precise as it influences the overall performance of the converter. In this paper, a simple yet effective technique has been investigated to design high-frequency transformers with adjustable leakage inductance. The transformer is designed to be used in a 100 kHz series resonant dc-dc converter, where the leakage inductance of the transformer is used as the resonant inductor. The proposed design technique utilizes the variation of the winding structures where a split bobbin separates primary and secondary windings. At first, the finite element analysis (FEA) based simulation is performed to estimate and analyze the leakage inductance with different winding structures, and then the experimental investigations are performed. Both the simulation and experimental results demonstrate that by simply varying the winding arrangements in the hybrid split-bobbin transformer, the leakage inductance can be changed while keeping the magnetizing inductance of the transformer constant.

The anti-scuffing bearing capacity of gears is a significant issue for their service lives, especially for the cases with heavy loads or high speeds. Generally, the anti-scuffing bearing capacity is evaluated according to the surface contact temperature that can be calculated with either analytical methods or finite element analysis (FEA) methods. The analytical methods usually apply the theory of Blok to efficiently obtain the results by simplifying some actual physical conditions, which are well considered in the FEA methods with accurate results but more computation time. Conversely, a new efficient and accurate analytical method is proposed by introducing the actual lubricant film thickness and continuous heat transfer for the theory of Blok. These two physical conditions are the key issues for the calculation of the two parts of surface contact temperature, flash temperature and bulk temperature, respectively. For the calculation of flash temperature, elastohydrodynamic lubrication (EHL) is introduced to consider the lubricant film thickness for the theory of Blok, and the result is obtained by solving the Reynolds equation efficiently with the finite difference method. For the bulk temperature, the result for a contacting point on the gear tooth surface is directly obtained according the theory of Blok, and the continuous heat transfer among the adjacent contacting points is considered with Gaussian heat morphology, which can accurately construct the bulk temperature field distribution in the contact region. The proposed method is validated as in good agreement with the FEA method and with less computation time.

In high-frequency transformers (HFTs), Litz wire is widely adopted to reduce eddy current loss and improve efficiency. Despite the advantages that Litz wire brings, calculating the leakage inductance is also more difficult. As one of the key parameters of HFT, leakage inductance directly affects the power transmission performance. This article proposes a new model to estimate the leakage inductance of transformers accurately in a wide frequency range. Unlike traditional models, the new model makes comprehensive analysis of leakage field and more accurate estimate of leakage inductance. In order to verify the precision of the proposed model, five transformers are built and analyzed by performance comparison. By comparing the results of measurement, finite element analysis (FEA), simulation and existing model, it is proved that the proposed model is more precise. Finally, the effect of winding layers and wire density on the variation of leakage inductance with frequency is revealed.

New and large synchronous condensers (SC) are required to improve the sub-transient voltage stability on the high voltage DC transmission, and the leakage inductance accurate calculation of SC is vital to meet the grid requirements. An improved end leakage inductance calculation method based on frozen permeability was proposed. Firstly, the end leakage inductance separation method by using 2D/3D finite element analysis was presented. Secondly, according to the actual structure of a 300 Mvar SC, 2D and 3D end FEA models were established respectively to analyze the magnetic saturation distribution in different operational states. Finally, the end leakage inductance under the different operation conditions was calculated and compared with the conventional method. The results show that to calculate the end-winding leakage inductance of SC, the effect of magnetic saturation and the rotor position should be considered, especially in the transient condition, and the saturation distribution of d and q-axis are also different under different working conditions.

Inductive power transfer (IPT) is gaining popularity across a wide range of battery charging applications like biomedical, consumer electronics and electric vehicle (EV) charging. One of the major challenges in designing IPT charge pads is determining the optimal physical sizes of the magnetic couplers resulting in efficient power transfer and low cost of materials. In EV applications, it is especially difficult due to the variation in nominal air gap, required power levels associated with different vehicle classes, and charging locations that may be encountered. This paper aims to determine the relationship between optimal coupler sizes and the nominal air gap of an IPT system. Finite element analysis (FEA) is used to model the electromagnetic behavior of the magnetic couplers. A multi-objective optimization framework is built to reveal the Pareto fronts which show the trade-offs between the power transfer efficiencies and the coupler power densities at different air gaps. This method is applied on polarized double-D (DD) couplers for a 5 kW IPT system at different air gaps. Analyzing the power densities of the Pareto Optimal designs an approximate relation between optimal pad sizes and the air gap is derived. Results show that there is an exponential relationship between the optimal coupler sizes and the nominal air gap.

Premature failures of stator insulation account for a large percentage of repairs of marine generator systems. The failure mechanisms of such faults have been presented in many parts of the literature. Partial discharge activity, thermal degradation, thermal cycling, harmonics and transients are some examples of such failure mechanisms. Whilst there has been an insight into the failure mechanisms, there is still no definite answer to how these defects manifest in the first place. Most of the failures that have been identified within literature are on end windings, especially slot ends. Some failure mechanisms have also been linked with thermal cycling. Frequent and rigorous stop/start cycles stress coils by inducing mechanical forces between elements of the coil and housing owing to differential thermal expansion. This differential expansion is dependent on the rate of rise of temperature and also the different coefficients of thermal expansion of the materials. The present paper will evaluate the thermal degradation of insulation systems used on marine generators using Finite Element Analysis (FEA) methods. On board temperature measurements of stator coils during a high speed run are used as one of the parameters within the FEA simulations, to investigate if there is any risk of differential thermal expansions during such an operational cycle. Different ramp rates are also analyzed within the FEA simulations to understand the effect of uneven thermal expansions and the risk of material degradation of the insulation in coils on marine systems. A brief review of the standards available for thermal cycling and testing are also presented within the paper.

Resonant converters rely on a precise knowledge of leakage inductance of the equipped transformers. Resonant circuit topologies such as LLC usually utilize the transformer leakage as an inductive component in the resonant tank, allowing for a drastic reduction in the converter weight, size and volume. The existence of the secondary leakage inductance affects the whole operation of the LLC resonant converter. This paper reveals that placing the secondary winding near the air gap would increase the resonant tank input impedance, vertically shrink the voltage-gain curve of the converter, and consequently minimize the frequency range (i.e frequency bandwidth with respect to load variation). On contrary, placing the secondary winding in a close contact with the magnetic core would decrease the resonant tank input impedance, vertically stretches the voltage-gain curve of the converter, and widen the frequency variation range. It has been reported that the winding location with respect to the air gap has an impact on the leakage inductance value. In other words, placing the secondary winding in a close contact with the magnetic core (zero mmf position) would maximize the leakage energy storage originated from the secondary winding, and hence maximize the secondary leakage inductance and vice versa. The theoretical discussion is presented which is merely based on Ampere's law and Dowell's model. Furthermore, transformer prototypes had been constructed and tested in a 390V/12V-220W LLC converter prototype to evaluate the proposed analysis.

Offshore pipeline on-bottom roughness analysis is generally performed to understand pipe stress and areas of free spanning. In this paper, the predicted pipeline profiles, by finite element analysis (FEA) modeling, are compared with survey data. Several case studies are presented and parametric effects are assessed. The FEA modeling procedures are presented in this paper along with several project experiences. The pipeline on-bottom roughness analysis is conducted to determine the pipe stress and the associated fatigue damage due to internal pressure and temperature fluctuation and vortex-induced vibration (VIV) of free span sections due to seabed unevenness. The analysis presented in this paper can aid the design of pipeline free spans and mitigation, if required. The parametric effects of higher and lower bound soil stiffness, friction resistance, pipeline bottom tension, external / internal pressure, and content density are considered. The predicted pipeline profiles by FEA modeling are compared with surveyed profiles under several loading conditions. A strong correlation between survey data and finite element analysis (FEA) is achieved. This paper shows that the FEA stress prediction is adequate, and the FEA modeling is suitable as an advanced design tool for pipeline on-bottom roughness assessment and free span behavior analysis. A commonly used mitigation method for VIV fatigue is to install VIV suppression strakes. For overstresses due to pipeline bending effect, the common mitigation methods are to install mechanical supports, use heavy wall pipe and correct the seabed unevenness among others. It is important to reliably predict the pipeline profiles in order to precisely assess the pipeline free span response and to provide guidance to determine a proper free span mitigation strategy. The FEA method can be utilized to realistically simulate the pipeline on-bottom roughness behavior affected by the pipe properties, pipe-soil interaction including penetration and soil friction resistance, the internal and external pressure, product content, temperature profile, and the bottom tension from pipe-lay. An accurately built FEA model can provide a reliable prediction for the pipeline profile, free spanning length and gap under all conditions, which are crucial for the stress and fatigue assessment as well as for the design of free span mitigation.

This paper presents a general method based on a permeance network (PN) in order to study stator turn faults in permanent-magnet synchronous machines (PMSMs). This approach includes two main parts: first, static computations are performed to identify the various parameters of a faulty machine. Leakage inductances as well as self and cross saturations are taken into account to improve the results without increasing the CPU time compared to finite element analysis (FEA). Then, a faulty model of the PMSM is used rather than time-stepping finite element method (TSFEM) which requires large CPU time. The model gives dynamical results and it is suitable to studying PMSM's behavior under faults, testing, or investigating fault detection methods under parameter variations. The method can be applied for any type of winding arrangements and different fault configurations. Various comparisons validate the proposed approach to determine precisely the parameters of the PMSM model under turn faults including the saturation effect and leakage inductances.

Slot leakage field accounts for an important quota of the total leakage flux in electric machines. The computation of unsaturated slot leakage inductances can rely on analytical formulas for simple open slot shapes, while the case of semiclosed slots is more critical and typically requires finite element analysis (FEA) or analytically solving the field over the whole machine domain. This paper sets forth an analytical procedure for computing the leakage field in semiclosed slots of unsaturated electric machines. The method is based on solving Maxwell's equations in the slot domain alone, which is made possible by appropriately defining boundary conditions in the slot opening region. The method proposed is assessed by comparison with FEA. Validations indicate that a good accuracy is achieved by the presented approach in predicting unsaturated leakage inductances, while FEA is required when magnetic saturation effects need to be taken into account.

The paper studies the magnetic field distribution of three degree-of-freedom (3-DOF) permanent magnet (PM) spherical motor adopting the 3-D magnetic equivalent circuits (MEC) method. Compared with the analytical method and finite element analysis (FEA) method, the MEC has such desirable attributes as moderate computational effort and reasonable accuracy. The model of PM spherical motor is evenly meshed into elements in spherical coordinates, and the expressions of reluctances and magnetomotive force (MMF) sources in the element have been deduced. Given that magnetic field of the PM spherical motor distributes in the whole space, to reduce the number of elements and increase the solving speed, an approximate equipotential surface is adopted based on the simplified magnetic circuit, and the different magnetic boundary conditions are represented by the corresponding states of nodes and branches of the elements. Finally, the MEC network, which represents half of the magnetic pole and the corresponding air region of the motor, is built. Flux density distribution is calculated by means of the proposed model and verified by the FEA method.

In this paper, the coupling factor between the primary and secondary windings of low profile planar transformer (LPPT) is studied with Finite Element Analysis (FEA) method, focusing on the coupling factor, the different planar structure is discussed. The electromagnetism simulation model is created in ANSOFT HFSS, and the coupling factor can reach 0.92976. Results of the simulation say agree with that of the prototype experimental test.