Leakage Inductances Calculation for Power Transformers Interturn Fault Studies

The inter-turn fault is a common fault of oil-immersed transformers. Due to the deterioration of inter-turn insulation, its resistance decreases, which leads to an increase in the winding coil current and loss, causing the winding temperature to rise. Therefore, analyzing the electrothermal characteristics of inter-turn short circuit faults in oil-immersed transformers can provide a theoretical basis for the diagnosis of inter-turn faults in transformers. This paper studies the equivalent circuit under inter-turn faults and establishes a field–circuit coupling model to calculate the current characteristics under different inter-turn short circuit faults of transformers. The distribution of coil losses under faults is calculated as thermal source excitations, and a thermal–fluid-coupled calculation model for oil-immersed transformers is established. After the experimental verification, it is found that both the errors between the winding and tank surface temperatures do not exceed the acceptable limits, validating the effectiveness of this model. Using this model to calculate the temperature distribution for various inter-turn short circuit faults in transformers reveals their hot-spot characteristics. The results indicate that under inter-turn fault conditions, the temperature at faulty turns will gradually increase towards a limit, eventually leading to coil damage. This research provides theoretical support for enhancing transformer detection and diagnostic capabilities.

Leakage inductance is one of the key parameters of a transformer, and it is often intentionally integrated into transformers. Rogowski’s equation is generally used for leakage inductance calculation; however, it is only applicable to concentric winding transformers where windings have the same height. Consequently, it has limited applications. This paper proposes a transformer leakage inductance calculation method using a double Fourier series. The limitation of Rogowski’s leakage inductance equation was analyzed in practical applications, and a new model for calculating the leakage inductance of a double-group-overlapping winding transformer was derived. Experimental prototypes of transformers were developed, and their simulation models were built in Ansys. The correctness of the proposed calculation method for transformer leakage inductance using a double Fourier series was verified by comparing the calculation results with the simulation and measured ones. A sensitivity analysis was also conducted by studying the variations in different parameters that might affect the leakage inductance value. The proposed calculation model gives an intuitive and simple method with less calculation and design effort while maintaining reasonable accuracy for leakage inductance calculation. In addition, the featured double Fourier series approach has a wider range of applications than Rogowski’s equation.

The transformer leakage inductance (TLI) is an important parameter in the design phase of the isolated power supplies. Hence, the TLI estimation before the transformer construction is very useful for the designers. The previous works considered an ordered winding turn arrangement (WTA) for the transformers. This assumption considers only ideal windings which may result in a significant error from what will be achieved after the construction of the transformer. This article concentrates on the transformers with nonideal windings in which the turns are not ordered. The uneven distribution of the turns in the layers is mainly due to the wrapping machine error. Hence, for a specific transformer with determined electrical specifications, different WTAs will be possible. Thus, the corresponding TLIs will be different. This will cause uncertainties about the TLI values for the designer. The article proposes a method for considering a large number of possible WTAs of nonideal windings. Hence, the proposed method can be used as a probability tool to plot the probability distribution of the TLIs. Furthermore, based on the obtained results, effective guidelines are recommended for the designers to avoid critical situations according to the transformer specifications. The accuracy of the method is evaluated using finite-element (FE) analysis and experimental measurements. The FE and experimental results both are in conformity with the statistical analysis of the article.

It is important to understand the relationship between iron core configurations and leakage flux distributions to get a better design of synchronous machines. This paper presents a method for calculating the steadyand transient-state leakage flux distributions in salient-pole synchronous machines. The method provides information on leakage flux distributions that cannot be obtained by terminal quantities. The method analyzes the leakage inductances that properly represent the corresponding leakage fluxes. They are calculated using the gap flux distributions by finite elements with magnetic saturation. The calculated leakage inductances of a synchronous machine under various loads are also shown and the relationship between the inductances and magnetic saturation is discussed.

The leakage inductance of a high-frequency transformer affects the operating mode and performance in dc/dc converters, so it is necessary to calculate the leakage inductance accurately. In the existing analytical calculation methods of leakage inductance of high-frequency transformers with Litz wire winding, the nonarea-equivalent high-frequency analytical method is applied to calculate leakage inductance. However, the calculated leakage inductance value is lower than its actual value due to the neglect of the irregular region between turns. In order to improve the calculation accuracy, this article proposes an analytical calculation method of leakage inductance for the high-frequency transformer with Litz wire winding, which considers the irregular region between turns. The 2-D magnetic field distribution in the transformer window and attenuation caused by high-frequency effects on magnetic field energy are analyzed and applied in this proposed method, to take the energy stored in the irregular region between turns into account indirectly. Thus, the proposed analytical expression for leakage inductance is derived correspondingly. Finally, the accuracy of the proposed method is verified by simulations and experiments. The results indicate that the relative error of calculating leakage inductance can be reduced from 16.25% to 3.79% by the proposed method within a certain range of wire densities.

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.

An equivalent circuit for the leakage inductance of three-winding transformers is presented. The model is derived from the principle of duality (between electric and magnetic circuits) and matches terminal leakage inductance measurements. The circuit consists of a set of mutually coupled inductances and does not contain negative inductances. Each inductance can be computed from both: the geometrical information of the windings and from terminal leakage measurements taking two windings at a time. The new model is suitable for steady state, electromechanical transients and electromagnetic transient studies. The circuit can be assembled in any circuit simulation program such as EMTP, PSPICE, etc. programs using standard mutually coupled inductances.

The effects of the transformer leakage inductance in a LLC converter that exploits the integrated magnetic concept are investigated. The vast literature on this subject always models the transformer considering its magnetizing inductance, together with a lumped leakage inductance located at the primary side. However, when the transformer windings are arranged so as to increase the leakage magnetic flux with the aim of achieving the desired value, two leakage inductances are indeed created, one associated to each winding. Using the Fundamental Harmonic Approximation (FHA), the converter behavior at steady-state is revised so as to highlight the effects of a split leakage inductance, while the dynamic behavior is investigated using the Generalized Averaging Method. A suitable design procedure is proposed that accounts for the more complex transformer model. Measurements taken on a 100 W rated LLC converter prototype confirm the theoretical forecasts.

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.

The efficiency is affected by the parameters of components in the DC high current generator. The leakage inductance of the rectifier transformer will affect the output and filtering effect of the device and reduce the power quality of the public network. To improve the output and filtering effect of the DC high current generator, the 3-phase 6-pulsation rectifier bridge arm with the transformer T-type equivalent circuit is proposed. Through the topology model of each conduction state circuit of the semiconductor components, the expressions of load output, high-order harmonic content, and transformer leakage inductance are calculated. Then the actual generator is simulated in the MATLAB-Simulink module and variation law between the primary and secondary side leakage inductance and the output DC voltage, the total harmonic distortion(THD), and the fifth harmonic content rate is obtained. Finally, the output waveform is analyzed under the rated condition. The results show that the influence of transformer leakage inductance on output efficiency and high order harmonic filtering effect can be obtained by the proposed calculation method, and the simulation results verify the validity and correctness of the theoretical analysis.

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.

In this paper, comparisons are made on various parameters of electromagnetic fields like air gap flux density (radial), flux distribution, phase currents, speed and torque of a healthy and stator inter-turn fault induction motor (IM). Using FEM (Finite Element Method), the inter-turn short circuit fault analysis of PWM (Pulse Width Modulated) inverter fed 3 phase IM is analyzed. The inter-turn fault is the initial stage of a short circuit in the stator winding and it progresses to a phase to phase fault or phase to ground fault if left undetected. When the IM is directly fed from the mains, the inter-turn fault can be identified using a popular technique known as MCSA (Motor Current Signature Analysis). But this method fails when the IM is fed from a PWM inverter due to rich noise content observed in the current spectrum due to high frequency inverter switching making it difficult to detect the fault. The electromagnetic field analysis of PWM inverter fed 3 phase IM with 12.5% and 25% stator winding inter-turn fault is carried out on a 7.5kW IM using ANSYS Maxwell FEA (Finite Element Analysis) tool. The spatial FFT spectrum of air gap flux density (radial) indicates the presence of stator winding inter-turn fault with rich noise content compared to healthy motor.

An interturn short-circuit in the stator windings can lead to the breakdown of electrical machines. In the case of induction machines, several fault detection methods and faulted models have been developed in the recent decades. These models differ mainly in how the leakage inductances of the faulted winding are modeled. This work provides a generalized model for interturn short-circuit faults, using different assumptions for the leakage inductances. The model is validated with experimental results for an exhaustive set of fault parameters, and the leakage inductances influence is analyzed. Moreover, the model is used to analyze the drawbacks of the negative-sequence fundamental current as a traditional fault signature. A high-frequency injection method for converter-fed machines is presented to overcome these limits. The proposed fault signature is the negative-sequence current at the injection frequency and it is evaluated experimentally at different operating conditions. The fault severity and its location are proved to be related to the proposed fault signature.

Winding and core geometries are described for a matrix transformer constructed from integrated core and z-folded flex circuits. The magnetizing inductance is derived using the reluctance method and exploiting structural periodicity and symmetry. The internal leakage inductance is computed from the magnetic field distribution, and the interconnect leakage inductance from inductance formulas and current distribution. The results show that the interconnects are responsible for most of the leakage inductance. The modeling predicts inductance values that agree well with experimental measurements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The paper at hand proposes to employ a multisource DC-DC converter to interconnect energy sources, storage devices, drives and the motion control unit of an electric vehicle. This converter topology is well suited to interconnect more than 2 sources/loads that need galvanic isolation. It is particularly advantageous in the case of different voltage levels to be connected, with the power flowing in any direction. The multisource DC-DC converter employs a single magnetic core with multiple windings. The maximum transmissible power for each pair of sources, the energy efficiency and the controllability of the system depend on the multiwinding transformer's leakage inductances. The paper presents a solution to adjust the leakage inductances in order to obtain a given converter characteristic. The approach works with uneven transformation ratios and is validated experimentally for 4 sources/loads.