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The purpose of this paper is to present a new type of equivalent scheme of multi‐winding transformers.

An inventory representation of relations between currents and flux linkages has been interpreted as a multi‐port purely inductive circuit.

An equivalent scheme in the form of a multi‐port circuit, and a method of its parameters determination from field computations.

Core losses are not considered in the multi‐port equivalent scheme.

A new equivalent scheme could become a basic tool for modeling multi‐winding transformers.

The introduced multi‐port equivalent scheme eliminates disadvantages of classical T‐type equivalent scheme of transformers.

The traction cable is paralleled with the existing traction network of electrified railway through transverse connecting line to form the scheme of long distance power supply for the traction network. This paper aims to study the scheme composition and power supply distance (PSD) of the scheme.

Based on the structure of parallel traction network (referred to as “cable traction network (CTN)”), the power supply modes (PSMs) are divided into cable + direct PSM and cable + autotransformer (AT) PSM (including Japanese mode, French mode and new mode). Taking cable + Japanese AT PSM as an example, the scheme of long distance power supply for CTN under the PSMs of co-phase and out-of-phase power supply are designed. On the basis of establishing the equivalent circuit model and the chain circuit model of CTN, taking the train working voltage as the constraint condition, and based on the power flow calculation of multiple train loads, the calculation formula and process for determining the PSD of CTN are given. The impedance and PSD of CTN under the cable + AT PSM are simulated and analyzed, and a certain line is taken as an example to compare the scheme design.

Results show that the equivalent impedance of CTN under the cable + AT PSM is smaller, and the PSD is about 2.5 times of that under the AT PSM, which can effectively increase the PSD and the flexibility of external power supply location.

The research content can effectively improve the PSD of traction power supply system and has important reference value for the engineering application of the scheme.

In electric system of high-speed trains, neutral sections are set to balance the three-phase load. When passing neutral sections, the train should detach from the power supply for a short time. To permanent magnet synchronous motors (PMSMs) traction system, the voltage of DC link will increase quickly due to the back-EMF of PMSM during this time. Although the energy consumption braking method can be adopted to consume the feedback energy. It not only wastes energy, but also causes more speed drop of the train. The paper aims to discuss these issues.

In order to get better performance when the train is under passing neutral section condition, a suitable control method is proposed, in which the torque command is set to zero and d-axis current order remains unchanged during passing neutral section. Based on a co-simulation model, the influences of this method on the PMSMs traction system are compared with that of traditional method, which is used in induction motors traction system. This model combines both control strategy and finite element model of motor, which can take the effects of magnetic saturation and power loss into consideration.

In PMSMs traction system, PMSMs work as generators during neutral section, and charge to DC bus, which may cause over-voltage damage. Moreover, there would be strong torque shock at the moment of power cut-off. It is finally found that, with the suitable control method, the high-speed train can pass the neutral section with less speed drop, less torque shock and little DC link voltage rise.

The control method proposed in this paper is easier to achieve and gets a better performance of PMSMs traction system in high-speed train compared with the traditional method. Furthermore, the co-simulation model is much closer to reality than the analytical model.

This paper aims to propose a new design for high-power compact solid-state transformers (SSTs) made with grain-oriented electrical steel (GOES) wound cores that benefit from the natural reduction of iron losses at high temperatures.

An experimental approach, coupled with numerical and analytical investigations, is widely used for proving the validity of the proposed concept.

With cores much hotter than coils, the new design of medium frequency transformers can be used for building compact SSTs that rated powers and common-mode insulation voltages much higher than existing ones with similar efficiencies.

The thermal design must provide a large difference between core and coil temperatures in a reasonable volume.

The increasing number of intermittent renewable sources place electric grid stability at risk. Smart nodes, made of SSTs, improve the global grid stability because they are able to provide real-time control of energy fluxes at critical points. In railway applications, high-power SST cells can be distributed along the train providing a larger volume for passengers.

The increasing part of electricity in a flexible grid requires performant and high-power SSTs made with components that have an environmental footprint as low as possible.

This paper proves that the design of high-power transformers with GOES wound cores much hotter than coils is possible. It proposes also a thermal equivalent circuit that helps the design.

The purpose of this paper is to propose a DC-port voltage balance strategy realizing it by logic combination modulation (LCM). This voltage balance strategy is brief and high efficient, which can be used in many power electronic devices adopting the cascaded H-bridge rectifier (CHBR) such as power electronic transformer (PET).

The CHBR is typically as a core component in the power electronic devices to implement the voltage or current conversion. The modulation method presented here is aiming to solve the voltage imbalance problem occurred in the CHBR with more stable work station and higher reliability in ordinary operating conditions. In particular, by changing the switch states smoothly and quickly, the DC-port voltage can be controlled as the ideal value even one of the modules in CHBR is facing the load-removed problem.

By using the voltage balance strategy of LCM, the problem of voltage imbalance occurring in three-phase cascaded rectifiers has been solved properly. With the lower modulation depth, the efficiency of the strategy is shown to be better and stronger. The strategy can work reliably and quickly no matter facing the problem as load-removed change or the ordinary operating conditions.

The limitation of the proposed DC-port voltage balance strategy is calculated and proved, in a three-module CHBR, the LCM could balance the DC-port voltage while one module facing the load-removed situation under 0.83 modulation depth.

This paper provides a useful and particular voltage balance strategy which can be used in the topology of three-phase cascaded rectifier. The value of the strategy is that a brief and reliable voltage balance method in the power electronic devices can be achieved. What is more, facing the problem, such as load-removed, in outport, the strategy can response quickly with no switch jump and switch frequency rising.

Auxiliary power system is an indispensable part of the train; the auxiliary systems of both electric locomotives and EMUs mainly are powered by one of the two ways, which are either from auxiliary windings of traction transformers or from DC-link voltage of traction converters. Powered by DC-link voltage of traction converters, the auxiliary systems were maintained of uninterruptable power supply with energy from electric braking. Meanwhile, powered by traction transformers, the auxiliary systems were always out of power while passing the neutral section of power supply grid and control system is powered by battery at this time.

Uninterrupted power supply of auxiliary power system powered by auxiliary winding of traction transformer was studied. Failure reasons why previous solutions cannot be realized are analyzed. An uninterruptable power supply scheme for the auxiliary systems powered by auxiliary windings of traction transformers is proposed in this paper. The validity of the proposed scheme is verified by simulation and experimental results and on-site operation of an upgraded HXD3C type locomotive. This scheme is attractive for upgrading practical locomotives with the auxiliary systems powered by auxiliary windings of traction transformers.

This scheme regenerates braking power supplied to auxiliary windings of traction transformers while a locomotive runs in the neutral section of the power supply grid. Control objectives of uninterrupted power supply technology are proposed, which are no overvoltage, no overcurrent and uninterrupted power supply.

The control strategies of the scheme ensure both overvoltage free and inrush current free when a locomotive enters or leaves the neutral section. Furthermore, this scheme is cost low by employing updated control strategy of software and add both the two current sensors and two connection wires of hardware.

This paper aims to present an engineering computational method for fatigue life evaluation of welded structures on large-scale equipment under random vibration load.

Based on a case study of the traction transformers, virtual fatigue test (VFT) was proposed via numerical simulation approach. Static analysis was conducted to identify the risky zone and then dynamic response of the risky welds under random vibration load was calculated based on frequency-domain structural stress method (FDSSM) theory, life distribution and associated survivability at various locations of the structure were obtained. Structural modification was finally performed according to the evaluation results. Moreover, experimental test was carried out and compared with the virtual test result.

By applying the virtual test, fatigue life of the complex welded structures on large-scale equipment can be accurately and efficiently obtained considering dynamic effect under random vibration load. Meanwhile, risky welds can be directly determined and targeted modification scheme can be accordingly concluded. Validity of the VFT result was proved by comparing with the experimental test.

The proposed method can help obtain equivalent structural stress and fatigue life distribution of the welded structure at any position with various survivability and make quantitative evaluation on the life-extending effect of the structural modification. This method shows significant cost and efficiency advantages over experimental test during design stage of the large-scale structures in numerous manufacturing industries.

The purpose of this paper is to determine the external magnetic field density of the traction transformer for EMU and to find the model for its computation.

The magnetic flux density in the surrounding region of the traction transformer was modeled and calculated using FEM. The transformer was modeled in a way that tank, clamps and current sources were taken into account. Most frequent operating modes for the basic 50 Hz current harmonic, and most represented higher harmonic of 1,950 Hz loading current, were analyzed.

Matching calculated and measured values were obtained on the finished transformer. The developed calculation has proved to be a useful tool for the stray field calculation outside this type of transformer. Calculated values of the flux density are lower then the maximum permitted values defined by the DIN VDE 0848 standard.

This paper presents a study of calculation compared to measurement of magnetic field density outside an oil immersed transformer.

The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for Kth winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The purpose of this paper is to first determine a hysteresis nonlinearity involved in Φ(Θ) function using modified Preisach theory and second to develop new analytical formula of Preisach distribution function (PDF).

It is assumed in this paper that flux linkage characteristics Ψ(i) of each winding have nonlinear component due to the magnetization characteristic of the steel core and sum of linear components due to the self and mutual leakage fluxes. This nonlinear component of Ψ(i) characteristic can be expressed as a flux common Φ to all windings vs ampere-turns Θ of all windings. The nonlinear flux linkage characteristics Ψ(i) of the tested transformer are calculated from the set of measured terminal voltages and terminal currents. To simulate magnetic behavior of the iron core the feedback scalar Preisach model of hysteresis is proposed which gives more accurate predictions than classical model. For this hysteresis model the PDF and feedback function are needed. The intend of this paper is to find these function as an analytical formulas which are convenient for numerical simulations. For identification of the PDF and feedback function parameters of the considered iron core of tested transformer the Levenberg-Marquardt optimization algorithm was used.

The flux common to all windings is calculated by integrating the induced voltages of the appropriate windings. In this paper the PDF is proposed as a functional series including two dimensional Gauss expressions. In order to proper approximation of hysteresis nonlinearity of the tested iron core the first three terms of functional series of the PDF have been used. In the optimization algorithm only initial and descending limiting hysteresis curves Φ(Θ) were utilized. The feedback function for proposed hysteresis model is assumed as third-order polynomial. The hysteresis model has been successfully validated by comparing the calculated and measured results of Φ(Θ) hysteresis curves. This hysteresis model can be used in transient and steady state simulations of tested transformer taking into account the hysteresis phenomenon. The developed hysteresis model can be also used for analysis of the influence of remnant flux on the operation of tested transformer especially in transient states.

In this paper the feedback Preisach hysteresis model is involved in the flux common to all windings vs ampere-turns of all windings. The new PDF is proposed as functional series including two dimensional Gauss expressions. For tested transformer the three first terms of this functional series may be used for proper approximation of hysteresis nonlinearities.