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Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The purpose of this paper is to design a cascaded Multilevel inverter with reduce number of switches for high power applications. This paper came up with an innovative three-phase multilevel inverter (MLI) topology, which is a cascaded structure based on classical three-legged voltage source inverter (VSI) bridges as an individual module. The prominent advantage of this topology is that it requires only one direct current (DC) link system. The main characteristic of it is that a higher number of voltage levels can be achieved with considerably a smaller number of semiconductor switches, which improves the reliability, power quality, cost and size of the system significantly.

The individual modules are cascaded through three-phase transformers to provide higher voltage at the output with the higher number of voltage levels. In this work, the phase-shifted pulse width modulation technique is implemented to verify the result.

The proposed topology is compared with three-phase cascaded H-bridge MLI (CHB-MLI) and a modified CHB-MLI topology and found better in many aspects. The proposed MLI can produce a higher number of voltage levels with fewer semiconductor switches and associated triggering circuitry. As the device count in the proposed MLI is less compared to other MLI discussed, it tends to have less switching and conduction loss which increases the efficiency and reliability. As the number of level increases, the voltage profile and the total harmonic distortion of the proposed MLI improves.

This is a transformer-based modular cascaded MLI, which is based on classical VSI bridges. Here in this topology, a single module provides all three phases. So, a single string of cascaded modules is enough for three-phase multilevel voltage generation.

The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.

In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.

The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.

Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

Many authors reported the decrease of performances when electric machines and electromagnetic devices were supplied by pulse width modulated (PWM) voltages. However, these statements are rarely supported by measurements performed under fair conditions. The aim of this paper is to compare the performances of a single‐phase transformer and a three‐phase permanent magnet synchronous motor (PMSM) supplied by sinusoidal and PWM voltages and to find a way to evaluate the decrease of performances when PWM voltages are applied.

In order to perform a fair comparison between performances of the tested objects supplied by sinusoidal and PWM voltages, an experimental system was built. It contains a single‐phase and a three‐phase linear rectifier for supply with sinusoidal voltages and an H‐bridge inverter and a three‐phase inverter for supply with PWM voltages. The tests and measurements were performed on a single‐phase transformer and three‐phase PMSM, where different constant loads and different modulation frequencies were used. The test conditions were identical for the supply by sinusoidal and PWM voltages. The measured data, used for the evaluation of performances, were the input and output power and the time behaviours of currents and voltages together with their THDs.

The results presented in the paper clearly show that the efficiency of the singe‐phase transformer and three‐phase PMSM decreases with the increasing level of voltage THD. To properly determine the THD of PWM voltage, the sampling frequencies above 1 MHz and special equipment are normally required. However, if the modulation frequency is not too high, also the current THD, which can be easily determined, can be used to evaluate the decrease of efficiency in the case of supply by PWM voltages.

The results presented in the paper clearly show that the efficiency of the singe‐phase transformer and three‐phase PMSM decreases with the increasing level of voltage THD.

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.

The majority of three‐phase dynamic transformer models used in commercially available electric power system transient simulation programs offer only saturated three‐phase transformer models built from three single‐phase transformer models. This paper sets out to deal with the modelling and transient analysis of a saturated three‐limb core‐type transformer.

Three iron core models I‐III are given by the current‐dependent characteristics of flux linkages. In the first model, these characteristics are given by a set of piecewise linear functions, which include saturation. In the second model, the piecewise linear functions are replaced by the measured nonlinear characteristic. The more complex third model is given by a set of measured flux linkage characteristics.

The behaviour of transformers used in electric power applications depends considerably on the properties of magnetically nonlinear iron core. The best agreement between the calculated and measured results is obtained by use of the most complex iron core model III, which takes into account magnetic cross‐couplings between different limbs, caused by saturation.

Measurement of the current‐dependent flux linkage characteristics of the 0.4 kV, 3.5 kVA laboratory transformer requires corresponding excitation of windings by three independent linear amplifiers. Current‐dependent flux linkage characteristics of the larger power transformer can be determined either by similar measurement with linear amplifiers of an appropriate power or by extracting them from the calculated magnetic field, which is done by the finite element method.

A three‐phase dynamic transformer model with the obtained iron core model III is suitable for the numerical analysis of nonsymmetric transient states in power systems.

This paper presents a three‐phase dynamic transformer model with an original iron core model III, which accounts for magnetic cross‐couplings between different limbs, caused by saturation.

The aim is to develop a nonlinear transformer model to achieve an accurate model to obtain the frequency components of the magnetizing current based on the harmonic voltages at the primary and secondary side. So, it can easily be implemented in a harmonic load‐flow program.

The transformer model is based on the harmonic balance method. The electric and magnetic equations of the transformer are derived from the electric and magnetic equivalent circuits.

The transformer model can be easily implemented in a harmonic load‐flow program. The accuracy of the model has been shown by comparing it with a finite element simulation. The transformer model can be used with asymmetrical supply voltages, because different saturation levels of the phases can occur. There is a coupling between the phases which can be concluded out of the asymmetrical currents in the transformer under symmetrical supply voltages.

The transformer model does not consider the iron losses and the interharmonics. In future work the transformer model will be used to study the harmonic losses in distribution networks, so the transformer losses due to these harmonics have to be considered. This can be achieved with a postcalculation process where the magnetic flux density is used to calculate the eddy current losses and the magnetic field intensity will be applied in a static Preisach model to quantify the hysteresis losses.

The model can be used in a harmonic load‐flow program in order to obtain more accurate simulations for the power system analysis and design.

The model presented in this paper is more detailed than similar papers found in literature (saturation of the yokes, coupling between the phases, interaction between different harmonics) and still it takes a brief simulation time.

Despite its well-founded criticism and lack of proper justification under core saturation conditions, the T-equivalent transformer model (Steinmetz scheme) is obviously championing in the literature. This educational paper aims to explain in a simple manner the limitations of the T-model of a low-frequency transformer and critically analyses some attempts to improve it.

Using a simplified examination of magnetic fluxes in the core and windings and using the modeling in ATPDraw, it is shown that transient transformer models with the indivisible leakage inductance allow circumventing the drawbacks of the T-model.

The authors show the absence of valid grounds for subdividing the leakage inductance of a transformer between its primary and secondary windings. The connection between the use of individual leakage inductances and inaccurate prediction of inrush current peaks is outlined as an important example.

The presented models can be used either as independent tools or serve as a reference for subsequent developments.

Over generations, the habitual transformer T-equivalent is widely used by engineers and Electromagnetic Transients Program experts with no attention to its inadequacy under core saturation conditions. Having studied typical winding configurations, the authors have shown that neither of them has any relation to the T-equivalent.

This educational paper will contribute to the correct understanding of the transients occurring in a transformer under abnormal conditions such as inrush current or ferroresonance events, as well as during an out-of-phase synchronization of step-up generator transformers.

The purpose of this paper is to present an application of a multidisciplinary multi-level design optimization methodology for the optimal design of a complex device from the field of electrical engineering throughout discipline-based decomposition. The considered benchmark is a single-phase low voltage safety isolation transformer.

The multidisciplinary optimization of a safety isolation transformer is addressed within this paper. The bi-level collaborative optimization (CO) strategy is employed to coordinate the optimization of the different disciplinary analytical models of the transformer (no-load and full-load electromagnetic models and thermal model). The results represent the joint decision of the three distinct disciplinary optimizers involved in the design process, under the coordination of the CO's master optimizer. In order to validate the proposed approach, the results are compared to those obtained using a classical single-level optimization method – sequential quadratic programming – carried out using a multidisciplinary feasible formulation for handling the evaluation of the coupling model of the transformer.

Results show a good convergence of the CO process with the analytical modeling of the transformer, with a reduced number of coordination iterations. However, a relatively important number of disciplinary models evaluations were required by the local optimizers.

The CO multi-level methodology represents a new approach in the field of electrical engineering. The advantage of this approach consists in that it integrates decisions from different teams of specialists within the optimal design process of complex systems and all exchanges are managed within a unique coordination process.

The influence of overlap joints in transformer cores on the local flux and eddy current distribution and on overall transformer characteristics is studied by means of two‐dimensional finite element (2D FE) models. A simplified 2D FE model of a single overlap joint is used for estimating the resulting increased magnetomotive force and increased eddy current losses. Both effects can be accounted for in a 2D FE model of the complete transformer by locally adopting modified material characteristics (viz. BH‐curve and electrical conductivity) in the cross‐section of the core. This novel method is demonstrated and validated by applying it to a three phase transformer. The calculated no‐load currents and losses are compared to the measured ones.