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The paper presents the analysis of magnetic field that surrounds the power transformer after it has been switched off. The purpose of this paper is to determine the possibility of defining the residual fluxes in the legs of the transformer based on the measurement of this field. It was also intended to determine the type and the location of magnetic sensors.

Numerical analysis of the magnetic field was performed. A three-dimensional model of the transformer’s magnetic core was created in the Flux 3D simulation program. The analysis was concerned with an oil-filled transformer and a dry transformer. The magnetic field of Earth was taken into account.

The research has shown that magnetic induction of the leakage field produced by residual magnetization of the core is comparable to the magnetic induction of the Earth’s field. It was also found that the measurement of the magnetic induction should be performed as close as possible to the core. The interior of the tank turned out to be a convenient space for the placement of the sensors.

The influence of external ferromagnetic objects, and devices generating magnetic field, on the measurement was not considered. It should be taken into account in the future work.

On the basis of the analysis, it was proposed to measure the magnetic induction vector of the leakage field at three points. The sensors should be placed in front of the columns at a position that is half of their height. The measurement can be performed with satisfactory accuracy by sensors located on the surface of the windings.

In spite of the vehicle, magnetic field interference can be reduced by some measures and techniques in ammunition design and manufacturing stage, the corruption of the vehicle magnetic field can still reach hundreds to thousands of nanoteslas. Besides, the magnetic field that the ferromagnetic materials generate in response to the strong magnetic field in the vicinity of the body. So, a real-time and accurate vehicle magnetic field calibration method is needed to improve the real-time measurement accuracy of the geomagnetic field for spinning projectiles.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time. In the method, the elliptical model of magnetometer measurement is established to convert the coefficients of hard and soft iron errors into the parameters of the elliptic equation. Then, the parameters are estimated by recursive least square estimator in real-time. Finally, the initial conditions for the estimator are established using prior knowledge method or static calibration method.

Studies show the proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real-time. A turntable experiments indicate that the post-calibration residuals approximate the measurement noise of the magnetometer and the roll accuracy is better than 1°. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers' calibration in real-time.

Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time and the calculation is small. Besides, it does not take up storage space. The proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real time. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers’ calibration in real-time.

Magnetization is one of the most important parameters of magnetic fluids. The shape of the magnetization curve often determines the application of a fluid in a device. On the basis of the magnetization curve, it is also possible to estimate, for example, the distribution and size of the particles in a magnetic fluid carrier fluid. The aim of this paper is to present a new approach for estimating the magnetization curve.

The proposed method is an iterative method based on the measurement of magnetic induction on a test stand. To determine the magnetization curve, a numerical simulation of the magnetic field distributions for the preliminary magnetization curve should also be performed. Numerical simulations for modified forms of the magnetization curve are performed until the difference between the results obtained by the measurement and numerical simulation are the smallest.

This paper presents the results of magnetization curve research for ferrofluids and magnetorheological fluids.

The discussed method shows the possibilities of using numerical simulations of magnetic field distribution to determine the magnetic properties of magnetic fluids. This method may be an alternative for estimating the magnetization curve of the magnetic fluid compared to other methods.

The purpose of the paper is to analyze the impact of coupling on the distribution of the magnetic field and study the characteristics of the magnetic flux density in the transmission process of the magnetic coupling resonant wireless power transmission (MCR-WPT) system, which provides guidance on the design of the WPT system.

In this study, a finite element simulation analysis was conducted and a three-dimensional (3D) electromagnetic field measurement platform was used.

It is shown that the distribution of the magnetic field, as well as the position of maximum magnetic flux density, will change when the coils are coupled. The simulation results of the magnetic field distribution, as well as the transmission performance, are different from those in practice. It cannot describe the actual performance of WPT system.

A 3D electromagnetic field measurement system and the host computer software are designed to help optimize the simulation and carry out more accurate and efficient research. The 3D electromagnetic field measurement system can be used to study the distribution of the spatial electromagnetic field, influencing factor, exposure and interoperability between different coils.

This paper aims to present the use of magnetic gradient, and magnetic potential measurements in the specific case of magnetization identification for a thin sheet. Usually, induction measurements are only used.

After a brief description of the magnetic gradient and magnetic scalar potential notions, methods to calculate them are presented and validated. These two kinds of measurements are tested for a numerical identification case. Then, virtual measurements can be generated and used for inverse problem resolution. Advantages of using induction, magnetic gradient or magnetic potential measurements are then discussed.

A previous method to solve inverse problem based on induction measurement has been increased by the capability of using other kind of measurements. A numerical approach has allowed to validate the use of magnetic gradient or magnetic scalar potential measurement as information sources.

Usually, induction measurements are only used. Inversion resolution using other kind of measurements than the induction can be made. An experimental validation has been done for gradient measurements.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The paper gives a new measurement method of the parameters characterising the magnetic laminations for broadband low‐level signals defined at any operational point.

High frequency phenomena machines fed by PWM inverters are related to low‐level signals corresponding to minor hysteresis loops around the instantaneous working point, which moves on the main loop at the basic frequency. The minor loops are assimilated to ellipses, which are characterised by only two parameters: the incremental magnetic permeability (μ) and the electric conductivity (σ).

For small signals high frequency field components, the laminated steel behaviour can be described by two local parameters (μ, σ) and skin effect. The values of μ and σ do not depend on frequency up to 1 MHz, but only on the operating point.

The proposed broadband characterisation should be associated with a Priesach model that defines the operating point for computer simulation of high frequency phenomena.

The broadband characterisation of magnetic laminations is useful for studying the behaviour of the windings of the PWM‐fed machines.

Broadband measurements are now possible on small magnetic steel lamination samples.

The definition of a simple model of low frequency magnetic field created by power industrial installations can be approached by using an equivalent source system (ESS). Given a set of measured magnetic field points, the ESS, made by a limited set of current carrying wires or turns, must be placed and supplied in order to fit the measured magnetic field values. An optimisation procedure can be used to define the current values and the location of the ESS which minimize the error between the measured and computed magnetic field values.

A two‐step optimal procedure is defined: in the outer step a stochastic optimisation routine is used to drive the geometric control parameters of the ESS while, in the inner step, the current values flowing through the sources are computed to find the minimization of the error with respect to a set of measured magnetic field values. The optimisation procedure is based on an artificial immune system algorithm which focuses on a deep exploration of the search space and gave interesting results both in terms of accuracy and computational efficiency.

The results show that the proposed approach is able to reconstruct the magnetic field created by complex source system and give some accuracy measure on the reconstruction error. The optimisation process carried out also on conductor positions has allowed to find out the location of the real sources in an accurate way, also in presence of measurement errors.

The approach proposed uses optimisation procedures to solve the inverse problem of source reconstruction starting by a set of measured magnetic field values. The definition of a simple equivalent source structure, together with an optimisation procedure to set its control parameters, allows to simulate complex magnetic field sources, like power substations or cable systems, in a very efficient and compact way.

The purpose of this paper is to establish the mathematical foundations of magnetic measurement methods based on translating-coil and rotating-coil magnetometers for accelerator magnets and solenoids. These field transducers allow a longitudinal scanning of the field distribution, but require a sophisticated post-processing step to extract the coefficients of the Fourier–Bessel series (known as pseudo-multipoles or generalized gradients) as well as a novel design of the rotating coil magnetometers.

Calculating the transversal field harmonics as a function of the longitudinal position in the magnet, or measuring these harmonics with a very short, rotating induction-coil scanner, allows the extraction of the coefficients of a Fourier–Bessel series, which can then be used in the thin lens approximation of the end regions of accelerator magnets.

The extraction of the leading term in the Fourier–Bessel series requires the solution of a differential equation by means of a Fourier transform. This yields a natural way to de-convolute the measured distribution of the multipole content. The author has shown that the measurement technique requires iso-parametric coils to avoid interception of the longitudinal field component. The compensation of the main signal cannot be done with the classical arrangement of search coils at different radii, because no easy scaling law exists. A new design of an iso-perimetric induction coil has been found.

In the literature, it is stated that the pseudo-multipoles can be extracted from field computations or measurements. While this is true for computations, the author shows that the measurement of the field harmonics must be done with iso-parametric coils because otherwise the leading term in the Fourier–Bessel series cannot be extracted.

The author has now established the theory behind a number of field transducers, such as the moving fluxmeter, the rotational coil scanner and the solenoidal field transducer.

This paper brought together the known theory of the orthogonal expansion method with the methods and tools for magnetic field measurements to establish a field description in accelerator magnets.

To describe the wide range of possible applications of high temperature superconductors (HTSCs) (e.g. magnetic bearings, levitation systems or electrical machines) several appropriate calculation algorithms have been developed. They determine the force interaction between a superconductor and any even multidimensional magnetic field excitation system. Especially good agreements between experiments and computed results have been obtained for the Vector‐Controlled Model, which seems to be the best approximation of the macroscopic superconductivity behaviour. The validation of this model by means of measurements makes it a powerful tool for the design and optimisation of any HTSC application in the field of force generation. It can be used not only for the designing of levitation applications, but also to help the understanding of the flux penetration, flux trapping and magnetisation of bulk superconductors in non‐uniform magnetic fields. By means of this model, the force interaction between superconductors and external magnetic fields for practical multi‐polar configurations, e.g. superconducting levitation systems or inherently stable superconducting bearings has been determined. Furthermore, the time dependency of the forces taking flux flow and flux creep into account, can be considered.